The quadratic dimensional reduction method for parameter identification

Abstract

This paper presents the Quadratic Dimensional Reduction Method (QDRM) for parameter identification. The QDRM involves a quadratic adaptation to the existing, linear Dimensional Reduction Method (DRM). Gradient descent methods can halt prematurely when curvature of the objective surface is low near the optimal parameter choices. The QDRM identifies curved hyper-surfaces that capture the domain where premature gradient descent convergence occurs. Parameter identification is then restricted to those surfaces allowing continued convergence. The performance of the novel QDRM and existing DRM is compared across two models. A theoretical model was used with exaggerated curvature in the objective surfaces in order to test the optimality of the QDRM. Second, a thermal model representing a typical first order ‘real-world’ case was solved using the DRM and QDRM. The QDRM out-performed the DRM in all cases tested with improved performance most prominent in problems subject to minimal noise as well as in problems whose objective surface exhibits more pronounced curvature. Thus, the QDRM extends the set of problems over which the DRM framework is applicable and effective.