CN116149186A - A Kalman filter method for fault estimation of satellite attitude control system - Google Patents
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Abstract
本发明公开了一种卫星姿态控制系统故障估计的Kalman滤波方法,属于航天器故障诊断技术领域,具体为:考虑可建模干扰和状态时滞,执行器和传感器故障为附加变量,建立时滞广义系统模型;设计非奇异鲁棒Kalman滤波器;基于泰勒级数展开时滞广义系统的非线性项和非线性时滞项,并给出鲁棒上界;通过改进的鲸鱼优化算法优化噪声协方差矩阵,并用优化后的噪声协方差矩阵代替原有噪声协方差;执行时滞广义系统的状态估计和可建模干扰估计,完成卫星姿态控制系统的状态估计和复合故障估计。采用上述一种卫星姿态控制系统故障估计的Kalman滤波方法,解决了复杂运行环境下卫星姿态控制系统的多种故障估计问题,提高了故障估计的精度。
The invention discloses a Kalman filtering method for fault estimation of a satellite attitude control system, which belongs to the technical field of spacecraft fault diagnosis. Generalized system model; design non-singular robust Kalman filter; expand the nonlinear term and nonlinear time-delay term of the time-delay generalized system based on Taylor series, and give a robust upper bound; optimize the noise coherence through the improved whale optimization algorithm variance matrix, and replace the original noise covariance with the optimized noise covariance matrix; perform state estimation and modelable interference estimation for time-delay generalized systems, and complete state estimation and composite fault estimation for satellite attitude control systems. Using the Kalman filter method for fault estimation of the satellite attitude control system mentioned above, various fault estimation problems of the satellite attitude control system in complex operating environments are solved, and the accuracy of fault estimation is improved.
Description
技术领域Technical Field
本发明涉及航天器故障诊断技术领域,尤其是涉及一种卫星姿态控制系统故障估计的Kalman滤波方法。The invention relates to the technical field of spacecraft fault diagnosis, and in particular to a Kalman filtering method for fault estimation of a satellite attitude control system.
背景技术Background Art
随着卫星在轨服务的快速发展,在轨卫星数量不断增加。相应地,对卫星稳定性和安全性的要求也日益提升。姿态控制系统(ACSs)作为卫星的重要分系统,其正常工作关系到星上有效载荷、遥控、遥测和轨道控制等重要任务的有效展开。但是,由于系统设备众多、运行机制复杂,ACSs也较易发生故障。因此,需要对ACSs的故障进行诊断,以及时发现系统异常,避免安全事故发生,保证卫星的在轨正常运行。因此,结合现代故障诊断技术,有效诊断出ACSs的故障,具有重要的现实意义。With the rapid development of satellite on-orbit services, the number of satellites in orbit continues to increase. Correspondingly, the requirements for satellite stability and safety are also increasing. As an important subsystem of the satellite, the normal operation of the attitude control system (ACSs) is related to the effective implementation of important tasks such as on-board payload, remote control, telemetry and orbit control. However, due to the large number of system equipment and complex operating mechanisms, ACSs are also prone to failure. Therefore, it is necessary to diagnose the faults of ACSs to detect system anomalies in time, avoid safety accidents, and ensure the normal operation of satellites in orbit. Therefore, it is of great practical significance to effectively diagnose the faults of ACSs in combination with modern fault diagnosis technology.
在基于模型的故障诊断方法中,设计残差生成器是一种行之有效的方法。目前,诸如观测器、滤波器等残差生成器已广泛用于ACSs的故障诊断。为实现ACSs的前两个任务阶段,即:故障检测与分离(FDI),未知输入观测器(UIO)已结合H-/H∞检测方法得到了广泛应用。而对于故障诊断的最后一个任务阶段:故障估计,因该过程不仅能够判断故障信号的具体形式和幅值,而且能够为主动容错控制提供基础,故尤为重要。有鉴于此,自适应观测器、滑模观测器、区间观测器等已结合鲁棒H∞方法,保证了系统的稳定性和鲁棒性。但是,当系统存在运行噪声时,需要考虑噪声对于故障估计精度的影响。为此,另一种残差生成器-Kalman滤波器已被用于噪声下的ACSs故障估计。In the model-based fault diagnosis method, designing residual generators is an effective method. At present, residual generators such as observers and filters have been widely used in fault diagnosis of ACSs. To achieve the first two task stages of ACSs, namely, fault detection and isolation (FDI), unknown input observers (UIO) have been widely used in combination with H- / H∞ detection methods. As for the last task stage of fault diagnosis: fault estimation, it is particularly important because this process can not only determine the specific form and amplitude of the fault signal, but also provide a basis for active fault-tolerant control. In view of this, adaptive observers, sliding mode observers, interval observers, etc. have been combined with robust H∞ methods to ensure the stability and robustness of the system. However, when there is operating noise in the system, it is necessary to consider the impact of noise on the accuracy of fault estimation. For this reason, another residual generator-Kalman filter has been used for ACSs fault estimation under noise.
