Search Results (467)

This paper studies the properties of the Fourier transform of the fuzzy function, and extends the classical Poisson integral formula on the half plane to the fuzzy case, obtaining the composition of the fuzzy set generated by a point in the complex field under the action of the fuzzy function. Further, we define and study the fuzzy Hilbert transform of fuzzy functions and their properties. We prove that when the fuzzy function degenerates to the classical case, the fuzzy Hilbert transform will degenerate to the classical Hilbert transform, which proves that the fuzzy Hilbert transform is an extension of classical transformations in the fuzzy function space. In addition, we point out and prove some properties of the fuzzy Hilbert transform. For some fuzzy functions that meet certain requirements, their fuzzy Hilbert transform is a fuzzy point on 0. Full article

This study investigates the hypothesis that meteorological anomalies may precede earthquake events. Long-term time series of observations for air temperature, atmospheric pressure and precipitation at a meteorological station in Kamchatka are considered. Time series are subjected to Huang decomposition into sequences of levels of empirical oscillation modes (intrinsic mode functions—IMFs), forming a set of orthogonal components with decreasing average frequency. For each IMF level, the instantaneous amplitudes of envelopes are calculated using the Hilbert transform. A comparison with the earthquake sequence is made using a parametric model of the intensity of two interacting point processes, which allows one to quantitatively estimate the “measure of the lead” of the time instants of the compared sequences. For each IMF level, the number of time moments of the largest local maxima of instantaneous amplitudes which is equal to the number of earthquakes is selected. As a result of the analysis, it turned out that for the sixth IMF level (periods of 8–16 days), the “lead measure” of the instantaneous amplitude maxima of meteorological parameters in comparison with earthquake time moments significantly exceeds the inverse lead, which confirms the existence of prognostic changes in meteorological parameters in the problem of “atmosphere–lithosphere” interaction. This study reveals that certain meteorological anomalies can be a precursor for seismic activity. Full article

The issue of power quality disturbances in modern power systems has become increasingly complex and severe, with multiple disturbances occurring simultaneously, leading to a decrease in the recognition accuracy of traditional algorithms. This paper proposes a composite power quality disturbance identification method based on the integration of improved Complementary Ensemble Empirical Mode Decomposition (CEEMDAN), Hilbert Transform (HT), and Extreme Learning Machine (ELM). Addressing the limitations of traditional signal processing techniques in handling nonlinear and non-stationary signals, this study first preprocesses the collected initial power quality signals using the improved CEEMDAN method to reduce modal aliasing and spurious components, thereby enabling a more precise decomposition of noisy signals into multiple Intrinsic Mode Functions (IMFs). Subsequently, the HT is utilized to conduct a thorough analysis of the reconstructed signals, extracting their time-amplitude information and instantaneous frequency characteristics. This feature information provides a rich data foundation for subsequent classification and identification. On this basis, an improved ELM is introduced as the classifier, leveraging its powerful nonlinear mapping capabilities and fast learning speed to perform pattern recognition on the extracted features, achieving accurate identification of composite power quality disturbances. To validate the effectiveness and practicality of the proposed method, a simulation experiment is designed. Upon examination, the approach introduced in this study retains a fault diagnosis accuracy exceeding 95%, even amidst significant noise disturbances. In contrast to conventional techniques, such as Convolutional Neural Network (CNN) and Support Vector Machine (SVM), this method achieves an accuracy enhancement of up to 5%. Following optimization via the Particle Swarm Optimization (PSO) algorithm, the model’s accuracy is boosted by 3.6%, showcasing its favorable adaptability. Full article

