Probabilistic Engineering Mechanics最新文献

{"title":"An estimation method for limit-state failure probability of cascade dam groups: from a systematic state function to enhanced subset simulation","authors":"Jiayi Wang,&nbsp;Qiming Zhong,&nbsp;Yibo Shan,&nbsp;Siyuan Xu,&nbsp;Chenfei Shao","doi":"10.1016/j.probengmech.2026.104057","DOIUrl":"10.1016/j.probengmech.2026.104057","url":null,"abstract":"<div><div>Cascade dam groups are critical infrastructure systems whose failure can lead to catastrophic consequences, yet their reliability assessment remains challenging due to the complex interdependencies among individual dams and the uncertainties in their operational states. Traditional probabilistic methods frequently struggle to address these uncertainties comprehensively, particularly when data are limited. To overcome these limitations, a method is proposed for constructing a systematic state function to represent various failure scenarios in a cascade dam group, which is grounded in an analysis of the state function construction principles for individual dams. An analytical model employing an ellipsoidal convex set is developed to define the variability range of variables influencing the uncertainty of an individual dam's service state. Non-probabilistic reliability estimation for individual dams is conducted by integrating the Face-Centred Cubic (FCC) design method with a Particle Swarm Optimisation (PSO) algorithm, which identifies the most critical state function based on the scale factor of the convex set. The most hazardous state function for each individual dam is identified using the response surface method. The hierarchical analysis method is employed to evaluate the risk impact of each individual dam within the cascade dam system under specific key factors of inherent resistance characteristics. The weights of each key factor's impact on inherent resistance characteristics are quantified by integrating the Improved Criteria Importance Through Intercriteria Correlation (ICRITIC) method with the hierarchical analysis method. In combination with the difference coefficient method, a weighting approach is proposed to assess the risk impact of each individual dam on the entire cascade dam group. Following the enhancement of the subset simulation sampling method, an estimation method for the limit state failure probability of the cascade dam system is proposed. Results show that the limit-state failure probability of the cascade dam group is calculated as 1.51 × 10⁻⁶, indicating a very low risk of limit state failure for the cascade dam group, consistent with its current operational performance.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"86 ","pages":"Article 104057"},"PeriodicalIF":4.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205037","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}

{"title":"Scalable reliability analysis of structures under earthquake via sparse graph data and state-space metamodel","authors":"Manh-Hung Ha,&nbsp;Viet-Hung Dang","doi":"10.1016/j.probengmech.2026.104058","DOIUrl":"10.1016/j.probengmech.2026.104058","url":null,"abstract":"<div><div>Existing approaches for earthquake reliability analysis of large structures are often tailored for fixed structural layouts, making them inapplicable to different configurations, even those with minor modifications such as removing or adding elements. This study introduces a framework, named Sa3, in which a single model covers a set of structural configurations declared in advance, obtained from one training run and one hyperparameter setting. Furthermore, the proposed method offers several advantages, including fast inference time, high accuracy, and reliability results for various safety criteria. The framework’s core idea involves, first, designing a sparse graph representation for structural data, including geometric topology and material properties; second, utilizing a selective state-space-based learning component to transform the graph representation, ground motions, and historical responses into latent data that are beneficial to forecasting tasks. The viability and performance of Sa3 are demonstrated, via three 3D spatial structures of different complexities. The results show that Sa3 can provide reliability results with high accuracy for all investigated structures without requiring retraining or modifications of the framework architecture or parameters, while significantly reducing time complexity. Moreover, ablation and sensitivity studies provide a deeper understanding of the Sa3 framework’s operation.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"86 ","pages":"Article 104058"},"PeriodicalIF":4.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149282902","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}

{"title":"Higher-order skyhook mechanical network synthesis and realization in HMDV inertial suspension using electromechanical inerter","authors":"Xiaofeng Yang,&nbsp;Yihong Ping,&nbsp;Yi Yang,&nbsp;Yujie Shen,&nbsp;Shaocong Zeng,&nbsp;Rongji Ma,&nbsp;Miao Xu,&nbsp;Hongbo Yang,&nbsp;Changning Liu","doi":"10.1016/j.probengmech.2026.104056","DOIUrl":"10.1016/j.probengmech.2026.104056","url":null,"abstract":"<div><div>Hub motor-driven vehicles (HMDVs) face the challenge of a rise in unsprung mass accompanied by radially unbalanced electromagnetic forces, which significantly aggravate vehicle body acceleration within low-frequency range. Existing skyhook suspension systems can partially suppress low-frequency vibrations but fail to fully exploit mechanical network characteristics, leading to degraded vibration isolation and even performance deterioration at higher frequencies. This study presents a higher-order generalized skyhook inertial suspension to enhance vibration suppression over a wider frequency band. An HMDV suspension model based on a switched reluctance motor is established, and seven higher-order suspension configurations are optimized to identify the optimal structure. To investigate a potential practical implementation, a fuzzy sliding-mode controller is designed and a ball-screw-based electromechanical inerter is developed. Component-level bench tests show that the mechanical output force varies with the external electrical loading condition. Relative to the conventional passive suspension, the optimized ideal L6 configuration reduces the RMS values of body acceleration, suspension working space, and dynamic tire load by 28.0%, 31.9%, and 3.0%, respectively. The resulting controllable S4 suspension is configured to reproduce the dynamic response of L6, with simulation results showing reductions of 24.5%, 32.6%, and 2.4% in the same three RMS measures, respectively. Frequency-domain analysis further shows that L6 reduces the maximum body-acceleration gain in the 0–5 Hz range by 69.2%, while S4 provides broadband vibration isolation, improves low-frequency ride comfort, and maintains dynamic tire-load performance.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"86 ","pages":"Article 104056"},"PeriodicalIF":4.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205036","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}