鉴于ACSs系统的非线性特性,基于奇偶向量法的扩展Kalman滤波器、融合无迹Kalman滤波器、强跟踪容积Kalman滤波器等改进的非线性滤波器已用于估计ACSs的故障。另外,考虑ACSs噪声的未知特性,自适应滤波、变分贝叶斯滤波等方法已结合上述非线性Kalman器,用于更好地估计系统噪声,从而实现更优的故障估计。然而,ACSs的非线性Kalman滤波方法仍有一定不足。首先,系统的并发执行器、传感器并发故障(复合故障)估计精度仍需进一步提高。通常,卫星的执行器故障表现为飞轮卡死、空转和斜坡漂移等;传感器故障主要表现为:陀螺敏感器卡死、恒偏差、斜坡变化等。极端情况下,若复合故障同时发生,故障信号的耦合可能导致估计精度不高。尽管传感器故障可视为伪执行器故障,但该等效方法的偏差可能影响估计精度。其次,系统的外部干扰对故障估计的精度具有一定的影响。尽管扰动观测器等方法已用于估计ACSs的外部干扰,但随机噪声和未知外部干扰通常同时存在,给Kalman滤波器的设计带来了一定的挑战。再次,ACSs的速度时滞也会影响滤波精度。目前,针对具有时滞环节ACSs的Kalman滤波器设计主要集中于具有测量时滞的ACSs,但这些方法的本质是系统的高维变换,导致变量维度高、算法负载较大等不足。因此,考虑上述因素的综合影响,设计行之有效的故障估计Kalman滤波器,以提高ACSs的复合故障估计精度,是十分必要的。In view of the nonlinear characteristics of ACSs, improved nonlinear filters such as extended Kalman filter based on parity vector method, fused unscented Kalman filter, and strong tracking cubature Kalman filter have been used to estimate the faults of ACSs. In addition, considering the unknown characteristics of ACSs noise, adaptive filtering, variational Bayesian filtering and other methods have been combined with the above nonlinear Kalman filter to better estimate the system noise, thereby achieving better fault estimation. However, the nonlinear Kalman filtering method of ACSs still has certain shortcomings. First, the estimation accuracy of concurrent actuator and sensor concurrent faults (compound faults) of the system still needs to be further improved. Usually, the actuator faults of satellites are manifested as flywheel jamming, idling and slope drift; sensor faults are mainly manifested as gyro sensor jamming, constant deviation, slope change, etc. In extreme cases, if compound faults occur at the same time, the coupling of fault signals may lead to low estimation accuracy. Although sensor faults can be regarded as pseudo-actuator faults, the deviation of this equivalent method may affect the estimation accuracy. Secondly, the external interference of the system has a certain impact on the accuracy of fault estimation. Although methods such as disturbance observers have been used to estimate external disturbances of ACSs, random noise and unknown external disturbances usually exist at the same time, which brings certain challenges to the design of Kalman filters. Thirdly, the speed delay of ACSs will also affect the filtering accuracy. At present, the design of Kalman filters for ACSs with time-delay links mainly focuses on ACSs with measurement delays, but the essence of these methods is the high-dimensional transformation of the system, which leads to shortcomings such as high variable dimension and heavy algorithm load. Therefore, considering the combined influence of the above factors, it is necessary to design an effective fault estimation Kalman filter to improve the estimation accuracy of composite faults of ACSs.
另外,对于ACSs而言,因其长期运行于复杂工况下,诸多不确定因素可能导致测量元件异常,从而导致噪声的测量值和真实值存在一定的偏差,进一步降低了滤波精度。目前,已有诸如蝗虫算法、野山羊算法、灰狼算法和鲸鱼优化算法(WOA)等群体智能算法用于优化系统噪声,从而降低系统噪声测量偏差对于滤波精度的影响。但已有的研究和应用表明,上述方法不同程度地具有收敛速度慢、寻优精度低和易陷入局部最优解等不足。因此,结合有效的方法改进现有的群体智能寻优方法,对于增强算法性能、提高噪声寻优精度,进而提高ACSs的故障估计精度,具有重要的意义。In addition, for ACSs, because they operate under complex working conditions for a long time, many uncertain factors may cause abnormal measurement components, resulting in a certain deviation between the measured value and the true value of the noise, further reducing the filtering accuracy. At present, swarm intelligence algorithms such as locust algorithm, wild goat algorithm, gray wolf algorithm and whale optimization algorithm (WOA) have been used to optimize system noise, thereby reducing the impact of system noise measurement deviation on filtering accuracy. However, existing research and applications have shown that the above methods have shortcomings such as slow convergence speed, low optimization accuracy and easy to fall into local optimal solutions to varying degrees. Therefore, combining effective methods to improve the existing swarm intelligence optimization method is of great significance for enhancing algorithm performance, improving noise optimization accuracy, and thus improving the fault estimation accuracy of ACSs.
考虑ACSs的速度时滞、可建模扰动和系统测量偏差,视执行器、传感器故障为系统的附加状态变量,则得到时滞广义系统。故而,ACSs的故障估计转化为时滞广义系统的状态估计。近年来,广义系统的Kalman滤波估计成为国内外研究的热点。由于广义系统的动态项中存在奇异矩阵,导致现有奇异结构的Kalman滤波器解算困难,且其协方差矩阵可能出现奇异值,不易于应用。同时,目前针对状态时滞广义系统的Kalman滤波估计方法仍较为有限。另外,上述的外部干扰和系统测量偏差给非线性广义系统的Kalman滤波器设计带来了额外的挑战。因此,本发明视执行器、传感器复合故障为ACSs的附加变量,建立时滞广义系统;基于扰动观测器设计鲁棒Kalman滤波器,设计鲁棒参数以解决系统非线性项和非线性时滞项的线性化误差问题;基于精英集合策略的改进退火模拟算法(ISA)和自适应参数改进WOA,以更好地寻优系统噪声,降低噪声测量偏差对滤波精度的影响。结合鲁棒H方法、KalmanConsidering the speed time delay, modelable disturbance and system measurement deviation of ACSs, and regarding the actuator and sensor faults as additional state variables of the system, a time-delay generalized system is obtained. Therefore, the fault estimation of ACSs is transformed into the state estimation of the time-delay generalized system. In recent years, Kalman filter estimation of generalized systems has become a hot topic of research at home and abroad. Due to the existence of singular matrices in the dynamic terms of generalized systems, the existing singular structure Kalman filter is difficult to solve, and its covariance matrix may have singular values, which is not easy to apply. At the same time, the current Kalman filter estimation methods for state-delay generalized systems are still relatively limited. In addition, the above-mentioned external disturbances and system measurement deviations bring additional challenges to the design of Kalman filters for nonlinear generalized systems. Therefore, the present invention regards the combined faults of actuators and sensors as additional variables of ACSs and establishes a time-delay generalized system; designs a robust Kalman filter based on a disturbance observer and designs robust parameters to solve the linearization error problem of the system nonlinear terms and nonlinear time-delay terms; improves the WOA based on the improved annealing simulation algorithm (ISA) of the elite set strategy and adaptive parameters to better optimize the system noise and reduce the influence of noise measurement deviation on the filtering accuracy.
