Optimization-Based Network Identification for Thermal Transient Measurements

Nils J Ziegeler,Peter W Nolte,Stefan Schweizer

doi:10.3390/en14227648

Abstract

Network identification by deconvolution is a proven method for determining the thermal structure function of a given device. The method allows to derive the thermal capacitances as well as the resistances of a one-dimensional thermal path from the thermal step response of the device. However, the results of this method are significantly affected by noise in the measured data, which is unavoidable to a certain extent. In this paper, a post-processing procedure for network identification from thermal transient measurements is presented. This so-called optimization-based network identification provides a much more accurate and robust result compared to approaches using Fourier or Bayesian deconvolution in combination with Foster-to-Cauer transformation. The thermal structure function obtained from network identification by deconvolution is improved by repeatedly solving the inverse problem in a multi-dimensional optimization process. The result is a non-diverging thermal structure function, which agrees well with the measured thermal impedance. In addition, the associated time constant spectrum can be calculated very accurately. This work shows the potential of inverse optimization approaches for network identification.

Highlights

IntroductionA system is exposed to a change in heating or cooling power and the response of the system, i.e. the resulting temperature change, is monitored
In thermal response measurements, a system is exposed to a change in heating or cooling power and the response of the system, i.e. the resulting temperature change, is monitored
The precise computation time of an optimization-based network identification depends on the trajectory the solver takes in parameter space, which is mainly affected by the quality of the initial values and the noise level

Summary

Introduction

A system is exposed to a change in heating or cooling power and the response of the system, i.e. the resulting temperature change, is monitored. The impulse response or the step response is measured with the goal to reconstruct the relevant thermal properties of the system. For the one-dimensional case, this corresponds to the construction of an equivalent Cauer network with known resistances and capacitances. One method to achieve this is known as the “network identification by deconvolution” method [1]. The method is regularly used as an analysis tool for transient thermal analysis [2,3,4]. The methodology itself is subject to intense discussions [5,6,7,8]

Methods

Results

Conclusion