Complexity evaluation of hydro-climatic datasets is a challenging but essential pre-requisite for accurate modeling and subsequent planning. Changes in climate and anthropogenic interventions amplify the complexity of hydro-climatic time-series. Understanding persistence and fractal features may help us to develop new and robust modeling frameworks which can work well under non-stationary and non-linear environments. Classical fractal hydrology, rooted in statistical physics, has been developed since the 1980s and the modern alternatives based on de-trending, complex network, and time–frequency principles have been developed since 2002. More specifically, this review presents the procedures of Multifractal Detrended Fluctuation Analysis (MFDFA) and Arbitrary Order Hilbert Spectral Analysis (AOHSA), along with their applications in the field of hydro-climatology. Moreover, this study proposes a complex network-based fractal analysis (CNFA) framework for the multifractal analysis of daily streamflows as an alternative. The case study proves the efficacy of CNMFA and shows that it has the flexibility to be applied in visibility and inverted visibility schemes, which is effective in complex datasets comprising both high- and low-amplitude fluctuations. The comprehensive review showed that more than 75% of the literature focuses on characteristic analysis of the time-series using MFDFA rather than modeling. Among the variables, about 70% of studies focused on analyzing fine-resolution streamflow and rainfall datasets. This study recommends the use of CNMF in hydro-climatology and advocates the necessity of knowledge integration from multiple fields to enhance the multifractal modeling applications. This study further asserts that transforming the characterization into operational hydrology is highly warranted. Full article

Signal analysis is a fundamental field in engineering and data science, focused on the study of signal representation, transformation, and manipulation. The accurate estimation of harmonic vibration components and their associated parameters in vibrating mechanical systems presents significant challenges in the presence of very similar frequencies and mode mixing. In this context, a hybrid strategy to estimate harmonic vibration modes in weakly damped, multi-degree-of-freedom vibrating mechanical systems by combining Empirical Mode Decomposition and Variational Mode Decomposition is described. In this way, this hybrid approach leverages the detection of mode mixing based on the analysis of intrinsic mode functions through Empirical Mode Decomposition to determine the number of components to be estimated and thus provide greater information for Variational Mode Decomposition. The computational time and dependency on a predefined number of modes are significantly reduced by providing crucial information about the approximate number of vibratory components, enabling a more precise estimation with Variational Mode Decomposition. This hybrid strategy is employed to compute unknown natural frequencies of vibrating systems using output measurement signals. The algorithm for this hybrid strategy is presented, along with a comparison to conventional techniques such as Empirical Mode Decomposition, Variational Mode Decomposition, and the Fast Fourier Transform. Through several case studies involving multi-degree-of-freedom vibrating systems, the superior and satisfactory performance of the hybrid method is demonstrated. Additionally, the advantages of the hybrid approach in terms of computational efficiency and accuracy in signal decomposition are highlighted. Full article

Tree species are important factors affecting the carbon sequestration capacity of forests and maintaining the stability of ecosystems, but trees are widely distributed spatially and located in complex environments, and there is a lack of large-scale regional tree species classification models for remote sensing imagery. Therefore, many studies aim to solve this problem by combining multivariate remote sensing data and proposing a machine learning model for forest tree species classification. However, satellite-based laser systems find it difficult to meet the needs of regional forest species classification characters, due to their unique footprint sampling method, and SAR data limit the accuracy of species classification, due to the problem of information blending in backscatter coefficients. In this work, we combined Sentinel-1 and Sentinel-2 data to construct a machine learning tree classification model based on optical features, vegetation spectral features, and PolSAR polarization observation features, and propose a forest tree classification feature selection method featuring the Hilbert–Huang transform for the problem of mixed information on the surface of SAR data. The PSO-RF method was used to classify forest species, including four temperate broadleaf forests, namely, aspen (Populus L.), maple (Acer), peach tree (Prunus persica), and apricot tree (Prunus armeniaca L.), and two coniferous forests, namely, Chinese pine (Pinus tabuliformis Carrière) and Mongolian pine (Pinus sylvestris var. mongolica Litv.). In this study, some experiments were conducted using two Sentinel-1 images, four Sentinel-2 images, and 550 measured forest survey sample data points pertaining to the forested area of Fuxin District, Liaoning Province, China. The results show that the fusion model constructed in this study has high accuracy, with a Kappa coefficient of 0.94 and an overall classification accuracy of 95.1%. In addition, this study shows that PolSAR data can play an important role in forest tree species classification. In addition, by applying the Hilbert–Huang transform to PolSAR data, other feature information that interferes with the perceived vertical structure of forests can be suppressed to a certain extent, and its role in the classification of forest species, combined with PolSAR, should not be ignored. Full article

