Reducing numerical work in non-linear parameter identification

TL;DR

This paper introduces a hierarchical minimization method that reduces computational effort in non-linear parameter identification by constructing a noise-free follower merit function and skipping local minima caused by noise.

Contribution

It proposes a novel hierarchical minimization approach based on an implicit projection map to efficiently handle complex merit functions in parameter identification.

Findings

The method effectively skips noise-induced local minima.

It simplifies the minimization process in high-dimensional parameter spaces.

The approach is applicable to sensitivity analysis and reliability testing.

Abstract

The real-life merit functions have an unimaginable complexity of an M-dimensional topography, where M is the number of the parameters. It is shown that there is an underlying noise-free merit function, called follower merit function which can be constructed from simulated, noise-free data using the solution of a Least Squares minimization. The difference of these is controlled by the norm of the error vector. The local minima arisen from the noise can be skipped during such minimization that apply adjustable, large step sizes, depending on the norm of the error vector. The suggested hierarchical minimisation - based on the implicit function of a projection map - makes the minimisation in two steps. In the first step some parameters are eliminated with conditional minimisation, resulting in a kind of deepest section of the merit function, called clever section with respect to the remainder parameters. Then the clever section is minimized. The method can be used to handle a quasi-degenerate global minimum, in sensitivity analyses, reliability testing.