CN107703911B - A kind of diagnosability analysis method of uncertain system - Google Patents

Abstract

The invention discloses a kind of diagnosability analysis methods of uncertain system, the influence of the disturbing factors such as process noise and observation noise and uncertainty has been fully considered in the analysis process, give the statistical model of multivariate probability distribution of control system, it can detect uncertainty radius and uncertain radius can be isolated, and the probabilistic detectability analysis indexes of consideration and isolability analysis indexes are obtained based on statistical model of multivariate probability distribution and uncertain radius, simultaneously based on the rational judgment for considering probabilistic detectability analysis indexes and isolability analysis indexes progress diagnosticability, it ensure that the stability of complex control system and the accuracy of design.

Description

A kind of diagnosability analysis method of uncertain system

Technical field

The invention belongs to technical field of spacecraft control more particularly to a kind of diagnosability analysis sides of uncertain system Method.

Background technique

In the latest 20 years, domestic and foreign scholars to the research of spacecraft control system failure diagnostic techniques achieve it is huge at Just.As the important prerequisite of method for diagnosing faults design, fault diagnosability starts to cause the concern of scholars.By to being The diagnosticability of system is analyzed, can learn system for the diagnosis capability of different faults, and can the design phase be improve The diagnosticability energy and design level of system itself provide theoretical direction.However, being analyzed at this stage for fault diagnosability Research be still in the budding stage.Therefore, it is highly desirable that the diagnosticability of uncertain system is carried out further to deepen to grind Study carefully.

Uncertain (including: model error, observation and process noise etc.) is the main of progress fault diagnosability analysis Consideration.Uncertainty directly affects the accuracy of fault diagnosis result.For example, when systematic uncertainty is affected, Lesser failure is often difficult to be detected and isolated.Therefore, the analysis knot of the uncertain diagnosticability energy for influencing control system Fruit, and then to the two class key factors for influencing control system system: uncertain and failure, compare and analyze, analyze this two Relationship between person can be conducive to the weak link that designer finds out fault diagnosis in entire control system, and be system Configuration and diagnostic method design provide theoretical direction.As it can be seen that diagnosable for carrying out with probabilistic control system Property analysis method research have important engineering significance.

Diagnosticability is the important attribute that general control systems itself have, and is to measure fault detection and isolation hardly possible A kind of important indicator of easy degree.However, existing most of achievements about diagnosticability research focus mostly in qualitative description, only Only to be out of order can be detected or different failures between can segregate conclusion.For designer, further The complexity (analysis) for understanding fault detection and isolation is more convenient for the weak link of analysis system, to instruct diagnosis algorithm The configuration of design and system.

It is different for the element considered in analytic process, usually system diagnosability can be divided into intrinsic diagnosticability With two kinds of practical diagnosability analysis.Indigenous fault diagnosability analysis is defined as: do not consider in the analysis process interference because Element influence, only by the analytic modell analytical model of system, output and input information, detectability and isolability are analyzed.Closely Nian Lai obtains certain achievement for the research of indigenous fault diagnosability analysis.However, in the actual course of work of system In all inevitably by probabilistic influence.However, by known to investigation: existing about considering uncertain influence The achievement of control system diagnosability analysis is less；Meanwhile existing diagnosability analysis method is also less than satisfactory.For example, The newest fruits in the field in 2013 " Automatica " handle the Gaussian Profile that uncertainty is 0 as mean value.It is real On border, it uncertainty be simply considered as random distribution will lead to analysis result and lose accuracy, and this method can not be to not Deterministic influence is analyzed.

Summary of the invention

Technology of the invention solves the problems, such as: overcoming the deficiencies of the prior art and provide a kind of diagnosticability of uncertain system Analysis method is carried out the rational judgment of system diagnosability based on detectability index and isolability index, ensure that complexity The stability of control system and the accuracy of design.

In order to solve the above-mentioned technical problem, the invention discloses a kind of diagnosability analysis method of uncertain system, packets It includes:

According to probabilistic discrete control spatial model is had, it is iterated in temporal sequence, takes length of window s, obtain To have probabilistic control system statistical model of multivariate probability distribution:

N_HLz_s=N_HFf_s+N_HEe_s+N_HΛΔ_s

Wherein, z_s、f_s、e_sAnd Δ_sRespectively indicate observation, failure, noise and the time heap for not knowing 20 property of control system Stack vector；N_HThe left orthogonal basis of representing matrix H kernel, N_HH=0；L, H, F, E and Λ are respectively the coefficient matrix of corresponding dimension；

According to the statistical model of multivariate probability distribution with probabilistic control system, obtain control system can Detect uncertain radius R_i,NFIt is isolated uncertain radius R with control system_i,j:

Wherein, η_i,NF=max2 | | N_HΛΔ_θi|||||Δ_c(m^*)||≤α,||Δ_o(m^*)||≤β,m^*=k ..., k-s+ 1}；

