飞行器非定常气动力稀疏识别建模方法

doi:10.7527/S1000-6893.2025.32764

Abstract

Abstract:

To enable efficient， high-fidelity construction of white-box reduced-order aerodynamic models， a frequency-domain unsteady aerodynamic modeling approach is proposed based on Sparse Identification of Nonlinear Dynamics （SINDy）. The proposed method uses simulation data of harmonic aircraft motions at representative amplitudes and frequencies， constructs a candidate function library guided by classical algebraic aerodynamic model architectures， and applies sparse regression to select optimal terms and identify parameters-thereby automatically yielding sparse， highly interpretable reduced-order aerodynamic models. Leveraging both classical algebraic model structures and Theodorsen’s unsteady aerodynamic theory， we formulate a globally sampled unified model （SINDyA） and a parameter-varying local model （SINDyB）. The approach is validated on two canonical problems-transonic pitch oscillations of the NACA64A010 airfoil and of the CHN-T1 aircraft-using lift and pitching-moment coefficients as modeling targets.Results indicate that the identified models require only a small number of dominant terms to capture the key nonlinear and hysteretic features of the unsteady aerodynamics； the SINDyB model， which performs local interpolation of coefficients， achieves higher prediction accuracy. Because the pitching-moment coefficient exhibits stronger nonlinearity， its prediction proves markedly more challenging than that of lift. The models predict aerodynamic responses accurately under small-amplitude excitations， while performance degrades for large-amplitude， high-frequency cases. These findings demonstrate the promise of symbolic machine-learning methods for constructing high-accuracy， interpretable unsteady aerodynamic models and highlight their potential for engineering application.

Key words: unsteady aerodynamics, machine learning, sparse identification, CFD, reduced-order model

CLC Number:

V212.11

Jinyang TONG, Jiaqing KOU, Weiwei ZHANG. Sparse identification modeling method for unsteady aerodynamics of aircraft[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(16): 132764.

Figures/Tables 24

Fig.1

Fig.2

Table 1

Geometric parameters

参数	数值
参考面积/ $m 2$	0.129 37
机翼半展长/ $m$	0.774 38
平均气动弦长/ $m$	0.193 7
力矩参考点/ $m$	（0.660 87，0，0）

Table 1

Table 2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Table 3

Coefficients of each term in SINDyA model for NACA 64A010 airfoil

参数	系数
参数	$α$	$α k$	$α k 2$	$α k 3$	$α ˙ l g k$	$α ˙ k$	$α ˙ k 2$	$α ˙ k 3$	$α ˙ α ˙ l g k$	$α ˙ α ˙ k$	$α ˙ α ˙ k 2$	$α ˙ α ˙ k 3$
C_L	1.487	-1.327	1.714	-0.884	0.685	0.894	-0.577	-0.385	-1.162	2.246	0	-1.367
C_m	-1.577	1.519	-1.762	0.811	-0.772	-1.261	0	0.791	0.462	1.688	-1.849	0.53

Table 3

Fig.10

Fig.11

Table 4

Fig.12

Fig.13

Table 5

Coefficients of each term in SINDyA model for CHN-T1 standard model

参数	系数
参数	$α$	$α k$	$α k 2$	$α k 3$	$α ˙ l g k$	$α ˙ k$	$α ˙ k 2$	$α ˙ k 3$	$α α ˙ k 3$	$α ˙ α ˙ l g k$	$α ˙ α ˙ k$	$α ˙ α ˙ k 3$
C_L	1.244	-0.981	2.348	-1.556	-0.119	0	-0.697	0.653	-0.008	-0.094	-0.319	0.242
C_m	-0.995	1.753	-4.041	2.575	0.380	-2.706	6.169	-3.875	-0.815	0.811	0	0

Table 5

Table 6

Number of terms in SINDyB model

工况	项数
工况	C_L	C_m
$α m a x = 1 °, k = 0.102$	8	13
$α m a x = 1 °, k = 0.026$	7	7
$α m a x = 1 °, k = 0.015$	5	7
$α m a x = 4 °, k = 0.051$	11	10
$α m a x = 4 °, k = 0.02$ 0	15	9
$α m a x = 4 °, k = 0.013$	14	12
$α m a x = 8 °, k = 0.102$	12	13
$α m a x = 8 °, k = 0.026$	16	15
$α m a x = 8 °, k = 0.015$	15	14

Table 6

Fig.14

Table 7

Fig.15

Fig.16

Fig.17

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网格	总网格量	第1层网格高度	y^＋
粗网格	2 318 948	1.44×10^-6	1.0
中等网格	5 952 147	1.00×10^-6	0.6
细网格	17 249 562	6.93×10^-7	0.4

模型	E_R/%		E_RMS/10^-3
模型	C_L	C_m	C_L	C_m
SINDyA	16.14	17.65	23.858	8.134
SINDyB	2.72	9.69	12.654	6.293

模型	C_L 的E_RMS	C_m 的E_RMS
SINDyA	0.108 9	0.284 7
SINDyB	0.047 7	0.221 0

Sparse identification modeling method for unsteady aerodynamics of aircraft

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