CN103699119A - Fault diagnosability analysis method applicable to affine nonlinear system - Google Patents

Abstract

The invention discloses a fault diagnosability analysis method applicable to an affine nonlinear system. Through mathematical manipulation, a closed loop system considering nonlinear factors such as friction can be converted into a type of affine nonlinear system. By aiming at the type of system, the definition and the criterion of the fault diagnosability (including detectability and isolability) are given on the basis of the differential geometry theory; two kinds of quantitative indexes are respectively designed by aiming at the fault detectability and isolability; according to the indexes, the fault diagnosability analysis of the nonlinear closed loop system is realized through controlling the distribution conditions of output/output quantity and a mathematical model of the system. The fault diagnosability analysis method has the advantages that the fault diagnosis of the nonlinear closed loop control system can be brought forward to the design stage under the condition of not relying on any fault diagnosis algorithm, and in addition, the theoretical basis is provided for the design of the fault diagnosis algorithm.

Description

A kind of Method for Analysing Sensitivity of Fault that is applicable to affine nonlinear system

Technical field

The present invention relates to a kind of Method for Analysing Sensitivity of Fault that is applicable to affine nonlinear system, belong to satellite control field.

Background technology

Control system is to realize the important subsystem that the attitude of satellite, track control and each parts drive (as the sun wing, satellite antenna etc.), because the moving component comprising is many and mode of operation is complicated, makes its on-orbit fault rate high.Show according to statistics: 32 years of from 1975 to 2007, in the fault that 272 satellites occur control system accounted for wherein 37%.Consider that control system bears the importance of task, once it breaks down, will produce very serious consequence.For the fault effects of Guarantee control system, be down to minimumly, need to just consider in the design phase trouble diagnosibility of satellite.The height of control system trouble diagnosibility depends on that diagnosability analysis and diagnosis algorithm design two aspects, and the former is the latter's prerequisite and basis.Because for the fault with undetectability, design detection and isolation which kind of diagnosis algorithm all can not be realized fault.Yet the research for satellite failure diagnostic field at present focuses mostly on aspect diagnosis algorithm, less for the research of diagnosability analysis aspect.

In the technology of analyzing at existing control system fault diagnosability, mainly comprise following 4 kinds: by closing series structure incidence matrix between I/O information and fault; Can the new system observability after being augmented to transport function, state variable between output according to fault and the realizations such as existence of the residual error vector based on output and input message structure detect the system failure and can isolate and analyze.But there is following problem in above-mentioned technology: 1) research object is all linear system.Satellite control system is the Complex Nonlinear System that topworks, sensor, controller etc. form, and it is carried out to linearization process and will ignore the impact of non-linear factor.Particularly, because topworks (as momenttum wheel, the SADA etc.) fault that non-linear friction causes cannot be studied, and this fault is a typical fault pattern of control system.Therefore, the system failure that cause such non-linear factor is carried out diagnosability analysis, must consider that various non-linear factors are to the system modeling that becomes more meticulous; 2) analysis result is qualitatively, can only explain that can fault be diagnosed, and the complexity that can not specific explanations fault can be diagnosed.Quantitative analysis results can be found out the weak link of the system failure, and instructs the design of diagnosis algorithm with this, and this is that the qualitative analysis cannot relate to.

Summary of the invention

Technical matters to be solved by this invention is: overcome the deficiencies in the prior art, a kind of Method for Analysing Sensitivity of Fault that is applicable to affine nonlinear system is provided, the become more meticulous control system of modeling of the non-linear factors such as friction is carried out to the quantitative analysis of fault diagnosability, and instruct the design of fault diagnosis algorithm to guarantee the stability of satellite control system and the accuracy of design with this.

Technical solution of the present invention is:

A kind of Method for Analysing Sensitivity of Fault that is applicable to affine nonlinear system comprises that step is as follows:

(1) Nonlinear Closed-Loop is processed, made it become standard affine nonlinear system;

(2) affine nonlinear system of utilizing step (1) to obtain, obtains minimum antithesis corresponding to each output quantity and distributes;

(3) utilize the minimum antithesis distribution failure judgement that step (2) obtains whether can detect, if can detect, enter step (4), otherwise judge that fault can not detect, enter step (9);

(4) detectability fault step (3) being obtained, carries out detectability quantitative test;

(5) whether the quantitative analysis results that judges detectability fault is 0, if 0 is judged that fault can not be detected and enters step (9); Otherwise judgement fault can detect and enter step (6);

(6) judge whether other detectable failures, if having, entered step (7), otherwise judged that this fault can not be isolated, entered step (9);

(7) the detectability fault and other detectable failures that in step (4), obtain are carried out to the quantitative test of isolability;

(8) whether the quantitative analysis results that judges isolability fault is 0, if 0 is judged that fault can not be isolated and enters step (9); Otherwise judge that fault can be isolated fault and enter step (9);

(9) judge whether to travel through all output quantities of affine nonlinear system, if do not enter step (2), if travel through all steps (10) that enter;

(10) finish.