In recent years, preventive maintenance has emerged as a focal point of research in the aerospace field. The concept of equipment maintenance, exemplified by prognosis and health management (PHM), has permeated every aspect of development and design. Extracting degradation features presents a fundamental and challenging task for health assessment and remaining useful life prediction. To facilitate the efficient operation of the incipient fault diagnosis model, this paper proposes a data-driven feature extraction process for converters, which consists of two main stages. First, feature extraction and comparison are conducted in the time domain, frequency domain, and time–frequency domain. By employing wavelet decomposition and the Hilbert transform method, a highly correlated time–frequency domain feature is obtained. Second, an improved feature selection approach that combines the ReliefF algorithm with the correlation coefficient is proposed to effectively minimize redundancy within the feature subset. Furthermore, an incipient fault diagnosis model is established using neural networks, which verifies the effectiveness of the data-driven feature extraction process presented herein. Experimental results indicate that this method not only maintains fault diagnosis accuracy but also significantly reduces training time. Full article

Flywheels have been largely used in rotating machine engines to save inertial energy and to limit speed fluctuations. A stress distribution problem is created due to the centrifugal forces that are formed when the flywheel is spinning around, which leads to different levels of pressure and decompression inside its structure. Lack of balance leads to high energy losses through various mechanisms, which deteriorate both the flywheel’s expectancy and their ability to rotate at high speeds. Deviation in the design of flywheels from their optimum performance can cause instability issues and even a catastrophic failure during operation. This paper aims to analytically examine the stress distribution of radial and tangential directions along the flywheel structure within a linear elastic range. The eigenvalues and eigenvectors, which are representative of free vibrational features, were extracted by applying finite element analysis (FEA). Natural frequencies and their corresponding vibrating mode shapes and mass participation factors were identified. Furthermore, Kirchhoff–Love plate theory was employed to model the transverse vibration of the system. A general solution for the radial component of the equation of flywheel motion was derived with the help of the Bessel function. The results show certain modes of vibration identified as particularly influential in specific directions. Advanced time-frequency analysis techniques, including but not limited to continuous wavelet transform (CWT) and Hilbert–Huang transform (HHT), were applied to extract transverse vibration features of the flywheel system. It was also found that using CWT, low-frequency vibrations contribute to the majority of the energy in the extracted signal spectrum, while HHT exposes the high-frequency components of vibration that may cause significant structural damage if not addressed in time. Full article

Fluid–structure interaction introduces critical failure modes due to varying stiffness and changing contact states in rotor-stator systems. This is further aggravated by stress fluctuations due to shaft impact with a fixed stator when the shaft rotates. In this paper, the investigation of imbalance and rotor-stator contact on a rotating shaft was carried out in viscous fluid. The shaft was modelled as a vertical elastic rotor system based on a vertically oriented elastic rotor operating in an incompressible medium. Implicit representation of the rotating system including the rotor-stator contact and the hydrodynamic resistance was formulated for the coupled system using the energy principle and the Navier–Stokes equations. Additionally, the monolithic approach included an implicit strategy of the rotor-stator fluid interaction interface conditions in the solution methodology. Advanced time-frequency methods, such as Hilbert transform, continuous wavelet transform, and estimated instantaneous frequency maps, were applied to extract the vibration features of the dynamic response of the faulted rotor. Time-varying stiffness due to friction is thought to be the main reason for the frequency fluctuation, as indicated by historical records of the vibration displacement, whirling orbit patterns of the centre shaft, and the amplitude–frequency curve. It has also been demonstrated that the augmented mass associated with the rotor and stator decreases the natural frequencies, while the amplitude signal remains relatively constant. This behaviour indicates a quasi-steady-state oscillatory condition, which minimises the energy fluctuations caused by viscous effects. Full article

