A method for diagnosing faults of an attitude determination sensor of a drag-free satellite in displacement mode
By establishing a dynamic model of the dragless satellite and using an extended Kalman filter for state estimation, residual sequences are generated for fault detection and isolation. This solves the problem of hardware redundancy in fault diagnosis of dragless satellite sensors and achieves efficient fault detection and isolation.
Patent Information
- Application Number
- CN202211604614.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-12-13
- Publication Date
- 2025-11-25
- Estimated Expiration
- 2042-12-13
AI Technical Summary
Existing technologies for diagnosing attitude determination sensors for dragless satellites rely on hardware redundancy, which makes it difficult to effectively diagnose faults when multiple sensors fail simultaneously. Furthermore, attitude determination for dragless satellites requires consideration of the interaction between the satellite body and the inspection quality, which traditional methods are not applicable to.
By defining the coordinate system of the dragless system, a dynamic model of the dragless satellite in displacement mode is established. The extended Kalman filter is used for state estimation, residual sequence is generated, and residual chi-square test and generalized likelihood function value calculation are performed to achieve fault detection and isolation without hardware redundancy.
It enables efficient diagnosis of drag-free satellite attitude determination sensor faults, simplifies the fault detection process, reduces reliance on hardware redundancy, and has significant economic benefits and application prospects.
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Figure CN115855110B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The application belongs to the field of drag-free satellite fault diagnosis, and is a displacement mode drag-free satellite attitude determination sensor fault diagnosis method. BACKGROUND
[0002] With the rapid development of science and technology, people's demand for exploration of outer space is increasing, and more and more research needs a spacecraft to provide a stable and low-interference environment, so the drag-free space technology emerges as the times require. The drag-free satellite isolates external interference by placing a test mass inside the satellite, and uses high-precision displacement detection technology to measure the motion of the test mass relative to the satellite. In the displacement mode, the displacement signal is input to the control system to control the thruster to generate thrust, so that the satellite follows the test mass.
[0003] Considering that in space, the drag-free satellite will be affected by various uncertain factors, resulting in system failure. If no active and effective measures are taken to deal with it, it may lead to the failure of the space mission, resulting in huge waste of resources and adverse social impact.
[0004] The attitude determination of the drag-free satellite is crucial to the control of the satellite and the realization of drag-free. Based on the measurement data of the attitude determination sensor, the relative displacement and attitude of the test mass relative to some known reference target in space are determined, and then the controller can give control instructions to generate the required control torque, so as to realize the satellite attitude control and drag-free control.
[0005] Traditional satellite attitude determination sensors include optical sensors and inertial sensors. The optical sensors include sun sensors and star sensors, and the inertial sensors are represented by gyroscopes. The general satellite attitude determination sensor fault detection method mainly uses the hardware redundancy of the sensor, such as comparing the measurement data of gyroscopes at different angles to diagnose faults. However, if multiple sensors fail at the same time and cannot meet the hardware redundancy condition, this fault diagnosis method cannot be used. In addition, the interaction between the satellite body and the test mass also needs to be considered in the attitude determination of the drag-free satellite. In addition to traditional sensors, the electrode cage sensor is also very important. However, the electrode cage sensor cannot meet the hardware redundancy condition, so the fault diagnosis method based on hardware redundancy is not suitable for the drag-free satellite. SUMMARY
[0006] The purpose of the present application is to solve the problems in the prior art and provide a displacement mode drag-free satellite attitude determination sensor fault diagnosis method, which can realize the fault diagnosis of the displacement mode drag-free satellite attitude determination sensor without hardware redundancy.
[0007] In order to achieve the above object, the present application adopts the following technical solutions to achieve the above object:
[0008] A sensor fault diagnosis method for attitude determination of a drag-free satellite in displacement mode, comprising the following steps:
[0009] A coordinate system of a drag-free system is defined, the dynamic composition of a single test mass drag-free satellite and an electrostatic coupling force model are determined, and a dynamic model of the single test mass drag-free satellite in displacement mode is established;
[0010] According to the established dynamic model, a nonlinear state space equation is constructed;
[0011] According to the constructed nonlinear state space equation, state estimation is performed on the drag-free satellite in the attitude determination process, and a residual sequence of attitude-related state quantities is generated;
[0012] Using the generated residual sequence of attitude-related state quantities, residual chi-square test is performed, a chi-square statistic is constructed, and whether the chi-square statistic exceeds the set threshold is judged to perform fault detection of the attitude determination sensor of the drag-free satellite;
[0013] For the fault detected in the fault detection, primary isolation of the fault is performed, and after isolating the faulty sensor, final isolation of the fault is performed.
