Parameter identification and sensitivity analysis of the differential model of hysteresis

Hysteresis is a highly nonlinear and hereditary behavior encountered in many structural systems of engineering interest. Structures often exhibit this behavior under severe dynamic loadings, such as those associated with earthquakes, strong winds and waves, when repeated excursions are made into the inelastic range of deformation. Under cyclic excitation, hysteretic behavior is often characterized by hysteresis loops, where the enclosed area of each loop is a measure of the energy dissipated through internal friction. The ability to model hysteresis loops realistically, thereby predicting the response, deterioration, and energy absorption capacity of structural elements, is a crucial task in modern structural design.; Due to the lack of understanding of structural internal friction, it is difficult to develop a theory of hysteresis from the fundamental postulates of mechanics. Instead, this work seeks to produce practical models of hysteretic loops by conducting parameter identification on the extended Bouc-Wen differential model of hysteresis.; The extended Bouc-Wen differential model of hysteresis contains a set of thirteen undetermined parameters and it can curve-fit practically any hysteretic trace. Three computationally efficient parameter identification algorithms are developed to estimate the thirteen parameters of the differential model in order to match experimental observations. These algorithms are based upon the simplex, extended Kalman filter, and generalized reduced gradient methods. Noise filtering and constrained optimization techniques are incorporated to facilitate convergence and stability. Effectiveness of the devised algorithms is demonstrated through simulations of two nonlinear systems with pinching and degradation characteristics in their hysteresis trace. Because of their very modest computing requirements, these identification algorithms may become acceptable as a design tool for mapping the hysteretic features of inelastic structures.; A critical issue in modeling systems with hysteresis is to decide on an appropriate energy dissipation index, which measures the energy absorption capability of hysteretic systems. The energy dissipation index is also crucial in determining key features of hysteresis loops, such as strength degradation, stiffness degradation and pinching. However, the original energy dissipation index associated with the Bouc-Wen differential model of hysteresis fluctuates if plotted against time. This behavior violates the basic principle that any energy dissipation functional of a passive system should be non-decreasing. A new index is proposed in this research in order to correct this problem.; Finally, for the first time, this research addresses the parameter sensitivity issue of the extended Bouc-Wen differential model of hysteresis. Sensitivity analysis is vital in identifying key parameters whose variation has significant effects on the model output. Successful identification of sensitive and insensitive parameters facilitates the simplification of hysteresis model and bolsters the effective application of the model in engineering design. Both the one-factor-at-a-time approach and the Sobol global sensitivity indices have been applied to determine the relative importance and the interaction of the thirteen model parameters. Monte Carlo simulation and variance reduction techniques, such as Latin hypercube sampling, are utilized in generating the sensitivity indices.