基于混沌多项式的RBCC飞行器上升段鲁棒轨迹快速优化

doi:10.7527/S1000-6893.2023.28349

Abstract

Abstract:

The ascent trajectory design for Rocket-Based Combined Cycle （RBCC） hypersonic vehicle has many typical characteristics， including complex power system working modes， strong coupling between thrust and flight state， highly nonlinear models， numerous complex constraints， parameter uncertainties， etc. In this paper， a robust trajectory optimization method for RBCC power ascent based on non-intrusive polynomial chaos， the Gaussian quadrature strategy， and sequential convex optimization is proposed to enhance the trajectory’s anti-interference ability and process reliability. Firstly， a robust trajectory optimization model for the RBCC hypersonic ascent， accounting for parameter uncertainties， is established. An uncertainty quantification propagation algorithm based on the Gaussian quadrature strategy and non-intrusive polynomial chaos is designed to transform the robust optimization model into a deterministic trajectory optimization problem with extended dimensions. Then， the extend model is convexified and discretized using convex optimization theory， and a trajectory optimization solution strategy based on sequential convex optimization algorithm is established to achieve a solution of this high-dimensional deterministic optimization problem. The optimaization results of a certain air-based vehicle’s ascent trajectory indicate that based on the constructed model and trajectory method， the robust trajectory optimization of the ascent phase of the RBCC hypersonic aircraft can be effectively completed， and the optimization results are in line with the working characteristics of the RBCC power system. Compared with the traditional deterministic trajectory optimization algorithm， the proposed method can effectively reduce the influence of random disturbances on the ascent trajectory， thereby improving the reliability and robustness of the trajectory.

Key words: Rocket-Based Combined Cycle (RBCC), hypersonic vehicle, ascent trajectory, robust optimization, uncertainty, non-intrusive polynomial chaos, Gaussian quadrature strategy, convex optimization

CLC Number:

V412

Xunliang YAN, Peichen WANG, Shumei WANG, Yuxuan YANG, Kuan WANG. Rapid robust trajectory optimization for RBCC vehicle ascent based on polynomial chaos[J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(21): 528349-528349.

Figures/Tables 16

Table 1

Correspondence between distribution type of random variables and orthogonal basis functions［31］

分布类型	基多项式	概率密度函数
高斯分布	Hermite	$1 2 π e x p - x 2 2$
均匀分布	Legendre	$12$
指数分布	Laguerre	$e x p (- x)$
$β$ 分布	Jacobi	$(1 - x) γ (1 + x) β / 2 γ + β + 1 B (γ + 1, β + 1)$

Table 1

Fig.1

Table 2

Parameter uncertainties setting

不确定参数	符号	分布类型	$3 σ$
大气密度	$δ ρ$	高斯	15%
升力系数	$δ C L$	高斯	15%
阻力系数	$δ C D$	高斯	15%
推力大小	$δ P$	高斯	1%

Table 2

Fig.2

Fig.3

Fig.4

Fig.5

Table 3

Table 4

Weight coefficients setting

工况	$k g$	$k J$	$k x$
工况1	3	0	0
工况2	3	3	0
工况3	3	3	3

Table 4

Fig.6

Fig.7

Table 5

MC shooting results of optimization control quantity under different conditions

情况	$μ (t f)$ /s	$μ (m f)$ /kg	$μ (h f)$ /km	$μ / M a f$	$σ (h f)$ /km	$σ (V f)$ /（m·s^-1）	P_e/%
标准	120.9	1 218.4	49.72	10.97	1.46	66.92	54.60
工况1	122.1	1 210.7	50.01	11.00	1.36	66.03	0.10
工况2	128.8	1 177.9	50.00	11.00	0.48	61.61	0.03
工况3	130.2	1 152.8	50.02	11.20	0.48	61.19	0.01

Table 5

Fig.8

Fig.9

Table 6

MC shooting data comparison of optimization results between GP-PC and CO-PC

算法	$μ (t f)$ /s	$μ (m f)$ /kg	$μ (h f)$ /km	$μ (M a f)$	$σ (h f)$ /km	$σ (V f)$ /（m·s^-1）	Pe/%
标准	120.9	1 218.4	49.72	10.97	1.46	66.92	54.60
CO-PC	130.2	1 152.8	50.02	11.20	0.48	61.19	0.01
GP-PC	132.1	1 131.2	50.03	11.23	0.52	61.97	0.02

Table 6

Table 7

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方法	均值		标准差
方法	结果/km	误差/%	结果/km	误差/%
MC	49.734 5		1.459 3
n=2，p=1	49.726 7	0.015 6	1.448 6	0.739 0
n=2，p=2	49.726 7	0.015 6	1.458 9	0.032 7
n=2，p=3	49.726 7	0.015 6	1.878 1	28.694 4
n=3，p=2	49.725 1	0.018 8	1.462 2	0.193 0
n=3，p=3	49.725 1	0.018 8	1.462 3	0.201 9

优化算法	待优化变量数	迭代步数	优化耗时/s
GP-PC	3 024	6	6 250.2
CO-PC	2 562	9	862.8

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Rapid robust trajectory optimization for RBCC vehicle ascent based on polynomial chaos

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