Probabilistic Engineering Mechanics最新文献

Mellin transform for the probabilistic characterization of random variables and stochastic processes

IF 3 3区工程技术

Probabilistic Engineering Mechanics Pub Date : 2025-04-01 DOI: 10.1016/j.probengmech.2025.103766

S. Russotto , A. Pirrotta

{"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}

引用次数: 0

An improved AK-IS based on the adaptive radial-based importance sampling for reliability analysis

IF 3 3区工程技术

Probabilistic Engineering Mechanics Pub Date : 2025-04-01 DOI: 10.1016/j.probengmech.2025.103759

Bo Wang, Junkai Zhang, Shuo Wu, Shengnan Lyu, Tianxiao Zhang

{"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}

引用次数: 0

Detecting and quantifying stochastic resonance in a coupled fractional-order bistable system driven by Lévy noises via statistical complexity measure

IF 3 3区工程技术

Probabilistic Engineering Mechanics Pub Date : 2025-04-01 DOI: 10.1016/j.probengmech.2025.103762

Xiao-jing Zhuo, Yong-feng Guo

{"title":"Detecting and quantifying stochastic resonance in a coupled fractional-order bistable system driven by Lévy noises via statistical complexity measure","authors":"Xiao-jing Zhuo, Yong-feng Guo","doi":"10.1016/j.probengmech.2025.103762","DOIUrl":"10.1016/j.probengmech.2025.103762","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103762"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873130","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}

引用次数: 0

System identification and reliability assessment of hyperelastic materials via an efficient sparsity-promoting variational Bayesian approach

IF 3 3区工程技术

Probabilistic Engineering Mechanics Pub Date : 2025-04-01 DOI: 10.1016/j.probengmech.2025.103763

Rohan Vittal Thorat, Mohammad Anas, Rajdip Nayek, Sabyasachi Chatterjee

{"title":"System identification and reliability assessment of hyperelastic materials via an efficient sparsity-promoting variational Bayesian approach","authors":"Rohan Vittal Thorat, Mohammad Anas, Rajdip Nayek, Sabyasachi Chatterjee","doi":"10.1016/j.probengmech.2025.103763","DOIUrl":"10.1016/j.probengmech.2025.103763","url":null,"abstract":"<div><div>In this study, an efficient data-driven approach to identify constitutive models for isotropic hyperelastic materials is introduced, which is crucial for predicting material behavior and subsequently evaluating its reliability. This innovative method allows for reliability assessment, even when the precise material model is unknown beforehand. First, a data-driven physics-preserving approach for identifying constitutive models that describe the stress–strain relationships of isotropic hyperelastic materials is developed. A manually designed library of polynomial basis functions inspired by existing models for rubber-like materials is utilized. To achieve a sparse selection of features from this library, a Bayesian sparse regression technique is employed, implementing a sparsity-promoting spike-and-slab prior. Instead of using the computationally intensive Markov Chain Monte Carlo (MCMC) method for Bayesian posterior inference, a more efficient Variational Bayesian (VB) approach is opted for, significantly reducing computational time. The effectiveness of the constitutive model identification procedure is demonstrated through various numerical examples. Next, attention is turned to the estimation of reliability for hyperelastic materials under parametric uncertainty. Given that the constitutive model is unknown beforehand, multiple specimens of the material are utilized to determine a common underlying model and identify parameter distributions. These parameter distributions are then employed to estimate the Probability of Failure (PF) through Monte Carlo simulations. The results showcase the versatility of the proposed approach, not only in predicting material behavior and calibrating models but also in calculating the PF for hyperelastic materials, even in situations where the underlying model is not known in advance.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103763"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143873132","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}

引用次数: 0

Multi-source data-driven conjugate Bayesian inference of the distributions of soil shear strength parameter moments

IF 3 3区工程技术

Probabilistic Engineering Mechanics Pub Date : 2025-04-01 DOI: 10.1016/j.probengmech.2025.103758

Yibiao Liu, Weizhong Ren

{"title":"Multi-source data-driven conjugate Bayesian inference of the distributions of soil shear strength parameter moments","authors":"Yibiao Liu, Weizhong Ren","doi":"10.1016/j.probengmech.2025.103758","DOIUrl":"10.1016/j.probengmech.2025.103758","url":null,"abstract":"<div><div>The distributions of soil shear strength parameter moments are crucial for slope reliability analyses. The expressions for the joint posterior distributions of the mean and variance of shear strength parameters <span><math><mrow><mi>c</mi></mrow></math></span> and <span><math><mrow><mi>φ</mi></mrow></math></span> are derived based on conjugate Bayesian inference under the assumptions of normality and lognormality. To fuse prior distributions obtained from multiple data sources, the expression of the Jensen–Shannon (JS) divergence is generalized to two-dimensional cases. The generalized JS divergence can measure the similarity between the prior and posterior distributions so that it is adopted as the metric to determine the weights of different prior distributions. An illustrative example demonstrates that the posterior distribution inferred from the fused prior distribution can effectively integrate the information from each individual prior distribution. The weighting method based on the generalized JS divergence enhances the anti-interference ability of the fused prior distribution. Comparisons of the maximum a posteriori estimation results of the mean and variance reveal that the inference results based on the two distributional assumptions differ slightly, which can also be drawn from the comparison of the standard values. The illustrative example reveals that the proposed method can provide a reference for the posterior distribution inference of geotechnical parameter statistics.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103758"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143737979","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}

