CN105300406A - Gyro fault diagnosis method based on equivalence of balance equations - Google Patents

Abstract

The invention relates to a gyro fault diagnosis method based on equivalence of balance equations, and discloses a gyro fault diagnosis method suitable for an aircraft. The gyro fault diagnosis method comprises the following steps of firstly, using five gyros with redundancy measurement to form five gyro groups by using four gyros as one group, and optionally selecting one balance equation from each gyro group to calculate the coefficient and error of the balance equation; for each gyro group, according to the coefficient of the balance equation, calculating to obtain the parameter related with configuration, and using a product of the parameter and the setting fault threshold value as the fault judging reference value; finally, comparing the error of the balance equation of each gyro group and the calculated fault judging reference value, and positioning the faulted gyro according to the comparing results of all gyro groups. The gyro fault diagnosis method has the advantages that according to the equivalence conclusion between the balance equations of the gyro groups, the accurate diagnosis result of the gyro fault is realized on the basis of minimum calculation amount of algorithm; the clear selection principle is put forward for the fault judging threshold value, and the engineering operability and controllability are higher.

Description

Gyro fault diagnosis method based on equivalence of balance equations

Technical Field

The invention relates to the field of spacecraft attitude control, in particular to a gyroscope fault diagnosis method based on equilibrium equation equivalence, which is used for fault diagnosis of a gyroscope configured on a spacecraft.

Background

In a satellite control system, measurement of an attitude measurement sensor gyroscope is a key component for obtaining the angular velocity of a star body to realize effective control of the attitude of the star body, and is a key factor for influencing the stable operation of a spacecraft and restricting the on-orbit service life of the spacecraft. Although the spacecraft system can realize the measurement of the angular velocity of the three axes of the star body only by configuring 3 gyros with non-coplanar measuring axes, in order to ensure the long service life and high-reliability and stable operation of the spacecraft, the control system is generally configured with more than three redundant gyros.

The spacecraft gyroscope fault diagnosis is generally used for judging gyroscope faults based on errors of balance equations formed by measurement of four gyroscopes in redundant gyroscopes, namely, projections of star angular velocities obtained by calculation of 3 gyroscope measurement values in the directions of other gyroscope measurement axes and measured deviations of the star angular velocities are used as fault judgment bases. In order to locate the fault gyro, the number of gyros participating in fault diagnosis of the balance equation gyro cannot be less than 5. Any four gyro combinations in the 5 gyros are not marked as { i, j, k, l }, and the output delta g can be measured according to the combinations_i、Δg_j、Δg_k、Δg_lAnd its installation unit vector VG_i、VG_j、VG_k、VG_lFour different forms of equilibrium equations are established as follows:

_ijkl＝|k_ijkl,iΔg_i+k_ijkl,jΔg_j+k_ijkl,kΔg_k-Δg_l|(1a)

_ijlk＝|k_ijlk,iΔg_i+k_ijlk,jΔg_j+k_ijlk,lΔg_l-Δg_k|(1b)

_ilkj＝|k_ilkj,iΔg_i+k_ilkj,lΔg_l+k_ilkj,kΔg_k-Δg_j|(1c)

_jkli＝|k_jkl,lΔg_l+k_jkli,jΔg_j+k_jkli,kΔg_k-Δg_i|(1d)

wherein,_ijkl、_ijlk、_ilkj、_jklito account for the error of the equilibrium equation, the 3 coefficients in the four equilibrium equation are sequentially the first 3 elements of the corresponding four vectors as follows, i.e.

$k_{ijkl}=\[\begin{array}{cccc}{k}_{ijkl,i}& k_{ijkl,j}& k_{ijkl,k}& k_{ijkl,l}\end{array}\]=\[\begin{array}{cc}{\mathrm{VG}}_l^T\·A_{ijk}& -1\end{array}\]$

$k_{ijlk}=\[\begin{array}{cccc}{k}_{ijlk,i}& k_{ijlk,j}& k_{ijlk,l}& k_{ijlk,k}\end{array}\]=\[\begin{array}{cc}{\mathrm{VG}}_k^T\·A_{ijl}& -1\end{array}\]$

