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C. Jiang - One of the best experts on this subject based on the ideXlab platform.

  • A novel evidence theory model dealing with correlated variables and the corresponding structural Reliability Analysis Method
    Structural and Multidisciplinary Optimization, 2017
    Co-Authors: Z. Zhang, C. Jiang, X.x. Ruan, Fengjiao Guan
    Abstract:

    Evidence theory serves as a powerful tool to deal with epistemic uncertainty which widely exists in the design stages of many complex engineering systems or products. However, the traditional evidence theory model cannot handle parameter correlations that may have profound influences on the Reliability Analysis results. This paper is supposed to develop a novel evidence theory model with consideration of parameter correlations and its corresponding structural Reliability Analysis Method. First, a multidimensional parallelepiped uncertainty domain which takes into account the influence of parameter correlations is constructed. Second, the corresponding joint basic probability assignments are established for each focal element in the uncertainty domain. Finally, the Reliability interval composed of the belief and plausibility measures are computed. Several numerical examples are investigated to demonstrate the effectiveness of the proposed model and the corresponding Reliability Analysis Method.

  • a time variant Reliability Analysis Method for structural systems based on stochastic process discretization
    International Journal of Mechanics and Materials in Design, 2017
    Co-Authors: C. Jiang, X P Huang
    Abstract:

    In this paper, we propose a new Method for analyzing time-variant system Reliability based on stochastic process discretization, which provides an effective tool for Reliability design of many relatively complex structures considering the whole lifecycle. Within a design lifetime, the stochastic process is discretized into a series of random variables, and meanwhile, we can derive a time-invariant limit-state function in each time interval; the discretized random variables from the stochastic processes and the original random variables are transformed to the independent normal space, and a conventional time-invariant system Reliability problem is derived through the linearization to each discretized limit-state functions; by solving this time-invariant system Reliability problem, we can obtain the structural Reliability or failure probability within the design lifetime. Finally, in this paper, we provide four numerical examples to verify the effectiveness of the Method.

  • A probabilistic and interval hybrid Reliability Analysis Method for structures with correlated uncertain parameters
    International Journal of Computational Methods, 2015
    Co-Authors: C. Jiang, Jing Zheng, X. Han
    Abstract:

    This paper proposes a probability-interval mixed uncertainty model considering parametric correlations and a corresponding structural Reliability Analysis Method. First of all, we introduce the sample correlation coefficients to express the correlations between different kinds of uncertain variables including probability and interval variables. Then dependent parameters are transformed into independent ones through a matrix transformation. A Reliability Analysis model is put forward, and an efficient Method is built to obtain the Reliability index or failure probability interval of the structure. Finally, four numerical examples are provided to verify the validity of the Method.

  • A Vine-Copula-Based Reliability Analysis Method for Structures With Multidimensional Correlation
    Journal of Mechanical Design, 2015
    Co-Authors: C. Jiang, X. Han, W. Zhang, Lijun Song
    Abstract:

    This paper proposed a vine-copula-based structural Reliability Analysis Method which is an effective approach for performing a Reliability Analysis on complex multidimensional correlation problems. A joint probability distribution function (PDF) among multidimensional random variables was established using a vine copula function, based on which a Reliability Analysis model was constructed. Two solution algorithms were proposed to solve this Reliability Analysis model: one was based on Monte Carlo simulation (MCS) and another one was based on the first-order Reliability Method (FORM). The former Method provides a generalized computational Method for a Reliability Analysis based on vine copula functions and can provide so-called “precise solutions”; the latter Method has high computational efficiency and can be used to solve actual complex engineering problems. Finally, three numerical examples were provided to verify the effectiveness of the Method.

  • a time variant Reliability Analysis Method based on stochastic process discretization
    Journal of Mechanical Design, 2014
    Co-Authors: C. Jiang, X P Huang, Dequan Zhang
    Abstract:

    Time-variant Reliability problems caused by deterioration in material properties, dynamic load uncertainty, and other causes are widespread among practical engineering applications. This study proposes a novel time-variant Reliability Analysis Method based on stochastic process discretization (TRPD), which provides an effective analytical tool for assessing design Reliability over the whole lifecycle of a complex structure. Using time discretization, a stochastic process can be converted into random variables, thereby transforming a time-variant Reliability problem into a conventional time-invariant system Reliability problem. By linearizing the limit-state function with the first-order Reliability Method (FORM) and furthermore, introducing a new random variable, the converted system Reliability problem can be efficiently solved. The TRPD avoids the calculation of outcrossing rates, which simplifies the process of solving time-variant Reliability problems and produces high computational efficiency. Finally, three numerical examples are used to verify the effectiveness of this approach.

Jie Liu - One of the best experts on this subject based on the ideXlab platform.

