Adaptive algorithms for the identification of nonlinear structural systems

This dissertation presents two variations of adaptive least-square algorithms (or of Kalman filtering algorithms) for the identification of nonlinear structural systems: the variable trace and the adaptive forgetting factor algorithms. At each time step, the variable trace method properly upgrades the diagonal elements of the adaptation gain matrix by comparing the values of estimated parameters between two consecutive time steps, while the adaptive forgetting factor method uses a newly defined adaptive forgetting factor for the upgrading of such a matrix. Both these two adaptive algorithms contain a procedure to stabilize the adaptation gain matrix that sustains the adaptive properties of the identification algorithms, resolving a typical problem of purely recursive least-square algorithms. These two algorithms enforce a smooth convergence of the parameter values, a fast tracking of the parameter changes and remain adaptive as time progresses so that they are capable of detecting parameter changes induced by damage. For real-life applications, it is important to emphasize that the proposed adaptive algorithms use only the time histories of the input excitation and of the structural accelerations. Measurement noise in structural accelerations will be transferred to structural velocities and displacements through an integration process. This is a much more realistic way of including the effect of noise into the identification process, compared to the cases where measurement noise is directly applied to the “correct” velocity and displacement time histories. These two adaptive approaches have been implemented and analyzed for both parametric and non-parametric identification studies. For the non-parametric analysis where no a priori information on the type of the structural model is available, an analytical method based on a power series of a multivariable polynomial expansion has been proposed. Such a power series expansion is capable of recovering general polynomial-type nonlinear models such as Duffing and Van der Pole oscillators as well as the “generalized” Bouc-Wen hysteretic model, models that are commonly used in civil engineering applications. With this methodology, it will be possible to induce an accurate and controllable on-line identification either for the estimation of time-invariant or time-varying structural parameters (for damage detection purposes) or for the prediction of the future structural response to dynamic loading. In addition, in order to obtain an exact-parameterization of the system's model, a quantitative tool derived from the residual coherence function has been introduced. To obtain accurate response signals (e.g. velocities and displacements from accelerations) for successful identifications, a generalization of the Predictor-Connector integration scheme has been presented and further analyzed for selecting a proper order of convergence.