∞∞
滤波器和扰动估计思想,利用改进的群体智能算法设计优化的鲁棒Kalman滤波器,从而提高复杂工况下的ACSs复合故障估计精度,具有重要的现实意义。The idea of filter and disturbance estimation is used to design an optimized robust Kalman filter using an improved swarm intelligence algorithm, thereby improving the estimation accuracy of ACSs compound faults under complex working conditions, which has important practical significance.
发明内容Summary of the invention
本发明的目的是提供一种卫星姿态控制系统故障估计的Kalman滤波方法,实现航天器的高精度故障估计。The purpose of the present invention is to provide a Kalman filtering method for fault estimation of a satellite attitude control system, so as to achieve high-precision fault estimation of a spacecraft.
为实现上述目的,本发明提供了一种卫星姿态控制系统故障估计的Kalman滤波方法,具体步骤如下:To achieve the above object, the present invention provides a Kalman filtering method for satellite attitude control system fault estimation, and the specific steps are as follows:
步骤S1:考虑可建模干扰和状态时滞,将执行器故障和传感器故障为卫星姿态控制系统的附加变量,建立时滞广义系统模型;Step S1: Considering the modelable disturbance and state time delay, actuator failure and sensor failure are taken as additional variables of the satellite attitude control system, and a time-delay generalized system model is established;
步骤S2:针对建立的时滞广义系统,基于鲁棒滤波和扰动观测器设计非奇异鲁棒Kalman滤波器;Step S2: for the established time-delay descriptor system, a non-singular robust Kalman filter is designed based on robust filtering and disturbance observer;
非奇异鲁棒Kalman滤波器包括干扰估计项和非线性状态估计项,The non-singular robust Kalman filter includes interference estimation terms and nonlinear state estimation terms.
基于扰动观测器的干扰估计项用于估计可建模干扰;The disturbance estimation term based on the disturbance observer is used to estimate the modelable disturbance;
非线性状态估计项用于估计时滞广义系统的状态变量;The nonlinear state estimation term is used to estimate the state variables of the time-delay descriptor system;
步骤S3:基于泰勒级数展开时滞广义系统的非线性项和非线性时滞项,并给出泰勒级数展开截断误差的鲁棒上界;Step S3: Based on the Taylor series expansion of the nonlinear term and the nonlinear time-delay term of the time-delay descriptor system, a robust upper bound of the Taylor series expansion truncation error is given;
步骤S4:基于精英集合策略得到改进的模拟退火算法,通过改进的模拟退火算法和自适应参数改进鲸鱼优化算法,得到改进的鲸鱼优化算法,通过改进的鲸鱼优化算法优化系统的噪声协方差矩阵,并用优化后的噪声协方差矩阵代替系统原有噪声协方差;Step S4: an improved simulated annealing algorithm is obtained based on the elite set strategy, and the whale optimization algorithm is improved by the improved simulated annealing algorithm and adaptive parameters to obtain an improved whale optimization algorithm, and the noise covariance matrix of the system is optimized by the improved whale optimization algorithm, and the original noise covariance of the system is replaced by the optimized noise covariance matrix;
步骤S5:执行时滞广义系统的状态估计和可建模干扰估计,完成卫星姿态控制系统的状态估计和多种故障估计。Step S5: Execute state estimation and modelable interference estimation of the time-delay generalized system, and complete state estimation and multiple fault estimation of the satellite attitude control system.
优选的,在步骤S1中,Preferably, in step S1,
所述可建模干扰具有谐波特性,且等效为外源干扰;The modelable interference has harmonic characteristics and is equivalent to external interference;
所述时滞为定常时滞,即时滞常数为正整数;The time lag is a steady-state time lag, that is, the time lag constant is a positive integer;
所述执行器和所述传感器的故障分布矩阵和可建模干扰分布矩阵均为列满秩矩阵。The fault distribution matrix and the modelable interference distribution matrix of the actuator and the sensor are both column full rank matrices.
优选的,所述卫星姿态控制系统的模型为:Preferably, the model of the satellite attitude control system is:
其中,xk、xk-l、g(xk)、gd(xk-l)、uk、yk分别为:卫星的三轴角速度、角速度时滞、非线性项、非线性时滞项、控制输入、测量输出;l代表时滞常数且为正整数,fk和sk分别表示执行器故障和传感器故障;A、Ad和C为常数矩阵;常数矩阵B为控制输入uk的系数矩阵;Fa和Fs分别为执行器故障fk和传感器故障sk的分布矩阵;wk和vk分别为过程白噪声和测量白噪声,dk为可建模干扰,常数矩阵Fd为其分布矩阵;Among them, xk , xkl , g( xk ), gd ( xkl ), uk , yk are: the satellite's three-axis angular velocity, angular velocity time delay, nonlinear term, nonlinear time delay term, control input, and measurement output, respectively; l represents the time delay constant and is a positive integer, fk and sk represent actuator fault and sensor fault, respectively; A, Ad , and C are constant matrices; the constant matrix B is the coefficient matrix of the control input uk ; Fa and Fs are the distribution matrices of actuator fault fk and sensor fault sk , respectively; wk and vk are process white noise and measurement white noise, respectively; dk is the modelable interference, and the constant matrix Fd is its distribution matrix;
可建模干扰的等效公式如下:The equivalent formula for modeling interference is as follows:
dk=D1ηk+D2,ηk+1=Wηk d k =D 1 η k +D 2 , η k+1 =Wη k
其中,ηk为外源干扰,D1、D2和W为常数矩阵;Among them, η k is the external interference, D 1 , D 2 and W are constant matrices;
令x=[xT fT sT]T,yr,k=Crfk+vr,k,vr,k为白噪声,且其协方差矩阵为Rr,k,令fk+1≈fk,则得到时滞广义系统如下:Let x = [x T f T s T ] T , y r,k = C r f k + v r,k , v r,k is white noise, and its covariance matrix is R r,k , let f k+1 ≈ f k , then the time-delay generalized system is as follows:
其中:E=diag(I,0),I代表设定维数的单位阵;为时滞广义系统的状态变量,为状态时滞变量, Where: E = diag(I,0), I represents the unit matrix of set dimension; is the state variable of the time-delay descriptor system, is the state lag variable,
系统白噪声wk和vk的协方差为Qk和Rk,和的协方差为和 The covariance of the system white noise w k and v k is Q k and R k , and The covariance of and
优选的,与时滞广义系统和所设计的非奇异鲁棒Kalman滤波器有关的非奇异矩阵G和矩阵H满足如下公式:Preferably, the non-singular matrix G and the matrix H related to the time-delay descriptor system and the designed non-singular robust Kalman filter satisfy the following formula:
非奇异矩阵G和矩阵H的通解为:The general solution for non-singular matrices G and H is:
其中,Y为自由度矩阵,为伪逆。in, Y is the degree of freedom matrix, It is a pseudo-reverse.