NF indicates non-fault mode, Δ_θiIt indicates to correspond to failure f at time series θ_iProbabilistic specific manifestation shape Formula；Representing matrix [H F_j] kernel left orthogonal basis；F_jIndicate failure f_jCorresponding position in matrix F；Δ_cWith Δ_oRespectively indicate the uncertainty of executing agency and sensor；α and β respectively indicates the upper bound of control system uncertainty norm And lower bound；K indicates sampling time point；S indicates length of window；I and j indicates failure serial number；

According to the statistical model of multivariate probability distribution with probabilistic control system, control system it is detectable Uncertain radius R_i,NFIt is isolated uncertain radius R with control system_i,j, obtain considering detectable uncertain radius Detectability analysis indexesWith the isolability analysis indexes for considering that uncertain radius can be isolated

Wherein, θ indicates time series；

According to the detectability analysis indexes for considering detectable uncertain radiusIt can be every with the consideration Isolability analysis indexes from uncertain radiusObtain comparative analysis result.

In the diagnosability analysis method of above-mentioned uncertain system, the basis is empty with probabilistic discrete control Between model, be iterated in temporal sequence, take length of window s, obtain the multivariate probability point with probabilistic control system Cloth statistical model, comprising:

It determines and has probabilistic discrete control spatial model:

Wherein, x (k) ∈ Rⁿ, u (k) ∈ R^m, y (k) ∈ R^qWith f (k) ∈ R^pRespectively indicate the state vector, defeated of control system Incoming vector, output vector and fault vectors；w(k)∈R^lWith v (k) ∈ R^tThe process noise and observation for respectively indicating control system are made an uproar Sound；Matrix A ∈ R^n×n、B_u∈R^n×m、C∈R^q×n、D_u∈R^q×m、B_f∈R^n×p、D_f∈R^q×p、B_w∈R^n×lAnd D_v∈R^q×tTable respectively Show the corresponding coefficient matrix of control system, Δ A, Δ B_u, Δ C and Δ D_uIt is uncertain to respectively indicate dimension control system appropriate Matrix；Rⁿ、R^m、R^q、R^p、R^lAnd R^tN dimension, m dimension, q dimension, the p dimension, l peacekeeping t dimensional vector being illustrated respectively in real number field, n, m, Q, p, l and t are positive integer；

According to the uncertain Δ of executing agency_cWith the uncertain Δ of sensor_o, to probabilistic discrete control Spatial model processed carries out simplifying processing, has probabilistic discrete control spatial model after being simplified:

Wherein, Δ_c(k)=Δ Ax (k)+Δ B_uu(k)∈R^n×1, Δ_o(k)=Δ Cx (k)+Δ D_uu(k)∈R^q×1；||Δ_c (k) | |≤α, | | Δ_o(k)||≤β；| | | | indicate two norms；

It is iterated in temporal sequence, takes length of window s, obtain standardized model:

Lz_s=Hx_s+Ff_s+Ee_s+ΛΔ_s

Wherein, x_sIndicate the time heap stack vector of the state of control system；

According to equivalent space shift theory, to standardized model equal sign both sides while premultiplication matrix N_H, obtain described Statistical model of multivariate probability distribution:

N_HLz_s=N_HFf_s+N_HEe_s+N_HΛΔ_s。

In the diagnosability analysis method of above-mentioned uncertain system,

z_s∈R^(m+q)s、x_s∈R^n(s+1)、f_s∈R^ps、e_s∈R^(L+t)s、Δ_s∈R^(n+q)s；

L∈R^{(n+q)s×(m+q)s}、H∈R^{(n+q)s×n(s+1)}、F∈R^(n+q)s×ps、E∈R^{(n+q)s×(l+t)s}、Λ∈R^{(n+q)s×(n+q)s}；

Wherein, O and I respectively indicate null matrix and unit matrix；Table Show the operation of direct product of matrix.

It is described to be with probabilistic control according in the diagnosability analysis method of above-mentioned uncertain system The statistical model of multivariate probability distribution of system obtains the detectable uncertain radius R of control system_i,NFWith control system can be every From uncertain radius R_i,j, comprising:

According to failure f_iThe corresponding probability density function at time series θWith another failure f_jAll probability it is close The set of degreeBetween minimum K-L divergence, obtain failure f in control system model_iDetectability assay index with And failure f_iWith failure f_jBetween isolability assay index；

According to failure f in the control system model_iDetectability assay index and ideal detectability analyze Evaluation indexComparison result, determine the detectable uncertain radius R of the control system_i,NF；And according to Failure f in the control system model_iWith failure f_jBetween isolability assay index commented with ideal isolability analysis Valence indexComparison result, determine the control system is isolated uncertain radius R_i,j。

In the diagnosability analysis method of above-mentioned uncertain system,

Wherein, F_iIndicate failure f_iCorresponding position in matrix F；

In the diagnosability analysis method of above-mentioned uncertain system, consider to can detect uncertain radius according to described Detectability analysis indexesThe isolability analysis indexes of uncertain radius can be isolated with the consideration Obtain comparative analysis result, comprising:

Judge the detectability analysis indexes for considering detectable uncertain radiusIt whether is 0；

IfIt is 0, it is determined that control system failure cannot be detected and cannot be isolated；

IfIt is not 0, it is determined that control system failure is detectable, and judges that uncertainty can be isolated in the consideration The isolability analysis indexes of radiusIt whether is 0；

IfIt is 0, it is determined that control system failure can be detected but can not be isolated；

IfIt is not 0, it is determined that control system failure can be detect and isolated.