$k_{ilkj}=\[\begin{array}{cccc}{k}_{ilkj,i}& k_{ilkj,l}& k_{ilkj,k}& k_{ilkj,j}\end{array}\]=\[\begin{array}{cc}{\mathrm{VG}}_j^T\·A_{ilk}& -1\end{array}\]$

$k_{jkli}=\[\begin{array}{cccc}{k}_{jkli,j}& k_{jkli,k}& k_{jkli,l}& k_{jkli,i}\end{array}\]=\[\begin{array}{cc}{\mathrm{VG}}_i^T\·A_{jkl}& -1\end{array}\]$

At present, a gyro fault method based on a balance equation generally judges 5 balance errors obtained by 5 gyros according to a specific gyro sequence and a fixed fault judgment threshold value selected in advance. But due to any combination { i, j, k, l } of them being obtained under the same gyro measurement_ijkl、_ijlk、_ilkj、_jkliThe error values may be different, and therefore, even if the same combination may have different judgment results due to different selection of the balance equation, the judgment of the gyro fault may be inaccurate, and the preset fixed threshold may not be completely adaptive to other different gyro combinations. In order to solve the problem of the method, another commonly adopted method is to use all balance equation errors of the gyroscope for gyroscope fault judgment and aim atAnd designing a fault judgment threshold value for each balance equation. As 5 gyros have 4 gyro groups and each gyro group has 4 balance equations, the error values of 20 balance equations are calculated and 20 fault judgment threshold values are designed. Although the method can improve the accuracy of gyro fault diagnosis, the method is obtained at the expense of gyro fault diagnosis calculation amount and system design amount.

The invention provides a gyro fault diagnosis method based on balance equation equivalence, which is based on a theoretical analysis result and obtained for four balance equation equivalence conclusions of formulas (1a) - (1d) under the same gyro combination, namely for any gyro combination, the ratio of coefficients of gyro measurement values in any balance equation of the gyro combination to the ratio of coefficients arranged in the same gyro sequence in other balance equations of the combination has a fixed proportional relation.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the gyro fault diagnosis method based on the equivalence of the balance equations is provided, the balance equations consisting of five gyros are used for accurately diagnosing the gyro faults, and the problems that misdiagnosis or missed diagnosis is caused by inaccurate judgment of the balance equations in the judgment method in the prior art or the problems that the calculated amount is too large and the design amount is too complex in other existing gyro fault diagnosis methods are solved.

The technical scheme of the invention is as follows:

a gyro fault diagnosis method based on equivalence of balance equations comprises,

s1, numbering the five gyros as i, j, k, l and m respectively, and dividing the gyros into five groups in a way that four gyros form a group: fault detection of a balance equation is respectively carried out by { i, j, k, l }, { i, j, k, m }, { i, j, l, m }, { i, k, l, m }, and { j, k, l, m };

s2, for the gyro group { i, j, k, l }, measuring the unit vector VG of the installation of the axes on the star body by the gyros i, j, k, l_i、VG_j、VG_k、VG_lCorresponding to its gyro to measure output delta g_i、Δg_j、Δg_k、Δg_lCalculating the coefficient vector k of the balance equation_ijklAnd error of balance equation_ijkl：

$A_{ijk}={\left[\begin{array}{c}{\mathrm{VG}}_i^T\\ {\mathrm{VG}}_j^T\\ {\mathrm{VG}}_k^T\end{array}\right]}^{-1}$

$k_{ijkl}=\[\begin{array}{cc}{\mathrm{VG}}_l^T\·A_{ijk}& -1\end{array}\],{\mathrm{\ϵ}}_{ijkl}=k_{ijkl}\×\left[\begin{array}{c}\mathrm{\Δ}{g}_i\\ {\mathrm{\Δg}}_j\\ {\mathrm{\Δg}}_k\\ {\mathrm{\Δg}}_l\end{array}\right]$

Calculating k according to the set of gyroscopes (i, j, k, l)_ijklAnd_ijklin the process of (1), the balance equation coefficient vector k is respectively obtained for other four gyro groups { i, j, k, m }, { i, j, l, m }, { i, k, l, m }, { j, k, l, m }, and { j, k, l, m }, respectively_ijkm、k_ijlm、k_iklm、k_jklmAnd error of its equilibrium equation_ijkm、_ijlm、_iklm、_jklm。

