Structural SafetyPub Date : 2023-11-06DOI: 10.1016/j.strusafe.2023.102399
Amir H. Khodabakhsh, Seid H. Pourtakdoust
{"title":"Solution of FPK equation for stochastic dynamics subjected to additive Gaussian noise via deep learning approach","authors":"Amir H. Khodabakhsh, Seid H. Pourtakdoust","doi":"10.1016/j.strusafe.2023.102399","DOIUrl":"https://doi.org/10.1016/j.strusafe.2023.102399","url":null,"abstract":"<div><p>The Fokker-Plank-Kolmogorov (FPK) equation is an idealized model representing many stochastic systems commonly encountered in the analysis of stochastic structures as well as many other applications. Its solution thus provides an invaluable insight into the performance of many engineering systems. Despite its great importance, the solution of the FPK equation is still extremely challenging. For systems of practical significance, the FPK equation is usually high dimensional, rendering most of the numerical methods ineffective. In this respect, the present work introduces the FPK-DP Net as a physics-informed network that encodes the physical insights, i.e. the governing constrained differential equations emanated out of physical laws, into a deep neural network. FPK-DP Net is a mesh-free learning method that can solve the density evolution of stochastic dynamics subjected to additive white Gaussian noise without any prior simulation data and can be used as an efficient surrogate model afterward. FPK-DP Net uses the dimension-reduced FPK equation. Therefore, it can be used to address high-dimensional practical problems as well. To demonstrate the potential applicability of the proposed framework, and to study its accuracy and efficacy, numerical implementations on five different benchmark problems are investigated.</p></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"106 ","pages":"Article 102399"},"PeriodicalIF":5.8,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91686951","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Structural SafetyPub Date : 2023-11-06DOI: 10.1016/j.strusafe.2023.102402
Ziqi Wang
{"title":"Optimized equivalent linearization for random vibration","authors":"Ziqi Wang","doi":"10.1016/j.strusafe.2023.102402","DOIUrl":"https://doi.org/10.1016/j.strusafe.2023.102402","url":null,"abstract":"<div><p>A fundamental limitation of various Equivalent Linearization Methods (ELMs) in nonlinear random vibration analysis is that they are approximate by their nature. A quantity of interest estimated from an ELM has no guarantee to be the same as the solution of the original nonlinear system. In this study, we tackle this fundamental limitation. We sequentially address the following two questions: (i) given an equivalent linear system obtained from any ELM, how to construct an estimator such that, as the linear system simulations are guided by a limited number of nonlinear system simulations, the estimator converges on the nonlinear system solution? (ii) how to construct an optimized equivalent linear system such that the estimator approaches the nonlinear system solution as quickly as possible? The first question is theoretically straightforward since classic Monte Carlo techniques, such as the control variates and importance sampling, can improve upon the solution of any surrogate model. We adapt the well-known Monte Carlo theories into the specific context of equivalent linearization. The second question is challenging, especially when rare event probabilities are of interest. We develop specialized methods to construct and optimize linear systems. In the context of uncertainty quantification (UQ), the proposed optimized ELM can be viewed as a <em>physical surrogate model</em>-based UQ method. The embedded physical equations endow the surrogate model with the capability to handle high-dimensional uncertainties in stochastic dynamics analysis.</p></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"106 ","pages":"Article 102402"},"PeriodicalIF":5.8,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167473023000899/pdfft?md5=a10237d76767366b4f233aaf9be4c845&pid=1-s2.0-S0167473023000899-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92045888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Structural SafetyPub Date : 2023-11-06DOI: 10.1016/j.strusafe.2023.102403
B. Barros , B. Conde , B. Riveiro , O. Morales-Nápoles
{"title":"Gaussian Copula-based Bayesian network approach for characterizing spatial variability in aging steel bridges","authors":"B. Barros , B. Conde , B. Riveiro , O. Morales-Nápoles","doi":"10.1016/j.strusafe.2023.102403","DOIUrl":"https://doi.org/10.1016/j.strusafe.2023.102403","url":null,"abstract":"<div><p>Finite Element (FE) modeling often requires unavoidable simplifications or assumptions due to a lack of experimental data, modeling complexity, or non-affordable computational cost. One such simplification is modeling corrosion phenomena or material properties, which are usually assumed to be uniform throughout the structure. However, e.g., corrosion has a local nature and severe consequences on the behavior of steel structures that should not be overlooked. To improve the current numerical modeling techniques in aging steel bridges, this paper proposes a Gaussian Copula-based Bayesian Network (GCBN) approach to model the spatial variability of structural element properties. Accordingly, a study of the automatic Bayesian network generation process is first conducted. Subsequently, the methodology is applied to a severely damaged riveted steel bridge built in 1897. The results show that the methodology has excellent flexibility for generating properties variability in FE models at a low computational cost, thus ensuring its practical feasibility and robustness for accurate numerical modeling.