Non-probabilistic method to consider uncertainties in frequency response function for vibration-based damage detection using Artificial Neural Network

Abstract Artificial neural network (ANN) has become a popular computational approach in the field of vibration-based damage detection, based on its ability to relate the nonlinear relationship between structural vibration characteristics and damage information. In the meantime, frequency response function (FRF) estimation has been proven effective as a dynamic parameter for damage detection due to its prevention of information leakage. In this regard, FRF is chosen as the input variable for ANN to detect structural damage in this study. However, the main concern in damage detection using FRF with ANN is the size of FRF data. A full-size FRF data will result in a wide composition range of the ANN input layer, thus affecting the iteration divergence in the network training process and resulting in the computational inefficiency. In most applications, principal component analysis (PCA) has been used to reduce the size of the FRF data before being fed to an ANN model. However, as the structures become more complex, the FRF data size also increases. The large size of FRF data may result in the PCA not being effective in selecting important information from the actual FRF data, leading to false damage detection. Moreover, the existence of uncertainties from modelling error and measurement error may also amplify the error in damage detection. Hence, this study proposes a combination of a non-probabilistic method with PCA to consider the problem of the existing uncertainties and the inefficiency of using FRF data in ANN-based damage detection. In this study, ANN is used to relate the FRF data to a damage feature. The input data for the network are the compressed real FRFs and the outputs are the elemental stiffness parameter (ESP). The compressed FRF data obtained from PCA provide a new damage index (DI) that is used as the input layer of the ANN. Based on the interval analysis method, the uncertainties in the new DI are considered to bind together to obtain the interval bound (lower and upper bounds) of the DI changes. The possibility of damage existence (PoDE) is designed to ascertain the relationship between the input and output parameters in the form of undamaged and damaged conditions. The verification conducted on a numerical model and a laboratory tested steel truss bridge model demonstrated that the proposed method is efficient in dealing with uncertainties using FRF for damage detection.

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