Sustainable Optimizing Performance and Energy Efficiency in Proof of Work Blockchain: A Multilinear Regression Approach

Abstract

The energy-intensive characteristics of the computations performed by graphics processing units (GPUs) in proof-of-work (PoW) blockchain technology are readily apparent. The optimization of GPU feature configuration is a complex subject that significantly impacts a system’s energy consumption and performance efficiency. The primary objectives of this study are to examine and improve the energy consumption characteristics of GPUs, which play a crucial role in the functioning of blockchains and the mining of cryptocurrencies. This study examines the complex relationship between GPU configurations and system architecture components and their effects on energy efficiency and sustainability. The methodology of this study conducts experiments involving various GPU models and mining software, evaluating their effectiveness across various configurations and environments. Multilinear regression analysis is used to study the complex relationships between critical performance indicators like power consumption, thermal dynamics, core speed, and hash rate and their effects on energy efficiency and performance. The results reveal that strategically adjusting GPU hardware, software, and configuration can preserve substantial energy while preserving computational efficiency. GPU core speed, temperature, core memory speed, ETASH algorithms, fan speed, and energy usage significantly affected the dependent computational-efficiency variable (p = 0.000 and R² = 0.962) using multilinear regression analysis. GPU core speed, temperature, core memory speed, fan speed, and energy usage significantly affected efficient energy usage (p = 0.000 and R² = 0.989). The contributions of this study offer practical recommendations for optimizing the feature configurations of GPUs to reduce energy consumption, mitigate the environmental impacts of blockchain operations, and contribute to the current research on performance in PoW blockchain applications.

1. Introduction

By thriving in a global economy, blockchain technology has been integrated into the current digital ecosystem for secure and private enterprises [1]. Blockchain technology has numerous applications in everyday life and business with a decentralized [2] and immutable ledger structure. In addition, using decentralized ledger technology, blockchain enables individuals and institutions to trace and verify transactions in real-time, thereby enhancing data security, transparency, and traceability and giving rise to transformative applications in numerous fields. For example, blockchain systems can deal with automated complex and secure business processes for supply chain management [3], secure and interoperable education [4,5], government [5], finance [6,7], health [8,9], and self-executing smart contracts [9,10]. In the field of financial technology, blockchain technology is the foundational concept that underpins cryptocurrencies and infrastructures. Central processing units (CPUs) initially dominated mining, but their processing power and speed were insufficient for proof-of-work (PoW) algorithm computational demands. The graphics processing units (GPUs) and application-specific integrated circuits (ASICs) information system architectures used for parallel processing capabilities of blockchain mining provide an edge in executing multiple operations simultaneously in a new era of efficiency and speed, making them well-suited for blockchain computations [11]. GPUs’ ability to execute multiple operations simultaneously is essential for solving complex computations in many areas, such as neural networks, deep learning, image processing, distilled image processing, and blockchain technology for cryptographic puzzles using PoW algorithms [12], which evolved from cryptocurrency mining. Cryptocurrency mining particularly uses the PoW method in many blockchain networks to support public smart contracts, especially Ethereum networks. Mining operations require energy-intensive computational processes facilitated by GPUs and ASICs. Mining algorithms are computationally intensive to secure the network. GPUs outperform CPUs due to their thousands of cores and computational power. A wealth of benchmarking studies shows GPU mining’s performance, speed, and efficiency advantages over other encryption processing hardware [13]. Moreover, GPUs are designed to use many platform architectures, from smartphones, edge computing, personal computers, and game-playing stations to supercomputers.

In recent years, the integration of GPUs with information system architecture in blockchain technology has gained considerable attention. Such synergy magnifies the capabilities of blockchain networks, ensuring efficient transaction processing and improved security protocols [9]. Many studies have begun unraveling the transformative potential of this convergence in various sectors. On the other hand, information system architecture defines the framework that aligns technology, data, and business processes [14]. A synergy between the two is observed in blockchain networks where the computational prowess of GPUs augments the system architecture to enhance throughput and security [2]. Several studies have underscored the impact of integrating GPUs into blockchain’s information system architecture. For instance, Iliakis et al. [15] showcased how the adaptability of GPUs can be harnessed to increase transaction throughput in a blockchain network. Also, the research of Cocco et al. [16] delved into how the architectural components of a blockchain can be optimized using GPU-based systems, leading to performance enhancement and better scalability. Energy efficiency is also a significant theme in the discourse on GPUs and information system architecture synergy. By addressing the energy-intensive nature of blockchain computations, the authors explore GPU architectures that optimize energy usage without compromising the speed or security of transactions [17]. The synergy between GPUs and the information system architecture in blockchain technology promises to optimize computational processes and usher in an era of enhanced performance and sustainability. Thus, the exploration and understanding of this synergy can likely continue to be a focal point for innovations in blockchain technologies.

While the growing demand for real-world applications emphasizes the escalating significance of blockchain technology [18], the complex blockchain framework significantly impacts energy efficiency and system performance. Not only are GPU information system architectures essential for blockchain technology, but many factors relating to the hardware, software, data management, and network structures should also be considered as a foundation of blockchain performance, such as energy per transaction [17], energy cost per coin [19], power usage effectiveness [20], and hash rate [21]. Many studies have indicated that blockchain and other digital ecosystem data centers are highly energy-intensive [22]. Coroamă [23] confirmed that the PoW consensus mechanism dominates blockchain energy consumption, while storage and coordination messages require significantly less energy. Ghosh and Das [24] highlighted blockchains’ exorbitant energy consumption due to the creation algorithm. Powell et al. [25] emphasized the importance of making blockchain greener and compared energy consumption among consensus protocols. Corbet et al. [26] mentioned the growing electricity consumption and carbon production from cryptocurrency mining, emphasizing the need for further assessment of environmental impacts. Schinckus et al. [27] found a positive correlation between crypto-currency trading volumes and energy consumption, indicating a significant influence of cryptocurrency activities on energy consumption. Therefore, this study prioritizes energy-efficient blockchain technology solutions that can reduce environmental impact and manage resources for optimizing blockchain implementation.

The primary objective of this work is to address the existing research gaps by investigating GPU configurations, system architecture components, and their interactions based on the PoW blockchain implementation to optimize performance indicators and ensure that the maximum performance of GPUs can deal with low energy consumption. It includes evaluating related factors of GPU information system architecture for promoting sustainable blockchain PoW ecosystems. Our challenge is to quantify the environmental impact, reveal energy consumption reduction potential, and provide practical advice to a diverse PoW blockchain stakeholder audience. To achieve this goal, the authors explore the following research questions:

• What are the energy and sustainable energy efficiency concerns of blockchain frameworks based on PoW cryptocurrency mining?
• How can GPU information system architecture enhance energy efficiency for PoW algorithms? This research question encompasses GPU hardware, software, and configuration settings.
• What results of practical recommendations can be provided for PoW blockchain?

This study uncovers and addresses the complexities of energy consumption in GPU-based blockchain technologies, making practical, policy, and environmental contributions. The research contribution represents the global economy thriving amid rapid technological advancements while maintaining environmental integrity as follows:

• This study explores ways to reduce energy consumption in PoW blockchain frameworks, focusing on GPU information system architecture. It highlights the balance between blockchain security and environmental sustainability and offers actionable insights. This study advances energy-efficient PoW blockchain systems by decoding GPU performance and energy consumption dynamics.
• A systematic multilinear regression analysis provides empirical insights into GPU information system architecture optimization. It analyzes the many variables affecting energy consumption and GPU performance to make data-driven decisions. These findings help technology developers, policymakers, and users improve blockchain energy efficiency.
• Concerns about the environmental impact of blockchain technology are growing as it is adopted across various sectors. This research illuminates these issues by analyzing energy consumption and proposing solutions. This study underpins ongoing and future efforts to optimize blockchain technologies’ energy footprint in finance, healthcare, and other fields.
• This study is crucial for promoting sustainable blockchain ecosystems in a world facing digital transformation and environmental sustainability challenges. It explains GPU-based blockchain technology and how to combine technology and environmental stewardship. The contributions will influence policies, practices, and academic discourse to create a worldwide sustainable, energy-efficient PoW blockchain ecosystem.

The subsequent sections of this article are structured in the following manner: Section 2 provides a theoretical background about blockchain technology and framework. Section 3 of this study presents a comprehensive analysis of the research model and methodology that underpins the design, development, and evaluation of the framework for information system architecture optimization. Additionally, this study provides an overview of the outcomes employed by the optimizing blockchain framework, which are subsequently summarized. The results are presented in Section 4 and discussed in Section 5, whereas Section 6 summarizes the optimizing blockchain framework and the findings derived from this study.

2. Theoretical Background

2.1. Blockchain Technologies

Blockchain technology has emerged as a transformative force, shaping many industries beyond its original application for Bitcoin [28]. Blockchain offers a decentralized ledger system, promoting transparency and data integrity without a centralized authority [29]. The appeal of decentralization is undeniable. Unlike traditional centralized systems, which may introduce bottlenecks or single points of failure, blockchain operates across multiple nodes, ensuring no single point of control or failure, enhancing its security and reliability [30].

Blockchain’s security in transactions and data management is enhanced by incorporating cryptographic techniques [2,9,31]. Each block in the chain carries a cryptographic hash of the previous block, forming an unchangeable and tamper-evident chain [32,33]. Altering data in a block retroactively requires modification of all following blocks, needing consensus from all system participants [34]. Transparency, another key feature of blockchain, ensures every transaction is visible and unalterable, tracing data back to their source [32]. This feature proves invaluable in areas like supply chain management, where tracking product life cycles is crucial [3]. Introducing smart contracts, self-executing contracts with agreement terms encoded into code [9,10,35], extends blockchain’s utility. These contracts autonomously verify or enforce transactions, offering innovative solutions in finance, energy, and healthcare [9].

However, blockchain technology faces scalability and energy consumption challenges, particularly in networks using the PoW consensus algorithm [36,37]. The initial consensus mechanism in blockchain technology, PoW [7], involves validating transactions through nodes, referred to as mining. This process requires significant computational capacity for brute-force calculations. Alternative consensus mechanisms, like proof of stake (PoS) [23,24,25] and proof of authority (PoA) [33], are being explored to address these issues [38]. Unlike the PoW consensus mechanism, where miners solve complex mathematical problems to authenticate transactions and generate new blocks [10], PoS depends on participants having a financial interest in the network’s coin. Additionally, the PoA consensus process is often used in blockchain networks based on the identity and reputation of the validators, specifically in permissioned or private blockchains.

2.2. GPUs in Blockchain Technologies

GPUs have evolved beyond their traditional role in rendering graphics, becoming instrumental in blockchain technologies. GPUs are crucial in optimizing and enhancing blockchain technologies, contributing computational power and speed for transaction validation and consensus mechanisms. The initiation of cryptocurrencies, such as Bitcoin and Ethereum, demonstrated the need for computational execution to solve complex cryptographic puzzles, a process known as mining [23]. GPUs emerged as a pivotal element in significantly optimizing the mining process [11]. GPUs outperform CPUs in mining due to their parallel processing capabilities, which are critical for solving computationally intensive PoW algorithms [39]. The algorithms necessitate numerous calculations to validate transactions and secure the blockchain network [40]. An and Seo [41] observed that GPUs provided thousands of cores capable of executing operations simultaneously, dramatically accelerating the resolution of cryptographic challenges.

