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Wei Wang - One of the best experts on this subject based on the ideXlab platform.
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non linear partial least squares response surface method for Structural Reliability Analysis
Reliability Engineering & System Safety, 2017Co-Authors: Wei Zhao, Wei WangAbstract:An important challenge in Structural Reliability is to minimize the number of calls to the numerical models, so the current Structural Reliability Analysis of multidimensional variable, the surrogate model with the uniform design are widely used because of fewest sample points used in the construction of the surrogate model. However, fewer points may lead to correlation exiting between the samples. The surrogate model, obtained by the original Least Squares (LS) regression using these samples, is not accurate, which leads to inaccuracies in the Structural Reliability Analysis. To deal with the limitation of fitting the models in the original LS regression, an effective technique is introduced to the Reliability Analysis, and a new approach based on this technique has been proposed. The aim of this paper is to establish a new surrogate model based on the theory of Partial Least Squares (PLS) under the condition of multi-dimensional small samples data with correlation, to assess the Reliability of structures in a more efficient way. The method is called the UD-BP-PLS surrogate model method, combining uniform design, non-linearity B-spline function and PLS technique. It is shown to be efficient as the probability of failure obtained by UD-BP-PLS surrogate model method is very accurate, which only needs a small number of calls to the performance function. Several examples from literature are used to illustrate the methodology and to prove its efficiency, particularly for problems dealing with high non-linearity and high dimensionality.
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an improved radial basis function network for Structural Reliability Analysis
Journal of Mechanical Science and Technology, 2011Co-Authors: Wei Zhao, Wei WangAbstract:Approximation methods such as response surface method and artificial neural network (ANN) method are widely used to alleviate the computation costs in Structural Reliability Analysis. However most of the ANN methods proposed in the literature suffer various drawbacks such as poor choice of parameter setting, poor generalization and local minimum. In this study, a support vector machine-based radial basis function (RBF) network method is proposed, in which the improved RBF model is used to approximate the limit state function and then is connected to a Reliability method to estimate failure probability. Since the learning algorithm of RBF network is replaced by the support vector algorithm, the advantage of the latter, such as good generalization ability and global optimization are propagated to the former, thus the inherent drawback of RBF network can be defeated. Numerical examples are given to demonstrate the applicability of the improved RBF network method in Structural Reliability Analysis, as well as to illustrate the validity and effectiveness of the proposed method.
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Application of Cokriging Technique to Structural Reliability Analysis
2011 International Conference on Future Computer Sciences and Application, 2011Co-Authors: Wei Zhao, Wei WangAbstract:Approximation techniques are widely used in Structural Reliability Analysis to build computationally inexpensive surrogate models to replace expensive-to-run computer Analysis codes. Recently, kriging models are frequently utilized to construct surrogate approximations; however, they may be inefficient for systems having with a large number of design variables. Therefore, a new method-cokriging, which is an extension of kriging for creating surrogate models, is proposed for large-scale systems. In this paper, our intention is to discuss the suitability of cokriging models for Structural Reliability Analysis, especially in high-dimensional problems. First, This paper explores the use of the cokriging method for Structural Reliability problems by comparing it with the kriging method based on two numerical examples. Secondly, comparisons between the two different database augmenting schemes in the cokriging models are made based on the examples. Finally, this paper suggests the points for which the cokriging model could be improved to get better results for Structural Reliability problems.
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Structural Reliability Analysis based on the cokriging technique
IOP Conference Series: Materials Science and Engineering, 2010Co-Authors: Wei Zhao, Wei WangAbstract:Approximation methods are widely used in Structural Reliability Analysis because they are simple to create and provide explicit functional relationships between the responses and variables in stead of the implicit limit state function. Recently, the kriging method which is a semi-parameter interpolation technique that can be used for deterministic optimization and Structural Reliability has gained popularity. However, to fully exploit the kriging method, especially in high-dimensional problems, a large number of sample points should be generated to fill the design space and this can be very expensive and even impractical in practical engineering Analysis. Therefore, in this paper, a new method—the cokriging method, which is an extension of kriging, is proposed to calculate the Structural Reliability. cokriging approximation incorporates secondary information such as the values of the gradients of the function being approximated. This paper explores the use of the cokriging method for Structural Reliability problems by comparing it with the Kriging method based on some numerical examples. The results indicate that the cokriging procedure described in this work can generate approximation models to improve on the accuracy and efficiency for Structural Reliability problems and is a viable alternative to the kriging.
