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\"Based on material taught at the University of California, Berkeley, this textbook offers a modern, rigorous and comprehensive treatment of the methods of structural and system reliability analysis. It covers the first- and second-order reliability methods for components and systems, simulation methods, time- and space-variant reliability, and Bayesian parameter estimation and reliability updating. It also presents more advanced, state-of-the-art topics such as finite element reliability methods, stochastic structural dynamics, reliability-based optimal design, and Bayesian networks. A wealth of well-designed examples connect theory with practice, with simple examples demonstrating mathematical concepts and larger examples demonstrating their applications. End-of-chapter homework problems are included throughout\"-- Provided by publisher.

Active-learning surrogate model–based reliability analysis is widely employed in engineering structural reliability analysis to alleviate the computational burden of the Monte Carlo method. To date, most of these methods are built based on the single-fidelity surrogate model, such as the Kriging model. However, the computational burden of constructing a fine Kriging model may be still expensive if the high-fidelity (HF) simulation is extremely time-consuming. To solve this problem, an active-learning method based on the multi-fidelity (MF) Kriging model for structural reliability analysis (abbreviated as AMK-MCS+AEFF), which is an online data-driven method fusing information from different fidelities, is proposed in this paper. First, an augmented expected feasibility function (AEFF) is defined by considering the cross-correlation, the sampling density, and the cost query between HF and low-fidelity (LF) models. During the active-learning process of AMK-MCS+AEFF, both the location and fidelity level of the updated sample can be determined objectively and adaptively by maximizing the AEFF. Second, a new stopping criterion that associates with the estimated relative error is proposed to ensure that the iterative process terminates in a proper iteration. The proposed method is compared with several state-of-the-art methods through three numerical examples and an engineering case. Results show that the proposed method can provide an accurate failure probability estimation with a less computational cost.

Epistemic uncertainty widely exists in the early design stage of complex engineering structures or throughout the full-life cycle of innovative structure design, which should be appropriately quantified, managed, and controlled to ensure the reliability and safety of the product. Evidence theory is usually regarded as a promising model to deal with epistemic uncertainty, as it employs a general and flexible framework, the basic probability assignment function, which enables the quantification and propagation of epistemic uncertainty more effective. Due to its strong ability, evidence theory has been applied in the field of structural reliability during the past few decades, and a series of important progresses have been achieved. Evidence-theory-based reliability analysis thus provides an important means for engineering structure design, especially under epistemic uncertainty, and it has become one of the research hotspots in the field of structural reliability. This paper reviews the four main research directions of evidence-theory-based reliability analysis, and each one is focused on solving one critical issue in this field, namely, computational efficiency, parameter correlation, hybrid uncertainties, and reliability-based design optimization. It summarizes the main scientific problems, technical difficulties, and current research status of each direction. Based on the review, this paper also provides an outlook for future research in evidence-theory-based structural reliability analysis.

The paper presents a hybrid active-learning approach for structural reliability analysis via adaptive Kriging surrogate models. The quasi first-order reliability method is first proposed for characteristic truncation point of a structural performance function. This is used to define a truncation boundary via the joint probability distribution function of input random variables. To reduce simulation time for new training samples, a U-function based criterion is further implemented to refine the candidate sample set. Since the reliability-based expected improvement function and U functions are combined together to evaluate new training samples, it finalizes a hybrid active-learning Kriging (HALK) to develop adaptive surrogate models for the structural reliability analysis. Several numerical examples are presented to demonstrate potential applications of the proposed HALK algorithm. Compared to benchmark results provided by the brutal force Monte-Carlo simulation method, the effectiveness of the HALK approach has been justified by dealing with various structural reliability problems.

In structural reliability analysis, the HL-RF method may not converge in some nonlinear cases. The chaos control based first-order second-moment method (CC) achieves convergence by controlling the step length with chaotic control factors, but it commonly requires very time-consuming computation. In this paper, an Armijo-based hybrid step length release method based on chaos control is proposed to surmount the above issue. An iterative control angle is introduced for the proposed method to select an adaptive adjustment step length strategy. Then, a step length release method is proposed to speed up the convergence when the iterative rotation angle is less than the rotation control angle. When the iterative rotation angle exceeds the rotation control angle, an adaptive adjustment method for step length is defined based on the Armijo rule to provide an optimal choice of adaptive step length for the iterative process and guarantee convergence. After that, the robustness and efficiency of the proposed method are proved through several examples. The examples show that the proposed method is capable of generating a suitable adaptive step length, therefore accessing a more stable and accurate solution with greater efficiency in both high and low nonlinearity cases. It can well combine the advantages of HL-RF and the CC methods, and the efficiency is further improved without sacrificing its robustness. Finally, a discussion is brought out to investigate the selection of optimal parameters and how the two step length selection strategy cooperates and co-action with one another. It can be seen that the efficiency improvement of the proposed method mainly contributed to the step length release method, while the Armijo-based adaptive adjustment method for step length guaranteed convergence.

