Surrogate-based modeling and dimension reduction techniques for multi-scale mechanics problems

Abstract

Successful modeling and/or design of engineering systems often requires one to address the impact of multiple "design variables" on the prescribed outcome. There are often multiple, competing objectives based on which we assess the outcome of optimization. Since accurate, high fidelity models are typically time consuming and computationally expensive, comprehensive evaluations can be conducted only if an efficient framework is available. Furthermore, informed decisions of the model/hardware's overall performance rely on an adequate understanding of the global, not local, sensitivity of the individual design variables on the objectives. The surrogate-based approach, which involves approximating the objectives as continuous functions of design variables from limited data, offers a rational framework to reduce the number of important input variables, i.e., the dimension of a design or modeling space. In this paper, we review the fundamental issues that arise in surrogate-based analysis and optimization, highlighting concepts, methods, techniques, as well as modeling implications for mechanics problems. To aid the discussions of the issues involved, we summarize recent efforts in investigating cryogenic cavitating flows, active flow control based on dielectric barrier discharge concepts, and lithium (Li)-ion batteries. It is also stressed that many multi-scale mechanics problems can naturally benefit from the surrogate approach for "scale bridging."

Optimization of a Single Lithium-Ion Battery Cell with a Gradient-Based Algorithm

“…A Pareto front contains solutions that are not dominated by any other points in the design space, i.e. the solutions on the Pareto front have the best objective functions at their respective constraints [46,47]. It offers valuable insight into multi-objective optimization in numerous applications [46,48].…”

“…the solutions on the Pareto front have the best objective functions at their respective constraints [46,47]. It offers valuable insight into multi-objective optimization in numerous applications [46,48]. In this case the Pareto front is formed from the set of points with the maximum achievable cell energy capacity for each required power level.…”

Value-driven design and sensitivity analysis of hybrid energy systems using surrogate modeling

“…Surrogate models are constructed from the results of a predetermined set of simulations designed to sample the parameter space (design of experiments or DOE), and have been previously utilized to study a variety of engineering problems [3,4]. An important advantage of the surrogate modeling approach is a significant reduction in simulation time compared to the original model, since most classes of surrogate models are analytically defined.…”

A Systematic Optimization Design Method for Complex Mechatronic Products Design and Development

“…Li et al [25] presented a new meta-model-based global optimization method using fuzzy clustering for design space reduction. Forrester and Keane [26] reviewed the work on constructing surrogate models and their use in optimization strategies, while Shyy et al [27] reviewed the fundamental issues arising in surrogate-based analysis and optimization. Zhang et al [28] presented a new method to identify the key design variables based on the sensitivity analysis for high-speed train design.…”

“…[27,32] Back-propagation neural network (BPN) is one of these effective surrogate models, and its structure is shown in Figure 4. The design performances of a complex product are considered at the same time with different performance indexes.…”