Probabilistic Engineering Mechanics最新文献

{"title":"Explicit closed-form solution for the evolutionary power spectral density function of the stochastic response of structures subjected to artificial accelerograms consistent with pulse-like ground motions","authors":"Federica Genovese ,&nbsp;Giuseppe Muscolino","doi":"10.1016/j.probengmech.2024.103718","DOIUrl":"10.1016/j.probengmech.2024.103718","url":null,"abstract":"<div><div>The near-fault pulse-like ground motions are of great practical interest in seismic engineering. In fact, they tend to cause more serious damage to some types of structures than ordinary ground motions. However, the limited availability of pulse-like records significantly constrains studies involving the randomness of ground motion, such as reliability analysis. To address the scarcity of records, ground motion simulation methods should be used. In the literature, the most efficient one, according to the theory of random processes, is based on the generation of artificial accelerograms as samples of fully non-stationary Gaussian processes. By operating in this way, it is possible to reproduce the typical characteristics of recorded time histories, with both temporal and spectral non-stationarities, which fill the absence of available actual data. In this framework, the authors recently proposed a new model of the <em>evolutionary power spectral density</em> (<em>EPSD</em>) function to generate artificial accelerograms in such a way that a given target accelerogram can be considered as one of its own samples. The <em>EPSD</em> function can be simply evaluated once the frequency of peaks, the zero-level up-crossings, and the total energy of the target accelerogram are determined. This approach, previously applied to the case of ordinary accelerograms, is here extended to pulse-like ones. To effectively achieve this extension, some measures must be taken in the definition of the modulating function and the sub-processes that characterize the <em>EPSD</em> function.</div><div>In this study, once the way to define the <em>EPSD</em> function of the input process is described, a procedure to evaluate in explicit closed form the <em>EPSD</em> function of the output process, in terms of displacements and velocities of the structural response, is proposed. Finally, the statistics of the structural response are evaluated, and a reliability analysis is performed in order to demonstrate the accuracy and efficiency of the proposed formulation.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"79 ","pages":"Article 103718"},"PeriodicalIF":3.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143147055","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}

{"title":"Vibration fatigue analysis of structures under non-stationary and non-Gaussian random excitation","authors":"Wuyang Lei ,&nbsp;Yu Jiang ,&nbsp;Xiao Zhou ,&nbsp;Hongbo Tang ,&nbsp;Jinhao Zhang","doi":"10.1016/j.probengmech.2025.103744","DOIUrl":"10.1016/j.probengmech.2025.103744","url":null,"abstract":"<div><div>Non-stationary and non-Gaussian random excitation is widely used in the operation of various mechanical systems; therefore, it is necessary to explore the effects of the non-stationary and non-Gaussian excitation signal characteristics on vibration fatigue. A novel method for generating non-stationary and non-Gaussian signals based on amplitude and phase modulation is proposed. The effects of the non-stationary and non-Gaussian random excitation characteristics and their response characteristics on vibration fatigue damage are analyzed in detail by simulation, theoretical derivation, and experiments. The results indicate that as the fatigue exponent <em>b</em> increases, the difference in fatigue damage caused by non-stationary and non-Gaussian signals, stationary and non-Gaussian signals, and stationary and Gaussian signals with the same level becomes more pronounced. Stationary non-Gaussian signals have a significant impact on fatigue damage compared to Gaussian signals when the fatigue exponent <em>b</em> is large. For non-stationary and non-Gaussian signals, kurtosis is more noteworthy than the non-stationary index because changes in the non-stationary index do not have a significant impact on fatigue damage. The fatigue damage of a structure under non-stationary and non-Gaussian random excitation is linearly related to the <em>b</em>-th moment of the absolute value of the structural response, which facilitates an efficient assessment of the fatigue damage.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"79 ","pages":"Article 103744"},"PeriodicalIF":3.