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采用截断三阶Volterra级数模型来研究空气动力二阶核函数的辨识问题,选取一簇正交化的切比雪夫多项式对二阶核函数进行参数化处理,并将非参数辨识问题转化成参数辨识问题。相比于其他方法,本文模型能有效降低对激励信号幅值的敏感程度,保证辨识出的核函数具有较好的保真度;只针对三阶Volterra降阶模型中的一阶、二阶核函数进行辨识,即可提升原系统一阶、二阶核函数的辨识精度,却不会显著增加辨识过程的工作量;参数化辨识方法属于整体性辨识,根据已有的部分数据对(输入、输出数据)就能完成系统辨识,且能达到较好的辨识精度,从而有效地减少了执行计算流体力学(CFD)代码程序的总次数,节约了大量的时间成本。算例表明,与目前流行的非参数化方法相比,本文提出的切比雪夫函数辨识方法,精度上达到预期要求,辨识过程消耗的CFD总时间量至少可降低一个数量级。
The truncated third-order Volterra series model is used to study the identification of aerodynamic second-order kernel function. A set of orthogonal Chebyshev polynomials is used to parameterize the second-order kernel function, and the non-parametric identification problem is transformed into the parameter Identify the problem. Compared with other methods, this model can effectively reduce the sensitivity to the amplitude of the excitation signal and ensure that the identified kernel function has a good fidelity. Only for the first-order and second-order kernels in the third-order Volterra reduction model Function to identify the original system can improve the first-order, second-order kernel function identification accuracy, but does not significantly increase the identification process workload; parameter identification method belongs to the overall identification, based on the existing part of the data (input, Output data) to complete the system identification, and can achieve better identification accuracy, thus effectively reducing the total number of CFD code implementation process, saving a lot of time and cost. The numerical example shows that compared with the popular nonparametric method, the proposed method of Chebyshev identification achieves the expected accuracy, and the total CFD time consumed by the identification process can be reduced by at least an order of magnitude.