CN111259553B - Spacecraft system fault detection obtaining method based on distance similarity - Google Patents

Spacecraft system fault detection obtaining method based on distance similarity Download PDF

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CN111259553B
CN111259553B CN202010062129.0A CN202010062129A CN111259553B CN 111259553 B CN111259553 B CN 111259553B CN 202010062129 A CN202010062129 A CN 202010062129A CN 111259553 B CN111259553 B CN 111259553B
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王大轶
李文博
刘文静
刘成瑞
张香燕
林海淼
韩洪波
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Beijing Institute of Spacecraft System Engineering
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Abstract

A spacecraft system fault detection performance acquisition method based on distance similarity belongs to the technical field of space. The method provided by the invention is based on the vector-subspace distance, and considers the influence of unknown input on the system detectability, so that the mathematical description of complete fault detection and condition detection is realized, and the accuracy of the detectability acquisition result of the conventional system is greatly improved. Compared with the existing method, the method has the advantages of wider application range, enough flexibility and stronger applicability. The method is proved to be effective and feasible by application on a control system.

Description

Spacecraft system fault detection obtaining method based on distance similarity
Technical Field
The invention relates to a spacecraft system fault detection performance acquisition method based on distance similarity, and belongs to the technical field of space.
Background
The method has the advantages that accurate and quantitative detectability acquisition is carried out on the complex spacecraft system nonlinear model, basic guarantee and important premise for improving the design level of the detectability of the system are provided, the reduction of the space risk is facilitated, the space safety is guaranteed, and the spacecraft can smoothly complete the flight task. The fault detectability is an important attribute of the system, and the fault detectability is incorporated into the design process of the spacecraft system, so that the fault detection difficulty of the system can be fundamentally reduced, the system has high natural detectability, and the on-orbit operation quality of the spacecraft is effectively improved.
The fault detectability acquisition generally includes: qualitative judgment and quantitative description. The main consideration of qualitative judgment is whether a fault can be detected, and most of the existing detectability acquisition research results are attributed to the fault. With respect to qualitative judgments, the question that quantitatively describes the primary answer is how difficult the fault detection is. At present, scientific researchers at home and abroad also obtain certain achievements on the research of quantitative description of detectability. However, most of the existing research focuses on the detectability acquisition of a linear system model or the qualitative judgment of the detectability of a nonlinear system model, and the quantitative acquisition of the detectability of the nonlinear system model is not realized, that is, the difficulty of the detection of the fault cannot be known through the existing detectability criterion, and the quantitative acquisition result is helpful for optimizing the configuration and algorithm of the spacecraft system in the system design and fault detection algorithm design stages. At the present stage, only a few documents consider quantitative description of a nonlinear system model, and influence of unknown input on fault detectability is not considered in the existing method. In fact, in engineering practice, a spacecraft system is inevitably affected by unknown input factors such as external interference and model uncertainty, and meanwhile, as the functional structure of the spacecraft is increasingly complex, the nonlinear model of the spacecraft system is linearized at a working point, so that a fault detection result generates certain deviation. In conclusion, the method for obtaining the detectability of the nonlinear system model by considering the unknown input influence has important theoretical research significance and practical application value.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method comprises the steps of overcoming the defects of the prior art, aiming at a nonlinear affine model influenced by unknown input factors, providing a spacecraft system fault detection obtaining method based on distance similarity, and converting a fault detection obtaining problem into a mathematical problem of minimum distance measurement between a fault vector and invariable minimum dual distribution by utilizing the invariance of the output of the existing nonlinear affine model to input; by comparing the existing definition and connotation of the fault detectability, the detectability acquisition result obtained by calculation is further refined, and mathematical description of the complete detectability and the condition detectability of the fault is given. By utilizing the obtained fault detection result and the obtained fault detectability type, the configuration of the spacecraft system and the optimization of a fault diagnosis algorithm can be realized, and the on-orbit monitoring of the health state of the spacecraft system is realized.
