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Journal ArticleDOI

Sequential Stochastic Response Surface Method Using Moving Least Squares-Based Sparse Grid Scheme for Efficient Reliability Analysis

13 Nov 2017-International Journal of Computational Methods (World Scientific Publishing Company)-Vol. 16, Iss: 05, pp 1840017
TL;DR: In this article, an efficient method for reliability analysis using sequential development of the stochastic response surface is presented. But the method is not suitable for the case of nonlinear finite element analysis of plates.
Abstract: The present work demonstrates an efficient method for reliability analysis using sequential development of the stochastic response surface. Here, orthogonal Hermite polynomials are used whose unknown coefficients are evaluated using moving least square technique. To do so, collocation points in the conventional stochastic response surface method (SRSM) are replaced by the sparse grid scheme so as to reduce the number of function evaluations. Moreover, the domain is populated sequentially by the sparse grid based on the outcome of the optimization to find out the most probable failure point. Hence, the support points are generated based on a coupled effect of the optimization for failure region and the sub-grids hierarchy. Continuous and differentiable penalty function is imposed to determine multiple failure points, if any, by repeating the optimization. Once the response surface is developed, reliability analysis is carried out using importance sampling. Five different benchmark examples are presented in this study to validate the performance of the proposed modeling. As the accuracy of the method is established, two reliability-based design examples involving nonlinear finite element (FE) analysis of plates are demonstrated. Numerical study shows the efficiency of the proposed sequential SRSM in terms of accuracy and number of time-exhaustive evaluation of the original performance function, as compared to other methods available in the literature. Based on these results, it may be concluded that the proposed method works satisfactorily for a large class of reliability-based design problems.
Citations
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Journal ArticleDOI
TL;DR: It is shown that the reliability-based design optimization method can not only satisfy the reliability constraints of the lattice boom, but also ensure the safety and economy of crawler crane boom as well as minimize the structure weight.

9 citations

Journal ArticleDOI
TL;DR: This paper presents the state-of-the-art on different moving least square (MLS) based dimension decomposition schemes for reliability analysis and demonstrates a modified version for high fidelity analysis.
Abstract: This paper presents the state-of-the-art on different moving least square (MLS)-based dimension decomposition schemes for reliability analysis and demonstrates a modified version for high fidelity

7 citations

Journal Article
TL;DR: This study demonstrates the necessity of the design of experiment schemes for the Physics-Informed Neural Network (PINN), which belongs to the supervised learning class, and sees that the Hammersley sampling-based PINN performs better than other DoE sample strategies.
Abstract: This paper presents a comprehensive review of the design of experiments used in the surrogate models. In particular, this study demonstrates the necessity of the design of experiment schemes for the Physics-Informed Neural Network (PINN), which belongs to the supervised learning class. Many complex partial differential equations (PDEs) do not have any analytical solution; only numerical methods are used to solve the equations, which is computationally expensive. In recent decades, PINN has gained popularity as a replacement for numerical methods to reduce the computational budget. PINN uses physical information in the form of differential equations to enhance the performance of the neural networks. Though it works efficiently, the choice of the design of experiment scheme is important as the accuracy of the predicted responses using PINN depends on the training data. In this study, five different PDEs are used for numerical purposes, i.e., viscous Burger’s equation, Shrödinger equation, heat equation, Allen-Cahn equation, and Korteweg-de Vries equation. A comparative study is performed to establish the necessity of the selection of a DoE scheme. It is seen that the Hammersley sampling-based PINN performs better than other DoE sample strategies.

7 citations

Journal ArticleDOI
TL;DR: In this paper, a hybrid dimension adaptive model representation (hdA-HDMR) is proposed for stochastic finite element analysis of laminated composite plate whose material properties are considered as homogeneous non-normal random fields.

3 citations

Journal ArticleDOI
TL;DR: The improvement of PFR method can solve the RBDO problem with unfixed constraint boundary and has better adaptability, and three applications, a nonlinear mathematical problem, a highly non linear mathematical problem and an engineering design problem, are presented to illustrate the accuracy of the improvement.
Abstract: The decoupled methods for reliability-based design optimization (RBDO) problems are efficient and accurate. Sequential optimization and reliability analysis (SORA) method and probabilistic feasible...

3 citations

References
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Book
20 Dec 1990
TL;DR: In this article, a representation of stochastic processes and response statistics are represented by finite element method and response representation, respectively, and numerical examples are provided for each of them.
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TL;DR: The use of composite materials in engineering structures continues to increase dramatically, and there have been significant advances in modeling for general and composite materials and structures in particular as discussed by the authors. But the use of composites is not limited to the aerospace domain.
Abstract: The use of composite materials in engineering structures continues to increase dramatically, and there have been equally significant advances in modeling for general and composite materials and structures in particular. To reflect these developments, renowned author, educator, and researcher J.N. Reddy created an enhanced second edit

5,301 citations

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1,412 citations

Journal ArticleDOI
TL;DR: In this paper, a method for numerical integration of a well-behaved function over a finite range of argument is described, which consists essentially of expanding the integrand in a series of Chebyshev polynomials, and integrating this series term by term.
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919 citations