{"title":"Probabilistic life-cycle optimization in structural design and maintenance: A systematic review","authors":"Sunyong Kim,&nbsp;Dan M. Frangopol","doi":"10.1016/j.probengmech.2026.104060","DOIUrl":"10.1016/j.probengmech.2026.104060","url":null,"abstract":"<div><div>Probabilistic life-cycle optimization provides a rational framework for designing and managing structures under uncertainty by considering time-dependent structural performance, deterioration, maintenance, life-cycle cost, and service life. To provide a systematic review of probabilistic life-cycle optimization, this paper first summarizes probabilistic performance indicators, including reliability, risk, redundancy, vulnerability, robustness, resilience, life-cycle cost, and sustainability. Inspection, nondestructive evaluation, structural health monitoring, Bayesian updating, and value of information are then briefly reviewed as tools for reducing uncertainty and improving life-cycle decision-making. Optimization methods for single- and multi-objective problems are reviewed, including mathematical programming, metaheuristic methods, reliability-based design optimization, surrogate-assisted optimization, evolutionary algorithms, and multi-criteria decision-making approaches. This paper distinguishes life-cycle design optimization of new structures, which emphasizes selecting optimal initial design alternatives for long-term performance, from life-cycle optimization for managing existing deteriorating structures, which requires sequential and adaptive decision models for inspection, maintenance, repair, retrofit, and replacement planning. Practical implementation challenges, including data availability, model uncertainty, computational complexity, decision constraints, asset management integration, and artificial intelligence-based life-cycle optimization, are discussed. Future research needs are identified for data-informed adaptive optimization, uncertainty quantification, resilience and sustainability integration, and practical decision-support frameworks.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"86 ","pages":"Article 104060"},"PeriodicalIF":4.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149253024","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}

{"title":"Learning across scales for multiscale characterization of complex materials","authors":"Zhengtao Yao,&nbsp;Philippe Hawi,&nbsp;Venkat Aitharaju,&nbsp;Jay Mahishi,&nbsp;Roger Ghanem","doi":"10.1016/j.probengmech.2026.104059","DOIUrl":"10.1016/j.probengmech.2026.104059","url":null,"abstract":"<div><div>We propose a physics-guided probabilistic representation framework for multiscale learning in heterogeneous materials. The framework combines established microscale-to-mesoscale homogenization with a measure-matched generalized Polynomial Chaos representation, Projection Pursuit Adaptation, and a transfer-learned neural surrogate at the structural scale.</div><div>The key idea is to learn a low-dimensional, physically consistent mesoscale representation that acts as a sufficient statistic for structural response. The gPC–PPA stage compresses high-dimensional microscale uncertainty into a small set of adapted coordinates and interpretable descriptors, including the homogenized stiffness tensor and mixed-mode failure metrics, while preserving orthogonality, reciprocity, and analytic uncertainty propagation.</div><div>By separating homogenization from structural prediction, the proposed operator chain reduces dimensionality, enforces physical consistency, and aligns probability measures across scales. For the calibrated material and loading regime considered here, this representation improves data efficiency and interpretability compared with direct learning from the full microscale parameter space.</div><div>A case study on delamination in laminated composites demonstrates that the approach achieves higher accuracy with orders-of-magnitude fewer simulations, while exposing physically meaningful directions governing stiffness and failure. The resulting surrogate reduces structural evaluation time from approximately 1.5 h on 16 cores to below 1 ms during inference. The framework generalizes to other heterogeneous systems by replacing the mesoscale operator with appropriate effective descriptors.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"86 ","pages":"Article 104059"},"PeriodicalIF":4.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149253025","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}

