Pub Date : 2025-10-01Epub Date: 2025-09-17DOI: 10.1016/j.probengmech.2025.103847
Yan Zhang , Zhengyang Zhang , Guanlan Xu , Yunsen Ren , Xiaoxiao Bai , You Qin , Kai Zhao , Guoxing Chen , Zhenglong Zhou , Jiawei Jiang
The reasonable determination of correlation distances serves as the prerequisite for ensuring the accuracy of random field simulation results for geotechnical parameters, and also constitutes a critical challenge in random field simulations that remains difficult to resolve. The Bootstrap method was employed to perform resampling on correlation distances. Utilizing the sampling results, a weighted prior probability density function for correlation distances was constructed. By applying Bayesian principles in conjunction with Hoffman's conditional random field simulation method, the decoupling and simultaneous updating of correlation distance determinations and geotechnical parameter estimations in random field simulations were achieved. Taking a seabed site as an example, this study simulated the spatial variability of marine soil SPT-N values and their influence on seabed liquefaction probability. The research revealed the impacts of correlation distances, constraints from measured borehole data, and heterogeneity of original site stratigraphy on random field simulation outcomes and seabed liquefaction probability. The validity of the proposed methodology was confirmed through verification against reserved measurement results at actual borehole locations.
{"title":"Improved conditional random field simulation method based on bootstrap- Bayesian inference and its application in identification of seafloor liquefaction","authors":"Yan Zhang , Zhengyang Zhang , Guanlan Xu , Yunsen Ren , Xiaoxiao Bai , You Qin , Kai Zhao , Guoxing Chen , Zhenglong Zhou , Jiawei Jiang","doi":"10.1016/j.probengmech.2025.103847","DOIUrl":"10.1016/j.probengmech.2025.103847","url":null,"abstract":"<div><div>The reasonable determination of correlation distances serves as the prerequisite for ensuring the accuracy of random field simulation results for geotechnical parameters, and also constitutes a critical challenge in random field simulations that remains difficult to resolve. The Bootstrap method was employed to perform resampling on correlation distances. Utilizing the sampling results, a weighted prior probability density function for correlation distances was constructed. By applying Bayesian principles in conjunction with Hoffman's conditional random field simulation method, the decoupling and simultaneous updating of correlation distance determinations and geotechnical parameter estimations in random field simulations were achieved. Taking a seabed site as an example, this study simulated the spatial variability of marine soil SPT-<em>N</em> values and their influence on seabed liquefaction probability. The research revealed the impacts of correlation distances, constraints from measured borehole data, and heterogeneity of original site stratigraphy on random field simulation outcomes and seabed liquefaction probability. The validity of the proposed methodology was confirmed through verification against reserved measurement results at actual borehole locations.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103847"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097515","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 : 2025-10-01Epub 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":"2025-10-01","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}
Pub Date : 2025-10-01Epub 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":"2025-10-01","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 : 2025-10-01Epub Date: 2025-11-15DOI: 10.1016/j.probengmech.2025.103864
Huanping Li , Guo-Peng Bai , Guilin Wen , Jie Liu , Guo-Kang Er
This paper proposes a novel TS-PINN framework, a physics-informed neural network incorporating trial and shape functions, for the probabilistic analysis of complex systems with strong even-powered nonlinearities. The presence of such nonlinearities in stochastic systems consistently induces asymmetry in probabilistic solutions. Unlike Gaussian closure which collapses under strong even-powered nonlinearities, TS-PINN delivers precise probabilistic solutions for these challenging stochastic systems. Within TS-PINN, the probabilistic solution takes the form of an exponential trial function applied to the sum of a Gaussian shape function and a neural network output. This solution formulation offers two key advantages: the exponential trial function guarantees solution positivity, preserving the physical interpretation of probability; and the Gaussian shape function provides an informed initial estimate, accelerating neural network convergence. The effectiveness of TS-PINN is validated through four numerical examples, demonstrating its capability to characterize asymmetric probabilistic solutions for stochastic oscillators with strong even-powered nonlinearities under correlated multiplicative and additive excitations. Verification is performed through comparative analysis with both Gaussian closure method and Monte Carlo simulation, confirming the framework’s accuracy and reliability.
