CN102736616A - Dulmage-Mendelsohn (DM)-decomposition-based measuring point optimal configuration method for closed loop system - Google Patents

Dulmage-Mendelsohn (DM)-decomposition-based measuring point optimal configuration method for closed loop system Download PDF

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CN102736616A
CN102736616A CN2012102057753A CN201210205775A CN102736616A CN 102736616 A CN102736616 A CN 102736616A CN 2012102057753 A CN2012102057753 A CN 2012102057753A CN 201210205775 A CN201210205775 A CN 201210205775A CN 102736616 A CN102736616 A CN 102736616A
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CN102736616B (en
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刘文静
王南华
王大轶
何英姿
邢琰
刘成瑞
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Beijing Institute of Control Engineering
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Abstract

The invention discloses a Dulmage-Mendelsohn (DM)-decomposition-based measuring point optimal configuration method for a closed loop system. The method comprises the following steps of: first establishing a quantitative model of the closed loop system, and giving analytic relations between variables and between failures and the variables; then representing the obtained analytic relations by utilizing a parity adjacency matrix; next decomposing the parity adjacency matrix to obtain constraint relations between the variables by utilizing a DM decomposition technology; and finally obtaining an optimal measuring point set making a failure set detectable, an optimal measuring point set making a single failure fi maximally separable and an optimal measuring point set making the failures separable according to the constraint relations between the variables. The failures can be detected and separated as many as possible under the condition of satisfaction of resource constraints, and a basis can be provided for the diagnostic design of a satellite control system.

Description

A kind of closed-loop system measuring point that decomposes based on DM is distributed method rationally
Technical field
The present invention relates to a kind of closed-loop system measuring point and distribute method rationally, relate in particular to a kind of closed-loop system measuring point that decomposes based on DM and distribute method rationally, belong to fault diagnosis field.
Background technology
Satellite control system except depending on effective method for diagnosing faults, also follows the quantity and the quality of the metrical information that is used for fault diagnosis closely related in rail fault adaptibility to response.And the quantity of metrical information and quality depend on the measuring point of system design stage configuration, but it is considerably less with the diagnosticability to be that the measuring point of target is distributed pertinent literature rationally at present.At present; In the satellite control system design; Though also considered the demand of partial fault diagnosis in the measuring point layoutprocedure; But just by rule of thumb, add measuring point, do not proceed from the situation as a whole as yet to provide the optimum measuring point of containing all faults through the redundancy relationship of analyzing between each measuring point through analysis of failure one by one.
Document (1.Erik Frisk; Mattias Krysander and Jan Aslund.Sensor placement for fault isolation in linear differential-algebraic systems, Automatica, 2009; 45: 364-371.2.Mattias Krasander and Erik Frisk.Sensor placement for fault diagnosis; IEEE Transactions on Systems, Man, and Cybernetics-Part a:systems and humans; 2008; 38 (6): disclose 1398-1410.) and utilized the DM decomposition technique to carry out the method that measuring point is distributed rationally, weak point is that given method only is applicable to open cycle system, does not relate to the situation that system has feedback loop as yet; The closed-loop system measuring point based on the DM decomposition for the present invention is given is distributed method rationally, does not have disclosed method with complete meaning at present.
Summary of the invention
Technology of the present invention is dealt with problems and is: the deficiency that overcomes prior art; Provide a kind of closed-loop system measuring point that decomposes based on DM to distribute method rationally; Guarantee to detect and separate fault as much as possible satisfying under the situation of resource constraint, for the design of satellite control system diagnosticability provides foundation.
Technical solution of the present invention is: a kind of closed-loop system measuring point that decomposes based on DM is distributed method rationally, and step is following:
(1) set up the quantitative model of closed-loop system, provide the analytic relationship between variable and variable, fault and the variable, the closed-loop system quantitative model adopts following form to represent:
e 1∶x 1＝g 1(x 1，x 2，…，x n)+h 1(f 1，f 2，…，f m)
e 2∶x 2＝g 2(x 1，x 2，…，x n)+h 2(f 1，f 2，…，f m)
. . .
. . .
