Fault and state decoupling method based on dimension reduction energy observation matrix
By decomposing the observable matrix into a shared subspace and subspace residual term in the space aircraft autonomous diagnosis system, and calculating the pseudo-inverse matrix and the left zero space, the problem of high computational complexity of the left zero space of the observable matrix in the prior art is solved, and efficient fault and state decoupling is achieved.
Patent Information
- Application Number
- CN202411503918.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-10-25
- Publication Date
- 2025-02-25
AI Technical Summary
In the autonomous diagnosis system of space aircraft, it is difficult for the prior art to simply calculate the left zero space of the energy-observing matrix, resulting in high computational complexity and difficult to implement on space aircraft with limited computing capabilities.
A fault and state decoupling method based on the dimensionality reduction energy observation matrix is proposed. By determining the Lie derivative calculation rules of the space aircraft autonomous diagnosis system, the energy observation matrix O is established, and it is decomposed into a common subspace and subspace residual term, the pseudo-inverse matrix and the left zero space are calculated, and the left zero space of the energy observation matrix is obtained.
This method greatly reduces the difficulty of left zero space calculation of the energy-observing matrix, improves the calculation accuracy, reduces the calculation complexity, and makes it suitable for independent calculations on space vehicles, realizing effective decoupling of faults and states.
Smart Images
Figure CN119512908A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a fault and state decoupling method based on a dimension reduction energy observable matrix, and belongs to the technical field of space autonomous operation. Background Art
[0002] Deep space exploration is one of the important development directions in the aerospace field. In the future, exploration of celestial bodies in deep space will be carried out, and the healthy flight time of spacecraft will continue to increase. Space autonomous operation technology will be the key technology for deep space exploration missions, and autonomous diagnosis is one of the core technologies for achieving safe, reliable and autonomous operation of spacecraft.
[0003] To realize autonomous diagnosis of spacecraft, it is first necessary to decouple the state quantity of the observation equation in the autonomous diagnosis system of the spacecraft from the fault information, which requires calculating the left null space of the observable matrix of the spacecraft. Given the limited computing power of the spacecraft, how to easily calculate the left null space of the observable matrix is one of the keys.
[0004] The traditional calculation of the left null space of the energy observable matrix includes the linear equation solving method and the matrix elementary transformation method. Among them, the linear equation solving method requires the transposition of the energy observable matrix and then calculates the eigenvector with zero eigenvalue. For high-order energy observable matrices, this calculation process involves a complex eigenvector calculation process, which is difficult to perform on a spacecraft; the matrix elementary transformation method requires the use of elementary matrix transformation matrices to find the vector that makes the linear combination of each row of the energy observable matrix a zero vector, and then obtain the left null space of the matrix. This method is usually used for theoretical derivation and is difficult to implement programmatically. Summary of the invention
[0005] The technical problem solved by the present invention is: to overcome the deficiencies of the prior art, to provide a method for decoupling faults and states based on a reduced-dimensional energy-observable matrix, and to realize left null space calculation of the energy-observable matrix.
[0006] The technical solution of the present invention is:
[0007] In a first aspect, the present invention proposes a fault and state decoupling method based on a dimension-reduced energy matrix, comprising the following steps:
[0008] S1. Determine the calculation rules of Lie derivatives of the spacecraft autonomous diagnosis system;
[0009] S2. Using the Lie derivative calculation rule, establish the observable matrix O of the spacecraft autonomous diagnosis system;
[0010] S3, determining the common subspace and subspace residual items of the observable matrix O of the spacecraft autonomous diagnosis system;
[0011] S4, calculating the pseudo-inverse matrix of the subspace residual items;
[0012] S5, calculating the left null space of the common subspace;
[0013] S6, multiplying the pseudo-inverse matrix and the left null space to obtain the left null space of the observable matrix of the spacecraft autonomous diagnosis system;
[0014] S7. Multiply the left null space of the observable matrix of the spacecraft autonomous diagnosis system by the observation function of the spacecraft autonomous diagnosis system to achieve fault and state decoupling.
[0015] Furthermore, the Lie derivative calculation rule of the spacecraft autonomous diagnosis system is:
[0016]
[0017] L 0 f h=h(X,F)
[0018] Wherein, h(X) is the observation function of the spacecraft autonomous diagnosis system; f(X) is the state function of the spacecraft autonomous diagnosis system; X is the system state quantity; k is the Lie derivative order; F is the system fault quantity; L k f is the k-th Lie derivative of the system, L 0 f is the 0th-order Lie derivative of the system, h is the abbreviated form of h(X);
[0019] The calculation rules are:
[0020] g∈C ∞ , C is a set of continuous functions.
[0021] Furthermore, the observable matrix O of the spacecraft autonomous diagnosis system is established, which is:
[0022]
[0023] Furthermore, the method for constructing the common subspace and subspace residual items of the observable matrix of the spacecraft autonomous diagnosis system is as follows:
[0024] Perform polar coordinate transformation on the system state, and the new system state is Then the observable matrix O is rewritten as:
[0025]
[0026] in, It is the common subspace of the observable matrix of the spacecraft autonomous diagnosis system;
[0027] is the remaining term in the subspace.
