Pub Date : 2024-10-01DOI: 10.1016/j.probengmech.2024.103706
Rossella Laudani, Giovanni Falsone
This work shows the use of the Probability Transformation Method (PTM) for deriving a closed-form probability density function (PDF) of the eigenpair of stochastic real-valued symmetric matrices. In particular, the PTM allows the direct evaluation of the eigenpair PDF starting from the joint PDF (JPDF) of the system’s uncertainties. The impact of the linear stochastic systems’ randomness in the natural frequencies and mode shape is investigated through some numerical applications. Even if the structural samples investigated are intentionally simple, that aspect is only linked to the authors’ use of the Mathematica software that, in some ways, limits the resolution for high dimensional problems. From a theoretical perspective, though, this is not a restriction, and the problem’s dimension has no impact on the method’s accuracy. The obtained analytical results compared with Monte Carlo simulations have confirmed the goodness of the proposed stochastic procedure.
{"title":"Closed-form expressions for eigenvalue and eigenvectors of stochastic symmetric matrices using the probability transformation method","authors":"Rossella Laudani, Giovanni Falsone","doi":"10.1016/j.probengmech.2024.103706","DOIUrl":"10.1016/j.probengmech.2024.103706","url":null,"abstract":"<div><div>This work shows the use of the Probability Transformation Method (PTM) for deriving a closed-form probability density function (PDF) of the eigenpair of stochastic real-valued symmetric matrices. In particular, the PTM allows the direct evaluation of the eigenpair PDF starting from the joint PDF (JPDF) of the system’s uncertainties. The impact of the linear stochastic systems’ randomness in the natural frequencies and mode shape is investigated through some numerical applications. Even if the structural samples investigated are intentionally simple, that aspect is only linked to the authors’ use of the Mathematica software that, in some ways, limits the resolution for high dimensional problems. From a theoretical perspective, though, this is not a restriction, and the problem’s dimension has no impact on the method’s accuracy. The obtained analytical results compared with Monte Carlo simulations have confirmed the goodness of the proposed stochastic procedure.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103706"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142700925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.probengmech.2024.103708
Jian-Bing Chen , Xin Huang , Jie Li
The response analysis of high-dimensional and strongly nonlinear systems with random parameters remains a significant challenge in stochastic computational mechanics. To address this challenge, some methods based on the high-efficacy point sets have been developed, in which efficient global-point-set methods represented by low-discrepancy are of paramount importance in generating representative point sets. Several discrepancies including the extended F-discrepancy (EF-discrepancy) and the generalized F-discrepancy (GF-discrepancy) have been introduced to assess the uniformity and the efficacy of a representative point set. In such context, a maximal marginal EF-discrepancy (MF-discrepancy), which is an extended form of the GF-discrepancy, is proposed in this paper and then the properties of the MF-discrepancy are studied in detail. The probability distribution of the MF-discrepancy is derived, including a rigorous proof for random point sets and a model based on an assumption for some generic point sets. A generalized Koksma-Hlawka inequality is established accordingly to govern the worst error estimate. The lowest bound of the MF-discrepancy is given, and two intuitive quantitative indices are proposed to measure the goodness of the MF-discrepancy. Based on the lowest bound, an enhanced point-selection strategy with a unified theoretical framework for minimizing the MF-discrepancy is proposed. In this framework, locally minimizing the MF-discrepancy yields the two-step point-selection method, and a new point-selection strategy is proposed based on the global minimization of the MF-discrepancy, which is verified to be efficient and robust, especially in high-dimensional cases. Several numerical examples, including a 2-story shear frame, a 10-story shear frame, and a 10-story reinforced concrete frame structure modeled by the finite element method, are studied, verifying the efficiency and the robustness of the proposed point-selection strategy.