S3, for the gyro group { i, j, k, l }, according to the vector k_ijklIs the sum variable k of the absolute values of the elements_{ijkl_sum}And the set gyro bonus judgment threshold value_gelim1And a division judgment threshold value_gelim2And (3) performing addition and subtraction processing on each gyro in the gyro combination with the same score:

if it is_ijklLess than k_{ijkl_sum}×_gelim1In the time, scoring of the gyros i, j, k and l is subjected to scoring processing;

if it is_ijklGreater than k_{ijkl_sum}×_gelim2And (4) carrying out division reduction processing on the scores of the gyros i, j, k and l.

According to the same processing process of the gyro sets { i, j, k and l }, the sum k of absolute values of coefficient vector elements of each balance equation is respectively solved for other four gyro sets { i, j, k and m }, { i, j, l and m }, { i, k, l and m }, and { j, k, l and m }, and_{ijkm_sum}、k_{ijlm_sum}、k_{iklm_sum}、k_{iklm_sum}in combination with setting a threshold value_gelim1、_gelim2And sequentially carrying out addition and subtraction processing on the gyros in each gyro group.

S4, judging a fault gyro: and after the processing of S2 and S3 is completed and the situation that the score of the gyro is reduced to the maximum score occurs, judging that the gyro with the maximum score is reduced in the gyros i, j, k, l and m as a fault gyro.

Further, the method includes setting a threshold value according to a configuration determined by the gyro mounting unit vector_gelim1、_gelim2And satisfy_gelim2＞_gelim1；

In order to avoid misdiagnosis of the gyroscope as a fault when the gyroscope measurement is normal, a threshold value is selected_gelim1Greater than the normal measurement error index range b given by the gyro_norm；

In order to avoid the condition of misdiagnosis caused by the fact that scores of a plurality of gyros are reduced equally when one gyro is in fault, selecting_gelim2Generally satisfy_gelim2＞2_gelim1。

Compared with the prior art, the invention has the advantages that:

(1) the method is provided based on the equivalence principle of the balance equation, the possible situation that fault gyro diagnosis results are different due to different balance equation selections in diagnosis in the prior art is avoided, and the accuracy of the diagnosis results and the consistency of the diagnosis results are improved on the basis of keeping the minimum calculation amount of a diagnosis algorithm.

(2) The invention provides a definite fault diagnosis threshold value selection principle, can effectively avoid the misdiagnosis condition caused by unreasonable diagnosis threshold value selection in the prior art, and greatly simplifies the complexity of system parameter design.

Drawings

FIG. 1 is a flowchart of gyro fault diagnosis based on equivalence of balance equations according to the present invention;

Detailed Description

As shown in FIG. 1, the gyro fault diagnosis method based on the equivalence of the balance equation of the invention comprises the following steps:

(1) five gyros i, j, k, l and m are utilized to form five groups: the method comprises the following steps of { i, j, k, l }, { i, j, k, m }, { i, j, l, m }, { i, k, l, m }, { j, k, l, m } balance equation for fault detection.

(2) Measuring unit vector VG of installation of axes on star body by gyros i, j, k, l and k_i、VG_j、VG_k、VG_l、VG_kCalculating the coefficient vector k of the balance equation_ijkl、k_ijkm、k_ijlm、k_iklm、k_jklm：

$k_{ijkl}=\[\begin{array}{cccc}{k}_{ijkl,i}& k_{ijkl,j}& k_{ijkl,k}& k_{ijkl,l}\end{array}\]=\[\begin{array}{cc}{\mathrm{VG}}_l^T\·A_{ijk}& -1\end{array}\]$

$k_{ijkm}=\[\begin{array}{cccc}{k}_{ijkm,i}& k_{ijkm,j}& k_{ijkm,k}& k_{ijkm,m}\end{array}\]=\[\begin{array}{cc}{\mathrm{VG}}_m^T\·A_{ijk}& -1\end{array}\]$