优选的,所述非奇异鲁棒Kalman滤波器结构为:Preferably, the non-singular robust Kalman filter structure is:
其中,和分别用以估计时滞广义系统的状态变量状态时滞变量和外源干扰ηk;Kk和Vk为待设计的增益矩阵;in, and They are used to estimate the state variables of the time-delay descriptor system State Delay Variable and external interference η k ; K k and V k are gain matrices to be designed;
令 定义变量J的误差为得到和η的联合估计误差为:make Define the error of variable J as get The joint estimation error of and η is:
其中, in,
优选的,非线性误差项和采用泰勒级数展开方式进行线性化,利用等式表示非线性高阶项和非线性时滞高阶项后,得到:Preferably, the nonlinear error term and After linearization using Taylor series expansion and using equations to represent nonlinear high-order terms and nonlinear time-delay high-order terms, we get:
其中,Ni,k(i=1,2)为关于 关于求导得到的矩阵;L1和L2为常数矩阵,φ1,k和φ2,k为未知有界矩阵,满足 in, N i,k (i=1,2) is about about The matrix obtained by derivative; L 1 and L 2 are constant matrices, φ 1,k and φ 2,k are unknown bounded matrices satisfying
基于不等式引理,得到的协方差矩阵鲁棒上界Pk+1为:Based on the inequality lemma, we get The robust upper bound P k+1 of the covariance matrix is:
其中,标量μ>0,γ1和γ2为设计的鲁棒参数, Among them, the scalar μ>0, γ1 and γ2 are the designed robust parameters,
滤波增益矩阵满足:The filter gain matrix satisfies:
且估计误差对于增广噪声和的鲁棒性由如下不等式保证:And the estimated error For the augmented noise and The robustness of is guaranteed by the following inequality:
其中,P0 -1代表估计误差协方差上界初始值P0的逆;对于矩阵或变量X、Z,有 Among them, P 0 -1 represents the inverse of the initial value P 0 of the upper bound of the estimated error covariance; for matrices or variables X, Z, there is
优选的,改进的鲸鱼优化算法具体步骤如下:Preferably, the specific steps of the improved whale optimization algorithm are as follows:
步骤S41a:设置自适应参数ps;Step S41a: setting the adaptive parameter ps ;
步骤S42a:基于自适应参数ps,执行鲸鱼优化算法的搜索过程:Step S42a: Based on the adaptive parameter ps , the search process of the whale optimization algorithm is performed:
若rand()>ps,鲸鱼对猎物进行局部搜索:If rand()> ps , the whale performs a local search for prey:
其中,p是0和1之间的随机数,Ui,k+1是当前粒子位置,Ui,k *是最优粒子的位置,是定义螺旋形状的常数,ω在-1和1之间, ζ=2arl1-a,ξ=2rl2,rl1和rl2是0和1之间的随机数,a是收敛因子,从2线性下降到0;Where p is a random number between 0 and 1, U i,k+1 is the current particle position, U i,k * is the position of the optimal particle, is a constant that defines the shape of the spiral, ω is between -1 and 1, ζ=2ar l1 -a,ξ=2r l2 ,r l1 and r l2 are random numbers between 0 and 1, a is the convergence factor, which decreases linearly from 2 to 0;
若rand()≤ps,鲸鱼对猎物进行全局搜索:If rand() ≤ps , the whale conducts a global search for prey:
其中, 是随机粒子在当前总体中的位置。in, is the position of the random particle in the current population.
步骤S43a:通过精英集合策略判断是否进入集合,假设选择集合的大小为Y,定义则精英集合策略步骤为:Step S43a: Determine by elite set strategy Whether to enter the collection, assuming that the size of the selected collection is Y, define Then the steps of elite set strategy are:
①对于适应度函数ψ,若则进入集合;否则,转至步骤④;①For the fitness function ψ, if but Enter the collection; otherwise, go to
②若j<Y,则j=j+1,进入集合;若j=Y-1,则进入集合,退出集合;②If j<Y, then j=j+1, Enter the set; if j = Y-1, then Enter the collection, Exit the collection;
③将集合中的元素从大到小排列,即 ③ Arrange the elements in the set from large to small, that is
④结束判断;④End the judgment;
步骤S44a:基于精英集合策略,执行模拟退火算法,用Mertopolis接受概率判断是否接受新的解:Step S44a: Based on the elite set strategy, execute the simulated annealing algorithm and use the Mertopolis acceptance probability Determine whether to accept the new solution:
其中,是随机粒子在精英集合中的位置, in, is the position of the random particle in the elite set,
若则否则 like but otherwise
若则否则Ui,k+1=Ui,k。like but Otherwise U i,k+1 =U i,k .
