Probabilistic Engineering Mechanics最新文献

{"title":"Reliability analysis of cutting tools using transformed inverse Gaussian process-based wear modelling considering parameter dependence","authors":"Monojit Das ,&nbsp;V.N.A. Naikan ,&nbsp;Subhash Chandra Panja","doi":"10.1016/j.probengmech.2024.103698","DOIUrl":"10.1016/j.probengmech.2024.103698","url":null,"abstract":"<div><div>Reliability analysis is crucial for ensuring the performability of the desired function. The cutting tool performs the machining operation at varied conditions to manufacture diverse products. During operation, the tool degrades stochastically in the form of wear. To avoid the unfavourable consequences occurring from severe tool wear, appropriate formulation of the tool reliability, considering threshold degradation level as the failure criterion, is crucial. However, the degradation of the tool during machining is impacted by the current state of the tool wear and operating conditions. Considering these, the present study proposes a state-dependent transformed inverse Gaussian (TIG) process incorporating the effects of operating conditions to develop the tool wear model. In order to evaluate the proposed method, tool wear experiments are conducted at different operating conditions following the Taguchi orthogonal array experimental design. The experimental data are utilised to estimate the parameters of the developed model using the Bayesian approach. Following the parameter estimation, tool reliability is evaluated under varying operating conditions. The comparison of the estimated median time to failure of the tools with the failure time observed in the validation experiments ensures the effectiveness of the proposed model. The proposed approach has the potential to estimate the reliability of the industrial products subjected to state-dependent degradation under varied operating conditions.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103698"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531093","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":"Laplace and Mellin transform for reconstructing the probability distribution by a limited amount of information","authors":"Lizhi Niu ,&nbsp;Mario Di Paola ,&nbsp;Antonina Pirrotta ,&nbsp;Wei Xu","doi":"10.1016/j.probengmech.2024.103700","DOIUrl":"10.1016/j.probengmech.2024.103700","url":null,"abstract":"<div><div>A method for reconstructing the Probability Density Function (PDF) of a random variable using the Laplace transform is first introduced for one-sided PDFs. This approach defines new complex quantities, referred as Shifted Characteristic Functions, which allow the PDF to be computed using a classical Fourier series expansion. The method is then extended to handle double-sided PDFs by redefining the double-sided Laplace transform. This new definition remains applicable even when the integral in the inverse Laplace transform is discretized along the imaginary axis. For comparison, a new definition of double-sided Complex Fractional Moments based on Mellin transform is also introduced, addressing the singularity at zero that arises during PDF reconstruction.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103700"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142531094","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":"Real-time anomaly detection of the stochastically excited systems on spherical (S2) manifold","authors":"Satyam Panda ,&nbsp;Breiffni Fitzgerald ,&nbsp;Budhaditya Hazra","doi":"10.1016/j.probengmech.2024.103689","DOIUrl":"10.1016/j.probengmech.2024.103689","url":null,"abstract":"<div><div>Advanced analytical tools have become crucial in today’s constantly changing and complex systems. Real-time Principal Geodesic Analysis (RPGA) is a novel technique that provides a unique perspective for analyzing nonlinear data on differentiable manifolds. Traditional linear methods are often inadequate when exploring the complexities of such data. Orthogonal transformation techniques such as Principal Component Analysis (PCA) and Principal Geodesic Analysis (PGA) are highly desirable for condition monitoring stochastically excited systems in domains like mechanical, aerospace, and civil engineering. However, uncertainties and dynamic fluctuations necessitate robust analytical methods for early change detection to ensure safety, performance, and cost-effectiveness. Limitations posed by linear orthogonal transformation techniques such as PCA and its recursive counterparts make it imperative to adapt these techniques to nonlinear situations where data does not evolve in a flat Euclidean space. Significant advancements have been made in this field over recent decades, with data-driven real-time algorithms such as RPCA, RCCA, and RSSA providing reliable solutions for complex multidimensional problems. However, for curved space, the nonlinear RPGA technique takes center stage. It is known for its effectiveness in extracting meaningful information from the complex data stream. This paper explores the foundational concepts and methodologies underlying the transition from linear to nonlinear data analysis. By examining examples such as stochastic geometric oscillator on <span><math><msup><mrow><mtext>S</mtext></mrow><mrow><mn>2</mn></mrow></msup></math></span>, and the inverted spherical pendulum cart system navigating a rough surface, we illustrate the significance of reliable, real-time damage detection techniques provided by tools such as RPGA.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103689"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142420998","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":"Quantified active learning Kriging model for structural reliability analysis","authors":"Ioannis Prentzas,&nbsp;Michalis Fragiadakis","doi":"10.1016/j.probengmech.2024.103699","DOIUrl":"10.1016/j.probengmech.2024.103699","url":null,"abstract":"<div><div>A <em>quantified</em> active learning Kriging-based (qAK) methodology for structural reliability analysis is presented. The proposed approach is based on an updated probability density function (PDF), which is dominant in the vicinity of the limit-state surface. This PDF is created using weights based on an improved learning function called the <em>most probable misclassification</em> function. This function is used as a metric for efficiently updating the Kriging model, as it symmetrically quantifies the uncertainty of candidate points in terms of the model’s accuracy. The proposed approach accurately approximates the points that lie on the limit-state surface. Moreover, a probabilistic-based stopping criterion is proposed. The new support points are selected using the weighted <span><math><mi>K</mi></math></span>-means algorithm and the sample from the updated PDF. Thus, the method does not require solving an optimization problem or using a sampling algorithm. The proposed qAK methods are more reliable and robust than previous implementations of the Kriging method for structural reliability assessment. The proposed approach is presented within the framework of standard reliability methods, i.e., the Monte Carlo and the Subset Simulation methods. The efficiency of the proposed qAK methods is demonstrated with the aid of six case studies.