[0014] Further, the coordinate system of the drag-free system includes a satellite body coordinate system b, an electrode cage coordinate system h, a test mass coordinate system tm, and an inertial coordinate system i; the single test mass drag-free satellite includes a satellite body, an electrode cage, and a test mass, and the electrostatic coupling force model in the electrode cage coordinate system h is:
[0015]
[0016] Wherein, the superscript h represents the equation in the electrode cage coordinate system, K trans and K rot respectively represent the coupling horizontal elastic coefficient and the coupling rotational elastic coefficient, D trans and D rot respectively represent the horizontal damping coefficient and the rotational damping coefficient, f tm,sc and T tm,sc respectively represent the electrostatic coupling force and the torque suffered by the test mass, r h,tm and θ h,tm respectively represent the displacement and the rotation angle of the test mass relative to the electrode cage.
[0017] Further, the dynamic model of the single test mass drag-free satellite in displacement mode is:
[0018]
[0019]
[0020] where superscript b denotes the equation in the satellite body frame, r b,tm and ω b,tm denote the displacement and angular velocity of the proof mass relative to the satellite body, ω i,b denotes the angular velocity of the satellite body, m tm and m sc denote the mass of the proof mass and the satellite body, I tm denotes the inertia matrix of the proof mass, f tm,dist , f tm,sc , and f tm,grav denote the disturbance force, electrostatic coupling force, and gravitational force experienced by the proof mass, f sc,dist , f sc,tm , f sc,grav , and f sc,cont denote the disturbance force, electrostatic coupling force, gravitational force, and control force experienced by the satellite, T tm.dist , T tm.sc , and T tm.grav denote the disturbance torque, electrostatic coupling torque, and gravitational torque experienced by the proof mass.
[0021] Further, in constructing the nonlinear state space equation, the rotation angle θ rel , angular velocity ω rel , displacement r rel , velocity v rel , attitude angle θ sc , and angular velocity ω sc of the proof mass relative to the satellite are selected as state variables, and the state vector and nonlinear state space equation are:
[0022] x = [ θ rel ω rel r rel v rel θ sc ω sc ] T
[0023]
[0024] where f() is a nonlinear function, and w is system noise, including the uncertainty terms of the disturbance force and disturbance torque experienced by the proof mass and the satellite body, and is specifically w = [ Δf tm,dist ΔT tm,dist Δf sc,dist ΔT sc,dist ] T .
[0025] Further, the state of the untowed satellite in the attitude determination process is estimated by using an extended Kalman filter, and the linearized state space equation in the extended Kalman filter is:
[0026]
[0027] where F and G are the Jacobian matrices of the function f() with respect to the state vector and the system noise respectively;
[0028] The sensors used in the attitude determination process of the untowed satellite include optical sensors, inertial sensors and electrode cage sensors, and the measurement vector is:
[0029] z=[θ z,rel r z,rel θ z,sc ω z,sc ] T
[0030] where θ z,rel and r z,rel represent the measurement values of the rotation angle and displacement of the proof mass measured by the electrode cage sensor, θ z,sc represents the measurement value of the satellite body attitude angle measured by the optical sensor, and ω z,sc represents the measurement value of the satellite body rotation angular velocity measured by the inertial sensor.
[0031] The kth step residual sequence obtained is:
[0032] r k =z k -Hx k / k-1
[0033] where z k represents the measurement vector of the kth step, H represents the coefficient matrix of the measurement equation, and x k / k-1 represents the prior estimate of the kth step.
[0034] Further, the chi-square statistic is:
[0035]
[0036] where V k represents the covariance matrix of the kth step residual, and specifically:
[0037] V k =HP k / k-1 H T +R
[0038] where P k / k-1 represents the covariance matrix of the prior estimate of the kth step, and R is the covariance matrix of the measurement noise.
[0039] Further, the determination rule of the fault detection is:
[0040] According to the significance level, the threshold is set as T D If the chi-square statistic λ k >T D , it indicates that the sensor is faulty from the kth step, otherwise, the sensor is normal.