[0028] Furthermore, the pseudo-inverse matrix of the residual term of the computation subspace is specifically:
[0029] {γ + |γ + γ=I}
[0030] Where I is the identity matrix; γ + Represents the pseudo-inverse matrix of the obtained subspace residual.
[0031] Furthermore, the left null space of the calculated common subspace is specifically:
[0032] χ - ·χ=0
[0033] Among them, χ - is the left null space of the common subspace.
[0034] Furthermore, the pseudo-inverse matrix is multiplied by the left null space to obtain the left null space of the observable matrix of the spacecraft autonomous diagnosis system, which is specifically:
[0035] O - = x - γ +
[0036] Among them, O - It is the left null space of the observable matrix of the spacecraft autonomous diagnosis system.
[0037] Furthermore, the left null space O of the observable matrix of the spacecraft autonomous diagnosis system is - Multiplying with the observation function of the spacecraft autonomous diagnosis system to achieve fault and state decoupling, specifically:
[0038]
[0039] in, The new observation function of the spacecraft autonomous diagnosis system is obtained by decoupling the fault and the state.
[0040] In a second aspect, the present invention further proposes a non-volatile storage medium, comprising: a computer program product, which, when executed, executes the fault and state decoupling method based on reduced-dimensional energy observable matrix.
[0041] In a third aspect, the present invention further proposes a computer program product, which, when executed by a processor, implements the fault and state decoupling method based on a reduced-dimensional energy observable matrix.
[0042] The beneficial effects of the present invention compared with the prior art are:
[0043] (1) Compared with the traditional energy observable matrix left null space calculation method, the energy observable matrix left null space calculation method provided by the present invention greatly reduces the difficulty of energy observable matrix left null space calculation by decomposing the energy observable matrix into common subspaces and subspace residual items;
[0044] (2) The method of the present invention does not linearize or truncate the state equation and observation equation of the spacecraft, and the left null space calculation method of the energy observable matrix provided has higher accuracy;
[0045] (3) Compared with the traditional method, the observable matrix left null space given by the method of the present invention involves matrix calculations in which the highest dimension of the matrix is the dimension of the system state. Therefore, the calculation complexity is lower and it is suitable for autonomous calculation on a spacecraft. BRIEF DESCRIPTION OF THE DRAWINGS
[0046] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION
[0047] The specific embodiments of the present invention are further described in detail below with reference to the accompanying drawings.
[0048] like Figure 1 As shown, the present invention proposes a fault and state decoupling method based on a dimension reduction energy matrix, comprising the following steps:
[0049] S1. Give the calculation rules of Lie derivative of spacecraft autonomous diagnosis system;
[0050] S2, using the Lie derivative calculation rules given in S1, establish the observable matrix of the spacecraft autonomous diagnosis system;
[0051] S3, give the common subspace and subspace residual items of the observable matrix of the spacecraft autonomous diagnosis system in S2;
[0052] S4, calculate the pseudo-inverse matrix of the remaining items of the subspace in S3;
[0053] S5, calculate the left null space of the common subspace in S3;
[0054] S6, multiplying the pseudo-inverse matrix in S4 and the left null space in S5 to obtain the left null space of the observable matrix of the spacecraft autonomous diagnosis system;
[0055] S7. Decoupling the fault and state is achieved by combining the left null space of the observable matrix of the spacecraft autonomous diagnosis system in S6 with the observation function of the spacecraft autonomous diagnosis system.
[0056] The left null space calculation method of the observable matrix of the spacecraft autonomous diagnosis system obtained by the present invention reduces the calculation complexity, and the algorithm is reliable and occupies less calculation resources.
[0057] The following is a detailed introduction to steps S1 to S7. The steps are as follows:
[0058] S1. The calculation rules of Lie derivative of spacecraft autonomous diagnosis system are given:
[0059]
[0060] L 0 f h=h(X)
[0061] Where h(X) is the observation function of the spacecraft autonomous diagnosis system; f(X) is the state function of the spacecraft autonomous diagnosis system; X is the system state quantity; k is the Lie derivative order; L k f is the k-th Lie derivative of the system, L 0 f is the 0th-order Lie derivative of the system, h is the abbreviated form of h(X);
[0062] The calculation rules are:
[0063] g∈C ∞ , C is a set of continuous functions.
[0064] S2. Using the Lie derivative calculation rules given in S1, the observable matrix of the spacecraft autonomous diagnosis system is established:
[0065]
[0066] S3. Give the common subspace and subspace residual items of the observable matrix of the spacecraft autonomous diagnosis system in S2:
[0067] Perform polar coordinate transformation on the system state, and the new system state is Then the energy observable matrix described in S2 can be rewritten as:
[0068]
[0069] in, It is the common subspace of the observable matrix of the spacecraft autonomous diagnosis system;
[0070] is the remaining term in the subspace.
[0071] S4. Calculate the pseudo-inverse matrix of the remaining items in the subspace in S3:
[0072] {γ + |γ + γ=I}
[0073] Where I is the identity matrix; γ + Represents the pseudo-inverse matrix of the obtained subspace residual.