{"title":"Quantitative property of MF-discrepancy and efficient point-selection strategy for the nonlinear stochastic response analysis of structures with random parameters","authors":"Jian-Bing Chen , Xin Huang , Jie Li","doi":"10.1016/j.probengmech.2024.103708","DOIUrl":"10.1016/j.probengmech.2024.103708","url":null,"abstract":"<div><div>The response analysis of high-dimensional and strongly nonlinear systems with random parameters remains a significant challenge in stochastic computational mechanics. To address this challenge, some methods based on the high-efficacy point sets have been developed, in which efficient global-point-set methods represented by low-discrepancy are of paramount importance in generating representative point sets. Several discrepancies including the extended F-discrepancy (EF-discrepancy) and the generalized F-discrepancy (GF-discrepancy) have been introduced to assess the uniformity and the efficacy of a representative point set. In such context, a maximal marginal EF-discrepancy (MF-discrepancy), which is an extended form of the GF-discrepancy, is proposed in this paper and then the properties of the MF-discrepancy are studied in detail. The probability distribution of the MF-discrepancy is derived, including a rigorous proof for random point sets and a model based on an assumption for some generic point sets. A generalized Koksma-Hlawka inequality is established accordingly to govern the worst error estimate. The lowest bound of the MF-discrepancy is given, and two intuitive quantitative indices are proposed to measure the goodness of the MF-discrepancy. Based on the lowest bound, an enhanced point-selection strategy with a unified theoretical framework for minimizing the MF-discrepancy is proposed. In this framework, locally minimizing the MF-discrepancy yields the two-step point-selection method, and a new point-selection strategy is proposed based on the global minimization of the MF-discrepancy, which is verified to be efficient and robust, especially in high-dimensional cases. Several numerical examples, including a 2-story shear frame, a 10-story shear frame, and a 10-story reinforced concrete frame structure modeled by the finite element method, are studied, verifying the efficiency and the robustness of the proposed point-selection strategy.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103708"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.probengmech.2024.103704
Beatrice Pomaro , Pol D. Spanos
This work focuses on determining the stochastic response properties, in the frequency domain, of a general class of nonlinear systems with polynomial nonlinearities. Specifically, the results are presented in terms of the stationary power spectral densities of the system's displacement and velocity. This is pursued by revisiting the conditional power spectrum concept, with the assumption that the response process is both ergodic and pseudo-harmonic and characterized by an amplitude, and a phase. A theoretical elucidation of an existing formula for the conditional spectrum is attempted. In particular, this concept is interpreted in conjunction with the time averaging approximation made in the definition of the stationary probability density function of a response amplitude quantity, associated with the original nonlinear system. It is shown that a proper definition of the stationary probability density of the response amplitude, along with a reasonable treatment of the distribution over the frequency domain of the amplitude contribution, lead to an improved approximation of the stationary response power spectral density. The treatment involves the averaging of a population of surrogate spectral densities of stationary random responses conforming with the system responses associated with individual values of the amplitudes of the responses. The semi-analytical results have been quite favourably juxtaposed with a large suite of à propos Monte Carlo simulations, both in terms of the shape and of the range of the involved germane frequencies, even for strongly nonlinear systems.
