Damage Location in Mechanical Structures by Multi-Objective Pattern Search

authored by: Christian Günther, Benedikt Hofmeister, Clemens Hübler, Clemens Jonscher, Jasper Ragnitz, Jenny Schubert, Marc C. Steinbach
Abstract: We propose a multi-objective global pattern search algorithm for the task of locating and quantifying damage in flexible mechanical structures. This is achieved by identifying eigenfrequencies and eigenmodes from measurements and matching them against the results of a finite element simulation model, which leads to a nonsmooth nonlinear bi-objective parameter estimation problem. A derivative-free optimization algorithm is required since the problem is nonsmooth and also because complex mechanical simulation models are often solved using commercial black-box software. Moreover, the entire set of non-dominated solutions is of interest to practitioners. Most solution approaches published to date are based on meta-heuristics such as genetic algorithms. The proposed multi-objective pattern-search algorithm provides a mathematically well-founded alternative. It features a novel sorting procedure that reduces the complexity in our context. Test runs on two experimental structures with multiple damage scenarios are used to validate the approach. The results demonstrate that the proposed algorithm yields accurate damage locations and requires moderate computational resources. From the engineer's perspective it represents a promising tool for structural health monitoring.
Organisation(s): Institute of Applied Mathematics
Institute of Structural Analysis
Type: Preprint
Publication date: 02.04.2024
Publication status: E-pub ahead of print

BibTeX

@techreport{7eb3e1a0088142e49afe0aacfd9f7360,
title = "Damage Location in Mechanical Structures by Multi-Objective Pattern Search",
abstract = "We propose a multi-objective global pattern search algorithm for the task of locating and quantifying damage in flexible mechanical structures. This is achieved by identifying eigenfrequencies and eigenmodes from measurements and matching them against the results of a finite element simulation model, which leads to a nonsmooth nonlinear bi-objective parameter estimation problem. A derivative-free optimization algorithm is required since the problem is nonsmooth and also because complex mechanical simulation models are often solved using commercial black-box software. Moreover, the entire set of non-dominated solutions is of interest to practitioners. Most solution approaches published to date are based on meta-heuristics such as genetic algorithms. The proposed multi-objective pattern-search algorithm provides a mathematically well-founded alternative. It features a novel sorting procedure that reduces the complexity in our context. Test runs on two experimental structures with multiple damage scenarios are used to validate the approach. The results demonstrate that the proposed algorithm yields accurate damage locations and requires moderate computational resources. From the engineer's perspective it represents a promising tool for structural health monitoring.",
keywords = "math.OC, 70J10, 74R99, 90C26, 90C29, 90C59",
author = "Christian G{\"u}nther and Benedikt Hofmeister and Clemens H{\"u}bler and Clemens Jonscher and Jasper Ragnitz and Jenny Schubert and Steinbach, {Marc C.}",
year = "2024",
month = apr,
day = "2",
language = "English",
type = "WorkingPaper",
}