Pub Date : 2025-04-01DOI: 10.1016/j.probengmech.2025.103767
Andrea Burlon , Mario Di Paola , Giuseppe Failla , Pol D. Spanos
The discretized paths-based sequential integration method (SIM) is a quite versatile approach for solving various problems, including barrier problems, first passage problems, reflecting barrier problems and so on. This method builds upon the Chapman–Kolmogorov equation and is not applicable to non-Markovian problems, as in the case of fractional Brownian motion (FBM). In this paper, it is shown that the loss of the Markovian property can be overcome by utilizing the self-similarity of the FBM. In order to apply the discretized paths-based SIM, we have to solve a specific stochastic boundary value problem, also called stochastic “bridge” problem, which involves selecting only the trajectories of the FBM that ends at an assigned value, say at , at the beginning of the time interval . It is shown that, due to self-similarity, the stochastic “bridge” problem may be solved only once, regardless of the value at . It is also shown that the trajectories of the stochastic “bridge” problem exhibit self-similarity, which circumvents the loss of Markovian property in FBM, thus allowing the discretized paths-based SIM to be employed without invoking the classical Chapman–Kolmogorov equation. Further, an application involving the classical first passage problem is presented.
基于离散路径的顺序积分法（SIM）是一种非常通用的方法，可用于解决各种问题，包括障碍问题、首通道问题、反映障碍问题等。该方法建立在Chapman-Kolmogorov方程的基础上，不适用于非马尔可夫问题，如分数布朗运动（FBM）的情况。本文证明了利用FBM的自相似性可以克服马尔可夫性质的损失。为了应用离散的基于路径的SIM，我们必须解决一个特定的随机边值问题，也称为随机“桥”问题，这涉及到只选择FBM的轨迹，该轨迹在指定值处结束，例如在时间间隔tk−tk+1开始时的x ā at tk。结果表明，由于自相似性，随机“桥”问题可能只被解决一次，而不管x在tk处的值是多少。研究还表明，随机“桥”问题的轨迹表现出自相似性，这规避了FBM中马尔可夫性质的损失，从而允许在不调用经典Chapman-Kolmogorov方程的情况下使用基于路径的离散化SIM。此外，还提出了一个涉及经典第一通道问题的应用。
{"title":"A discretized paths-based sequential integration method involving the self-similarity of the fractional Brownian motion","authors":"Andrea Burlon , Mario Di Paola , Giuseppe Failla , Pol D. Spanos","doi":"10.1016/j.probengmech.2025.103767","DOIUrl":"10.1016/j.probengmech.2025.103767","url":null,"abstract":"<div><div>The discretized paths-based sequential integration method (SIM) is a quite versatile approach for solving various problems, including barrier problems, first passage problems, reflecting barrier problems and so on. This method builds upon the Chapman–Kolmogorov equation and is not applicable to non-Markovian problems, as in the case of fractional Brownian motion (FBM). In this paper, it is shown that the loss of the Markovian property can be overcome by utilizing the self-similarity of the FBM. In order to apply the discretized paths-based SIM, we have to solve a specific stochastic boundary value problem, also called stochastic “bridge” problem, which involves selecting only the trajectories of the FBM that ends at an assigned value, say <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> at <span><math><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>, at the beginning of the time interval <span><math><mrow><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>−</mo><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msub></mrow></math></span>. It is shown that, due to self-similarity, the stochastic “bridge” problem may be solved only once, regardless of the value <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>̄</mo></mrow></mover></math></span> at <span><math><msub><mrow><mi>t</mi></mrow><mrow><mi>k</mi></mrow></msub></math></span>. It is also shown that the trajectories of the stochastic “bridge” problem exhibit self-similarity, which circumvents the loss of Markovian property in FBM, thus allowing the discretized paths-based SIM to be employed without invoking the classical Chapman–Kolmogorov equation. Further, an application involving the classical first passage problem is presented.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103767"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143935802","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 : 2025-04-01DOI: 10.1016/j.probengmech.2025.103769
Peifang Sun , Yongbo Peng
As a promising device for seismic mitigation of structures, the tuned mass-damper-inerter (TMDI) has attracted considerable attention in recent years. However, existing design methods of TMDI such as the fixed-point theory-based formulas and stochastic optimization methods, often suffer from insufficient control gains or excessive computational demands. To address these issues, this study develops a reliability-informed multi-parameter design table (MPDT) for optimizing TMDI in a fast, accurate, and non-iterative manner. The MPDT is developed through repeated reliability-based design optimization (RBDO), integrating the probability density evolution method (PDEM) with genetic algorithms. It ensures robust TMDI performance under stochastic ground motions and facilitates efficient selection of key parameters, including mass ratio, inertance-to-mass ratio, damping ratio, and frequency ratio, across varying structural periods and seismic conditions. Additionally, it provides guidance for rational selection of TMDI topology, such as TMD, TID, or full TMDI. The MPDT is validated via case studies on a base-isolated structure and a five-story shear frame structure with various TMDI configurations. The results demonstrate that the MPDT-based TMDI designs achieve comparable control performance to full RBDO designs while significantly reducing computational effort. Key influences such as structural modal frequency, inerter connection, and TMDI placement are examined, revealing the robustness of the proposed method even if the design assumptions are partially fulfilled. Furthermore, design trends, such as the relationship between inertance and structural period are uncovered. Overall, the MPDT provides a reliable, efficient, and scalable framework for performance-based seismic design of TMDI systems, supporting practical engineering applications.
