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"Reliability (Engineering) Mathematics."
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Structural and system reliability
\"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.
Book
Accident Precursor Analysis and Management
In the aftermath of catastrophes, it is common to find prior indicators, missed signals, and dismissed alerts that, had they been recognized and appropriately managed before the event, could have resulted in the undesired event being averted. These indicators are typically called \"precursors.\" Accident Precursor Analysis and Management: Reducing Technological Risk Through Diligence documents various industrial and academic approaches to detecting, analyzing, and benefiting from accident precursors and examines public-sector and private-sector roles in the collection and use of precursor information. The book includes the analysis, findings and recommendations of the authoring NAE committee as well as eleven individually authored background papers on the opportunity of precursor analysis and management, risk assessment, risk management, and linking risk assessment and management.
eBook
A new directional stability transformation method of chaos control for first order reliability analysis
The HL-RF iterative algorithm of the first order reliability method (FORM) is popularly applied to evaluate reliability index in structural reliability analysis and reliability-based design optimization. However, it sometimes suffers from non-convergence problems, such as bifurcation, periodic oscillation, and chaos for nonlinear limit state functions. This paper derives the formulation of the Lyapunov exponents for the HL-RF iterative algorithm in order to identify these complicated numerical instability phenomena of discrete chaotic dynamic systems. Moreover, the essential cause of low efficiency for the stability transform method (STM) of convergence control of FORM is revealed. Then, a novel method, directional stability transformation method (DSTM), is proposed to reduce the number of function evaluations of original STM as a chaos feedback control approach. The efficiency and convergence of different reliability evaluation methods, including the HL-RF algorithm, STM and DSTM, are analyzed and compared by several numerical examples. It is indicated that the proposed DSTM method is versatile, efficient and robust, and the bifurcation, periodic oscillation, and chaos of FORM is controlled effectively.
Journal Article
Hyperparameter Tuning of Machine Learning Algorithms Using Response Surface Methodology: A Case Study of ANN, SVM, and DBN
This study applies response surface methodology (RSM) to the hyperparameter fine-tuning of three machine learning (ML) algorithms: artificial neural network (ANN), support vector machine (SVM), and deep belief network (DBN). The purpose is to demonstrate RSM effectiveness in maintaining ML algorithm performance while reducing the number of runs required to reach effective hyperparameter settings in comparison with the commonly used grid search (GS). The ML algorithms are applied to a case study dataset from a food producer in Thailand. The objective is to predict a raw material quality measured on a numerical scale. K-fold cross-validation is performed to ensure that the ML algorithm performance is robust to the data partitioning process in the training, validation, and testing sets. The mean absolute error (MAE) of the validation set is used as the prediction accuracy measurement. The reliability of the hyperparameter values from GS and RSM is evaluated using confirmation runs. Statistical analysis shows that (1) the prediction accuracy of the three ML algorithms tuned by GS and RSM is similar, (2) hyperparameter settings from GS are 80% reliable for ANN and DBN, and settings from RSM are 90% and 100% reliable for ANN and DBN, respectively, and (3) savings in the number of runs required by RSM over GS are 97.79%, 97.81%, and 80.69% for ANN, SVM, and DBN, respectively.
Journal Article
An enhanced finite step length method for structural reliability analysis and reliability-based design optimization
The finite step length (FSL) method is extensively used for structural reliability analysis due to its robustness and efficiency compared with traditional Hasofer–Lind and Rackwitz–Fiessler (HL-RF) method. However, it may generate a large computational effort when it faces some complex nonlinear limit state functions. This study explains the basic reason of inefficiency of the FSL method and proposes an enhanced finite step length (EFSL) method to improve the ability for solving complex nonlinear problems, and then apply it to reliability-based design optimization (RBDO). The tactic is to present an iterative control criterion to compensate for the deficiency of the FSL method in the oscillation amplitude criterion, which solves the problem of large computational effort caused by unchanged step length during the iterative process. Then, a comprehensive step length adjustment formula is presented, which can adaptively adjust the step length to achieve fast convergence for limit state functions with different degrees of nonlinearity. Following that, the proposed method is combined with the double loop method (DLM) to improve the efficiency and robustness for solving complex RBDO problems. The robustness and efficiency of the proposed method compared to other commonly used first-order reliability analysis methods are demonstrated by five numerical examples. In addition, four design problems are used to validate the proposed EFSL-based DLM which is effective for solving complex nonlinear RBDO problems.
Journal Article
Algorithms for computing Pythagorean fuzzy average edge connectivity of Pythagorean fuzzy graphs
Average edge connectivity is a fundamental metric in classical and fuzzy graph theory. It is a key parameter in evaluating the reliability of a network. Fuzzy average edge connectivity more accurately describes the overall stability of links in the network by providing a more precise measure of the connectivity of the fuzzy graphs. It is particularly significant in situations where connectivity strength and dependability possess a degree of fuzziness, including communication networks with variable signal intensities or transit systems with unpredictable travel durations. In this article, we describe the types of edges in Pythagorean fuzzy graphs and the ideas of the Pythagorean fuzzy trees and cycles. We define the Pythagorean fuzzy average edge connectivity of Pythagorean fuzzy graphs using the concept of minimal Pythagorean fuzzy local edge cut. We provide the bounds for the Pythagorean fuzzy average edge connectivity of Pythagorean fuzzy graphs and strong Pythagorean fuzzy graphs. We discuss the Pythagorean fuzzy average edge connectivity of edge-deleted Pythagorean fuzzy subgraphs of Pythagorean fuzzy graphs. Moreover, we determine the effect of the different types of edges on the Pythagorean fuzzy average edge connectivity. We establish some results on Pythagorean fuzzy average edge connectivity. Furthermore, we design some algorithms to compute the Pythagorean fuzzy average edge connectivity of particular Pythagorean fuzzy graphs as complete Pythagorean fuzzy graphs and saturated Pythagorean fuzzy cycles. We provide the application of Pythagorean fuzzy average edge connectivity in human trafficking. Finally, we compare the suggested approach with an existing model to illustrate its viability and applicability.