The invention has the following advantages that

The invention discloses a kind of diagnosability analysis methods of uncertain system, give the multivariate probability of control system Statistical distribution model and uncertain radius, and controlled based on the statistical model of multivariate probability distribution and uncertain radius The system failure processed considers the uncertain detectability of radius and the analysis indexes of isolability, is under noise circumstance with not true The determination of qualitative control system fault diagnosis provides accurate mathematical model and analytical standard, while based on consideration Probabilistic detectability analysis indexes and isolability analysis indexes carry out the rational judgment of diagnosticability, ensure that complexity The stability of control system and the accuracy of design.

Secondly, the present invention in the analytic process of spacecraft control diagnosticability, has fully considered process noise, has seen Survey the disturbing factors such as noise and uncertainty to diagnosticability can influence, the accurate description fault diagnosability of control system Can, to improve the accuracy and robustness for having indeterminate fauit diagnosability analysis result under noise circumstance.

Again, the fault diagnosis of uncertain system is advanceed to the design phase by the present invention, and regard analysis result as one kind Index is brought into Complex control system design system, while can find out the weak spot of fault diagnosis based on the analysis results, excellent The design method for having changed control system improves the controllability of Control System Design.

In addition, the present invention does not need to design any fault diagnosis algorithm, dynamics, the movement of complex control system are only relied on Configuration/installation situation of the system informations such as, controller model and sensor and actuator, can be realized failure it is detectable and The determination of isolability simplifies the failure diagnostic process of complex control system, while can provide for the design of diagnosis algorithm Theoretical foundation.

Detailed description of the invention

Fig. 1 is a kind of step flow chart of the diagnosability analysis method of uncertain system in the embodiment of the present invention；

Fig. 2 is a kind of schematic diagram analyzed based on K-L divergence failure isolability in the embodiment of the present invention；

Fig. 3 is a kind of schematic diagram analyzed based on K-L divergence failure isolability in the embodiment of the present invention.

Specific embodiment

To make the object, technical solutions and advantages of the present invention clearer, public to the present invention below in conjunction with attached drawing Embodiment is described in further detail.

A kind of diagnosability analysis method of uncertain system, is sufficiently examined in the determination process described in the embodiment of the present invention The influence for considering the disturbing factors such as process noise and observation noise and uncertainty gives the multivariate probability distribution of control system Statistical model, detectable uncertain radius and uncertain radius can be isolated, and based on statistical model of multivariate probability distribution and Uncertain radius has obtained the probabilistic detectability analysis indexes of consideration and isolability analysis indexes, while being based on examining Consider probabilistic detectability analysis indexes and isolability analysis indexes carry out the rational judgment of diagnosticability, ensure that multiple The stability of miscellaneous control system and the accuracy of design.

Referring to Fig.1, the step of showing a kind of diagnosability analysis method of uncertain system in embodiment of the present invention stream Cheng Tu.In the present embodiment, the diagnosability analysis method of a kind of uncertain system, comprising:

Step 101, it according to probabilistic discrete control spatial model is had, is iterated in temporal sequence, takes window Length s obtains the statistical model of multivariate probability distribution with probabilistic control system.

In the present embodiment, the following formula of the statistical model of multivariate probability distribution:

N_HLz_s=N_HFf_s+N_HEe_s+N_HΛΔ_s

Wherein, z_s、f_s、e_sAnd Δ_sRespectively indicate observation, failure, noise and the probabilistic time storehouse of control system Vector；N_HFor the left orthogonal basis of matrix H kernel, N_HH=0；L, H, F, E and Λ are respectively the coefficient matrix of corresponding dimension.

In the present embodiment, following form can be generally described as with probabilistic discrete control spatial model:

Wherein, k indicates sampling time point；x(k)∈Rⁿ, u (k) ∈ R^m, y (k) ∈ R^qWith f (k) ∈ R^pRespectively indicate control State vector, input vector, output vector and the fault vectors of system；w(k)∈R^lWith v (k) ∈ R^tRespectively indicate control system Process noise and observation noise；Matrix A ∈ R^n×n、B_u∈R^n×m、C∈R^q×n、D_u∈R^q×m、B_f∈R^n×p、D_f∈R^q×p、B_w∈R^{n ×l}And D_v∈R^q×tRespectively indicate the corresponding coefficient matrix of control system, Δ A, Δ B_u, Δ C and Δ D_uIt is appropriate to respectively indicate dimension Control system uncertainty matrix；Rⁿ、R^m、R^q、R^p、R^lAnd R^tN dimension, m dimension, q dimension, p dimension, the l dimension being illustrated respectively in real number field With t dimensional vector, n, m, q, p, l and t are positive integer.

