Nanzheng Zou , Chunlin Gong , Licong Zhang , Yunwei Zhang , Xiaowei Wang , Chunna Li
{"title":"一种基于边界最可能点轨迹的混合时变可靠性分析方法","authors":"Nanzheng Zou , Chunlin Gong , Licong Zhang , Yunwei Zhang , Xiaowei Wang , Chunna Li","doi":"10.1016/j.probengmech.2023.103558","DOIUrl":null,"url":null,"abstract":"<div><p><span><span>In the engineering field, time-variant reliability analysis (TRA) is used to measure the safety level of structures under time-variant uncertainties. Lacking in information or data, some uncertainties cannot be directly quantified as stochastic models, which results in the simultaneous existence of aleatory and </span>epistemic uncertainties<span><span> in most of problems. In general, stochastic and interval models are respectively used to describe aleatory and epistemic uncertainties. For the hybrid TRA (HTRA) problem considering the two kinds of uncertainties, the existing method needs to excessively evaluate the original time-variant limit-state function, which is too expensive for engineering problems. To address this issue, we propose the concept of bound-most-probable point trajectory (BMPPT) which can be used to construct the approximation of the limit-state hyper-surface. Moreover, we develop a HTRA method based on approximating BMPPT which can further improve the computational efficiency. First, based on time discretization, we transform the HTRA problem into a time-independent series-system reliability problem which can be solved by searching the bound-most-probable point (BMPP) at all discrete time instants. Then, with the BMPPT, the lower and upper bounds of the time-variant limit-state function are linearized into two Gaussian processes. Finally, the expansion optimal linear estimation and Monte Carlo simulation are performed to estimate the time-variant reliability. To avoid excessive BMPP searches, the active learning Kriging is used to approximate the BMPPT. Two numerical examples including a </span>cantilever beam, and a 10-bar truss, and two </span></span>engineering applications<span> of the solid rocket engine shell and the rocket inter-stage structure are investigated, and the results reveal that the proposed method can solve the HTRA problems with high accuracy and efficiency.</span></p></div>","PeriodicalId":54583,"journal":{"name":"Probabilistic Engineering Mechanics","volume":null,"pages":null},"PeriodicalIF":3.0000,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A novel hybrid time-variant reliability analysis method through approximating bound-most-probable point trajectory\",\"authors\":\"Nanzheng Zou , Chunlin Gong , Licong Zhang , Yunwei Zhang , Xiaowei Wang , Chunna Li\",\"doi\":\"10.1016/j.probengmech.2023.103558\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span><span>In the engineering field, time-variant reliability analysis (TRA) is used to measure the safety level of structures under time-variant uncertainties. Lacking in information or data, some uncertainties cannot be directly quantified as stochastic models, which results in the simultaneous existence of aleatory and </span>epistemic uncertainties<span><span> in most of problems. In general, stochastic and interval models are respectively used to describe aleatory and epistemic uncertainties. For the hybrid TRA (HTRA) problem considering the two kinds of uncertainties, the existing method needs to excessively evaluate the original time-variant limit-state function, which is too expensive for engineering problems. To address this issue, we propose the concept of bound-most-probable point trajectory (BMPPT) which can be used to construct the approximation of the limit-state hyper-surface. Moreover, we develop a HTRA method based on approximating BMPPT which can further improve the computational efficiency. First, based on time discretization, we transform the HTRA problem into a time-independent series-system reliability problem which can be solved by searching the bound-most-probable point (BMPP) at all discrete time instants. Then, with the BMPPT, the lower and upper bounds of the time-variant limit-state function are linearized into two Gaussian processes. Finally, the expansion optimal linear estimation and Monte Carlo simulation are performed to estimate the time-variant reliability. To avoid excessive BMPP searches, the active learning Kriging is used to approximate the BMPPT. Two numerical examples including a </span>cantilever beam, and a 10-bar truss, and two </span></span>engineering applications<span> of the solid rocket engine shell and the rocket inter-stage structure are investigated, and the results reveal that the proposed method can solve the HTRA problems with high accuracy and efficiency.</span></p></div>\",\"PeriodicalId\":54583,\"journal\":{\"name\":\"Probabilistic Engineering Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.0000,\"publicationDate\":\"2023-11-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probabilistic Engineering Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0266892023001479\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probabilistic Engineering Mechanics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0266892023001479","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
A novel hybrid time-variant reliability analysis method through approximating bound-most-probable point trajectory
In the engineering field, time-variant reliability analysis (TRA) is used to measure the safety level of structures under time-variant uncertainties. Lacking in information or data, some uncertainties cannot be directly quantified as stochastic models, which results in the simultaneous existence of aleatory and epistemic uncertainties in most of problems. In general, stochastic and interval models are respectively used to describe aleatory and epistemic uncertainties. For the hybrid TRA (HTRA) problem considering the two kinds of uncertainties, the existing method needs to excessively evaluate the original time-variant limit-state function, which is too expensive for engineering problems. To address this issue, we propose the concept of bound-most-probable point trajectory (BMPPT) which can be used to construct the approximation of the limit-state hyper-surface. Moreover, we develop a HTRA method based on approximating BMPPT which can further improve the computational efficiency. First, based on time discretization, we transform the HTRA problem into a time-independent series-system reliability problem which can be solved by searching the bound-most-probable point (BMPP) at all discrete time instants. Then, with the BMPPT, the lower and upper bounds of the time-variant limit-state function are linearized into two Gaussian processes. Finally, the expansion optimal linear estimation and Monte Carlo simulation are performed to estimate the time-variant reliability. To avoid excessive BMPP searches, the active learning Kriging is used to approximate the BMPPT. Two numerical examples including a cantilever beam, and a 10-bar truss, and two engineering applications of the solid rocket engine shell and the rocket inter-stage structure are investigated, and the results reveal that the proposed method can solve the HTRA problems with high accuracy and efficiency.
期刊介绍:
This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.