基于GPR模型的多保真气动力建模方法

Multi-fidelity aerodynamic modeling method based on GPR model

  • 摘要: 多保真气动力建模通过整合不同保真度的数据,能够有效提升飞行器气动特性分析的计算效率和预测精度。为了更好处理高低保真数据之间同时存在的线性和非线性的混合复杂相关性,本文在非线性自回归高斯过程(nonlinear autoregressive Gaussian process, NARGP)模型的基础上,提出了一种新的多保真高斯过程回归模型(multi-fidelity Gaussian process regressive, MFGPR)。该模型通过结合线性核函数和非线性核函数,扩展了NARGP的能力,能够同时处理多保真数据中复杂的非线性关系和线性依赖性。为验证MFGPR的有效性,通过两个解析函数进行测试,并与传统的多保真建模方法进行对比分析。研究结果表明,在处理线性相关性问题时,MFGPR的性能与CoKriging非常接近;而在应对复杂非线性相关性问题时,MFGPR展现出最高的预测精度,同时其建模效率也表现出显著优势。最后,本文将MFGPR应用于两个工程算例,进一步展示了该模型在气动力建模中的应用潜力和优越性能。

     

    Abstract: Multi-fidelity aerodynamic modeling, which integrates experimental and simulation data of varying fidelity levels, effectively enhances computational efficiency and prediction accuracy in analyzing aircraft aerodynamic characteristics. Traditional multi-fidelity modeling methods typically assume ‌a single type of mapping relationship (either linear or nonlinear)‌ between high- and low-fidelity aerodynamic data. However, practical analyses under complex flight conditions, such as transonic flows and high-angle-of-attack scenarios, reveal that multi-fidelity data often exhibit hybrid correlations ‌that combine‌ both linear and nonlinear features. To better address these coexisting ‌complex linear-nonlinear interdependencies‌ across fidelity levels, the present study proposes a novel ‌Multi-fidelity Gaussian Process Regression (MFGPR)‌ model based on the ‌Nonlinear Autoregressive Gaussian Process (NARGP)‌ framework. By integrating linear and nonlinear kernel functions, the MFGPR extends the capabilities of NARGP to simultaneously capture ‌both‌ intricate nonlinear relationships and linear dependencies inherent in multi-fidelity datasets. To validate the effectiveness of MFGPR, two analytical functions were tested and compared with conventional multi-fidelity modeling approaches. The results demonstrate that MFGPR achieves performance comparable to ‌CoKriging‌ in handling linearly correlated problems, ‌while exhibiting‌ superior prediction accuracy and significant efficiency advantages ‌in addressing‌ complex nonlinear correlations. Finally, the application of MFGPR to two engineering cases further illustrates its potential and outstanding performance in aerodynamic ‌force modeling‌ applications.

     

/

返回文章
返回