An evaluation of data-driven identification strategies for complex nonlinear dynamic systems

The development of suitable mathematical models on the basis of dynamic measurements from dispersed structural systems that may be undergoing significant nonlinear behavior is an important and very challenging problem in the field of Applied Mechanics that has drawn the attention of numerous investigators and motivated the development of many approaches for extracting reduced-order, reduced-complexity models from such systems. However, even though numerous nonlinear system identification techniques that are focused on the class of problems encountered in the structural dynamics field have been developed over the past decades, there are no systematic studies available that rigorously compare the performance and fidelity of such methods under similar operating conditions, and when encountering challenging nonlinear phenomena (such as hysteresis) that are present in physical systems, at different scales. This paper explores a variety of data-driven identification techniques for complex nonlinear systems and provides a much needed critical comparison of the accuracy and performance of each method. The Volterra/Wiener neural network (VWNN), a more recent development in nonlinear identification, is featured and compared against several existing methods, including polynomial-based nonlinear estimators and other artificial neural network systems. A representative three degree-of-freedom structure with nonlinear restoring force elements is used as the primary means of comparison for the different methods, and a variety of nonlinear models were investigated, including bilinear hysteresis, polynomial stiffness, and Bouc–Wen hysteresis. Performance comparisons were based on the ability to estimate the acceleration responses for both training and testing simulations. The results showed that, in general, the VWNN provided better accuracy in its estimates for each model. The VWNN also performed best when evaluated for scenarios in which numerical integration is required to find velocity and displacement information from measured accelerations or sensor noise is present in the measured responses.