[0041] Further, the primary isolation of the fault is to set a plurality of parallel extended Kalman filters, respectively receiving different types of sensor measurement data for state estimation, and generating residual sequences, and using the generated residual sequences, the faulty sensor is isolated;
[0042] The final isolation of the fault is to calculate the generalized likelihood function value of the faulty sensor in different directions using the generated residual sequences, and according to the residual generalized likelihood function value in the fault direction, the specific fault direction of the faulty sensor is isolated.
[0043] Further, the generalized likelihood function expression is:
[0044]
[0045] Wherein, i (i=1, 2, 3) represents the assumed fault direction, r k,i represents the residual in the assumed fault direction of the kth step, V k,i represents the residual covariance matrix in the assumed fault direction of the kth step, Π k,i is a quantity related to the assumed fault direction, specifically:
[0046]
[0047] Wherein, λ k,i is a geometric constraint coefficient related to the assumed fault direction.
[0048] Compared with the prior art, the present application has the following beneficial effects:
[0049] The application provides a displacement mode satellite attitude determination sensor fault diagnosis method, which comprises the following steps: establishing a dynamic model of a displacement mode satellite without drag, using an extended Kalman filter to perform state estimation and generate a residual, performing fault detection based on a residual chi-square test method, and determining whether a sensor is faulty. BRIEF DESCRIPTION OF DRAWINGS
[0050] In order to more clearly illustrate the technical solutions of the embodiments of the application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some of the embodiments of the application, and therefore should not be regarded as a limitation to the scope. For those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.
[0051] Figure 1 The figure is an implementation flowchart of the displacement mode satellite attitude determination sensor fault diagnosis method of the application.
[0052] Figure 2 The figure is a chi-square statistical quantity change curve diagram in the fault detection stage under a fault-free condition.
[0053] Figure 3 The figure is a chi-square statistical quantity change curve diagram in the fault primary isolation stage under a fault-free condition.
[0054] Figure 4 The figure is a chi-square statistical quantity change curve diagram in the fault detection stage under a fault condition.
[0055] Figure 5 The figure is a chi-square statistical quantity change curve diagram in the fault primary isolation stage under a fault condition.
[0056] Figure 6 The figure is a likelihood function value diagram in different directions in the fault final isolation stage under a fault condition. DETAILED DESCRIPTION
[0057] Exemplary embodiments of the present application are described herein below with reference to the accompanying drawings, in which various specific details are set forth to assist in providing a thorough understanding of the embodiments. It will be apparent, however, to one of ordinary skill in the art that the embodiments described herein can be practiced without many of the specific details. In other instances, well-known structures and functions have not been described in detail in order to avoid obscuring the embodiments.
[0058] It is apparent that the described embodiments are merely some, but not all, of the embodiments of the present application. Based on the embodiments described in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of the present application.
[0059] It should be noted that the terminal involved in the embodiments of the present application can include, but is not limited to, a mobile phone, a personal digital assistant (PDA), a wireless handheld device, a tablet computer, a personal computer (PC), an MP3 player, an MP4 player, a wearable device (for example, smart glasses, a smart watch, a smart bracelet, etc.), a smart home device, and the like.
[0060] In addition, the term "and / or" in the present application is merely a description of the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B can represent the three cases of A alone, A and B together, and B alone. In addition, the character " / " in the present application generally represents an "or" relationship between the front and rear associated objects.
[0061] The present application will be further described in detail below with reference to the accompanying drawings:
[0062] Referring to Figure 1 The present application provides a sensor fault diagnosis method for attitude determination of a drag-free satellite in a displacement mode, comprising the following steps:
[0063] S1, defining a coordinate system of a drag-free system, and explicitly defining the dynamics composition and electrostatic coupling force model of a single proof mass drag-free satellite;
[0064] Without considering the cross-coupling term in the electrostatic coupling force, the electrostatic coupling force model in the defined electrode cage coordinate system h is:
[0065]
[0066] The superscript h represents that the equation is expressed in the electrode cage coordinate system, K trans and K rot respectively represent the coupling horizontal elastic coefficient and the coupling rotation elastic coefficient, Dtrans and D rot represent horizontal and rotational damping coefficients, respectively, f tm,sc and T tm,sc represent electrostatic coupling force and moment on the proof mass, respectively, r h,tm and θ h,tm represent displacement and rotation angle of the proof mass relative to the electrode cage.
