Nonlinear state-space modeling for structural dynamics in aerospace structures = Nonlinear state-space modeling for structural dynamics in aerospace structures

This thesis develops a comprehensive methodology for the identification of nonlinear state-space models for complex engineering structures, with a focus on making advanced techniques applicable to real-world systems. The process begins with a non-parametric analysis using the Best Linear Approximation (BLA) to characterize the system's dynamics and nonlinearity type across various excitation levels. This information is then used to identify a robust "underlying linear model" in modal coordinates through a state-of-the-art pipeline combining Polymax and Maximum Likelihood Modal Model (MLMM) estimators. ???? A key contribution of this work is a systematic modal selection approach. By analyzing BLA distortion metrics and sine-sweep data, a small subset of the most nonlinearly-active modes is identified. This targeted selection transforms the modeling problem from a high-dimensional black-box challenge into a parsimonious, grey-box framework. It enables a focused extension of the linear model where nonlinear terms are only applied to the selected modal states. ???? This selected-state architecture makes the identification of high-order systems computationally tractable, drastically reducing the number of parameters and making even the traditionally intensive Polynomial Nonlinear State-Space (PNLSS) model significantly more manageable. Despite this improvement, the Decoupled Model (DM) and a custom-designed gray-box Neural Network (NN) provide a superior representation when combined with the modal approach due to their inherent structure. The complete methodology is validated on several numerical and complex experimental datasets. Results consistently show that the Decoupled Model provides the best performance in terms of accuracy. The Neural Network model is confirmed as the most computationally efficient alternative, offering an excellent trade-off between accuracy and required resources. The research culminates in a robust, semi-automated procedure capable of delivering accurate, physically-interpretable nonlinear models for complex engineering systems. ??