On the use of GP-NARX model for damage detection in intrinsically nonlinear systems

Damage detection is the first and main step in applying Structural Health Monitoring (SHM) procedures. Vibration-based damage detection methods are commonly applied because the signals are affected by structural changes, related to the structural dynamics. Usually, signals measured with the structure operating in unknown conditions are compared with reference signals predicted using baseline models. This step is not trivial when the structure to be monitored operates in a nonlinear regime of motion because linear models lose the capability to predict the baseline-dynamic behavior, inducing the false-positive occurrence, i.e., the confusion between the presence of damage and the presence of nonlinear phenomena. To overcome this issue, this work proposes the use of a GP-NARX nonlinear model as a baseline model for structure monitoring. The GP-NARX model is constructed using the Gaussian Process (GP) machine learning method considering the framework of a nonlinear autoregressive with an eXogenous (NARX) input model. The advantage of doing so is the natural capability of calculating the model uncertainty, related to the GP model, and the versatility to describe various types of nonlinearities with minor changes in the model structure. The procedure was implemented considering both experimental and simulated data, in a detailed analysis, demonstrating the advantages of using the GP-NARX model for monitoring structures that can operate in a nonlinear motion regime.