In practical engineering problems, scenarios frequently emerge where random parameters follow multimodal probability distributions. Traditional time-variant uncertainty propagation methods, originally designed for unimodal distributions, risk incurring significant inaccuracies when applied to such multimodal cases. To address this challenge this paper introduces a time-variant uncertainty propagation analysis framework tailored for multimodal probability distributions. Initially, the time-variant response function is discretized into a series of instantaneous response functions. Subsequently, an improved point estimation method is employed to compute high-order statistical moments and correlation coefficients of these instantaneous responses. Following this, the maximum entropy method is used to reconstruct the probability density function of each instantaneous response function from its derived statistical moments. The highest order of statistical moments is adaptively determined through entropy-based criteria to balance computational efficiency and accuracy. Ultimately, the validity and effectiveness of the proposed framework are demonstrated through three examples.
{"title":"A time-variant uncertainty propagation analysis method for multimodal probability distributions","authors":"Boqun Xie , Xinpeng Wei , Qiang Gu , Chao Jiang , Jinwu Li","doi":"10.1016/j.probengmech.2025.103840","DOIUrl":"10.1016/j.probengmech.2025.103840","url":null,"abstract":"<div><div>In practical engineering problems, scenarios frequently emerge where random parameters follow multimodal probability distributions. Traditional time-variant uncertainty propagation methods, originally designed for unimodal distributions, risk incurring significant inaccuracies when applied to such multimodal cases. To address this challenge this paper introduces a time-variant uncertainty propagation analysis framework tailored for multimodal probability distributions. Initially, the time-variant response function is discretized into a series of instantaneous response functions. Subsequently, an improved point estimation method is employed to compute high-order statistical moments and correlation coefficients of these instantaneous responses. Following this, the maximum entropy method is used to reconstruct the probability density function of each instantaneous response function from its derived statistical moments. The highest order of statistical moments is adaptively determined through entropy-based criteria to balance computational efficiency and accuracy. Ultimately, the validity and effectiveness of the proposed framework are demonstrated through three examples.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103840"},"PeriodicalIF":3.5,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050190","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 : 2025-09-09DOI: 10.1016/j.probengmech.2025.103841
Boqun Xie , Xin Liu , Kai Liu , Shaowei Wu , Jiachang Tang
Multimodal random variables are widely encountered in practical engineering problems, such as the structural fatigue stress of a steel bridge accommodating both highway and railway traffic and the vibratory load experienced by a blade under stochastic dynamic excitations. Because of the error amplification effect caused by nonlinear response function in uncertainty propagation, traditional uncertainty analysis methods may yield large computational errors when multimodal distributions are involved. Herein, an uncertainty propagation method for multimodal distributions is proposed. First, the probability density function of multimodal random variables is modelled using a Gaussian mixture model. Second, the higher-order statistical moments of the response function are calculated through a bivariate dimension reduction method. Finally, the probability density function of the response function is computed using the maximum entropy method, and the desired statistical moment orders are means of an adaptive convergence framework. The effectiveness of the proposed method is demonstrated through two numerical examples and one engineering application.