{"title":"Reliability-informed design table for optimizing tuned mass-damper-inerter systems to improve structural seismic performance","authors":"Peifang Sun , Yongbo Peng","doi":"10.1016/j.probengmech.2025.103769","DOIUrl":"10.1016/j.probengmech.2025.103769","url":null,"abstract":"<div><div>As a promising device for seismic mitigation of structures, the tuned mass-damper-inerter (TMDI) has attracted considerable attention in recent years. However, existing design methods of TMDI such as the fixed-point theory-based formulas and stochastic optimization methods, often suffer from insufficient control gains or excessive computational demands. To address these issues, this study develops a reliability-informed multi-parameter design table (MPDT) for optimizing TMDI in a fast, accurate, and non-iterative manner. The MPDT is developed through repeated reliability-based design optimization (RBDO), integrating the probability density evolution method (PDEM) with genetic algorithms. It ensures robust TMDI performance under stochastic ground motions and facilitates efficient selection of key parameters, including mass ratio, inertance-to-mass ratio, damping ratio, and frequency ratio, across varying structural periods and seismic conditions. Additionally, it provides guidance for rational selection of TMDI topology, such as TMD, TID, or full TMDI. The MPDT is validated via case studies on a base-isolated structure and a five-story shear frame structure with various TMDI configurations. The results demonstrate that the MPDT-based TMDI designs achieve comparable control performance to full RBDO designs while significantly reducing computational effort. Key influences such as structural modal frequency, inerter connection, and TMDI placement are examined, revealing the robustness of the proposed method even if the design assumptions are partially fulfilled. Furthermore, design trends, such as the relationship between inertance and structural period are uncovered. Overall, the MPDT provides a reliable, efficient, and scalable framework for performance-based seismic design of TMDI systems, supporting practical engineering applications.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103769"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143912411","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 : 2025-04-01DOI: 10.1016/j.probengmech.2025.103770
Fengwei Lai , Tan Nguyen , Jim Shiau , Ming Huang
Understanding the influence of spatial variability in soil friction angle on trapdoor stability remains crucial, particularly in commonly encountered shallow active trapdoor configurations within sandy deposits. This study presents a probabilistic stability assessment of shallow active trapdoors in spatially random sands, employing Random Adaptive Finite Element Limit Analysis (RAFELA) integrated with Monte Carlo simulations (MCs). The numerical solutions, expressed in terms of stability number, are validated through both deterministic and probabilistic analyses. A comprehensive parametric study examines the effects of cover depth, soil friction angle, and spatial variability parameters (including coefficient of variation and horizontal/vertical correlation lengths) on the probability of failure (PF) corresponding to selected factors of safety (FoS). The observed failure mechanisms reveal distinctively variable sliding surfaces, highlighting the nature of random field problems in geomechanics. The study culminates in the development of practical contour-based design charts for a quick assessment of PF in active shallow trapdoors embedded in spatially random sands. These research outcomes offer valuable guidance for engineers, facilitating informed decision-making during preliminary design of buried structures.