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103699"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552657","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":"Stochastic design optimization of nonlinear structures under random seismic excitations using incremental dynamic analysis","authors":"Pinghe Ni ,&nbsp;Zhishen Yuan ,&nbsp;Jinlong Fu ,&nbsp;Yulei Bai ,&nbsp;Liang Liu","doi":"10.1016/j.probengmech.2024.103707","DOIUrl":"10.1016/j.probengmech.2024.103707","url":null,"abstract":"<div><div>The increasing demand for mitigating earthquake hazards has prompted substantial research attention towards performance-based seismic design of civil structures. Nevertheless, there remains limited exploration into optimizing complex structures while accounting for seismic uncertainties. This study seeks to address this gap by introducing an effective approach for optimizing designs of nonlinear structures under random seismic excitations. The key innovation lies in approximating structural failure probability through incremental dynamic analysis (IDA), leading to the development of a novel double-loop optimization method tailored for designing nonlinear structures exposed to stochastic seismic loading conditions. In the outer loop, geometric variables of structures are optimized using sequential quadratic programming; within the inner loop, IDA is adopted for structural analysis to quantify seismic uncertainty, and the resulting failure probability is then served as the optimization constraint for the outer loop. To validate its accuracy and efficacy, numerical investigations have been performed on two representative case studies utilizing <em>OpenSees</em>: a reinforced concrete column and a three-story steel frame. The findings affirm that IDA can precisely estimate failure probabilities associated with nonlinear structures experiencing random ground motions and demonstrate that this proposed methodology can effectively determine optimal geometries aimed at enhancing structural resilience against earthquakes across various levels of failure probabilities and bound constraints.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103707"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142572221","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":"Confidence-based design optimization using multivariate kernel density estimation under insufficient input data","authors":"Yongsu Jung ,&nbsp;Minjik Kim ,&nbsp;Hyunkyoo Cho ,&nbsp;Weifei Hu ,&nbsp;Ikjin Lee","doi":"10.1016/j.probengmech.2024.103702","DOIUrl":"10.1016/j.probengmech.2024.103702","url":null,"abstract":"<div><div>The uncertainty quantification of the input statistical model in reliability-based design optimization (RBDO) has been widely investigated for accurate reliability analysis, and it could be estimated through its characteristics, cumulative experiences, and available data. However, uncertainty quantification of random variables in existing RBDO studies has exploited parametric distributions quantifying the uncertainty through the Bayes' theorem. In addition, a correlation between random variables is often underestimated due to a lack of knowledge and difficulty to describe the high-dimensional correlation. Hence, it has been a challenge to properly quantify input statistical model and its uncertainty. Therefore, a multivariate kernel density estimation (KDE) is employed to perform data-driven confidence-based design optimization (CBDO) for effective quantification of input model uncertainty. Any assumption on input distribution is not necessary since it is established only with the given input data. Moreover, the input model uncertainty due to insufficient data is quantified using bootstrapping and optimal adaptive bandwidth matrices through the Bayes’ theorem using cross-validation error. Consequently, the proposed CBDO with given input data is capable of finding a conservative optimum of RBDO accounting for both aleatory uncertainty of random variables and epistemic uncertainty induced by a limited number of input data through the multivariate KDE.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103702"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142437726","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 data-driven maximum entropy method for probability uncertainty analysis based on the B-spline theory","authors":"Gang Li ,&nbsp;Yiyuan Wang ,&nbsp;Wanxin He ,&nbsp;Changting Zhong ,&nbsp;Yixuan Wang","doi":"10.1016/j.probengmech.2024.103688","DOIUrl":"10.1016/j.probengmech.2024.103688","url":null,"abstract":"<div><div>The probability density function (PDF) is quite important for structural reliability analysis; thus, accurate PDF modeling methods draw increasing attention. This paper proposes a novel metaheuristic data-driven paradigm of the maximum entropy method (MEM) based on the B-spline function theory. Firstly, a B-spline proxy of the MEM PDF is proposed for probability uncertainty analysis. We derive the parameter calculation formulation and calculate the undetermined parameters via the raw data of structural responses. Then, to determine the knots of the B-spline functions, we propose a novel data-driven approach with the aid of a powerful metaheuristic algorithm and the response data information. Different from the traditional MEM, the proposed method is a complete data-driven solution approach and does not involve the statistical moment calculation and the nonlinear equations composed of statistical moments. Combining the advantages of the B-spline theory and the MEM, the proposed method can reconstruct the response PDF with a complex shape, such as the PDF with multiple peaks or heavy tails. For verification, two numerical examples and one engineering example are analyzed, and compared with some classical PDF modeling methods. The results show that the proposed method is superior to the compared methods in terms of computational accuracy, when the same sample data is used.