Use Δ_cIndicate the uncertainty of executing agency, Δ_oIndicate the uncertainty of sensor, then it, can be according to the machine of execution The uncertain Δ of structure_cWith the uncertain Δ of sensor_o, simplify to probabilistic discrete control spatial model Processing has probabilistic discrete control spatial model after being simplified:

Wherein, Δ_c(k)=Δ Ax (k)+Δ B_uu(k)∈R^n×1, Δ_o(k)=Δ Cx (k)+Δ D_uu(k)∈R^q×1；Assuming that Control system uncertainty norm-bounded, has: | | Δ_c(k) | |≤α, | | Δ_o(k)||≤β；| | | | indicate two norms；α and β Respectively indicate the upper bound and the lower bound of control system uncertainty norm.

In order to analyze control system diagnosticability, control system can be iterated in temporal sequence, take window Mouth length s, can obtain standardized model:

Lz_s=Hx_s+Ff_s+Ee_s+ΛΔ_s

Wherein, x_sIndicate the time heap stack vector of the state of control system.

Preferably, in the present embodiment, z_s∈R^(m+q)s、x_s∈R^n(s+1)、f_s∈R^ps、e_s∈R^(L+t)s、Δ_s∈R^(n+q)s；

Wherein, O and I respectively indicate null matrix and unit matrix；Table Show the operation of direct product of matrix.Lz_sIt can be used to indicate that the controlling behavior by observing available control system, Hx_s、Ff_sAnd Ee_sIt can To be respectively used to indicate control system state, fault vectors and interference vector.

Before further analyzing the diagnosticability of the system, following hypothesis can be provided:

Assuming that 1: for standardized model, [H E] is row non-singular matrix.

Substantially, when all sensors all have measurement noise, i.e. D_vWhen for row full rank, it is assumed that 1 sets up.

According to equivalent space shift theory, to standardized model equal sign both sides while premultiplication matrix N_H, available described Statistical model of multivariate probability distribution:

N_HLz_s=N_HFf_s+N_HEe_s+N_HΛΔ_s。

Wherein, as previously mentioned, N_HThe left orthogonal basis of representing matrix H kernel, N_HH=0；

It should be noted that above-mentioned hypothesis 1 makes N_HEe_sCovariance matrix be it is nonsingular.The controlling behavior of control system N_HLz_sBy fault vectors N_HFf_s, interference vector N_HEe_sAnd systematic uncertainty N_HΛΔ_sInfluence.Wherein, N_HEe_sTo obey The random vector of normal distribution, N_HFf_sAnd N_HΛΔ_sFor certainty vector, then pass through observation N_HLz_sIt is available about failure Random distribution.When no fault occurs, there is f_s=0, N at this time_HLz_sObedience mean value is N_HΛΔ_s, variance σ_neNormal distribution, That is N_HLz_s~N (N_HΛΔ_s,σ_ne), whereinTo interfere vector N_HEe_sVariance matrix；Work as f_s≠ 0, There is N at this time_HLz_s~N (N_HFf_s+N_HΛΔ_s,σ_ne).As it can be seen that failure N_HFf_sWith the uncertain N of control system_HΛΔ_sIt is right simultaneously Random distribution N_HLz_sMean value have an impact, the variance without influencing the distribution.Therefore, each fault mode can be retouched It states as the set of one group of multivariate probability density.

Step 102, it according to the statistical model of multivariate probability distribution with probabilistic control system, is controlled The detectable uncertain radius R of system_i,NFIt is isolated uncertain radius R with control system_i,_j。

In the present embodiment, R_i,NFAnd R_i,jSpecific manifestation form it is as follows:

η_i,NF=max2 | | N_HΛΔ_θi|||||Δ_c(m^*)||≤α,||Δ_o(m^*)||≤β,m^*=k ..., k-s+1 }

Wherein, NF indicates non-fault mode, Δ_θiIt indicates to correspond to failure f at time series θ_iIt is probabilistic specific The form of expression；Representing matrix [H F_j] kernel left orthogonal basis；F_jIndicate failure f_jCorrespondence position in matrix F It sets；I and j indicates failure serial number.