{"title":"Probabilistic stability analyses of active shallow trapdoor in spatially random sand","authors":"Fengwei Lai , Tan Nguyen , Jim Shiau , Ming Huang","doi":"10.1016/j.probengmech.2025.103770","DOIUrl":"10.1016/j.probengmech.2025.103770","url":null,"abstract":"<div><div>Understanding the influence of spatial variability in soil friction angle on trapdoor stability remains crucial, particularly in commonly encountered shallow active trapdoor configurations within sandy deposits. This study presents a probabilistic stability assessment of shallow active trapdoors in spatially random sands, employing Random Adaptive Finite Element Limit Analysis (RAFELA) integrated with Monte Carlo simulations (MCs). The numerical solutions, expressed in terms of stability number, are validated through both deterministic and probabilistic analyses. A comprehensive parametric study examines the effects of cover depth, soil friction angle, and spatial variability parameters (including coefficient of variation and horizontal/vertical correlation lengths) on the probability of failure (<em>PF</em>) corresponding to selected factors of safety (<em>FoS</em>). The observed failure mechanisms reveal distinctively variable sliding surfaces, highlighting the nature of random field problems in geomechanics. The study culminates in the development of practical contour-based design charts for a quick assessment of <em>PF</em> in active shallow trapdoors embedded in spatially random sands. These research outcomes offer valuable guidance for engineers, facilitating informed decision-making during preliminary design of buried structures.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103770"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143935801","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 : 2025-04-01DOI: 10.1016/j.probengmech.2025.103773
R. Bourkaib , M. Kok , H.C. Seyffert
This paper aims at estimating both unidirectional and multi-directional waves from noisy measured ship motion data, with a focus on the inclusion of the vessel’s forward speed to reflect real-world operating conditions. The technique is based on an Adaptive Kalman Filter for estimating wave elevation and wave spectrum parameters, including significant wave height, peak period, and wave direction. The proposed method was tested using simulated ship motion data, and its performance was evaluated by comparing the estimated wave spectrum with reference values used in the simulation model and with results from a widely used baseline frequency domain approach. The results demonstrate that the method effectively estimates the wave spectrum in a short measuring window with a reasonable degree of accuracy when accounting for varying forward speed, indicating strong potential for real-time wave estimation to aid in improving navigation, safety, and operational efficiency.
{"title":"Unidirectional and multi-directional wave estimation from ship motions using an Adaptive Kalman Filter with the inclusion of varying forward speed","authors":"R. Bourkaib , M. Kok , H.C. Seyffert","doi":"10.1016/j.probengmech.2025.103773","DOIUrl":"10.1016/j.probengmech.2025.103773","url":null,"abstract":"<div><div>This paper aims at estimating both unidirectional and multi-directional waves from noisy measured ship motion data, with a focus on the inclusion of the vessel’s forward speed to reflect real-world operating conditions. The technique is based on an Adaptive Kalman Filter for estimating wave elevation and wave spectrum parameters, including significant wave height, peak period, and wave direction. The proposed method was tested using simulated ship motion data, and its performance was evaluated by comparing the estimated wave spectrum with reference values used in the simulation model and with results from a widely used baseline frequency domain approach. The results demonstrate that the method effectively estimates the wave spectrum in a short measuring window with a reasonable degree of accuracy when accounting for varying forward speed, indicating strong potential for real-time wave estimation to aid in improving navigation, safety, and operational efficiency.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103773"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144146775","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 : 2025-04-01DOI: 10.1016/j.probengmech.2025.103760
Tushar , Souvik Chakraborty
The well-known governing physics in science and engineering often relies on certain assumptions and approximations, resulting in approximate analyses and designs. The emergence of data-driven models has, to a certain degree, addressed this challenge; however, the purely data-driven models often (a) lack interpretability, (b) are data-hungry, and (c) do not generalize beyond the training window. Operator learning has emerged as a potential solution, but the challenges are still persistent. A promising alternative resides in data-physics fusion, where data-driven models are employed to correct or identify the missing physics. Accordingly, we here introduce a novel Differentiable Physics Augmented Wavelet Neural Operator (DPA-WNO) for solving stochastic mechanics problems. The proposed DPA-WNO blends the concepts of differentiable physics with the Wavelet Neural Operator (WNO). This framework harnesses WNO’s ability to learn from data while retaining the interpretability and generalization of physics-based solvers. We illustrate the applicability of the proposed approach in solving uncertainty quantification and reliability analysis problems due to randomness in the initial condition. Three benchmark examples and one practical application from various fields of science and engineering are solved using the proposed approach. The results presented illustrate the efficacy of the proposed approach.