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395535","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 analytical approach for response power spectral density determination of linear systems using stochastic harmonic function","authors":"Fan Kong ,&nbsp;Yijian Xu ,&nbsp;Xu Hong ,&nbsp;Lunhai Zhi ,&nbsp;Hongyou Cao","doi":"10.1016/j.probengmech.2025.103739","DOIUrl":"10.1016/j.probengmech.2025.103739","url":null,"abstract":"<div><div>Fractional derivatives have emerged as a powerful tool for characterizing memory-dependent or non-local mechanical behaviors of materials and structures. This paper presents an alternative yet novel method for determining the analytical solution for the non-stationary response of linear dynamic systems with/without fractional derivative elements subjected to stochastic excitation. The technique simplifies the derivation by representing the stochastic excitation as a single harmonic component with random frequency and phase angle, effectively transforming the stochastic dynamic problem into a deterministic one of harmonic response analysis. This significantly reduces the complexity of calculating system response statistics by simply taking mathematical expectations on stochastic harmonic responses. The proposed approach not only offers a new analytical framework for re-deriving conventional Caughey’s solution but also extends readily to linear stochastic systems with fractional derivative elements. Validation through comparison with conventional analytical methods for fractional-order systems developed recently demonstrates the accuracy of the results, providing new insights for further stochastic analysis of fractional-order dynamic systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"79 ","pages":"Article 103739"},"PeriodicalIF":3.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143376539","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":"Joint probabilistic modelling and sampling from small data via probabilistic learning on manifolds and decoupled multi-probability density evolution method","authors":"Zhiqiang Wan ,&nbsp;Meng-ze Lyu ,&nbsp;Xu Hong ,&nbsp;Yupeng Song ,&nbsp;Jianbing Chen ,&nbsp;Roger Ghanem","doi":"10.1016/j.probengmech.2025.103736","DOIUrl":"10.1016/j.probengmech.2025.103736","url":null,"abstract":"<div><div>Computational models are of utmost importance in various aspects of structural design and optimization, uncertainty quantification, risk assessment, and other engineering fields. Among numerous critical issues for model-based uncertainty quantification, the issue of joint probabilistic modelling of dependent model parameters under the condition of small data is investigated in this work. In contrast to most viewpoints, which see model parameters by observation or experiment as mere data, we regard them as stochastic responses that are realized through implicit (and possibly complicated) physical processes with respect to underlying random variables. Based on this thought, a novel approach for estimating the joint probabilistic model of <span><math><mi>n</mi></math></span>-dimensional dependent model parameters is proposed in two stages: Firstly, the probabilistic learning on manifolds (PLoM) is adopted to generate ample “virtual” realizations of model parameters that are statistically consistent with the original small data. This aims to construct an approximately dependent probability structure of model parameters; Secondly, the decoupled multi-probability density evolution method (PDEM) is employed to calculate the joint probabilistic model from a perspective of uncertainty propagation, where the original small data are equipped with assigned probabilities that are calculated from the dependent probability structure via PLoM. Moreover, taking the advantages of the proposed method, a low-dimensional data storing and a novel acceptance–rejection sampling technique are proposed, which is particularly convenient for the case that <span><math><mrow><mi>n</mi><mo>≥</mo><mn>3</mn></mrow></math></span>. A benchmark case is studied to illustrate and verify the proposed method, which is found to be robust to complex engineering data. Three applications, including double doughnut configuration-type’s data, mechanical parameters of concrete, and location and time parameters of typhoon genesis, are presented to demonstrate the new capacities of the proposed method.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"79 ","pages":"Article 103736"},"PeriodicalIF":3.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143146063","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":"Full probability conversion model for predicting concrete compressive strength using the rebound method","authors":"Jinju Tao ,&nbsp;Xiao Fu ,&nbsp;Sicheng Ren","doi":"10.1016/j.probengmech.2025.103730","DOIUrl":"10.1016/j.probengmech.2025.103730","url":null,"abstract":"<div><div>The conversion model forms the basis for predicting concrete compressive strength using the rebound method and plays a crucial role in improving prediction accuracy. Traditional approaches, such as regression and calibration methods, primarily estimate the mean compressive strength while neglecting the full probabilistic relationship between the rebound number and compressive strength. To overcome this limitation, a full probability conversion model is proposed using the Copula function method, which effectively captures the joint probability distribution between the rebound number and compressive strength. In addition, a Bayesian full probability conversion model is introduced, enabling the integration of core sample data to enhance the predictive accuracy of compressive strength. To validate and compare the proposed method, 20 datasets comprising 1838 rebound number and compressive strength pairs were analysed. Results demonstrate that the proposed full probability conversion model improves the prediction accuracy, particularly when combined with the Bayesian update method. Moreover, the proposed method delivers comprehensive probabilistic information for predicting concrete compressive strength, offering a more complete and reliable understanding than traditional approaches.