{"title":"A perspective on conditional spectrum-based determination of response statistics of nonlinear systems","authors":"Beatrice Pomaro , Pol D. Spanos","doi":"10.1016/j.probengmech.2024.103704","DOIUrl":"10.1016/j.probengmech.2024.103704","url":null,"abstract":"<div><div>This work focuses on determining the stochastic response properties, in the frequency domain, of a general class of nonlinear systems with polynomial nonlinearities. Specifically, the results are presented in terms of the stationary power spectral densities of the system's displacement and velocity. This is pursued by revisiting the conditional power spectrum concept, with the assumption that the response process is both ergodic and pseudo-harmonic and characterized by an amplitude, and a phase. A theoretical elucidation of an existing formula for the conditional spectrum is attempted. In particular, this concept is interpreted in conjunction with the time averaging approximation made in the definition of the stationary probability density function of a response amplitude quantity, associated with the original nonlinear system. It is shown that a proper definition of the stationary probability density of the response amplitude, along with a reasonable treatment of the distribution over the frequency domain of the amplitude contribution, lead to an improved approximation of the stationary response power spectral density. The treatment involves the averaging of a population of surrogate spectral densities of stationary random responses conforming with the system responses associated with individual values of the amplitudes of the responses. The semi-analytical results have been quite favourably juxtaposed with a large suite of à propos Monte Carlo simulations, both in terms of the shape and of the range of the involved germane frequencies, even for strongly nonlinear systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103704"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1016/j.probengmech.2024.103701
Atin Roy , Tanmoy Chatterjee , Sondipon Adhikari
Reliability analysis of highly sensitive structures is crucial to prevent catastrophic failures and ensure safety. Therefore, these safety-critical systems are to be designed for extremely rare failure events. Accurate statistical quantification of these events associated with a very low probability of occurrence requires millions of evaluations of the limit state function (LSF) involving computationally expensive numerical simulations. Variance reduction techniques like importance sampling (IS) reduce such repetitions to a few thousand. The use of a data-centric metamodel can further cut it down to a few hundred. In data-centric metamodeling approaches, the actual complex numerical analysis is performed at a few points to train the metamodel for approximating the structural response. On the other hand, a physics-informed neural network (PINN) can predict the structural response based on the governing differential equation describing the physics of the problem, without a single evaluation of the complex numerical solver, i.e., data-free. However, the existing PINN models for reliability analysis have been effective only in estimating a large range of failure probabilities (10−1∼10−3). To address this issue, the present study develops a PINN-based data-free reliability analysis for low failure probabilities (<10−5). In doing so, a two-stage PINN integrated with IS (PINN-IS) is proposed. The first stage is employed to approximate the most probable failure point (MPP) appropriately while the second stage enhances the accuracy of LSF predictions at the IS population centred on the approximated MPP. The effectiveness of the proposed approach is numerically illustrated by three structural reliability analysis examples.
高敏感结构的可靠性分析对于防止灾难性故障和确保安全至关重要。因此，这些安全关键型系统必须针对极其罕见的故障事件进行设计。要对这些发生概率极低的事件进行精确的统计量化，需要对极限状态函数（LSF）进行数百万次评估，其中涉及计算成本高昂的数值模拟。重要度采样（IS）等降低方差技术可将此类重复计算减少到数千次。使用以数据为中心的元模型可将重复次数进一步减少到几百次。在以数据为中心的元模型方法中，实际的复杂数值分析是在几个点上进行的，以训练元模型来逼近结构响应。另一方面，物理信息神经网络（PINN）可以根据描述问题物理特性的控制微分方程预测结构响应，而无需对复杂的数值求解器进行一次评估，即无需数据。然而，现有的用于可靠性分析的 PINN 模型只能有效估计较大范围的失效概率（10-1∼10-3）。针对这一问题，本研究开发了一种基于 PINN 的无数据可靠性分析方法，适用于低故障概率（10-5）。为此，我们提出了一种与 IS 集成的两阶段 PINN（PINN-IS）。第一阶段用于适当近似最可能故障点 (MPP)，第二阶段则提高以近似 MPP 为中心的 IS 群的 LSF 预测精度。通过三个结构可靠性分析实例对所提方法的有效性进行了数值说明。
