CN111324036B - A method for quantifying the diagnosability of time-varying systems under the influence of bounded disturbances - Google Patents

Abstract

A method for quantifying the diagnosability of a time-varying system under the influence of bounded interference belongs to the field of space technology. The invention converts the spacecraft system described in the state space into a time stack dynamic model, so that the diagnosability quantification problem of the system is transformed into the similarity calculation problem of a fully symmetric polytope, and the detectability and isolation of system faults are given. The mathematical definition of , and the diagnosability of faults (including detectability and isolation) are quantified by Hausdorff distance. Compared with the existing method, the method of the invention not only extends the spacecraft system model from the existing time-invariant model to the time-varying model, but also only needs to know the boundary of the interference without clarifying its specific form, which is more in line with the actual engineering needs. It is convenient for designers to operate and execute.

Description

A method for quantifying the diagnosability of time-varying systems under the influence of bounded disturbances

technical field

The invention relates to a method for quantifying the diagnosability of a time-varying system under the influence of bounded interference, and belongs to the field of space technology.

Background technique

With the continuous improvement of investment scale and system complexity, more stringent requirements are put forward for the accuracy and speed of autonomous fault diagnosis of spacecraft systems. On the one hand, a diagnostic algorithm with higher performance is directly proposed to meet the specific requirements of fault diagnosis in practical engineering; on the other hand, by quantifying the fault diagnosability of the system, the autonomous diagnostic capability of the spacecraft system is fundamentally improved.

Fault diagnosability is an inherent property of the system itself, and it is an important indicator to measure the difficulty of fault detection and isolation. Diagnosis mainly includes two parts: detectability and isolation. Generally, diagnostic evaluation can be divided into: qualitative evaluation and quantitative evaluation. Among them, the qualitative evaluation considers the problem from the perspective of whether the fault can be detected or isolated. Different from qualitative evaluation, quantitative evaluation results reflect the ease with which system faults can be detected or isolated, and the latter can provide more necessary observable information for the optimization of hardware configuration and diagnostic algorithms of spacecraft systems.

At this stage, the research on the quantification of system diagnosability has achieved certain results. However, the existing quantitative research results of diagnosability based on K-L divergence, Babbitt distance and directional similarity are all specific research work on linear time-invariant system models, and do not consider or only consider the influence of noise in known distribution forms. . In essence, in many engineering practices, such as the field of space technology, usually only the upper and lower bounds of system interference (including noise) can be known, but its specific statistical characteristics cannot be grasped; at the same time, the model uncertainty of the system can also be described as The exact form is unknown but bounded disturbance. To sum up, it is of more important theoretical research significance and practical application value to study the quantification method of the diagnosability of time-varying systems under the influence of bounded disturbance.

SUMMARY OF THE INVENTION

The technical problem solved by the present invention is: overcoming the deficiencies of the prior art, a method for quantifying the diagnosability of a time-varying system under the influence of bounded interference is proposed, which converts the spacecraft system described in the state space into a time-stack dynamic model, so that the failure The quantification problem of system diagnosability is transformed into the similarity calculation problem of fully symmetric polytope, and the mathematical definition of system fault detectability and isolation is given, and the diagnosability of faults is determined by Hausdorff distance ( Including detectability and isolation) for quantification. Compared with the existing method, the method of the invention not only extends the spacecraft system model from the existing time-invariant model to the time-varying model, but also only needs to know the boundary of the interference without clarifying its specific form, which is more in line with the actual engineering needs. Easy for designers to operate and execute.

The technical solution of the present invention is: a method for quantifying the diagnosability of a time-varying system under the influence of bounded interference, comprising the following steps:

S1, establish a time-varying equivalent space model of the spacecraft system based on the model standardization processing method and the equivalent space transformation processing method;

S2, establishing a fault set according to the time-varying equivalent space model of the spacecraft system;

S3, using the time-varying equivalent space model and the fault set of the spacecraft system, according to the first preset condition to determine whether the fault can be detected; if it can be detected, then enter S4; otherwise, end;

S4, using the time-varying equivalent space model of the spacecraft system to calculate the detectability metric value through the Hausdorff distance;

S5, using the time-varying equivalent space model and the fault set of the spacecraft system, according to the second preset condition to determine whether the fault can be isolated; if it can be isolated, then enter S6; otherwise, end;

S6, the time-varying equivalent space model of the spacecraft system is used to calculate the isolation metric value through the Hausdorff distance, which is used to optimize the spacecraft system configuration and fault diagnosis algorithm, so as to realize the stability of the spacecraft system health status. track monitoring.