[0067] S2, according to the electrostatic coupling force model in S1, a dynamic model of a single proof mass undragged satellite in displacement mode is established as:
[0068]
[0069]
[0070] The superscript b indicates that the equation is in the satellite body coordinate system, r b,tm and ω b,tm represent displacement and rotation angular velocity of the proof mass relative to the satellite body, ω i,b represents rotation angular velocity of the satellite body, m tm and m sc represent mass of the proof mass and the satellite body, I tm represents inertia matrix of the proof mass, f tm,dist , f tm,sc , and f tm,grav represent disturbance force, electrostatic coupling force, and gravity on the proof mass, f sc,dist , f sc,tm , f sc,grav , and f sc,cont represent disturbance force, electrostatic coupling force, gravity, and control force on the satellite, T tm.dist , T tm.sc , and T tm.grav represent disturbance moment, electrostatic coupling moment, and gravity moment on the proof mass.
[0071] S3, according to the dynamic model of the single proof mass undragged satellite in displacement mode established in S2, appropriate state variables are selected, and a nonlinear state space equation is constructed;
[0072] The rotation angle θ rel , angular velocity ω rel , displacement r rel , velocity v rel , attitude angle θ sc , and rotation angular velocity ω sc of the proof mass relative to the satellite are selected as state variables, and the state vector is
[0073] x = [ θ rel ωrel r rel v rel θ sc ω sc ] T (4)
[0074] The dynamic equation of the system can be obtained from the dynamic model of the single proof mass non-towed satellite in displacement mode, the electrostatic coupling force model, and the kinematics and dynamics model of the satellite, as follows:
[0075]
[0076] is the rotation matrix from the proof mass coordinate system to the satellite body coordinate system, and f1() and f2() are nonlinear functions of the satellite attitude kinematics and dynamics, respectively, which are not specifically given here, wherein the kinematics equation is in the order of "312".
[0077] The system noise includes the uncertain terms of the disturbance force and the disturbance torque received by the proof mass and the satellite body, and is specifically w = [Δf tm,dist ΔT tm,dist Δf sc,dist ΔT sc,dist ] T The covariance matrix of which is Q, and the form of the nonlinear state space equation can be obtained as follows:
[0078]
[0079] S4, according to the nonlinear state space equation constructed in S3, the state of the non-towed satellite in the attitude determination process is estimated by using an extended Kalman filter, and a residual sequence of the attitude-related state quantity is generated.
[0080] The linearized state space equation in the designed extended Kalman filter is as follows:
[0081]
[0082] wherein F and G are the Jacobian matrices of the nonlinear function f() with respect to the state vector and the system noise, respectively. Since the state space equation shown in equation (7) is a continuous equation, it needs to be discretized, and the coefficient matrix of the discretization is as follows:
[0083] Φ k ≈I+FT s (8)
[0084] wherein T s is the sampling time.
[0085] The discretized system noise covariance matrix is as follows:
[0086]
[0087] Three sensors are mainly used in the process of attitude determination of the untowed satellite: optical sensor, inertial sensor and electrode cage sensor. The Kalman filter in the fault detection stage receives all the measurement information, and the measurement vector is specifically:
[0088] z = [θ z,rel r z,rel θ z,sc ω z,sc ] T (10)
[0089] Where θ z,rel and r z,rel represent the measurement values of the angle and displacement of the test mass relative to the satellite measured by the electrode cage sensor, θ z,sc represents the measurement value of the attitude angle of the satellite body measured by the optical sensor, and ω z,sc represents the measurement value of the rotation angular velocity of the satellite body measured by the inertial sensor.
[0090] The measurement equation is:
[0091] z = Hx + v (11)
[0092] Where v is the measurement noise, its covariance matrix is R, and H is the coefficient matrix of the measurement equation, which is specifically:
[0093]
[0094] The expression of the residual sequence of the kth step obtained by the extended Kalman filter is:
[0095] r k = z k -Hx k / k-1 (13)
[0096] Where z k represents the measurement vector of the kth step, and x k / k-1 represents the prior estimate of the kth step.
