Surrogate modeling for efficient analysis and design of engineering systems
Date
2021
Authors
Li, Min, author
Jia, Gaofeng, advisor
Ellingwood, Bruce, committee member
van de Lindt, John, committee member
Gao, Xinfeng, committee member
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Abstract
Surrogate models, trained using a data-driven approach, have been extensively used to approximate the input/output relationship for expensive high-fidelity models (e.g., large-scale physical experiments and high-resolution computationally expensive numerical simulations). The computational efficiency of surrogate models is greatly increased compared with the high-fidelity models. Once trained, the original high-fidelity models can be replaced by the surrogate models to facilitate efficient subsequent analysis and design of engineering systems. The quality of surrogate based analysis and design of engineering systems relies largely on the prediction accuracy of the constructed surrogate model. To ensure the prediction accuracy, the training data should be adequate in terms of the size of the training data and their sampling. Unfortunately, constrained by limited computational budgets, typically it is challenging to obtain a lot of training data by running high-fidelity models. Furthermore, significant challenge arises in obtaining sufficient training data for problems with high-dimensional model inputs due to the well-known curse of dimensionality. In order to build surrogate models with high prediction accuracy and generalization performance while using as less computational resources as possible, this dissertation proposes several advanced strategies and examines their performances within several practical engineering applications. The fundamental idea of the proposed strategies is to embed extra knowledge about the high-fidelity models in the surrogate model by enriching the training data (e.g., leverage additional low-fidelity data, or censored/bounded data) and enhancing model assumption (e.g., explicitly incorporate prior knowledge about the physics of the problem, or explore low-dimensional latent structures/features), which reduces the required size of high-fidelity training data and meanwhile effectively boosts the prediction accuracy of the established surrogate model. Among different surrogate models, Gaussian process models have been gaining popularity due to its flexibility in modeling complex functions and ability to provide closed-form predictive distributions. Therefore, the strategies are developed in the context of Gaussian process model, but the ideas are expected to be applicable to other types of surrogate models. In particular, this dissertation (i) develops a physics-constrained Gaussian process model to efficiently incorporate our prior knowledge about physical constraints/characteristics of the input/output relationship by designing specific kernels, (ii) proposes a general multi-fidelity Gaussian process model capable of integrating training data with different level of accuracy (i.e., both high-fidelity data and low-fidelity data) and completeness (i.e., both accurate data and censored data), and (iii) develops an efficient surrogate modeling approach for problems with high-dimensional binary model inputs by integrating dimension reduction technique and Gaussian process model, and investigates its application in design optimization problems. The excellent performance of the proposed strategies are then validated through analysis and design of several different engineering systems, including (i) calculating hydrodynamic characteristics of wave energy converters (WECs) in an array, (ii) predicting the deformation capacity of reinforced concrete columns under cyclic loading, and (iii) optimizing topology of periodic structures.
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Subject
Gaussian process model
optimization
surrogate model
multi-fidelity
dimension reduction
physics-constrained