Further, the time-varying equivalent space model of the spacecraft system is v _s (k)y _s -v _s (k)H _us (k)u _s =v _s (k)F(k)f _s +v _s (k)E(k)d _s ; where v _s (k) is the time-varying equivalent vector of the spacecraft system, f _s is the time stack vector of the spacecraft system failure, y _s , u _s and d _s are respectively are the time stack vectors of spacecraft system outputs, control inputs and bounded disturbances, and _Hus (k), F(k) and E(k) are time-varying coefficient matrices of corresponding dimensions.

其中，f_i表示第i个故障向量；F_i(k)表示矩阵F(k)对应向量f_i所在的行；b^m表示由m个单位区间[-1,1]组成的单位盒子，即表示m维的区间向量。Further, the fault set is

Among them, f _i represents the ith fault vector; F _i (k) represents the row of the matrix F(k) corresponding to the vector f _i ; b ^m represents the unit box composed of m unit intervals [-1, 1], that is Represents an m-dimensional interval vector.

Further, the first preset condition is: if and only if P _s (k)F _i (k)f _i ≠0, the fault can be detected; wherein, P _s (k) is composed of time-varying equivalent vectors The time-varying space-equivalent set of spacecraft systems.

其中，

为有向的豪斯多夫距离，具体而言，

表示故障f_i所对应时变全对称多胞形

与无故障所对应时变全对称多胞形c_NF(k)之间的有向豪斯多夫距离，

表示无故障所对应时变全对称多胞形c_NF(k)与表示故障f_i所对应时变全对称多胞形

之间的有向豪斯多夫距离；w_i→NF和w_NF→i为对应的有向豪斯多夫距离所占比例，且w_i→NF+w_NF→i＝1、w_i→NF≥0、w_NF→i≥0；

由

给出，c_NF(k)由c_NF(k)＝{v_s(k)E(k)d_s:d_s∈b^m}给出。Further, the detectability metric is

in,

is the directed Hausdorff distance, specifically,

represents the time-varying fully symmetric polytope corresponding to the fault f _i

is the directed Hausdorff distance to the time-varying fully symmetric polytope c _NF (k) corresponding to the fault-free,

represents the time-varying fully symmetric polytope c _NF (k) corresponding to no fault and the time-varying fully symmetric polytope corresponding to the fault f _i

The _{directed Hausdorff distance between the NF} ≥ 0, w _NF→i ≥ 0;

Depend on

Given, c _NF (k) is given by c _NF (k) = {v _s (k)E(k)d _s :d _s ∈ b ^m }.

时，故障f_i与故障f_j之间可隔离。Further, the second preset condition is: if and only if

When , the fault f _i and the fault f _j can be isolated.

其中，

表示故障f_i所对应时变全对称多胞形

与故障f_j所对应时变全对称多胞形

之间的有向豪斯多夫距离；

表示故障f_j所对应时变全对称多胞形

与故障f_i所对应时变全对称多胞形

之间的有向豪斯多夫距离；w_i→j和w_j→i表示对应的有向豪斯多夫距离所占比例，且w_i→j+w_j→i＝1、w_i→j≥0、w_j→i≥0。Further, the isolation metric is

in,

represents the time-varying fully symmetric polytope corresponding to the fault f _i

The time-varying fully symmetric polytope corresponding to the fault f _j

the directed Hausdorff distance between;

represents the time-varying fully symmetric polytope corresponding to the fault f _j

The time-varying fully symmetric polytope corresponding to the fault f _i

The _{directed Hausdorff distances between the j} ≥ 0, w _j→i ≥ 0.

The advantages of the present invention compared with the prior art are:

①The patent of the present invention no longer requires the specific statistical characteristics of the system interference to be known, only the upper and lower bounds of the system interference need to be known, and the quantitative results of the system diagnosability can be given by using the set element analysis method, and the system can be guided based on the quantitative results. Optimized design of configuration and diagnosis algorithms, which are more in line with actual engineering needs and are easy to implement;

②The patent of the present invention can realize the quantification of the diagnosability based on the time-varying equivalent space model in the non-statistical sense, has a wider range of use, sufficient flexibility and stronger applicability, and will improve the work focus of the system's self-diagnosis ability Moving forward to the design stage can provide technical reserves for the design of background models for subsequent deep space exploration missions such as Mars and asteroids and the development of related stand-alone products;

③The patent of the present invention can be extended and applied to large-scale industrial equipment such as large-scale complex industrial control, flight control, equipment manufacturing, electric power, etc., to realize online monitoring of the health status of the above-mentioned equipment; The goal is to guide the evaluation and design of the hardware configuration and software algorithm in the above-mentioned large-scale equipment, which has a wide range of needs in China.