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application of low discrepancy sampling method in Structural Reliability Analysis
Structural Safety, 2009Co-Authors: Wei WangAbstract:This study introduces and investigates various low-discrepancy sequences and then develops a new procedure in which the low-discrepancy sequences are combined with the importance sampling technique to estimate the failure probability. This proposed low-discrepancy sampling method is based on the concept that the deterministic low-discrepancy sequences of points can significantly improve the accuracy of the classical Monte Carlo (MC) method over purely random sampling. Different benchmark examples verify that the proposed method is more accurate with the same number of samples and has a faster rate of convergence in order to achieve a given accuracy when compared with the MC method. Therefore, the low-discrepancy sampling method shows great potential for improving the accuracy and efficiency of the MC-based simulation method for Structural Reliability Analysis.
Jian Deng - One of the best experts on this subject based on the ideXlab platform.
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Structural Reliability Analysis for implicit performance function using radial basis function network
International Journal of Solids and Structures, 2006Co-Authors: Jian DengAbstract:Abstract This is the second paper of our work on Structural Reliability Analysis for implicit performance function. The first paper proposed Structural Reliability Analysis methods using multilayer perceptron artificial neural network [Deng, J., Gu, D.S., Li, X.B., Yue, Z.Q., 2005. Structural Reliability Analysis for implicit performance function using artificial neural network. Structural Safety 25 (1), 25–48]. This paper presents three radial basis function network (RBF) based Reliability Analysis methods, i.e. RBF based MCS, RBF based FORM, and RBF based SORM. In these methods, radial basis function network technique is adopted to model and approximate the implicit performance functions or partial derivatives. The RBF technique uses a small set of the actual data of the implicit performance functions, which are obtained via physical experiments or normal numerical Analysis such as finite element methods for the complicated Structural system, and are used to develop a trained RBF generalization algorithm. Then a large number of the function values and partial derivatives of implicit performance functions can be readily obtained by simply extracting information from the established and successfully trained RBF network. These function values and derivatives are used in conventional MCS, FORM or SORM to constitute RBF based Reliability Analysis algorithms. Examples are presented in the paper to illustrate how the proposed RBF based methods are used in Structural Reliability Analysis. The results are well compared with those obtained by the conventional Reliability methods such as the Monte-Carlo simulation, multilayer perceptrons networks, the response surface method, the FORM method 2, and so on. The examples showed the proposed approach is applicable to Structural Reliability Analysis involving implicit performance functions.
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Structural Reliability Analysis for implicit performance functions using artificial neural network
Structural Safety, 2005Co-Authors: Jian Deng, Desheng Gu, Xibing LiAbstract:Abstract The Monte-Carlo simulation (MCS), the first-order Reliability methods (FORM) and the second-order Reliability methods (SORM), are three Reliability Analysis methods that are commonly used for Structural safety evaluation. The MCS requires the calculations of hundreds and thousands of performance function values. The FORM and SORM demand the values and partial derivatives of the performance function with respect to the design random variables. Such calculations could be time-consuming or cumbersome when the performance functions are implicit. Such implicit performance functions are normally encountered when the Structural systems are complicated and numerical Analysis such as finite element methods has to be adopted for the prediction. To address this issue, this paper presents three artificial neural network (ANN)-based Reliability Analysis methods, i.e. ANN-based MCS, ANN-based FORM, and ANN-based SORM. These methods employ multi-layer feedforward ANN technique to approximate the implicit performance functions. The ANN technique uses a small set of the actual values of the implicit performance functions. Such a small set of actual data is obtained via normal numerical Analysis such as finite element methods for the complicated Structural system. They are used to develop a trained ANN generalization algorithm. Then a large number of the values and partial derivatives of the implicit performance functions can be obtained for conventional Reliability Analysis using MCS, FORM or SORM. Examples are given in the paper to illustrate why and how the proposed ANN-based Structural Reliability Analysis can be carried out. The results have shown the proposed approach is applicable to Structural Reliability Analysis involving implicit performance functions. The present results are compared well with those obtained by the conventional Reliability methods such as the direct Monte-Carlo simulation, the response surface method and the FORM method 2.
