Implementation and Performance Evaluation of a Bivariate Cut-HDMR Metamodel for Semiconductor Packaging Design Problems with a Large Number of Input Variables

Yu-Hsiang Yang; Hsiu-Ping Wei; Bongtae Han; Chao Hu

doi:10.3390/ma14164619

Implementation and Performance Evaluation of a Bivariate Cut-HDMR Metamodel for Semiconductor Packaging Design Problems with a Large Number of Input Variables

Materials (Basel). 2021 Aug 17;14(16):4619. doi: 10.3390/ma14164619.

Authors

Yu-Hsiang Yang¹, Hsiu-Ping Wei¹, Bongtae Han¹, Chao Hu²

Affiliations

¹ Mechanical Engineering Department, University of Maryland, College Park, MD 20742, USA.
² Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA.

Abstract

A metamodeling technique based on Bivariate Cut High Dimensional Model Representation (Bivariate Cut HDMR) is implemented for a semiconductor packaging design problem with 10 design variables. Bivariate Cut-HDMR constructs a metamodel by considering only up to second-order interactions. The implementation uses three uniformly distributed sample points (s = 3) with quadratic spline interpolation to construct the component functions of Bivariate Cut-HDMR, which can be used to make a direct comparison with a metamodel based on Central Composite Design (CCD). The performance of Bivariate Cut-HDMR is evaluated by two well-known error metrics: R-squared and Relative Average Absolute Error (RAAE). The results are compared with the performance of CCD. Bivariate Cut HDMR does not compromise the accuracy compared to CCD, although the former uses only one-fifth of sample points (201 sample points) required by the latter (1045 sample points). The sampling schemes and the predictions of cut-planes and boundary-planes are discussed to explain possible reasons for the outstanding performance of Bivariate Cut HDMR.

Keywords: R-squared; bivariate cut-HDMR; central composite design; relative average absolute error; semiconductor packaging.