Hyperchaotic and delayed oscillators for system identification with application to damage assessment

In this dissertation, system identification techniques are introduced through the use of hyperchaotic and delayed oscillators. In particular, the existing attractor-based technique of chaotic interrogation for damage assessment is extended by employing hyperchaotic excitation signals, resulting in a hyperchaotic interrogation technique which is more sensitive to small amounts of structural damage. Also, the extended Kalman-Bucy filter (EKBF) is employed for the consistent estimation of parameters and states of chaotic and hyperchaotic systems from noise-corrupted nonlinear incomplete measurements, and its advantages are highlighted by comparing the performance of the EKBF with that of some common discrete filtering techniques.;Next, a novel approach in parameter and delay estimation of time-delayed systems is proposed through exploiting the estimation technique of EKBF in conjunction with continuous time approximation based on Chebyshev spectral collocation. The proposed approach is implemented on a variety of linear, nonlinear, chaotic and hyperchaotic delayed oscillators with constant and time-varying delay. Also, an innovative technique is proposed to approximately compute the Lyapunov exponents of delayed chaotic and hyperchaotic oscillators through the use of the Chebyshev spectral continuous time approximation (CSCTA). Later, the proposed approach is extended for state, parameter, and delay estimation in time-delayed systems with distributed delay, or delayed integro-differential equations (DIDEs), in which the upper bound of the distributed delay can also be estimated by this proposed technique.;Eventually in this dissertation, the concept of hyperchaotic excitation is combined with stochastic estimation using the EKBF to develop an innovative technique for system identification in nonlinear structural systems. This feasible new technique, which has promising potential applications in smart or self-healing structures, is then applied for real-time identification of damage in nonlinear structures.