A study by Shuaib et al. [13] underscored the adaptability of GPUs for blockchain applications. GPUs can be efficiently utilized for cryptocurrency mining and enhancing the transaction throughput of a blockchain network. GPUs have facilitated the implementation of smart contracts on blockchain platforms, offering security and performance [15]. The application of GPUs in blockchain technologies is full of challenges. GPUs have been illustrated and implemented in various other technological domains, including machine learning [42], natural processing [42,43], and data analytics [44,45]. However, the major GPU issues have emerged as prominent concerns of energy consumption and environmental sustainability [17]. This study of innovations in GPU architectures aims to address these concerns by optimizing energy efficiency without compromising performance [15].

2.3. Blockchain Security Domains

Blockchain security can be divided into two domains: private and public blockchains. Both have distinctive features and applications catering to different market and organization needs. Public blockchains like Bitcoin and Ethereum networks are open and accessible to participants [46]. These decentralized networks ensure transparency and security by employing cryptographic techniques and consensus mechanisms for PoW [47]. The participants, often called nodes, can engage in transaction validation and block mining, thereby maintaining the security and integrity of the entire network [5].

On the other hand, private blockchains are confined to specific organizations or groups and are not open to public participation. These private blockchains are typically faster and more scalable due to the restricted number of participants, ensuring secure, fast, and efficient transaction processing [48]. This approach makes them particularly prevalent in financial institutions and enterprises. Platforms like Hyperledger, Ethereum, Quorum, and Corda facilitate the creation of these secure and efficient private blockchains [49].

A comparative analysis of public and private blockchains reveals trade-offs between transparency, security, speed, and control. While public blockchains promote community transparency and decentralization, private blockchains emphasize speed, efficiency, and regional privacy [50]. Buterin [51] explores hybrid models of public and private blockchains. For example, consortium blockchains operate under the control of a group of organizations rather than a single entity, thus ensuring a degree of decentralization while maintaining privacy and efficiency.

The dichotomy between private and public blockchains opens up a world of possibilities for diverse applications. The ongoing exploration and comparison of these technologies promise a future where the potential of blockchain technology can be fully realized across various domains. Distinguishing between public and private blockchain technologies requires an exploration of several aspects, including trustlessness, permissions, efficiency, privacy, and governance, among others, as illustrated in

Table 1. Comparison of private versus public blockchain security domains.

Factors	Public Blockchain	Private Blockchain
Trustlessness [52]	Defining attribute. Functions autonomously without reliance on central authorities.	Irrelevant. Capable of functioning efficiently with legal contracts, trust relationships, and trusted third parties.
Permissions [53,54]	Each node possesses both read and write permissions.	Write access is limited to specific nodes. Access to information and the ability to transact are limited to authorized users only.
Efficiency [52]	The speed can be reduced as a result of consensus mechanisms such as PoW or PoS.	It can exhibit exceptional efficiency and efficacy, particularly when integrated with legal agreements and regulatory structures.
Privacy [54]	Transactions are characterized by transparency and accessibility to all participants.	They are designed for transactions that necessitate data privacy and confidentiality. Enables exclusive data access for authorized users.
Hybrid [55]	-	A hybrid architecture integrates the privacy features of private blockchains with the transparency and traceability of public blockchains.
Applications [56]	Cryptocurrencies, supply chain management, voting systems, and smart contracts.	Supply chains, healthcare, digital identity, asset tokens, and transactions involving data privacy.
Security and consensus mechanism	Enhanced security achieved through mechanisms such as PoW or PoS.	Consensus mechanisms such as practical byzantine fault tolerance (PBFT) prioritize efficiency to achieve faster transaction processing.
Governance	It is characterized by decentralization and open-source nature.	Centralized governance refers to the management and decision-making authority held by either a single organization or a consortium.
Smart contracts customization [57]	-	Customization options are available for private smart contract platforms, allowing for parameter adjustments such as block time size, among others.
Role of legal contracts [52]	-	Able to operate effectively in conjunction with legal contracts and reputable third parties.

. Table 1 provides a comparative analysis of key differences and unique characteristics of public and private blockchains, showcasing the potential of each.

2.4. Blockchain Technology for Private Enterprises

Blockchain technology holds transformative potential for private enterprises, revolutionizing traditional business processes from supply chain management to customer relationship management (CRM). Its adoption in the private sector is largely driven by its capacity to establish trust, enhance transparency, and promote sustainable practices. As Saberi et al. [58] have highlighted, blockchain’s role in sustainable supply chain management is particularly notable, ensuring the integrity and sustainability of operations.

As discussed by Xiang et al. [59], private and consortium blockchains address the limitations of public blockchains, making them more suitable for enterprise adoption. Lacity and Khan [60] noted their potential to eliminate reconciliations and ensure data provenance. The security, reliability, transparency, immutability, and accountability of blockchain, as Matsenko et al. [61] have pointed out, are its key characteristics that benefit internet-of-things applications and data management. Tariq et al. [62] emphasized optimizing processes and protecting personal data as major advantages. Moreover, Gatomatis and Bogonikolos [63] and Xia et al. [64] recognized blockchain’s role in enhancing precision in business operations, reducing costs, and improving financial transactions. Blockchain technology is not limited to financial applications but extends to business model innovation and organizational performance enhancement, as suggested by Aini et al. [65]. Swan [8] discussed its role in advancing enterprise artificial intelligence systems, offering clean data and efficient net settlement in supply chains. Konstantinidis et al. [66] underscored the technology’s disruptive potential across various business sectors.

Despite its benefits, blockchain technology raises concerns regarding energy consumption, especially in PoW blockchain frameworks. Matsenko et al. [61] pointed out the need for a unified regulatory framework as a significant drawback. The energy-intensive nature of blockchain operations, particularly in PoW mining, poses sustainability challenges, prompting a need for more energy-efficient blockchain solutions in private enterprises. In summary, blockchain technology presents a compelling proposition for private enterprises, offering process optimization, data security, and business model innovation benefits. However, its adoption is challenging, especially regarding energy consumption and regulatory complexity. Addressing these issues is crucial for realizing the full potential of blockchain in transforming private enterprise operations.

2.5. Blockchain Framework for Private Enterprises

Blockchain frameworks tailored for private enterprises have evolved to offer various consensus mechanisms, such as PoA, PoS, and PoW. However, blockchain frameworks, such as Hyperledger Fabric and Hyperledger Besu, provide a modular architecture that allows for flexibility in choosing consensus mechanisms and has been extensively investigated. Hyperledger Fabric offers a flexible and modular architecture to support various consensus mechanisms tailored for enterprise needs [67]. Belotti et al. [68] described Hyperledger Fabric as a permissioned blockchain platform that allows plug-and-play components such as consensus mechanisms. By employing PoA, Hyperledger Fabric ensures that transactions are validated by designated authorities, thus, optimizing for performance and scalability. Syed et al. [69] further delved into how PoA facilitates a streamlined and efficient consensus process within private enterprises. Additionally, discussions regarding implementing PoS mechanisms in Hyperledger Fabric continue to gain momentum in the blockchain community.

Hyperledger Besu, an Ethereum client designed to be enterprise-friendly, stands out for its versatility in supporting multiple consensus mechanisms. Tkachuk et al. [70] explained that Besu can operate on public Ethereum networks using PoW and on private networks using PoA and PoS. Besu makes a particularly attractive choice for enterprises looking for a customizable solution.

Comparatively, other blockchain frameworks have also been employed by private enterprises. Corda, as highlighted by Brown et al. [71], is designed for business interactions and provides a unique consensus mechanism that ensures transaction privacy. Yli-Huumo et al. [72] noted that Quorum’s adaptability is especially beneficial for enterprises requiring transaction privacy and high throughput.

Private enterprises seeking blockchain solutions have a variety of frameworks and consensus mechanisms to consider. Hyperledger Fabric and Besu, with their support for PoA, PoS, and PoW, offer customizable solutions, while frameworks like Corda and Quorum provide alternative approaches tailored to specific enterprise needs. Several enterprise blockchain frameworks have emerged to cater to the needs of private enterprises, as illustrated in

Table 2. Comparison of enterprise blockchain systems among different requirements.

Aspect	Hyperledger Fabric [67,68]	Hyperledger Besu [70,73]	Enterprise Ethereum [50]	Ethereum Quorum [72]	Hyperledger Sawtooth [74]	R3 Corda [71]
Consensus mechanism	PoA	PoW, PoA, PoS	PoA, PoS	PoA, PoS	PoET, PBFT	Notary-based
Governance	Permissioned	Permissioned/Public	Permissioned	Permissioned	Permissioned/Public	Permissioned
Smart contract support	Yes (Chaincode)	Yes (Solidity, EVM compatible)	Yes (Solidity)	Yes (Solidity)	Yes (Solidity, Python, JavaScript)	Yes (Corda contract)
Transaction privacy	Yes	Yes	Yes	Yes	Yes	Yes
Scalability	High	Moderate	Moderate	High	High	High
Industry focus	General	General	General	Finance	General	Finance, Healthcare
Data model	Ledger	Blockchain	Blockchain	Blockchain	Ledger	Ledger
Open source	Yes	Yes	Yes	Yes	Yes	Yes
Algorithms for public blockchain	None	Ethash (Proof of Work)	Ethash (Proof of Work)	None	None	None
Limitations	Hyperledger Fabric is designed exclusively for permission and private blockchains; public blockchains such as Ethereum (Ethash) or Binance chain are not supported natively.	Hybrid Besu has the capability to function on public Ethereum networks by employing the Ethash PoW algorithm. The Binance chain lacks support.	Enterprise Ethereum utilizes the Ethash PoW algorithm and is compatible with public Ethereum networks. The Binance chain lacks support.	Quorum for Ethereum is specifically designed to function on private blockchains and is not applicable to public networks such as Binance chain or Ethereum.	Hyperledger Sawtooth, which is exclusively intended for private networks, lacks native support for public blockchain algorithms such as Ethash or those implemented by Binance chain.	Corda is designed exclusively for confidential transactions involving known parties and does not provide support for public blockchain algorithms such as Ethash or those employed by Binance chain.

. The frameworks exhibit variances in consensus mechanisms, governance, privacy, and industry focus for supporting the different aims of leveraging blockchain’s decentralized ledger capabilities. A comparative analysis of enterprise blockchain frameworks based on Hyperledger Fabric, Hyperledger Besu, Enterprise Ethereum, Ethereum Quorum, Hyperledger Sawtooth, and R3 Corda facilitates a nuanced understanding of their features and applications.

2.6. GPU Acceleration for Improved Blockchain Performance in Enterprises

By enhancing the performance and efficiency of blockchain frameworks, GPUs benefit from blockchain frameworks in many areas of private enterprises. Kuznetsov et al. [75] explored the performance of various cryptographic hashing algorithms on GPUs and found that GPUs are effective for parallelizing hash calculations in blockchain networks. Pandya et al. [76] discussed the usage of GPUs for deploying blockchain in cryptocurrency mining and highlighted their high-power and high-performance computing capabilities and the usage of GPUs for deploying blockchain in cryptocurrency mining, indicating that GPUs are useful for solving complex mathematical equations and problems. Drakopoulos et al. [77] mentioned the application of GPU computing in accelerating blockchain for mobile health applications, emphasizing the computational intensity of encryption and verification tasks. Alkaeed et al. [78] discussed the benefits of using both CPUs and GPUs for cryptocurrency mining, highlighting the strength and speed of devices in solving mathematical problems and obtaining rewards. Previous studies have suggested that using GPUs for blockchain frameworks in private enterprises can provide benefits. Alkaeed et al. [78] compared the benefits of using both CPUs and GPUs for cryptocurrency mining and emphasized the speed and strength of GPUs in solving mathematical issues. Krishnaswamy [79] discussed the potential of blockchain technology at the edge of 5G networks and proposed a performance model for a permissioned private blockchain platform. These findings have indicated that GPUs can enhance the performance and efficiency of blockchain frameworks in private enterprises.

