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Towards Data-Driven Identification of Nonlinear Dynamical Systems for Building Interpretable Mathematical Models
The calibration and validation of computational models depend critically on experimental measurements. Engineers must recognize and consider the unmodeled and/or unpredictable dynamics when a model fails to replicate data to balance theoretical prediction and experimental observation. Although there are established linear identification tools, practicing engineers encounter significant challenges when identifying and building reduced-order models of the dynamics of nonlinear dynamical systems. This is because nonlinearities frequently introduce novel dynamical phenomena that do not exist in linear settings. This dissertation focuses on recently established tools for data-driven nonlinear system identification that makes it possible to identify, characterize, and model system nonlinearity with the help of experimental data and computational models. This task requires the coordinated application of numerous theoretical, computational, and experimental approaches, including wavelet and Hilbert transforms, empirical mode decomposition, and experimental modal analysis. This dissertation's first section focuses on creating a physics-based mathematical model for a local nonlinear attachment with clearance nonlinearity installed on a linear model airplane wing subjected to linear and nonlinear vibrations. The identification is carried out using the characteristic nonlinear system identification (CNSI) method, which identifies a mathematical model for a local nonlinear attachment without any prior knowledge of the basic structure or the attachment. The second portion relies on exploiting a single measurement instance to discover mathematical models for multiple nonlinear energy sinks, which introduces significant complexity to the system's dynamics. Later in the third portion, component-scaled signal reconstruction (CSSR), a new optimization-based signal denoising technique, is introduced. To find the best linear combination of the intrinsic mode functions (IMFs) obtained using empirical mode decomposition (EMD), the methodology uses the mode mixing issue that plagues EMD-based methods. The final section focuses on creating an inexpensive, simple-to-assemble automatic modal hammer with open-source hardware and software. An Arduino drives a servo driver that supports micro-stepping and is connected to a stepper motor with an encoder mounted with a commercial modal hammer.
Singh, Aryan, "Towards Data-Driven Identification of Nonlinear Dynamical Systems for Building Interpretable Mathematical Models" (2022). ETD collection for University of Nebraska - Lincoln. AAI29323206.