The standardization affine nonlinear system that described step (1) obtains is:

$\left\{\begin{array}{c}\stackrel{.}{x}\left(t\right)=q[x\left(t\right),t]+\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{G}_i[x\left(t\right),t]u_i\left(t\right)+\underset{e=1}{\overset{p}{\mathrm{\Σ}}}{P}_e[x\left(t\right),t]f_e\left(t\right)\\ y\left(t\right)=h[x\left(t\right),t]\end{array}\right.$

Wherein: x (t) ∈ R ⁿfor being defined in the state variable on equilibrium point neighborhood; Y (t) ∈ R ^mfor output quantity; u _i∈ R ^lfor input quantity; f _e∈ R ^pfor fault amount; Q ∈ R ⁿwith h ∈ R ^mfor abundant smooth nonlinear function, and meet q (0)=0 and h (0)=0; G _i∈ R ^{n * l}, i=1 ..., l and P _e∈ R ^{n * p}, e=1 ..., p is respectively the smooth vector field of input and fault; R ⁿ, R ^m, R ^land R ^pbe respectively n dimension, m dimension, l peacekeeping p dimensional vector in real number field, n, m, l and p are positive integer; T is time variable.

Each output quantity h in described step (2) _iminimum antithesis be distributed as:

$\left\{\begin{array}{c}{\mathrm{\Ω}}_0=\mathrm{span}\left\{{\mathrm{dh}}_j\right\}\\ {\mathrm{\Ω}}_{k+1}={\mathrm{\Ω}}_k+\underset{j=1}{\overset{p}{\mathrm{\Σ}}}{L}_{{\mathrm{\τ}}_j}{\mathrm{\Ω}}_k\end{array}\right.$

The end condition of above formula recursion is: have a positive integer k ^*, make

wherein, Ω ₀initial value for minimum antithesis distribution; K is the number of times of iteration;

for Lie derivative; J=1 ..., m.

In described step (3), the whether detectable criterion of failure judgement is---fault P _edo not belong to following distribution: this distribution is included in (dh) ^⊥in, and at vector field [q, G _i, P _e] in constant, write as:

$P_e\&NotElement;<q,G_i,P_e\left|\mathrm{span}\right\{\mathrm{dh}\}{>}^{\&perp;},e=1,...,p$

The computing formula of carrying out detectability quantitative test in described step (4) is:

$\mathrm{FD}\left(f_e\right)=\frac{{\left|\right|P_e\left|\right|}_2}{\max \left(P_e\right)}$

Wherein: || || ₂represent vectorial second order norm; Max (P _e) represent || P _e|| ₂the numerical value of middle norm maximum, e=1 ..., p;

The computing formula of carrying out isolability quantitative test in described step (7) is:

$\mathrm{FI}\left(f_{e1}\right|\left|f_{e2}\right)=\frac{{\left|\right|P_{e1}-P_{e2}\left|\right|}_2}{2*\max \left(P_e\right)},$ E1, e2=1 ..., p and e1 ≠ e2.

The present invention's beneficial effect is compared with prior art:

(1) the present invention advances to the design phase by the fault diagnosis of a class affine nonlinear system, and analysis result is brought in satellite control system design system as a kind of index.

(2) the present invention does not need to design any fault diagnosis algorithm, only relies on the system information such as dynamics, kinematics, controller model of nonlinear system, can realize fault and can detect and isolability analysis.

(3) the present invention can realize satellite sensor failure and can detect the quantitative analysis with isolability, can provide fault can detect and isolable complexity, and according to analysis result, find out the thin spot of fault detect and isolation, for the design of fault diagnosis algorithm provides theoretical foundation.

Accompanying drawing explanation

Fig. 1 is Method for Analysing Sensitivity of Fault process flow diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is further described in detail.