The integration of blockchain technology raises several development concerns, especially concerning its alignment with contemporary technologies such as GPUs, consensus mechanisms (PoW, PoS, PoA), and sustainability.

Table 3. Key concerns of blockchain frameworks for effective sustainability.

Development Concern	Methodology	Technologies/Factors
Scalability and performance [80,81]	Assess the performance and scalability of blockchain frameworks utilizing various consensus mechanisms.	GPUs, PoW, PoS, PoA
Security and privacy [82]	An analysis of the algorithms, privacy, and security protocols, hash chained storage, and anonymous signatures utilized in systems based on blockchain technology.	Blockchain frameworks, PoW, PoS, consensus Algorithms
Interoperability [83]	Examine the degree of interoperability between various blockchain frameworks.	Blockchain frameworks
Ease of development [50]	Evaluate the simplicity of application development on blockchain frameworks.	PoW, PoS, PoA, Blockchain Frameworks
Regulatory compliance [48]	Evaluate the adherence of blockchain frameworks to legal standards.	Blockchain Frameworks
Costs and investment [84]	Perform a cost analysis of the implementation of blockchain frameworks.	PoW, PoS, PoA, Blockchain Frameworks
Sustainability [17]	Observe the environmental impact and energy consumption of blockchain frameworks to determine their sustainability.	GPUs, PoW, PoS, PoA, Sustainability
Our study focuses on energy consumption	Utilizing linear regression, investigate the optimization of information system architecture for sustainable energy efficiency.	GPUs, PoW, energy consumption metrics

employs an analytical approach to understanding and addressing the developmental concerns of integrating blockchain technology in private enterprises. The table explores the relationship between consensus mechanisms, GPUs, blockchain frameworks, and sustainability that can be used to study intersections and optimization of blockchain implementations.

2.7. Sustainability in Optimizing Information System Architecture for Blockchain Framework

Blockchain frameworks, serving as distributed ledgers, enable the execution of smart contracts—self-executing agreements with terms directly written into code. The sustainability of blockchain systems, characterized by energy consumption, efficiency, and scalability, has been a focal point of research. Smart contracts, primarily popularized by Ethereum, introduce programmability into blockchain networks, expanding their use cases beyond cryptocurrency transactions [10]. However, concerns related to the energy-intensive nature of these platforms have spurred a quest for sustainable alternatives. For instance, Ethereum’s use of the PoW consensus mechanism, similar to Bitcoin, has been criticized for substantial energy consumption [23,24,85]. In recent years, the intersection of blockchain frameworks and smart contracts has attracted significant attention [9,10,39], particularly emphasizing the sustainability of underlying information system architectures.

Consensus techniques such as sharding and layer solutions (e.g., Plasma and the lightning network) have been examined to increase transaction throughput and scalability capacity while minimizing energy usage [2,37,86]. Alternative consensus mechanisms, such as PoS and delegated proof of stake (DPoS), have been studied to ensure sustainability while maintaining security and decentralization [38,87]. These mechanisms aim to significantly reduce the energy consumption of blockchain networks. By optimizing contract code for efficiency, the overall energy consumption of a blockchain network can be significantly reduced [39]. Wang et al. [11] delved into strategies for enhancing the energy efficiency of blockchain systems, proposing modifications in consensus algorithms and node management.

Furthermore, studies have explored the potential of employing optimized information system architectures tailored to the execution of smart contracts. Many existing studies that have focused on GPU optimization for PoW have spotlighted the urgency of mitigating the energy demands of cryptocurrency mining [12], including analysis of GPU hardware efficiency and refining mining algorithms to curtail the substantial electricity consumption characteristic of PoW tasks [11,88]. Iliakis et al. [15] explored energy-efficient GPU configurations that can sustain the performance needed for blockchain applications, including smart contracts. Stachowski et al. [89] dissected the energy consumption patterns of GPUs in blockchain mining, revealing opportunities for energy savings through the adaptive control of GPU operational states. These findings suggest that dynamically adjusting GPU frequencies can lead to substantial energy savings with minimal impact on mining efficiency. Concurrently, the study by Hijima et al. [90] illuminated the software techniques for mining software optimizations that can complement hardware adjustments to enhance overall efficient performance.

In addition, a particularly relevant factor has emerged from studies of the correlation between energy consumption and mining profitability. A study by Pathirana et al. [91] has shown that optimizing GPU settings for energy efficiency can maximize miners’ profits. Asdadi et al. [92] underscored the utility of multilinear regression in identifying the most impactful variables, thereby guiding the optimization process effectively. Ju et al. [93] introduced a parallel algorithm for multi-dimensional matrix profile mining on multiple GPUs, exploiting reduced precision modes for improved performance. Ronkin et al. [94] employed advanced regression analysis and neural networks to predict optimal GPU configurations to balance mining output and energy input. The efficacy of predictive models frequently hinges upon fast computation and accurate results, a resource not always readily accessible. This heightens diligence in efficiently utilizing computing power to process high-resolution images and large datasets. Many studies have collectively discussed the optimization of GPU mining using overclocking and undervolting techniques. Shuaib et al. [13] highlighted the benefits of using GPUs for cryptocurrency mining and compared the effectiveness of overclocking and undervolting in GPU optimization. Zamani et al. [95] also focused on energy-efficient GPU computing and presented an SAOU framework that reduces energy consumption through safe overclocking and undervolting without sacrificing performance.

Therefore, the sustainability of information system architectures for blockchain frameworks and smart contracts is an evolving area of research. Efforts are directed toward optimizing consensus mechanisms, enhancing scalability, and refining smart contract design to ensure efficient, secure, and sustainable operations. Optimizing information system architecture for blockchain frameworks and smart contracts thus presents a viable pathway toward sustainable solutions. By evaluating GPU factors for configurations through computational analysis and empirical evidence, this study can contribute to the development of blockchain systems that harmonize technological innovation with environmental responsibility.

3. Research Model and Methodology

Sustainability in blockchain technology emerges as a critical goal, particularly in energy consumption. The current study explores information system (IS) architecture, focusing on GPUs and their role in the energy dynamics of executing blockchain frameworks and smart contracts. The objective is to unearth strategies for enhancing the energy efficiency of proof of work (PoW) blockchain frameworks operated on GPUs.

A holistic research approach weaves together theoretical inquiry with empirical scrutiny. The journey begins with a comprehensive analysis of GPU information system architecture. Investigating the varied aspects of GPU architectures and their impact on the efficiency of blockchain processing sets the stage for identifying avenues for enhancement. A rigorous review of energy efficiency within the blockchain sphere follows this foundational analysis. By dissecting the existing body of literature and prevailing practices, this study not only situates itself within the current discourse but also casts light on the imperative for energy optimization within blockchain operations.

Our research methodology, which plays a pivotal role in achieving our goal, begins with formulating energy efficiency criteria. Benchmarks are established to appraise the energy consumption metrics across GPU-based blockchain systems. To untangle the intricacies of achieving a sustainable blockchain operation, multilinear regression analysis stands as a cornerstone analytical tool. This technique enables the quantification of relationships and the measurement of impacts stemming from a range of factors on energy consumption. Comparisons across GPU architectures, blockchain frameworks, and smart contracts are drawn, with the aim of eliciting profound insights that can inform future directions in sustainable blockchain technologies.

Our research culminates in a synthesized summary of methodological insights, underlining the potential that lies in optimizing GPU architectures for energy-efficient blockchain processing while preserving the best performance. The research propels the comprehension of achieving energy-efficient blockchain technology operation on GPUs and heralds a prospective shift to more sustainable practices in the blockchain field. These findings hold immense value for the future of sustainable blockchain technologies.

As illustrated in Figure 1, embarking on a mission to enhance sustainability in blockchain technology, a meticulous research methodology was crafted. The initial step delved into the literature, dissecting previous work on the energy efficiency of GPUs within blockchain frameworks. Here, a hypothesis was formed, laying the groundwork for the empirical investigation. Subsequently, the experimental design was articulated, focusing on selecting GPUs, mining software, and defining the variables critical to this study, such as core speed and energy consumption. This stage was instrumental in setting the parameters for the data collection that would fuel the research findings. The third phase centered on the development of a robust data collection protocol. Standardized procedures were established to ensure uniformity across the various tests, allowing for a reliable comparison of the results under controlled ambient conditions. Data preparation followed a crucial step where the collected data were organized and preprocessed, preparing the data for analysis. This phase was marked by rigorous attention to data integrity, ensuring the subsequent analysis would rest on a solid foundation of clean and well-structured data. With the data primed, multilinear regression analysis was then employed. This powerful statistical tool dissects the relationship between the chosen variables, shedding light on the intricate interplay between GPU settings and their impact on energy efficiency.

The research then transitioned to model validation and refinement. This study involved confirming that the regression model adhered to key statistical assumptions and tweaking the model where necessary to enhance its accuracy and reliability. Finally, the results were interpreted and reported. The regression analysis yielded insights that were carefully scrutinized and compared with existing studies. The outcomes were then compiled into a coherent narrative detailing the methodologies applied and the conclusions drawn. This final step was not just a summation of findings but also a reflection on this study’s implications, contributing valuable knowledge to the field and paving the way for future research endeavors.

3.1. Information System Architectures of Blockchain Technology

As illustrated in Figure 2, blockchain technology supports a robust and multifaceted layered architecture [96,97,98]. The development of a layered blockchain framework presents a multitude of benefits. Scalability is improved by segregating distinct layers for different functions in each layer, resulting in enhanced processing efficiency and facilitated upgrades. Adaptability renders it a desirable alternative for implementing blockchain technology. As each layer can be independently monitored and secured, the layered approach also improves security by decreasing the likelihood of system-wide vulnerabilities. Moreover, the layer design promotes compatibility among diverse blockchain systems and networks, augmenting connectivity and facilitating data exchange. Furthermore, the ability of a layered framework to accommodate a wide range of applications and services increases its adaptability to changing business requirements and technological developments.