引用次数: 0

Augmented weighted low-discrepancy simulation with hyper-spherical ring for general reliability analysis

IF 3 3区工程技术

Probabilistic Engineering Mechanics Pub Date : 2025-04-01 DOI: 10.1016/j.probengmech.2025.103756

Jian Ji , Tao Wang

{"title":"Augmented weighted low-discrepancy simulation with hyper-spherical ring for general reliability analysis","authors":"Jian Ji , Tao Wang","doi":"10.1016/j.probengmech.2025.103756","DOIUrl":"10.1016/j.probengmech.2025.103756","url":null,"abstract":"<div><div>Due to the increasing complexity of modern engineering systems, conventional reliability methods encounter significant challenges in dealing with high-dimensional stochastic problems. This study presents a hyper-spherical ring-augmented weighted low-discrepancy simulation (HSR-WLDS) method, which expands the applicability of original WLDS to high-dimensional reliability problems. Inspired from the geometric insights observed in the independent standard normal space, the proposed method innovatively integrates the well-established WLDS with a hyper-spherical transformation. This strategy leverages the rotational symmetry inherent in the joint probability density function (PDF), ensuring that the sample weights are solely dependent on the radius, thereby effectively mitigating the impact of extreme weights in high-dimensional spaces. Furthermore, by utilizing the important ring to concentrate computational efforts on critical areas, this method effectively mitigates computational complexity and enhances efficiency for estimating failure probabilities. The performance of the proposed method is verified through four numerical examples, encompassing highly nonlinear limit state function (LSF), multiple failure modes, and both component and system high-dimensional problems, as well as an engineering slope stability example. The results demonstrate the robustness and effectiveness of the proposed method, highlighting its superiority in high-dimensional reliability problems with improved computational efficiency.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103756"},"PeriodicalIF":3.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143748669","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}

引用次数: 0

Reliability assessment of stochastic dynamical systems based on physics-informed gaussian process regression

IF 3 3区工程技术

Probabilistic Engineering Mechanics Pub Date : 2025-03-12 DOI: 10.1016/j.probengmech.2025.103757

Zhiwei Bai , Shufang Song

{"title":"Reliability assessment of stochastic dynamical systems based on physics-informed gaussian process regression","authors":"Zhiwei Bai , Shufang Song","doi":"10.1016/j.probengmech.2025.103757","DOIUrl":"10.1016/j.probengmech.2025.103757","url":null,"abstract":"<div><div>The dynamic reliability function (DRF) can measure the performance of stochastic dynamic systems under random parameters or excitation in the whole life cycle, and it is required in the reliability-based design optimization under dynamic uncertainty. To construct a high-fidelity predictive model for analyzing complex dynamic systems and enhancing system reliability, a novel surrogate-based approach is proposed in this paper, leveraging physics-informed gaussian process regression (PIGPR). Two PIGPR-based frameworks are established, including PIGPR combined with Monte Carlo Simulation (PIGPR-MCS) for time-variant reliability under random parameters and PIGPR combined with first-passage (PIGPR-FP) for first-passage reliability under stochastic excitations. PIGPR-MCS applies PIGPR for the solution of the original dynamic equation and solves the DRF using MCS, while PIGPR-FP directly uses PIGPR to solve the backward Kolmogorov equation satisfied by the first-passage reliability. Compared with the traditional surrogate-based methods, the proposed PIGPR-based frameworks, by embedding the physical laws in DRF into the covariance function of Gaussian process, can handle uncertain and noisy data, offering better estimation of DRF as well as its uncertainty. Since PIGPR can effectively utilize the physical information of DRF, it effectively reduces the dependence on label samples and improve the physical interpretability, which is well illustrated by a numerical example. The effectiveness and applicability of the PIGPR-MCS and PIGPR-FP are demonstrated through two engineering examples, respectively. Through the proposed PIGPR approach, the safety degree of the stochastic dynamic systems can be efficiently evaluated.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103757"},"PeriodicalIF":3.0,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143679707","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}

引用次数: 0

Reliability-based design optimization incorporating extended Optimal Uncertainty Quantification

IF 3 3区工程技术

Probabilistic Engineering Mechanics Pub Date : 2025-03-12 DOI: 10.1016/j.probengmech.2025.103755