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"79 ","pages":"Article 103730"},"PeriodicalIF":3.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143147057","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":"A novel self-adaptive step size first-order method for structural reliability analysis based on modified Sigmoid function and Armijo rule","authors":"Yu Xia,&nbsp;Yiying Hu,&nbsp;Yingye Yu","doi":"10.1016/j.probengmech.2024.103721","DOIUrl":"10.1016/j.probengmech.2024.103721","url":null,"abstract":"<div><div>Among the first-order reliability methods (FORM), the Hasofer-Lind and Rackwitz-Fiessler method (HL-RF), and the chaos control method (CC) rely on a fixed step size and cannot generate an adaptive one, making it difficult to achieve a satisfactory trade-off between efficiency and robustness when dealing with highly nonlinear problems. To address these drawbacks, this paper proposes two innovative first-order reliability methods: the Sigmoid-based self-adaptive step size adjustment method (SSA) and the hybrid Sigmoid-based self-adaptive step size adjustment method (HSSA). The iterative rotation angle is first determined for both proposed methods. In the SSA method, a modified Sigmoid function is employed to enable nonlinear adaptive adjustments of the step size based on changes in the iterative turning angles, allowing for rapid convergence. Subsequently, the HSSA method incorporates the Armijo rule to further explore a more effective solution. Both proposed methods demonstrate strong computational merits, favorable performance, and user-friendly procedures, providing self-adaptive step sizes suitable for engineering problems, thus offering a broad range of applications. The paper introduces eight examples to showcase the remarkable performance of the two proposed methods. The results indicate that both methods exhibit significantly superior efficiency and robustness compared to other comparative analytical FORM methods when addressing highly nonlinear engineering challenges. Finally, a discussion is presented.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"79 ","pages":"Article 103721"},"PeriodicalIF":3.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143147063","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 model updating method and probabilistic damage identification based on an improved differential evolution adaptive Metropolis algorithm","authors":"Mingming Cao,&nbsp;Zhenrui Peng","doi":"10.1016/j.probengmech.2025.103743","DOIUrl":"10.1016/j.probengmech.2025.103743","url":null,"abstract":"<div><div>The Bayesian finite element model updating (FEMU) method is widely used in structural health monitoring. Traditional Bayesian FEMU methods face challenges such as dimensional limitations, slow convergence, and low computational efficiency. To improve the convergence speed and computational efficiency of the Bayesian FEMU method, this paper proposes a Bayesian FEMU method based on an improved Differential Evolution Adaptive Metropolis (DREAM) algorithm, named the DREAM_ZC algorithm, and constructs a probabilistic damage identification framework based on this method. The ZC strategies represent the centroid update and sampling difference vectors from past states. The effectiveness of the DREAM_ZC algorithm in FEMU is verified through numerical examples of a simply supported beam and experimental examples of a three-story frame structure. The updated model can serve as a baseline model for probabilistic damage identification. The results show that the proposed DREAM_ZC algorithm has high updating accuracy and fast convergence speed. Using the updated model as the baseline model for probabilistic damage identification can effectively locate the structural damage position and quantify the degree of structural damage, thereby improving the reliability of the damage identification results.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"79 ","pages":"Article 103743"},"PeriodicalIF":3.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143420351","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":"The influence of slope geometric parameters on the reliability of slope reinforced by micro-piles in spatially variable soils","authors":"Yuke Wang ,&nbsp;Haiwei Shang ,&nbsp;Yukuai Wan ,&nbsp;Yuyuan Chen","doi":"10.1016/j.probengmech.2024.103719","DOIUrl":"10.1016/j.probengmech.2024.103719","url":null,"abstract":"<div><div>Currently, the combined effects of soil spatial variability and slope geometric parameters on the reliability of micro-pile reinforced slopes remain unclear. To evaluate the influence of slope geometric parameters on the reliability of micro-pile reinforced slope, a reliability calculation program considering the spatial variability of soil strength parameters was proposed in this study. By combining the effective micro-pile side pressure formula with the simplified Bishop method, the limit equilibrium calculation method for micro-pile reinforced slope was obtained. The Karhunen–Loève (K-L) expansion method was employed to generate random fields. The failure probability and reliability index