The information system architecture of blockchain technology supports a layer design involving blockchain applications, framework, algorithms, networkchain, data, software, system, hardware, and sustainability concerns. Blockchain applications can primarily be used in many areas, such as logistics, finance, education, cryptocurrencies, healthcare, and government. The primary architectures are smart contracts and self-executing contractual states stored on the blockchain, which automate and enforce agreements without intermediaries, showcasing blockchain’s versatility beyond mere currency applications. Diving deeper into the blockchain framework, a variety of platforms, such as Hyperledger Fabric, Hyperledger Besu, Enterprise Ethereum, Quorum, Ant, and Corda, provide the infrastructure to implement blockchain solutions. These frameworks are built to accommodate different consensus mechanisms, including PoW, PoS, DPoS, PoA, and others, each with unique features to address various network security and governance challenges. Within these frameworks operate network chains like Ethereum, Binance smart chain, and others, some of which are compatible with the Ethereum virtual machine (EVM), facilitating interoperability and smart contract deployment. The data within these blockchains are organized into blocks that function across diverse system software environments, including Windows, Linux, and distributed operating systems, ensuring seamless integration and operation across various technological ecosystems. At the hardware level, the architecture extends to distributed computing and encompasses the emerging paradigm of edge computing, which brings computation and data storage closer to the needed location. Distributed computing contrasts with traditional client-server setups and is further enhanced by cloud and hybrid computing environments that offer scalable resources and services over the Internet. Incorporating GPUs into the blockchain’s information system architecture signifies a pivotal advancement, particularly in PoW blockchain operations. GPUs, renowned for their parallel processing capabilities, are instrumental in driving the performance and efficiency of blockchain computations. They are essential for accelerating transaction validations and consensus protocols and hold significant potential for optimizing energy consumption, a critical sustainability concern in blockchain operations. In juxtaposing GPUs with CPUs within the system architecture, the focus intensifies on balancing energy use with computational power, ensuring environmental considerations are heeded in the rapidly expanding digital ecosystem. As blockchain technology continues to evolve, the GPUs’ role in these architectures becomes increasingly central, emphasizing the need for continual innovation in hardware and software to meet the demand for sustainable, secure, and efficient blockchain systems.

The significance of optimizing GPU information system architecture for energy efficiency in blockchain mining cannot be overstated. Given the growing prevalence of blockchain technologies across industries and their associated high energy demands, the findings of this research hold immense relevance. This study aspires to usher in an era of sustainable blockchain operations by identifying the optimal combinations of GPUs and mining software. Our experiment aligns closely with the overarching objective of propelling the blockchain industry towards more sustainable practices. This study seeks to ascertain configurations that yield maximum efficiency by assessing each GPU and software combination. Furthermore, the research aims to create a data repository that can be instrumental for stakeholders in making informed choices regarding GPU investments and software applications for blockchain mining.

In conclusion, our research aims to provide a comprehensive guide for stakeholders looking for energy-efficient solutions in blockchain technologies. By investigating various configurations of GPUs and mining software, this study can significantly contribute to the discussion on energy efficiency in blockchain environments. Looking ahead, the knowledge gained from this study could profoundly impact the design of future GPU architectures and software applications specifically tailored for the efficient and sustainable mining of blockchain algorithms.

3.2. Sustainability of Energy Consumption Metrics

Understanding the energy consumption associated with blockchain technologies requires delving into specific metrics that encapsulate the nuances of power usage. Energy consumption metrics are pivotal indicators in evaluating the sustainability of information system (IS) architecture, particularly in blockchain frameworks and smart contracts. Various metrics have been proposed to assess energy consumption in blockchain operations. Among the key metrics, the energy consumed per transaction provides a granular insight into the efficiency of a blockchain network. The authors can draw comparisons between different networks and configurations by evaluating the amount of energy required to validate and add a single transaction to the blockchain, as illustrated in

Table 4. Evaluation criteria metrics and formula of energy consumption sustainability.

Metric	Description	Relevance to Blockchain	Calculating Formula	Relevant
Energy per transaction (EPT)	Quantifies the energy consumed (in kWh) for processing and validating a single transaction on the blockchain.	Provides insight into the energy efficiency of the blockchain network in handling transactions.	EPT = Total energy consumed/total transactions processed	[17]
Energy cost per coin (ECC)	Represents the energy cost (in kWh) incurred for mining a unit of cryptocurrency.	Allows assessment of the sustainability of cryptocurrency mining processes.	ECC = Total energy consumed/total coins mined	[19]
Power usage effectiveness (PUE)	Ratio of total energy consumed by a data center to the energy consumed by its IT equipment alone.	Indicates the efficiency of data centers used for blockchain operations.	PUE = Total data center energy/IT equipment energy	[20]
Data center infrastructure efficiency (DCiE)	Percentage representation of IT equipment energy consumption relative to total data center energy consumption.	Evaluates energy efficiency of data center infrastructure.	DCiE = (IT equipment energy/total data center energy) × 100%	[99]
Hash rate per watt (HPW)	Measures the number of hashes computed per watt of energy consumed.	Indicates better energy efficiency in cryptographic computations for blockchain validation.	HPW = Total hashes computed/total energy consumed	[100]
Energy footprint of smart contracts (EFSC)	Estimation of energy consumed by the execution of smart contracts on a blockchain network.	Sheds light on energy implications of deploying and executing smart contracts.	EFSC = Energy consumed by smart contracts/total executions	[101]

.

Another crucial metric is the energy cost per unit of cryptocurrency mined, often expressed in kWh per coin. This metric elucidates the direct relationship between the mining process and energy expenditure, providing a basis for assessing the sustainability of different mining hardware and algorithms. Additional metrics such as power usage effectiveness (PUE) and data center infrastructure efficiency (DCiE) extend the analysis to the infrastructure level. These metrics enable an examination of the energy efficiency of the entire data center or mining facility, including the computational elements and cooling systems, lighting, and other auxiliary components. By comprehensively evaluating these metrics, the research aims to present an encompassing view of the energy landscape in blockchain operations.

3.3. Data Collection

The focus has invariably shifted towards GPUs in the quest to unravel the intricacies of energy consumption within blockchain processes. These devices, celebrated for their ability to execute parallel operations seamlessly, have become integral to blockchain frameworks. The current research aims to analyze and optimize GPU information system architecture for the efficient execution of ETASH algorithms in blockchain mining for Eteruim cash (ETC) coin. It is crucial to emphasize the significance of proprietary large-scale real-world datasets to examine the ETASH algorithms using four distinct software applications utilizing Ethereum cash (ETC) coins as a practical application in a real-world environment. By doing so, the dataset performs as a real-world capability test and provides insightful information regarding the efficiency and effectiveness of these algorithms in practical operational mining ETASH blockchain scenarios. The duration of each test was approximately five minutes, and the gathered data are comprehensively presented as characteristics of GPU features in

Table 5. Data descriptive of GPU experiments.

Variables	RX5700	RX6700XT	RX6800XT	RTX2080Ti
GPU card	RX5700	RX6700XT	RX6800XT	RTX2080Ti
Memory (GB)	8 GB	12 GB	16 GB	11 GB
Core clock speed (MHz)	1350–1750 MHz	2000–2150 MHz	2000–2200 MHz	6700–7250 MHz
Memory clock speed (MHz)	1750–1850 MHz	2000–2150 MHz	2000–2200 MHz	7000–7500 MHz
Ambient temperature (°C)	26 °C	26 °C	26 °C	26 °C
Hash rate (MH/s)	Varies	Varies	Varies	Varies
Power consumption (wattH)	Varies	Varies	Varies	Varies
GPU temperature (°C)	Varies	Varies	Varies	Varies
Fan speed (%)	Up to 95%	Up to 95%	Up to 95%	Up to 95%
Compute units (CU)	Varies	Varies	Varies	Varies
Error rate (%)	Varies	Varies	Varies	Varies
Utilization rate (%)	Varies	Varies	Varies	Varies
Energy efficiency	Varies	Varies	Varies	Varies
GPU VDC (mV)	Varies	Varies	Varies	Varies
GPU VDC setting (mV)	Varies	Varies	Varies	Varies

. This methodology offers pragmatic observations regarding the efficacy of the methods within an authentic blockchain setting. The dataset incorporated a range of circumstances arising in extensive, proprietary datasets, including those utilized in public and private blockchain applications or systems with significantly biased data distributions. By conducting real-world sampling of ETASH-based coins, the dataset could illustrate the significance of findings applicable to a broader spectrum of real-world blockchain environments. Collecting data would contribute to a more inclusive comprehension of sustainability’s energy efficiency and performance in the face of diverse and demanding real-world circumstances. A diverse selection of hardware and software components underpinned the experimental setup designed for this investigation. On the hardware front, six GPUs were incorporated into a standard PC computer, including two Nvidia GTX 2080Ti, two AMD RTX 6800xt, one RTX 6700xt, and one RX 5700.

In an extensive empirical investigation, this study meticulously gathered data from a battery of tests performed on four GPUs: the rx5700, rx6700xt, rx6800xt, and the rtx2080ti. These GPUs were selected as they represent a cross-section of the current market offerings, each with unique performance characteristics and capabilities. The tests involved running four specialized mining software programs—SRBminer, Teamredminer, Gminer, and NBminer—chosen for their proven efficiency in executing the ETASH algorithm, a cryptographic puzzle integral to the Ethereum blockchain, on a system operating with Windows 11.

The GPUs underwent a detailed performance evaluation across a spectrum of operational settings, each chosen for its potential impact on GPU performance. The GPU clock speeds were varied from a base of 1350 MHz up to a peak of 1750 MHz to test their computational thresholds. Memory core speeds were also adjusted accordingly, with the rx5700 starting from 1750 MHz and ascending to 1850 MHz, the rx6700xt and rx6800xt ranging from 2000 MHz to 2150 MHz and 2200 MHz, respectively, and the rtx2080ti being pushed from a significant 6700 MHz to an impressive 7250 MHz. These adjustments allowed for an assessment of the GPU capabilities under different intensities of workload.

Crucial performance indicators were meticulously recorded to create a comprehensive dataset. Hash rates were measured to evaluate mining efficiency, while power consumption was monitored to gauge the energy requirements of each GPU configuration. GPU and ambient temperatures were logged to understand thermal dynamics and their implications for energy efficiency and hardware durability. Other recorded parameters included the GPU core and memory clock speeds, reflecting the operational frequency and memory usage, offering insights into the data handling capacity of each unit, as illustrated in Table 5.

The experiment also documented the cooling efficiency through fan speed and the number of computer units (CUs) essential for parallel processing tasks. Error rates provide insights into the stability and reliability of the GPUs under test conditions, while utilization rates reflect how intensely the GPUs are engaged during mining operations. Energy efficiency, a key sustainable metric, was calculated to provide a crucial balance between computational power and energy expenditure. The voltage supplied to and consumed by the GPU denoted as GPU VDC consumption and GPU VDC setting, was also captured to give a fuller picture of the power dynamics at play, as shown in

Table 6. Data collected for GPU optimizing performance indicators.

Performance Indicator	Description	Unit of Measurement
Hash rate	The computational speed at which a GPU can process data for mining.	Mega Hashes per second (MH/s)
Power consumption	The amount of electricity consumed by the GPU during operation.	Watts (W)
GPU temperature	The operating temperature of the GPUs, indicating potential overheating issues.	Celsius (°C)
Ambient temperature	The operating temperature of the experiment environment.	Celsius (°C)
GPU core clock speed	The speed at which the GPU’s core processes data.	Megahertz (MHz)
Memory clock speed	The speed at which the GPU’s memory (VRAM) operates.	Megahertz (MHz)
Memory usage	The amount of GPU memory (VRAM) utilized during operations.	Megabytes (MB) or Gigabytes (GB)
Fan speed	The speed at which the GPU’s cooling fans operates.	Revolutions per minute (RPM) or Percentage (%)
Compute units (CU)	The number of processing elements in a GPU, indicating parallel computing capabilities.	Count (units)
Error rate	The number of errors or failed attempts during operations.	Count (errors)
Utilization rate	The percentage of time the GPU is actively engaged in computations.	Percentage (%)
Energy efficiency	The hash rate per unit of power consumed.	Mega hashes per second per Watt (MH/s/W)
GPU Vdc consumption	Instances of the GPU voltage level consumption in a direct current (DC) electrical circuit.	millivolts (mV)
GPU Vdc setting	Limitation of the GPU voltage level consumption in a direct current (DC) electrical circuit.	millivolts (mV)

.