{"title":"A physics-informed neural network enhanced importance sampling (PINN-IS) for data-free reliability analysis","authors":"Atin Roy , Tanmoy Chatterjee , Sondipon Adhikari","doi":"10.1016/j.probengmech.2024.103701","DOIUrl":"10.1016/j.probengmech.2024.103701","url":null,"abstract":"<div><div>Reliability analysis of highly sensitive structures is crucial to prevent catastrophic failures and ensure safety. Therefore, these safety-critical systems are to be designed for extremely rare failure events. Accurate statistical quantification of these events associated with a very low probability of occurrence requires millions of evaluations of the limit state function (LSF) involving computationally expensive numerical simulations. Variance reduction techniques like importance sampling (IS) reduce such repetitions to a few thousand. The use of a data-centric metamodel can further cut it down to a few hundred. In data-centric metamodeling approaches, the actual complex numerical analysis is performed at a few points to train the metamodel for approximating the structural response. On the other hand, a physics-informed neural network (PINN) can predict the structural response based on the governing differential equation describing the physics of the problem, without a single evaluation of the complex numerical solver, i.e., data-free. However, the existing PINN models for reliability analysis have been effective only in estimating a large range of failure probabilities (10<sup>−1</sup>∼10<sup>−3</sup>). To address this issue, the present study develops a PINN-based data-free reliability analysis for low failure probabilities (<10<sup>−5</sup>). In doing so, a two-stage PINN integrated with IS (PINN-IS) is proposed. The first stage is employed to approximate the most probable failure point (MPP) appropriately while the second stage enhances the accuracy of LSF predictions at the IS population centred on the approximated MPP. The effectiveness of the proposed approach is numerically illustrated by three structural reliability analysis examples.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103701"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-24DOI: 10.1016/j.probengmech.2024.103685
Ilias G. Mavromatis, Ioannis A. Kougioumtzoglou
A joint time–space extrapolation approach within the Wiener path integral (WPI) technique is developed for determining, efficiently and accurately, the non-stationary stochastic response of diverse nonlinear dynamical systems. The approach can be construed as an extension of a recently developed space-domain extrapolation scheme to account also for the temporal dimension. Specifically, based on a variational principle, the WPI technique yields a boundary value problem (BVP) to be solved for determining a most probable path corresponding to specific final boundary conditions. Further, the most probable path is used for evaluating, approximately, a point of the system response joint probability density function (PDF) corresponding to a specific time instant. Remarkably, the BVP exhibits two unique features that are exploited in this paper for developing an efficient joint time–space extrapolation approach. First, the BVPs corresponding to two neighboring grid points in the spatial domain of the response PDF not only share the same equations, but also the boundary conditions differ only slightly. Second, information inherent in the time-history of an already determined most probable path can be used for evaluating points of the response PDF corresponding to arbitrary time instants, without the need for solving additional BVPs. In a nutshell, relying on the aforementioned unique and advantageous features of the WPI-based BVP, the complete non-stationary response joint PDF is determined, first, by calculating numerically a relatively small number of PDF points, and second, by extrapolating in the joint time–space domain at practically zero additional computational cost. Compared to a standard brute-force implementation of the WPI technique, the developed extrapolation approach reduces the associated computational cost by several orders of magnitude. Two numerical examples relating to an oscillator with asymmetric nonlinearities and fractional derivative elements, and to a nonlinear structure under combined stochastic and deterministic periodic loading are considered for demonstrating the reliability of the extrapolation approach. Juxtapositions with pertinent Monte Carlo simulation data are included as well.