[0074] S5. Calculate the left null space of the common subspace in S3:
[0075] χ - ·χ=0
[0076] Among them, χ - is the left null space of the common subspace.
[0077] S6. Multiply the pseudo-inverse matrix in S4 and the left null space in S5 to obtain the left null space of the observable matrix of the spacecraft autonomous diagnosis system:
[0078] O - = x - γ +
[0079] Among them, O - It is the left null space of the observable matrix of the spacecraft autonomous diagnosis system.
[0080] S7, multiply the left null space of the observable matrix of the spacecraft autonomous diagnosis system in S6 by the observation function of the spacecraft autonomous diagnosis system to achieve fault and state decoupling:
[0081]
[0082] Among them, The observation function of the spacecraft autonomous diagnosis system is a new observation function obtained by decoupling the fault and the state.
[0083] The fault and state decoupling method of the present invention can be decomposed into common subspaces and subspace residuals by using observability, which greatly reduces the difficulty of left null space calculation. The method does not linearize or truncate the state equation and observation equation of the spacecraft, and the left null space calculation method of the observable matrix given by the method has higher accuracy. Compared with the traditional method, the left null space of the observable matrix given by the method involves matrix calculation, and the highest dimension of the matrix is the dimension of the system state, so the calculation complexity is lower, which is suitable for autonomous calculation on the spacecraft.
[0084] Parts of the present invention that are not described in detail belong to common knowledge among those skilled in the art.
Claims
1. A fault and state decoupling method based on dimension reduction energy matrix, characterized in that include: Determine the Lie derivative calculation rules for the spacecraft autonomous diagnostic system; Using the Lie derivative calculation rule, the observable matrix O of the spacecraft autonomous diagnosis system is established; Determining the common subspace and subspace residual items of the observable matrix O of the spacecraft autonomous diagnosis system; Calculating a pseudo-inverse matrix of the subspace residual items; calculating the left null space of the common subspace; Multiplying the pseudo-inverse matrix and the left null space to obtain the left null space of the observable matrix of the spacecraft autonomous diagnosis system; The left null space of the observable matrix of the spacecraft autonomous diagnosis system is multiplied by the observation function of the spacecraft autonomous diagnosis system to achieve fault and state decoupling.
2. The fault and state decoupling method based on a dimension-reduced energy matrix according to claim 1 is characterized in that: The Lie derivative calculation rule of the spacecraft autonomous diagnosis system is: L 0 f h=h(X,F) Wherein, h(X) is the observation function of the spacecraft autonomous diagnosis system; f(X) is the state function of the spacecraft autonomous diagnosis system; X is the system state quantity; k is the Lie derivative order; F is the system fault quantity; L k f is the k-th Lie derivative of the system, L 0 f is the 0th-order Lie derivative of the system, h is the abbreviated form of h(X); The calculation rules are: g∈C ∞ , C ∞ is a set of continuous functions.
3. The fault and state decoupling method based on a dimension-reduced energy matrix according to claim 2 is characterized in that: The observable matrix O of the spacecraft autonomous diagnosis system is established, which is:
4. The fault and state decoupling method based on a dimension-reduced energy matrix according to claim 3 is characterized in that: The construction method of the common subspace and subspace residual items of the observable matrix of the spacecraft autonomous diagnosis system is as follows: Perform polar coordinate transformation on the system state, and the new system state is Then the observable matrix O is rewritten as: in, It is the common subspace of the observable matrix of the spacecraft autonomous diagnosis system; is the remaining term in the subspace.
5. The fault and state decoupling method based on dimension reduction energy matrix according to claim 4 is characterized in that: The pseudo-inverse matrix of the residual items of the computation subspace is specifically: {c} + |c + ·γ=I} Where I is the identity matrix; γ + Represents the pseudo-inverse matrix of the obtained subspace residual.
6. The fault and state decoupling method based on reduced-dimensional energy matrix according to claim 5 is characterized in that: The left null space of the calculated common subspace is specifically: x - ·x=0 Among them, χ - is the left null space of the common subspace.
7. The fault and state decoupling method based on reduced-dimensional energy matrix according to claim 6 is characterized in that: The pseudo-inverse matrix and the left null space are multiplied to obtain the left null space of the observable matrix of the spacecraft autonomous diagnosis system, which is specifically: The - =x - ·c + Among them, O - It is the left null space of the observable matrix of the spacecraft autonomous diagnosis system.
8. The fault and state decoupling method based on reduced-dimensional energy observable matrix according to claim 7 is characterized by: The left null space O of the observable matrix of the spacecraft autonomous diagnosis system - Multiplying with the observation function of the spacecraft autonomous diagnosis system to achieve fault and state decoupling, specifically: in, The new observation function of the spacecraft autonomous diagnosis system is obtained by decoupling the fault and the state.
9. A non-volatile storage medium, characterized in that: include: A computer program product, when the computer program product is executed, performs the method according to any one of claims 1 to 8.
10. A computer program product, characterized in that When the computer program product is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.