{"title":"An adaptive moment-based approach to uncertainty analysis considering multimodal random parameters","authors":"Boqun Xie , Xin Liu , Kai Liu , Shaowei Wu , Jiachang Tang","doi":"10.1016/j.probengmech.2025.103841","DOIUrl":"10.1016/j.probengmech.2025.103841","url":null,"abstract":"<div><div>Multimodal random variables are widely encountered in practical engineering problems, such as the structural fatigue stress of a steel bridge accommodating both highway and railway traffic and the vibratory load experienced by a blade under stochastic dynamic excitations. Because of the error amplification effect caused by nonlinear response function in uncertainty propagation, traditional uncertainty analysis methods may yield large computational errors when multimodal distributions are involved. Herein, an uncertainty propagation method for multimodal distributions is proposed. First, the probability density function of multimodal random variables is modelled using a Gaussian mixture model. Second, the higher-order statistical moments of the response function are calculated through a bivariate dimension reduction method. Finally, the probability density function of the response function is computed using the maximum entropy method, and the desired statistical moment orders are means of an adaptive convergence framework. The effectiveness of the proposed method is demonstrated through two numerical examples and one engineering application.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103841"},"PeriodicalIF":3.5,"publicationDate":"2025-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050189","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 : 2025-09-02DOI: 10.1016/j.probengmech.2025.103827
Qingwei Liang, Cheng Yang, Yuxin Lin, Hancheng Huang, Shanshan Hu
Structural reliability analysis is critical to the design and safety evaluation of engineering structures. However, conventional reliability methods often struggle with high-dimensional problems. This study proposes an adaptive Kriging method for high-dimensional reliability assessment based on multi-objective particle swarm optimization (MOPSO). The method uses the maximum information coefficient (MIC) to build a high-dimensional Kriging surrogate. Training samples for updating the surrogate are selected using MOPSO. Furthermore, a hybrid convergence criterion that incorporates an error-based stopping criterion (ESC) is introduced to ensure efficient termination. Four benchmark examples demonstrate the effectiveness and practicality of the method. The results show clear gains in surrogate modeling efficiency and accuracy for high-dimensional reliability problems.
{"title":"Adaptive Kriging high-dimensional reliability assessment method based on multi-objective particle swarm optimization algorithm","authors":"Qingwei Liang, Cheng Yang, Yuxin Lin, Hancheng Huang, Shanshan Hu","doi":"10.1016/j.probengmech.2025.103827","DOIUrl":"10.1016/j.probengmech.2025.103827","url":null,"abstract":"<div><div>Structural reliability analysis is critical to the design and safety evaluation of engineering structures. However, conventional reliability methods often struggle with high-dimensional problems. This study proposes an adaptive Kriging method for high-dimensional reliability assessment based on multi-objective particle swarm optimization (MOPSO). The method uses the maximum information coefficient (MIC) to build a high-dimensional Kriging surrogate. Training samples for updating the surrogate are selected using MOPSO. Furthermore, a hybrid convergence criterion that incorporates an error-based stopping criterion (ESC) is introduced to ensure efficient termination. Four benchmark examples demonstrate the effectiveness and practicality of the method. The results show clear gains in surrogate modeling efficiency and accuracy for high-dimensional reliability problems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103827"},"PeriodicalIF":3.5,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145007593","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 : 2025-08-29DOI: 10.1016/j.probengmech.2025.103828
Xiaoyu Yang , Liyang Xie , Jianpeng Chen , Bingfeng Zhao , Kangkang Wang
The three-parameter Weibull distribution is highly effective for modelling fatigue life data. This study aims to develop a method for the estimation of the three Weibull parameters using a back-propagation neural network (BPNN), specifically designed for small-sample fatigue life data. Initially, the range of the shape parameter for the three-parameter Weibull distribution in the context of fatigue life is determined based on a comprehensive review of the literature. Six statistical features (the sample minimum, maximum, median, mean, mode and coefficient of variation) and the sample size are then proposed as inputs to the neural network, with the three Weibull distribution parameters serving as outputs. A well-performing BPNN is achieved after training on 7000 data sets for parameter estimation. Furthermore, when compared with the correlation coefficient method (CCM) and the minimum discrepancy method(MDM) approach via Monte Carlo simulations, the proposed method demonstrates superior accuracy in estimating the Weibull distribution parameters. The effectiveness of the proposed method is validated using experimental fatigue life data of 6A02 aluminum alloy.
