Vol.:(0123456789) 1 3 Journal of the Brazilian Society of Mechanical Sciences and Engineering (2020) 42:241 https://doi.org/10.1007/s40430-020-02304-7 TECHNICAL PAPER Fuzzy clustering and AR models for damage detection in CFRP coupons considering loading efect Wagner Francisco Rezende Cano 1  · Samuel da Silva 2 Received: 13 May 2019 / Accepted: 20 March 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020 Abstract This paper proposes a strategy to avoid false alarms by distinguishing operation efects from damages efects in composite laminates. This strategy is based on active and sensing piezoelectric patches receiving Lamb waves that can be profoundly afected by operational factors such as load leading to false diagnostics. In order to overcome this drawback, this paper pro- poses an approach analyzing the use of prediction errors obtained by auto-regressive (AR) models. This index is computed using only the output signal received from sensors and combined with other traditional sensitive-damage indices. The fuzzy clustering technique is then applied for distinguishing the load efects from the efects of the damage. The method is evaluated using a carbon fber-reinforced polymer coupons subject to tension–tension fatigue and with layers of piezoelectric sensors and actuators bonded on this surface. The results revealed that fuzzy clustering using a fuzzy c-means (FCM) algorithm could distinguish these efects using one-step-ahead AR errors combined with other standard indices extracted in time and frequency domains. This strategy may be easily implemented for signal processing, making possible its online application in a real-world structure. Keywords Composite materials · Smart Structures · Lamb waves · AR models · Damage detection · Load variations · Fuzzy clustering 1 Introduction Structural health monitoring (SHM) techniques represent an essential tool in many mechanical, civil and aircraft struc- tures because of their ability to detect structural changes to prevent damage or the grown risk of failure throughout a service life [1, 2]. In the last years, SHM has become more attractive due to its potential to improve life-safety and gen- erate economic benefts [3]. Among all SHM strategies, the Lamb wave monitoring method is popular due to the excel- lent propagation and high damage sensitivity of this kind of wave besides conveniences of generation and acquisition [2]. Kessler et al. [4] performed the optimization of such methods capable of detecting many types of faws in com- posite structures, such as crack and delamination, in order to demonstrate their aptitude for SHM purposes. On the other hand, an approach that has been attracting attention for damage detection is the use of time series to perform system identifcation for a long time. The authors of the pre- sent paper in [12] already used an auto-regressive moving average with exogenous input (ARMAX) model for dam- age diagnosis based on prediction errors to assure structural changes identifcation with statistical confdence involving a smart structure composed by a beam. Park et al. [6] com- pared the performance of traditional frequency response function (FRF)-based analysis to auto-regressive models and demonstrated the latter capacity for SHM. This dem- onstrates a long time trend of the use of such models due to their simplicity and efectiveness for SHM purposes using well-known results from system identifcation and signal processing areas [7, 8]. Technical Editor: Pedro Manuel Calas Lopes Pacheco, D.Sc. * Samuel da Silva samuel.silva13@unesp.br Wagner Francisco Rezende Cano wagnerc@cpqd.com.br 1 Fundação Centro de Pesquisa e Desenvolvimento em Telecomunicações - CPqD, Rua Dr. Ricardo Benetton Martins, 1000, Campinas, SP 13086-902, Brazil 2 Departamento de Engenharia Mecânica, Faculdade de Engenharia, UNESP - Universidade Estadual Paulista, Av. Brasil 56, Ilha Solteira, SP 15385-000, Brazil