优选的,通过改进的鲸鱼优化算法优化系统的噪声协方差矩阵和得到的优化值分别为和将和代入非奇异鲁棒Kalman滤波器,具体步骤如下:Preferably, the noise covariance matrix of the system is optimized by an improved whale optimization algorithm and The optimized values obtained are and Will and Substitute into the non-singular robust Kalman filter, the specific steps are as follows:
步骤S41b:初始化,给定状态估计及其相应协方差矩阵的初始值;Step S41b: Initialization, giving the initial value of the state estimate and its corresponding covariance matrix;
步骤S42b:寻找最优噪声,通过改进的鲸鱼优化算法寻优到和的最优值和 Step S42b: Find the optimal noise, and use the improved whale optimization algorithm to find the optimal and The optimal value of and
步骤S43b:执行滤波估计,得到时滞广义系统状态变量和外源干扰ηk+1的联合估计值其相应的协方差鲁棒上界和滤波增益矩阵计算方式为:Step S43b: Execute filtering estimation to obtain the state variables of the time-delay generalized system and the joint estimate of the external interference η k+1 The corresponding covariance robust upper bound and filter gain matrix are calculated as follows:
步骤S44b:对下一组样本重复步骤S41b-步骤S43b。Step S44b: Repeat steps S41b to S43b for the next set of samples.
优选的,得到所述的联合估计值后,计算如下的估计值:Preferably, the joint estimate is obtained Then, the following estimates are calculated:
计算时滞广义系统的状态估计值和外源干扰的估计值 Compute state estimates for time-delay descriptor systems and estimates of external interference
由计算可建模干扰估计值 Depend on Compute modelable interference estimates
计算卫星姿态控制系统的状态估计值且计算执行器与传感器复合故障估计值和 Compute state estimates for satellite attitude control systems And calculate the estimated value of the combined fault of the actuator and sensor and
优选的,得到滤波算法的结果包括卫星状态估计曲线、基于执行器与传感器的复合故障估计曲线、改进的鲸鱼优化算法适应度函数迭代曲线以及用于评价滤波算法的指标数据,指标数据为均方根误差。Preferably, the results of the filtering algorithm include a satellite state estimation curve, a composite fault estimation curve based on actuators and sensors, an improved whale optimization algorithm fitness function iteration curve, and indicator data for evaluating the filtering algorithm, wherein the indicator data is a root mean square error.
因此,本发明采用上述一种卫星姿态控制系统故障估计的Kalman滤波方法,具有以下有益效果:Therefore, the present invention adopts the above-mentioned Kalman filtering method for satellite attitude control system fault estimation, which has the following beneficial effects:
(1)本发明的技术方案考虑可建模干扰和状态时滞,将执行器和传感器故障为卫星姿态控制系统的附加变量,建立时滞广义系统模型,充分考虑了ACSs的执行器故障、传感器故障、可建模干扰、状态定常时滞和系统测量偏差等复杂因素的影响,然后设计故障估计Kalman滤波器,不仅解决了复杂运行环境下卫星姿态控制系统的复合故障估计问题,而且拓展了Kalman滤波在时滞广义系统中的应用范围。(1) The technical solution of the present invention takes into account modelable interference and state time delay, regards actuator and sensor faults as additional variables of the satellite attitude control system, establishes a time-delay generalized system model, and fully considers the influence of complex factors such as actuator failure, sensor failure, modelable interference, state steady-state time delay and system measurement deviation of ACSs. Then, a fault estimation Kalman filter is designed, which not only solves the complex fault estimation problem of satellite attitude control systems under complex operating environments, but also expands the application scope of Kalman filtering in time-delay generalized systems.
(2)本发明的技术方案,针对建立的时滞广义系统,基于鲁棒滤波和扰动观测器设计非奇异鲁棒Kalman滤波器;非奇异鲁棒Kalman滤波器具有非奇异的结构,具有计算简单、实现容易等优点,在实现多种故障估计的同时,也实现了可建模外部干扰的估计;通过设计的鲁棒上界,降低了非线性项和非线性时滞项因泰勒级数展开导致的线性化误差,从而提高了滤波精度,进而得到了更精确的ACSs状态估计结果、可建模干扰估计结果和执行器、传感器故障估计结果。(2) The technical solution of the present invention is to design a non-singular robust Kalman filter based on robust filtering and disturbance observer for the established time-delay generalized system; the non-singular robust Kalman filter has a non-singular structure and has the advantages of simple calculation and easy implementation. While realizing multiple fault estimations, it also realizes the estimation of modelable external disturbances; through the designed robust upper bound, the linearization error of nonlinear terms and nonlinear time-delay terms caused by Taylor series expansion is reduced, thereby improving the filtering accuracy, and further obtaining more accurate ACSs state estimation results, modelable disturbance estimation results, and actuator and sensor fault estimation results.
(3)本发明的技术方案,针对系统的噪声测量偏差,基于精英集合策略改进退火模拟算法,并基于改进的退火模拟算法和自适应参数改进鲸鱼优化算法(WOA)。得到的改进的鲸鱼优化算法(IWOA)在一定程度上有效地避免了WOA优化精度低、收敛速度较慢和易陷入局部最优解等缺陷,从而更好地寻优了系统噪声,基于改进鲸鱼算法寻优得到的过程噪声和测量噪声协方差矩阵,执行优化滤波算法。该算法有效地降低了系统噪声测量偏差导致的滤波精度降低问题,从而更有效地估计出卫星姿态控制系统的状态值、可建模干扰值和多种故障值;相较于以往的优化滤波算法,得到了更高的估计精度。(3) The technical solution of the present invention aims at the noise measurement deviation of the system, improves the annealing simulation algorithm based on the elite set strategy, and improves the whale optimization algorithm (WOA) based on the improved annealing simulation algorithm and adaptive parameters. The obtained improved whale optimization algorithm (IWOA) effectively avoids the defects of low optimization accuracy, slow convergence speed and easy to fall into local optimal solution of WOA to a certain extent, so as to better optimize the system noise, and executes the optimization filtering algorithm based on the process noise and measurement noise covariance matrix obtained by optimizing the improved whale algorithm. The algorithm effectively reduces the problem of reduced filtering accuracy caused by the system noise measurement deviation, so as to more effectively estimate the state value, modelable interference value and various fault values of the satellite attitude control system; compared with the previous optimization filtering algorithm, a higher estimation accuracy is obtained.
