Use of Hybrid Surrogate in Sampling Process for Design and Analysis of Computer Experiments (DACE) applied on Multivariable Problems

Abstract

This work focuses on the improvement of Kriging in Design and Analysis of Computer Experiments (DACE) for multivariable problems through a specific sampling process that couples two methods already known in the literature: Adaptive Kriging and Genetic Algorithm. The special integration of these methods to enhance the sampling process is the main contribution of this dissertation. This procedure optimizes the sampling process of the metamodel finding specific location in the design space with relative few samples, which brings higher fidelity and better performance than conventional methods based on pure Conventional Kriging. Mean squared error (MSE) in Adaptive Kriging and its coupling with MSE derivative (dMSE) in objective functions of Genetic Algorithm are the metric used for sampling improvement. A dedicated random mesh is implemented in the design space covering all variables of the problem. The Adaptive Kriging works as a first contribution for sampling improvement, which is followed by the Genetic Algorithm based on the NSGAII code. The Genetic operations are used to exploit such mesh in order to identify specific locations with high potential for enhancement of metamodel fidelity with relative low quantity of sample points. All of these steps configure the proposed method called Hybrid Code that couples the Adaptive Kriging with Genetic Algorithm.

Three analytical problems are considered for Hybrid Code validation: Branin function and Product Peak Integrand Family function for two and ten variables. Once the validation is performed, the hybrid code is used to solve two numerical representative problems of FEM engineering applications: cantilever beam and underwater explosion effect on a submerged stiffened plate clamped at its edges. In each case, different commercial FEM code have been used: ANSYS for the former and ABAQUS for the latter. In the cantilever beam problem, the output analyzed for each individual sample point are the equivalent stress at the clamp location and vertical displacement at the free end of the beam. This problem contains ten variables defined as thickness of each section of the beam. For the underwater explosion problem by its turn, the output analyzed is the vertical displacement at the middle of the plate. This problem has six variables defined as the thickness of each structural element of the plate, such as planking, bar, flange, etc.

In all analyses, the metamodel performance obtained by the proposed method is compared with the one obtained from Conventional Kriging. The performance measurement parameters are based on non-dimensional error in comparison to the known response and the computational time required. The conclusion based on the results collected is that the Hybrid Code generates a higher fidelity metamodel in a faster manner than the Conventional Kriging for high-dimensional and/or more complex problems.