Ramana V Grandhi - One of the best experts on this subject based on the ideXlab platform.
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safety index calculation using intervening variables for Structural Reliability Analysis
Computers & Structures, 1996Co-Authors: Liping Wang, Ramana V GrandhiAbstract:Abstract This paper utilizes the intervening design variables concept for Structural Reliability Analysis. This procedure was traditionally used in Structural optimization, whereas this work applies to problems having stochastic information. The present algorithm is on the basis of a safety index algorithm present in Ref. [1] [L. P. Wang and R. V. Grandhi, Efficient safety index calculation for Structural Reliability Analysis. Comput. Struct. 52, 103–111 (1994)], which utilized the nonlinear approximation of performance function in the original space of random variables. The proposed algorithm further develops this procedure by (i) implementing the adaptive nonlinear approximation of performance function in the standard normal space of random variables, (ii) using an improved intervening variable procedure for more accurate approximation, and (iii) adding an additional convergency check on safety index calculation using approximate gradients. The efficiency and robustness of the proposed algorithm are demonstrated by several examples with highly nonlinear, complex, and explicit/implicit performance functions.
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efficient safety index calculation for Structural Reliability Analysis
Computers & Structures, 1994Co-Authors: Wang Liping, Ramana V GrandhiAbstract:Abstract This paper proposes an efficient Structural Reliability Analysis algorithm with an adaptive nonlinear approximation of performance function, in which the nonlinearity of the function is controlled by the feedback information from the previous iteration. The proposed Analysis procedure includes (1) identifying the most probable point of a limit state, (2) establishing an approximate nonlinear performance function by using intervening variables and (3) applying the HL-RF or the modified HL-RF method. The method is suitable not only for problems that involve explicit performance functions, but also for problems that need computer-intensive Structural Analysis. Several examples are presented in this paper to demonstrate the performance of the Analysis method using large coefficients of variation and nonnormal distribution of random variables.
Wei Zhao - One of the best experts on this subject based on the ideXlab platform.
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non linear partial least squares response surface method for Structural Reliability Analysis
Reliability Engineering & System Safety, 2017Co-Authors: Wei Zhao, Wei WangAbstract:An important challenge in Structural Reliability is to minimize the number of calls to the numerical models, so the current Structural Reliability Analysis of multidimensional variable, the surrogate model with the uniform design are widely used because of fewest sample points used in the construction of the surrogate model. However, fewer points may lead to correlation exiting between the samples. The surrogate model, obtained by the original Least Squares (LS) regression using these samples, is not accurate, which leads to inaccuracies in the Structural Reliability Analysis. To deal with the limitation of fitting the models in the original LS regression, an effective technique is introduced to the Reliability Analysis, and a new approach based on this technique has been proposed. The aim of this paper is to establish a new surrogate model based on the theory of Partial Least Squares (PLS) under the condition of multi-dimensional small samples data with correlation, to assess the Reliability of structures in a more efficient way. The method is called the UD-BP-PLS surrogate model method, combining uniform design, non-linearity B-spline function and PLS technique. It is shown to be efficient as the probability of failure obtained by UD-BP-PLS surrogate model method is very accurate, which only needs a small number of calls to the performance function. Several examples from literature are used to illustrate the methodology and to prove its efficiency, particularly for problems dealing with high non-linearity and high dimensionality.
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an improved radial basis function network for Structural Reliability Analysis
Journal of Mechanical Science and Technology, 2011Co-Authors: Wei Zhao, Wei WangAbstract:Approximation methods such as response surface method and artificial neural network (ANN) method are widely used to alleviate the computation costs in Structural Reliability Analysis. However most of the ANN methods proposed in the literature suffer various drawbacks such as poor choice of parameter setting, poor generalization and local minimum. In this study, a support vector machine-based radial basis function (RBF) network method is proposed, in which the improved RBF model is used to approximate the limit state function and then is connected to a Reliability method to estimate failure probability. Since the learning algorithm of RBF network is replaced by the support vector algorithm, the advantage of the latter, such as good generalization ability and global optimization are propagated to the former, thus the inherent drawback of RBF network can be defeated. Numerical examples are given to demonstrate the applicability of the improved RBF network method in Structural Reliability Analysis, as well as to illustrate the validity and effectiveness of the proposed method.