下面通过附图和实施例,对本发明的技术方案做进一步的详细描述。The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为本发明一种卫星姿态控制系统故障估计的Kalman滤波方法的结构示意图;FIG1 is a schematic diagram of the structure of a Kalman filtering method for fault estimation of a satellite attitude control system according to the present invention;
图2a为本发明卫星姿态控制系统的X轴状态估计结果图;FIG2a is a diagram showing the X-axis state estimation result of the satellite attitude control system of the present invention;
图2b为本发明卫星姿态控制系统的Y轴状态估计结果图;FIG2 b is a diagram showing the Y-axis state estimation result of the satellite attitude control system of the present invention;
图2c为本发明卫星姿态控制系统的Z轴状态估计结果图;FIG2c is a diagram showing the Z-axis state estimation result of the satellite attitude control system of the present invention;
图3为可建模扰动估计结果图;Figure 3 is a diagram of the modelable disturbance estimation results;
图4为执行器故障估计结果;Figure 4 shows the actuator fault estimation results;
图5为传感器故障估计结果;Figure 5 shows the sensor fault estimation results;
图6为IWOA-ODORKF与WOA-ORDRKF自适应函数迭代结果对比图。Figure 6 is a comparison of the iterative results of the adaptive functions of IWOA-ODORKF and WOA-ORDRKF.
具体实施方式DETAILED DESCRIPTION
实施例Example
为使本发明实施例的目的、技术方案和优点更加清楚,下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述,显然,所描述的实施例是本发明一部分实施例,而不是全部的实施例。通常在此处附图中描述和示出的本发明实施例的组件可以以各种不同的配置来布置和设计。In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.
因此,以下对在附图中提供的本发明的实施例的详细描述并非旨在限制要求保护的本发明的范围,而是仅仅表示本发明的选定实施例。基于本发明中的实施例,本领域普通技术人员在没有作出创造性劳动前提下所获得的所有其他实施例,都属于本发明保护的范围。Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
下面结合附图,对本发明的实施方式作详细说明。The embodiments of the present invention are described in detail below in conjunction with the accompanying drawings.
参考图1,一种卫星姿态控制系统故障估计的Kalman滤波方法,具体步骤如下:Referring to FIG1 , a Kalman filtering method for satellite attitude control system fault estimation is shown in the following specific steps:
步骤S1:考虑可建模干扰和状态时滞,将执行器和传感器故障为卫星姿态控制系统的附加变量,建立时滞广义系统模型。所述执行器和所述传感器的故障分布矩阵和可建模干扰分布矩阵均为列满秩矩阵。Step S1: Considering modelable interference and state time delay, actuator and sensor faults are taken as additional variables of the satellite attitude control system, and a time-delay generalized system model is established. The fault distribution matrix of the actuator and the sensor and the modelable interference distribution matrix are both column full rank matrices.
本实施例的卫星姿态控制系统的模型为:The model of the satellite attitude control system of this embodiment is:
其中,xk、xk-l、g(xk)、gd(xk-l)、uk、yk分别为:卫星的三轴角速度、角速度时滞、非线性项、非线性时滞项、控制输入、测量输出;l代表时滞常数且为正整数;fk和sk表示执行器和传感器故障;A、Ad和C为常数矩阵;常数矩阵B为控制输入uk的系数矩阵;Fa和Fs分别为执行器故障fk和传感器故障sk的分布矩阵;wk和vk分别为过程白噪声和测量白噪声,dk为可建模干扰,常数矩阵Fd为其分布矩阵。Among them, xk , xkl , g( xk ), gd ( xkl ), uk , and yk are the satellite's three-axis angular velocity, angular velocity lag, nonlinear term, nonlinear lag term, control input, and measurement output, respectively; l represents the lag constant and is a positive integer; fk and sk represent actuator and sensor faults; A, Ad, and C are constant matrices; the constant matrix B is the coefficient matrix of the control input uk ; Fa and Fs are the distribution matrices of actuator fault fk and sensor fault sk, respectively; wk and vk are process white noise and measurement white noise, respectively; dk is the modelable interference, and the constant matrix Fd is its distribution matrix.
可建模干扰具有谐波特性,且可等效为外源干扰;The modelable interference has harmonic characteristics and can be equivalent to external interference;
可建模干扰的等效公式如下:The equivalent formula for modeling interference is as follows:
dk=D1ηk+D2,ηk+1=Wηk d k =D 1 η k +D 2 , η k+1 =Wη k
其中,ηk为外源干扰,D1、D2和W为常数矩阵;Among them, η k is the external interference, D 1 , D 2 and W are constant matrices;
令yr,k=Crfk+vr,k,vr,k为白噪声,且其协方差矩阵为Rr,k,令fk+1≈fk,则得到时滞广义系统如下:make yr ,k = C rfk + vr,k , vr ,k is white noise, and its covariance matrix is Rr,k . Let fk+1 ≈ fk , then the time-delay generalized system is as follows:
其中:E=diag(I,0),I代表适当维数的单位阵,为时滞广义系统的状态变量,为状态时滞变量 其他矩阵的具体形式为:Where: E = diag(I,0), I represents the unit matrix of appropriate dimension, is the state variable of the time-delay descriptor system, is the state lag variable The specific forms of other matrices are:
另外,系统白噪声wk和vk的协方差为Qk和Rk,和的协方差为和由矩阵和D1的性质,保证了时滞广义系统的完全可检测性和滤波器设计的可行性。In addition, the covariance of the system white noise w k and v k is Q k and R k , and The covariance of and By matrix The properties of D1 and D2 guarantee the complete detectability of the time-delay descriptor system and the feasibility of filter design.
