Evolutionary-based sparse regression for the experimental identification of duffing oscillator

In this paper, an evolutionary-based sparse regression algorithm is proposed and applied onto experimental data collected from a Duffing oscillator setup and numerical simulation data. Our purpose is to identify the Coulomb friction terms as part of the ordinary differential equation of the system. Correct identification of this nonlinear system using sparse identification is hugely dependent on selecting the correct form of nonlinearity included in the function library. Consequently, in this work, the evolutionary-based sparse identification is replacing the need for user knowledge when constructing the library in sparse identification. Constructing the library based on the data-driven evolutionary approach is an effective way to extend the space of nonlinear functions, allowing for the sparse regression to be applied on an extensive space of functions. The results show that the method provides an effective algorithm for the purpose of unveiling the physical nature of the Duffing oscillator. In addition, the robustness of the identification algorithm is investigated for various levels of noise in simulation. The proposed method has possible applications to other nonlinear dynamic systems in mechatronics, robotics, and electronics

Sparse and low-rank methods in structural system identification and monitoring

This paper presents sparse and low-rank methods for explicit modeling and harnessing the data structure to address the inverse problems in structural dynamics, identification, and data-driven health monitoring. In particular, it is shown that the structural dynamic features and damage information, intrinsic within the structural vibration response measurement data, possesses sparse and low-rank structure, which can be effectively modeled and processed by emerging mathematical tools such as sparse representation (SR), and low-rank matrix decomposition. It is also discussed that explicitly modeling and harnessing the sparse and low-rank data structure could benefit future work in developing data-driven approaches towards rapid, unsupervised, and effective system identification, damage detection, as well as massive SHM data sensing and management

PySINDy: A comprehensive Python package for robust sparse system identification

Automated data-driven modeling, the process of directly discovering the governing equations of a system from data, is increasingly being used across the scientific community. PySINDy is a Python package that provides tools for applying the sparse identification of nonlinear dynamics (SINDy) approach to data-driven model discovery. In this major update to PySINDy, we implement several advanced features that enable the discovery of more general differential equations from noisy and limited data. The library of candidate terms is extended for the identification of actuated systems, partial differential equations (PDEs), and implicit differential equations. Robust formulations, including the integral form of SINDy and ensembling techniques, are also implemented to improve performance for real-world data. Finally, we provide a range of new optimization algorithms, including several sparse regression techniques and algorithms to enforce and promote inequality constraints and stability. Together, these updates enable entirely new SINDy model discovery capabilities that have not been reported in the literature, such as constrained PDE identification and ensembling with different sparse regression optimizers

Reduced-order Model Predictions of Wind Turbines via Mode Decomposition and Sparse Sampling

Wind turbine wakes are dominated by several energetic turbulent coherent structures that oscillate at specific Strouhal numbers. Implications on wind power harvesting of these dynamic, induced features require accurate unsteady modeling. Dynamic mode decomposition (DMD), a data-driven modal analysis, has demonstrated the ability to identify flow features based on specific frequencies. In this work, the selection of modes and data-driven DMD models pertaining to wakes with constant Strouhal number coherent structures are investigated using physically-informed criteria and sparse sampling. Both criteria are validated with a low Reynolds number flow behind a square cylinder. Next, the techniques are applied to data derived from the large-eddy simulation of a wind turbine wake. Modes related to tip vortices and hub vortex system are identified. Sparse identification shows remarkable ability to select the optimal modes for reduced-order modeling. Error becomes nearly independent of the number of modes when using fewer than 10% of the modes