  • A time-variant Reliability Analysis Method for non-linear limit-state functions with the mixture of random and interval variables
    Engineering Structures, 2020
    Co-Authors: Jie Liu, Yufei Yan, Jianhua Rong, Guilin Wen
    Abstract:

    Abstract Most of the current time-variant Reliability Analysis Methods are applicable for only random variables. However, some of the uncertain parameters can only be easily modeled by interval variables in many engineering applications. The main contribution of this paper is to propose a new time-variant Reliability Analysis Method for nonlinear limit state function with the coexistence of random variables and interval uncertain variables. Three primary strategies are put forward. Firstly, the stochastic process in the time-variant limit-state function is discretized, equivalently gaining several static limit-state functions at different time. Secondly, each static limit-state function is linearized at the most probable point (MPP) and the worst-case point (WCP) of interval variable, by doing which, the ordinary time-dependent Reliability problem is equally transformed into a static Reliability one with mixed uncertain variables. Finally, complex nested optimization problems using sequential iterations are effectively solved in mixed Reliability calculation. The proposed Method can obtain structural Reliability considering time effects and mixed uncertainties. The effectiveness and the efficiency of the proposed Method are demonstrated by four numerical examples.

  • A novel evidence-theory-based Reliability Analysis Method for structures with epistemic uncertainty
    Computers & Structures, 2013
    Co-Authors: C. Jiang, Zheng Zhang, X. Han, Jie Liu
    Abstract:

    Evidence theory has a strong ability to deal with the epistemic uncertainty, based on which the uncertain parameters existing in many complex engineering problems with limited information can be conveniently treated. However, the large computational cost caused by its discrete property severely influences the practicability of evidence theory. This paper aims to develop an efficient Method to evaluate the Reliability for structures with epistemic uncertainty, and hence improve the applicability of evidence theory in engineering problems. A uniformity approach is used to deal with the evidence variables, through which the original Reliability problem can be transformed to a traditional Reliability problem with only random uncertainty. It is then solved by using a response-surface-based Reliability Analysis Method, and a most probable point (MPP) is obtained. Based on the MPP, the most critical focal element which has the maximum contribution to failure can be identified. Then using an approximate model created based on this focal element, the Reliability interval can be efficiently computed for the original epistemic uncertainty problem. Three numerical examples are investigated to demonstrate the effectiveness of the present Method, which include two simple problems with explicit expressions and one engineering application.

Baopeng Liao - One of the best experts on this subject based on the ideXlab platform.

  • FORM and Out-Crossing Combined Time-Variant Reliability Analysis Method for Ship Structures
    IEEE Access, 2018
    Co-Authors: Baopeng Liao
    Abstract:

    In view of the varying characteristics of material properties, environmental conditions, and loading effects randomly with long time, the random and temporal characters of different variables should take into account when the structural Reliability Analysis Methods are adopted to estimate the Reliability of ship structures. Therefore, a time-variant Reliability Analysis Method combined the out-crossing approach and the first-order Reliability Method is proposed. In this paper, the research is conducted on the time-variant feature of ship structures under the corrosive action according to the environmental testing data. Furthermore, the limit state function is derived based on the time-variant feature Analysis results in which the strength and stress of ship structures are both regarded as variables with respect to time. Then, the time-dependent Reliability model of ship structures is established based on this combined Method, and the solving process of parameters in this model is illustrated. Finally, a case of a ship grillage structure under marine environment is given to prove that the proposed Method has a good application in evaluating the Reliability of ship structures. The comparison Analysis using different Methods is also conducted to study the accuracy and efficiency of this Method.

Hong-zhong Huang - One of the best experts on this subject based on the ideXlab platform.

  • Saddlepoint approximation-based Reliability Analysis Method for structural systems with parameter uncertainties
    Proceedings of the Institution of Mechanical Engineers Part O: Journal of Risk and Reliability, 2014
    Co-Authors: Ning-cong Xiao, Zhonglai Wang, Hong-zhong Huang
    Abstract:

    Due to epistemic uncertainty, precisely determining parameters of all distribution is impossible in engineering practice. In this article, a novel Reliability Analysis Method based on the saddlepoint approximation is proposed for structural systems with parameter uncertainties. The proposed Method includes four main steps: (1) sampling for random and probability-box variables, (2) approximating the cumulant generating functions for systems under the best and worst cases, (3) calculating saddlepoints for the best and worst cases, and (4) calculating the lower and upper bounds of the probability of failure. The proposed Method is effective because it does not require a large sample size or solving complicated integrals. Furthermore, the proposed Method provides results that have the same accuracy as the existing interval Monte Carlo simulation Method, but with significantly reduced computational effort. The effectiveness of the proposed Method is demonstrated with three examples that are compared against with the interval Monte Carlo simulation Method.

  • Reliability Analysis Method in the presence of fuzziness attached to operating time
    Microelectronics Reliability, 1995
    Co-Authors: Hong-zhong Huang
    Abstract:

    Abstract This paper makes an investigation into assessing the Reliability of a system in the presence of fuzziness attached to operating time. A crisp event is extended into a fuzzy one, and fuzzy Reliability etc. basic concepts are introduced. The fundamental calculation formulas of fuzzy Reliability are developed and the fuzzy Reliability models of unrepairable systems are established.