The present invention, in the satellite control system design phase, for a class affine nonlinear system, by the definition of fault of nonlinear system diagnosticability, criterion and index, can realize the quantitative analysis to fault diagnosability, and guides the design of diagnosis algorithm.

As shown in Figure 1, a class affine nonlinear system Method for Analysing Sensitivity of Fault of the present invention comprises the steps:

A kind of Method for Analysing Sensitivity of Fault that is applicable to affine nonlinear system comprises that step is as follows:

(1) Nonlinear Closed-Loop is processed, made it become standard affine nonlinear system;

Standardization affine nonlinear system is:

$\left\{\begin{array}{c}\stackrel{.}{x}\left(t\right)=q[x\left(t\right),t]+\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}{G}_i[x\left(t\right),t]u_i\left(t\right)+\underset{e=1}{\overset{p}{\mathrm{\&Sigma;}}}{P}_e[x\left(t\right),t]f_e\left(t\right)\\ y\left(t\right)=h[x\left(t\right),t]\end{array}\right.$

Wherein: x (t) ∈ R ⁿfor being defined in the state variable on equilibrium point neighborhood; Y (t) ∈ R ^mfor output quantity; u _i∈ R ^lfor input quantity; f _e∈ R ^pfor fault amount; Q ∈ R ⁿwith h ∈ R ^mfor abundant smooth nonlinear function, and meet q (0)=0 and h (0)=0; G _i∈ R ^{n * l}, i=1 ..., l and P _e∈ R ^{n * p}, e=1 ..., p is respectively the smooth vector field of input and fault; R ⁿ, R ^m, R ^land R ^pbe respectively n dimension, m dimension, l peacekeeping p dimensional vector in real number field, n, m, l and p are positive integer; T is time variable.

For above-mentioned affine nonlinear system, fault can not detect by output quantity h (x), i.e. output is not subject to fault effects, now claims fault not have detectability; Otherwise fault has detectability.The fault f with detectability _e1with f _e2if, f _e1impact on output vector h (x) is different from f _e2, claim f _e1with f _e2have isolability, its mathematic(al) representation is:

Δ=span{P _e1}∪span{P _e2}-span{P _e1}∩span{P _e2}

(2) affine nonlinear system of utilizing step (1) to obtain, obtains minimum antithesis corresponding to each output quantity and distributes;

Each output quantity h _iminimum antithesis be distributed as:

$\left\{\begin{array}{c}{\mathrm{\&Omega;}}_0=\mathrm{span}\left\{{\mathrm{dh}}_j\right\}\\ {\mathrm{\&Omega;}}_{k+1}={\mathrm{\&Omega;}}_k+\underset{j=1}{\overset{p}{\mathrm{\&Sigma;}}}{L}_{{\mathrm{\&tau;}}_j}{\mathrm{\&Omega;}}_k\end{array}\right.$

The end condition of above formula recursion is: have a positive integer k ^*, make

wherein, Ω ₀initial value for minimum antithesis distribution; K is the number of times of iteration;

for Lie derivative; J=1 ..., m.

(3) utilize the minimum antithesis distribution failure judgement that step (2) obtains whether can detect, if can detect, enter step (4), otherwise judge that fault can not detect, enter step (9);

The whether detectable criterion of failure judgement is: this fault P _edo not belong to following distribution: this distribution is included in (dh) ^⊥in, and at vector field [q, G _i, P _e] in constant, write as:

$P_e\&NotElement;<q,G_i,P_e\left|\mathrm{span}\right\{\mathrm{dh}\}{>}^{\&perp;},e=1,...,p$

Utilize the derive correctness of above-mentioned condition of reduction to absurdity

(a) adequacy: suppose vectorial P _emeet above-mentioned criterion, the system failure can not detect.By the detectable definition of affine nonlinear system fault, known: output is not subject to fault effects; Now, by the character of nonlinear system, can obtain:

P _e∈<q,G _i,P _e|span{dh ₁}> ^⊥...

P _e∈<q,G _i,P _e|span{dh _m}> ^⊥

${\mathrm{\&Omega;}}_1^{\&perp;}\&cap;{\mathrm{\&Omega;}}_2^{\&perp;}={({\mathrm{\&Omega;}}_1\&cup;{\mathrm{\&Omega;}}_2)}^{\&perp;}$

Based on above formula, and the algorithm distributing according to formula antithesis, can obtain:

P _e∈[<q,G,P _e|span{dh ₁}> ^⊥∩…∩<q,G,P _e|span{dh _m}> ^⊥]

=P _e∈<q,G,P _e|span{dh ₁}∪…∪span{dh _m}> ^⊥

=P _e∈<q,G,P _e|span{dh ₁…dh _m}> ^⊥

This and hypothesis test, adequacy must be demonstrate,proved.

