Solution of the LIMM equation by the polynomial regularization method and the L-curve algorithm for selection of the regularization parameter

Sidney B. Lang, Robert Fleming, Tadeusz Pawlowski

Research output: Contribution to journalConference articlepeer-review

Abstract

The determination of the polarization distribution by means of the Laser Intensity Modulation Method (LIMM) requires a solution of a Fredholm integral equation of the 1st kind. This is an ill-conditioned problem that can lead to multiple and very different solutions. One of the more frequently used methods of solution is based upon Tikhonov regularization. Previously, a new regularization method was developed for solving the LIMM equation with an 8th degree polynomial using smoothing to achieve a stable and optimal solution. This was named the Polynomial Regularization Method (PRM). In the current study, several simulated polarization distributions for polyvinylidene fluoride (PVDF) were selected. LIMM current versus frequency data were simulated using these distributions and Gaussian noise was added so as to emulate experimental data. The LIMM equation was solved using PRM. An algorithm based upon the L-curve method (LCM) was developed for the prediction of the optimal regularization parameter. Calculated distribution functions using PRM and LCM were in good agreement with the simulated polarization distributions.

Original languageEnglish
Pages (from-to)198-201
Number of pages4
JournalAnnual Report - Conference on Electrical Insulation and Dielectric Phenomena, CEIDP
StatePublished - 1 Dec 2004
Event2004 Annual Report - Conference on Electrical Insulation and Dielectric Phenomena, CEIDP - Boulder, CO, United States
Duration: 17 Oct 200420 Oct 2004

ASJC Scopus subject areas

  • General Engineering

Fingerprint

Dive into the research topics of 'Solution of the LIMM equation by the polynomial regularization method and the L-curve algorithm for selection of the regularization parameter'. Together they form a unique fingerprint.

Cite this