{"title":"Time-dependent reliability assessment of anchored rock slopes under cyclic loading considering degradation and spatial variability of anchor–rock interface performance","authors":"Hongsong Fu,&nbsp;Changfu Chen,&nbsp;Da Xiang,&nbsp;Binfeng Chen,&nbsp;Shimin Zhu,&nbsp;Huan Cai,&nbsp;Wenjie Liu","doi":"10.1016/j.probengmech.2026.104063","DOIUrl":"10.1016/j.probengmech.2026.104063","url":null,"abstract":"<div><div>With the rapid expansion of mountainous transportation networks, anchored rock slopes adjacent to roadways are increasingly subjected to long-term cyclic traffic loading. However, existing reliability analyses often neglect both the time-dependent degradation and stochastic variability of interface performance, making it difficult to accurately assess long-term slope safety. To address this issue, pull-out tests on tensile anchors under cyclic loading were first conducted at the element test, with multiple parallel samples designed to characterize the statistical properties of interface mechanical responses. Based on the experimental results, a non-stationary probabilistic degradation interface model (PDEIM) was established to characterize both the evolution of the anchor-rock interface <em>τ</em>-<em>s</em> response and the statistical uncertainty of anchor-rock interface performance. Subsequently, the PDEIM was adopted to develop a probabilistic cyclic load transfer model (PCLTM) to predict the degradation of the macroscopic anchor <em>P</em>–<em>s</em> response. The proposed model was validated against model test results. Furthermore, a 2D random field was introduced to characterize the spatial variability of anchor-rock interface performance, and combined with time-dependent limit state functions, a life-cycle degradation reliability assessment framework for anchored rock slopes was established. Finally, a time-dependent reliability analysis was performed on an engineering case study. The case study results show that the reliability index <em>β</em> decreases nonlinearly with service time and reaches approximately 3.21 at the end of the 50-year service period. The proposed framework provides a theoretical basis for life-cycle safety assessment and maintenance decision-making for anchored rock slopes in mountainous areas.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"86 ","pages":"Article 104063"},"PeriodicalIF":4.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149253023","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}

{"title":"Bayesian probabilistic calibration of steel-concrete bond strength models for beams with internal confinement","authors":"Hamid Mirshekar,&nbsp;Seyed Roohollah Mousavi,&nbsp;Mohammad Reza Sohrabi","doi":"10.1016/j.probengmech.2026.104045","DOIUrl":"10.1016/j.probengmech.2026.104045","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This study develops application-specific Bayesian reformulations of predictor structures motivated by three established bond-strength equations for reinforced-concrete beams with tension lap splices confined by internal transverse reinforcement. Bayesian inference and delayed-rejection adaptive Metropolis sampling are established methodological tools; the principal contribution of the study is their application to internal transverse-steel confinement using a heterogeneous literature-derived database of 273 beam-splice specimens. The original additive deterministic equations are not calibrated in an unchanged algebraic form. Instead, mechanically relevant variables associated with concrete strength, bar geometry, concrete cover, splice length, and transverse reinforcement are nondimensionalised and logarithmically transformed, resulting in three model-specific multiplicative power-law formulations. Posterior uncertainty and dependence in the retained regression coefficients were characterised using MCMC sampling, and an additional convergence assessment was performed using four independently initialised dispersed chains for each formulation, with 700,000 iterations per chain and the first 25% discarded as burn-in. Rank-normalized split &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mover&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mo&gt;ˆ&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, bulk and tail effective sample sizes, Monte Carlo standard errors, and autocorrelation diagnostics indicated stable sampling for all three formulations. The posterior samples were back-transformed to obtain conditional-median bond-strength estimates. A reproducible post-calibration 80:20 specimen-level partition was used only for descriptive performance reporting. On the 55-specimen subset, Bayesian Formulation 3 produced an RMSE of 0.82 MPa, a MAPE of 12.10%, and a coefficient of determination of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0.824&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. These metrics describe relative performance among the three Bayesian formulations and are not interpreted as evidence that Bayesian inference alone improves accuracy relative to the source deterministic equations, because the formulations differ in their predictors, transformations, coefficients, and calibration procedures. The reported 50% and 95% intervals are posterior credible intervals for the conditional-median response under the adopted fixed residual variance of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;σ&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, rather than posterior predictive intervals for future observations. Broad posterior dispersion and substantial coefficient dependence indicate possible weak identifiability and require cautious interpretation of individual coefficients. No structural reliability or code-calibration analysis is performed. The principal contribution is therefore the posterior characterisation of coefficient uncertainty and dependence for internally confined lap-splice bond-strength formulations, while ","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"86 ","pages":"Article 104045"},"PeriodicalIF":4.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149155305","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}

