9 RVM 69 / 6 x t = f x t + g x t u t + δ a x u t y t = h x t + δ h x t } x t R n u t R m f x t g x t 6 δ a x u t δ h x h x t RVM least square su

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1 5 9 9 ELECTRI C MACHINES AND CONTROL Vol. 5 No. 9 Sep. RVM 9 RVM RVM LSSVR RVM LSSVR RVM RVM V 448. A 7-449X Multi-fault detection for attitude control system based on RVM regression HU Di DONG Yun-feng School of Astronautics Beihang University Beijing 9 China Abstract As satellite attitude control system ACS failures have concurrent and multiple features both the sensors and actuators may occur faults. Model identification and residual evaluation were applied to ACS fault detection based on relevance vector machine RVM theory. RVM regression was utilized to perform offline regression modeling for the satellite s sun sensor gyro and reaction wheel and obtain the regression modeling through analyzing input /output history data stream. As a result the accuracy of modeling identification was affected by regression model. A comparison between least square support vector regression LSSVR and RVM regression was analyzed. The simulation result shows that the RVM is much better than LSSVR. Different scenarios with sun sensor gyro and reaction wheel to realize concurrent and multiple fault detection were simulated. The result shows that the RVM regression is convenient to the attitude control system. Key words sensor actuator attitude control system relevance vector machine regression least square support vector regression regression modeling multi-fault detection

2 9 RVM 69 / 6 x t = f x t + g x t u t + δ a x u t y t = h x t + δ h x t } x t R n u t R m f x t g x t 6 δ a x u t δ h x h x t RVM least square support vector regression - LSSVR sparse bayesian learning SBL 5 LSSVR support vector machine SVM semi - definite programming SDP support vector regression SVR Mercer SVM SVM SVM 6 LSSVR 3 LSS- n VR LSSVR m x y x m y m R n R m 7 8 y x w = m ω i K kernel x i x + ω i = x = x x x m w = ω ω 4 ω m T ω K kernel x i x unscented kalman filtering UKF x y 9 y measure = y ture + δ 3 relevance vector machine RVM δ δ ~ N y ture σ y true y measure

3 7 5 ( ) p T a w σ = πσ - K/ exp - T σ a - Φw 4 T a = δ δ δ n T Φ n m Φ ij = K kernel x i x j i = n j = m K Bayesian p w α = π -K / K α / i exp - α iω i ( ) 5 3. i = α = α α α K Bayesian p w T a α σ = π - K + / Σ - / exp[ - w - μ T Σ - w - μ ] 4 64 km ~ N μ Σ 6 3 Σ = σ - Φ T Φ + A μ = σ - ΣΦ T T a } 7 + X A = diag α α α K - B = - 3 p T a α σ = p Τ a w σ p w α dw x * T * p T * T a ~ N μ * σ * μ * = Fμ σ * = σ op I + F T ΣF } F = Φ x * Φ x * Φ K x * T Φ i x * = K kernel x x * i = K σ op s 4 s 8 s p T a α σ ~ N C 9 LSSVR RVM C = σ I + ΦA - Φ T I LSSVR 建模误差.5 RVM 建模误差 LSSVR RVM Fig. Model error between LSSVR model and RVM model of digital sun sensor 太敏测量角度 /( -3 )

4 9 RVM 7 LSSVR LSSVR. 5 RVM LSSVR RVM LSSVR S S S 3 LSSVR RVM Fig. 3 Model error between LSSVR model and RVM model of reaction wheel 3 LSSVR. r /minrvm RVM LSSVR 6 s 4 s 4 s LSSVR RVM 角速度 /( -3 s - ) Fig. LSSVR 建模误差 RVM 建模误差 Model error between LSSVR model and RVM model of gyro LSSVR RVM - 4 /s. RVM 3. 3 残差残差 e+ 残差评价 LSSVR RVM Fig. 4 3 转速 /( -3 r min - ) LSSVR 建模误差 RVM 建模误差 4 LSSVR RVM RVM 评价姿控计算机 e+ 残差 - 反作用轮辨识模型反作用轮地敏陀螺陀螺辨识模型太敏太敏辨识模型 + e 残差 - 空间环境干扰卫星运动学动力学残差评价 The schematic of satellite attitude control system fault diagnosis

5 7 5 k + X L k j = k + L k + = b + r j j = k + -b b r j -. L k + ε 3 L k + > ε ε 5 } MATLAB 3 6 Fig. 6 Residual evaluation of scenario Y 6 5 s A A 5. 4 s Y A 陀螺残差 /( s - ) 反作用轮残差 /(r min - ) Fig. 5 Residual evaluation of scenario RVM LSSVR 4s 7 5. A 5 s 陀螺残差 /( s - ) 反作用轮残差 /(r min - ) Y 3 s X 4 s 陀螺残差 /( s - ) 反作用轮残差 /(r min - ) Fig. 7 Residual evaluation of scenario s Y

6 9 RVM 73 4 s A spacecraft 5. 4 A 4 4 s X 8 陀螺残差 /( s - ) 反作用轮残差 /(r min - ) Fig. 8 Residual evaluation of scenario s RVM 6 RVM Acta Astronautica D. RVM LSSVR vector machine J of model based fault diagnosis method to propulsion system of J. Journal of propulsion technology XING Yan WEI Chunling. Fault location of single redundant gy-. roscopes based on estimated angular rate using quaternion J. J Journal of Astronautics BAOYAN Heshig JIANG Xingwei HUANG Wenhu. Application - 8. J S TIAN Kefeng LI Zhibin. Reaction wheel fault diagnosis based on adaptive observer J. Journal of Huazhong University of Science and Technology Nature Science Edition 9 37 S J JIN Lei XU Shijie. Extendted state observer-based fault detection and recovery for flywheels J. Journal of Beijing University of Aeronautics and Astronautics LI Zhongqi MA Liying KHORASANI Khashayar. Fault detection in reaction wheel of a satellite using observer-based dynamic neural networks J. Lecture Notes in Computer Science SVM J ZHAO Shilei ZHANG Yingchun. Application of SVM regression to fault diagnosis for satellite J. Electric Machines and Control LSSVM J WANG Jianfei JIANG Bin MAO Zehui. LSSVM based fault diagnosis for satellite attitude control systems J. Control Engineering of China HENRY D. Fault diagnosis of microscope satellite thrusters using H /H - filters J. Journal of guidance control and dynamics VALDES A KHORASANI K. A pulsed plasma thruster fault detection and isolation strategy for formation flying of satellites J. Applied Soft Computing Journal PIRMORADI F N SASSANI F DE SILVA C W. Fault detection and diagnosis in a spacecraft attitude determination system J TIPPING Michael E. Bayesian inference an introduction to principles and practice in machine learning J. Advanced lectures on machine learning TIPPING Michael E. Sparse bayesian learning and the relevance. Journal of Machine Learning Reaserch 3 LEI Liangyu ZHANG Qing. Relevance vector machine based bearing fault diagnosis C / /6 International Conference on Machine Learning and Cybernetics August Dalian China J.

SVM OA 1 SVM MLP Tab 1 1 Drug feature data quantization table

SVM OA 1 SVM MLP Tab 1 1 Drug feature data quantization table 38 2 2010 4 Journal of Fuzhou University Natural Science Vol 38 No 2 Apr 2010 1000-2243 2010 02-0213 - 06 MLP SVM 1 1 2 1 350108 2 350108 MIP SVM OA MLP - SVM TP391 72 A Research of dialectical classification