The technical solution of the invention is as follows: a spacecraft system fault detection obtaining method based on distance similarity comprises the following steps:
s1, establishing a nonlinear affine model of the spacecraft system;
s2, judging whether the model meets a preset condition or not according to the nonlinear affine model of the spacecraft system in the S1; if yes, judging that the fault can be detected, and entering S3; otherwise, judging that the fault is not detectable, and ending;
s3, according to the nonlinear affine model of the spacecraft system in the S1, respectively calculating the minimum fault detectability without considering the influence of unknown input and the maximum influence degree of the unknown input on the fault detectability by utilizing the vector-subspace distance;
s4, calculating the minimum fault detectability considering the influence of the unknown input according to the minimum fault detectability not considering the influence of the unknown input in the S3 and the maximum influence degree of the unknown input on the fault detectability;
and S5, judging the type of the fault detectability according to the minimum fault detectability considering the unknown input influence, optimizing the configuration of the spacecraft system and a fault diagnosis algorithm based on the acquired fault detectability and the type of the fault detectability, and monitoring the health state of the spacecraft system in an on-orbit manner.
Further, the spacecraft system nonlinear affine model is
Figure BDA0002374819360000031
Wherein,
Figure BDA0002374819360000032
is a state vector, R is a real number field, lxDimension of the state variable x;
Figure BDA0002374819360000033
as an input vector,/uIs the dimension of the input vector u;
Figure BDA0002374819360000034
as an output vector,/yDimension of the output vector y;
Figure BDA0002374819360000035
for a bounded unknown input vector containing system uncertainty, process noise, and unknown disturbances,/dDimension of unknown input vector d;
Figure BDA0002374819360000036
is a smooth vector function;
Figure BDA0002374819360000037
as a fault vector,/wDimension of the fault vector w; h isj(x) Is the jth observation vector.
Further, the preset condition is
Figure BDA0002374819360000038
And
Figure BDA0002374819360000039
wherein,
Figure BDA00023748193600000310
to comprise dual distribution
Figure BDA00023748193600000311
In the vector field
Figure BDA00023748193600000312
A minimum dual distribution with less variance;
Figure BDA00023748193600000313
to comprise
Figure BDA00023748193600000314
In the vector field
Figure BDA00023748193600000315
A lower invariant maximum distribution;
Figure BDA00023748193600000316
is a vector dhi,i＝1,…,lyA space formed by stretching
Figure BDA00023748193600000317
Further, the minimum fault detectability without considering the influence of unknown input is
Figure BDA00023748193600000318
Wherein, is distributed
Figure BDA00023748193600000319
E Δ, X is the set of all possible occurrences of the system state.
Further, the maximum influence degree of the unknown input on the fault detectability is
Figure BDA00023748193600000320
Further, the minimum fault detectability considering the influence of unknown input is
Figure BDA0002374819360000041
Wherein FDU(wi) To account for the minimum fault detectability of unknown input effects, a unit pulse function of (a) is satisfied
Figure BDA0002374819360000042
t is time.
Further, the fault detectability type includes full detectability and condition detectability; if it is
Figure BDA0002374819360000043
Then the fault wiThe method has complete detectability; if it is
Figure BDA0002374819360000044
So that FDU(wi) Is equal to 0 and
Figure BDA0002374819360000045
then the fault wiHas condition detectability.
Compared with the prior art, the invention has the advantages that:
the invention provides quantitative indexes of 'complete detectability' and 'condition detectability' aiming at a nonlinear affine model of a spacecraft system, so that the fault detectability of the spacecraft system under the influence of unknown input can be accurately and quantitatively obtained;
secondly, the invention breaks through the limitation that the specific characteristics of the unknown input need to be determined by the traditional method by analyzing the invariance of the system measurable information to the unknown input and the fault, enlarges the application range and the application prospect of the fault detectability acquisition algorithm and provides a clear theoretical basis for optimizing the system configuration and the diagnosis algorithm;
the invention breaks through the limitation that the traditional method can only measure the detectability of the linear system, expands the detectability acquisition method from the linear system with unknown input to the nonlinear system with unknown input, and better meets the requirements of actual engineering;
Detailed Description
The invention will be further explained and illustrated with reference to specific embodiments.
