SPARSE MODELING AND PREDICTION OF THE FLUID DYNAMICS SYSTEM FOR PITCHING AIRFOILS

This study delves into the nonlinear dynamics of complex fluid flows over a pitching airfoil under conditions of low Reynolds numbers and high angles of attack. By integrating multiple interrelated variables, the research successfully achieves a low-dimensional representation of high-dimensional flow field data through the use of principal component analysis (PCA) and isometric mapping (ISOMAP) dimensionality reduction techniques. ISOMAP, in particular, stands out for its superior ability to describe the nonlinear characteristics of the flow field, offering greater flexibility in managing the intricate structures inherent in highly nonlinear systems. This flexibility makes ISOMAP an invaluable tool in capturing the subtle, yet critical, aspects of fluid flow that may be overlooked by more traditional methods.Building on this dimensionality reduction, the study introduces the least absolute shrinkage and selection operator (LASSO) model to construct ordinary differential equations that govern the flow field. The LASSO model is particularly effective in automatically detecting and selecting the most relevant nonlinear terms, thus simplifying the complex descriptions of the flow field. This simplification not only enhances our understanding of the intricate relationships among multiple variables but also improves the model’s predictive power, making it a more practical tool for real-world applications. To further refine the model's accuracy, the research employs the 5(4) Explicit Runge-Kutta method, a numerical technique that allows for high-precision and rapid predictions of multivariable nonlinear fluid dynamics. This method significantly enhances the model’s capability to predict dynamic behaviors over time, making it a robust tool for both scientific research and practical engineering applications. Overall, this research framework transcends the limitations of traditional univariate analyses by integrating multidimensional data, thereby providing a more comprehensive understanding of the complexities inherent in fluid flow. By incorporating advanced techniques such as manifold learning and sparse modeling, this study not only demonstrates the potential for comprehensive modeling and accurate prediction in high-dimensional nonlinear dynamical systems but also paves the way for future innovations in the field. The insights and methodologies developed here offer substantial advancements for applied science and engineering, opening up new avenues for understanding and predicting the nonlinear dynamic behaviors that characterize complex flow fields.