. . .
e k∶x k＝g k(x 1，x 2，…，x n)+h k(f 1，f 2，…，f m)
E wherein iI equality in the expression closed-loop system quantitative model, g i(x 1, x 2..., x n) expression variable x 1, x 2..., x nWith variable x iBetween relation, h i(f 1, f 2..., f m) expression fault f 1, f 2..., f mWith variable x iBetween relation, i=(1,2 ... k), n is the variable number, and m is the fault number;
(2) with the contiguous matrix representation of analytic relationship utilization idol that obtains in the step (1), the behavior equality E={e of the contiguous matrix of idol 1, e 2..., e k, classify variable X={ x as 1, x 2..., x n, as variable x iBe present in equality e jThe time, x i∈ X, e j∈ E, the then (e in the contiguous matrix of idol j, x i) be 1, otherwise be 0;
(3) utilize the DM decomposition technique that the contiguous matrix of idol that step (2) obtains is decomposed the restriction relation that obtains between the variable; Concrete grammar is: the capable and rank transformation of the contiguous matrix of antithesis; Make it become upper triangular matrix, and the variable on the equality left side is positioned over diagonal positions, for variable x i, i=1,2 ..., n is if it is positioned at equality e zDiagonal positions, z=1,2 ... K is positioned at equality e simultaneously qNon-diagonal position, q=1,2 ... K, q ≠ z can know according to restriction relation: at equality e zIn, other variable can be to variable x iExert an influence, and x iThrough equality e qTo being positioned at e qThe variable of diagonal positions exerts an influence, and utilizes similar thinking can obtain the restriction relation between all variablees that closed-loop system comprises;
(4) obtain making failure collection F={f according to variable bound relation in the step (3) 1, f 2..., f mHave detectability the set of optimum measuring point, make single fault f iOptimum measuring point set with maximum separability, and i ∈ (1, m), make fault F={f 1, f 2..., f mOptimum measuring point set with separability.
The present invention's beneficial effect compared with prior art is:
(1) present; Mainly rely on designer's experience configuration measuring point in the system development stage; The measuring point that does not form system is distributed method rationally, and more lacking with fault detectability and separability is that the measuring point of target is distributed method rationally, and the present invention utilizes the DM decomposition technique to provide optimum measuring point and distributes method rationally; To be advanced to the design phase to the consideration of fault diagnosis, for Research on fault diagnosis method provides advantage.
(2) the measuring point method of distributing rationally conducts a research around open cycle system mostly; And the present invention has taken into full account the influence that feedback concerns variable bound in the closed-loop system; The portrayal of visual pattern complicated restriction relation between each variable in the closed-loop system; Solved the bottleneck problem that the closed-loop system measuring point is distributed rationally
(3) method of the present invention is simple, clear and definite, is suitable for engineering design.
Description of drawings
Fig. 1 is a FB(flow block) of the present invention.
Fig. 2 is DM decomposition result figure;
Fig. 3 is the DM decomposition result figure of momenttum wheel;
Fig. 4 is each variable bound relation of momenttum wheel;
Fig. 5 is the feedback loop in the momenttum wheel fault model;
Fig. 6 is deletion electric machine assembly fault F mAfter each variable bound relation.
Embodiment
As shown in Figure 1, step of the present invention is: the quantitative model of closed-loop system is set up in (1), provides the analytic relationship between variable and variable, fault and the variable, and the closed-loop system quantitative model adopts following form to represent:
e 1∶x 1＝g 1(x 1，x 2，…，x n)+h 1(f 1，f 2，…，f m)
e 2∶x 2＝g 2(x 1，x 2，…，x n)+h 2(f 1，f 2，…，f m)
. . .
. . .
. . .
e k∶x k＝g k(x 1，x 2，…，x n)+h k(f 1，f 2，…，f m)
E wherein iI equality in the expression closed-loop system quantitative model, g i(x 1, x 2..., x n) expression variable x 1, x 2..., x nWith variable x iBetween relation, h i(f 1, f 2..., f m) expression fault f 1, f 2..., f mWith variable x iBetween relation, i=(1,2 ... k), n is the variable number, and m is the fault number;
(2) with the contiguous matrix representation of analytic relationship utilization idol that obtains in the step (1), the behavior equality E={e of the contiguous matrix of idol 1, e 2..., e k, classify variable X={ x as 1, x 2..., x n, as variable x iBe present in equality e jThe time, x i∈ X, e j∈ E, the then (e in the contiguous matrix of idol j, x i) be 1, otherwise be 0;
(3) utilize the DM decomposition technique that the contiguous matrix of idol that step (2) obtains is decomposed the restriction relation that obtains between the variable, concrete grammar is: the capable and rank transformation of the contiguous matrix of antithesis makes it become upper triangular matrix, for e iUtilize the relation of the influence between the variable and variable in each equality, obtain the restriction relation between all variablees that closed-loop system comprises;
Based on the contiguous matrix of the idol that obtains in the step (2), utilize the DM decomposition technique to obtain the restriction relation between the variable, its basic ideas are: through row and rank transformation in the contiguous matrix of idol, it is become upper triangular matrix, the result is as shown in Figure 2, b among the figure p(p=1,2 ..., k) expression b pThe place corresponding variable of row is positioned at equality e pThe left side, and equality e pIn other variable be positioned at the right of equality and through equality e pVariable to being positioned at the equality left side exerts an influence, and thinking can draw the restriction relation between all variablees that system comprises according to this.