This detailed data collection lays the groundwork for a rigorous multilinear regression analysis, aiming to model the relationships between various operational parameters and their impact on GPU performance and energy consumption. The insights gleaned from these data will contribute significantly to understanding how to optimize GPU configurations for maximum efficiency in blockchain mining activities.

In this study, rigorous efforts were made to ensure the consistency and reliability of data collection by implementing several measures to control confounding variables and enhance the validity of the results. Firstly, a comprehensive strategy was employed to control confounding variables. Every extraneous factor that could potentially influence the GPU performance indicators, such as ambient temperature, software updates, and background processes, was systematically identified and controlled.

Randomization was another critical step taken to eliminate biases. The GPUs and mining software were assigned randomly to various tasks, ensuring no systematic errors skewed the results. Additionally, homogeneity of conditions was maintained by ensuring that all GPUs operated under the same environmental and system conditions, leveling the playing field for all the test cases.

Temporal stability was also addressed by conducting the experiments consistently, ensuring that time-related variables like system updates or network fluctuations did not influence the results. Manipulation checks were conducted periodically to ensure that the changes made in the independent variables were accurately reflected in the dependent variables.

The measurement precision was of paramount importance in this study. To ensure accurate data collection, software reports were meticulously scrutinized, and a digital multimeter was used to measure the energy consumption of the GPUs. By cross-verifying the data obtained from both sources, this study ensured the accuracy and reliability of the measurements.

In summary, this study consistently verified and ensured the integrity of the data collection processes through the diligent control of confounding variables, implementation of randomization and manipulation checks, assurance of homogeneity of conditions and temporal stability, and precision in measurements using software reports and a digital multimeter.

3.4. Optimization Techniques and Analysis

In pursuing the enhancement of blockchain technology with sustainable energy practices, the present research is dedicated to optimizing the architecture of GPU information systems for ETASH-based PoW blockchains. At the heart of this endeavor lies the energy efficiency score (EES), a sophisticated metric designed to evaluate the balance between high-level GPU performance and energy consumption. This study’s experimental foundation was built upon a robust PC setup, integrating an array of four GPUs, specifically RTX 2080Ti, RTX 6800xt, RTX 6700xt, and RX 5700.

In this exploration, the optimization techniques were centered on the dynamic adjustment of GPU clock speeds, precise calibration of memory bandwidth, and voltage settings. These parameters were meticulously modified to identify configuration yield maximum performance with minimal energy input, thereby elevating the energy efficiency score (EES). The EES, computed as the ratio of GPU performance to power consumption, further refined by weighted factors, provides a quantitative reflection of energy efficiency. This formula encapsulates both the raw power and the energy footprint of the mining operation, as expressed in Equation (1):

EES = (Hash rate/Power consumption) × Σ (Criterion weight × Normalized criterion score)

(1)

where performance represents a measure of the GPU’s mining performance, typically represented as the hash rate or mining speed; power consumption represents the amount of electrical power the GPU consumes during mining; weighted factors assign different weights to specific criteria based on their importance. For example, factors could be assigned based on the organization’s priorities, such as energy efficiency, cost-effectiveness, or environmental impact.

Here, the hash rate represents the GPU’s mining efficiency, while power consumption accounts for the electrical power utilized during the mining operation. The weighted factors offer a customizable framework to prioritize certain aspects over others, like cost-effectiveness, energy conservation, or environmental impact, depending on the organization’s strategic goals. The implications of an optimized EES are manifold. For organizations and miners, it is a benchmark of energy efficiency and a guide for configuring hardware setups and adopting energy-saving techniques. By advancing this metric, this study contributes to the broader dialogue on environmental stewardship and responsible resource management, aligning blockchain operations with overarching sustainability objectives.

This research illuminates the potential pathways to a more energy-conscious blockchain ecosystem, underscoring the importance of EES as a catalyst for continuous improvement and sustainable advancement in the GPU-powered landscapes of blockchain technology.

3.5. Verifications of Validation and Reliability Dataset

In this research, which delves into optimizing GPU information system architecture for ETASH-based PoW blockchains, particularly in simulating ETC mining coins, the imperative is to ensure the utmost validity and reliability of the analysis. The experiment entails a meticulous application of statistical methodologies to guarantee that the data acquired from a combination of four distinct GPUs and four mining software programs adhere stringently to the highest scientific rigor and precision standards.

The essence of validity in this context is accurately measuring the interplay between GPU performance and energy consumption. On the other hand, reliability refers to the consistency and repeatability of these measurements across various testing scenarios. The research journey commences with an exploratory data analysis, a critical step to unearth the underlying structure of the data and identify any anomalies or outliers that could influence the outcomes. Following this data analysis, hypothesis testing uses arbitrage pricing theory (APT) statistical methods to examine the dynamics between different variables.

Part of ensuring internal validity is the meticulous control and selection of variables to mitigate the impact of extraneous factors that could otherwise skew the results. However, in the realm of technical and empirical research like ours, where the primary goal is to understand the relationship between various independent hardware and software parameters of GPUs (such as clock speed, memory usage, and temperature) and a dependent variable (such as energy efficiency or hash rate), the concept of internal consistency measured by Cronbach’s alpha does not apply. Our study relies on the research objective, quantifiable performance indicators rather than subjective or abstract constructs that require consistency checks. The authors are dealing with direct measurements and technical specifications, where each variable independently contributes to the overall system performance and does not necessarily represent a unified latent construct.

In the process of this research, extensive efforts are dedicated to maintaining both internal and external validity, ensuring data integrity, and diligently checking for multicollinearity among variables. This study meticulously monitors multicollinearity among independent variables using variance inflation factors (VIFs), ensuring each predictor maintains its distinct predictive power.

Moreover, this comprehensive approach, combining rigorous planning and meticulous execution, ensures that this study adheres to the highest reliability, validity, and data integrity standards, thus offering robust and trustworthy insights into optimizing GPU performance for blockchain computations. Reliability is ascertained through repeated tests under uniform conditions, confirming the findings’ consistency and reproducibility. Additionally, measures such as randomized test sequences and manipulation checks are implemented to fortify internal validity, ensuring that the outcomes are a true reflection of the effects of GPU configurations rather than extraneous variables. To enhance external validity, a diverse array of GPUs and mining software is selected, thereby broadening the scope and applicability of the findings. This strategic selection ensures that the results are representative and can be generalized to similar real-world scenarios.

This study also emphasizes the integrity of data collection, employing rigorous record-keeping and automated logging systems to minimize human error and ensure uniform data collection. Linearity verification forms a crucial analysis component, examining relationships between independent and dependent variables through diagnostic plots and statistical tests. These plots’ absence of systemic deviations confirms the linearity assumption essential for multilinear regression analysis.

3.6. Multilinear Regression Analysis

In the dynamic areas of blockchain technology, especially within the blockchain framework-utilized PoW approach, the imperative of energy efficiency is paramount. This study ventures into this area by leveraging multilinear regression analysis as an exploratory tool. The focus is not on prediction but rather on deciphering the intricate interplay between GPU cards’ operational attributes and their efficient performance and energy consumption. This intricate analysis is applied to a dataset from four distinct GPU cards, each operating under various configurations and tested across four different mining software programs, and all executing ETASH algorithms. Central to this exploration is the utilization of multilinear regression to elucidate how various independent variables—such as hash rate, computation units, memory usage, GPU core and memory clock speeds, fan speeds, voltage settings, and operational temperature—influence energy consumption. This methodical approach uncovers which factors significantly impact energy usage, illuminating paths for potential optimization. The model posits a linear relationship among variables, suggesting a proportional contribution of each performance indicator to energy consumption, thus yielding deep insights into their correlations and interactions. The following formula of Equation (2) can represent the relationship between the dependent and independent variables:

E = β₀ + β₁ × HR + β₂ × MU + β₃ × CCS + β₄ × MCS + β₅ × T + ε

(2)

where E represents energy consumption (dependent variable); HR represents hash rate;

MU is memory usage;

CCS is core clock speed;

MCS is memory clock speed;

T is temperature

β₀ represents Y-intercept (constant term); and

β₁, β₂, β₃, β₄, β₅ are coefficients representing the change in E for a one-unit change in the corresponding independent variable.

ε: Error term

This formula effectively models how variations in hash rate, memory usage, core and memory clock speeds, and temperature can be linearly related to changes in energy consumption. By analyzing the coefficients β₁ to β₅, the authors can gauge the impact of each independent variable on energy consumption, thereby offering insights into potential optimization strategies. This study has applied a multilinear regression by dissecting data layers to reveal how various GPU operational aspects contribute to energy consumption in PoW blockchain technology. This approach aligns technological advancements with environmental stewardship, marking a significant stride in understanding sustainable practices in blockchain mining.

Energy consumption, the pivotal dependent variable, is a critical measure of operational efficiency and ecological responsibility. In a domain where energy-intensive processes are often scrutinized, optimizing energy usage becomes not just a technical endeavor but also a commitment to environmental sustainability. The analysis is meticulously designed to dissect the data’s complex relationships, offering a comprehensive understanding of how different GPU configurations affect energy efficiency. It delves into the subtleties of GPU behavior during mining, examining variables like hash rate and core clock speed, which indicate the GPU’s computational capacity and operational frequencies. These insights are instrumental in evaluating their impact on energy efficiency and overall performance. This study’s overarching goal is to optimize GPU performance while judiciously managing energy consumption. The research offers a detailed, nuanced perspective, enriching the discourse on efficient and sustainable GPU-based cryptocurrency mining through a detailed assessment and interpretation of GPU performances’ relationships. Eventually, this study explores the several variables to establish an information system architecture that emphasizes energy efficiency in blockchain applications.

4. Results

In this section of the study, the authors meticulously explore the intricacies of optimizing GPU information system architecture for enhanced energy efficiency within the realm of blockchain technology. Our findings express a detailed examination of descriptive statistics by providing a comprehensive overview of various performance metrics across multiple GPU configurations. These statistics vividly illustrate trends and patterns in hash rates, power consumption, and thermal dynamics. Rigorous checks for linearity and multicollinearity further strengthen the robustness of our analysis. These checks ensure the validity of our multilinear regression model, affirming that the relationships between independent and dependent variables are linear and that the predictors in our model are not unduly interdependent. A key highlight of this section is the comparative analysis, where the results of the multilinear regression are intricately dissected. This part of the study quantifies each variable’s impact on energy efficiency and offers crucial insights into how different GPU configurations can be optimized for energy efficiency in blockchain operations.

4.1. Descriptive Statistics Analysis of Dataset

As depicted in

Table 7. Descriptive statistics of the dataset.