与时滞广义系统和所设计的非奇异鲁棒Kalman滤波器有关的非奇异矩阵G和矩阵H满足如下公式:The non-singular matrices G and H related to the time-delay descriptor system and the designed non-singular robust Kalman filter satisfy the following formulas:
HE+GC=In,HE+GC=I n ,
非奇异矩阵G和矩阵H的通解为:The general solution for non-singular matrices G and H is:
其中,Y为自由度矩阵,为伪逆。in, Y is the degree of freedom matrix, It is a pseudo-reverse.
步骤S2:针对建立的时滞广义系统,基于鲁棒滤波和扰动观测器设计非奇异鲁棒Kalman滤波器。Step S2: For the established time-delay descriptor system, a non-singular robust Kalman filter is designed based on robust filtering and disturbance observer.
非奇异鲁棒Kalman滤波器包括干扰估计项和非线性状态估计项。基于扰动观测器的干扰估计项用于估计可建模干扰。非线性状态估计项用于估计时滞广义系统的状态变量。The non-singular robust Kalman filter includes disturbance estimation term and nonlinear state estimation term. The disturbance estimation term based on disturbance observer is used to estimate the modelable disturbance. The nonlinear state estimation term is used to estimate the state variables of the time-delay descriptor system.
非奇异鲁棒Kalman滤波器结构为:The structure of the non-singular robust Kalman filter is:
其中,和分别用以估计时滞广义系统的状态变量状态时滞变量和外源干扰ηk;Kk和Vk为待设计的增益矩阵;in, and They are used to estimate the state variables of the time-delay descriptor system State Delay Variable and external interference η k ; K k and V k are gain matrices to be designed;
令 定义变量J的误差为得到和η的联合估计误差为:make Define the error of variable J as get The joint estimation error of and η is:
其中, in,
步骤S3:基于泰勒级数展开时滞广义系统的非线性项和非线性时滞项,并给出泰勒级数展开截断误差的鲁棒上界。Step S3: Based on the Taylor series expansion, the nonlinear terms and nonlinear time-delay terms of the time-delay descriptor system are obtained, and a robust upper bound of the Taylor series expansion truncation error is given.
给定非线性高阶项和非线性时滞高阶项的鲁棒上界,非线性误差项和采用泰勒级数展开方式进行线性化,利用等式表示非线性高阶项和非线性时滞高阶项后,保留一阶导数项作为线性误差项,且截断误差表示为:得到:Given the robust upper bounds of the nonlinear high-order terms and the nonlinear time-delay high-order terms, the nonlinear error term and The Taylor series expansion method is used for linearization. After the nonlinear high-order terms and nonlinear time-delay high-order terms are expressed by equations, the first-order derivative terms are retained as linear error terms, and the truncation error is expressed as: get:
其中,Ni,k(i=1,2)为关于关于求导得到的矩阵。in, N i,k (i=1,2) is about about The matrix obtained by derivative.
基于不等式引理,给定正标量μ,设计鲁棒参数γ1和γ2,,得到的协方差矩阵鲁棒上界Pk+1为:Based on the inequality lemma, given a positive scalar μ, we design robust parameters γ 1 and γ 2 , and obtain The robust upper bound P k+1 of the covariance matrix is:
其中,标量μ>0,γ1和γ2为设计的鲁棒参数, Among them, the scalar μ>0, γ1 and γ2 are the designed robust parameters,
同时,设计的滤波增益矩阵满足:At the same time, the designed filter gain matrix satisfies:
且估计误差对于增广噪声和的鲁棒性由如下不等式保证:And the estimated error For the augmented noise and The robustness of is guaranteed by the following inequality:
其中,其中,P0 -1代表估计误差协方差上界初始值P0的逆,对于矩阵或变量X、Z,有 Among them, P 0 -1 represents the inverse of the initial value P 0 of the upper bound of the estimated error covariance. For matrices or variables X and Z, there is
步骤S4:基于精英集合策略得到改进的模拟退火算法,通过改进的模拟退火算法和自适应参数改进鲸鱼优化算法,得到改进的鲸鱼优化算法,通过改进的鲸鱼优化算法优化系统的噪声协方差矩阵,并用优化后的噪声协方差矩阵代替系统原有噪声协方差。Step S4: Based on the elite set strategy, an improved simulated annealing algorithm is obtained, and the whale optimization algorithm is improved by the improved simulated annealing algorithm and adaptive parameters to obtain an improved whale optimization algorithm. The noise covariance matrix of the system is optimized by the improved whale optimization algorithm, and the original noise covariance of the system is replaced by the optimized noise covariance matrix.
改进的鲸鱼优化算法具体步骤如下:The specific steps of the improved whale optimization algorithm are as follows:
步骤S41a:设置自适应参数ps;Step S41a: setting the adaptive parameter ps ;
步骤S42a:基于自适应参数ps,执行鲸鱼优化算法的搜索过程:Step S42a: Based on the adaptive parameter ps , the search process of the whale optimization algorithm is performed:
若rand()>ps,鲸鱼对猎物进行局部搜索:If rand()> ps , the whale performs a local search for prey:
其中,p是0和1之间的随机数,Ui,k+1是当前粒子位置,Ui,k *是最优粒子的位置,是定义螺旋形状的常数,ω在-1和1之间, ζ=2arl1-a,ξ=2rl2,rl1和rl2是0和1之间的随机数,a是收敛因子,从2线性下降到0。Where p is a random number between 0 and 1, U i,k+1 is the current particle position, U i,k * is the position of the optimal particle, is a constant that defines the shape of the spiral, ω is between -1 and 1, ζ=2ar l1 -a, ξ=2r l2 , r l1 and r l2 are random numbers between 0 and 1, and a is the convergence factor, which decreases linearly from 2 to 0.
若rand()≤ps,鲸鱼对猎物进行全局搜索:If rand() ≤ps , the whale conducts a global search for prey:
其中, 是随机粒子在当前总体中的位置。in, is the position of the random particle in the current population.
