1. Introduction
With the continuous improvement in social infrastructure construction techniques, structural safety is being confronted with the challenges of large volumes, complex structures, and harsh environments [
1,
2,
3]. This can result in complications, such as delayed structural damage diagnoses and inaccurate safety evaluations. A current focus in structural health monitoring research is exploring the correlation between monitoring data and structure service performance for quantitative evaluations based on existing safety evaluation methods.
Reinforced concrete (RC) has a wide range of applications in infrastructure, such as bridges and buildings. Over time, concrete structures may exhibit degraded stiffness and reduced bearing capacity due to cracking, corrosion of reinforcements, and other types of damage [
4]. Moradi et al. [
5] carried out four-point bending tests on RC slabs to extract the energy of the received signals to assess the loss of signal energy due to structural damage, verifying the applicability of ultrasound monitoring in assessments of damage in RC structures. Farhidzadeh et al. [
6] proposed a quantitative grading method for RC components based on the damage index of the residual cracking state. It was shown that the proposed method could more accurately assess the damage level of components and determine their relative stiffness loss through low-cycle reciprocating loading of two large RC shear walls. Xiao et al. [
7] introduced a damage detection method that considers the shear deformation of slender beam frame structures and precisely identifies damage by adjusting the structure parameters to match the measured displacements. Asjodi et al. [
8] developed a probabilistic framework to analyze the spatial distribution of cracking and crushing in RC shear walls. To demonstrate its validity, they carried out a comprehensive probabilistic spatial analysis of RC shear walls subjected to cyclic loading. In summary, the intrinsic relationship between damage states and the structural performance of RC structures is significant, reflecting changes in properties such as structural stiffness and load-carrying capacity.
The analytical hierarchy process (AHP) is essential for establishing an evaluation system within a comprehensive evaluation method by decomposing the evaluation object into multiple levels, such as the objective, guideline, and program levels [
9]. The key is to solve the weight coefficients of each level. However, this process depends entirely on the experience of experts to construct the judgment matrix; therefore, subjective problems remain that must be addressed by studying them in depth.
The fuzzy synthesis method is based on the theory of fuzzy mathematics, in which uncertain information is quantitatively represented and the evaluation results obtained with the help of a generalized fuzzy synthesis operation [
10]. Tesfamariam et al. [
11] developed a modeling approach based on a fuzzy rule knowledge base to assess the seismic vulnerability of buildings through fuzzy set theory. Sun et al. [
12] proposed a fuzzy theory-based model to assess the impact of explosion accidents (due to the use of hazardous materials) on bridge safety, established a hierarchical structure for bridge explosion disaster risk assessment, and validated the reasonableness of the proposed method by using relevant cases. Through the use of the fuzzy synthesis method, the fuzzy characteristics of things in the safety evaluation process can be better identified. However, there needs to be more objectivity in the determination criteria for the elements of the evaluation model, whose output is in the stage of qualitative determination [
13]. Contrastingly, the gray theoretical models make it possible to perform quantitative analyses of the dynamic development process of a system to identify the primary and secondary factors that influence the state of development of the system [
14]. This allows such models to effectively undertake evaluations using few data samples and to better reflect the uncertainty in knowledge, which is random [
15]. Zhao et al. [
16] considered the complex factors affecting the fatigue life of steel wire ropes by applying the gray theory to small-sample fatigue life data to effectively improve life prediction accuracy.
The emphasis on the static reaction of a structure is evident in the techniques employed for damage detection [
17] and sensor placement [
18] for SHM. Xiao et al. [
19] developed the stiffness separation method to divide the global stiffness into sub-stiffness matrices, making it possible to undertake precise evaluations of truss damage in space using static responses. On the other hand, the reliability theory is an evaluation method based on probabilistic statistics that establishes the uncertainty relationship between the loads and resistances in a structure and uses the reliability index or probability of failure to assess the safety status of that structure [
20]. Guo et al. [
21] developed a traffic load model based on monitoring data obtained from a vehicle dynamic weighing system, which was combined with probabilistic finite element (FE) analysis and applied to a fatigue reliability evaluation of an in-service bridge. To summarize, at the core of evaluation methods based on reliability theory is the need to determine the analytical formulas for loads and resistances, with particular focus on solving the systematic failure modes of complex structures.
With the rapid development of artificial intelligence technology, structural safety evaluations are shifting from traditional, model-driven modes to data-driven modes [
22]. The artificial neural network (ANN) is gradually being adopted by the civil engineering community due to its advantages of not requiring manual extraction of features and its superior ability to establish the mapping between inputs and outputs to enable end-to-end evaluations [
23,
24]. Shen et al. [
25] proposed a deep neural network-based structural safety state evaluation method that uses acceleration spectra and structural safety state as the model inputs and outputs, respectively. They verified the validity and accuracy of this approach through a five-layer RC framework structure. Liu et al. [
26] introduced a risk warning model based on a convolutional neural network according to the uncertainty characteristics of risk factors in engineering. Indeed, neural network models tend to require many samples for training, and the scarcity of such data is an ongoing issue [
27].