[0097] S5, using the residual sequence of the attitude-related state quantity generated in S4, performing residual chi-square test, constructing chi-square statistic, and setting a reasonable threshold according to the significance level, and judging whether the chi-square statistic exceeds the set threshold to perform fault detection of the attitude determination sensor of the untowed satellite;
[0098] In the residual chi-square test process, the following assumptions are made:
[0099]
[0100] Where, The critical value of chi-square test with significance level a and freedom m is λ k The chi-square distribution with freedom m is expressed as:
[0101]
[0102] where V k The covariance matrix of the residual of the kth step is expressed as:
[0103] V k = HP k / k-1 H T +R (16)
[0104] where P k / k-1 is the covariance matrix of the prior estimation of the kth step.
[0105] The criterion for fault is:
[0106] The threshold of fault detection is set according to the significance level If λ k >T D , it indicates that the sensor is faulty from the kth step, otherwise, the sensor is normal.
[0107] S6, if the fault detection method in S5 detects that the undragging satellite is faulty, primary isolation of the fault is performed, a plurality of parallel extended Kalman filters are set, which respectively receive different types of sensor measurement data to perform state estimation and generate residual sequences, and the generated residual sequences are used to isolate the faulty sensor by using the same method as S5.
[0108] Four parallel extended Kalman filters are set in the primary isolation stage of the fault, and the difference between the four filters and the filters in the fault detection stage is that the four filters respectively receive four different types of measurement data: relative angle θ z,rel , relative displacement r z,rel , satellite attitude angle θ z,sc and satellite rotation angular velocity ω z,sc , as shown in Table 1.
[0109] Table 1: Parallel sensor setting in primary isolation stage of fault
[0110]
[0111]
[0112] The state estimation is generated by using parallel filters respectively to generate residual and to perform residual chi-square test, since each filter only receives single type of measurement data, when the chi-square statistic exceeds the set threshold, it represents that the received measurement data is abnormal, so the faulty sensor can be determined to complete the primary isolation of fault.
[0113] S7、After the faulty sensor is isolated by S6, the final isolation of fault is performed, the residual sequence generated by S6 is used to calculate the generalized likelihood function value in different directions of the faulty sensor, since the residual generalized likelihood function value in the fault direction is obviously larger, the specific fault direction of the faulty sensor can be isolated according to the value.
[0114] The generalized likelihood function value of residual in different directions of the faulty sensor is calculated in the final isolation stage of fault, and the expression of the generalized likelihood function is as follows:
[0115]
[0116] Wherein, i (i=1, 2, 3) represents the assumed fault direction, r k,i represents the residual in the assumed fault direction, V k,i represents the residual covariance matrix in the assumed fault direction, Π k,i is a quantity related to the assumed fault direction, and is specifically as follows:
[0117]
[0118] Wherein, λ k,i is the i-th column of C k , which represents the geometric constraint coefficient related to the assumed fault direction, C k is obtained by Cholesky decomposition of V k,i .
[0119] As can be seen from formula (17), the generalized likelihood function value is a negative value, in order to better represent the difference of the likelihood function value in the fault direction in the form of image, the likelihood function value can be changed as follows:
[0120]
[0121] Since the generalized likelihood function value of residual in the fault direction is obviously larger, the fault direction of the faulty sensor can be determined by comparing the generalized likelihood function values of residual in different directions, and the final isolation of fault is completed.
[0122] The following simulation by Matlab / Simulink is used to illustrate the specific calculation process of the sensor fault diagnosis method for the attitude determination of the non-towed satellite.
[0123] The simulation parameters are set as follows:
[0124] The satellite orbit is a circular orbit with an altitude of 300 km, the satellite mass m sc = 1050 kg, the satellite inertia matrix I sc = diag{200, 2700, 2650} (kg-m 2 ), the proof mass mass m tm = 1 kg, the proof mass inertia matrix I tm = 0.2667 x 10 -3 I3(kg-m 2 ). Since the orbit is low earth orbit, the main external disturbance force on the satellite is atmospheric drag, so the atmospheric drag torque on the satellite is The atmospheric drag on the satellite The external disturbance torque on the proof mass The external disturbance on the proof mass The initial angular velocity of the satellite ω sc (0) = [-0.0023 -0.0017 0.0023] T (rad / s), the initial attitude angle of the satellite θ sc (0) = [0 0 0] T , the initial relative angle θ rel = [π / 180 π / 60 π / 90] T rad, the initial relative displacement r rel = [0.001 0.003 0.002] T (m / s). The sampling time T s = 0.1 s, and the simulation time t = 60 s.