$k_{ijlm}=\[\begin{array}{cccc}{k}_{ijlm,i}& k_{ijlm,j}& k_{ijlm,l}& k_{ijlm,m}\end{array}\]=\[\begin{array}{cc}{\mathrm{VG}}_m^T\·A_{ijl}& -1\end{array}\]$

$k_{iklm}=\[\begin{array}{cccc}{k}_{iklm,i}& k_{iklm,k}& k_{iklm,l}& k_{iklm,m}\end{array}\]=\[\begin{array}{cc}{\mathrm{VG}}_m^T\·A_{ikl}& -1\end{array}\]$

$k_{jklm}=\[\begin{array}{cccc}{k}_{jklm,i}& k_{jklm,k}& k_{jklm,l}& k_{jklm,m}\end{array}\]=\[\begin{array}{cc}{\mathrm{VG}}_m^T\·A_{jkl}& -1\end{array}\]$

Wherein

$A_{ijk}={\left[\begin{array}{c}{\mathrm{VG}}_i^T\\ {\mathrm{VG}}_j^T\\ {\mathrm{VG}}_k^T\end{array}\right]}^{-1},A_{ijl}={\left[\begin{array}{c}{\mathrm{VG}}_i^T\\ {\mathrm{VG}}_j^T\\ {\mathrm{VG}}_l^T\end{array}\right]}^{-1},A_{ikl}={\left[\begin{array}{c}{\mathrm{VG}}_i^T\\ {\mathrm{VG}}_k^T\\ {\mathrm{VG}}_l^T\end{array}\right]}^{-1},A_{jkl}={\left[\begin{array}{c}{\mathrm{VG}}_j^T\\ {\mathrm{VG}}_k^T\\ {\mathrm{VG}}_l^T\end{array}\right]}^{-1}$

Combining the above calculated balance equation coefficient vectors, the gyroscope correspondingly measures and outputs delta g_i、Δg_j、Δg_k、Δg_l、Δg_mCalculating the error of the equilibrium equation_ijkl、_ijkm、_ijlm、_iklm、_jklm：

_ijkl＝k_ijkl×[Δg_iΔg_jΔg_kΔg_l]^T

_ijkm＝k_ijkm×[Δg_iΔg_jΔg_kΔg_m]^T

_ijlm＝k_ijlm×[Δg_iΔg_jΔg_lΔg_m]^T

_iklm＝k_iklm×[Δg_iΔg_lΔg_lΔg_m]^T

_jklm＝k_jklm×[Δg_jΔg_kΔg_lΔg_m]^T

The right superscript "-1" of each variable represents the matrix inversion operation, and the right superscript "T" represents the transpose operation of the vector (matrix).

(3) Respectively taking absolute values of the coefficients of the five gyro equilibrium equations and summing the absolute values to obtain a variable k_{ijkl_sum}、k_{ijkm_sum}、k_{ijlm_sum}、k_{iklm_sum}、k_{iklm_sum}I.e. by

k_{ijkl_sum}＝|k_ijkl,i|+|k_ijkl,j|+|k_ijkl,k|+|k_ijkl,l|

k_{ijkm_sum}＝|k_ijkm,i|+|k_ijkm,j|+|k_ijkm,k|+|k_ijkm,m|

k_{ijlm_sum}＝|k_ijlm,i|+|k_ijlm,j|+|k_ijlm,l|+|k_ijlm,m|

k_{iklm_sum}＝|k_iklm,i|+|k_iklm,k|+|k_iklm,l|+|k_iklm,m|

k_{iklm_sum}＝|k_iklm,i|+|k_iklm,k|+|k_iklm,l|+|k_iklm,m|

And calculating the k_{ijkl_sum}、k_{ijkm_sum}、k_{ijlm_sum}、k_{iklm_sum}、k_{iklm_sum}Adding judgment threshold value with gyroscope_gelim1And a division judgment threshold value_gelim2Taking the multiplication result as the basis of adding and subtracting the scores of all the groups of gyros, taking the gyro group { i, j, k, l } as an example:

if it is_ijklLess than k_{ijkl_sum}×_gelim1When in use, the scores of the gyros i, j, k and l are all added with 1 score;

if it is_ijklGreater than k_{ijkl_sum}×_gelim2When the scores of the gyros i, j, k and l are all reduced by 1 point.