在维纳路径积分（WPI）技术中开发了一种时空联合外推法，用于高效、准确地确定各种非线性动力系统的非稳态随机响应。该方法可视为最近开发的空域外推方案的扩展，也考虑了时间维度。具体来说，基于变异原理，WPI 技术产生了一个边界值问题 (BVP)，用于确定与特定最终边界条件相对应的最可能路径。此外，最可能路径还可用于近似评估与特定时间瞬间相对应的系统响应联合概率密度函数 (PDF) 的一个点。值得注意的是，BVP 具有两个独特的特征，本文利用这两个特征开发了一种高效的联合时空外推方法。首先，响应 PDF 空间域中两个相邻网格点对应的 BVP 不仅方程相同，而且边界条件也只有细微差别。其次，已经确定的最可能路径的时间历史固有信息可用于评估响应 PDF 中对应任意时间时刻的点，而无需求解额外的 BVP。简而言之，依靠上述基于 WPI 的 BVP 的独特优势，首先通过数值计算相对较少的 PDF 点，其次通过在联合时空域进行外推，就能确定完整的非稳态响应联合 PDF，而额外的计算成本几乎为零。与 WPI 技术的标准强制执行相比，所开发的外推方法将相关计算成本降低了几个数量级。为了证明外推法的可靠性，我们考虑了两个与具有非对称非线性和分数导数元素的振荡器有关的数值示例，以及在随机和确定性周期性组合加载下的非线性结构。此外，还将相关的蒙特卡罗模拟数据并列在一起。
{"title":"A joint time–space extrapolation approach within the Wiener path integral technique for efficient stochastic response determination of nonlinear systems","authors":"Ilias G. Mavromatis, Ioannis A. Kougioumtzoglou","doi":"10.1016/j.probengmech.2024.103685","DOIUrl":"10.1016/j.probengmech.2024.103685","url":null,"abstract":"<div><div>A joint time–space extrapolation approach within the Wiener path integral (WPI) technique is developed for determining, efficiently and accurately, the non-stationary stochastic response of diverse nonlinear dynamical systems. The approach can be construed as an extension of a recently developed space-domain extrapolation scheme to account also for the temporal dimension. Specifically, based on a variational principle, the WPI technique yields a boundary value problem (BVP) to be solved for determining a most probable path corresponding to specific final boundary conditions. Further, the most probable path is used for evaluating, approximately, a point of the system response joint probability density function (PDF) corresponding to a specific time instant. Remarkably, the BVP exhibits two unique features that are exploited in this paper for developing an efficient joint time–space extrapolation approach. First, the BVPs corresponding to two neighboring grid points in the spatial domain of the response PDF not only share the same equations, but also the boundary conditions differ only slightly. Second, information inherent in the time-history of an already determined most probable path can be used for evaluating points of the response PDF corresponding to arbitrary time instants, without the need for solving additional BVPs. In a nutshell, relying on the aforementioned unique and advantageous features of the WPI-based BVP, the complete non-stationary response joint PDF is determined, first, by calculating numerically a relatively small number of PDF points, and second, by extrapolating in the joint time–space domain at practically zero additional computational cost. Compared to a standard brute-force implementation of the WPI technique, the developed extrapolation approach reduces the associated computational cost by several orders of magnitude. Two numerical examples relating to an oscillator with asymmetric nonlinearities and fractional derivative elements, and to a nonlinear structure under combined stochastic and deterministic periodic loading are considered for demonstrating the reliability of the extrapolation approach. Juxtapositions with pertinent Monte Carlo simulation data are included as well.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103685"},"PeriodicalIF":3.0,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The stability problem of a tunnel heading in clay remains a significant challenge in geotechnical engineering. Specifically, when considering the spatial variability of the soil, the stability factor may be influenced by geographically random fields. This study investigates the effect of random fields on a probabilistic analysis of a tunnel heading in undrained clay. The study assumes that the undrained shear strength of the clay increases linearly with depth due to a strength gradient factor. The random adaptive finite element limit analysis is employed to calculate the stability numbers for tunnel headings. Nonstationary random fields with varying vertical correlation lengths are simulated using Monte Carlo simulation technique. The stability analysis takes into account geometry parameters (i.e., cover depth ratio) and nonstationary random field of undrained shear strength parameters. (i.e., strength gradient, coefficient of variation, and vertical correlation length). The results of tunnel face stability using random adaptive finite element limit analysis have also been utilised to assess the probability of design failure over a practical range of deterministic factors of safety. In the context of probabilistic failure analysis, the failure mechanism resulting from varying vertical correlation lengths could influence the probability of design failure. The findings of this study can be of significant interest to tunnel engineering practitioners during the design phase of tunnel heading projects.
