Subspace-based identification of a distributed nonlinearity in time and frequency domains

Nonlinear system identification has become of great interest during the last decades. However, a common and shared framework is not present yet, and the identification may be challenging, especially when real engineering structures are considered with strong nonlinearities. Subspace methods have proved to be effective when dealing with local nonlinearities, both in time domain (TNSI method) and in frequency domain (FNSI method). This study reports an improvement for both methods, as a first attempt to account for distributed nonlinearities, which is still an open question in the research community. A numerical beam under moderately large oscillations that exhibits geometric nonlinearity is considered. The object of the identification process is to exploit its behavior through the correct identification of the parameters that define the nonlinearity. Results show a high level of confidence between the two methods, and suggest that a more complete analysis of distributed nonlinear phenomena can be conducted based on these approaches.