(4) obtain making failure collection F={f according to variable bound relation in the step (3) 1, f 2..., f mHave detectability the set of optimum measuring point, make single fault f iOptimum measuring point set with maximum separability, and i ∈ (1, m), make fault F={f 1, f 2..., f mOptimum measuring point set with separability.
For the system that has feedback loop, the step below adopting obtains to make fault to have the optimum measuring point set that various diagnosticabilities require.Obtain the relevant failure collection of each variable according to restriction relation; Travel through whole variable bound relation; Seek the failure collection relevant, and store respectively according to direct fault and indirect fault that (the direct fault of variable i is meant the fault of direct variation i, and the indirect fault of variable i is meant through influencing other variable with each variable; And utilize the relation between variable and the variable, and then have influence on the fault of variable i).
(a) make failure collection F={f 1, f 2..., f mHas a selection algorithm of the optimum measuring point of detectability
Obtain making failure collection F={f 1, f 2..., f mOptimum measuring point set with detectability, promptly no matter directly fault still be indirect fault, and whether the failure collection that judgment variable is relevant contains the fault of all considerations, the variable of any one all fault of covering can be surveyed all can make fault have detectability.Summarize and to say it then is that influence as if fault propagates in the feedback loop, then any variable of comprising of feedback loop can be surveyed and all can make fault have detectability.
(b) make single fault f iSelection algorithm with optimum measuring point of maximum separability
Make fault f iHave maximum separability and be meant fault f iWith F/f iIn all faults all have separability (F/f iBe meant that F removes f iAll faults afterwards).
Analysis of failure f iThe basic ideas that whether have maximum separability are: with fault f iThe equality of influence is deleted from the contiguous matrix of idol, sets up the restriction relation between variable in the contiguous matrix of residue idol, and the variable that makes the residue fault all have detectability is joined in the measuring point set.In addition also need to reflect fault f iThe measuring point that changes promptly directly comprises f in the fault iVariable join in the measuring point set.
Need to prove, for fault f iThe variable of influence, if this variable in-degree except that fault is 0 (in-degree be 0 mainly be the influence that this variable does not receive other variable and fault), then above-mentioned steps is no longer suitable, and this variable promptly is to make fault f iOptimum measuring point with maximum separability.
(c) make F={f 1, f 2..., f mIn all faults all have the selection algorithm of the optimum measuring point of separability.
If will realize F={f 1, f 2..., f mIn the separation of each fault, need m measuring point at least, in other words, for each fault mode, exist a measuring point can reflect its situation of change at least, and can this fault and other faulty section be separated, give the F={f that sends as an envoy to around this thinking below 1, f 2..., f mAll faults all have the optimum measuring point set of separability.
For fault f D, i(f D, i∈ F, f D, iBe variable x iDirect fault), according to variable bound relation, judge to receive variable x iThe next variable x of influence I+1Direct fault f D, i+1Whether be 0, if not, x then added iTo Measurable Set S IAnd with the f in the indirect failure collection of all variablees D, iDeletion, otherwise to x iIdentify, continue analysis according to the variable bound relation and receive variable x iThe next variable of influence is up to variable x hDirect fault f D, hNot till 0, for fault f D, iAll variablees that identified are:
Figure BSA00000737806100051
Adopt identical step to obtain the variable of all signs to the residue fault.
On the basis of above-mentioned steps, proceed to analyze: the fault that supposition does not search out suitable measuring point has q, and the corresponding identification variable is:
Figure BSA00000737806100052
J=1,2 ... Q is then at I (f D, j), j=1,2 ... Seek q unduplicated variable among the q and add Measurable Set S ICan obtain making all faults all to have the failure collection of separability.
