State Observer-Based Conditioned Reverse-Path Method for Nonlinear System Identification

In light of the complex behavior of vibrating structures, their reliable modeling plays a crucial role in the analysis and system design for vibration control. In this paper, the reverse-path (RP) method is revisited, further developed, and applied to modeling a nonlinear system, particularly with respect to the identification of the frequency response function for a nominal underlying linear system and the determination of the structural nonlinearities. The present approach aims to overcome the requirement for measuring all nonlinear system states all the time during operation. Especially in large-scale systems, this might be a tedious task and often practically infeasible since it would require having individual sensors assigned for each state involved in the design process. In addition, the proper placement and simultaneous operation of a large number of transducers would represent further difficulty. To overcome those issues, we have proposed state estimation in light of the observability criteria, which significantly reduces the number of required sensor elements. To this end, relying on the optimal sensor placement problem, the state estimation process reduces to the solution of Kalman filtering. On this ground, the problem of nonlinear system identification for large-scale systems can be addressed using the observer-based conditioned RP method (OBCRP) proposed in this paper. In contrast to the classical RP method, the current one can potentially handle local and distributed nonlinearities. Moreover, in addition to the state estimation and in comparison to the orthogonal RP method, a new frequency-dependent weighting is introduced in this paper, which results in superior nonlinear system identification performances. Implementation of the method is demonstrated on a multi-degree-of-freedom discretized lumped mass system, representing a substitute model of a physical counterpart used for the identification of the model parameters.