Detailed ways

The present invention will be further explained and illustrated below in conjunction with specific embodiments.

A method for quantifying the diagnosability of a time-varying system under the influence of bounded interference, comprising the following steps:

S1, establish a time-varying equivalent space model of the spacecraft system based on the model standardization processing method and the equivalent space transformation processing method;

S2, establishing a fault set according to the time-varying equivalent space model of the spacecraft system;

S3, using the time-varying equivalent space model and the fault set of the spacecraft system, according to the first preset condition to determine whether the fault can be detected; if it can be detected, then enter S4; otherwise, end;

S4, using the time-varying equivalent space model of the spacecraft system to calculate the detectability metric value through the Hausdorff distance;

S5, using the time-varying equivalent space model and the fault set of the spacecraft system, according to the second preset condition to determine whether the fault can be isolated; if it can be isolated, then enter S6; otherwise, end;

S6, the time-varying equivalent space model of the spacecraft system is used to calculate the isolation metric value through the Hausdorff distance, which is used to optimize the spacecraft system configuration and fault diagnosis algorithm, so as to realize the stability of the spacecraft system health status. track monitoring.

details as follows:

1. Establish a time-varying equivalent space model of the spacecraft system based on the model standardization processing method and the equivalent space transformation processing method;

A spacecraft system can generally be described as a time-varying discrete state-space model as follows:

其中d_i(k)表示向量d(k)的第i个元素，等价于||d(k)||_∞≤d_max；矩阵A(k)、B_u(k)、C(k)、D_u(k)、B_d(k)、D_d(k)、B_f(k)和D_f(k)分别为相应的系数矩阵。Where: k represents the kth moment; x(k), u(k) and y(k) are the state vector, input vector and output vector of the system, respectively; f(k) is the fault vector; d(k) is the system bounded interference of , and

where d _i (k) represents the ith element of the vector d(k), which is equivalent to ||d(k)|| _∞ ≤d _max ; matrices A(k), B _u (k), C(k) , D _u (k), B _d (k), D _d (k), B _f (k) and D _f (k) are the corresponding coefficient matrices, respectively.

The window length is selected as s, and the system model (1) is iterated according to the time series, and the analytical redundancy equation of the system model (1) from time k-s+1 (k≥s-1) to time k is obtained:

y _s -H _us (k)u _s =H(k)x(k-s+1)+F(k)f _s +E(k)d _s (2)

Among them, y _s , u _s and d _s are the spacecraft system output, control input and time stack vector of bounded disturbance, respectively; _Hus (k), H(k), F(k) and E(k) are the corresponding The coefficient matrix of the dimension, the specific form is:

where: the vectors u _s , d _s and f _s have the same structure as y _s , and the matrices F(k) and E(k) are obtained by replacing {B _u , D _u } in the matrix _Hus (k) with { B _f , D _f } and {B _d , D _d } are obtained.

For the analytical redundancy equation (2), y _s -H _us (k) u _s represents the dynamic behavior of the spacecraft system; H(k)x(k-s+1), Ff _s and Ed _s represent the state vector, Fault vectors and bounded disturbance vectors. The analytical redundancy equation (2) can be regarded as the static representation of the dynamic behavior of the spacecraft system time-varying model (1) in the time series (k-s+1, k-s+2,...,k).

According to the principle of equivalent space transformation, by simultaneously left-multiplying the equivalent vector v _s of the matrix H on both sides of the equal sign of formula (2), that is, v _s H=0, we can get

v _s (k)[y _s -H _us (k)u _s ]=v _s (k)F(k)f _s +v _s (k)E(k)d _s (3)

The set P _s (k)={v _s (k)|v _s (k)H _us (k)=0} of the time-varying equivalent vector v _s (k) of the spacecraft system is called a time-varying equivalent space set.

2. Establish a fault set according to the time-varying equivalent space model of the spacecraft system described in step 1:

Take the time series f=(f[t-n+1], f[t-n+2],...,f[t]) ^T , let f _i represent the specific form of the fault under the time series; Θ _i represents the fault fi has a specific form of failure under all time series _, that is, fi _{∈Θ i} .