In embodiments of the present invention, it is preferred that can be according to failure f_iThe corresponding probability density letter at time series θ NumberWith another failure f_jAll probability density set z_jBetween minimum K-L divergence, obtain in control system model therefore Hinder f_iDetectability assay index and failure f_iWith failure f_jBetween isolability assay index；Then, root According to failure f in the control system model_iDetectability assay index and ideal detectability assay indexComparison result, determine the detectable uncertain radius R of the control system_i,NF；And according to the control Failure f in system model_iWith failure f_jBetween isolability assay index and ideal isolability assay indexComparison result, determine the control system is isolated uncertain radius R_i,j。

During specific implementation:

It is possible, firstly, to take time series θ=(θ [t-s+1], θ [t-s+2] ..., θ [t])^T。

It enablesIndicate failure f_iThe corresponding probability density at time series θ Function；Wherein, N_HΛΔ_s+N_HF_iθ indicates stochastic variable N_HThe mean value of Lz, F_iIndicate failure f_iCorresponding position in matrix F. Particularly, p_NF=p (N_HLz,N_HΛΔ_s), it indicates trouble-free situation, there is θ ≡ 0 at this time.

Enable Θ_iIndicate failure f_iAll timing θ set, θ ∈ Θ_i,Indicate failure f_iAll probability density's Set.

For simplifying the analysis, without loss of generality, if interference vector N_HEe_sVariance matrix In fact, for arbitrarily interfering vector N in system model_HEe_s, variance matrix can make it meet σ by linear transformation_ne The case where=I.Utilize failure f_iThe corresponding probability density function at time series θWith another failure mode f_jInstitute There is the set of probability densityBetween minimum K-L divergence, to failure f_iWith failure f_jBetween detectability and isolability It is evaluated.For having probabilistic control system, the failure f under timing θ is given_iWith failure f_jBetween diagnosticability It is represented by Wherein, K (p | | q) indicates the K-L distance between p and q.It can be with Provide failure f in control system model_iDetectability assay index and failure f_iWith failure f_jBetween isolability Assay index:

Wherein, Δ₀、Δ_jWhen respectively indicating fault-free with break down f_jWhen systematic uncertainty the form of expression；f_i=θ_i Indicate failure f_iIn timing θ_iUnder specific version.It is worth noting that, working as θ_jWhen ≡ 0,It can be used as failure f_i's Detectability assay index is therefore, hereafter only rightIt is analyzed,It can indicate are as follows:

Wherein: Δ_θi,j=Δ_θi-Δ_j,Unlike existing diagnosability analysis method, Due to probabilistic presence, whenShi Wufa must be out of order f_iWith fault mode f_jNot isolable conclusion.It is worth It is noted that due to probabilistic specific manifestation form Δ_θi,jAnd Δ_θi,0All it is unknown, therefore can not directly passes throughFind out failure f_iWith fault mode f_jBetween isolability assay index.

Such as Fig. 2, a kind of signal analyzed based on K-L divergence failure isolability in the embodiment of the present invention is shown Figure.Wherein,WithIt is illustrated respectively in the set of corresponding probability density function under the influence of systematic uncertainty, You Tuzhong Dotted line frame indicates.In Fig. 2, left figure gives probability densityWith setBetween minimum range D_i,j(θ), meanwhile, D_i,j (θ) smaller distribution for indicating the two is more similar.Right figure according to fig. 2 is it is found that when failure mode is f=θ, stochastic variable N_HLz's Multivariate probability densityUnder the influence of uncertainty, it is extended to the set of multivariate probability densityMeanwhile relative to setAlso expand therewith.Due to uncertainty be it is unknown, can not accurately provide isolability evaluation indexTherefore, it defines and is with probabilistic isolability analysis indexesMinimum, maximum value value interval, can indicateIt is worth noting , the isolability analysis indexes that are proposedFor value interval, rather than a specific value, this be with it is existing Another important difference of analysis method.

It is intended to find out the isolability range with uncertain system, needs to consider following optimization problem:

Wherein, Δ_θi,j=Δ_θi-Δ_j,L=θ i, j respectively indicate the failure f under timing θ_iWith fault mode f_jExecuting agency and sensor uncertainty.Since restrictive condition is more, by traditional algorithms such as interior point methods directly to upper It states optimization problem and is solved more difficulty.Therefore, optimization problem can be simplified by norm uncertainty, finds out band There is the isolability range of uncertain system.

To that can be isolated before assessment analyzes with probabilistic system failure, following theorem is provided.

Theorem 1: for row non-singular matrix A ∈ R^m×nWith any vector b, if | | x | |≤α is such as drawn a conclusion:

max||Ax+b||²≤(η+||b||)²

Wherein, x ∈ Rⁿ, η=max | | Ax | | | | | x | |≤α }.

Theorem 2: failure f_iWith fault mode f_jBetween have probabilistic isolability analysis indexes are as follows:

Wherein:

And:

Wherein,Representing matrix [H F_j] kernel left orthogonal basis, i.e.,H is indicated The coefficient matrix known, F_jIndicate failure f_jCorresponding position in matrix F.

The influence that analysis system uncertainty evaluates system failure diagnosticability can obtain:

Wherein,Indicate failure f_iAt timing θ, with fault mode f_jIt Between ideal isolability analysis indexes.

Consider the situation the worst with uncertain system fault diagnosability evaluation result, can obtain

Obviously, only meetInfluence of the failure to final appraisal results is greater than uncertainty to evaluation result It influences, whenWhen meet the requirements.