(b), there is vectorial P in necessity: assumed fault is detectable _e, satisfy condition:

P _e∈<q,G _e,P _e|span{dh}> ^⊥

According to the definition of detectability, can obtain: fault can not be detected.This and hypothesis test, necessity must be demonstrate,proved.

(4) detectability fault step (3) being obtained, carries out detectability quantitative test;

The computing formula of detectability quantitative test is:

$\mathrm{FD}\left(f_e\right)=\frac{{\left|\right|P_e\left|\right|}_2}{\max \left(P_e\right)}$

Wherein: || || ₂represent vectorial second order norm; Max (P _e) represent || P _e|| ₂the numerical value of middle norm maximum, e=1 ..., p;

From the computing formula of above-mentioned detectability quantitative analysis, can find out: the span of result of calculation is [0,1].When it equals 0, show that this fault does not have detectability; When it equals 1, show the can detection level maximum in all faults of this fault, be the most easily detected; When it is between 0 and 1 time, value more approaches 1 and shows that the detectable degree of this fault is larger, otherwise, illustrate that this fault is more not easy to be detected.

The physical essence of above-mentioned computing formula is: by more vectorial P _eand the distance between null vector, realizes fault vectors P _ethe quantitatively evaluating of detectability.Nearer apart from null vector when it, the can detection level lower of this fault is described, be more not easy to be output vector and find; Otherwise, illustrate that this fault is more easily detected.

(5) whether the quantitative analysis results that judges detectability fault is 0, if 0 is judged that fault can not be detected and enters step (9); Otherwise judgement fault can detect and enter step (6);

(6) judge whether other detectable failures, if having, entered step (7), otherwise judged that this fault can not be isolated, entered step (9);

(7) the detectability fault and other detectable failures that in step (4), obtain are carried out to the quantitative test of isolability;

The computing formula of isolability quantitative test is:

$\mathrm{FI}\left(f_{e1}\right|\left|f_{e2}\right)=\frac{{\left|\right|P_{e1}-P_{e2}\left|\right|}_2}{2*\max \left(P_e\right)},$ E1, e2=1 ..., p and e1 ≠ e2.

(8) whether the quantitative analysis results that judges isolability fault is 0, if 0 is judged that fault can not be isolated and enters step (9); Otherwise judge that fault can be isolated fault and enter step (9);

(9) judge whether to travel through all output quantities of affine nonlinear system, if do not enter step (2), if travel through all steps (10) that enter;

(10) finish.

Specific embodiment with a satellite momenttum wheel illustrates principle of work of the present invention and concrete steps below:

Momenttum wheel is that satellite carries out the inertia topworks that attitude control is used, the relatively independent dynamo-electric execution unit being comprised of motor, flywheel and operation circuit etc.Its modeling accuracy depends primarily on the description degree of the electromechanical model of motor and flywheel body formation.

Electric moter voltage balance equation is described as:

$L\frac{\mathrm{di}\left(t\right)}{\mathrm{dt}}+i\left(t\right)R+e\left(t\right)=u\left(t\right)$

Wherein: L represents the inductance of armature; I (t) represents to flow through the electric current of armature; R represents the resistance of armature; U (t) represents Equivalent DC motor driven voltage; E (t) represents counter electromotive force of motor, is relevant to motor speed ω (t), and its relational expression is as follows:

e(t)=K _eω(t)

In formula: K _efor the coefficient of potential.

Motor torque balance equation is described as:

$J\frac{\mathrm{d\&omega;}\left(t\right)}{\mathrm{dt}}=T\left(t\right)$

In formula: J is the total moment of inertia of momenttum wheel; T (t) is motor dynamics output torque.

Add non-linear and uncertain rear accurate motor torque balance equation to be described as:

T(t)=T _r(t)+T _f(t)+T _d(t)

Wherein: T _d(t) be uncertain momenttum wheel disturbance torque, comprise noise of motor moment, bearing noise moment etc.; T _rand T (t) _f(t) be respectively momenttum wheel output torque and non-linear momentum wheel moment of friction, mathematic(al) representation is followed successively by:

T _r(t)=K _ri(t)

In formula, K _rfor motor torque coefficient.