{"title":"Differentiable physics augmented wavelet neural operator: A gray box model for a class of stochastic mechanics problem","authors":"Tushar , Souvik Chakraborty","doi":"10.1016/j.probengmech.2025.103760","DOIUrl":"10.1016/j.probengmech.2025.103760","url":null,"abstract":"<div><div>The well-known governing physics in science and engineering often relies on certain assumptions and approximations, resulting in approximate analyses and designs. The emergence of data-driven models has, to a certain degree, addressed this challenge; however, the purely data-driven models often (a) lack interpretability, (b) are data-hungry, and (c) do not generalize beyond the training window. Operator learning has emerged as a potential solution, but the challenges are still persistent. A promising alternative resides in data-physics fusion, where data-driven models are employed to correct or identify the missing physics. Accordingly, we here introduce a novel Differentiable Physics Augmented Wavelet Neural Operator (DPA-WNO) for solving stochastic mechanics problems. The proposed DPA-WNO blends the concepts of differentiable physics with the Wavelet Neural Operator (WNO). This framework harnesses WNO’s ability to learn from data while retaining the interpretability and generalization of physics-based solvers. We illustrate the applicability of the proposed approach in solving uncertainty quantification and reliability analysis problems due to randomness in the initial condition. Three benchmark examples and one practical application from various fields of science and engineering are solved using the proposed approach. The results presented illustrate the efficacy of the proposed approach.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103760"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143928287","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 : 2025-04-01DOI: 10.1016/j.probengmech.2025.103766
S. Russotto , A. Pirrotta
The probabilistic characterization of random variables and stochastic processes involves the evaluation of the probability density function or characteristic function. The latter is typically obtained by using integer-order statistical moments, that could lead to divergence problem for high-order moments especially in case of heavy-tailed distributions, such as the distribution of the α-stable random variables. On the other hand, recent approaches that use complex fractional moments, offer a more robust probabilistic description, but for particular cases.
In this paper, a novel approach based on Mellin transform for the probabilistic characterization of random variables is proposed. Starting from numerical data, this approach is effective for the evaluation of both the probability density function and the characteristic function, and then is valid for a wide class of random variables. Further, an extension of the approach from random variables to stochastic processes is proposed. The reliability of the proposed approach is assessed through several numerical simulations involving α-stable distributions, Gaussian distributions and α-stable stochastic processes.
{"title":"Mellin transform for the probabilistic characterization of random variables and stochastic processes","authors":"S. Russotto , A. Pirrotta","doi":"10.1016/j.probengmech.2025.103766","DOIUrl":"10.1016/j.probengmech.2025.103766","url":null,"abstract":"<div><div>The probabilistic characterization of random variables and stochastic processes involves the evaluation of the probability density function or characteristic function. The latter is typically obtained by using integer-order statistical moments, that could lead to divergence problem for high-order moments especially in case of heavy-tailed distributions, such as the distribution of the α-stable random variables. On the other hand, recent approaches that use complex fractional moments, offer a more robust probabilistic description, but for particular cases.</div><div>In this paper, a novel approach based on Mellin transform for the probabilistic characterization of random variables is proposed. Starting from numerical data, this approach is effective for the evaluation of both the probability density function and the characteristic function, and then is valid for a wide class of random variables. Further, an extension of the approach from random variables to stochastic processes is proposed. The reliability of the proposed approach is assessed through several numerical simulations involving α-stable distributions, Gaussian distributions and α-stable stochastic processes.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103766"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143870124","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 : 2025-04-01DOI: 10.1016/j.probengmech.2025.103768
Junjie Zhan, Jiangpeng Li, Yutong Liu
The advancement of soft robotics technology has spurred a growing interest in understanding the time-dependent reliability of continuum structures. This study introduces a novel non-probabilistic model for assessing the time-dependent reliability index of continuum structures under the influence of non-probabilistic bounded field uncertainties. Utilizing the non-probabilistic series expansion (NPSE), the field uncertainties are quantified through a collection of NPSE coefficients, offering a comprehensive representation of the uncertainty in the system. By considering the time variable as an uncertain parameter, the time-dependent reliability analysis can be reformulated as a time-independent problem, allowing for the development of a non-probabilistic reliability index that accounts for both time parameter and field uncertainties. A time-dependent reliability index is introduced utilizing the concerned performance method to assess the structural reliability throughout varying time intervals. Subsequently, the efficacy and applicability of the proposed non-probabilistic time-dependent reliability model were illustrated through three numerical example studies involving geometrically linear and nonlinear time-dependent structures. The findings highlight the effectiveness and practicality of the proposed approach in facilitating the evaluation of the reliability of time-dependent issues while accounting for field uncertainties.