步骤S43a:通过精英集合策略判断是否进入集合,假设选择集合的大小为Y,定义则精英集合策略步骤为:Step S43a: Determine by elite set strategy Whether to enter the collection, assuming that the size of the selected collection is Y, define Then the steps of elite set strategy are:
①对于适应度函数ψ,若则进入集合;否则,转至步骤④;①For the fitness function ψ, if but Enter the collection; otherwise, go to
②若j<Y,则j=j+1,进入集合;若j=Y-1,则进入集合,退出集合;②If j<Y, then j=j+1, Enter the set; if j = Y-1, then Enter the collection, Exit the collection;
③将集合中的元素从大到小排列,即 ③ Arrange the elements in the set from large to small, that is
④结束判断;④End the judgment;
步骤S44a:基于精英集合策略,执行模拟退火算法,用Mertopolis接受概率判断是否接受新的解:Step S44a: Based on the elite set strategy, execute the simulated annealing algorithm and use the Mertopolis acceptance probability Determine whether to accept the new solution:
其中,是随机粒子在精英集合中的位置, in, is the position of the random particle in the elite set,
若则否则 like but otherwise
若则否则Ui,k+1=Ui,k。like but Otherwise U i,k+1 =U i,k .
通过改进的鲸鱼优化算法优化系统的噪声协方差矩阵和得到的优化值分别为和将和代入非奇异鲁棒Kalman滤波器,得到的IWOA-DORKF滤波流程具体步骤如下:Optimizing the noise covariance matrix of the system by using the improved whale optimization algorithm and The optimized values obtained are and Will and Substituting into the non-singular robust Kalman filter, the specific steps of the IWOA-DORKF filtering process are as follows:
步骤S41b:初始化,给定状态估计及其相应协方差矩阵的初始值;Step S41b: Initialization, giving the initial value of the state estimate and its corresponding covariance matrix;
步骤S42b:寻找最优噪声,通过改进的鲸鱼优化算法寻优到和的最优值和 Step S42b: Find the optimal noise, and use the improved whale optimization algorithm to find the optimal and The optimal value of and
步骤S43b:执行滤波估计,得到时滞广义系统状态变量和外源干扰ηk+1的联合估计值其相应的协方差鲁棒上界和滤波增益矩阵计算方式为:Step S43b: Execute filtering estimation to obtain the state variables of the time-delay generalized system and the joint estimate of the external interference η k+1 The corresponding covariance robust upper bound and filter gain matrix are calculated as follows:
步骤S44b:对下一组样本重复步骤S41b-步骤S43b。Step S44b: Repeat steps S41b to S43b for the next set of samples.
步骤S5:执行时滞广义系统的状态估计和可建模干扰估计,完成卫星姿态控制系统的状态估计和复合故障估计。得到所述的联合估计值后,计算如下的估计值:Step S5: Execute the state estimation and modelable interference estimation of the time-delay generalized system to complete the state estimation and composite fault estimation of the satellite attitude control system. Obtain the joint estimation value Then, the following estimates are calculated:
(1)计算时滞广义系统的状态估计值和外源干扰的估计值 (1) Calculate the state estimate of the time-delay descriptor system and estimates of external interference
(2)由计算可建模干扰估计值 (2) By Compute modelable interference estimates
(3)计算卫星姿态控制系统的状态估计值且计算执行器与传感器复合故障估计值和 (3) Calculate the state estimate of the satellite attitude control system And calculate the estimated value of the combined fault of the actuator and sensor and
得到滤波算法的结果包括卫星状态估计曲线、基于执行器与传感器的复合故障估计曲线、改进的鲸鱼优化算法适应度函数迭代曲线以及用于评价滤波算法的指标数据,指标数据为均方根误差。The results of the filtering algorithm include the satellite state estimation curve, the composite fault estimation curve based on actuators and sensors, the improved whale optimization algorithm fitness function iteration curve, and the indicator data used to evaluate the filtering algorithm, the indicator data is the root mean square error.
为了验证本实施的性能,采用三种滤波器对目标ACSs的故障等进行估计,且将所获得的三种滤波器估计结果进行对比。三种滤波器分别为:DORKF、WOA-DORKF以及IWOA-DORKF。In order to verify the performance of this implementation, three filters are used to estimate the faults of target ACSs, and the estimation results of the three filters are compared. The three filters are DORKF, WOA-DORKF and IWOA-DORKF.
试验结果如图2a、图2b、图2c、图3、图4以及图5所示,基于本实施例的IWOA-DORKF滤波方法具有更快收敛速度、更高计算精度和更好跳出全局最优解能力,对目标ACSs的状态、可建模干扰和执行器、传感器复合故障估计结果最接近目标ACSs相应变量的真实值,因此表明本发明所提供的故障估计方法具有更精确的估计效果。于此同时,如图6所示,WOA-DORKF和本发明的IWOA-DORKF自适应函数迭代对比图。所述的估计精度由IWOA在估计期间内的更优自适应函数迭代方式保证。The test results are shown in Figures 2a, 2b, 2c, 3, 4 and 5. The IWOA-DORKF filtering method based on this embodiment has a faster convergence speed, higher calculation accuracy and better ability to jump out of the global optimal solution. The estimation results of the state of the target ACSs, modelable interference and actuator and sensor composite faults are closest to the true values of the corresponding variables of the target ACSs, thus indicating that the fault estimation method provided by the present invention has a more accurate estimation effect. At the same time, as shown in Figure 6, the WOA-DORKF and the IWOA-DORKF adaptive function iteration comparison diagram of the present invention. The estimation accuracy is guaranteed by the more optimal adaptive function iteration method of IWOA during the estimation period.
最后应说明的是:以上实施例仅用以说明本发明的技术方案而非对其进行限制,尽管参照较佳实施例对本发明进行了详细的说明,本领域的普通技术人员应当理解:其依然可以对本发明的技术方案进行修改或者等同替换,而这些修改或者等同替换亦不能使修改后的技术方案脱离本发明技术方案的精神和范围。Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.
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