{"title":"Asymmetric probabilistic solutions for stochastic oscillators with strong even-powered nonlinearities via a novel trial-shape function PINN framework","authors":"Huanping Li , Guo-Peng Bai , Guilin Wen , Jie Liu , Guo-Kang Er","doi":"10.1016/j.probengmech.2025.103864","DOIUrl":"10.1016/j.probengmech.2025.103864","url":null,"abstract":"<div><div>This paper proposes a novel TS-PINN framework, a physics-informed neural network incorporating trial and shape functions, for the probabilistic analysis of complex systems with strong even-powered nonlinearities. The presence of such nonlinearities in stochastic systems consistently induces asymmetry in probabilistic solutions. Unlike Gaussian closure which collapses under strong even-powered nonlinearities, TS-PINN delivers precise probabilistic solutions for these challenging stochastic systems. Within TS-PINN, the probabilistic solution takes the form of an exponential trial function applied to the sum of a Gaussian shape function and a neural network output. This solution formulation offers two key advantages: the exponential trial function guarantees solution positivity, preserving the physical interpretation of probability; and the Gaussian shape function provides an informed initial estimate, accelerating neural network convergence. The effectiveness of TS-PINN is validated through four numerical examples, demonstrating its capability to characterize asymmetric probabilistic solutions for stochastic oscillators with strong even-powered nonlinearities under correlated multiplicative and additive excitations. Verification is performed through comparative analysis with both Gaussian closure method and Monte Carlo simulation, confirming the framework’s accuracy and reliability.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103864"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571735","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 : 2025-10-01Epub Date: 2025-11-12DOI: 10.1016/j.probengmech.2025.103862
Hong Xiang, Jiajian Zhu, Yi Zhang, Yuting Zhang, Huadeng Wu, Zhonghang Lv
In structural reliability analysis, the first order reliability method (FORM) is an effective tool for identifying the most probable failure point (MPP), which represents the region where structural failure is most likely to occur. However, the traditional Hasofer-Lind and Rackwitz-Flessler (HL-RF) algorithm in FORM often encounters numerical instabilities in highly nonlinear scenarios, hindering the determination of the MPP. This paper proposes a novel momentum gradient based algorithm capable of accurately locating the MPP. It searches for the MPP along a novel direction determined by a weighted moving average of historical gradients, such that the highly oscillatory behavior caused by reliance on the current gradient alone is smoothed. Criteria based on the cosine of the angle between the position vector and gradient vector are introduced to guide the selection of the momentum factor to further enhance the computational efficiency, in light of different characteristics of iterative points. The effectiveness of the proposed algorithm is demonstrated through four nonlinear examples, including two benchmark numerical cases and two practical structural applications. The results indicate that the proposed algorithm significantly improves efficiency compared to some commonly used FORMs, establishing it as a reliable and practical solution for accurate MPP determination.
{"title":"Momentum gradient based first order reliability method for efficient identification of the most probable failure point","authors":"Hong Xiang, Jiajian Zhu, Yi Zhang, Yuting Zhang, Huadeng Wu, Zhonghang Lv","doi":"10.1016/j.probengmech.2025.103862","DOIUrl":"10.1016/j.probengmech.2025.103862","url":null,"abstract":"<div><div>In structural reliability analysis, the first order reliability method (FORM) is an effective tool for identifying the most probable failure point (MPP), which represents the region where structural failure is most likely to occur. However, the traditional Hasofer-Lind and Rackwitz-Flessler (HL-RF) algorithm in FORM often encounters numerical instabilities in highly nonlinear scenarios, hindering the determination of the MPP. This paper proposes a novel momentum gradient based algorithm capable of accurately locating the MPP. It searches for the MPP along a novel direction determined by a weighted moving average of historical gradients, such that the highly oscillatory behavior caused by reliance on the current gradient alone is smoothed. Criteria based on the cosine of the angle between the position vector and gradient vector are introduced to guide the selection of the momentum factor to further enhance the computational efficiency, in light of different characteristics of iterative points. The effectiveness of the proposed algorithm is demonstrated through four nonlinear examples, including two benchmark numerical cases and two practical structural applications. The results indicate that the proposed algorithm significantly improves efficiency compared to some commonly used FORMs, establishing it as a reliable and practical solution for accurate MPP determination.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103862"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145571736","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 : 2025-10-01Epub Date: 2025-09-17DOI: 10.1016/j.probengmech.2025.103850
Zhengwei Li , Wenping Gong , Zilong Zhang , Tianzheng Li
This study proposes a novel active learning-based method for reliability analysis, termed AK-EIG-ESC. The method integrates the adaptive Kriging metamodel with Monte Carlo simulation to estimate the probability of failure and, most importantly, introduces a novel active learning strategy to guide the selection of training samples. To achieve this, a random variable associated with the probability of failure is introduced and demonstrated to follow a Gaussian distribution according to the Central Limit Theorem. Building on this formulation, a new learning strategy is designed by quantifying the expected information gain from a hypothetical experiment. The information gain is expressed as the Kullback-Leibler divergence between the prior and posterior distributions of the introduced random variable associated with the probability of failure. Following this active learning strategy, a sequential sampling scheme is used to actively select new training samples, and the Kriging model is adaptively updated after each new sample is acquired. An error-based stopping criterion is adopted to evaluate the convergence of the proposed algorithm. Several illustrative examples are then used to assess the proposed AK-EIG-ESC algorithm, and the results show that the proposed algorithm exhibits high accuracy and efficiency for reliability analysis.