[0125] The electrostatic coupling coefficient matrix between the satellite body and the proof mass is:
[0126]
[0127] D trans = 1.4 x 10 -11 I3(N / m 2 ) (21)
[0128]
[0129] D rot = 1.4 x 10 -14 I3(N / m 2 ) (23)
[0130] All the noises in this simulation are zero-mean Gaussian white noises, and the measurement noises are set as follows: considering that the optical sensor is a sun sensor, the standard deviation of the measurement noise is 10 -3(rad / s), the measurement noise standard deviation of the relative displacement measured by the electrode cage sensor is 10 -4 (rad / s), the measurement noise standard deviation of the relative displacement measured by the electrode cage sensor is 10 -4 (rad / s), the measurement noise standard deviation of the relative displacement measured by the electrode cage sensor is 10 -3 (rad). Since the discretization of the state space equation will introduce correlated system noise, two more terms of system noise are set here, which are the satellite attitude kinematics discretization noise and the satellite attitude dynamics discretization noise, and the specific settings of the system noise are shown in Table 2.
[0131] Table 2 System noise settings
[0132] Noise type Noise standard deviation Interference torque noise experienced by the satellite 10 -6 (N·m) Interference force noise experienced by the satellite 10 -5 N]] Interference torque noise experienced by the test mass 10 -9 (N·m) Interference force noise experienced by the test mass 10 -7 N]] Satellite attitude kinematics discretization noise 10 -4 (rad / s) Satellite attitude dynamics discretization noise 5 x 10 -4 (rad / s 2 )]]>
[0133] The chi-square test critical value with a significance level of 0.01 for 12 degrees of freedom is selected as the threshold T in the fault detection stage D1 = 26.217, and the chi-square test critical value with a significance level of 0.001 for 3 degrees of freedom is selected as the threshold T in the primary fault isolation stage D2 = 16.266.
[0134] The fault parameters are set as follows: at 50s (i.e. 500 sampling points), sudden additive faults are applied to the three sensors, the fault amount of the gyroscope and the sun sensor is 20 times the noise standard deviation, and the fault amount of the electrode cage sensor is 40 times the noise standard deviation. The fault of the gyroscope is applied in the z-axis direction, the fault of the sun sensor is applied in the y-axis direction, the fault of the electrode cage sensor measuring the relative angle is applied in the x-axis direction, and the fault of the electrode cage sensor measuring the relative displacement is applied in the y-axis direction.
[0135] The simulation results under the fault-free condition are shown in Figure 2 and Figure 3 It can be seen from the simulation results that under the fault-free condition, the chi-square statistics of the fault detection stage and the primary fault isolation stage will not exceed the set threshold after stabilization.
[0136] The simulation results under the fault condition are shown in Figures 4 to 6It can be seen from the simulation results that in the case of fault, the chi-square statistics of the fault detection stage obviously exceeds the set threshold at 500 sampling points after the chi-square statistics is stable, and the fault can be detected; in the primary isolation stage of the fault, the chi-square statistics obtained by the four parallel filters also exceeds the threshold at 500 sampling points after the chi-square statistics is stable, and the fault sensor can be isolated; in the final isolation stage of the fault, the likelihood function values in different directions obtained by calculation can be seen, and the residual likelihood function values in the relative angle x-axis direction, the relative displacement y-axis direction, the satellite attitude angle y-axis direction and the satellite angular velocity z-axis direction are obviously larger than those in other non-fault directions, and the direction with larger likelihood function value is the fault direction, and the fault direction can be isolated.
[0137] The preferred embodiments of the present application have been described above by way of example only, not for limitation, and various changes and modifications can be made by those skilled in the art based on the principles and spirit of the present application. Any modification, equivalent replacement, improvement, etc. made within the principles and spirit of the present application shall be included in the protection scope of the present application.