It can be seen from formula (3) that when a fault f _i occurs, there is v _s (k)[y _s -H _us (k)us ]=M(k) _{d s +} N _i (k), where N _i (k )=vs( _k )Fi( _k )fi, M( _k )=vs( _k )E(k). Therefore, each failure can be represented by multiple sets in the form:

表示故障f_i的所有集合。不失一般性，为了简化分析，假设有界干扰d(k)为单位盒子，即d_max＝1，此时d_s为m阶单位盒子。实质上，对于任意盒子d_s，v_s(k)E(k)d_s+v_s(k)F_i(k)f_i总能化成M(k)b^m+N(k)的形式，其中b^m为m阶单位盒子，M(k)与N(k)为维数恰当的已知时变系数矩阵。in,

represents all sets of faults _fi . Without loss of generality, in order to simplify the analysis, it is assumed that the bounded interference d(k) is a unit box, that is, d _max =1, and d _s is an m-order unit box at this time. In essence, for any box d _s , v _s (k)E(k)d _s +v _s (k)Fi ( _k )fi can always be transformed into the form of M( _k )b ^m +N(k), where b ^m is a unit box of order m, and M(k) and N(k) are known time-varying coefficient matrices with appropriate dimensions.

为描述包括无故障以及故障f_i在内情况的所有全对称多胞形集合。显而易见，无故障时系统全对称多胞形的集合

为一个包含原点的全对称多胞形

值得注意的是，由于不同的故障有可能会对系统产生相同的影响，故不同的集合

与

有可能存在交集。为了区分不同时序下的不同故障，将时间序列下故障的全对称多胞形表示为：To sum up, each fault can be represented as a collection of multiple time-varying symmetric polytopes. When no fault f _i occurs, f _i ≡ 0; at this time,

to describe the set of all fully symmetric _polytopes including no faults and faults fi. Obviously, the set of fully symmetric polytopes of the system when there is no fault

is a fully symmetric polytope containing the origin

It is worth noting that since different failures may have the same impact on the system, different sets of

and

There may be an intersection. In order to distinguish different faults under different time series, the fully symmetric polytope of faults under time series is expressed as:

3. Use the time-varying equivalent space model and the fault set of the spacecraft system to determine whether the fault can be detected according to the first preset condition; if it can be detected, go to step 4; otherwise, end:

For the time-varying equivalent space model (3), the discriminant conditions for its detectability are:

For a failure form f _i ∈Θ _i under a specific time series, the failure f _i is detectable if and only if P _s (k)F _i (k)f _i ≠0.

4. Using the time-varying equivalent space model of the spacecraft system to calculate the detectability metric value through the Hausdorff distance;

The core of fault detectability quantification is to give the intrinsic relationship between measurable information and system faults and bounded disturbances.

It can be seen from formula (3) that the dynamic behavior of the system v _s (k)[y _s -H _us (k)u _s ] is simultaneously affected by the system state fault vector F(k)f _s and the bounded disturbance vector E(k)d The coupling effect of _s . In other words, the greater the difference between the system's measurable y _s and us _s before and after a fault occurs, the less difficult it is to achieve fault detection.

则故障f_i的可检测性度量值的计算公式如下：For the detectable fault f _i , the corresponding fully symmetric polytope can be obtained from equation (5)

Then the calculation formula of the detectability metric value of fault _fi is as follows:

为有向的豪斯多夫距离，具体而言，

表示故障f_i所对应时变全对称多胞形

与无故障所对应时变全对称多胞形c_NF(k)之间的有向豪斯多夫距离，

表示无故障所对应时变全对称多胞形c_NF(k)与表示故障f_i所对应时变全对称多胞形

之间的有向豪斯多夫距离；w_i→NF和w_NF→i为对应的有向豪斯多夫距离所占比例，且w_i→NF+w_NF→i＝1、w_i→NF≥0、w_NF→i≥0；

由

给出，c_NF(k)由c_NF(k)＝{v_s(k)E(k)d_s:d_s∈b^m}给出。in,

is the directed Hausdorff distance, specifically,

represents the time-varying fully symmetric polytope corresponding to the fault f _i

is the directed Hausdorff distance to the time-varying fully symmetric polytope c _NF (k) corresponding to the fault-free,

represents the time-varying fully symmetric polytope c _NF (k) corresponding to no fault and the time-varying fully symmetric polytope corresponding to the fault f _i

The _{directed Hausdorff distance between the NF} ≥ 0, w _NF→i ≥ 0;

Depend on

Given, c _NF (k) is given by c _NF (k) = {v _s (k)E(k)d _s :d _s ∈ b ^m }.