{"title":"Estimation of Weibull distribution using the back-propagation neural network for fatigue failure data","authors":"Xiaoyu Yang , Liyang Xie , Jianpeng Chen , Bingfeng Zhao , Kangkang Wang","doi":"10.1016/j.probengmech.2025.103828","DOIUrl":"10.1016/j.probengmech.2025.103828","url":null,"abstract":"<div><div>The three-parameter Weibull distribution is highly effective for modelling fatigue life data. This study aims to develop a method for the estimation of the three Weibull parameters using a back-propagation neural network (BPNN), specifically designed for small-sample fatigue life data. Initially, the range of the shape parameter for the three-parameter Weibull distribution in the context of fatigue life is determined based on a comprehensive review of the literature. Six statistical features (the sample minimum, maximum, median, mean, mode and coefficient of variation) and the sample size are then proposed as inputs to the neural network, with the three Weibull distribution parameters serving as outputs. A well-performing BPNN is achieved after training on 7000 data sets for parameter estimation. Furthermore, when compared with the correlation coefficient method (CCM) and the minimum discrepancy method(MDM) approach via Monte Carlo simulations, the proposed method demonstrates superior accuracy in estimating the Weibull distribution parameters. The effectiveness of the proposed method is validated using experimental fatigue life data of 6A02 aluminum alloy.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103828"},"PeriodicalIF":3.5,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010707","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 : 2025-07-29DOI: 10.1016/j.probengmech.2025.103818
Antonio P. Sberna , Angshuman Deb , Fabio Di Trapani , Joel P. Conte
This study presents a comprehensive, reliability-based methodology for the seismic retrofitting design of non-ductile reinforced concrete (RC) frame structures. Distinctively, it advances the innovative application of the Performance-Based Earthquake Engineering (PBEE) framework to the retrofitting of non-code-compliant buildings, an area where its use has been limited. By extending PBEE beyond its traditional scope, this research addresses critical challenges associated with assessing and improving the seismic performance of existing vulnerable structures.
The proposed methodology offers a cost-effective strategy that balances seismic performance, quantified in terms of the Mean Return Period (MRP) of limit state exceedances, with retrofit costs. This performance-cost optimization enables the identification of retrofit solutions that achieve or surpass MRP targets while minimizing expenditure, thereby providing practical guidance for engineers and decision-makers.
A central contribution of this work is the integration of collapse probability into the PBEE framework, enhancing the comprehensiveness of seismic risk assessment. This is particularly critical for existing non-ductile RC frame structures, which are inherently more vulnerable due to inadequate seismic detailing.
The applicability and effectiveness of the proposed methodology are demonstrated through a case study involving the performance-based retrofit design of a representative structure. The results highlight the computational efficiency and accuracy of the proposed approach, validating its utility in real-world scenarios. This framework has the potential to inform and advance current practices in the seismic retrofitting of non-ductile RC frames, contributing to the enhanced safety, resilience, and sustainability of aging infrastructure in seismically active regions.
{"title":"Reliability-based seismic retrofitting design methodology for non-ductile reinforced concrete frame structures","authors":"Antonio P. Sberna , Angshuman Deb , Fabio Di Trapani , Joel P. Conte","doi":"10.1016/j.probengmech.2025.103818","DOIUrl":"10.1016/j.probengmech.2025.103818","url":null,"abstract":"<div><div>This study presents a comprehensive, reliability-based methodology for the seismic retrofitting design of non-ductile reinforced concrete (RC) frame structures. Distinctively, it advances the innovative application of the Performance-Based Earthquake Engineering (PBEE) framework to the retrofitting of non-code-compliant buildings, an area where its use has been limited. By extending PBEE beyond its traditional scope, this research addresses critical challenges associated with assessing and improving the seismic performance of existing vulnerable structures.</div><div>The proposed methodology offers a cost-effective strategy that balances seismic performance, quantified in terms of the Mean Return Period (MRP) of limit state exceedances, with retrofit costs. This performance-cost optimization enables the identification of retrofit solutions that achieve or surpass MRP targets while minimizing expenditure, thereby providing practical guidance for engineers and decision-makers.</div><div>A central contribution of this work is the integration of collapse probability into the PBEE framework, enhancing the comprehensiveness of seismic risk assessment. This is particularly critical for existing non-ductile RC frame structures, which are inherently more vulnerable due to inadequate seismic detailing.</div><div>The applicability and effectiveness of the proposed methodology are demonstrated through a case study involving the performance-based retrofit design of a representative structure. The results highlight the computational efficiency and accuracy of the proposed approach, validating its utility in real-world scenarios. This framework has the potential to inform and advance current practices in the seismic retrofitting of non-ductile RC frames, contributing to the enhanced safety, resilience, and sustainability of aging infrastructure in seismically active regions.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103818"},"PeriodicalIF":3.5,"publicationDate":"2025-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145061039","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}