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Application of Cokriging Technique to Structural Reliability Analysis
2011 International Conference on Future Computer Sciences and Application, 2011Co-Authors: Wei Zhao, Wei WangAbstract:Approximation techniques are widely used in Structural Reliability Analysis to build computationally inexpensive surrogate models to replace expensive-to-run computer Analysis codes. Recently, kriging models are frequently utilized to construct surrogate approximations; however, they may be inefficient for systems having with a large number of design variables. Therefore, a new method-cokriging, which is an extension of kriging for creating surrogate models, is proposed for large-scale systems. In this paper, our intention is to discuss the suitability of cokriging models for Structural Reliability Analysis, especially in high-dimensional problems. First, This paper explores the use of the cokriging method for Structural Reliability problems by comparing it with the kriging method based on two numerical examples. Secondly, comparisons between the two different database augmenting schemes in the cokriging models are made based on the examples. Finally, this paper suggests the points for which the cokriging model could be improved to get better results for Structural Reliability problems.
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Structural Reliability Analysis with Uncertainty-but-Bounded Parameters Based on Meshless Method
Advanced Materials Research, 2010Co-Authors: Wei Zhao, Qiu Wei YangAbstract:The Structural Reliability Analysis with uncertainty-but-bounded parameters is considered in this paper. Each uncertain-but-bounded parameter is represented as an interval number or vector, an interval Reliability index is defined and discussed. Due to the wide application of the Meshless method, it is used in Structural stress and strain Analysis. The target variable of requiring Reliability Analysis is estimated via Taylor expansion. Based on optimization theory and vertex solution theorem, the upper and lower bounds of the target variables are obtained, and also the interval Reliability index. A typical elastostatics example is presented to illustrate the computational aspects of interval Reliability Analysis in comparison with the traditional probability method, it can be seen that the result calculated by the vertex solution theorem is consistent with that calculated by probability method.
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Structural Reliability Analysis based on the cokriging technique
IOP Conference Series: Materials Science and Engineering, 2010Co-Authors: Wei Zhao, Wei WangAbstract:Approximation methods are widely used in Structural Reliability Analysis because they are simple to create and provide explicit functional relationships between the responses and variables in stead of the implicit limit state function. Recently, the kriging method which is a semi-parameter interpolation technique that can be used for deterministic optimization and Structural Reliability has gained popularity. However, to fully exploit the kriging method, especially in high-dimensional problems, a large number of sample points should be generated to fill the design space and this can be very expensive and even impractical in practical engineering Analysis. Therefore, in this paper, a new method—the cokriging method, which is an extension of kriging, is proposed to calculate the Structural Reliability. cokriging approximation incorporates secondary information such as the values of the gradients of the function being approximated. This paper explores the use of the cokriging method for Structural Reliability problems by comparing it with the Kriging method based on some numerical examples. The results indicate that the cokriging procedure described in this work can generate approximation models to improve on the accuracy and efficiency for Structural Reliability problems and is a viable alternative to the kriging.
Jun Xu - One of the best experts on this subject based on the ideXlab platform.
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Structural Reliability Analysis based on polynomial chaos, Voronoi cells and dimension reduction technique
Reliability Engineering & System Safety, 2019Co-Authors: Jun Xu, Ding WangAbstract:Abstract Polynomial chaos expansions (PCEs) has been widely used to construct meta-models for Structural Reliability Analysis. The computational effort of classical PCEs is unaffordable as the required number of deterministic model analyses grows exponentially with the dimension. Alternatively, the sparse PCEs are always built to alleviate this problem. This paper proposes an efficient method, which combines the sparse PCE with a novel unequal-weighted sampling strategy, i.e. Voronoi cells and the dimension reduction technique for Structural Reliability Analysis. The unequal-weighted sampling strategy could converge fast to the ultimate goal of sequentially building a sparse PCE. Besides, when the dimension is high, the sliced inverse regression technique is employed to convert the original high-dimensional problem to a low-dimensional one. Then, a stepwise weighted regression method is involved to automatically determine the significant terms of the PCE and discard the insignificant ones for the reduced model. In this regard, the sparsity of the basis, the dimension reduction technique and the fast convergence of unequal-weighted sampling strategy lead to a considerably reduced computational cost. Four numerical examples with a large number of random variables are presented to validate the proposed method. The computational results show that the proposed method can establish fairly accurate meta-models for Structural Reliability assessment with low computational effort.