5. Use the time-varying equivalent space model and the fault set of the spacecraft system to determine whether the fault can be isolated according to the second preset condition; if it can be isolated, go to step six; otherwise, end;

For the time-varying equivalent space model (3), the discriminant condition for its isolation is:

则故障f_i与故障f_j之间可隔离；其中，P_s(k)＝{v_s(k)|v_s(k)H_us(k)＝0}表示s阶的时变等价空间。The failure form f _i ∈Θ _i under a specific time series if and only if

Then the fault f _i and the fault f _j can be isolated; among them, P _s (k)={v _s (k)|v _s (k) _Hus (k)=0} represents the time-varying equivalent space of order s .

6. Using the time-varying equivalent space model of the spacecraft system, calculate the isolation metric value by the Hausdorff distance:

和

得到故障f_i和f_j之间可隔离性度量值的计算公式为：Similarly, for the two detectable faults f _i and f _j , the corresponding fully symmetric polytope can be obtained from formula (5).

and

The calculation formula to obtain the measure of isolation between faults f _i and f _j is:

表示故障f_i所对应时变全对称多胞形

与故障f_j所对应时变全对称多胞形

之间的有向豪斯多夫距离；

表示故障f_j所对应时变全对称多胞形

与故障f_i所对应时变全对称多胞形

之间的有向豪斯多夫距离；w_i→j和w_j→i分别表示对应的有向豪斯多夫距离所占比例，且w_i→j+w_j→i＝1、w_i→j≥0、w_j→i≥0。in,

represents the time-varying fully symmetric polytope corresponding to the fault f _i

The time-varying fully symmetric polytope corresponding to the fault f _j

the directed Hausdorff distance between;

represents the time-varying fully symmetric polytope corresponding to the fault f _j

The time-varying fully symmetric polytope corresponding to the fault f _i

The _{directed Hausdorff distances between the →j} ≥0, w _j→i ≥0.

The quantification results of the detectability and isolation of the time-varying system under the influence of bounded interference obtained by the patent of the present invention can be used to optimize the configuration of the spacecraft system and the fault diagnosis algorithm, and realize the on-orbit monitoring of the health state of the spacecraft system.

Seventh, the working principle and concrete steps of the present invention are described below with a specific embodiment:

For the following time-varying MIMO system state space model considering the influence of bounded disturbances:

in:

||d₁(k)||_∞≤0.1，||d₂(k)||_∞≤0.2，||d₃(k)||_∞≤0.1。

||d ₁ (k)|| _∞ ≤0.1, ||d ₂ (k)|| _∞ ≤0.2, ||d ₃ (k)|| _∞ ≤0.1.

其中，矩阵S和U由矩阵

特征值分解得到，即

UU^T＝I，VV^T＝I，Σ＝[S 0]；

为矩阵S^-1U^TP_sF(P_sF)^TUS^-1最大特征值所对应的特征向量。Considering the moment k = 1, take the equivalent vector that maximizes the residual error-to-noise ratio

where the matrices S and U are determined by the matrix

The eigenvalue decomposition is obtained, that is,

^UUT = I, VVT = I, Σ = [ ^S 0];

is the eigenvector corresponding to the largest eigenvalue of the matrix S ^-1 U ^T P _s F(P _s F) ^T US ^-1 .

Considering the time window length s = 3, it is assumed that a constant deviation fault occurs, and the specific form is θ = [1.7 1.71.7] ^T ; at this time, the quantification results of the detectability and isolation of the system are shown in Table 1. . Among them, the column of NF represents the quantification result of fault detectability FD _f (fi , _k ), _i =1,...,4; the remaining values are the quantification result of isolation between corresponding faults FI _f (fi ,f _j ,k),i,j=1,...,4.

)Table 1 Diagnosable quantification results of constant deviation faults (θ=[1.7 1.7 1.7] ^T ,

)

It can be seen from Table 1 that the detectability of different faults varies greatly, and the order of detectability from high to low is: f ₁ >f ₂ >f ₄ >f ₃ ; The isolation between f ₁ and f ₂ is the best (4.118).

The content not described in detail in the specification of the present invention belongs to the well-known technology of those skilled in the art.