Based on above-mentioned analysis, it can provide:

It is similar, it can provide:

Step 103, according to statistical model of multivariate probability distribution, the control system with probabilistic control system Detectable uncertain radius R_i,NFIt is isolated uncertain radius R with control system_i,j, obtain considering detectable not true The detectability analysis indexes of qualitative radiusWith the isolability analysis indexes for considering that uncertain radius can be isolated

In the present embodiment, consider the detectability analysis indexes of detectable uncertain radiusIt can with consideration The isolability analysis indexes of uncertain radius are isolatedSpecific manifestation form it is as follows:

In embodiments of the present invention, based on above-mentioned definition 1, determining for credible detectability and credible isolability can be provided Justice:

It defines 2: considering standardized model, if ideal isolability assay index is more than or equal to corresponding isolability Uncertain radiusThen failure f_iAt timing θ with fault mode f_jIt is credible isolable；If ideal Detectability assay indexMore than or equal to corresponding detectability uncertainty radius Then failure f_iIt with non-fault mode is credible detectable at timing θ.

According to above-mentioned definition 2, if failure f_iWith fault mode f_jIt is not credible detectable, orderIt is then described Consider the detectability analysis indexes of detectable uncertain radiusIt is as follows:

Wherein,

In the present embodiment,The uncertain influence of expression is the smallest can Detection property index,Indicating uncertain influences maximum detectability index.For a value area Between,Bound is bigger, f_iDetectability it is higher；Conversely,Bound is smaller, f_iDetectability get over It is low；Detectability index is 0, i.e.,Indicate failure f_iIt can not detect.

Similarly, according to above-mentioned definition 2, consider the isolability analysis indexes that uncertain radius can be isolatedSuch as Under:

Wherein,

In the present embodiment,The uncertain influence of expression is the smallest can Isolation index,Indicating uncertain influences maximum isolability index；For a value interval,Bound is bigger, indicates f_iWith f_jBetween isolability can be stronger；Bound is smaller, and isolability can be got over It is weak；Isolability index is 0, i.e.,Indicate failure f_iIt can not be isolated；I and j is positive whole Number.

Step 104, according to the detectability analysis indexes for considering detectable uncertain radiusWith it is described Consider the isolability analysis indexes that uncertain radius can be isolatedObtain comparative analysis result.

In the present embodiment, it is possible, firstly, to judge that the detectability analysis for considering detectable uncertain radius refers to MarkIt whether is 0；IfIt is 0, it is determined that control system failure cannot be detected and cannot be isolated；IfBe not 0, it is determined that control system failure is detectable, and judge that the consideration can be isolated uncertain radius can be every From property analysis indexesIt whether is 0；IfIt is 0, it is determined that control system failure can be detected but can not be isolated； IfIt is not 0, it is determined that control system failure can be detect and isolated.

On the basis of the embodiment, below by a specific example, the invention will be further described.

Referring to Fig. 3, a kind of structural schematic diagram of the dc motor of armature control in the embodiment of the present invention is shown.For The Mechatronic Systems of dc motor shown in Fig. 3, state equation are as follows:

Wherein:

Subscript c indicates " continuous system "；

R_a=28 Ω, C_M=1.34, J=0.0028kgm², C_e=0.0028, L_a=0.82H, F_f=0.02Nm rad^-1·s^-1,

WithFor independent identically distributed Gaussian random vector, and there is w₁~N (0,0.02), w₂~N (0, 0.04), v₁~N (0,0.01), v₂~N (0,0.03)；

Uncertain vectorAnd Δ_oNorm-bounded, and have

If the sampling period is 0.1s, discretization is carried out to above-mentioned state equation, it is as follows to obtain discrete state equations:

Wherein:

It is analyzed with probabilistic detectability and isolability evaluation result:

Consider time window length s=6, for stepped fault mode, failure mode is θ=[1 1.2 1.4 1.6 1.8 2]^T.The system is under uncertain radius, such as following table of the evaluation result with probabilistic detectability and isolability Shown in 1:

Table 1

Table 1 has probabilistic diagnosable evaluation result table, gives the diagnosable evaluation knot under uncertain radius Fruit.Wherein, NF column indicates the value interval in the detectability evaluation result of specified failure Its remainder values is the isolability evaluation result between corresponding failureAs known from Table 1: different faults Detectability figure of merit and failure between the value interval length of isolability figure of merit it is different；For any two Failure f_iAnd f_j, the evaluation result of diagnosable value is usually asymmetric, i.e.,

Time window length evaluates impact analysis to detectability and isolability:

Consider time window length s=7, for stepped fault mode, failure mode is θ=[1 1.2 1.4 1.6 1.8 2.1 2.3]^T.The system is under uncertain radius, the evaluation result with probabilistic detectability and isolability It is as shown in table 2 below:

Table 2

Tables 1 and 2 is compared it is found that diagnosticability evaluation of estimate increases with the increase of length of window, this is indicated with can The increase of information realizes that detection and the accuracy of isolation all get a promotion to failure.With the increase of time window s, no There is different degrees of increase with the isolability figure of merit between the detectability figure of merit and failure of failure, this expression With the increase of available information, detection and the accuracy of isolation, which are all improved, to be realized to failure, this is consistent with actual conditions； However, evaluation procedure introduces more uncertain, the diagnosticability review number of different faults with the increase of time window s The value interval of value also increases with it, and the detection between failure is caused to increase with the comparison difficulty being isolated.It, can with the variation of s The comparing result of diagnostic evaluation value can also change.For example, for s=6.As known from Table 1, failure f₃With failure f₄Can There are intersections for detection property evaluation of estimate, i.e.,WithIt indicates, both can not judge the size relation of detection difficulty at this time, it, can be with however, work as s=7 It obtainsAs shown in Table 2, the difficulty for detecting failure 3 at this time is less than the difficulty of detection failure 4.

In conclusion giving control system the invention discloses a kind of diagnosability analysis method of uncertain system Statistical model of multivariate probability distribution and uncertain radius, and based on the statistical model of multivariate probability distribution and uncertain half The diameter system failure that is under control considers the uncertain detectability of radius and the analysis indexes of isolability, is noise circumstance The determination with probabilistic control system fault diagnosis provides accurate mathematical model and analytical standard down, together When based on considering that probabilistic detectability analysis indexes and isolability analysis indexes carry out the rational judgment of diagnosticability, It ensure that the stability of complex control system and the accuracy of design.And the present invention has fully considered process noise, observation noise With the disturbing factors such as uncertainty to diagnosticability can influence, the accurate description fault diagnosis of control system, from And improve the accuracy and robustness that indeterminate fauit diagnosticability definitive result is had under noise circumstance.

Secondly, the fault diagnosis of control system is advanceed to the design phase by the present invention, and using definitive result as a kind of finger Mark is brought into Complex control system design system, while the weak spot of fault diagnosis can be found out according to definitive result, is optimized The design method of control system, improves the controllability of Control System Design.The present invention does not need to design any fault diagnosis Algorithm only relies on the system informations such as the dynamics, kinematics, controller model of complex control system and sensor and actuator Configuration/installation situation, the determination of failure detectable and isolatable property can be realized, the failure for simplifying complex control system is examined Disconnected process, while theoretical foundation can be provided for the design of diagnosis algorithm.

In addition, the present invention takes full advantage of the own characteristic of complex control system structure, the reliable of definitive result ensure that Property and stability, greatly reduce operand, are conducive to obtain detectability and isolability in time in practical engineering applications Information.Moreover, this method be equally applicable to spacecraft control in the rail operation mode can the few situation of measured data.

Various embodiments are described in a progressive manner in this explanation, the highlights of each of the examples are with its The difference of his embodiment, the same or similar parts between the embodiments can be referred to each other.

The above, optimal specific embodiment only of the invention, but scope of protection of the present invention is not limited thereto, In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by anyone skilled in the art, It should be covered by the protection scope of the present invention.

The content that description in the present invention is not described in detail belongs to the well-known technique of professional and technical personnel in the field.

Claims (6)

1. a kind of diagnosability analysis method of uncertain system characterized by comprising

According to probabilistic discrete control spatial model is had, it is iterated in temporal sequence, takes length of window s, obtain band There is the statistical model of multivariate probability distribution of probabilistic control system:

N_HLz_s=N_HFf_s+N_HEe_s+N_HΛΔ_s

Wherein, z_s、f_s、e_sAnd Δ_sRespectively indicate observation, failure, noise and the probabilistic time heap stack vector of control system； N_HThe left orthogonal basis of representing matrix H kernel, N_HH=0；L, H, F, E and Λ are respectively the coefficient matrix of corresponding dimension；

According to the statistical model of multivariate probability distribution with probabilistic control system, the detectable of control system is obtained Uncertain radius R_i,NFIt is isolated uncertain radius R with control system_i,j:

Wherein, η_i,NF=max2 | | N_HΛΔ_θi||| ||Δ_c(m^*)||≤α,||Δ_o(m^*)||≤β,m^*=k ..., k-s+1 }；

NF indicates non-fault mode, Δ_θiIt indicates to correspond to failure f at time series θ_iProbabilistic specific manifestation form；Representing matrix [H F_j] kernel left orthogonal basis；F_jIndicate failure f_jCorresponding position in matrix F；Δ_cAnd Δ_o Respectively indicate the uncertainty of executing agency and sensor；α and β respectively indicates the upper bound of control system uncertainty norm under Boundary；K indicates sampling time point；S indicates length of window；I and j indicates failure serial number；

According to the statistical model of multivariate probability distribution with probabilistic control system, control system it is detectable not really Qualitative radius R_i,NFIt is isolated uncertain radius R with control system_i,j, obtain considering detectable uncertain radius can Detection property analysis indexesWith the isolability analysis indexes for considering that uncertain radius can be isolated

Wherein, θ indicates time series；

According to the detectability analysis indexes for considering detectable uncertain radiusIt can be isolated not with the consideration The isolability analysis indexes of certainty radiusObtain comparative analysis result.

