The use of a non-probabilistic artificial neural network to consider uncertainties in vibration-based-damage detection

The effectiveness of artificial neural networks (ANNs) when applied to pattern recognition in vibration-based damage detection has been demonstrated in many studies because they are capable of providing accurate results and the reliable identification of structural damage based on modal data. However, the use of ANNs has been questioned in terms of its reliability in the face of uncertainties in measurement and modeling data. Attempts to incorporate a probabilistic method into an ANN by treating the uncertainties as normally distributed random variables has delivered promising solutions to this problem, but the probabilistic method is less straightforward in practice because it is often not possible to obtain unbiased probabilistic distributions of the uncertainties. Moreover, the probabilistic ANN method is computationally complex, especially when generating output data. In this study, a non-probabilistic ANN is proposed to address the problem of uncertainty in vibration damage detection using ANNs. The input data for the network consist of natural frequencies and mode shapes, and the output is the Young's modulus (E values), which acts as an elemental stiffness parameter (ESP). Through the interval analysis method, the noise in measured frequencies and mode shapes are considered to be coupled rather than statistically distributed. This method calculates the interval bound (lower and upper bounds) of the ESP changes based on an interval analysis method. The ANN is used to predict the output of this interval bound by considering the uncertainties in the input parameters. To establish the relationship between the input parameters and output parameters, a possibility of damage existence (PoDE) parameter is defined for the undamaged and damaged states. A stiffness reduction factor (SRF) is also used to represent changes in the stiffness parameter. A numerical model and a laboratory-tested steel portal frame demonstrate the efficacy of the method in improving the accuracy of the ANN in the presence of uncertainties. The effect of different severity levels and the influence of different noise levels on the identification results are discussed.