Parsimonious Dynamic Mode Decomposition: A Robust and Automated Approach for Optimally Sparse Mode Selection in Complex Systems

This paper introduces the Parsimonious Dynamic Mode Decomposition (parsDMD), a novel algorithm designed to automatically select an optimally sparse subset of dynamic modes for both spatiotemporal and purely temporal data. By incorporating time-delay embedding and leveraging Orthogonal Matching Pursuit (OMP), parsDMD ensures robustness against noise and effectively handles complex, nonlinear dynamics. The algorithm is validated on a diverse range of datasets, including standing wave signals, identifying hidden dynamics, fluid dynamics simulations (flow past a cylinder and transonic buffet), and atmospheric sea-surface temperature (SST) data. ParsDMD addresses a significant limitation of the traditional sparsity-promoting DMD (spDMD), which requires manual tuning of sparsity parameters through a rigorous trial-and-error process to balance between single-mode and all-mode solutions. In contrast, parsDMD autonomously determines the optimally sparse subset of modes without user intervention, while maintaining minimal computational complexity. Comparative analyses demonstrate that parsDMD consistently outperforms spDMD by providing more accurate mode identification and effective reconstruction in noisy environments. These advantages render parsDMD an effective tool for real-time diagnostics, forecasting, and reduced-order model construction across various disciplines.

Efficient Transonic Aeroelastic Model Reduction Using Optimized Sparse Multi-Input Polynomial Functionals

Nonlinear aeroelastic reduced-order models (ROMs) based on machine learning or artificial intelligence algorithms can be complex and computationally demanding to train, meaning that for practical aeroelastic applications, the conservative nature of linearization is often favored. Therefore, there is a requirement for novel nonlinear aeroelastic model reduction approaches that are accurate, simple and, most importantly, efficient to generate. This paper proposes a novel formulation for the identification of a compact multi-input Volterra series, where Orthogonal Matching Pursuit is used to obtain a set of optimally sparse nonlinear multi-input ROM coefficients from unsteady aerodynamic training data. The framework is exemplified using the Benchmark Supercritical Wing, considering; forced response, flutter and limit cycle oscillation. The simple and efficient Optimal Sparsity Multi-Input ROM (OSM-ROM) framework performs with high accuracy compared to the full-order aeroelastic model, requiring only a fraction of the tens-of-thousands of possible multi-input terms to be identified and allowing a 96% reduction in the number of training samples.

A Data-driven Approach for Rapid Detection of Aeroelastic Modes from Flutter Flight Test Based on Limited Sensor Measurements

Flutter flight test involves the evaluation of the airframes aeroelastic stability by applying artificial excitation on the aircraft lifting surfaces. The subsequent responses are captured and analyzed to extract the frequencies and damping characteristics of the system. However, noise contamination, turbulence, non-optimal excitation of modes, and sensor malfunction in one or more sensors make it time-consuming and corrupt the extraction process. In order to expedite the process of identifying and analyzing aeroelastic modes, this study implements a time-delay embedded Dynamic Mode Decomposition technique. This approach is complemented by Robust Principal Component Analysis methodology, and a sparsity promoting criterion which enables the automatic and optimal selection of sparse modes. The anonymized flutter flight test data, provided by the fifth author of this research paper, is utilized in this implementation. The methodology assumes no knowledge of the input excitation, only deals with the responses captured by accelerometer channels, and rapidly identifies the aeroelastic modes. By incorporating a compressed sensing algorithm, the methodology gains the ability to identify aeroelastic modes, even when the number of available sensors is limited. This augmentation greatly enhances the methodology's robustness and effectiveness, making it an excellent choice for real-time implementation during flutter test campaigns.