This paper explores the application of Hilbert topological spaces and linear operator algebra in the modelling and analysis of OFDM signals and wireless channels, where the channel is considered as a linear time-invariant (LTI) system. The wireless channel, when subjected to an input OFDM signal, can be described as a mapping from an input Hilbert space to an output Hilbert space, with the system response governed by linear operator theory. By employing the mathematical framework of Hilbert spaces, we formalise the representation of OFDM signals, which are interpreted as elements of an infinite-dimensional vector space endowed with an inner product. The LTI wireless channel is characterised by using bounded linear operators on these spaces, allowing for the decomposition of complex channel behaviour into a series of linear transformations. The channel’s impulse response is treated as a kernel operator, facilitating a functional analysis approach to understanding the signal transmission process. This representation enables a more profound understanding of channel effects, such as fading and interference, through the eigenfunction expansion of the operator, leading to a spectral characterization of the channel. The algebraic properties of linear operators are leveraged to develop optimal solutions for mitigating channel distortion effects. Full article

In long-span bridges and high-rise buildings, closely spaced modes are commonly observed, which greatly increases the challenge of identifying modal parameters. Hilbert–Huang transform (HHT), a widely used method for modal parameter identification, first applies empirical mode decomposition (EMD) to decompose the acquired response and then uses the Hilbert transform (HT) to identify the modal parameters. However, the problem is that the deficiency of mode separation of EMD in HHT limits its application for structures with closely spaced modes. In this study, an improved HHT based on analytical mode decomposition (AMD) is proposed and is used to identify the modal parameters of structures with closely spaced modes. In the improved HHT, AMD is first employed to replace EMD for decomposing the measured response into several mono-component modes. Then, the random decrement technique is applied to the decomposed mono-component modes to obtain the free decay responses. Furthermore, the resulting free decay responses are analyzed by HT to estimate the modal parameters of structures with closely spaced modes. Examples of a simple three-degree-of-freedom system with closely spaced modes, a high-rise building under ambient excitation, and the Ting Kau bridge under typhoon excitations are adopted to validate the accuracy, effectiveness, and applicability of the proposed method. The results demonstrate that the proposed method can efficiently and accurately identify the natural frequencies and damping ratios of structures with closely spaced modes. Moreover, its identification results are more precise compared to those obtained using existing methods. Full article

We analyze the error estimates of a fully discrete scheme for solving a semilinear stochastic subdiffusion problem driven by integrated fractional Gaussian noise with a Hurst parameter $H\in (0,1)$. The covariance operator Q of the stochastic fractional Wiener process satisfies $\parallel A^{-\rho }{Q}^{1/2}{\parallel }_{HS}<\infty$ for some $\rho \in [0,1)$, where ${\parallel ·\parallel }_{HS}$ denotes the Hilbert–Schmidt norm. The Caputo fractional derivative and Riemann–Liouville fractional integral are approximated using Lubich’s convolution quadrature formulas, while the noise is discretized via the Euler method. For the spatial derivative, we use the spectral Galerkin method. The approximate solution of the fully discrete scheme is represented as a convolution between a piecewise constant function and the inverse Laplace transform of a resolvent-related function. By using this convolution-based representation and applying the Burkholder–Davis–Gundy inequality for fractional Gaussian noise, we derive the optimal convergence rates for the proposed fully discrete scheme. Numerical experiments confirm that the computed results are consistent with the theoretical findings. Full article

