An approximate optimization strategy using refined hybrid metamodel

Abstract

An approximate model called metamodel or surrogate model is a mathematical model that numerically approximates response of a system during an engineering simulation process or test. The introduction of a metamodel makes it possible to express response defined in the design problem as a simple mathematical function of design variables. A metamodel can be built with response surface method (RSM), kriging, neural network, radial basis function, and so on. Each method has its advantages and disadvantages. A combined metamodel called hybrid model, ensemble model, or multiple surrogates has been developed to maximize each metamodel's strength. The hybrid model of this research includes RSM and kriging. Besides, a strategy to refine the hybrid metamodel is implemented by reducing design space. In this process, information related to Hessian is utilized for an unconstrained optimization problem, on the contrary feasibility for a constrained optimization problem. This research presents a new hybrid metamodel‐based optimization strategy called refined hybrid metamodel. Five mathematical test problems, two‐bar design, spring design, and propeller shaft design problems are solved with the suggested method, verifying its usefulness. Most of the optimal results with the proposed method are closer to exact solutions with smaller function evaluations than existing methods.

Structural analysis and optimization of an automotive propeller shaft

“…In this study, y(x) can be weight, first natural frequency, or fatigue life. [13][14][15][16][17] If d y(x) is designated as the approximation model, and the mean squared errors of y(x) and d y(x) are minimized to satisfy the unbiased condition, y(x) can be estimated as…”

“…Kriging is an interpolation method named after a South African mining engineer named D. G. Krige, who developed the technique while increasing the accuracy in predicting ore reserves. [13][14][15][16][17] Kriging interpolation for an approximate model is well documented in the references. In general, a response function, y(x), is represented as…”

“…When the correlation parameters are determined, an approximated model can be constructed. Similarly to previous estimators, the unknown correlation parameters of u 1 , u 2 ,., u n are calculated from the formulation as follows [13][14][15][16][17] :…”

“…The design variables are the thicknesses and lengths of the tubes, so this corresponds to the shape optimization category that is very difficult to perform optimization. The optimization technique applied in this process is the metamodelbased optimization method [13][14][15][16][17] called the kriging interpolation method. The weight of the proposed optimal solution was reduced by 5.3% to the total weight of the propeller shaft and 14.1% when considering the tube alone.…”

Multiobjective optimization on adhesive bonding of aluminum‐carbon fiber laminate

“…35 ANOVA method is used to simplify the model keeping only the significant variables, with a significance value of 0.05. 36,37 3. The surrogate models for each objective function together with the operation constraints (4), (5), and (6) form the multi-objective optimization model for the problem.…”