{"title":"An adaptive Kriging-based method for reliability analysis with a new learning strategy","authors":"Zhengwei Li , Wenping Gong , Zilong Zhang , Tianzheng Li","doi":"10.1016/j.probengmech.2025.103850","DOIUrl":"10.1016/j.probengmech.2025.103850","url":null,"abstract":"<div><div>This study proposes a novel active learning-based method for reliability analysis, termed AK-EIG-ESC. The method integrates the adaptive Kriging metamodel with Monte Carlo simulation to estimate the probability of failure and, most importantly, introduces a novel active learning strategy to guide the selection of training samples. To achieve this, a random variable associated with the probability of failure is introduced and demonstrated to follow a Gaussian distribution according to the Central Limit Theorem. Building on this formulation, a new learning strategy is designed by quantifying the expected information gain from a hypothetical experiment. The information gain is expressed as the Kullback-Leibler divergence between the prior and posterior distributions of the introduced random variable associated with the probability of failure. Following this active learning strategy, a sequential sampling scheme is used to actively select new training samples, and the Kriging model is adaptively updated after each new sample is acquired. An error-based stopping criterion is adopted to evaluate the convergence of the proposed algorithm. Several illustrative examples are then used to assess the proposed AK-EIG-ESC algorithm, and the results show that the proposed algorithm exhibits high accuracy and efficiency for reliability analysis.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103850"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145097513","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 : 2025-10-01Epub Date: 2025-10-08DOI: 10.1016/j.probengmech.2025.103853
Sumit Singh Thakur , K.M. Pervaiz Fathima
This study presents a probabilistic approach for predicting fatigue crack growth (FCG) parameters in plain concrete beams under constant amplitude cyclic loading. The method incorporates a size-adjusted Paris’ law, treating the initial crack length () and Paris’ coefficients ( and ) as random variables. The inverse first-order reliability method (FORM) is used to determine the Paris’ law coefficients corresponding to a target reliability level of 0.95. A limit state function (LSF) is formulated based on the theoretical and experimental number of load cycles to failure. The theoretical value is derived from the crack growth rate law, while the experimental value is obtained from stress versus the number of cycles to failure (S-N curve) data. The effectiveness of the proposed method is evaluated by comparing its results with those from inverse Monte Carlo simulation (MCS). The model is validated using experimental data from various concrete compositions and specimen sizes, including alkali-activated concrete. Larger specimens yielded lower prediction errors for the parameter , while smaller specimens showed lower errors for . Additionally, a sensitivity analysis is conducted to investigate how variations in input parameters influence the predicted crack growth parameters. Among the input random variables, exhibited the highest sensitivity, followed by and . The proposed method improves fatigue life assessment and provides a predictive framework for structures where experimental data may be limited.
{"title":"A probabilistic evaluation of fatigue crack growth in plain concrete using inverse reliability approach","authors":"Sumit Singh Thakur , K.M. Pervaiz Fathima","doi":"10.1016/j.probengmech.2025.103853","DOIUrl":"10.1016/j.probengmech.2025.103853","url":null,"abstract":"<div><div>This study presents a probabilistic approach for predicting fatigue crack growth (FCG) parameters in plain concrete beams under constant amplitude cyclic loading. The method incorporates a size-adjusted Paris’ law, treating the initial crack length (<span><math><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>) and Paris’ coefficients (<span><math><mi>C</mi></math></span> and <span><math><mi>m</mi></math></span>) as random variables. The inverse first-order reliability method (FORM) is used to determine the Paris’ law coefficients corresponding to a target reliability level of 0.95. A limit state function (LSF) is formulated based on the theoretical and experimental number of load cycles to failure. The theoretical value is derived from the crack growth rate law, while the experimental value is obtained from stress versus the number of cycles to failure (S-N curve) data. The effectiveness of the proposed method is evaluated by comparing its results with those from inverse Monte Carlo simulation (MCS). The model is validated using experimental data from various concrete compositions and specimen sizes, including alkali-activated concrete. Larger specimens yielded lower prediction errors for the parameter <span><math><mi>m</mi></math></span>, while smaller specimens showed lower errors for <span><math><mi>C</mi></math></span>. Additionally, a sensitivity analysis is conducted to investigate how variations in input parameters influence the predicted crack growth parameters. Among the input random variables, <span><math><mi>m</mi></math></span> exhibited the highest sensitivity, followed by <span><math><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and <span><math><mi>C</mi></math></span>. The proposed method improves fatigue life assessment and provides a predictive framework for structures where experimental data may be limited.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103853"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267029","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 : 2025-10-01Epub Date: 2025-10-03DOI: 10.1016/j.probengmech.2025.103852
Qinghe Shi , Chen Xu , Lei Wang , Juxi Hu , Weimin Chen
This paper proposes an adaptive probabilistic regularization method for damage parameter identification in composite laminated plates. Element-level damage parameters are introduced to describe the damage extent of composite laminated plates. A regularization methodology incorporating adaptive weighting coefficients is developed, enabling the dynamic adjustment of the weights assigned to each unknown parameter within the regularization term based on damage identification results throughout the solution process. To address the uncertainties encountered in the damage identification process, a damage identification strategy based on probabilistic regularization is proposed. Building on the Generalized Cross-Validation (GCV) method, the influence of uncertain parameters on the selection of regularization parameters is considered, yielding more robust regularization parameter selection results. Meanwhile, probabilistic methods are employed to quantify the uncertainties in the identification results, obtaining the uncertainty distribution of damage parameters in composite materials, with a focus on the distribution of in-plane and out-of-plane damage parameters for each element. By incorporating the principles of system reliability theory, the damage probability of each element can be derived. The computational precision and robustness of the proposed methodology are validated through a series of numerical examples and experimental validation case.