{"title":"Time-dependent reliability index for continuum structures against field uncertainty based on non-probabilistic bounded field model","authors":"Junjie Zhan, Jiangpeng Li, Yutong Liu","doi":"10.1016/j.probengmech.2025.103768","DOIUrl":"10.1016/j.probengmech.2025.103768","url":null,"abstract":"<div><div>The advancement of soft robotics technology has spurred a growing interest in understanding the time-dependent reliability of continuum structures. This study introduces a novel non-probabilistic model for assessing the time-dependent reliability index of continuum structures under the influence of non-probabilistic bounded field uncertainties. Utilizing the non-probabilistic series expansion (NPSE), the field uncertainties are quantified through a collection of NPSE coefficients, offering a comprehensive representation of the uncertainty in the system. By considering the time variable as an uncertain parameter, the time-dependent reliability analysis can be reformulated as a time-independent problem, allowing for the development of a non-probabilistic reliability index that accounts for both time parameter and field uncertainties. A time-dependent reliability index is introduced utilizing the concerned performance method to assess the structural reliability throughout varying time intervals. Subsequently, the efficacy and applicability of the proposed non-probabilistic time-dependent reliability model were illustrated through three numerical example studies involving geometrically linear and nonlinear time-dependent structures. The findings highlight the effectiveness and practicality of the proposed approach in facilitating the evaluation of the reliability of time-dependent issues while accounting for field uncertainties.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103768"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143906876","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 : 2025-04-01DOI: 10.1016/j.probengmech.2025.103774
Wen Lu , Zhigen Wu , Dixiong Yang , Zeng Meng , Hanshu Chen
Uncertainties are inherently inevitable in the application of functionally graded materials (FGMs) structures. Existing analysis methods face challenges in terms of accuracy and efficiency when addressing these uncertainties, especially for dynamic problems. To this end, this paper proposes a direct probability integral method with improved smoothing technique (DPIM-IST) for the stochastic dynamic analysis of FGM cylinders. Subsequently, an adaptive framework is constructed based on the maximum entropy principle to determine the variable smoothing parameters at each representative point. To search for the proper smoothing parameter vector, a hybrid grey wolf optimizer is employed, which combines the grey wolf optimizer and BFGS method. Moreover, the dynamic responses at each representative point are evaluated by utilizing the differential quadrature method and Newmark algorithm. Several numerical and multiphase and multi-layer FGM hollow cylinder examples, involving nonlinear performance functions with Gaussian and non-Gaussian parameters, are investigated to validate the accuracy of the proposed DPIM-IST.
{"title":"Stochastic dynamic analysis of multi-layer functionally graded material cylinders using direct probability integral method with improved smoothing technique","authors":"Wen Lu , Zhigen Wu , Dixiong Yang , Zeng Meng , Hanshu Chen","doi":"10.1016/j.probengmech.2025.103774","DOIUrl":"10.1016/j.probengmech.2025.103774","url":null,"abstract":"<div><div>Uncertainties are inherently inevitable in the application of functionally graded materials (FGMs) structures. Existing analysis methods face challenges in terms of accuracy and efficiency when addressing these uncertainties, especially for dynamic problems. To this end, this paper proposes a direct probability integral method with improved smoothing technique (DPIM-IST) for the stochastic dynamic analysis of FGM cylinders. Subsequently, an adaptive framework is constructed based on the maximum entropy principle to determine the variable smoothing parameters at each representative point. To search for the proper smoothing parameter vector, a hybrid grey wolf optimizer is employed, which combines the grey wolf optimizer and BFGS method. Moreover, the dynamic responses at each representative point are evaluated by utilizing the differential quadrature method and Newmark algorithm. Several numerical and multiphase and multi-layer FGM hollow cylinder examples, involving nonlinear performance functions with Gaussian and non-Gaussian parameters, are investigated to validate the accuracy of the proposed DPIM-IST.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103774"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144069301","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 : 2025-04-01DOI: 10.1016/j.probengmech.2025.103759
Bo Wang, Junkai Zhang, Shuo Wu, Shengnan Lyu, Tianxiao Zhang
