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Stochastic Dynamic Analysis of Doubly Curved Composite Shells
Published in Sudip Dey, Tanmoy Mukhopadhyay, Sondipon Adhikari, Uncertainty Quantification in Laminated Composites, 2018
Sudip Dey, Tanmoy Mukhopadhyay, Sondipon Adhikari
In the surrogate based approach of uncertainty quantification, a virtual mathematical model is formed for the response quantity of interest that effectively replaces the actual expensive finite element model. The surrogate model is built up on the basis of information acquired regarding the behavior of the response quantity throughout the entire design space utilizing few algorithmically chosen design points. Besides the source-uncertainties due to stochastic nature of material and geometric attributes, there remains another inevitable source for second phase of uncertainty associated with the information acquired through the design points that needs further attention (refer to Fig. 5.4). In the present chapter, this second source of uncertainty associated with the surrogate model formation has been addressed by developing an algorithm to account it in the form of random noise (Mukhopadhyay et al. 2016a). The effect of such simulated noise can be regarded as considering other sources of uncertainty besides conventional material and geometric uncertainties, such as error in measurement of responses, error in modelling and computer simulation and various other epistemic uncertainties involved with the system. Noise effects are found to be accounted in several other studies in available literature (Nejad et al. 2005, Friswell et al. 2015, Mukhopadhyay 2018a) dealing with deterministic analysis. In the present chapter an algorithm has been presented to quantify the effect of noise for Kriging based stochastic analysis of doubly curved composite shells.
Dimension reduction and surrogate based approach for optimal seismic risk mitigation of large-scale transportation network
Published in Hiroshi Yokota, Dan M. Frangopol, Bridge Maintenance, Safety, Management, Life-Cycle Sustainability and Innovations, 2021
The idea of surrogate model is to establish a simple mathematical relationship between the inputs and outputs based on a database of input-output results. Since it is a mathematical model, surrogate model is very efficient when used for prediction (Jia & Taflanidis 2013). In terms of surrogate model, we use the kriging surrogate model, which is known as the Best Linear Unbiased Predictor (BLUP). More importantly, it not only gives the prediction but also the associated uncertainty, namely the local variance of the prediction error (Jia & Taflanidis 2013), which can be used to guide adaptive design of experiments to iteratively improve the accuracy of the surrogate model and facilitate effective optimization within the context of EGO.
Shape optimization of closed-box girder considering dynamic and aerodynamic effects on flutter: a CFD-enabled and Kriging surrogate-based strategy
Published in Engineering Applications of Computational Fluid Mechanics, 2023
Jie Zheng, Genshen Fang, Zilong Wang, Lin Zhao, Yaojun Ge
The accuracy of the first generation of the surrogate model is usually inadequate due to insufficient samples or nonlinearity of the problem. To further increase the accuracy, surrogate model is usually updated by introducing more samples. The hybrid infill sampling criteria, including the expected improvement (EI), probability of improvement (PI), minimize prediction (MP) and root mean square error (RMSE) are employed. The EI criterion accounts for the effects of the predicted value of the function and the error of the prediction achieved by the Kriging model. The EI value of the Kriging model at any unknown point x can be formulated as: where (·) and (·) indicate the CDF and PDF of the standard normal distribution, respectively. ymax is the maximum value in the known samples.
An optimisation method for anti-blast performance of corrugated sandwich plate structure based on neural network and sparrow search algorithm
Published in Ships and Offshore Structures, 2023
Wei-Jian Qiu, Kun Liu, Shuai Zong, Tong-qiang Yu, Jia-xia Wang, Zhen-guo Gao
Surrogate model is a kind of model using known parameters to predict unknown responses, which can simulate the original model with high precision. Combining the surrogate model with the intelligent optimisation algorithm can significantly reduce the optimisation efficiency. The commonly used surrogate models include response surface model (RSM), Kriging model, radial basis function (RBF) and BP neural network, and these surrogate models have been applied in the design of sandwich plates (Karsh et al. 2022; Mao et al. 2022; Wei et al. 2022; Peng et al. 2023). Based on the finite element simulation samples, Lim et al. (2013) developed a surrogate model using the Kriging model to quickly calculate the blast resistance of hybrid sandwich plates in design optimisation. Qi et al. (2013) studied the multi-objective design optimisation of aluminium foam core sandwich plate, in which the artificial neural network is used to approximate the blast load. Chen et al. (2019) combined the adaptive RSM with a multi-objective genetic algorithm to study the dynamic response and design optimisation of sandwich plates with layered gradient. These studies show that the surrogate model can effectively replace the finite element calculation in the optimisation process and perform well in the optimisation of structural blast resistance. However, for various surrogate models, improvement of accuracy sometimes is still necessary(Chu et al. 2020; Zhang et al. 2020), which is one of the focuses in this study as well.
Gaussian Process Assisted Active Learning of Physical Laws
Published in Technometrics, 2021
Jiuhai Chen, Lulu Kang, Guang Lin
Alternatively, we can build a surrogate model of based on the current available observations for , where n is the currently available sample size. The surrogate model is an empirical statistical model that is often used to analyze the outputs from computer experiments or simulations, in which the functional relationship between the input variables and outputs is complex and highly nonlinear. For example, many computer experiments are run through complex numerical PDE solvers. Among all statistical modeling methods, GP regression, also known as kriging, has been widely used for computer experiments (Santner et al. 2003) for several reasons. First, due to the mathematical simplicity of the GP assumption, it is relatively easy to obtain the prediction and statistical inference. Second, the GP predictor with nugget effect (or the posterior mean if Bayesian framework is used) is identical to the kernel ridge regression based on reproducing kernel Hilbert space (RKHS) (Kanagawa et al. 2018). Therefore, the GP regression possesses the same theoretical properties of RKHS regression which provides a clear analysis of the approximation error (Wendland 2004).