Niklas Miska, Daniel Balzani

{"title":"Reliability-based design optimization incorporating extended Optimal Uncertainty Quantification","authors":"Niklas Miska, Daniel Balzani","doi":"10.1016/j.probengmech.2025.103755","DOIUrl":"10.1016/j.probengmech.2025.103755","url":null,"abstract":"<div><div>Reliability-based design optimization (RBDO) approaches aim to identify the best design of an engineering problem, whilst the probability of failure (PoF) remains below an acceptable value. Thus, the incorporation of the sharpest bounds on the PoF under given constraints on the uncertain input quantities strongly strengthens the significance of RBDO results, since unjustified assumptions on the input quantities are avoided. In this contribution, the extended Optimal Uncertainty Quantification framework is embedded within an RBDO context in terms of a double loop approach. By that, the mathematically sharpest bounds on the PoF as well as on the cost function can be computed for all design candidates and compared with acceptable values. The extended OUQ allows the incorporation of aleatory as well as epistemic uncertainties, where the definition of probability density functions is not necessarily required and just given data on the input can be included. Specifically, not only bounds on the values themselves, but also bounds on moment constraints can be taken into account. Thus, inadmissible assumptions on the data can be avoided, while the optimal design of a problem can be identified. The capability of the resulting framework is firstly shown by means of a benchmark problem under the influence of polymorphic uncertainties. Afterwards, a realistic engineering problem is analyzed, where the positioning of laser-hardened lines within a steel sheet for a car crash structure are optimized.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103755"},"PeriodicalIF":3.0,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Novel symmetric divergence based importance measures for engineering simulation models under uncertainty

IF 3 3区工程技术

Probabilistic Engineering Mechanics Pub Date : 2025-02-28 DOI: 10.1016/j.probengmech.2025.103753

Wei Li , Peng Xu , Xueying Wang , Jialong He , Hongshuang Li

{"title":"Novel symmetric divergence based importance measures for engineering simulation models under uncertainty","authors":"Wei Li , Peng Xu , Xueying Wang , Jialong He , Hongshuang Li","doi":"10.1016/j.probengmech.2025.103753","DOIUrl":"10.1016/j.probengmech.2025.103753","url":null,"abstract":"<div><div>Uncertainty importance assessment of engineering simulation models provides information on how difference sources of uncertainty in the model inputs contribute to the uncertainty in the model output. This paper develops new importance measures based on symmetric statistical divergences, including the symmetric Kullback-Leibler (SKL) divergence and Jensen-Shannon divergence (JSD). These measures aim at assessing the global sensitivity of individual inputs, the joint effect of multiple inputs, the impact of uncertainty on specific output regions of interest, and the influence of input uncertainty on the reliability of engineering system performance. The Mathematical properties of the new importance measures are explored and compared with the conventional asymmetric Kullback-Leibler divergence (KLD) based measure. The analysis indicates that the proposed measures preserve the flexibility of the KLD based measure while addressing its limitations in terms of robustness and interpretability. A comparative study investigates the proposed JSD and SKL based measures, alongside the KLD based importance measure, the moment-independent <em>δ</em><sub><em>i</em></sub> index, and Sobol's indices, through two numerical cases and a composite beam example. The results demonstrate that the new importance measures not only ensure calculation accuracy and efficiency, but also exhibit improved robustness compared to the asymmetric approach. Finally, the proposed importance measures are applied to a quayside container crane structure to analyze how uncertainties in the input parameters affect the system's performance and reliability.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103753"},"PeriodicalIF":3.0,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143579520","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}

引用次数: 0

A modified Fourier model for stochastic jumping loads on rigid floors

IF 3 3区工程技术

Probabilistic Engineering Mechanics Pub Date : 2025-02-28 DOI: 10.1016/j.probengmech.2025.103754

Sunil Kumar Maurya , Anil Kumar

{"title":"A modified Fourier model for stochastic jumping loads on rigid floors","authors":"Sunil Kumar Maurya , Anil Kumar","doi":"10.1016/j.probengmech.2025.103754","DOIUrl":"10.1016/j.probengmech.2025.103754","url":null,"abstract":"<div><div>This paper introduces a modified Fourier model for accurately simulating the induced stochastic dynamic jumping force exerted by an individual during jumping motion on a rigid floor. The contact ratio, pace frequency, and amplification factor are the critical parameters in the force modeling. These parameters are considered as random variables. The mean, standard deviation, and interval of variation for the parameters have been computed based on experimental records of individual jumping force-time history. Correlation analysis indicates that the pace frequency and the contact ratio are weakly dependent variables. Moreover, analysis of experimental data shows that the amplification factor depends on both the contact ratio and pacing frequency. To account for this, the modified amplification factor has been incorporated into a truncated Fourier series to model the continuous rhythmic jumping force. The bootstrap resampling technique has been utilized to capture the inherent randomness in the jumping force. Additionally, successive corrections, in terms of the time difference between the metronome beat frequency and the achieved jumping frequency, have been applied in each load cycle to produce the jumping force. Comparisons between the measured force signals and the model-generated forces demonstrate strong agreement. Finally, the jumping vandal loading is simulated on a steel floor in a finite element model, and the responses for both, i.e., the model and the experimental forces, are compared. The results demonstrate that the proposed jumping force model is simple and can be easily used for the vibration serviceability assessment of structures.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"80 ","pages":"Article 103754"},"PeriodicalIF":3.0,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143562532","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}

引用次数: 0