{"title":"Reliability analysis of DC-DC converters using RIAC 217Plus and Bayesian Belief Networks","authors":"Akanksha Chaturvedi,&nbsp;Sanjay K. Chaturvedi,&nbsp;Monalisa Sarma","doi":"10.1016/j.probengmech.2026.104040","DOIUrl":"10.1016/j.probengmech.2026.104040","url":null,"abstract":"<div><div>DC-DC converters are critical in electric vehicles and other modern power systems, yet their reliability assessment remains complex due to interdependent subsystem failures and degradation across multiple components. This paper presents a comprehensive reliability modeling framework integrating RIAC 217Plus and Bayesian Belief Networks (BBNs) for hierarchical DC-DC converter systems. The hierarchical structure of the proposed BBN enables scalable and modular modeling from component-level to system-level, allowing extension to complex converter architectures. To identify critical subsystems and estimate converter-level reliability, a two-state BBN is first developed, and failure rates are derived from RIAC 217Plus in the absence of field reliability data. This BBN model is further extended to a multi-state framework, capturing the degradation of key components using physics-based degradation models. The framework further incorporates degradation thresholds and logistic regression are used to classify components into working, degraded, and failed states, enabling representation of long-term stress effects. To capture degradation propagation from critical components to other subsystems, α-scaled conditional probabilities are used to model sequential dependent failures. A partial-output scenario is also assessed to represent converters operating in degraded performance modes. The proposed framework is demonstrated using a DC-DC converter used in electric scooters. The analysis shows that the core circuit dominates system failure behavior, with MOSFETs identified as the most critical components. Sensitivity analysis reveals that degradation severity (via α) and threshold selection significantly influence the modeled reliability outcomes. The proposed approach enables a dynamic, unified reliability assessment framework that could potentially support diagnostics and predictive-maintenance planning under the stated modeling assumptions. However, these potential applications require future empirical validation. The reported reliability values are scenario-dependent model outputs rather than validated absolute reliability estimates. This makes the framework well-suited for safety-critical and long-lifetime applications where converters operate under gradual degradation and partial failure conditions.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"86 ","pages":"Article 104040"},"PeriodicalIF":4.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149155370","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}

{"title":"An improved multiscale dispersion entropy with application to rolling bearing fault diagnosis","authors":"Haiming Wang,&nbsp;Yongqiang Liu,&nbsp;Shaopu Yang,&nbsp;Yanli Wang","doi":"10.1016/j.probengmech.2026.104053","DOIUrl":"10.1016/j.probengmech.2026.104053","url":null,"abstract":"<div><div>Due to the complex engineering conditions, the vibration signals of rolling bearings exhibit nonlinear characteristics. To effectively enhance fault diagnosis accuracy, an improved multiscale dispersion entropy (IMDE) method is proposed for feature extraction. For IMDE, the enhanced multiscale approach is first designed to coarse-grain the signal, which considers the connection of data before and after the breakpoint. Secondly, a more reasonable entropy value solving process is put forward, considering the dynamic diversities between adjacent elements in the dispersion pattern. Furthermore, the experimental results indicate that IMDE compares favorably with other advanced entropy methods in terms of effectiveness and robustness. IMDE consistently outperforms all competing methods under different classifiers. Crucially, IMDE demonstrates exceptional stability and low estimation error even for extremely short data sequences with a point count of 400. This capability suggests that IMDE has the potential for industrial monitoring applications, particularly in scenarios where short data lengths are advantageous for early fault detection.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"86 ","pages":"Article 104053"},"PeriodicalIF":4.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149205038","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}

{"title":"Generalized Gaussian distributions in Fourier domain via Maximum Entropy Principle","authors":"Gaia Prezioso,&nbsp;Massimiliano Zingales,&nbsp;Mario Di Paola","doi":"10.1016/j.probengmech.2026.104052","DOIUrl":"10.1016/j.probengmech.2026.104052","url":null,"abstract":"<div><div>In this paper, a new approach for reconstructing the wide variety of Generalized Gaussian distributions is proposed.</div><div>In particular, in order to reconstruct the most rational approximation of the probability density function of these distributions, the Maximum Entropy Principle method is used. The main novelty of this approach consists in introducing values of the Characteristic Function, as constraints to which the entropy functional is subjected, in order to overcome the drawbacks linked to the use of integer order moments as constraints.</div><div>The new method is tested for the reconstruction of both symmetric Generalized Gaussian distributions (<span><math><mrow><mi>μ</mi><mo>=</mo><mn>0</mn></mrow></math></span>) and also non-symmetric distributions (<span><math><mrow><mi>μ</mi><mo>≠</mo><mn>0</mn></mrow></math></span>) by means of a translation formula.</div><div>Finally, numerical simulations are proposed to assess the accuracy and the engineering applicability of the approach.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"86 ","pages":"Article 104052"},"PeriodicalIF":4.1,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149200961","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}