Subsea control systems are crucial for ensuring the safe and stable operation of subsea oil and gas production. However, traditional reliability assessment methods face challenges in handling uncertain or incomplete fault data in deep-sea environments. In this study, an integrated approach combining Fuzzy Fault Tree Analysis (FFTA) and Bayesian Network (BN) is proposed to improve the reliability assessment of subsea control systems under uncertainty. Firstly, the fault tree model with ‘subsea control systems failure’ as the primary event is constructed and 42 basic events are identified as contributing factors. To address the lack of precise failure data, fuzzy set theory is applied to estimate failure probabilities at different confidence levels (denoted by λ) to represent varying degrees of certainty. When λ = 1, the failure probability is calculated as 0.0003904, while when λ = 0, the failure probability falls within the fuzzy interval [0.1121 × 10−3, 0.6334 × 10−3]. Subsequently, the Bayesian probabilistic prediction model is constructed based on uncertain data and small sample conditions, enabling the determination of the systems expected reliability value. Finally, the corresponding Bayesian network model is constructed based on the fault tree analysis outcomes to further enhance the reliability assessment of subsea control systems. The quantitative analysis is performed under the condition of λ = 1, and the systems failure probability is calculated as 0.00038979759, which is highly consistent with the calculated value of the fault tree analysis. Subsequently, reverse diagnostic inference is performed to obtain the posterior probability of the root node. However, relying solely on posterior probability for diagnosis may lack reliability. To enhance diagnostic accuracy, integrating probabilistic importance, critical importance and sensitivity analyses is essential to pinpoint the primary factors influencing system failure. Various diagnostic metrics consistently highlight nodes BF39 (Sand sensor fault), BF26 (Subsea control module optical fiber coupler fault) and BF19 (Subsea allocation device jumper fault) as system vulnerabilities. These findings validate the method's efficacy and establish a theoretical basis for risk-informed decision-making in subsea oil and gas systems reliability management.
{"title":"Reliability analysis of subsea control systems based on FFTA and Bayesian network","authors":"Chuankun Zhou , Jian Liu , Zihao Jiao , Guangfei Zhang , Yuqing Chen","doi":"10.1016/j.probengmech.2025.103831","DOIUrl":"10.1016/j.probengmech.2025.103831","url":null,"abstract":"<div><div>Subsea control systems are crucial for ensuring the safe and stable operation of subsea oil and gas production. However, traditional reliability assessment methods face challenges in handling uncertain or incomplete fault data in deep-sea environments. In this study, an integrated approach combining Fuzzy Fault Tree Analysis (FFTA) and Bayesian Network (BN) is proposed to improve the reliability assessment of subsea control systems under uncertainty. Firstly, the fault tree model with ‘subsea control systems failure’ as the primary event is constructed and 42 basic events are identified as contributing factors. To address the lack of precise failure data, fuzzy set theory is applied to estimate failure probabilities at different confidence levels (denoted by λ) to represent varying degrees of certainty. When λ = 1, the failure probability is calculated as 0.0003904, while when λ = 0, the failure probability falls within the fuzzy interval [0.1121 × 10<sup>−3</sup>, 0.6334 × 10<sup>−3</sup>]. Subsequently, the Bayesian probabilistic prediction model is constructed based on uncertain data and small sample conditions, enabling the determination of the systems expected reliability value. Finally, the corresponding Bayesian network model is constructed based on the fault tree analysis outcomes to further enhance the reliability assessment of subsea control systems. The quantitative analysis is performed under the condition of λ = 1, and the systems failure probability is calculated as 0.00038979759, which is highly consistent with the calculated value of the fault tree analysis. Subsequently, reverse diagnostic inference is performed to obtain the posterior probability of the root node. However, relying solely on posterior probability for diagnosis may lack reliability. To enhance diagnostic accuracy, integrating probabilistic importance, critical importance and sensitivity analyses is essential to pinpoint the primary factors influencing system failure. Various diagnostic metrics consistently highlight nodes BF39 (Sand sensor fault), BF26 (Subsea control module optical fiber coupler fault) and BF19 (Subsea allocation device jumper fault) as system vulnerabilities. These findings validate the method's efficacy and establish a theoretical basis for risk-informed decision-making in subsea oil and gas systems reliability management.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103831"},"PeriodicalIF":3.5,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144925743","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 : 2025-07-01DOI: 10.1016/j.probengmech.2025.103817