A spacecraft system fault detection obtaining method based on distance similarity comprises the following steps:
s1, establishing a nonlinear affine model of the spacecraft system;
s2, judging whether the model meets a preset condition or not according to the nonlinear affine model of the spacecraft system in the S1; if yes, judging that the fault can be detected, and entering S3; otherwise, judging that the fault is not detectable, and ending;
s3, according to the nonlinear affine model of the spacecraft system in the S1, respectively calculating the minimum fault detectability without considering the influence of unknown input and the maximum influence degree of the unknown input on the fault detectability by utilizing the vector-subspace distance;
s4, calculating the minimum fault detectability considering the influence of the unknown input according to the minimum fault detectability not considering the influence of the unknown input in the S3 and the maximum influence degree of the unknown input on the fault detectability;
and S5, judging the type of the fault detectability according to the minimum fault detectability considering the unknown input influence, optimizing the configuration of the spacecraft system and a fault diagnosis algorithm based on the acquired fault detectability and the type of the fault detectability, and monitoring the health state of the spacecraft system in an on-orbit manner.
The method comprises the following specific steps:
establishing a nonlinear affine system model of a spacecraft system based on a model standardization processing method;
spacecraft systems can be generally described as a non-linear affine model as shown below:
Figure BDA0002374819360000051
wherein,
Figure BDA0002374819360000052
is a state vector, R is a real number field, lxDimension of the state variable x;
Figure BDA0002374819360000053
as an input vector,/uIs the dimension of the input vector u;
Figure BDA0002374819360000054
as an output vector,/yDimension of the output vector y;
Figure BDA0002374819360000055
for containing system uncertainty, process noiseBounded unknown input vector, l, including acoustic and unknown perturbationsdDimension of unknown input vector d;
Figure BDA0002374819360000056
is a smooth vector function;
Figure BDA0002374819360000057
as a fault vector,/wDimension of the fault vector w; h isj(x) Is the jth observation vector.
Secondly, judging whether the model meets a preset condition or not according to the nonlinear affine system model of the spacecraft system in the step one; if yes, judging that the fault can be detected, and entering a third step; otherwise, the fault is not detectable, and the process is finished;
when a system (1) fails, the failure is said to be detectable if it can cause a change in the measurable information. The heart of the fault detectability qualitative criterion is to give the relationship between the measurable information and the fault as well as the unknown input. The qualitative criterion for the system (1) fault detectability is given below:
for the non-linear affine model (1), the following conditions are met if and only if:
Figure BDA0002374819360000061
Figure BDA0002374819360000062
fault wiIt can be detected.
Wherein,
Figure BDA0002374819360000063
the representation comprises a dual distribution
Figure BDA0002374819360000064
In the vector field
Figure BDA0002374819360000065
Minimum of lower varianceDual distribution; accordingly, the method can be used for solving the problems that,
Figure BDA0002374819360000066
the representation comprises
Figure BDA0002374819360000067
In the vector field
Figure BDA0002374819360000068
A lower invariant maximum distribution;
Figure BDA0002374819360000069
representation by vector dhi,i＝1,…,lyA space formed by stretching and having
Figure BDA00023748193600000610
The qualitative criterion gives a testability criterion by analyzing the internal coupling incidence relation between the fault and the unknown input and the measurable information, and the specific physical meaning is as follows: if and only if the output y is faulted wiWithout being influenced by unknown input di,i＝1,…ldIn the influence of (d), fault wiIt can be detected.
Thirdly, according to the nonlinear affine system model of the spacecraft system obtained in the first step, respectively calculating the minimum fault detectability without considering the influence of unknown input and the maximum influence degree of the unknown input on the fault detectability by utilizing the vector-subspace distance;
as can be seen from equations (2) and (3): by analysing vector functions
Figure BDA00023748193600000611
And subspace
Figure BDA00023748193600000612
The relationship between them, the detectability obtaining result can be obtained. Through analysis, only the dependency relationship between the vector function and the subspace is considered in the acquisition process, and the relationship between the vector function and the subspace is not further quantitatively subdivided. Based on this, we consider using vectorsThe subspace distance transforms the fault detectability acquisition problem into a mathematical problem of similarity measure between the fault vector function and the output versus fault invariant maximum distribution.
Firstly, a general vector-subspace distance calculation method is provided, and the specific form is as follows:
Figure BDA00023748193600000613
where u represents a given vector, V represents a subspace of euclidean space W, | | | · | |, is a 2-norm symbol. As can be seen from the formula (4), d (u, V) is not less than 0, and the equal sign is established if and only if u belongs to V; the larger the value of d (u, V), the larger the distance between the vector and the subspace.
Notably, p isi,i＝1,…,lwAnd
Figure BDA0002374819360000071
all are functions of the state vector x, and when the fault detectability is obtained, in order to ensure the robustness of the algorithm, the worst condition of the system detectability needs to be considered.