The same addition and subtraction processing is carried out on the other four gyroscope groups { i, j, k, m }, { i, j, l, m }, { i, k, l, m }, { j, k, l, m }, respectively.

(4) And (3) judging a fault gyro: and after the addition and subtraction processing of each gyro group is completed, when the situation that the scores of the gyros are subtracted is present, reducing the total scores of the gyros i, j, k, l and m to the maximum, and judging the gyro with the fault.

In the above steps, the selection of the threshold value needs to satisfy the following conditions:

selecting threshold value_gelim2＞_gelim1；

Selecting threshold value_gelim1Greater than the range b of the normal measurement error index of the gyroscope_norm；

Threshold value_gelim2The selection is required according to the configuration of the gyro combination, and the selection is generally preferred_gelim2＞2_gelim1。

Example 1: and the five gyros i, j, k, l and m work, and gyro fault diagnosis is carried out based on an equivalent balance equation.

(1) The fault detection is carried out by utilizing five gyros i, j, k, l and m to form five groups of balance equations (i, j, k and l), (i, j, k and m), (i, j, l and m), (i, k, l and m) and (j, k, l and m).

The installation unit vector of 5 gyros in the embodiment is as follows:

VG_i＝[-0.52483389，-0.62547267，0.57735027]^T；

VG_j＝[0.80409216，-0.14178314，0.57735027]^T；

VG_k＝[-0.27925828，0.76725581，0.57735027]^T；

VG_l＝[0.70710678，0.40824829，0.57735027]^T；

VG_m＝[-0.70710678，0.40824829，0.57735027]^T；

setting gyro i as fault, and the measurement output of each gyro is:

Δg_i＝-0.008384377516774；

Δg_j＝0.014048585562026；

Δg_k＝-0.004859446568903；

Δg_l＝0.012355871354728；

Δg_m＝-0.012326811593622；

according to the normal measurement error index b of the gyroscope_normLess than 0.00002, and selecting an addend threshold by a threshold selection mode_gelim1And a division threshold_gelim2Are respectively as

_gelim1＝0.00002，_gelim2＝0.00004；

(2) Taking the gyro group { i, j, k, l } as an example, calculate_ijklThe algorithm of (1) is as follows:

$\begin{array}{c}{A}_{ijk}={\left[\begin{array}{c}{\mathrm{VG}}_i^T\\ {\mathrm{VG}}_j^T\\ {\mathrm{VG}}_k^T\end{array}\right]}^{-1}\\ \begin{array}{ccc}=\[-0.52483388288& 0.80409216343& -0.27925828055\\ -0.62547266863& -0.14178314464& 0.76725581327\\ 0.57735026534& 0.57735027302& 0.57735026676\];\end{array}\end{array}$

$\begin{array}{c}{k}_{ijkl}=\[\begin{array}{cc}{\mathrm{VG}}_l^T\·A_{ijk}& -1\end{array}\]\\ =\[\begin{array}{cccc}-0.29312841278& 0.84402963017& 0.44909878261& -1\end{array}\];\end{array}$

k_{ijkl_sum}＝2.5862568255；

_ijkl＝k_ijkl×[Δg_iΔg_jΔg_kΔg_l]^T＝2.23121e-004；

k_{ijkl_sum}×_gelim2＝0.00008776；

due to the fact that_ijklGreater than k_{ijkl_sum}×_gelim2The scores of the gyros i, j, k and l are respectively reduced by 1.

Processing similar to the gyro sets { i, j, k, m }, { i, j, l, m }, { i, k, l, m }, { j, k, l, m }, and the like is performed on the gyro sets { i, j, k, l, m }, and the obtained scoring conditions of the gyro sets are shown in table 1.

(3) And accumulating the scores of each gyro in different gyro groups, and judging that the score-4 of gyro i is the lowest according to the result, so that the gyro i is judged to be a fault.