Claims (3)

1. A method for diagnosably quantifying a time-varying system under the influence of bounded interference, comprising the steps of:

s1, establishing a time-varying equivalent space model of the spacecraft system based on a model standardization processing method and an equivalent space transformation processing method;

s2, establishing a fault set according to the time-varying equivalent space model of the spacecraft system;

s3, judging whether the fault can be detected or not according to a first preset condition by using the time-varying equivalent space model and the fault set of the spacecraft system; if so, go to S4; otherwise, ending;

s4, calculating a detectability metric value through a Hausdorff distance by using a time-varying equivalent space model of the spacecraft system;

s5, judging whether the fault can be isolated or not according to a second preset condition by using the time-varying equivalent space model and the fault set of the spacecraft system; if so, go to S6; otherwise, ending;

s6, calculating an isolatability measurement value through a Hausdorff distance by using the time-varying equivalent space model of the spacecraft system, and optimizing the configuration and fault diagnosis algorithm of the spacecraft system to realize the on-orbit monitoring of the health state of the spacecraft system;

the time-varying discrete state space model of the spacecraft system is as follows:

wherein: k represents the kth time; x (k), u (k), and y (k) are the state vector, input vector, and output vector of the system, respectively; f (k) is a fault vector; d (k) is the bounded interference of the system, and

wherein d is_i(k) The i-th element representing the vector d (k), equivalent to | | d (k) | purple_∞≤d_max(ii) a Matrices A (k), B_u(k)、C(k)、D_u(k)、B_d(k)、D_d(k)、B_f(k) And D_f(k) Respectively corresponding coefficient matrixes;

the time-varying equivalent space model of the spacecraft system is v_s(k)y_s-v_s(k)H_us(k)u_s＝v_s(k)F(k)f_s+v_s(k)E(k)d_s(ii) a Wherein v is_s(k) Is a time-varying equivalent vector of the spacecraft system, f_sTime stack vector, y, for spacecraft system failure_s、u_sAnd d_sTime stack vectors, H, for spacecraft system output, control input and bounded interference, respectively_us(k) F (k) and E (k) are time-varying coefficient matrices of corresponding dimensions;

the set of faults is

Wherein f is_iRepresenting the ith fault vector; f_i(k) Representing the corresponding vector f (k) of the matrix F_iThe row in which it is located; b^mIs represented by m unit intervals [ -1,1 [)]A unit box is formed, namely an m-dimensional interval vector is represented;

the first preset condition is as follows: if and only if P_s(k)F_i(k)f_iNot equal to 0, fault detection; wherein, P_s(k) The method comprises the steps of (1) forming a spacecraft system time-varying equivalent space set consisting of time-varying equivalent vectors;

the detectability metric is

Wherein,

x is a directed hausdorff distance, and is used to explain the concrete form of the hausdorff distance formula, and in particular,

indicates a fault f_iCorresponding time-varying fully-symmetrical multi-cell shape

Time-varying fully symmetrical multi-cell c corresponding to no fault_NF(k) The directed hausdorff distance there between,

representing time-varying fully symmetric polytope c corresponding to no fault_NF(k) And represents a fault f_iCorresponding time-varying fully-symmetrical multi-cell shape

Directed hausdorff distance in between; w is a_i→NFAnd w_NF→iIs the proportion of the corresponding directed Hausdorff distance, and w_i→NF+w_NF→i＝1、w_i→NF≥0、w_NF→i≥0；

By

Give a result of_NF(k) From c_NF(k)＝{v_s(k)E(k)d_s:d_s∈b^mGiving.

2. The method of claim 1, further comprising determining the amount of diagnosability of the time-varying system under the influence of the disturbanceThe chemical conversion method is characterized in that the second preset condition is as follows: if and only if

Time, fault f_iAnd fault f_jCan be isolated.

3. The method of claim 2, wherein the isolatability metric value is

Wherein,

indicates a fault f_iCorresponding time-varying fully-symmetrical multi-cell shape

And fault f_jCorresponding time-varying fully-symmetrical multi-cell shape

Directed hausdorff distance in between;

indicates a fault f_jCorresponding time-varying fully-symmetrical multi-cell shape

And fault f_iCorresponding time-varying fully-symmetrical multi-cell shape

Directed hausdorff distance in between; w is a_i→jAnd w_j→iRepresents the proportion of the corresponding directed Hausdorff distance, and w_i→j+w_j→i＝1、w_i→j≥0、w_j→i≥0。