{"title":"Stability analysis of tunnel heading in clay with nonstationary random fields of undrained shear strength","authors":"Weeradetch Tanapalungkorn , Wittawat Yodsomjai , Suraparb Keawsawasvong , Thanh Son Nguyen , Weeraya Chim-Oye , Suched Likitlersuang","doi":"10.1016/j.probengmech.2024.103692","DOIUrl":"10.1016/j.probengmech.2024.103692","url":null,"abstract":"<div><div>The stability problem of a tunnel heading in clay remains a significant challenge in geotechnical engineering. Specifically, when considering the spatial variability of the soil, the stability factor may be influenced by geographically random fields. This study investigates the effect of random fields on a probabilistic analysis of a tunnel heading in undrained clay. The study assumes that the undrained shear strength of the clay increases linearly with depth due to a strength gradient factor. The random adaptive finite element limit analysis is employed to calculate the stability numbers for tunnel headings. Nonstationary random fields with varying vertical correlation lengths are simulated using Monte Carlo simulation technique. The stability analysis takes into account geometry parameters (i.e., cover depth ratio) and nonstationary random field of undrained shear strength parameters. (i.e., strength gradient, coefficient of variation, and vertical correlation length). The results of tunnel face stability using random adaptive finite element limit analysis have also been utilised to assess the probability of design failure over a practical range of deterministic factors of safety. In the context of probabilistic failure analysis, the failure mechanism resulting from varying vertical correlation lengths could influence the probability of design failure. The findings of this study can be of significant interest to tunnel engineering practitioners during the design phase of tunnel heading projects.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103692"},"PeriodicalIF":3.0,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142316043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-21DOI: 10.1016/j.probengmech.2024.103694
Yuhua Yan , Zhenzhou Lu
Under random-interval uncertainty, the failure probability function (FPF) represents the failure probability variation as a function of the random input distribution parameter. To quickly capture the effect of the distribution parameters on failure probability and decouple the reliability-based design optimization, a novel Bayesian updating method is proposed to efficiently estimate the FPF. In the proposed method, the prior augmented failure probability (AFP) is first estimated in the space spanned by random input and distribution parameter vectors. Subsequently, by treating the distribution parameter realization as an observation, the FPF can be estimated using posterior AFP based on Bayesian updating. The main novelty of this study is the elaborate treatment of the distribution parameter realization as an observation, whereby the FPF is transformed into the posterior AFP based on Bayesian updating, and can be obtained by sharing the prior AFP simulation samples. The computational cost of the proposed method is the same as that of estimating the prior AFP. To improve the efficiency of recognizing the sample state, and improve AFP and in turn FPF estimation, the adaptive Kriging model for random-interval uncertainty was inserted into the proposed method. The feasibility and novelty of the proposed method were verified on several examples.
{"title":"Novel Bayesian updating based interpolation method for estimating failure probability function in the presence of random-interval uncertainty","authors":"Yuhua Yan , Zhenzhou Lu","doi":"10.1016/j.probengmech.2024.103694","DOIUrl":"10.1016/j.probengmech.2024.103694","url":null,"abstract":"<div><div>Under random-interval uncertainty, the failure probability function (FPF) represents the failure probability variation as a function of the random input distribution parameter. To quickly capture the effect of the distribution parameters on failure probability and decouple the reliability-based design optimization, a novel Bayesian updating method is proposed to efficiently estimate the FPF. In the proposed method, the prior augmented failure probability (AFP) is first estimated in the space spanned by random input and distribution parameter vectors. Subsequently, by treating the distribution parameter realization as an observation, the FPF can be estimated using posterior AFP based on Bayesian updating. The main novelty of this study is the elaborate treatment of the distribution parameter realization as an observation, whereby the FPF is transformed into the posterior AFP based on Bayesian updating, and can be obtained by sharing the prior AFP simulation samples. The computational cost of the proposed method is the same as that of estimating the prior AFP. To improve the efficiency of recognizing the sample state, and improve AFP and in turn FPF estimation, the adaptive Kriging model for random-interval uncertainty was inserted into the proposed method. The feasibility and novelty of the proposed method were verified on several examples.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103694"},"PeriodicalIF":3.0,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-21DOI: 10.1016/j.probengmech.2024.103691
Qiushi Wang , Hui Zhao , Dao Gong , Jinlong Qiu , Pengfei Wu , Xiaoming Li , Xiyang Zhu , Hongyi Xiang , Tengfei Wang , Zhongmin Xiao , Jinsong Zhou
The irregularity excitation experienced by subway vehicles is mainly the result of the interaction between the track and wheel. However, in the early system design and simulation analysis of subway vehicles, most only used the traditional standard track irregularity spectrum as the input excitation, ignoring or underestimating the contribution of the wheel irregularity. Based on our statistical analysis of 200 000 km of tracking test data of subway vehicle wheel irregularities, we found that the short-wave irregularity caused by the wheels far exceeds the traditional standard track irregularity. The service condition of the vehicle is seriously affected, especially in the final stage of a wheel re-profile period. To address the above issues: Firstly, the sensitive wavelength range (16. 67–2500 mm) of subway vehicles was derived based on the axle box acceleration spectrum of IEC61373: 2010, which was very close to the wavelength range (50–2627 mm) of the wheel irregularity spectrum proposed later, demonstrating the importance of compiling a wheel irregularity spectrum; Secondly, based on the large number of tracking test data of wheel out-of-roundness, a calculation method of the wheel irregularity quantile spectrum under the Johnson non-normal transformation system was proposed; Thirdly, according to the different stages of the wheel re-profile period, the wheel irregularity spectrum is introduced to correct the short-wave segments of the traditional standard track irregularity spectrum to compile a wheel-rail comprehensive irregularity spectrum.