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a new bivariate dimension reduction method for efficient Structural Reliability Analysis
Mechanical Systems and Signal Processing, 2019Co-Authors: Jun Xu, Chao DangAbstract:Abstract This paper presents a new bivariate dimension reduction method (BDRM) for statistical moments evaluation and Structural Reliability Analysis with accuracy and efficiency. A high-order unscented transformation (HUT) is introduced to evaluate the two-dimensional integrals involved in BDRM, and the free parameter involved in HUT is suggested. In this regard, the proposed BDRM can be formulated accordingly for statistical moments assessment. Then, the performance function’s probability density function (PDF) is reconstructed by the shifted generalized lognormal distribution (SGLD) with the available statistical moments as constraints. Thus, the failure probability can be straightforwardly obtained by a simple integral over the PDF. The proposed method is verified by five numerical examples, including linear and non-linear, explicit and implicit performance functions. Besides, some other existing methods are also employed to demonstrate the advantages of the proposed method. It is found that the proposed method can keep the trade-off of accuracy and efficiency for Structural Reliability Analysis.
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adaptive scaled unscented transformation for highly efficient Structural Reliability Analysis by maximum entropy method
Structural Safety, 2019Co-Authors: Jun Xu, Fan KongAbstract:Abstract The approximation of the probability density function (PDF) of the performance function, especially for the tail distribution, is of paramount importance in Structural Reliability Analysis. In this paper, a new method is proposed to derive the PDF of the performance function with accuracy and high efficiency. The derivation is based on the maximum entropy method(MEM), where the fractional moments are adopted as constraints. Since the MEM dose not involve deterministic Structural Analysis, the efficiency and accuracy of the proposed method is dependent on the evaluation of fractional moments. In this regard, an adaptive scaled unscented transformation (ASUT) is developed to obtain the fractional moments with only a few of sample evaluations. The proposed ASUT is applicable to problems with correlated/uncorrelated random variables. Besides, it can circumvent the so-called “curse of dimensionality” to some extent. Thus, the proposed method could be taken as a general tool for highly efficient Structural Reliability Analysis. Numerical examples involving explicit and implicit performance functions are used to illustrate the implementation of the proposed method, which shows the great efficacy of the proposed method, particularly for a high-dimensional problem. The problems to be further investigated are also pointed out.
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A cubature collocation based sparse polynomial chaos expansion for efficient Structural Reliability Analysis
Structural Safety, 2018Co-Authors: Jun Xu, Fan KongAbstract:Abstract Polynomial chaos expansion (PCE) is widely used to build a surrogate meta-model of the performance function for Structural Reliability Analysis. The number of terms to be determined in PCE grows exponentially with the number of input random variables, which makes the computational effort intractable in practices. Although several sparse PCEs have been developed, a large number of deterministic model evaluations may be still required to achieve a satisfactory accuracy since equal-weighted collocation samples are used. To address such problems, this paper proposes a cubature collocation based sparse PCE for efficient Structural Reliability Analysis. An iterative scheme is actually involved in the proposed method, which automatically selects the significant terms in PCE contributing to the variance of the performance function. The cubature formula not only generates unequal-weighted collocation samples, which has much faster convergent rate, but also provides the target variance of the performance function to terminate the iterative process. In this regard, a weighted regression method is employed in each step to determine the coefficients of PCE. As a consequence, a rather small number of terms in PCE are retained. Since the number of cubature collocation points is relatively small, the construction of a sparse PCE is quite efficient. Several numerical examples are investigated to validate the proposed method for Structural Reliability Analysis. The results show the effectiveness of the proposed method for different Reliability problems.