Claims
1. A method for fault diagnosis of an attitude determination sensor of a drag-free satellite in displacement mode, characterized in that, The method comprises the following steps: a coordinate system of a non-dragging system is defined, a dynamic composition of a single test mass non-dragging satellite and an electrostatic coupling force model are determined, and a dynamic model of the single test mass non-dragging satellite in a displacement mode is established; a nonlinear state space equation is constructed according to the established dynamic model; state estimation is performed on the non-dragging satellite in an attitude determination process according to the constructed nonlinear state space equation, and a residual sequence of attitude-related state quantities is generated; residual chi-square test is performed by using the generated residual sequence of the attitude-related state quantities, a chi-square statistic is constructed, and fault detection of a sensor in the attitude determination of the non-dragging satellite is performed by judging whether the chi-square statistic exceeds a set threshold value; primary isolation of the fault is performed, and final isolation of the fault is performed after isolation of the faulty sensor; In the construction of the nonlinear state space equation process, the rotation angle of the test mass relative to the satellite is selected as the state variable , angular velocity , displacement , velocity , attitude angle of the satellite and rotation angular velocity , the state vector and nonlinear state space equation are: wherein, is a nonlinear function, is a system noise including uncertainties of the disturbance force and the disturbance torque received by the proof mass and the satellite body, specifically , denotes the disturbance force received by the proof mass, denotes the disturbance force received by the satellite, denotes the disturbance torque received by the proof mass, denotes the disturbance torque received by the satellite; state estimation is performed on the non-dragging satellite in the attitude determination process by using an extended Kalman filter, and a linearized state space equation in the extended Kalman filter is: wherein and are functions the Jacobian matrix of the state vector and system noise; the sensor used in the attitude determination process of the non-dragging satellite comprises an optical sensor, an inertial sensor and an electrode cage sensor, and a measurement vector is: wherein, and respectively represent the measured values of the test mass with respect to the satellite rotation angle and displacement measured by the electrode cage sensor, respectively represent the measured values of the satellite body attitude angle measured by the optical sensor, respectively represent the measured values of the satellite body rotation angular velocity measured by the inertial sensor; a kth step residual sequence obtained is: wherein denotes the measurement vector of the kth step, denotes the coefficient matrix of the measurement equation, denotes the a priori estimate of the kth step.
2. The method according to claim 1, wherein the coordinate system of the non-dragging system comprises a satellite body coordinate system b, an electrode cage coordinate system h, a test mass coordinate system tm and an inertial coordinate system i; the single test mass non-dragging satellite comprises a satellite body, an electrode cage and a test mass, and an electrostatic coupling force model in the electrode cage coordinate system h is: where the superscript h denotes the equation in the electrode cage coordinate system, and denote the coupling horizontal and coupling rotational stiffness, respectively, and denote the horizontal and rotational damping, respectively, and denote the electrostatic coupling force and torque on the proof mass, respectively, and denote the displacement and rotation angle of the proof mass with respect to the electrode cage, respectively.
3. The method according to claim 1, wherein the dynamic model of the single test mass non-dragging satellite in the displacement mode is: where the superscript b denotes the equation is in the satellite body coordinate system, and denote the displacement and angular velocity of the proof mass relative to the satellite body, respectively, denote the angular velocity of the satellite body, and denote the mass of the proof mass and the satellite body, respectively, denote the inertia matrix of the proof mass, and denote the electrostatic coupling force and the gravity experienced by the proof mass, respectively, , and denote the electrostatic coupling force, the gravity and the control force experienced by the satellite, respectively, and denote the electrostatic coupling moment and the gravity moment experienced by the proof mass, respectively.
4. The method according to claim 1, wherein the chi-square statistic is: wherein, denotes the covariance matrix of the kth step residual, in particular: wherein denotes the covariance matrix of the k-step a priori estimate, is the covariance matrix of the measurement noise.
5. The method of claim 1, wherein, a judgment rule of the fault detection is: According to the significance level, the threshold is set as If the chi-square statistic It means that the sensor is malfunctioning from the kth step, otherwise, the sensor is normal.
6. The method of claim 1, wherein the primary isolation of the fault is to set a plurality of parallel extended Kalman filters, receive state estimation of measurement data of different types of sensors, and generate a residual sequence, and isolate the faulty sensor by using the generated residual sequence; the final isolation of the fault is to calculate a generalized likelihood function value in different directions of the faulty sensor by using the generated residual sequence, and isolate the specific fault direction of the faulty sensor according to the residual generalized likelihood function value in the fault direction.
7. The method according to claim 6, wherein the generalized likelihood function expression is: wherein represents a hypothetical fault direction, represents the residual in the kth step in the hypothetical fault direction, represents the residual covariance matrix in the kth step in the hypothetical fault direction, is a quantity related to the hypothetical fault direction, specifically: wherein is a geometric constraint coefficient related to the assumed fault direction.