Reliability analysis remains a cornerstone for quantifying uncertainty in probabilistic engineering, yet its practical implementation is constrained by the prohibitive computational cost of repeatedly evaluating limit-state functions. To address this challenge, Importance Sampling (IS) emerges as a variance reduction technique that significantly enhances assessment efficiency. Building upon the hybrid meta-modeling paradigm of the Adaptive Kriging Importance Sampling (AK-IS) method, this research proposes an advanced computational framework through the development of a novel adaptive radial-based sampling strategy. The proposed methodology advances the field in three key aspects. Firstly, a general formulation for radial sampling is derived to ensure dimensional invariance and scalability across high-dimensional spaces. Secondly, a non-intrusive adaptive procedure termed secondary sorting is introduced to accurately determine the optimal sampling radius through iterative refinement. Finally, a systematic algorithmic architecture is established for integrative reliability analysis. Extensive numerical validation demonstrates that the proposed approach achieves superior sampling efficiency compared to conventional techniques, with significant reductions in computational burden while maintaining comparable accuracy levels. The results confirm that this adaptive radial sampling strategy effectively balances exploration-exploitation trade-offs, leading to enhanced robustness and generalizability in probabilistic reliability assessments.
{"title":"An improved AK-IS based on the adaptive radial-based importance sampling for reliability analysis","authors":"Bo Wang, Junkai Zhang, Shuo Wu, Shengnan Lyu, Tianxiao Zhang","doi":"10.1016/j.probengmech.2025.103759","DOIUrl":"10.1016/j.probengmech.2025.103759","url":null,"abstract":"<div><div>Reliability analysis remains a cornerstone for quantifying uncertainty in probabilistic engineering, yet its practical implementation is constrained by the prohibitive computational cost of repeatedly evaluating limit-state functions. To address this challenge, Importance Sampling (IS) emerges as a variance reduction technique that significantly enhances assessment efficiency. Building upon the hybrid meta-modeling paradigm of the Adaptive Kriging Importance Sampling (AK-IS) method, this research proposes an advanced computational framework through the development of a novel adaptive radial-based sampling strategy. The proposed methodology advances the field in three key aspects. Firstly, a general formulation for radial sampling is derived to ensure dimensional invariance and scalability across high-dimensional spaces. Secondly, a non-intrusive adaptive procedure termed secondary sorting is introduced to accurately determine the optimal sampling radius <span><math><msup><mrow><mi>β</mi></mrow><mrow><mtext>opt</mtext></mrow></msup></math></span> through iterative refinement. Finally, a systematic algorithmic architecture is established for integrative reliability analysis. Extensive numerical validation demonstrates that the proposed approach achieves superior sampling efficiency compared to conventional techniques, with significant reductions in computational burden while maintaining comparable accuracy levels. The results confirm that this adaptive radial sampling strategy effectively balances exploration-exploitation trade-offs, leading to enhanced robustness and generalizability in probabilistic reliability assessments.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103759"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143829863","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 : 2025-04-01DOI: 10.1016/j.probengmech.2025.103762
Xiao-jing Zhuo, Yong-feng Guo
In this work, we analyze stochastic resonance phenomenon in two fractional-order bistable systems that are mutually coupled and stimulated by independent Lévy noises. Statistical complexity and normalized Shannon entropy are utilized to characterize stochastic resonance by modulating the parameters of Lévy noise and the given system. It has been determined that the maximum of statistical complexity and minimum of normalized Shannon entropy are regarded as indicators of the severity of dynamical complexity and the occurrence of stochastic resonance, at an optimal level of noise intensity. Then, the influences of various parameters on stochastic resonance are also revealed by the statistical complexity measures. The numerical results demonstrate that the appropriate coupling strength can be found to enhance stochastic resonance effect. The consistency of the complexity of two subsystems is positively correlated to the degree of coupling between them. At lower noise levels, there exists an optimal fractional-order derivative that increases complexity of the system and makes stochastic resonance phenomenon more pronounced. At higher noise levels, the fractional-order derivative suppresses the appearance of stochastic resonance by rendering the evolution of system completely random. Furthermore, stochastic resonance is bolstered by increasing the amplitude of the external periodic signal and stability index, while it is weakened by a larger skewness parameter.
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