Lugre Dynamic friction model equation is:

$\left\{\begin{array}{c}\stackrel{.}{z}\left(t\right)=\mathrm{\&omega;}\left(t\right)-\left|\mathrm{\&omega;}\left(t\right)\right|z\left(t\right)/g\left[\mathrm{\&omega;}\left(t\right)\right]\\ T_f={\mathrm{\&sigma;}}_{0}z\left(t\right)+{\mathrm{\&sigma;}}_1\stackrel{.}{z}\left(t\right)+{\mathrm{\&sigma;}}_2\mathrm{\&omega;}\left(t\right)\\ {\mathrm{\&sigma;}}_{0}g\left[\mathrm{\&omega;}\left(t\right)\right]=T_c+(T_m-T_c)\exp \left\{{[-\mathrm{\&omega;}\left(t\right)/{\mathrm{\&omega;}}_s\left(t\right)]}^2\right\}\end{array}\right.$

In formula: z (t) describes in boundary lubrication friction process, the relative deformation amount of frictional contact surface; σ ₀, σ ₁and σ ₂be respectively stiffness coefficient, ratio of damping and viscous friction coefficient; T _cand T _mbe respectively static friction moment and maximum static friction moment; ω _s(t) be critical Stribeck speed.

The PI controller mathematical model of Torque Control form is:

u(t)=K _i∫i(t)dt+K _pi(t)

In sum, writ state variable x=[i ω z x _k] ^t(x _kthe system state variables that represents controller), the mathematical model that obtains closed loop momenttum wheel affine nonlinear system is:

$\left\{\begin{array}{c}\stackrel{.}{x}=q\left(x\right)+\underset{i=1}{\overset{8}{\mathrm{\&Sigma;}}}{P}_i\left(x\right)f_i\left(t\right)+D\left(x\right)T_d\\ y={\left[\begin{array}{cc}{x}_1& x_2\end{array}\right]}^T\end{array}\right.$

Wherein:

$q\left(x\right)=\left[\begin{array}{c}\frac{K_p-R}{L}{x}_1-\frac{K_e}{L}{x}_2+\frac{1}{L}{x}_4\\ \frac{K_r}{J}+\frac{{\mathrm{\&sigma;}}_0+{\mathrm{\&sigma;}}_2}{J}{x}_2+\frac{1}{J}[{\mathrm{\&sigma;}}_1-\frac{\left|x_2\right|}{g\left(x_2\right)}]x_3\\ x_2-\frac{\left|x_2\right|}{g\left(x_2\right)}{x}_3\\ K_i{x}_1\end{array}\right],P_1{=\left[\begin{array}{cccc}0& \frac{1}{J}({2x}_2-\frac{\left|x_2\right|}{g\left(x_2\right)}{x}_3)& 0& 0\end{array}\right]}^T,$

$P_2={\left[\begin{array}{cccc}0& \frac{1}{J}({2x}_2-\frac{\left|x_2\right|}{g\left(x_2\right)}{x}_3)& 0& 0\end{array}\right]}^T,P_3={\left[\begin{array}{cccc}0& \frac{1}{J}(x_3-\frac{{\mathrm{\&sigma;}}_1\left|x_2\right|}{{\mathrm{\&sigma;}}_{0}g\left(x_2\right)}{x}_3)& \frac{\left|x_2\right|}{{\mathrm{\&sigma;}}_{0}g\left(x_2\right)}{x}_3& 0\end{array}\right]}^T,$

P ₄=D=[0?1/J?0?0] ^T，P ₅=P ₆=P ₇=P ₈=[1/L?0?0?0] ^T。

For above-mentioned closed loop momenttum wheel Affine nonlinear model, obtain: comprise distribution span{dh ₁at vector field [q, p ₁..., p ₈] in constant minimum antithesis distribution Ω be:

Ω=<q,p|span{dh ₁}>=span{Ω ₀,L _qdh ₁}

By vectorial p _ii=1 ..., 8 successively with Ω ₀and L _qdh ₁carry out dot product: if result of calculation is 0, p is described _i∈ Ω ^⊥, i=1 ..., 8, i.e. vectorial p _ican not be detected; If result of calculation is not 0, p is described _ican be detected.Result of calculation shows: 8 kinds of faults all can be output variable x ₁detect, fault all can display by the ANOMALOUS VARIATIONS of current i; In like manner, can obtain: all faults all can be passed through state variable x ₂the ANOMALOUS VARIATIONS of (rotational speed omega) detects.