Features	Records	Mean	Std Dev	Min.	25%	50%	75%	Max.
GPU card	7992	2.81	0.97	1.00	2.00	3.00	4.00	4.00
ETASH	7992	2.00	0.82	1.00	1.00	2.00	3.00	3.00
Memory Gb	7992	8.00	0.00	8.00	8.00	8.00	8.00	8.00
Core speed MHz	7992	1499.10	125.47	1300	1400	1500	1600	1750
Core memory MHz	7992	3535.48	2283.37	1750	2050	2100	6800	7200
Ambient temperature	7992	27	0	27	27	27	27	27
Bandwidth	7992	265.89	62.54	192	192	256	352	352
Core units	7992	3699.89	976.04	2304	2560	4352	4608	4608
Fan speed	7992	2919.34	588.89	2200	2600	2700	2900	4700
Fan %	7992	90.98	4.35	64.00	85.00	92.00	95.00	95.00
Core temperature (°C)	7992	51.26	4.87	44.00	44.00	54.00	55.00	55.00
Used Vdc (mV)	7992	877.48	11.5	800	875	880	880	910
Vdc (mV)	7992	977.61	70.57	780	920	980	1040	1100
Energy (Wh)	7992	129.6	20.14	100	108	130	153	163
Hash rate (MH/s)	7992	53.93	6.64	43.67	47.15	53.80	60.87	64.80
EES (MH/s/Wh)	7992	0.418	0.017	0.380	0.406	0.431	0.457	0.482

, the statistical analysis of the GPU descriptive dataset, encompassing 7992 records, reveals significant insights into various performance metrics. The GPU card and ETASH, with average values of 2.81 and 2.00, respectively, demonstrate GPU types and configuration diversity. A uniform memory capacity of 8 GB across all units points to a standardized memory allocation. Core speed MHz, averaging 1499.10 MHz, shows variability in processing speeds, a crucial factor for computational efficiency. Similarly, core memory MHz displays a wide range, emphasizing the variance in memory speeds among different GPUs. The consistent ambient temperature of 27 °C across all records suggests a controlled testing environment, essential for accurate performance assessment. Bandwidth and core units, averaging 265.89 and 3699.89, respectively, highlight differences in data transfer capabilities and processing power. Fan speed and fan percentage variability indicate the GPUs’ differing cooling requirements and efficiencies, which are crucial for maintaining optimal operating conditions. With a narrow range, core temperature underscores the effective thermal management in these units. The operational voltages were reflected by used Vdc (mV) and Vdc (mV) averages of 877.48 mV and 977.61 mV, outlining the power needs and efficiency of the GPUs. Energy consumption, averaging 129.6 Wh, and hash rate, averaging 53.93 MH/s, are critical for evaluating the GPUs’ power efficiency and computational output. The EES (MH/s/Wh), with a mean value of 0.418, provides a quantifiable measure of how efficiently these GPUs convert energy into computational power. This comprehensive analysis highlights the diverse capabilities and efficiencies of the GPUs in the dataset and provides understanding and optimizes the resources of GPUs’ performance.

4.2. Distributions Analysis of Dataset

The multilinear regression analysis of skewness and kurtosis ensures that the data adhere to the necessary assumptions for accurate modeling and interpretation. Skewness, which measures the asymmetry of the data distribution, is particularly important for assessing the normality of residuals in the regression model. Significant skewness can indicate that the linear model needs to fully capture the underlying relationships in the data, potentially due to outliers or a non-linear relationship. Kurtosis, indicating the ‘tailedness’ of the distribution, is essential for identifying outliers. High kurtosis in the residuals suggests that the model’s errors are not evenly distributed, with extreme values not well-explained by this model. Both skewness and kurtosis are vital diagnostic tools in regression analysis. The descriptive statistics of skewness and kurtosis help determine the need for data transformation, assess the model’s accuracy, and ensure the reliability of confidence intervals and hypothesis tests. Understanding these aspects of data distribution is key to applying multilinear regression effectively, leading to more robust, reliable, and interpretable results.

The skewness and kurtosis analysis of various features in the GPU dataset provides significant insights into their distribution characteristics, as shown in

Table 8. Skewness and kurtosis distribution of the dataset.

Variable	Skewness	Kurtosis	Skewness Interpretation	Kurtosis Interpretation
GPU card	−0.23	−1.05	Fairly symmetrical	Less outliers
ETASH	0.00	−1.50	Fairly symmetrical	Less outliers
Memory Gb	0.00	0.00	Fairly symmetrical	Less outliers
Core speed MHz	0.14	−1.02	Fairly symmetrical	Less outliers
Core memory MHz	0.86	−1.25	Moderately skewed	Less outliers
Ambient temperature	0.00	0.00	Fairly symmetrical	Less outliers
Bandwith	0.29	−1.33	Fairly symmetrical	Less outliers
Core units	−0.42	−1.76	Fairly symmetrical	Less outliers
Fan speed	2.56	4.98	Highly skewed	More outliers
Fan %	−0.76	−0.26	Moderately skewed	Less outliers
Core temperature	−0.77	−1.33	Moderately skewed	Less outliers
Used Vdc mV	−3.29	20.45	Highly skewed	More outliers
Vdc mV	−0.08	−0.83	Fairly symmetrical	Less outliers
Energy Wh	0.24	−1.37	Fairly symmetrical	Less outliers
Hash rate MH/s	0.08	−1.26	Fairly symmetrical	Less outliers

. Variables like GPU card, ETASH, memory Gb, core speed MHz, ambient temperature, bandwidth, core units, Vdc mV, energy Wh, and hash rate MH/s exhibit fairly symmetrical distributions with skewness values close to zero, indicating a balanced spread around the mean. This symmetry is further supported by their kurtosis values, which suggest fewer outliers than a normal distribution. On the other hand, core memory MHz and fan % show moderate skewness, indicating slight asymmetry in their distributions. While core memory MHz is moderately skewed towards higher values, fan % leans towards lower values, but both still have fewer outliers.

However, fan speed and used Vdc mV stand out with their highly skewed distributions. Fan speed has a significant positive skewness, indicating a long tail towards higher values, and its high kurtosis points to more pronounced outliers in the data. Conversely, used Vdc mV exhibits a substantial negative skewness, suggesting a concentration of data points at the higher end and a tail stretching towards lower values, along with an exceptionally high kurtosis, indicating a large number of extreme outliers.

These skewness and kurtosis values collectively offer a detailed view of the data’s distribution, highlighting the balance, asymmetry, and presence of outliers in each feature. Such insights are critical for data preprocessing, guiding decisions on normalization and transformation, and informing the choice of statistical models and methods for further analysis.

4.3. Multicollinearity Analysis of Features

Multilinear regression analysis is the identification of the optimal set of correlating features. This study involves finding features that correlate significantly with the dependent variable while minimizing multicollinearity among themselves. Multicollinearity occurs when two or more independent variables in a regression model are highly correlated, leading to unreliable and unstable estimates of regression coefficients. This issue can compromise the model’s reliability and make it difficult to determine the individual effects of predictors on the dependent variable. The first step is to conduct a correlation analysis using a correlation matrix of all variables to address this variable. This matrix is crucial in identifying pairs of variables that are highly correlated. A common practice is to set a threshold for significance, often a minimum value of 0.65 for correlation, which indicates a meaningful linear relationship. However, this threshold is not absolute and may vary based on the study’s context. A correlation above 0.65 is substantial enough to imply a significant relationship but not so high as to suggest likely multicollinearity, as illustrated in Figure 3.

The scatter plots in Figure 4 illustrate the correlation between various GPU parameters (core speed, fan speed, core memory, and core units) and watt hours (Wh) of energy consumption. The purpose of every plot is to evaluate the degree of linearity in the correlation between these characteristics and energy consumption, which is an essential component in comprehending how GPU configurations affect power efficiency. Each graph features a linear regression line (possibly the orange line) to facilitate the visualization of this relationship. While the scatter plots provide insights into the potential correlations between specific GPU characteristics and energy usage, they fail to account for the collective impacts that these characteristics may have. Multiple linear regression emerges as an especially significant statistical technique in this study by fitting a linear equation to the observed data to model the relationship between two or more explanatory variables (or features) and a response variable.

Multilinear regression enables the examination of the collective impact of various GPU configurations on the consumption of power. As an illustration, while core speed alone does not substantially affect energy consumption, its combined influence with fan speed and core memory becomes more conspicuous. Interaction effects are incorporated to determine whether the impact of one feature on energy consumption varies with the value of another feature. By employing this methodology, intricate correlations that are imperceptible when examining individual features can be unveiled. Consider the possibility that latent variables influence both the characteristics and the energy usage. When this occurs, multilinear regression can be utilized to control for these confounding variables; thereby, quantifying the impact of each feature while keeping the others constant and revealing a more precise correlation between the desired characteristics and energy consumption. This approach discerns the comparative significance of every setting concerning its impact on energy consumption. Therefore, multilinear regression is a structural framework for hypothesis testing to ascertain whether a correlation between the set of characteristics and energy consumption is statistically significant.

The ANOVA summaries, displayed in

Table 9. Summary ANOVA analysis of the efficient performance model.

	Sum Square	df	Mean Square	F	p-Value
Total	352,444.139	7991	0.000	0.000	0.000
Error	13,376.345	7985	1.675	0.000	0.000
Regression	339,067.794	6	56,511.299	33,734.381	0.000

and

Table 10. Summary ANOVA analysis of the efficient energy model.

	Sum Square	df	Mean Square	F	p-Value
Total	3,239,869.455	7991	0.000	0.000	0.000
Error	36,167.183	7986	4.529	0.000	0.000
Regression	3,203,702.272	5	640,740.454	141,480.560	0.000

, perform a statistical analysis of two distinct models pertaining to GPU performance: one is concerned with energy efficiency, while the other is concerned with efficient performance. By decomposing the variability in the dependent variables into components ascribed to the models and random error, both summaries provide valuable information regarding the predictive accuracy of the models with respect to real-world results.

Table 9 presents the details of the efficient performance model. The sum of squares represents a significant portion of the total variance in the data. The substantial degree of freedom, which indicates the presence of diverse and substantial data, is noteworthy. Notably, the mean square error is negligible, indicating that the amount of variability the model cannot account for is minimal. The exceptionally high F-statistic signifies that the model possesses a substantial explanatory capacity; the analyzed performance metric is significantly influenced by the predictors as a whole. The p-value, effectively zero, emphasizes this significance, suggesting that the regression model predicts performance significantly.

Table 10 additionally delineates the model of efficient energy. Likewise, the sum of squares is substantial in this case, suggesting that energy consumption is highly variable overall. The five predictors comprising the model are represented by the degrees of freedom for regression. The mean squared error deviates slightly from the performance model, suggesting a marginally greater amount of unexplained variability. However, the F-statistic is significantly elevated, further indicating the strong correlation between the predictors and energy consumption. Reaffirming the statistical significance of these results, the p-value is negligible.

The variance inflation factors (VIFs) for each feature in two models—an efficient energy model and an efficient performance model—is displayed in

Table 11. VIF Multicollinearity verification of the models.

Features	VIF’s Efficient Performance Model	VIF’s Efficient Energy Model
ETASH	1.000	-
Core memory MHz	1.485	1.485
Core speed MHz	1.057	1.057
Used Vdc mV	1.096	1.096
Fan speed	1.224	1.224
Core temperature	1.338	1.338

. The VIF quantifies the increase in variance of an estimated regression coefficient due to correlation among the predictors. Without correlation among any factors, all VIFs will equal 1.

The VIFs for the efficient performance model range from 1.000 to 1.485, which is extremely close to 1, suggesting that the predictors in this model exhibit minimal to no multicollinearity. In general, a VIF value below five indicates that multicollinearity is not significantly affecting the model; the closer the VIF is to one, the less significant the multicollinearity’s effect. Except for ETASH, which is omitted from the energy model, the efficient energy model includes the same features with identical VIF values. This consistency indicates that the efficient energy model does not exhibit multicollinearity.