Then, from equation (4), the calculation formula that yields the minimum fault detectability without considering the influence of unknown inputs is obtained as:
Figure BDA0002374819360000072
wherein p isiIs obtained by the system (1) and is,
Figure BDA0002374819360000073
representing the subspace of the distributions and X representing the set of all possible occurrences of the system state.
From equation (5): FD (w)i) Is not less than 0, if and only if
Figure BDA0002374819360000077
So that p isi(x0)∈Δ(x0) The time equal sign is established; FD (w)i) The larger the value of (A), the higher the detectability of the failure, if and only if FD (w)i) When 0, the fault wiIs not detectable.
Similarly, in order to quantify the influence of the unknown input on the fault detectability, the maximum condition of the influence of the unknown input of the system is considered, and the calculation formula of the maximum influence degree of the unknown input on the fault detectability can be obtained as follows:
Figure BDA0002374819360000074
wherein q isiIs obtained by the system (1) and is,
Figure BDA0002374819360000075
representing a subspace of distributions, U (d)i) Representing unknown input diThe degree of influence on the detectability of the fault.
From equation (6): u (d)i) Is not less than 0, if and only if
Figure BDA0002374819360000076
So that q isi(x0)∈Δ(x0) The time equal sign is established; u (d)i) The larger the value of (d), the greater the influence of the unknown input on the fault detectability, if and only if U (d)i) When 0, the unknown input does not affect the failure detectability.
Fourthly, calculating the minimum fault detectability considering the influence of the unknown input according to the minimum fault detectability not considering the influence of the unknown input in the third step and the maximum influence degree of the unknown input on the fault detectability;
from equations (5) and (6), the domains of influence of the unknown input on the system measurable information are substantially obtained, regardless of the minimum fault detectability of the influence of the unknown input and the maximum degree of influence of the unknown input on the fault detectability. Thus, after considering the effect of unknown input on fault detectability, we give the following calculation formula for minimum fault detectability considering the effect of unknown input:
Figure BDA0002374819360000081
wherein FD (w)i) And U (d)i) Represents the minimum fault w in equations (5) and (6), respectively, without considering the effect of unknown inputsiAnd the detectability of the obtained result and the unknown input diA calculation of the impact on the detectability of the fault;
a unit pulse function of
Figure BDA0002374819360000082
As can be seen from equation (8): FDU(wi) Is not less than 0, if and only if
Figure BDA0002374819360000083
Satisfies pi(x0)∈Δ(x0) Or
Figure BDA0002374819360000084
The time equal sign is established; FDU(wi) A large value of (d) indicates that the minimum fault detectability considering the influence of unknown input is higher if and only if FDU(wi) When 0, the fault wiIs not detectable.
Judging the type of the fault detectability according to the minimum fault detectability considering the influence of unknown input: the specific fault detectability types and discrimination conditions are as follows:
(1) complete detectability:
for the nonlinear affine model (1), if the output information is not subjected to unknown input d at any timei,i＝1,…,ldAnd is simultaneously affected by the fault wiIs called a fault wiIs completely detectable; in other words, if
Figure BDA0002374819360000085
Then the fault wiHas complete detectability.
(2) Condition detectability:
for the nonlinear affine model (1), except for part of time, the output information is not subjected to unknown input di,i＝1,…,ldAnd is simultaneously affected by the fault wiIs called a fault wiThe condition is detectable; in other words, if
Figure BDA0002374819360000086
So that FDU(wi) Is equal to 0 and
Figure BDA0002374819360000087
then the fault wiHas condition detectability.
The method can optimize the configuration of the spacecraft system and a fault diagnosis algorithm based on the fault detectability and the fault detectability type obtained by the method, and is used for monitoring the health state of the spacecraft system in an on-orbit manner.
Sixthly, the working principle and the specific steps of the invention are explained in a specific embodiment.
A non-linear affine model for a multiple-input multiple-output system containing bounded unknown inputs as follows:
Figure BDA0002374819360000091
the following can be obtained:
Figure BDA0002374819360000092
Figure BDA0002374819360000093
a sequence calculation formula generated from the invariant minimum-pair distribution as follows:
Figure BDA0002374819360000094
obtain a distribution containing dual
Figure BDA0002374819360000095
In the vector field
Figure BDA0002374819360000096
Lower, constant minimum dual distribution
Figure BDA0002374819360000097
Wherein the recurrence termination condition of equation (10) is:
Figure BDA0002374819360000098
this time is:
Figure BDA0002374819360000099
then its orthogonal distribution is:
Figure BDA00023748193600000910
further, the results of obtaining the failure detectability of the system (9) are specifically shown in table 1.
