Analytical and experimental studies in nonlinear system identification and modeling for structural control

This work represents a three-part study of several dynamics modeling issues relevant to modern structural control applications. A straight-forward procedure is presented for representing nonstationary random process data in a compact probabilistic format which can be used as excitation input in multi-degree-of-freedom (MDOF) analytical random vibration studies. The compaction is performed in two stages: (1) the orthogonal decomposition of the input covariance matrix by the Karhunen-Loeve expansion, and (2) the least-squares fitting of the dominant eigenvectors with Chebyshev polynomials to yield an analytical approximation. Linear MDOF system random vibration studies are conducted, resulting in good agreement with exact solutions. The response formulation is derived for nonlinear problems using statistical linearization techniques.; Various parametric and nonparametric system identification techniques are investigated for their capability to model general nonlinear dynamical systems, and for their ability to indicate structural modifications from changes in their model parameters. Both the time-domain least-squares based and neural network techniques adequately model the dynamics of an unknown physical system. All of the methods detect change through the lack of agreement in model output from one modified structure to the next; however only the equivalent linear model shows consistent model parameter changes. The nonparametric techniques, although able to model nonlinearities accurately, yield non-unique optimal solutions.; A method based on adaptive estimation approaches is presented for the on-line parametric identification of hysteretic systems. The availability of such an identification approach is crucial for the on-line control and monitoring of time-varying structural systems. Through single-degree-of-freedom (SDOF) and MDOF simulation studies, the method, which incorporates a Bouc-Wen hysteresis element model with additional polynomial-type nonlinear terms, proves to be quite robust. Application of the proposed method is, however, limited to situations where inertial quantities are directly or indirectly available, and to certain system topologies.