Comparatively, via cloud theory, which is based on probability theory and fuzzy theory, the concept of an affiliation cloud was proposed; this is a novel mathematical tool and decision-making instrument for solving the quantification of uncertainty knowledge [
28,
29,
30]. Cloud theory, as an artificial intelligence algorithm, is currently being widely used in several fields, including data mining and knowledge discovery [
31], decision analysis [
32], mechanical diagnosis [
33], and safety evaluation [
34]. Zhou et al. [
35] proposed a cloud model method with entropy-containing weights for the classification prediction of rock bursts, verifying the validity by zoning 209 sets of rock burst samples from underground rock engineering. Wang et al. [
36] suggested a new connected cloud model for the multiple uncertainties and distribution characteristics of slope stability evaluation indexes. Lin et al. [
37] combined variable-weight theory with cloud theory to construct a new computational model for assessing the construction risk of karst tunnels with respect to the risk evaluation of tunnel construction safety regarding sudden water hazards.
Based on the above, a new structural safety evaluation method, named multi-source fusion uncertainty cloud inference (MFUCI), is proposed in this paper. It may be used to assess the uncertainty caused by initial defects and monitoring errors in practical engineering structures. The method focuses on studying the relationship between characterization condition indexes and structural performance in order to quantitatively evaluate the structural health status of RC structures, from the component level to the whole structural level. An evaluation was performed through damage experiments on RC components and FE simulations of single-story RC frame structures. The proposed method facilitates comprehensive safety evaluations by considering the individual components and the whole structure separately.
Regarding the rest of this paper,
Section 2 describes cloud theory.
Section 3 describes the mathematical theory, architectural design, and evaluation index system of the proposed method.
Section 4 and
Section 5 present the numerical simulations and experimental studies used to evaluate and validate the performance of all aspects of the proposed method at the component and structural levels, respectively. The conclusions are reported in
Section 6.
6. Conclusions
This paper presents a novel structural safety evaluation method, named multi-source fusion uncertainty cloud inference, to address the uncertainties arising from initial defects and monitoring errors in practical engineering structures. Leveraging the advantages of cloud modeling theory in handling uncertainty in knowledge, this method provides a comprehensive approach to assessing structural safety. Focusing on RC structures, this study investigates methods of safety evaluation from the component level to the structural level. The evaluation is conducted through experimental damage tests on RC components and FE simulations of a single-story RC frame structure. By considering both the individual components and the entire structure, a comprehensive evaluation of safety is achieved. Based on the above work, the conclusions of this paper are as follows:
This study is focused on investigating the relationship between characterizing condition indexes and structural performance to quantitatively evaluate the structural health status. Considering the influence of multi-source data in structural safety evaluations, a multi-source fusion uncertainty cloud inference architecture is proposed as a theoretical basis for quantifying the structural safety degree;
A single-story RC structure was investigated for damage under low-cycle reciprocating loads. The safety level was quantified by extracting characteristic points from the skeleton curve, and the effectiveness of the proposed approach in conducting safety evaluations at the structural level was validated;
Damage experiments on two RC T-beams were conducted to analyze the failure process in terms of the specimen condition index and specimen stiffness degradation. A safety evaluation system for reinforcement strain, concrete strain, and deflection was developed based on the proposed MFUCI, demonstrating that it is suitable for safety evaluations at the component level;
Considering the variations of civil building O&M environments, the model was tested for different levels of immunity by injecting uncertainty information, i.e., adding noise only to the inference samples. The results show that the proposed model has excellent noise immunity under different noise levels;
Considering the non-uniformity of the material and the influence of the fabrication process of the components, the excellent generalizability and robustness of the proposed study are demonstrated by using SJ-T-2 as the basis of the architecture and SJ-T-1 as the inference samples in RC T-beams.
When dealing with a complicated structural system using the proposed method, it is suggested that the system be divided into substructural systems. On the one hand, the proposed method permits the direct evaluation of critical substructure systems, thus facilitating evaluations of critical components. On the other hand, each substructure is considered an information source when employing multi-source fusion inference to evaluate the whole structure. The critical point is to apply representational signals that can be easily and directly monitored by the in-service structure as local condition indexes. In future work, we will focus on developing a digital twin framework for finite element synergy, where a physically synergistic finite element model is taken as the architectural set of the proposed method, while the response signals of the real structure are taken as the inference set to accurately evaluate the in-service structure.