</p></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"106 ","pages":"Article 102403"},"PeriodicalIF":5.8,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0167473023000905/pdfft?md5=fe1f3fa0ae0696b641df9a809a94a580&pid=1-s2.0-S0167473023000905-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91686564","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Structural SafetyPub Date : 2023-10-31DOI: 10.1016/j.strusafe.2023.102395
Yuanqin Tao , Kok-Kwang Phoon , Honglei Sun , Jianye Ching
{"title":"Variance reduction function for a potential inclined slip line in a spatially variable soil","authors":"Yuanqin Tao , Kok-Kwang Phoon , Honglei Sun , Jianye Ching","doi":"10.1016/j.strusafe.2023.102395","DOIUrl":"https://doi.org/10.1016/j.strusafe.2023.102395","url":null,"abstract":"<div><p>Variance reduction function for a spatially variable soil property is an important factor that affects the spatial average-based characteristic value, which in turn influences the design of a geotechnical structure in the context of Eurocode 7. This study derives the theoretical and approximate variance reduction functions (VRFs) for a potential inclined slip line in a spatially variable soil. Only stationary random fields are studied but more general spatial variability characteristics including smoothness and hole effect are considered. First, the closed-form one-dimensional (1D) VRFs are investigated, including the VRFs for classical one-parameter autocorrelation models, the non-classical two-parameter Whittle-Matérn (WM) model, and the most general three-parameter cosine Whittle-Matérn (CosWM) model proposed to date. It is found that closed-form solutions are not available or not practical to compute in general and the simple approximate VRF (equal to scale of fluctuation/averaging length) is not adequate for the non-classical autocorrelation models (WM and CosWM). Two approximate VRFs are developed in this study for the 1D WM and 1D CosWM models. For a spatial average over an inclined line, this paper derives the theoretical scales of fluctuation (SOFs) and VRFs for five commonly used 2D autocorrelation models. The theoretical solutions show that the equivalent SOFs proposed in the literature are only applicable under special conditions which are clarified in this paper. More general approximations for the VRF over an inclined line are proposed. The range of applicability for each approximation is stated. The proposed approximate VRFs are shown to be reasonably accurate when they are applied to the spatial average-based characteristic value and for the design of a vertical pile and an inclined soil nail.</p></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"106 ","pages":"Article 102395"},"PeriodicalIF":5.8,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90017504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A conditional extreme value distribution method for dynamic reliability analysis of stochastic structures","authors":"Ye-Yao Weng , Xuan-Yi Zhang , Zhao-Hui Lu , Yan-Gang Zhao","doi":"10.1016/j.strusafe.2023.102398","DOIUrl":"https://doi.org/10.1016/j.strusafe.2023.102398","url":null,"abstract":"<div><p>An efficient post-processing simulation method is proposed to estimate small failure probabilities of stochastic dynamic structures involving the inherent randomness of structural physical-geometrical parameters and external excitations. To extract a small failure probability, the proposed method introduces an intermediate event to represent the realizations of extreme structural response in the tail of distribution. With the aid of this intermediate event, structural failure probability is reformulated as a product of the event’s occurrence probability and the conditional exceedance probability of extreme response when the event occurs. The latter corresponds to a distribution of extreme response under the condition of the intermediate event, referred to as the conditional extreme value distribution (CEVD). Accordingly, the proposed method is termed the CEVD method. To reconstruct the CEVD, a truncated shifted generalized lognormal distribution model is employed. Bayesian estimation method is utilized to determine the two shape parameters of this model based on the samples of both original extreme value distribution and CEVD, where the CEVD samples are generated by Markov chain Monte Carlo sampling. The efficiency and accuracy of the proposed method are demonstrated through two numerical examples considering seismic reliability analyses of a 10-story nonlinear frame and a soil-foundation-structure interaction system.</p></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"106 ","pages":"Article 102398"},"PeriodicalIF":5.8,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91686565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Structural SafetyPub Date : 2023-10-25DOI: 10.1016/j.strusafe.2023.102397