Aleatory and epistemic uncertainties usually coexist within a mechanistic model, which motivates the hybrid structural reliability analysis considering random and interval variables in this paper. An introduction of the interval variable requires one to recursively evaluate embedded optimizations for the extremum of a performance function. The corresponding structural reliability analysis, hence, becomes a rather computationally intensive task. In this paper, physical characteristics for potential optima of the interval variable are first derived based on the Karush-Kuhn-Tucker condition, which is further programmed as a simulation procedure to pair qualified candidate samples. Then, an outer truncation boundary provided by the first-order reliability method is used to link the size of a truncation domain with the targeted failure probability, whereas the U function is acted as a refinement criterion to remove inner samples for an increased learning efficiency. Given new samples detected by the revised reliability-based expected improvement function, an adaptive Kriging surrogate model is determined to tackle the hybrid structural reliability analysis. Several numerical examples in the literature are presented to demonstrate applications of this proposed algorithm. Compared to benchmark results provided by the brute-force Monte Carlo simulation, the high accuracy and efficiency of this proposed approach have justified its potentials for the hybrid structural reliability analysis.

PurposeAssessing the failure probability of engineering structures is still a challenging task in the presence of various uncertainties due to the involvement of expensive-to-evaluate computational models. The traditional simulation-based approaches require tremendous computational effort, especially when the failure probability is small. Thus, the use of more efficient surrogate modeling techniques to emulate the true performance function has gained increasingly more attention and application in recent years. In this paper, an active learning method based on a Kriging model is proposed to estimate the failure probability with high efficiency and accuracy.Design/methodology/approachTo effectively identify informative samples for the enrichment of the design of experiments, a set of new learning functions is proposed. These learning functions are successfully incorporated into a sampling scheme, where the candidate samples for the enrichment are uniformly distributed in the n-dimensional hypersphere with an iteratively updated radius. To further improve the computational efficiency, a parallelization strategy that enables the proposed algorithm to select multiple sample points in each iteration is presented by introducing the K-means clustering algorithm. Hence, the proposed method is referred to as the adaptive Kriging method based on K-means clustering and sampling in n-Ball (AK-KBn).FindingsThe performance of AK-KBn is evaluated through several numerical examples. According to the generated results, all the proposed learning functions are capable of guiding the search toward sample points close to the LSS in the critical region and result in a converged Kriging model that perfectly matches the true one in the regions of interest. The AK-KBn method is demonstrated to be well suited for structural reliability analysis and a very good performance is observed in the investigated examples.Originality/valueIn this study, the statistical information of Kriging prediction, the relative contribution of the sample points to the failure probability and the distances between the candidate samples and the existing ones are all integrated into the proposed learning functions, which enables effective selection of informative samples for updating the Kriging model. Moreover, the number of required iterations is reduced by introducing the parallel computing strategy, which can dramatically alleviate the computation cost when time demanding numerical models are involved in the analysis.

Structural health monitoring (SHM) is the most direct and advanced method for understanding the evolution laws of structures and ensuring structural safety. The essence of SHM lies in diagnosing structural health by analyzing monitoring data. Since the introduction of machine learning paradigm for SHM, using machine learning methods to analyze the monitoring data, identify, and evaluate structural health status has become a prominent research topic in this field. For complex bridge structures, diagnosing structural health based on highly incomplete monitoring data presents an inherent high-dimensional problem. Machine learning methods are particularly well-suited for addressing these issues due to their capabilities in effective feature extraction, efficient optimization, and robust scalability. This article provides a brief review of the developments in machine learning-based structural health diagnosis, including data cleaning, structural modal parameters estimation, structural damage identification, digital twin technology, and structural reliability assessment. Additionally, the paper discusses related open questions and potential directions for future research.

PurposeThe purpose of this paper is to briefly summarize and review the theories and methods of complex structures’ dynamic reliability. Complex structures are usually assembled from multiple components and subjected to time-varying loads of aerodynamic, structural, thermal and other physical fields; its reliability analysis is of great significance to ensure the safe operation of large-scale equipment such as aviation and machinery.Design/methodology/approachIn this paper for the single-objective dynamic reliability analysis of complex structures, the calculation can be categorized into Monte Carlo (MC), outcrossing rate, envelope functions and extreme value methods. The series-parallel and expansion methods, multi-extremum surrogate models and decomposed-coordinated surrogate models are summarized for the multiobjective dynamic reliability analysis of complex structures.FindingsThe numerical complex compound function and turbine blisk are used as examples to illustrate the performance of single-objective and multiobjective dynamic reliability analysis methods. Then the future development direction of dynamic reliability analysis of complex structures is prospected.Originality/valueThe paper provides a useful reference for further theoretical research and engineering application.

Importance sampling methods are widely used in structural reliability analysis. However, owing to the complex shape of optimal importance sampling densities, it is usually difficult to fit the optimal importance sampling densities and sample from the fitted distributions using conventional importance sampling methods. In this paper, a novel importance sampling method based on interpretable deep generative network (IDGN-IS) is proposed for structural reliability analysis. The proposed IDGN-IS model can be directly trained using the data from original distribution of random variables and efficiently sampling from an arbitrary importance sampling density. The developed interpretable deep generative network consists of a deep generative network and a monotonic network, which enables the network to fit and sample from the target distributions while being interpretable. Using the interpretability of the deep generative network, the IDGN-IS method can sample from an arbitrary conditional probability distribution of the fitted distributions by choosing an appropriate threshold of the input Gaussian distribution samples. When the threshold of the input Gaussian distribution samples is set to a value close to zero, the IDGN-IS method can efficiently sample from the optimal importance sampling density and provide accurate estimation of the failure probability. The calculation efficiency and estimation accuracy of the proposed IDGN-IS method in structural reliability analysis are demonstrated using four examples.