Rajib Adhikari - Academia.edu (original) (raw)
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Indian Institute of Engineering Science and Technology, Shibpur
University of Oxford
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Papers by Rajib Adhikari
Applied Mathematical Modelling, 2010
This paper presents a generic high dimensional model representation (HDMR) method for approximati... more This paper presents a generic high dimensional model representation (HDMR) method for approximating the system response in terms of functions of lower dimensions. The proposed approach, which has been previously applied for problems dealing only with random variables, is extended in this paper for problems in which physical properties exhibit spatial random variation and may be modelled as random fields. The formulation of the extended HDMR is similar to the spectral stochastic finite element method in the sense that both of them utilize Karhunen-Loève expansion to represent the input, and lowerorder expansion to represent the output. The method involves lower dimensional HDMR approximation of the system response, response surface generation of HDMR component functions, and Monte Carlo simulation. Each of the low order terms in HDMR is sub-dimensional, but they are not necessarily translating to low degree polynomials. It is an efficient formulation of the system response, if higher-order variable correlations are weak, allowing the physical model to be captured by the first few lower-order terms. Once the approximate form of the system response is defined, the failure probability can be obtained by statistical simulation. The proposed approach decouples the finite element computations and stochastic computations, and consecutively the finite element code can be treated as a black box, as in the case of a commercial software. Numerical examples are used to illustrate the features of the extended HDMR and to compare its performance with full scale simulation.
Engineering Computations, 2010
Purpose���High-dimensional model representation (HDMR) is a general set of quantitative model ass... more Purpose���High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. It is an efficient formulation of the system response, if higher-order cooperative effects are weak, allowing the physical model to be captured by the lower-order terms. The paper's aim is to develop a new computational tool for estimating probabilistic sensitivity of structural/mechanical systems subject to random ...
Applied Mathematical Modelling, 2010
This paper presents a generic high dimensional model representation (HDMR) method for approximati... more This paper presents a generic high dimensional model representation (HDMR) method for approximating the system response in terms of functions of lower dimensions. The proposed approach, which has been previously applied for problems dealing only with random variables, is extended in this paper for problems in which physical properties exhibit spatial random variation and may be modelled as random fields. The formulation of the extended HDMR is similar to the spectral stochastic finite element method in the sense that both of them utilize Karhunen-Loève expansion to represent the input, and lowerorder expansion to represent the output. The method involves lower dimensional HDMR approximation of the system response, response surface generation of HDMR component functions, and Monte Carlo simulation. Each of the low order terms in HDMR is sub-dimensional, but they are not necessarily translating to low degree polynomials. It is an efficient formulation of the system response, if higher-order variable correlations are weak, allowing the physical model to be captured by the first few lower-order terms. Once the approximate form of the system response is defined, the failure probability can be obtained by statistical simulation. The proposed approach decouples the finite element computations and stochastic computations, and consecutively the finite element code can be treated as a black box, as in the case of a commercial software. Numerical examples are used to illustrate the features of the extended HDMR and to compare its performance with full scale simulation.
Engineering Computations, 2010
Purpose���High-dimensional model representation (HDMR) is a general set of quantitative model ass... more Purpose���High-dimensional model representation (HDMR) is a general set of quantitative model assessment and analysis tools for capturing the high-dimensional relationships between sets of input and output model variables. It is an efficient formulation of the system response, if higher-order cooperative effects are weak, allowing the physical model to be captured by the lower-order terms. The paper's aim is to develop a new computational tool for estimating probabilistic sensitivity of structural/mechanical systems subject to random ...