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A Comparative Study on Metamodel Based Stochastic Analysis of Composite Structures
Published in Sudip Dey, Tanmoy Mukhopadhyay, Sondipon Adhikari, Uncertainty Quantification in Laminated Composites, 2018
Sudip Dey, Tanmoy Mukhopadhyay, Sondipon Adhikari
This chapter presents a critical comparative assessment of different metamodels (such as polynomial regression, kriging, high dimensional model representation, polynomial chaos expansion, artificial neural network, moving least square, support vector regression, multivariate adaptive regression splines, radial basis function and polynomial neural network) for stochastic natural frequency analysis of composite laminates from the viewpoint of accuracy (with respect to traditional Monte Carlo simulation) and computational efficiency. First three stochastic natural frequencies of a laminated composite plate are considered for individual and combined variation of layer-wise random input parameters. A comparative investigation is presented on different design of experiment methods (such as 2k factorial designs, central composite design, A-Optimal design, I-Optimal, D-Optimal, Taguchi’s orthogonal array design, Box-Behnken design) in conjunction with the polynomial regression technique. D-optimal design is found to obtain the most satisfactory results compared to others. For each of the metamodeling techniques, the rate of convergence with respect to traditional Monte Carlo simulation has been studied considering both low and high dimensional input parameter space. Probabilistic descriptions of the natural frequencies obtained on the basis of different metamodeling techniques are presented along with direct Monte Carlo simulation results.
Analysis of Interpolation-Based Image In-Painting Approaches
Published in Rashmi Gupta, Arun Kumar Rana, Sachin Dhawan, Korhan Cengiz, Advanced Sensing in Image Processing and IoT, 2022
Mustafa Zor, Erkan Bostanci, Mehmet Serdar Güzel, Erinç Karataş
Karaca and Tunga[10], who consider image in-painting as an interpolation problem, have designed this problem using the high-dimensional model representation (HDMR) method and Lagrange interpolation, which allows a multivariate function to be expressed as the sum of multiple functions with fewer variables.
Structural damage identification of bridge using high dimensional model representation
Published in International Journal for Computational Methods in Engineering Science and Mechanics, 2021
Damage identification of tested reinforced concrete (RC) frame is carried out using sensitivity based updating method by Fang et al. [20] by utilizing a two-dimensional planar FE to model RC frame followed by minimizing the discrepancies of modal frequencies and mode shapes. By design optimization using response surface based model updating, damage can be identified by developing explicit relationships between inputs and outputs of a physical system. Improved particle swam optimization (PSO) technique has been used in damage identification by framing objective function using vibration data [31], and PSO technique is carried out by updating the FEM to predict the damage location and intensity using experimentally determined natural frequencies. However, the efficiency of the technique will be dependent on the accuracy and sensitivity of the objective function which is essentially obtained through relating the input and output. High Dimensional Model Representation (HDMR) is a particular family of representations which reflect the individual or cooperative contributions of the inputs upon the output [32, 33].
Shape optimization for blended-wing–body underwater glider using an advanced multi-surrogate-based high-dimensional model representation method
Published in Engineering Optimization, 2020
Ning Zhang, Peng Wang, Huachao Dong, Tianbo Li
Metamodelling construction is the most important phase in surrogate-based optimization methods. Well-known metamodelling techniques include the polynomial response surface method (PRS) (Box and Draper 1987), radial basis function (RBF) (Fang and Horstemeyer 2006), neural network (Papadrakakis, Lagaros, and Tsompanakis 1998), support vector regression (SVR) (Smola and Schölkopf 2004) and kriging (Cressie 1988). However, the samples increase exponentially and the established high-dimensional surrogate models are not accurate with finite samples when the dimension of the underlying problem grows. Various approaches based on surrogate model techniques have been developed to tackle these challenges (Regis and Shoemaker 2013; Regis 2014; Bouhlel et al.2019). High-dimensional model representation (HDMR) is one of the most promising techniques among these approaches. It has been proposed to solve high-dimensional expensive black-box (HEB) problems (Rabitz et al.1999; Rabitz and Aliş 1999), as introduced by Sobol (1993). There are two main types of HDMR: analysis of variance–HDMR (ANOVA-HDMR) and cut-HDMR (Rabitz et al.1999; Li, Rosenthal, and Rabitz 2001). The ANOVA-HDMR is commonly used for sensitivity analysis and identifying important variables and correlations. Differently from ANOVA-HDMR, the cut-HDMR is relatively more efficient and integral computation is completely unnecessary. Accordingly, the cut-HDMR has been widely studied to generate highly accurate approximation for HEB problems (Shan and Wang 2010, 2011; Cai et al.2016; Chen et al.2019).