Shailesh Garg , Souvik Chakraborty
In this paper, we propose a novel data-driven operator learning framework termed the Randomized Prior Wavelet Neural Operator (RP-WNO). The proposed RP-WNO is an extension of the recently proposed wavelet neural operator, which, while boasts excellent generalizing capabilities, cannot estimate the uncertainty associated with its predictions in its vanilla form. RP-WNO, unlike the vanilla WNO, has an inherent predictive uncertainty quantification module and is expected to be useful for tasks where some form of decision-making is involved. RP-WNO is set in a deterministic framework, which makes it easier to implement than its Bayesian counterpart, especially for large, complex deep-learning architectures. It utilizes randomized prior networks that can account for prior information, and in this paper, we extend the theory of randomized prior networks by using the underlying concept to incorporate seamlessly, a physics-based prior. Three examples, covering datasets originating from two-dimensional partial differential equations, have been shown to test the efficacy of the proposed framework. Two of these examples utilize a randomly initialized prior network, and the remaining example utilizes a physics-based prior along with the randomly initialized prior network. The results produced favorably advocate for the efficacy of the proposed RP-WNO framework.
{"title":"Randomized prior wavelet neural operator for uncertainty quantification","authors":"Shailesh Garg , Souvik Chakraborty","doi":"10.1016/j.probengmech.2025.103817","DOIUrl":"10.1016/j.probengmech.2025.103817","url":null,"abstract":"<div><div>In this paper, we propose a novel data-driven operator learning framework termed the <em>Randomized Prior Wavelet Neural Operator</em> (RP-WNO). The proposed RP-WNO is an extension of the recently proposed wavelet neural operator, which, while boasts excellent generalizing capabilities, cannot estimate the uncertainty associated with its predictions in its vanilla form. RP-WNO, unlike the vanilla WNO, has an inherent predictive uncertainty quantification module and is expected to be useful for tasks where some form of decision-making is involved. RP-WNO is set in a deterministic framework, which makes it easier to implement than its Bayesian counterpart, especially for large, complex deep-learning architectures. It utilizes randomized prior networks that can account for prior information, and in this paper, we extend the theory of randomized prior networks by using the underlying concept to incorporate seamlessly, a physics-based prior. Three examples, covering datasets originating from two-dimensional partial differential equations, have been shown to test the efficacy of the proposed framework. Two of these examples utilize a randomly initialized prior network, and the remaining example utilizes a physics-based prior along with the randomly initialized prior network. The results produced favorably advocate for the efficacy of the proposed RP-WNO framework.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103817"},"PeriodicalIF":3.5,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144904007","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 : 2025-07-01DOI: 10.1016/j.probengmech.2025.103822
Xianrui Lyu, Xiaodan Ren, Jie Li
The inherent uncertainty of the microstructure in random porous materials propagates to the macroscopic response uncertainty through the underlying physical laws. Accurately characterizing this uncertainty necessitates the use of high-dimensional joint probability density functions, which need to be coupled with nonlinear, cross-scale propagation. This integration poses significant challenges for quantifying macroscopic performance uncertainty. To overcome these challenges, this study proposes an uncertainty analysis framework based on manifold space sampling. Specifically, manifold learning is employed to map the complex, high-dimensional microstructure to a low-dimensional manifold space. Within this manifold space, the uncertainty of the microstructure is comprehensively characterized via the probabilistic distribution of latent variables, enabling effective dimensionality reduction while preserving essential statistical characteristics of the original microstructure. Subsequently, a sampling strategy guided by maximal marginal EF-discrepancy (MF-discrepancy) is used to select representative latent variables, which are then decoded to reconstruct representative microstructure samples. These samples and their corresponding mechanical responses are subsequently input into a physically-based probability density evolution method (PDEM), which transforms the high-dimensional stochastic problem into a set of deterministic partial differential equations. This provides a full probabilistic evolution process of the homogenized stress response, thereby enabling the propagation of microstructural uncertainty to macroscopic performance uncertainty. The accuracy and computational efficiency of the proposed method are validated by comparing its results with the reference values obtained from Monte Carlo simulations (MC) using an sufficiently large sample size. The results demonstrate that the framework offers significant advantages in handling high-dimensional random variables and nonlinear cross-scale propagation, providing an efficient and feasible approach for uncertainty quantification in complex material systems.