{"title":"Compilation of wheel-rail comprehensive irregularity spectrum for subway vehicle","authors":"Qiushi Wang , Hui Zhao , Dao Gong , Jinlong Qiu , Pengfei Wu , Xiaoming Li , Xiyang Zhu , Hongyi Xiang , Tengfei Wang , Zhongmin Xiao , Jinsong Zhou","doi":"10.1016/j.probengmech.2024.103691","DOIUrl":"10.1016/j.probengmech.2024.103691","url":null,"abstract":"<div><div>The irregularity excitation experienced by subway vehicles is mainly the result of the interaction between the track and wheel. However, in the early system design and simulation analysis of subway vehicles, most only used the traditional standard track irregularity spectrum as the input excitation, ignoring or underestimating the contribution of the wheel irregularity. Based on our statistical analysis of 200 000 km of tracking test data of subway vehicle wheel irregularities, we found that the short-wave irregularity caused by the wheels far exceeds the traditional standard track irregularity. The service condition of the vehicle is seriously affected, especially in the final stage of a wheel re-profile period. To address the above issues: Firstly, the sensitive wavelength range (16. 67–2500 mm) of subway vehicles was derived based on the axle box acceleration spectrum of IEC61373: 2010, which was very close to the wavelength range (50–2627 mm) of the wheel irregularity spectrum proposed later, demonstrating the importance of compiling a wheel irregularity spectrum; Secondly, based on the large number of tracking test data of wheel out-of-roundness, a calculation method of the wheel irregularity quantile spectrum under the Johnson non-normal transformation system was proposed; Thirdly, according to the different stages of the wheel re-profile period, the wheel irregularity spectrum is introduced to correct the short-wave segments of the traditional standard track irregularity spectrum to compile a wheel-rail comprehensive irregularity spectrum.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103691"},"PeriodicalIF":3.0,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142316044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-20DOI: 10.1016/j.probengmech.2024.103686
Haodong Zhao, Changcong Zhou
The study focuses on the reliability and global sensitivity analysis of fiber-reinforced composite radome structures, considering uncertainty from a multiscale perspective. Macroparameters are estimated based on microparameters using the multiscale analysis method for composites, and a reliability analysis model of the composite structure at the macrolevel is constructed. The material performance mechanism is explored in depth, both "from bottom to top" and "from top to bottom", to reveal its inherent laws. Due to insufficient variable distribution information, an imprecise probabilistic model is introduced to characterize the uncertainty effect in multiscale composite analysis. A nested optimization calculation method is applied to obtain reliability and sensitivity results. To ensure both calculation accuracy and efficiency, the regression and classification problems encountered in the proposed framework are addressed using two support vector machine models. The reliability and sensitivity analysis under the imprecise probabilistic framework can help engineers identify significant influential factors, thereby guiding the design of composite radome structures.
