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Robust damage detection in uncertain nonlinear systems

Grant number: 15/25676-2
Support type:Scholarships in Brazil - Doctorate (Direct)
Effective date (Start): March 01, 2016
Effective date (End): December 31, 2019
Field of knowledge:Engineering - Mechanical Engineering - Mechanics of Solids
Principal researcher:Samuel da Silva
Grantee:Luis Gustavo Giacon Villani
Home Institution: Faculdade de Engenharia (FEIS). Universidade Estadual Paulista (UNESP). Campus de Ilha Solteira. Ilha Solteira , SP, Brazil
Associated research grant:12/09135-3 - Structural health monitoring in nonlinear mechanical systems through Volterra models, AP.JP
Associated scholarship(s):17/24977-4 - Experimental nonlinear damage detection in uncertain nonlinear systems, BE.EP.DD


The damage detection problem in mechanical systems through measurements of vibration is a solved problem in the literature. Numerous tools are able to detect any structural variation by changes in the vibration pattern, mainly, because damages induce nonlinear behavior. However, a more difficult problem is to detect structural variation associated with damage, when the mechanical system has nonlinear behavior without damage. In these cases, more sophisticated methods are needed to detect if the changes in the response are based on some structural variation or changes in the vibration regime, because both can generate strong nonlinearities. Among the many ways to solve this problem, the use of the Volterra series has several favorable points, because they are a generalization of the linear convolution and the contributions linear and nonlinear of the response can be separated through the Volterra kernels. However, their estimation is very uncertain, because it is based on experimental data contaminated by noise and is function of the parameters used to describe orthonormal functions to reduce difficulties related to convergence. Thus, the methods for damage detection should be robust to these uncertainties, which makes a challenger problem. This problem is not resolved in the literature and shows deficiency of new proposals and application tests. In this sense, this thesis proposes to develop and test a new algorithm able to detect variations associated with damage and separate these effects of possible nonlinear behavior, even in the presence of different kinds of uncertainties. The prediction is based on the use of Volterra series identified for stochastic manner in reference conditions (no damage) already assuming strongly nonlinear behavior. The decision whether or not to match any structural variation is estimated based on the probability density functions of sensitive indicators of structural variation, as well as robust hypothesis testing. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
YANO, MARCUS OMORI; VILLANI, LUIS G. G.; DA SILVA, SAMUEL; FIGUEIREDO, ELOI. Autoregressive model extrapolation using cubic splines for damage progression analysis. Journal of the Brazilian Society of Mechanical Sciences and Engineering, v. 43, n. 1, . (15/25676-2, 17/15512-8, 19/19684-3)
VILLANI, LUIS G. G.; DA SILVA, SAMUEL; CUNHA, JR., AMERICO. Damage detection in uncertain nonlinear systems based on stochastic Volterra series. MECHANICAL SYSTEMS AND SIGNAL PROCESSING, v. 125, p. 288-310, . (12/09135-3, 15/25676-2)
VILLANI, LUIS G. G.; DA SILVA, SAMUEL; CUNHA JR, AMERICO; TODD, MICHAEL D.. Damage detection in an uncertain nonlinear beam based on stochastic Volterra series: An experimental application. MECHANICAL SYSTEMS AND SIGNAL PROCESSING, v. 128, p. 463-478, . (15/25676-2, 17/15512-8, 12/09135-3, 17/24977-4)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
VILLANI, Luis Gustavo Giacon. Robust damage detection in uncertain nonlinear systems. 2019. Doctoral Thesis - Universidade Estadual Paulista (Unesp). Faculdade de Engenharia. Ilha Solteira Ilha Solteira.

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