Journal Article
Robustness of subsystem-based reliability for complete-transposition network
System reliability assessment is of great significance since it determines whether the system can perform properly or not. As an effective metric, subsystem-based reliability is defined to be the probability that at least one of the fault-free subsystems of a given size remains available in the event of node failure. In this work, we propose two distinct strategies to measure the subsystem reliability of complete-transposition network
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and investigate the robustness of its reliability bounds. Specifically, by virtue of the probability fault model, we establish the upper and lower bounds of subsystem reliability for
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in terms of at most four subgraphs intersecting. Subsequently, the approximation of subsystem reliability for
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is derived by ignoring the intersection among subgraphs. Furthermore, we investigate the robustness of subsystem reliability bounds for
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and determine the critical time point such that the bounds are valid. Numerical simulations are performed to verify the established analytic inference, which shows that the approximation of subsystem reliability is sufficient to characterize the exact value of subsystem reliability.
Journal Article
Surrogate-assisted reliability-based design optimization: a survey and a unified modular framework
Reliability-based design optimization (RBDO) is an active field of research with an ever increasing number of contributions. Numerous methods have been proposed for the solution of RBDO, a complex problem that combines optimization and reliability analysis. Classical approaches are based on approximation methods and have been classified in review papers. In this paper, we first review classical approaches based on approximation methods such as FORM, and also more recent methods that rely upon surrogate modelling and Monte Carlo simulation. We then propose a generalization of the existing surrogate-assisted and simulation-based RBDO techniques using a unified framework that includes three independent blocks, namely adaptive surrogate modelling, reliability analysis, and optimization. These blocks are non-intrusive with respect to each other and can be plugged independently in the framework. After a discussion on numerical considerations that require attention for the framework to yield robust solutions to various types of problems, the latter is applied to three examples (using two analytical functions and a finite element model). Kriging and support vector machines regression together with their own active learning schemes are considered in the surrogate model block. In terms of reliability analysis, the proposed framework is illustrated using both crude Monte Carlo and subset simulation. Finally, the covariance matrix adaptation-evolution scheme (CMA-ES), a global search algorithm, or sequential quadratic programming (SQP), a local gradient-based method, is used in the optimization block. The comparison of the results to benchmark studies shows the effectiveness and efficiency of the proposed framework.
Journal Article
A new computational scheme for structural static stochastic analysis based on Karhunen–Loève expansion and modified perturbation stochastic finite element method
Due to uncertainties, deterministic analysis cannot sufficiently reflect the performance of structures. Stochastic analysis can consider the influence of multiple uncertainties factors and improve the confidence of the analysis results. A new stochastic computational scheme, which has the features of Karhunen–Loève (K–L) expansion and modified perturbation stochastic finite element method (MPSFEM), is proposed for the structures with low-level uncertainties, called KL-MPSM for short. The material parameters are regarded as random fields and discretized by K–L expansion. The random variables obtained are substituted into MPSFEM to get the estimates of the first two order moments (mean and variance) of the structural responses. JC method is introduced to compute the reliability indexes and structures failure probability by utilizing the second-order estimates. A deep beam and a plane frame structure are presented as numerical examples to demonstrate the feasibility of KL-MPSM, and some random filed properties are studied. The results show that KL-MPSM has good accuracy, efficiency, and advantages in programming. Therefore, KL-MPSM is well suited for static stochastic analysis of structures with low-level uncertainties.
Journal Article
Second-order reliability methods: a review and comparative study
Second-order reliability methods are commonly used for the computation of reliability, defined as the probability of satisfying an intended function in the presence of uncertainties. These methods can achieve highly accurate reliability predictions owing to a second-order approximation of the limit-state function around the Most Probable Point of failure. Although numerous formulations have been developed, the lack of full-scale comparative studies has led to a dubiety regarding the selection of a suitable method for a specific reliability analysis problem. In this study, the performance of commonly used second-order reliability methods is assessed based on the problem scale, curvatures at the Most Probable Point of failure, first-order reliability index, and limit-state contour. The assessment is based on three performance metrics: capability, accuracy, and robustness. The capability is a measure of the ability of a method to compute feasible probabilities, i.e., probabilities between 0 and 1. The accuracy and robustness are quantified based on the mean and standard deviation of relative errors with respect to exact reliabilities, respectively. This study not only provides a review of classical and novel second-order reliability methods, but also gives an insight on the selection of an appropriate reliability method for a given engineering application.
Journal Article