{"title":"Research on Adaptive Probabilistic Regularization (APR) method for damage parameter identification of laminated structures","authors":"Qinghe Shi , Chen Xu , Lei Wang , Juxi Hu , Weimin Chen","doi":"10.1016/j.probengmech.2025.103852","DOIUrl":"10.1016/j.probengmech.2025.103852","url":null,"abstract":"<div><div>This paper proposes an adaptive probabilistic regularization method for damage parameter identification in composite laminated plates. Element-level damage parameters are introduced to describe the damage extent of composite laminated plates. A regularization methodology incorporating adaptive weighting coefficients is developed, enabling the dynamic adjustment of the weights assigned to each unknown parameter within the regularization term based on damage identification results throughout the solution process. To address the uncertainties encountered in the damage identification process, a damage identification strategy based on probabilistic regularization is proposed. Building on the Generalized Cross-Validation (GCV) method, the influence of uncertain parameters on the selection of regularization parameters is considered, yielding more robust regularization parameter selection results. Meanwhile, probabilistic methods are employed to quantify the uncertainties in the identification results, obtaining the uncertainty distribution of damage parameters in composite materials, with a focus on the distribution of in-plane and out-of-plane damage parameters for each element. By incorporating the principles of system reliability theory, the damage probability of each element can be derived. The computational precision and robustness of the proposed methodology are validated through a series of numerical examples and experimental validation case.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103852"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145267043","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 : 2025-10-01Epub Date: 2025-10-10DOI: 10.1016/j.probengmech.2025.103854
Cosmin Safta , Reese E. Jones , Ravi G. Patel , Raelynn Wonnacot , Dan S. Bolintineanu , Craig M. Hamel , Sharlotte L.B. Kramer
We propose an inference hypernetwork as a general model of history-dependent processes. The framework is a hybrid between purely sampling- and optimization-based uncertainty quantification methods. The flexible data model is based on a neural ordinary differential equation (NODE) representing the evolution of internal states together with a trainable observation model subcomponent. The posterior distribution corresponding to the data model parameters (weights and biases) follows a stochastic differential equation with a drift term related to the score of the posterior that is learned jointly with the data model parameters. This Langevin sampling approach offers flexibility in balancing the computational budget between the evaluation cost of the data model and the approximation of the posterior density of its parameters. We demonstrate performance of the ensemble sampling hypernetwork on chemical reaction and material physics data and compare it to standard variational inference.
{"title":"Uncertainty quantification of neural network models of evolving processes via Langevin sampling","authors":"Cosmin Safta , Reese E. Jones , Ravi G. Patel , Raelynn Wonnacot , Dan S. Bolintineanu , Craig M. Hamel , Sharlotte L.B. Kramer","doi":"10.1016/j.probengmech.2025.103854","DOIUrl":"10.1016/j.probengmech.2025.103854","url":null,"abstract":"<div><div>We propose an inference hypernetwork as a general model of history-dependent processes. The framework is a hybrid between purely sampling- and optimization-based uncertainty quantification methods. The flexible data model is based on a neural ordinary differential equation (NODE) representing the evolution of internal states together with a trainable observation model subcomponent. The posterior distribution corresponding to the data model parameters (weights and biases) follows a stochastic differential equation with a drift term related to the score of the posterior that is learned jointly with the data model parameters. This Langevin sampling approach offers flexibility in balancing the computational budget between the evaluation cost of the data model and the approximation of the posterior density of its parameters. We demonstrate performance of the ensemble sampling hypernetwork on chemical reaction and material physics data and compare it to standard variational inference.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"82 ","pages":"Article 103854"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145321011","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 : 2025-10-01Epub 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":"2025-10-01","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}
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