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Improving Flexibility of Multivariate Spline Model Structures for Aerodynamic Modeling

机译:提高用于空气动力学建模的多元样条模型结构的灵活性

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Recently, multivariate simplex B-splines (MVSB) function approximators have been investigated with the aim of providing accurate global aerodynamic models for use in adaptive flight control systems. In this paper, a new approach for constructing multivariate spline models is presented in the form of the tensor-product MVSB (TP-MVSB) that consists of tensor products of ordinary MVSB. The key advantage of this new approach is that it provides more flexibility in the definition of the spline model structure than the standard multivariate spline approach. This flexibility allows the user to include a priori (expert) knowledge of the system in the definition of the spline model structure leading to more efficient and physically meaningful models. The TP-MVSB maintains the desirable properties of the MVSB in the sense that the global B-form regression vector is normalized, each basis polynomial is guaranteed to be well-conditioned numerically, and differentiability is maintained along each input dimension. The new approach is validated using data obtained from a nonlinear F-16 model. Simulation results show that the new approach can achieve a higher level of approximation accuracy using fewer parameters when modeling the aerodynamic moment coefficients, and in addition can provide accurate estimations of the control effectiveness matrix in cases where the system is affine in the inputs. (C) 2017 American Society of Civil Engineers.
机译:最近,研究了多元单纯形B样条(MVSB)函数逼近器,目的是提供用于自适应飞行控制系统的准确的全局空气动力学模型。本文以张量积MVSB(TP-MVSB)的形式提出了一种构建多元样条模型的新方法,该张量积MVSB由普通MVSB的张量积组成。这种新方法的主要优点是,与标准的多变量样条方法相比,它在样条模型结构的定义上提供了更大的灵活性。这种灵活性允许用户在样条模型结构的定义中包括系统的先验知识(专家知识),从而获得更有效和更有意义的模型。 TP-MVSB保持了MVSB的理想属性,即全局B形式回归向量已归一化,每个基本多项式均保证在数值上处于良好状态,并且沿每个输入维数保持可微性。使用从非线性F-16模型获得的数据验证了该新方法。仿真结果表明,在对空气动力力矩系数进行建模时,该新方法可以使用较少的参数来获得更高的逼近精度,此外,如果系统在输入中仿射,则可以提供对控制有效性矩阵的准确估算。 (C)2017年美国土木工程师学会。

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  • 来源
    《Journal of aerospace engineering》 |2017年第5期|04017044.1-04017044.18|共18页
  • 作者单位

    Beihang Univ, Sch Aeronaut Sci & Engn, Beijing 100191, Peoples R China;

    Delft Univ Technol, Fac Aerosp Engn, Dept Control & Operat, NL-2600 GB Delft, Netherlands;

    Delft Univ Technol, Fac Aerosp Engn, Dept Control & Operat, NL-2600 GB Delft, Netherlands;

    Beihang Univ, Sch Aeronaut Sci & Engn, Beijing 100191, Peoples R China;

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