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中文核心期刊

俯仰翼型流体动力学系统的稀疏建模与预测

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

  • 摘要: 重点探讨了在低雷诺数和大攻角条件下, 俯仰翼型复杂流体流动的非线性动力学特性. 研究通过整合多个相互关联的变量, 利用主成分分析(principal component analysis, PCA)和等距特征映射(isometric mapping, ISOMAP)降维技术, 成功实现了对高维流场数据的低维表达. 其中, 特别强调了ISOMAP在描述非线性流场特征方面的卓越性能, 该算法具有更强的灵活性, 能够有效处理高度非线性系统的复杂结构. 在此基础上, 研究进一步引入最小绝对收缩和选择算子(least absolute shrinkage and selection operator, LASSO)模型, 构建了流场的常微分控制方程. 这一模型通过自动检测和筛选非线性项, 显著简化了流场的描述, 提高了对多变量复杂关系的理解. 最后, 研究采用5(4)显式龙格-库塔方法, 实现了对多变量非线性流体动力学的高精度快速预测. 这项研究框架不仅突破了传统单一变量分析的局限性, 还通过整合多维信息, 全面揭示了流场的复杂特性. 引入流形学习和稀疏建模等先进技术, 展示了在高维非线性动力系统中的全面建模与精确预测的潜力. 这一研究为应用科学和工程领域提供了重要的理论方法学进展, 为深入理解和预测复杂流场中的非线性动态行为开辟了新的路径. 这不仅为相关科学研究提供了强有力的工具, 也为工程应用中的流体动力学问题提供了有效的解决方案.

     

    Abstract: 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.

     

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