  • Time-variant system Reliability Analysis Method for a small failure probability problem
    Reliability Engineering & System Safety, 1
    Co-Authors: Hua-ming Qian, Hong-zhong Huang
    Abstract:

    Abstract This paper proposes a time-variant system Reliability Analysis Method by combining multiple response Gaussian process (MRGP) and subset simulation (SS) to solve the small failure probability problem. One common Method for time-variant Reliability Analysis is based on the double-loop procedure where the inner loop is the optimization for extreme values and the outer loop is extreme-value-based Reliability Analysis. In this paper, a new single-loop strategy is firstly proposed to decouple the double-loop procedure by using the best value in current initial samples to approximate the extreme value, thus the extremal optimization in inner loop can be avoided. Then the MRGP model is used to construct the surrogate model of extreme value response surface for time-variant system Reliability Analysis based on the approximated extremums. Meanwhile, the Kriging model is also constructed based on the initial samples to assist in searching the new sample point. Furthermore, for selecting the new point that resides as close to the extreme value response surface as possible from the Monte Carlo simulation (MCS) sample pool, three learning functions (U-function, EFF-function and H-function) are respectively used to find the new random variable sample point based on the MRGP model and the expected improvement (EI) function is used to find the new time sample point based on the Kriging model. Finally, for reducing the size of candidate sample pool and the computing burden, the SS Method is combined with the MRGP model to deal with the small failure probability problem. The effectiveness of the proposed Method is also demonstrated by several examples.

Chao Jiang - One of the best experts on this subject based on the ideXlab platform.

  • A frequency domain Reliability Analysis Method for electromagnetic problems based on univariate dimension reduction Method
    Science China Technological Sciences, 2019
    Co-Authors: Menghao Ping, Chao Jiang, Xu Han, Jianfeng Zhong, Xiaoya Xiao, Zhiliang Huang, Zhonghua Wang
    Abstract:

    In this paper, a class of electromagnetic field frequency domain Reliability problem is first defined. The frequency domain Reliability refers to the probability that an electromagnetic performance indicator can meet the intended requirements within a specific frequency band, considering the uncertainty of structural parameters and frequency-variant electromagnetic parameters. And then a frequency domain Reliability Analysis Method based on univariate dimension reduction Method is proposed, which provides an effective calculation tool for electromagnetic frequency domain Reliability. In electromagnetic problems, performance indicators usually vary with frequency. The Method firstly discretizes the frequency-variant performance indicator function into a series of frequency points’ functions, and then transforms the frequency domain Reliability problem into a series system Reliability problem of discrete frequency points’ functions. Secondly, the univariate dimension reduction Method is introduced to solve the probability distribution functions and correlation coefficients of discrete frequency points’ functions in the system. Finally, according to the above calculation results, the series system Reliability can be solved to obtain the frequency domain Reliability, and the cumulative distribution function of the performance indicator can also be obtained. In this study, Monte Carlo simulation is adopted to demonstrate the validity of the frequency domain Reliability Analysis Method. Three examples are investigated to demonstrate the accuracy and efficiency of the proposed Method.

  • an efficient evidence based Reliability Analysis Method via piecewise hyperplane approximation of limit state function
    Structural and Multidisciplinary Optimization, 2018
    Co-Authors: Chao Jiang
    Abstract:

    For evidence-based Reliability Analysis, whether a focal element belongs to the failure domain is commonly judged by the corresponding extreme values of a performance function in its response domain. In contrast, in this paper, an efficient Method by which the ownership relationship between a focal element and the failure domain is directly determined in uncertain variable domain, is proposed via the piecewise hyperplane approximation of limit state function (LSF). The whole uncertainty domain is divided into several sub uncertainty domains on the defined reference direction. The approximate LSF is constructed by the piecewise hyperplane in each sub uncertainty domain, the belief measure and the plausibility measure of Reliability Analysis can be directly calculated in uncertainty domain through the approximate piecewise hyperplanes of LSF. The proposed evidence-based Reliability Analysis Method is demonstrated by two numerical examples and two engineering applications.

  • a non probabilistic structural Reliability Analysis Method based on a multidimensional parallelepiped convex model
    Acta Mechanica, 2014
    Co-Authors: Chao Jiang, Q F Zhang, Y H Qian
    Abstract:

    Compared with a probability model, a non-probabilistic convex model only requires a small number of experimental samples to discern the uncertainty parameter bounds instead of the exact probability distribution. Therefore, it can be used for uncertainty Analysis of many complex structures lacking experimental samples. Based on the multidimensional parallelepiped convex model, we propose a new Method for non-probabilistic structural Reliability Analysis in which marginal intervals are used to express scattering levels for the parameters, and relevant angles are used to express the correlations between uncertain variables. Using an affine coordinate transformation, the multidimensional parallelepiped uncertainty domain and the limit-state function are transformed to a standard parameter space, and a non-probabilistic Reliability index is used to measure the structural Reliability. Finally, the Method proposed herein was applied to several numerical examples.