{"title":"Uncertainty quantification of the mechanical response of random porous materials based on manifold space sampling","authors":"Xianrui Lyu, Xiaodan Ren, Jie Li","doi":"10.1016/j.probengmech.2025.103822","DOIUrl":"10.1016/j.probengmech.2025.103822","url":null,"abstract":"<div><div>The inherent uncertainty of the microstructure in random porous materials propagates to the macroscopic response uncertainty through the underlying physical laws. Accurately characterizing this uncertainty necessitates the use of high-dimensional joint probability density functions, which need to be coupled with nonlinear, cross-scale propagation. This integration poses significant challenges for quantifying macroscopic performance uncertainty. To overcome these challenges, this study proposes an uncertainty analysis framework based on manifold space sampling. Specifically, manifold learning is employed to map the complex, high-dimensional microstructure to a low-dimensional manifold space. Within this manifold space, the uncertainty of the microstructure is comprehensively characterized via the probabilistic distribution of latent variables, enabling effective dimensionality reduction while preserving essential statistical characteristics of the original microstructure. Subsequently, a sampling strategy guided by maximal marginal EF-discrepancy (MF-discrepancy) is used to select representative latent variables, which are then decoded to reconstruct representative microstructure samples. These samples and their corresponding mechanical responses are subsequently input into a physically-based probability density evolution method (PDEM), which transforms the high-dimensional stochastic problem into a set of deterministic partial differential equations. This provides a full probabilistic evolution process of the homogenized stress response, thereby enabling the propagation of microstructural uncertainty to macroscopic performance uncertainty. The accuracy and computational efficiency of the proposed method are validated by comparing its results with the reference values obtained from Monte Carlo simulations (MC) using an sufficiently large sample size. The results demonstrate that the framework offers significant advantages in handling high-dimensional random variables and nonlinear cross-scale propagation, providing an efficient and feasible approach for uncertainty quantification in complex material systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103822"},"PeriodicalIF":3.5,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144813867","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 : 2025-07-01DOI: 10.1016/j.probengmech.2025.103814
Leonidas Taliadouros, Ilias G. Mavromatis, Ioannis A. Kougioumtzoglou
A quantum computing approach is developed for eigenvalue analysis of stochastic structural systems. Specifically, within a Monte Carlo simulation (MCS) solution framework, both the subspace-search variational quantum eigensolver (SSVQE) and the variational quantum deflation (VQD) algorithms are employed and appropriately adapted for treating the random eigenvalue problem in structural dynamics. Compared to alternative quantum-based solution efforts in the literature, the herein-developed approach yields statistics for the complete set of the system eigenvalues. Further, certain advantageous properties of the system parameter matrices, such as symmetry and sparsity, are also exploited for enhancing the efficiency of the approach. Furthermore, an efficient strategy is proposed for addressing the challenging problem of initialization of the SSVQE and VQD algorithms, and calibration of the associated hyperparameters. Two representative examples exhibiting random parameter matrices are considered. They relate to a chain-like system that is widely used in structural dynamics for modeling, for instance, shear-type building structures, and to a system with cyclic symmetry that is of relevance to the dynamics of rotating machines such as turbine blades. The accuracy degree of the approach is demonstrated by comparing eigenvalue statistics obtained based on classical computing (Python) with estimates obtained by employing a quantum computer simulator and, for a specific case, an actual quantum computer (IBM Sherbrooke). The latter achievement has its own merit since, for the first time, an MCS approach is employed on a real quantum computer for conducting eigenvalue analysis of a stochastic structural system. This serves as a proof-of-concept that quantum computing can, potentially, treat challenging stochastic dynamics problems in the near future.
