Regularization for the inversion of fibre Bragg grating spectra. Issue 13 (23rd December 2021)

• Record Type: Journal Article
• Authors: Gerth, Daniel; Hannusch, Susann; Ernst, Oliver G.; Ihlemann, Jörn
• Is Part Of: Inverse problems in science and engineering. Volume 29:Issue 13(2021)
• Page Start: 2629
• Page End: 2655
• Publication Date: 2021-12-23
• Subjects: Fibre Bragg grating -- regularization -- Tikhonov regularization -- strain sensor -- nonlinear inverse problem; 65Z05; Engineering mathematics -- Periodicals; Inverse problems (Differential equations) -- Periodicals; 620.001515357
• DOI: 10.1080/17415977.2021.1943383
• Languages: English
• ISSNs: 1741-5977

Abstract

Abstract : Fibre Bragg Gratings have become widespread measurement devices in engineering and other fields of application. In all but a few cases, the relation between cause and effect is simplified to a proportional model. However, at its mathematical core lies a nonlinear inverse problem which appears not to have received much attention in the literature. In this paper, we present this core problem to the mathematical community and provide a first report on opportunities and limitations of a regularization approach. In particular, we show that difficulties arise from non-uniqueness and the absence of established parameter selection rules for nonlinear inverse problems with multiple regularization parameters. Nevertheless, the paper takes a first step toward extracting more information from a single FBG measurement.