TABLE 1 Fault detectability acquisition results for System (9)
Figure BDA00023748193600000911
For the nonlinear affine model shown in equation (9), table 1 gives the detectivity acquisition results obtained based on the vector-subspace distance. Wherein, 0cIndicating that the output information is not subject to unknown input except for part of the timeiI is 1,2 and is simultaneously affected by the fault wiI is 1, …, 4.
The fault detectability type and the judgment condition can be known as follows: fault w1And fault w3All have complete detectability, fault w4With conditional detectability, fault w1Is less difficult than the fault w3The difficulty of detection of (c); fault w2It is not detectable.
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 (2)

1. A spacecraft system fault detection obtaining method based on distance similarity is characterized by comprising the following steps:
s1, establishing a nonlinear affine model of the spacecraft system;
s2, judging whether the model meets a preset condition or not according to the nonlinear affine model of the spacecraft system in the S1; if yes, judging that the fault can be detected, and entering S3; otherwise, judging that the fault is not detectable, and ending;
s3, according to the nonlinear affine model of the spacecraft system in the S1, respectively calculating the minimum fault detectability without considering the influence of unknown input and the maximum influence degree of the unknown input on the fault detectability by utilizing the vector-subspace distance;
s4, calculating the minimum fault detectability considering the influence of the unknown input according to the minimum fault detectability not considering the influence of the unknown input in the S3 and the maximum influence degree of the unknown input on the fault detectability;
s5, judging a fault detectability type according to the minimum fault detectability considering unknown input influence, optimizing spacecraft system configuration and a fault diagnosis algorithm based on the acquired fault detectability and fault detectability type, and monitoring the health state of the spacecraft system in an on-orbit manner;
the non-linear affine model of the spacecraft system is
Figure FDA0002590446430000011
Wherein,
Figure FDA0002590446430000012
is a state vector, R is a real number field, lxDimension of the state variable x;
Figure FDA0002590446430000013
as an input vector,/uIs the dimension of the input vector u;
Figure FDA0002590446430000014
as an output vector,/yAs an output vectorThe dimension of y;
Figure FDA0002590446430000015
for a bounded unknown input vector containing system uncertainty, process noise, and unknown disturbances,/dDimension of unknown input vector d;
Figure FDA0002590446430000016
is a smooth vector function;
Figure FDA0002590446430000017
as a fault vector,/wDimension of the fault vector w; h isj(x) Is the jth observation vector;
the preset condition is that
Figure FDA0002590446430000021
And
Figure FDA0002590446430000022
wherein,
Figure FDA0002590446430000023
to comprise dual distribution
Figure FDA0002590446430000024
In the vector field
Figure FDA0002590446430000025
A minimum dual distribution with less variance;
Figure FDA0002590446430000026
to comprise
Figure FDA0002590446430000027
In the vector field
Figure FDA0002590446430000028
A lower invariant maximum distribution;
Figure FDA0002590446430000029
is a vector dhi,i＝1,…,lyA space formed by stretching
Figure FDA00025904464300000210
The minimum fault detectability without considering the influence of unknown input is
Figure FDA00025904464300000211
Wherein, is distributed
Figure FDA00025904464300000212
E is delta, and X is a set of all possible system states;
the maximum influence degree of the unknown input on the fault detectability is
Figure FDA00025904464300000213
The minimum fault detectability considering the influence of unknown input is
Figure FDA00025904464300000214
Wherein FDU(wi) To account for the minimum fault detectability of unknown input effects, a unit pulse function of (a) is satisfied
Figure FDA00025904464300000215
t is time.
2. The method for acquiring the fault detectability of the spacecraft system based on the distance similarity according to claim 1, wherein the fault detectability types comprise complete detectability and condition detectability; if it is
Figure FDA00025904464300000216
Then the fault wiThe method has complete detectability; if it is
Figure FDA00025904464300000217
So that FDU(wi) Is equal to 0 and
Figure FDA00025904464300000218
then the fault wiHas condition detectability.
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