Min Li , Srinivasan Arunachalam , Seymour M.J. Spence
{"title":"A multi-fidelity stochastic simulation scheme for estimation of small failure probabilities","authors":"Min Li , Srinivasan Arunachalam , Seymour M.J. Spence","doi":"10.1016/j.strusafe.2023.102397","DOIUrl":"https://doi.org/10.1016/j.strusafe.2023.102397","url":null,"abstract":"<div><p>Computing small failure probabilities is often of interest in the reliability analysis of engineering systems. However, this task can be computationally demanding since many evaluations of expensive high-fidelity models are often required. To address this, a multi-fidelity approach is proposed in this work within the setting of stratified sampling. The overall idea is to reduce the required number of high-fidelity model runs by integrating the information provided by different levels of model fidelity while maintaining accuracy in estimating the failure probabilities. More specifically, strata-wise multi-fidelity models are established based on Gaussian process models to efficiently predict the high-fidelity response and the system collapse from the low-fidelity response. Due to the reduced computational cost of the low-fidelity models, the multi-fidelity approach can achieve a significant speedup in estimating small failure probabilities associated with high-fidelity models. The effectiveness and efficiency of the proposed multi-fidelity stochastic simulation scheme are validated through an application to a two-story two-bay steel building under extreme winds.</p></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"106 ","pages":"Article 102397"},"PeriodicalIF":5.8,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91686949","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Structural SafetyPub Date : 2023-10-03DOI: 10.1016/j.strusafe.2023.102393
Jianhua Xian, Ziqi Wang
{"title":"Relaxation-based importance sampling for structural reliability analysis","authors":"Jianhua Xian, Ziqi Wang","doi":"10.1016/j.strusafe.2023.102393","DOIUrl":"https://doi.org/10.1016/j.strusafe.2023.102393","url":null,"abstract":"<div><p><span>This study presents an importance sampling formulation based on adaptively relaxing parameters from the indicator function and/or the probability density function<span>. The formulation embodies the prevalent mathematical concept of relaxing a complex problem into a sequence of progressively easier sub-problems. Due to the flexibility in constructing relaxation parameters, relaxation-based importance sampling provides a unified framework for various existing variance reduction techniques, such as subset simulation, sequential importance sampling, and annealed importance sampling. More crucially, the framework lays the foundation for creating new importance sampling strategies, tailoring to specific applications. To demonstrate this potential, two importance sampling strategies are proposed. The first strategy couples annealed importance sampling with subset simulation, focusing on low-dimensional problems. The second strategy aims to solve high-dimensional problems by leveraging spherical sampling and scaling techniques. Both methods are desirable for fragility analysis in performance-based engineering, as they can produce the entire fragility surface in a single run of the sampling algorithm. Three numerical examples, including a 1000-dimensional </span></span>stochastic dynamic problem, are studied to demonstrate the proposed methods.</p></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"106 ","pages":"Article 102393"},"PeriodicalIF":5.8,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49699006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Structural SafetyPub Date : 2023-09-29DOI: 10.1016/j.strusafe.2023.102382
Xuejing Wang , Xin Ruan , Joan R. Casas , Mingyang Zhang
{"title":"Probabilistic model of traffic scenarios for extreme load effects in long-span bridges","authors":"Xuejing Wang , Xin Ruan , Joan R. Casas , Mingyang Zhang","doi":"10.1016/j.strusafe.2023.102382","DOIUrl":"https://doi.org/10.1016/j.strusafe.2023.102382","url":null,"abstract":"<div><p>The traffic scenarios that may cause extreme load effects are of great importance to the safety assessment of bridge structures. The traditional simulation method of traffic flow cannot depict the distribution pattern of vehicles on the bridge deck when the maximum effect is induced. In this paper, a probabilistic Gaussian mixture model (GMM) for heavy vehicle scenarios on the bridge deck under free-flow condition is proposed for long-span bridges based on collected Weigh in Motion (WIM) data. The scenarios of extreme response under free-flow occur more frequently than congestion scenarios and are of similar value and relevance in the daily management and safety assessment of long-span bridges.