By above-mentioned all faults that can be detected, to carry out detecting and isolable quantitative analysis, concrete result of calculation is as shown in table 1.

Table 1 momenttum wheel fault diagnosability analysis result

From table 1, can obviously find: fault f ₃detectability is the strongest, is the most easily detected, and f ₄detectability is the most weak; If isolation estimate result between each fault is used as to the matrix on 8 * 8 rank, this matrix is that a diagonal entry is 0 symmetric matrix entirely.Wherein, fault f ₁with f ₂can not be isolated; f ₅, f ₆, f ₇and f ₈in all can not be isolated between the two arbitrarily.Fault f ₄and between all the other faults can degree of isolation with respect to being minimum between other faults, this is due to f ₄can detection level minimum causing.

The unspecified part of the present invention belongs to general knowledge as well known to those skilled in the art.

Claims (5)

1. be applicable to a Method for Analysing Sensitivity of Fault for affine nonlinear system, it is characterized in that step is as follows:

(1) Nonlinear Closed-Loop is processed, made it become standard affine nonlinear system;

(2) affine nonlinear system of utilizing step (1) to obtain, obtains minimum antithesis corresponding to each output quantity and distributes;

(3) utilize the minimum antithesis distribution failure judgement that step (2) obtains whether can detect, if can detect, enter step (4), otherwise judge that fault can not detect, enter step (9);

(4) detectability fault step (3) being obtained, carries out detectability quantitative test;

(5) whether the quantitative analysis results that judges detectability fault is 0, if 0 is judged that fault can not be detected and enters step (9); Otherwise judgement fault can detect and enter step (6);

(6) judge whether other detectable failures, if having, entered step (7), otherwise judged that this fault can not be isolated, entered step (9);

(7) the detectability fault and other detectable failures that in step (4), obtain are carried out to isolability quantitative test;

(8) whether the quantitative analysis results that judges isolability fault is 0, if 0 is judged that fault can not be isolated and enters step (9); Otherwise judge that fault can be isolated fault and enter step (9);

(9) judge whether to travel through all output quantities of affine nonlinear system, if do not enter step (2), if travel through all steps (10) that enter;

(10) finish.

2. a kind of Method for Analysing Sensitivity of Fault that is applicable to affine nonlinear system according to claim 1, is characterized in that: the standardization affine nonlinear system that described step (1) obtains is:

Wherein: x (t) ∈ R ⁿfor being defined in the state variable on equilibrium point neighborhood; Y (t) ∈ R ^mfor output quantity; u _i∈ R ^lfor input quantity; f _e∈ R ^pfor fault amount; Q ∈ R ⁿwith h ∈ R ^mfor abundant smooth nonlinear function, and meet q (0)=0 and h (0)=0; G _i∈ R ^{n * l}, i=1 ..., l and P _e∈ R ^{n * p}, e=1 ..., p is respectively the smooth vector field of input and fault; R ⁿ, R ^m, R ^land R ^pbe respectively n dimension, m dimension, l peacekeeping p dimensional vector in real number field, n, m, l and p are positive integer; T is time variable.

3. a kind of Method for Analysing Sensitivity of Fault that is applicable to affine nonlinear system according to claim 1, is characterized in that: each the output quantity h in described step (2) _iminimum antithesis be distributed as:

The end condition of above formula recursion is: have a positive integer k ^*, make

wherein, Ω ₀initial value for minimum antithesis distribution; K is the number of times of iteration;

for Lie derivative; J=1 ..., m.

4. a kind of Method for Analysing Sensitivity of Fault that is applicable to affine nonlinear system according to claim 1, is characterized in that: in described step (3), the whether detectable criterion of failure judgement is: fault P _edo not belong to following distribution: this distribution is included in (dh) ^⊥in, and at vector field [q, G _i, P _e] in constant, write as:

。

5. a kind of Method for Analysing Sensitivity of Fault that is applicable to affine nonlinear system according to claim 1, is characterized in that: the computing formula of carrying out detectability quantitative test in described step (4) is:

Wherein: || || ₂represent vectorial second order norm; Max (P _e) represent || P _e|| ₂the numerical value of middle norm maximum, e=1 ..., p;

The computing formula of carrying out isolability quantitative test in described step (7) is:

e1, e2=1 ..., p and e1 ≠ e2.

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