{"title":"Eigenvalue analysis of stochastic structural systems: A quantum computing approach","authors":"Leonidas Taliadouros, Ilias G. Mavromatis, Ioannis A. Kougioumtzoglou","doi":"10.1016/j.probengmech.2025.103814","DOIUrl":"10.1016/j.probengmech.2025.103814","url":null,"abstract":"<div><div>A quantum computing approach is developed for eigenvalue analysis of stochastic structural systems. Specifically, within a Monte Carlo simulation (MCS) solution framework, both the subspace-search variational quantum eigensolver (SSVQE) and the variational quantum deflation (VQD) algorithms are employed and appropriately adapted for treating the random eigenvalue problem in structural dynamics. Compared to alternative quantum-based solution efforts in the literature, the herein-developed approach yields statistics for the complete set of the system eigenvalues. Further, certain advantageous properties of the system parameter matrices, such as symmetry and sparsity, are also exploited for enhancing the efficiency of the approach. Furthermore, an efficient strategy is proposed for addressing the challenging problem of initialization of the SSVQE and VQD algorithms, and calibration of the associated hyperparameters. Two representative examples exhibiting random parameter matrices are considered. They relate to a chain-like system that is widely used in structural dynamics for modeling, for instance, shear-type building structures, and to a system with cyclic symmetry that is of relevance to the dynamics of rotating machines such as turbine blades. The accuracy degree of the approach is demonstrated by comparing eigenvalue statistics obtained based on classical computing (Python) with estimates obtained by employing a quantum computer simulator and, for a specific case, an actual quantum computer (IBM Sherbrooke). The latter achievement has its own merit since, for the first time, an MCS approach is employed on a real quantum computer for conducting eigenvalue analysis of a stochastic structural system. This serves as a proof-of-concept that quantum computing can, potentially, treat challenging stochastic dynamics problems in the near future.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"81 ","pages":"Article 103814"},"PeriodicalIF":3.5,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144781326","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 : 2025-07-01DOI: 10.1016/j.probengmech.2025.103806
Stjepan Salatovic , Sebastian Krumscheid , Florian Wittemann , Luise Kärger
Fiber orientation is decisive for the mechanical performance of composite materials. During manufacturing, variations in material and process parameters can influence fiber orientation. We employ multilevel polynomial surrogates to model the propagation of uncertain material properties in the injection molding process. To ensure reliable uncertainty quantification, a key focus is deriving novel error bounds for statistical measures of a quantity of interest. Numerical experiments employ the Cross-WLF viscosity model and Hagen–Poiseuille flow to investigate the impact of uncertainties in fiber length and matrix temperature on the fractional anisotropy of fiber orientation. The Folgar–Tucker equation and the improved anisotropic rotary diffusion model, incorporating analytical solutions, are used for verification. Results show that the method improves significantly upon standard Monte Carlo estimation, while also providing error guarantees. These findings offer the first step towards a reliable and practical tool for optimizing fiber-reinforced polymer manufacturing processes in the future.
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