</p><p>A non-stationary Poisson process is utilized to simulate the uneven occurrence of heavy vehicles in different lanes, and it is assumed that they are located within the artificially defined cells on the bridge deck. Then, Nataf transformation is employed to consider the correlation of gross vehicle weights (GVWs) within close range in the same lane. The numerical study is carried out on a long-span cable-stayed bridge to investigate the effects of correlation in GVWs and stationarity of vehicle distribution location on the structural responses. The load responses calculated by the proposed model and Monte Carlo method for different effects are compared with the values derived from code model. The results show that with the increase of the correlation level of the neighboring GVWs, the simulated responses are more prone to get extreme values, which means an increasing probability of the most unfavorable spatial distribution of on-bridge vehicles. The same results are also found under the non-stationary simulation state for vehicle location. The non-stationary Poisson process provides an efficient, highly feasible method, which is also in the safe side, for simulating the vehicle spatial distribution for specific effects.</p></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"106 ","pages":"Article 102382"},"PeriodicalIF":5.8,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49877424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Soft Monte Carlo Simulation for imprecise probability estimation: A dimension reduction-based approach","authors":"Azam Abdollahi , Hossein Shahraki , Matthias G.R. Faes , Mohsen Rashki","doi":"10.1016/j.strusafe.2023.102391","DOIUrl":"https://doi.org/10.1016/j.strusafe.2023.102391","url":null,"abstract":"<div><p><span>This paper proposes an efficient solution for solving hybrid reliability problems involving random and interval variables. To meet this aim, using the soft Monte Carlo (SMC) method, a solution is proposed that breaks the random variables space into local 1-D coordinates and then, considers 1-D coordinate as an additional dimension of interval variables. Accordingly, using an optimization in increased interval variables space, the upper and lower bounds of failure probability for each 1-D problem are estimated. In addition, the total failure probabilities are presented as the </span>mathematical expectation<span> of the obtained probability bounds for 1-D coordinates. Then, it is shown that this approach is fit for application of univariate dimension reduction method to reduce the function calls of analysis in the optimization phase. This approach is validated by solving benchmark reliability problems as well as the application of the proposed method for solving real world engineering problems investigated by solving hybrid reliability analysis of reinforced concrete columns. It is shown that the proposed approach efficiently approximates the failure probability bound of problems with moderate nonlinear limit state functions with high accuracy.</span></p></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"106 ","pages":"Article 102391"},"PeriodicalIF":5.8,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49698997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Structural SafetyPub Date : 2023-09-23DOI: 10.1016/j.strusafe.2023.102394
Qiangqiang Zhao, Tengfei Wu, Jinyan Duan, Jun Hong
{"title":"A novel Bayesian-inference-based method for global sensitivity analysis of system reliability with multiple failure modes","authors":"Qiangqiang Zhao, Tengfei Wu, Jinyan Duan, Jun Hong","doi":"10.1016/j.strusafe.2023.102394","DOIUrl":"https://doi.org/10.1016/j.strusafe.2023.102394","url":null,"abstract":"<div><p><span>Global reliability sensitivity analysis aims at quantifying the effects of each random source on failure probability or reliability over their whole distribution range and is highly concerned in reliability design and uncertainty control. And in practice, a structure or product usually has more than one component impacting their performance safety, which is essentially a system reliability problem. Therefore, this paper proposes a novel Bayesian-inference-based method for moment-based global sensitivity analysis of system reliability with multiple failure modes. First, the limit-state function of each component involved in the system is linearly approximated based on the reliability index. Then, the global reliability sensitivity is transformed into a problem of multivariable Gaussian probability within a given safe region where the dimension number is double of the failure modes. In this case, the Bayesian-inference-driven expectation propagation technique is introduced to solve this intractable problem in an analytical manner, based on which the closed-form solution to the global reliability sensitivity for system with multiple components is accordingly derived. Finally, a numerical case, a vehicle subjected to impact, a cantilever beam and a practical </span>engineering application to a four-panel spaceborne deployable plane antenna are studied to demonstrate the effectiveness of the proposed method by comparison with Monte Carlo simulation.</p></div>","PeriodicalId":21978,"journal":{"name":"Structural Safety","volume":"106 ","pages":"Article 102394"},"PeriodicalIF":5.8,"publicationDate":"2023-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49698994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}