of the slope were calculated by Monte Carlo Simulation (MCS). The effects of different reinforcement parameters and random parameters on the mean safety factor and reliability of micro-pile reinforced slope were studied, and the influence of slope geometric parameters on the reliability of micro-pile reinforced slope was analyzed. The results indicate that the stability of the slope is effectively improved by micro-pile reinforcement. After reinforcement, the reliability index is less affected by the change of slope geometric parameters. Compared to reducing the slope height, decreasing the slope ratio can more effectively ensure the enhancement of the slope's reliability. The reinforcement efficiency is the highest when the micro-pile is set near the foot of the slope. With the increase of slope ratio, the influence of the change of pile length on the reliability index increases. The influence of each random parameter on the reliability of the slope is different, and the influence of <em>L</em>_<em>v</em> is more significant. The influence of random parameters on the reliability index and safety factor of micro-pile reinforced slopes is essentially consistent across different geometric parameters.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"79 ","pages":"Article 103719"},"PeriodicalIF":3.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143147033","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 efficient strategy for information reuse in probability density evolution method considering large shift of distributions with multiple random variables","authors":"Jia-Shu Yang ,&nbsp;Zhiqiang Wan ,&nbsp;Hector Jensen","doi":"10.1016/j.probengmech.2024.103728","DOIUrl":"10.1016/j.probengmech.2024.103728","url":null,"abstract":"<div><div>The probability density evolution method (PDEM) is a versatile approach for analyzing stochastic dynamical systems. When combined with the change of probability measure (COM), it provides a tool to efficiently deal with the aleatory and epistemic uncertainties, where shifts of probability distributions are frequently encountered. However, when the shifts of distributions are too large, the PDEM-COM method can lead to increasing numerical errors. This paper aims to propose an extension of the PDEM-COM that can address the large shifts of distributions involving multiple random variables. In the proposed method, the concepts of the multi-dimensional augmented support and the augmented probability density function (PDF) are introduced based on the differences between the original and updated distributions. Then, an efficient numerical procedure is established for selecting a small set of additional representative points based on the augmented PDF. These additional representative points serve as a complement to the representative point set selected according to the original distributions. By incorporating the augmented representative point set and solving the generalized probability density evolution equation (GDEE), the stochastic response of the system considering the updated distributions can be evaluated. Numerical examples are presented to demonstrate the capability and effectiveness of the proposed approach. The results demonstrate that the proposed approach offers improved accuracy compared to the PDEM-COM method, particularly for large distribution shifts, while maintaining a relatively lower computational cost.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"79 ","pages":"Article 103728"},"PeriodicalIF":3.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143147059","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 method for multiple failure modes with overlapping failure domains","authors":"Aoyang Zhang ,&nbsp;Zhenzhong Chen ,&nbsp;Qianghua Pan ,&nbsp;Xiaoke Li ,&nbsp;Pei Feng ,&nbsp;Xuehui Gan ,&nbsp;Ge Chen ,&nbsp;Liang Gao","doi":"10.1016/j.probengmech.2025.103741","DOIUrl":"10.1016/j.probengmech.2025.103741","url":null,"abstract":"<div><div>In reliability analysis, the problem of multiple failure modes with overlapping failure domains has long attracted significant attention. Traditional methods, such as direct integral methods and approximate analytical methods, cannot deal with this issue effectively. Typically, simulation techniques, such as Monte Carlo simulation and kriging, are employed. However, these methods require extensive sampling and computation, resulting in lower efficiency. Therefore, this paper proposes a new reliability analysis method for multiple failure modes with overlapping failure domains and multiple design points. The method combines a simplified formula for the hyperspherical cap area, applicable to both odd and even integer values, with the curved surface integral method, significantly simplifying the failure probability calculation process. Furthermore, by incorporating the hypersphere cap intersection region area, structures or systems with multiple failure modes can be efficiently handled. Five examples demonstrate that the proposed method outperforms traditional methods in both computational efficiency and accuracy.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"79 ","pages":"Article 103741"},"PeriodicalIF":3.0,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143395536","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}