{"title":"An imprecise multiscale uncertainty quantification framework for fiber reinforced composites","authors":"Haodong Zhao, Changcong Zhou","doi":"10.1016/j.probengmech.2024.103686","DOIUrl":"10.1016/j.probengmech.2024.103686","url":null,"abstract":"<div><div>The study focuses on the reliability and global sensitivity analysis of fiber-reinforced composite radome structures, considering uncertainty from a multiscale perspective. Macroparameters are estimated based on microparameters using the multiscale analysis method for composites, and a reliability analysis model of the composite structure at the macrolevel is constructed. The material performance mechanism is explored in depth, both \"from bottom to top\" and \"from top to bottom\", to reveal its inherent laws. Due to insufficient variable distribution information, an imprecise probabilistic model is introduced to characterize the uncertainty effect in multiscale composite analysis. A nested optimization calculation method is applied to obtain reliability and sensitivity results. To ensure both calculation accuracy and efficiency, the regression and classification problems encountered in the proposed framework are addressed using two support vector machine models. The reliability and sensitivity analysis under the imprecise probabilistic framework can help engineers identify significant influential factors, thereby guiding the design of composite radome structures.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103686"},"PeriodicalIF":3.0,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Tall buildings with long service periods inevitably face multiple hazards, and the uncertainty associated with various factors has a considerable impact on life-cycle structural safety estimation. This study presents a hybrid Bayesian-Copula-based methodology for evaluating the damage risk e of tall buildings under concurrent seismic and strong wind excitations that incorporate various uncertainties. The main contributions of this study to the field of probabilistic multi-hazard risk assessment include the following: (1) The Bayes statistic method is employed to develop posterior probability distributions of the unknown parameters in the marginal probability models of an individual earthquake and strong wind as well as parameters involved in the multi-hazard demand model for fragility estimation. (2) The Bayesian-based method is applied to update the existing joint probabilistic model of earthquakes and strong winds. (3) A new method is presented to estimate the muti-hazard fragility bounds. The damage risk assessment quantifies the epistemic uncertainties of the unknown demand model parameters by calculating the total probability in the domain of the definition of the model parameters. A representative composite building with 42 floors is selected to perform this multi-hazard damage risk assessment method. The application of this study highlights the considerable impact of epistemic uncertainties and loading directions on damage risk. This presented Bayesian-Copula-based method is beneficial for decision-making involving tall buildings subjected to multiple hazards.
{"title":"Hybrid Bayesian-Copula-based damage probability estimation for steel-concrete composite tall buildings under concurrent seismic and wind loads","authors":"Xiao-Wei Zheng , Jie Cheng , Ling-Xin Zhang , Xian-Xin Xie","doi":"10.1016/j.probengmech.2024.103693","DOIUrl":"10.1016/j.probengmech.2024.103693","url":null,"abstract":"<div><div>Tall buildings with long service periods inevitably face multiple hazards, and the uncertainty associated with various factors has a considerable impact on life-cycle structural safety estimation. This study presents a hybrid Bayesian-Copula-based methodology for evaluating the damage risk e of tall buildings under concurrent seismic and strong wind excitations that incorporate various uncertainties. The main contributions of this study to the field of probabilistic multi-hazard risk assessment include the following: (1) The Bayes statistic method is employed to develop posterior probability distributions of the unknown parameters in the marginal probability models of an individual earthquake and strong wind as well as parameters involved in the multi-hazard demand model for fragility estimation. (2) The Bayesian-based method is applied to update the existing joint probabilistic model of earthquakes and strong winds. (3) A new method is presented to estimate the muti-hazard fragility bounds. The damage risk assessment quantifies the epistemic uncertainties of the unknown demand model parameters by calculating the total probability in the domain of the definition of the model parameters. A representative composite building with 42 floors is selected to perform this multi-hazard damage risk assessment method. The application of this study highlights the considerable impact of epistemic uncertainties and loading directions on damage risk. This presented Bayesian-Copula-based method is beneficial for decision-making involving tall buildings subjected to multiple hazards.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103693"},"PeriodicalIF":3.0,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142311995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
扫码关注我们
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号