ETASH has a VIF of 1.000 in the performance model, which indicates that it is not correlated with any other variables. The VIFs of ‘core memory MHz’, ‘core speed MHz’, ‘used Vdc mV’, ‘fan speed’, and ‘core temperature’ indicate minimal multicollinearity in both models, which is advantageous. This result indicates that every feature contributes distinct information not duplicated or encoded by the other features.

The significance of the results ought not to be exaggerated. The absence of multicollinearity between variables increases the likelihood that the estimated regression coefficients for both the efficient performance and energy models are dependable and stable. From a practical standpoint, this stability enhances the assurance of interpreting the influence of each variable on the dependent variable. For example, by manipulating the value of ‘core speed MHz’, the value becomes more feasible to ascertain with greater certainty that the fluctuations observed in the dependent variable are attributable to this particular attribute and not to a proxy for another correlated variable.

4.4. Multilinear Regression Analysis

An examination of the correlation between energy consumption, efficient performance, and PoW blockchain technology was conducted. The research inquiry pertains to the characteristics that most impact effective energy consumption. The dependent variable of efficient energy consumption was regressed against the predicting variables of fan speed, used Vdc mV, core speed MHz, and core temperature MHz, as shown in Figure 5 on the right. With an F-statistic of 141,480.560 and a p-value below 0.000, the independent variables explain efficient energy consumption significantly. This result indicates that the five factors investigated substantially influence efficient energy consumption. In addition, the R-squared value of 0.989 indicates that the model serves as a significant explanatory power, accounting for 98.9% of the variance in efficient energy consumption.

Furthermore, an evaluation was conducted on the coefficients to determine the extent to which each factor affected the criterion variable of energy efficiency. The findings indicate a significant positive relationship between core memory MHz and efficient energy consumption (B = 0.622, t = 431.810, p < 0.000). This result indicates that substantial improvements in energy efficiency are associated with increases in core memory speed. On the other hand, the model can observe that core temperature exerts a substantial adverse effect (B = −1.144, t = 836.190, p < 0.000), suggesting that elevated temperatures have a detrimental effect on energy efficiency. This result may be attributed to the augmented cooling demands or suboptimal operational circumstances. Additional variables, such as used Vdc mV (B = 0.118, t = 95.549, p < 0.000), core speed MHz (B = 0.079, t = 64.962, p < 0.000), and fan speed (B = 0.087, t = 66.205, p < 0.000), despite possessing smaller coefficients, continue to contribute positively and statistically significantly to the improvement of energy efficiency. The comprehensive analysis conducted in this study offers significant insights that can be utilized to optimize GPU settings to conserve energy in PoW blockchain applications.

To deal with analysis, a regression analysis was conducted on the dependent performance variable using the predictor variables: ETASH, fan speed, core speed (MHz), core temperature, core memory MHz, and used Vdc mV. The performance of the five examined factors is substantially influenced, as indicated by the F-statistic of 33,734.381 and the p-value of less than 0.000 for these independent variables, which significantly predict performance. Moreover, as depicted in Figure 5 on the left, the R-squared value of 0.962 indicates that the model explains 96.2% of the variance in performance, suggesting a substantial degree of explanatory capability.

An analysis was conducted on the coefficients of the independent variables to ascertain their distinct contributions to the model. The results reveal that enhancements in core memory speed are linked with significant performance gains (B = 0.666, t = 250.511, p < 0.000). This result demonstrates that core memory frequency is crucial in boosting performance, which should greatly interest our audience. The negative correlation between core temperature and performance (B = −1.125, t = 446.168, p < 0.000) suggests that increased temperatures may hinder performance due to heat-related inefficiencies or thermal throttling. ETASH, a variable potentially associated with a particular facet of the GPU’s hashing capability, shows a statistically significant and positive correlation with performance (B = 0.056, t = 25.681, p < 0.000). Although fan speed and used Vdc mV have smaller coefficients, they remain positively correlated with performance (B = 0.137, t = 56.671, p < 0.000; B = 0.069, t = 30.440, p < 0.000, respectively). This suggests that improved voltage control and cooling contribute to enhanced performance outcomes.

The results of a multiple linear regression analysis on an efficient performance model are presented in

Table 12. Summary coefficients of multilinear regression for efficient performance model.

Features	Standardized Coefficients	SE	T Value	p-Value	2.5%	97.5%
Core Speed MHz	0.041	0.000	18.283	0.000	0.002	0.002
Core Temperature	−1.125	0.003	446.168	0.000	−1.541	−1.527
Core Memory MHz	0.666	0.000	250.511	0.000	0.002	0.002
ETASH	0.056	0.018	25.681	0.000	0.421	0.490
Fan Speed	0.137	0.000	56.671	0.000	0.001	0.002
Used Vdc mV	0.069	0.001	30.440	0.000	0.038	0.043
Intercept	0.000	1.206	67.879	0.000	79.496	84.224

and

Table 13. Summary coefficients of multilinear regression for efficient energy model.

Features	Standardized Coefficients	SE	T Value	p-Value	2.5%	97.5%
Core Speed MHz	0.079	0.000	64.962	0.000	0.012	0.013
Core Memory MHz	0.622	0.000	431.810	0.000	0.005	0.006
Core Temperature	−1.144	0.006	836.190	0.000	−4.739	−4.716
Fan Speed	0.087	0.000	66.205	0.000	0.003	0.003
Used Vdc mV	0.118	0.002	95.549	0.000	0.203	0.211
Intercept	0.000	1.982	72.259	0.000	139.335	147.105

, which detail the impact of different GPU features on a dependent variable related to performance. The significance of each feature in performance prediction is denoted by the standardized coefficients, where the sign of the relationship indicates the direction of the association.

The standardized positive coefficient for the megahertz (MHz) core speed is marginal but statistically significant; this indicates that a slight performance improvement can be anticipated as the core speed increases. The conclusion that this is statistically significant is supported by a very high T value and a p-value of 0.000. The narrowness of the confidence interval serves to strengthen the estimation’s precision.

On the contrary, the standardized coefficient for core temperature is significantly negative, indicating a strong inverse correlation with performance. This result is crucial for our audience to note, as it suggests that maintaining optimal core temperature is essential for achieving high performance. The extremely high T and p-values of 0.000 further confirm the significance of this predictor. The fact that the confidence interval does not intersect zero provides confirmation that the relationship between core temperature and performance is robust. The standardized coefficient for core memory MHz is substantially positive, indicating that memory speed has a substantial positive effect on performance. The statistical significance of the result is supported by the T value and p-value, while the narrow confidence interval signifies an estimate that is precise.

The standardized coefficient of ETASH, which may be an efficiency metric, is also positive. This result is a significant finding that our audience should note, indicating a robust and noteworthy correlation between ETASH and performance. The T value is statistically significant, and the p-value is 0.000, further emphasizing the importance of this correlation.

A positive fan speed coefficient signifies that an increase in fan speed is correlated with enhanced performance. The T value and p-value support the statistical significance of this relationship.

Despite having a smaller positive coefficient, the utilized Vdc in millivolts (mV) remains a significant predictor of performance, as indicated by its T value and p-value.

In this model, the intercept, which denotes the anticipated value of the dependent variable under the condition that all predictors are set to zero, is generally not significant. However, with a p-value of 0.000 and a significant T value, the model intercept differs significantly from zero.

The ‘core speed MHz’ variable exhibits a marginally positive standardized coefficient, indicating that an increase in core speed is linked to a marginal enhancement in energy efficiency. The considerably larger positive coefficient for ‘core memory MHz’ indicates that memory speed is a substantial determinant of energy efficiency in this model.

In contrast, the coefficient associated with ‘core temperature’ is considerably negative, suggesting that an increase in core temperature substantially reduces energy efficiency. The reason for this may be the result of increased cooling demands, which necessitate a more significant amount of energy, or the result could indicate that higher temperatures reduce the GPU’s efficiency.

Although their coefficients are small, the positive correlations between ‘fan speed’ and ‘used Vdc mV’ indicate that these variables also enhance energy efficiency, albeit to a lesser degree than core memory speed. It is noteworthy that within this model, fan speed, which is conventionally linked to cooling and consequently may result in increased energy consumption, exhibits a positive correlation with energy efficiency. This observation suggests that efficient cooling enhances overall energy efficiency by enabling the GPU to function at its peak performance.

All features exhibit remarkably high T values and p-values of 0.000, signifying that the associations they denote are statistically significant and that the probability that they are the result of random variation is exceedingly small.

The narrow confidence intervals for each coefficient, which span from the 2.5th to the 97.5th percentiles, indicate that the estimates are highly precise. The strength of the observed relationships is further reinforced by the fact that none of the confidence intervals intersect zero.

4.5. Quality of Multilinear Regression Results

Two plots frequently employed in statistical analysis to evaluate the normality of residuals and the existence of autocorrelation in a regression model are illustrated in Figure 6 and Figure 7, using SmartPLS 4 software. The methodological overview of the diagnostic steps of the regression model is presented in these plots. The findings indicate that although the model exhibits a satisfactory fit for most of the data (as indicated by the Q-Q plot), concerns may arise regarding outliers, extreme values, and potential autocorrelation. These issues may necessitate the implementation of a robust regression technique or, if the data are sequential, direct modeling of the time series components.

The Q-Q (quantile–quantile) plot on the left is a graphical instrument for assessing whether a given dataset adheres to a specific distribution, typically the normal distribution. The quantiles of the residuals from the regression model are symbolized by the blue data points, plotted against the expected quantiles of a normal distribution, denoted by the red line. Assuming the residuals follow a normal distribution, the points should be positioned close to this reference line. The plot indicates that a significant proportion of the data points, particularly in the central quantiles, closely align with the reference line. However, certain deviations are observed in the tails, which may indicate the existence of outliers or heavy tails in the residual distribution.

The residual autocorrelation plot on the right illustrates the autocorrelations of the residuals across various time lags. The authors anticipate that in the absence of autocorrelation, the plot would exhibit points arbitrarily dispersed around the zero line, as denoted by the blue dashed lines corresponding to confidence intervals for the autocorrelation estimates. The graph illustrates that the autocorrelations fall within the anticipated range for the absence of autocorrelation for most lags. However, certain points lie beyond the confidence bands, suggesting the possibility of autocorrelation at specific lags.

The Q-Q plot is significant because it verifies the normality of residuals, a fundamental assumption of numerous statistical models, including linear regression. Unusual expectation values may compromise the dependability of specific hypothesis tests linked to the model. The observation that most data points lie along the reference line implies that the assumption of normality for the central range of the data is approximately satisfied. However, additional investigation may be necessary for the tails. The residual autocorrelation plot holds considerable importance as it evaluates an additional fundamental assumption: the independence of the residuals derived from the model. Non-independent residuals, as evidenced by autocorrelation, have the potential to impact the estimated coefficients and standard errors of a model.

5. Discussion

5.1. Performance and Energy Efficiency in PoW Blockchain Technology

Examining the results explores the complexities of GPU performance within the framework of proof-of-work blockchain technology, particularly emphasizing performance and energy efficiency. The results obtained from multilinear regression analyses provide valuable insights into the effects of different GPU configurations on the sustained functionality of blockchain operations.

Upon analyzing the optimizing effects of voltage and temperature dynamics on the efficiency of PoW blockchains, the result was discovered that increased voltage settings have an adverse effect on energy efficiency (p < 0.001, coefficients for Vdc mV are negative). Voltage settings that can potentially increase the energy efficiency of mining are crucial for ensuring the sustainability of blockchain operations. On the contrary, the significant positive correlation coefficient (p < 0.001) between core temperature and heat management highlights the importance of effective heat control to ensure efficient mining operations. This result highlights the criticality of maintaining a precise equilibrium between energy usage and operational temperature.