TABLE 1 Gyro scoring Condition judged by the equilibrium equations of the various groups

Gyro set	GCi	GCj	GCk	GCl	GCm
						{i、j、k、l}	-1	-1	-1	-1	0
{i、j、k、m}	-1	-1	-1	0	-1
						{i、j、l、m}	-1	-1	0	-1	-1
{i、k、l、m}	-1	0	-1	-1	-1
						{j、k、l、m}	0	+1	+1	+1	+1
Score accumulation	-4	-2	-2	-2	-2

Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.

Claims (4)

1. A gyro fault diagnosis method based on balance equation equivalence is characterized by comprising the following steps:

s1, numbering the five gyros as i, j, k, l and m respectively, and dividing the gyros into five groups in a mode that four gyros form a group: fault detection of a balance equation is respectively carried out by { i, j, k, l }, { i, j, k, m }, { i, j, l, m }, { i, k, l, m }, and { j, k, l, m };

s2, for the gyro group { i, j, k, l }, measuring the unit vector VG of the installation of the axes on the star body by the gyros i, j, k, l_i、VG_j、VG_k、VG_lCorresponding to its gyro to measure output delta g_i、Δg_j、Δg_k、Δg_lCalculating the coefficient vector k of the balance equation_ijklAnd error of balance equation_ijkl：

$A_{ijk}={\left[\begin{array}{c}V{G}_i^T\\ {\mathrm{VG}}_j^T\\ {\mathrm{VG}}_k^T\end{array}\right]}^{-1}$

$k_{ijkl}=\[\begin{array}{cc}{\mathrm{VG}}_l^T\·A_{ijk}& -1\end{array}\]$

${\mathrm{\ϵ}}_{ijkl}=k_{ijkl}\×\left[\begin{array}{c}\mathrm{\Δ}{g}_i\\ {\mathrm{\Δg}}_j\\ {\mathrm{\Δg}}_k\\ {\mathrm{\Δg}}_l\end{array}\right]$

Calculating k according to the set of gyros { i, j, k, l } mentioned above_ijklAnd_ijklin the process of (1), the balance equation coefficient vector k is respectively obtained for other four gyro groups { i, j, k, m }, { i, j, l, m }, { i, k, l, m }, { j, k, l, m }, and { j, k, l, m }, respectively_ijkm、k_ijlm、k_iklm、k_jklmAnd error of its equilibrium equation_ijkm、_ijlm、_iklm、_jklm；

S3, for gyro group { i, j, k, l }, according toVector k_ijklIs the sum variable k of the absolute values of the elements_{ijkl_sum}And the set gyro bonus judgment threshold value_gelim1And a division judgment threshold value_gelim2And (3) performing addition and subtraction processing on each gyro in the gyro combination with the same score:

if it is_ijklLess than k_{ijkl_sum}×_gelim1In the time, scoring of the gyros i, j, k and l is subjected to scoring processing;

if it is_ijklGreater than k_{ijkl_sum}×_gelim2When the distance between the gyros i, j, k and l is less than the threshold value, the scores of the gyros i, j, k and l are all reduced;

according to the same processing process of the gyro sets { i, j, k and l }, the sum k of absolute values of coefficient vector elements of each balance equation is respectively solved for other four gyro sets { i, j, k and m }, { i, j, l and m }, { i, k, l and m }, and { j, k, l and m }, and_{ijkm_sum}、k_{ijlm_sum}、k_{iklm_sum}、k_{iklm_sum}in combination with setting a threshold value_gelim1、_gelim2Sequentially adding and subtracting gyros in each gyro group;

s4, judging a fault gyro:

and after the processing of S2 and S3 is completed and the situation that the score of the gyro is reduced to the maximum score occurs, judging that the gyro with the maximum score is reduced in the gyros i, j, k, l and m as a fault gyro.

2. The method of claim 1, further comprising: setting threshold value according to configuration determined by gyro installation unit vector_gelim1、_gelim2And satisfy_gelim2>_gelim1。

3. The method of claim 2, wherein the threshold is selected_gelim1Greater than the normal measurement error index range b given by the gyro_norm。

4. The method of claim 2, further comprising:

selecting_gelim2Satisfy the requirement of_gelim2>2.0_gelim1。