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103688"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421054","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":"Closed-form expressions for eigenvalue and eigenvectors of stochastic symmetric matrices using the probability transformation method","authors":"Rossella Laudani,&nbsp;Giovanni Falsone","doi":"10.1016/j.probengmech.2024.103706","DOIUrl":"10.1016/j.probengmech.2024.103706","url":null,"abstract":"<div><div>This work shows the use of the Probability Transformation Method (PTM) for deriving a closed-form probability density function (PDF) of the eigenpair of stochastic real-valued symmetric matrices. In particular, the PTM allows the direct evaluation of the eigenpair PDF starting from the joint PDF (JPDF) of the system’s uncertainties. The impact of the linear stochastic systems’ randomness in the natural frequencies and mode shape is investigated through some numerical applications. Even if the structural samples investigated are intentionally simple, that aspect is only linked to the authors’ use of the Mathematica software that, in some ways, limits the resolution for high dimensional problems. From a theoretical perspective, though, this is not a restriction, and the problem’s dimension has no impact on the method’s accuracy. The obtained analytical results compared with Monte Carlo simulations have confirmed the goodness of the proposed stochastic procedure.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103706"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142700925","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":"Quantitative property of MF-discrepancy and efficient point-selection strategy for the nonlinear stochastic response analysis of structures with random parameters","authors":"Jian-Bing Chen ,&nbsp;Xin Huang ,&nbsp;Jie Li","doi":"10.1016/j.probengmech.2024.103708","DOIUrl":"10.1016/j.probengmech.2024.103708","url":null,"abstract":"<div><div>The response analysis of high-dimensional and strongly nonlinear systems with random parameters remains a significant challenge in stochastic computational mechanics. To address this challenge, some methods based on the high-efficacy point sets have been developed, in which efficient global-point-set methods represented by low-discrepancy are of paramount importance in generating representative point sets. Several discrepancies including the extended F-discrepancy (EF-discrepancy) and the generalized F-discrepancy (GF-discrepancy) have been introduced to assess the uniformity and the efficacy of a representative point set. In such context, a maximal marginal EF-discrepancy (MF-discrepancy), which is an extended form of the GF-discrepancy, is proposed in this paper and then the properties of the MF-discrepancy are studied in detail. The probability distribution of the MF-discrepancy is derived, including a rigorous proof for random point sets and a model based on an assumption for some generic point sets. A generalized Koksma-Hlawka inequality is established accordingly to govern the worst error estimate. The lowest bound of the MF-discrepancy is given, and two intuitive quantitative indices are proposed to measure the goodness of the MF-discrepancy. Based on the lowest bound, an enhanced point-selection strategy with a unified theoretical framework for minimizing the MF-discrepancy is proposed. In this framework, locally minimizing the MF-discrepancy yields the two-step point-selection method, and a new point-selection strategy is proposed based on the global minimization of the MF-discrepancy, which is verified to be efficient and robust, especially in high-dimensional cases. Several numerical examples, including a 2-story shear frame, a 10-story shear frame, and a 10-story reinforced concrete frame structure modeled by the finite element method, are studied, verifying the efficiency and the robustness of the proposed point-selection strategy.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103708"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142663357","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 perspective on conditional spectrum-based determination of response statistics of nonlinear systems","authors":"Beatrice Pomaro ,&nbsp;Pol D. Spanos","doi":"10.1016/j.probengmech.2024.103704","DOIUrl":"10.1016/j.probengmech.2024.103704","url":null,"abstract":"<div><div>This work focuses on determining the stochastic response properties, in the frequency domain, of a general class of nonlinear systems with polynomial nonlinearities. Specifically, the results are presented in terms of the stationary power spectral densities of the system's displacement and velocity. This is pursued by revisiting the conditional power spectrum concept, with the assumption that the response process is both ergodic and pseudo-harmonic and characterized by an amplitude, and a phase. A theoretical elucidation of an existing formula for the conditional spectrum is attempted. In particular, this concept is interpreted in conjunction with the time averaging approximation made in the definition of the stationary probability density function of a response amplitude quantity, associated with the original nonlinear system. It is shown that a proper definition of the stationary probability density of the response amplitude, along with a reasonable treatment of the distribution over the frequency domain of the amplitude contribution, lead to an improved approximation of the stationary response power spectral density. The treatment involves the averaging of a population of surrogate spectral densities of stationary random responses conforming with the system responses associated with individual values of the amplitudes of the responses. The semi-analytical results have been quite favourably juxtaposed with a large suite of à propos Monte Carlo simulations, both in terms of the shape and of the range of the involved germane frequencies, even for strongly nonlinear systems.</div></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":"78 ","pages":"Article 103704"},"PeriodicalIF":3.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552656","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}