Upon scrutinizing variables associated with memory clock speed, it is discovered that a negative coefficient (p < 0.001) for core memory MHz challenges conventional wisdom, which prioritizes faster clock speeds. This research suggests that increased velocities could result in improved energy efficiency. This research discovery is critical for the long-term sustainability of blockchain mining, as it prompts a reassessment of the clock speed configurations of graphics processing units.

Based on the evaluation of algorithm efficiency, a statistically significant correlation (p < 0.001) is observed between performance and the ETASH algorithm. This result implies that the selection and improvement of algorithms are pivotal elements in augmenting the energy efficiency of blockchain processes. Additionally, the analysis findings revealed a statistically significant inverse correlation (p < 0.001) between the core speed in megahertz and the performance. This finding suggests that there is no guarantee that higher velocities will result in improved energy efficiency. This study’s results demonstrate a significant correlation (p < 0.001) between fan speed and performance, emphasizing the critical need for efficient cooling systems to preserve mining productivity at its highest level.

The strategies presented herein for GPU configuration that facilitate sustainable PoW blockchain mining are supported by empirical evidence. Consequently, their actions serve to advance the cause of sustainability in the mining sector. By examining the effects of voltage, temperature, and clock speeds on energy efficiency, this research paper contributes to the comprehension of the intricate relationship between GPU performance and energy consumption and paves the way for the development of more environmentally sustainable mining techniques. It is imperative to attain a comprehensive comprehension of this subject matter to facilitate the development of blockchain technologies that are ecologically conscious and capable of reconciling computational requirements with sustainability. The research findings significantly contribute to the progress of energy-efficient blockchain operations by balancing technological innovation and sustainability in response to growing concerns about the environmental impact of proof-of-concept blockchain technology.

Furthermore, through comprehensive statistical analyses, stakeholders are empowered to make informed decisions regarding configuring GPUs for blockchain technologies. As mentioned earlier, the decisions are grounded in empirical evidence and seek to maximize efficiency while reducing power usage. This study provides substantial contributions to understanding GPU selection and administration in PoW blockchain applications. This article highlights the importance of energy efficiency and sustainability and provides empirical evidence regarding the impact of different GPU features on energy consumption. The overarching objective is to encourage the adoption of blockchain methodologies that are more environmentally sustainable.

5.2. Computational Complexity Analysis

This study involved conducting an exhaustive computational complexity analysis of the ETASH mining software depending on various GPU configurations, specifically emphasizing three critical elements: space complexity pertaining to the performance utilization of GPU memory, energy power consumption measured in mVDC, and overall electricity consumption measured in watts per hour. To guarantee a rigorous and uniform assessment, every configuration underwent three trials under distinct conditions (worst, best, and average cases) with a strict time constraint of five minutes per test.

In the initial assessment, the authors assessed the space complexity of the ETASH algorithm by measuring memory allocation and utilization patterns throughout the mining process while imposing a specific GPU memory constraint of up to 8 GB. This investigation aimed to determine the algorithm’s scalability regarding memory usage across various operational parameters, including hash rate and block size. The significance of this analysis is based on its ability to detect inefficiencies and scalability issues in mining operations that heavily rely on GPUs.

The authors analyzed the system’s performance across three separate scenarios to obtain a comprehensive understanding of its capabilities and limitations. The worst-case scenario was designed to determine the system’s upper limits by simulating the most demanding conditions with maximal resource consumption and processing time. The objective of the best-case scenario was to determine the optimal operational conditions under which the software functions with the fewest resources utilized and the quickest processing time that would yield valuable insights regarding the potential for maximum efficiency. The average-case scenario provided an impartial depiction of the system in its typical operational state by calculating the average values of resource consumption and processing times across all experiments.

A comprehensive assessment of the energy efficiency of every configuration was conducted by measuring power usage in mVDC and overall electricity consumption in watts per hour. The results identified configurations that maximize energy efficiency, a critical element for the operation of PoW blockchains in a sustainable manner. By comparing energy consumption across various configurations, it is possible to quantify each arrangement’s energy consumption and efficacy, thereby emphasizing the compromises between energy utilization and computation performance.

The findings of this research are crucial in furthering the progress of environmentally conscious and energy-efficient PoW blockchain technologies. The results reveal the significance of striking a balance between computational requirements and minimal energy usage in the practical context of sustainable blockchain operations. More specifically, identifying configurations that maximize energy efficiency can guide the development of more sustainable mining practices, potentially reducing the environmental impact of PoW blockchain technologies.

5.3. Extending Approach and Framework

Investigating various explanatory analytical techniques may enhance future research’s comprehension and implementation of GPU optimization in PoW blockchain systems. Logistic regression or other alternative methods may be essential for categorical outcomes. This method may uncover classifications of GPU performance and energy efficiency. Principal component regression (PCR) and partial least squares regression (PLS) are indispensable in situations involving dimensional complexity and multicollinearity. These approaches facilitate comprehension of GPU configurations’ impact on energy efficiency, underscoring their utility in optimizing GPUs. The reliability of Ridge and Lasso regression is undeniable when it comes to enhancing the precision of predictions and warding off overfitting. These robust methods can determine the most influential factors in GPU energy efficiency. Given the complex nature of blockchain systems and the myriad variables that affect GPU performance, the adaptability of ensemble methodologies like boosting and random forests is reassuring. These methods are more adept at handling high-dimensional data and intricate connections than linear models, potentially elevating prediction models.

A multifaceted strategy is imperative for developing intelligent and sustainable infrastructures, with advanced data analysis as a critical component. Subsequent research endeavors may explore the predictive performance of machine learning methodologies, including multi-layer perceptron networks. While the present study does not explore predictive modeling, it would be highly beneficial to comprehend the capacity of such models to predict smart infrastructure trends and behaviors. The capability of these models to analyze extensive datasets, detect concealed patterns, and forecast forthcoming states are critical attributes in the administration and enhancement of intelligent infrastructures. Furthermore, the convergence of artificial intelligence and blockchain technology offers an optimistic pathway for forthcoming scholarly investigations. Through enhanced data analysis, decision-making capabilities, and automation, artificial intelligence (AI) can increase the efficacy and efficiency of blockchain applications in intelligent infrastructures. Integrating blockchain technology’s intrinsic security and transparency functionalities with AI’s predictive capabilities can shift the paradigm in numerous facets of intelligent and sustainable infrastructure, including supply chain optimization and energy management.

6. Conclusions

This study represents a substantial advance in blockchain technology, explicitly concerning sustainable energy methodologies. Through the establishment of a connection between optimal GPU performance and minimal energy consumption, this research establishes a foundation for blockchain technology that is more environmentally sustainable. The practical suggestions and insights presented in this document function as a manual for stakeholders to navigate the intricate terrain of PoW blockchain, ensuring that technological progress is in harmony with sustainability principles.

6.1. Theoretical Contributions

The findings of this research demonstrate a substantial advance in solving the fundamental issues associated with energy and sustainable energy efficiency in blockchain frameworks, specifically those that rely on proof-of-work cryptocurrency mining. This study comprehensively analyzed GPU configurations, system architecture components, and their interaction within the PoW blockchain implementation. The primary aim of this investigation was to optimize performance metrics, ensuring that GPUs function at their utmost capability while reducing their energy usage.

One of the most important aspects of this research was to quantify the ecological damage caused by these technologies. Through an in-depth exploration of GPU architecture’s operational characteristics and subtleties, the research unveiled prospective pathways for mitigating energy consumption. The implications of these discoveries extend beyond environmental considerations and are of the utmost importance for all parties engaged in PoW blockchain ecosystems. The research findings present practical recommendations and guidance specifically designed to address the varied requirements of the stakeholders involved.

Before addressing the research inquiries, this study emphasized the concerns about energy and sustainable energy efficiency linked to PoW blockchain frameworks. The result became apparent that, although these frameworks provide robust security measures and advantages of decentralization, their high energy consumption presents considerable obstacles. This study’s particular facet garnered significant attention within cryptocurrency mining owing to its substantial energy requirements.

The second research inquiry explored potential optimizations to the architecture of GPU information systems to improve the energy efficiency of proof-of-work algorithms. Through rigorous examination and empirical investigation, the current research demonstrated that significant energy conservation could be achieved without sacrificing computational performance by strategically modifying GPU hardware, software, and configuration settings. Implementing this comprehensive optimization strategy was necessary to attain sustainable energy efficiency.

The research concluded with actionable suggestions for PoW blockchain technology. The above recommendations are based on an exhaustive examination of GPU performance across various configurations and operational circumstances. A collection of actionable strategies is the final product, which can be adopted by stakeholders to strike a balance between energy consumption and operational efficiency. This study holds particular significance for organizations involved in PoW blockchain mining, as energy expenditures comprise a substantial proportion of overall operational costs.

6.2. Practical Implications

This research has significant implications for the real world, specifically blockchain technology. The outcomes revolve around optimizing GPU configurations to improve energy efficiency in PoW blockchain technologies; a critical conclusion confirms that higher voltages reduce energy efficiency. Hardware manufacturers and blockchain operators can utilize this discovery to optimize GPU voltage configurations, achieving a more sustainable trade-off between performance and energy usage. The positive correlation between core temperature and heat control underscores thermal management’s practical nature. Acquiring this knowledge is necessary to develop cooling solutions for mining rigs that effectively mitigate overheating and energy waste, prolonging the hardware’s lifespan and enhancing the system’s overall efficiency. The results challenge the traditional preference for increased memory clock speeds and advocate for re-evaluating clock speed configurations. In practical terms, fine-tuned clock speeds could significantly enhance the energy efficiency of blockchain technology. This insight should inspire blockchain practitioners and GPU manufacturers to consider this finding when developing energy-efficient mining rigs.

This study also highlights the significance of algorithm selection in optimizing blockchain processes. The correlation between algorithm performance and efficiency implies that PoW blockchain algorithms have the potential to influence energy usage substantially. This discovery may assist blockchain operators and software developers in selecting or creating more efficient algorithms, thereby advancing the sustainability of blockchain technology, and offering a strategic roadmap for implementing energy-conserving blockchain technology. GPU configuration would balance performance and sustainability for stakeholders by shedding light on GPU configurations and energy efficiency. As the environmental impact of blockchain technology becomes increasingly apparent, these insights instill hope for the long-term viability of blockchain systems in a progressively sustainable world.

6.3. Limitations and Future Work

Nevertheless, the current research has limitations. The restricted scope of this study, which centered on particular GPU models and the ETASH algorithm, might restrict the generalizability of the results to alternative blockchain technologies. Moreover, future study is possible to examine whether the controlled experimental configuration, which maintained a constant room temperature, does not precisely replicate the diverse environmental circumstances in practical blockchain mining scenarios.

There is vast potential for further investigation in this area, which could delve into a wider array of GPU models and blockchain algorithms. This would augment the results’ applicability and spark intrigue as well as hope for future advancements. The insights into the performance and energy consumption of GPUs could be rendered more realistic by implementing experiments conducted under various environmental conditions. Longitudinal studies that track the performance of GPUs over extended periods of time may yield more comprehensive insights into the enduring viability of optimized configurations. Moreover, the incorporation of nascent technologies such as artificial intelligence and machine learning has the potential to fundamentally transform the forecasting and enhancement of GPU performance in the context of blockchain mining.