At present, researchers in the field of pipeline inspection focus on pipe wall defects while neglecting pipeline defects in special situations such as welds. This poses a threat to the safe operation of projects. In this paper, a multi-node fusion and modal projection algorithm of steel pipes based on guided wave technology is proposed. Through an ANSYS numerical simulation, research is conducted to achieve the identification, localization, and quantification of axial cracks on the surface of straight pipelines and internal cracks in circumferential welds. The propagation characteristics and vibration law of ultrasonic guided waves are theoretically solved by the semi-analytical finite element method in the pipeline. The model section is discretized in one-dimensional polar coordinates to obtain the dispersion curve of the steel pipe. The T(0,1) mode, which is modulated by the Hanning window, is selected to simulate the axial crack of the pipeline and the L(0,2) mode to simulate the crack in the weld, and the correctness of the dispersion curve is verified. The results show that the T(0,1) and L(0,2) modes are successfully excited, and they are sensitive to axial and circumferential cracks. The time–frequency diagram of wavelet transform and the time domain diagram of the crack signal of Hilbert transform are used to identify the echo signal. The first wave packet peak point and group velocity are used to locate the crack. The pure signal of the crack is extracted from the simulation data, and the variation law between the reflection coefficient and the circumferential and radial dimensions of the defect is calculated to evaluate the size of the defect. This provides a new and feasible method for steel pipe defect detection. Full article

In today’s era, it is important to analyze and utilize various signals in industrial or laboratory applications. Measured signals provide critical information about the controlled system, which can be contained precisely within a narrow frequency range. Many methods and algorithms exist to process such signals in both the time and frequency domains. In particular, signal processing in the frequency domain is primary in industrial practice because dominant components within a specific narrow frequency band are sought. The discrete Fourier transformation (DFT) algorithm is the tool used in practice to find these frequency components. The DFT algorithm provides the full frequency spectrum with a higher number of calculation steps, and its spectrum frequency resolution is low. Therefore, research has focused on finding a method to achieve high-frequency spectrum resolution. An important factor in selecting the technique was that such an algorithm should be implementable on a microprocessor-based system under harsh industrial conditions. Research results showed that the DFT ZOOM method meets these requirements. The frequency zoom has many advantages but requires some modification. It is implemented in high-performance analyzers, but a thorough and detailed description of the respective algorithm is lacking in technical articles and literature. This article mathematically and theoretically describes the modified frequency zoom algorithm in detail. The steps of the frequency zoom, from creating an analytical signal through frequency shifting and decimation to the frequency analysis of the signal, are realized. The algorithm allows for the analysis of a signal with high-frequency resolution in a limited frequency band. A significant modification of DFT ZOOM is that of using the Hilbert transform to create an analytic signal. This resolves the aliasing issue caused by the overlap between fundamental and sideband spectra. Results from processing deterministic and stochastic signals using the modified DFT ZOOM are presented. The presented experimental results contribute to a more detailed frequency analysis of the signal. As part of this scientific research, the issues of frequency zoom were thoroughly addressed, solving the partial problems of this algorithm, both in theory and in the context of signal theory. Full article

Epoxy chip seals are widely used to improve the skid resistance of cement concrete pavements, which is significantly affected by surface texture. However, current methods for characterizing the surface texture structure are not precise, and the standard is not uniform. Therefore, a high-toughness modified epoxy resin chip seal structure was developed to conduct an indoor accelerated abrasion test. The elevation data of the epoxy chip seal under different abrasion times and different abrasion loads were obtained using laser scanning, and the Density/Sharpness combination parameters were obtained using the Hilbert–Huang transform and spectral analysis. The correlation between the texture parameters and the dynamic friction coefficient was analyzed using a stepwise multivariate quadratic polynomial method. The results showed that the texture structure of the epoxy chip seal surface is positively distributed, and the macroscopic texture occupies 49.45%, while the probability of the microscopic texture is only 4.55%. Meanwhile, the correlation coefficient between the texture parameters and the dynamic friction coefficient is 0.9307, which demonstrates that the selected texture parameters discard the texture components unrelated to skid resistance performance and reflect the distribution of the pavement texture and the skid resistance performance well. Full article