2. the diagnosability analysis method of uncertain system according to claim 1, which is characterized in that the basis has Probabilistic discrete control spatial model, is iterated in temporal sequence, takes length of window s, obtains with probabilistic The statistical model of multivariate probability distribution of control system, comprising:

It determines and has probabilistic discrete control spatial model:

Wherein, x (k) ∈ Rⁿ, u (k) ∈ R^m, y (k) ∈ R^qWith f (k) ∈ R^pRespectively indicate the state vector of control system, input to Amount, output vector and fault vectors；w(k)∈R^lWith v (k) ∈ R^tRespectively indicate the process noise and observation noise of control system； Matrix A ∈ R^n×n、B_u∈R^n×m、C∈R^q×n、D_u∈R^q×m、B_f∈R^n×p、D_f∈R^q×p、B_w∈R^n×lAnd D_v∈R^q×tRespectively indicate control The corresponding coefficient matrix of system processed, Δ A, Δ B_u, Δ C and Δ D_uRespectively indicate dimension control system uncertainty matrix appropriate； Rⁿ、R^m、R^q、R^p、R^lAnd R^tN dimension, m dimension, q dimension, the p dimension, l peacekeeping t dimensional vector being illustrated respectively in real number field, n, m, q, p, l It is positive integer with t；

According to the uncertain Δ of executing agency_cWith the uncertain Δ of sensor_o, to empty with probabilistic discrete control Between model carry out simplify processing, after being simplified have probabilistic discrete control spatial model:

Wherein, Δ_c(k)=Δ Ax (k)+Δ B_uu(k)∈R^n×1, Δ_o(k)=Δ Cx (k)+Δ D_uu(k)∈R^q×1；||Δ_c(k)| |≤α, | | Δ_o(k)||≤β；| | | | indicate two norms；

It is iterated in temporal sequence, takes length of window s, obtain standardized model:

Lz_s=Hx_s+Ff_s+Ee_s+ΛΔ_s

Wherein, x_sIndicate the time heap stack vector of the state of control system；

According to equivalent space shift theory, to standardized model equal sign both sides while premultiplication matrix N_H, obtain described polynary general Rate statistical distribution model:

N_HLz_s=N_HFf_s+N_HEe_s+N_HΛΔ_s。

3. the diagnosability analysis method of uncertain system according to claim 2, which is characterized in that z_s∈R^(m+q)s、x_s ∈R^n(s+1)、f_s∈R^ps、e_s∈R^(L+t)s、Δ_s∈R^(n+q)s；L∈R^{(n+q)s×(m+q)s}、H∈R^{(n+q)s×n(s+1)}、F∈R^(n+q)s×ps、E ∈R^{(n+q)s×(l+t)s}、Λ∈R^{(n+q)s×(n+q)s}；

Λ=I_(n+q)s；

Wherein, O and I respectively indicate null matrix and unit matrix； Representing matrix Operation of direct product.

4. the diagnosability analysis method of uncertain system according to claim 1, which is characterized in that described according to Statistical model of multivariate probability distribution with probabilistic control system obtains the detectable uncertain radius of control system R_i,NFIt is isolated uncertain radius R with control system_i,j, comprising:

According to failure f_iThe corresponding probability density function at time series θWith another failure f_jAll probability density SetBetween minimum K-L divergence, obtain failure f in control system model_iDetectability assay index and therefore Hinder f_iWith failure f_jBetween isolability assay index；

According to failure f in the control system model_iDetectability assay index refer to ideal detectability assay MarkComparison result, determine the detectable uncertain radius R of the control system_i,NF；And according to the control Failure f in system model processed_iWith failure f_jBetween isolability assay index and ideal isolability assay indexComparison result, determine the control system is isolated uncertain radius R_i,j。

5. the diagnosability analysis method of uncertain system according to claim 4, which is characterized in that

Wherein, F_iIndicate failure f_iCorresponding position in matrix F；

6. the diagnosability analysis method of uncertain system according to claim 1, which is characterized in that according to the consideration The detectability analysis indexes of detectable uncertainty radiusWith the consideration can be isolated uncertain radius can be every From property analysis indexesObtain comparative analysis result, comprising:

Judge the detectability analysis indexes for considering detectable uncertain radiusIt whether is 0；

IfIt is 0, it is determined that control system failure cannot be detected and cannot be isolated；

IfIt is not 0, it is determined that control system failure is detectable, and judges that uncertain radius can be isolated in the consideration Isolability analysis indexesIt whether is 0；

IfIt is 0, it is determined that control system failure can be detected but can not be isolated；

IfIt is not 0, it is determined that control system failure can be detect and isolated.