With the momenttum wheel is example, and the present invention is elaborated.
(1) sets up the momenttum wheel model, provide the analytic relationship between each variable and other variable and the fault respectively;
Consider that the momenttum wheel model after the various faults is:
e 1 : L di ( t ) dt = u ( t ) - R · i ( t ) - K e · w ( t ) + F d e 2 : m e ( t ) = K m · i ( t ) + F m e 3 : J dw ( t ) dt = m d ( t ) e 4 : m d ( t ) = m e ( t ) + m f , 0 ( t ) + F b e 5 : u ( t ) = ( K p + K i s ) ( w 0 ( t ) - i ( t ) ) + F c
Wherein L is the inductance of armature, and i (t) is for flowing through the electric current of armature, and R is the resistance of armature, and u (t) is the direct current generator driving voltage of equivalence, and w (t) is a rotating speed of motor, K eBe the coefficient of potential, K mBe motor torque coefficient, m e(t) be the motor output torque, J is the total moment of inertia of momenttum wheel, m d(t) be the dynamic output torque of momenttum wheel, m F, 0(t) be moment of friction,
Figure BSA00000737806100062
(T RepExpression desired output moment), K pBe current controller scale-up factor, K iBe the current controller integral coefficient.F dBe driving circuit fault, F mBe electric machine assembly fault, F bBe bearing assembly fault, F cBe the control circuit fault.
(2) the contiguous matrix of analytic relationship utilization idol that obtains in the step (1) is represented;
The analytic relationship that obtains in the step (1) is sorted out by known quantity, known variables and fault, and corresponding set adopts Y={y respectively 1, y 2..., y p, X={x 1, x 2..., x qAnd F={f 1, f 2..., f mExpression, be designated row with equality, with set X, Y and F are for row, and according to the incidence relation between variable and the fault in each equality, the contiguous matrix of the momenttum wheel of foundation idol is as shown in table 1.
The contiguous matrix of table 1 momenttum wheel idol
Figure BSA00000737806100063
Figure BSA00000737806100071
(3) based on the contiguous matrix of the idol that obtains in the step (2), utilize the DM decomposition technique to obtain the restriction relation between the variable;
To the contiguous matrix of the momenttum wheel shown in the table 1 idol, the result who utilizes the DM decomposition technique to obtain is as shown in Figure 3, and it is as shown in Figure 4 to get between each variable of momenttum wheel restriction relation thus.If there is restriction relation, then adopts the straight line that has arrow that both are connected, and identify relevant equality label between variable and the variable on the straight line next door.
As can be seen from Figure 4, there are two feedback loops in the momenttum wheel variable bound relation, are respectively { current i (t), motor output torque m e(t), momenttum wheel output torque m d(t), rotating speed w (t) } and { current i (t), driving voltage u (t) }, and also two feedback loops have common point { current i (t) }, and as shown in Figure 5.
(4), provide and satisfy the optimum measuring point set that various diagnosticabilities require according to the variable bound relation that obtains in the step (3).
Travel through variable bound relation shown in Figure 4, seek the failure collection relevant with each variable, and store respectively according to direct fault and indirect fault, variable that obtains and the relation between the fault are i (F d/ { F b, F m, F c), m e(F m/ { F b, F d, F c), m d(/ { F b, F d, F c, F m), w (/ { F b, F d, F c, F m), u (F c/ { F b, F d, F m), m f(F b/), wherein for i (F d/ { F b, F m, F c), the F on symbol/left side dRepresent the direct fault relevant with variable i, and { the F on symbol/the right b, F m, F cRepresent the indirect fault relevant with variable i, other is similarly.
1. make all faults have the optimum measuring point set of detectability
No matter can know according to the related content that provides in the step 4 embodiment, be direct fault or indirect fault, owing to driving voltage u (t), current i (t), rotating speed w (t), motor output torque m e(t) and momenttum wheel output torque m d(t), all contained the fault of all considerations, so any one variable can be surveyed and can both make all faults have detectability.From the another one angle analysis, have two feedback loops in the momenttum wheel model, and two feedback loops have common point, so any one variable in these two feedback loops can survey and all can make fault have detectability, optimum measuring point set is as shown in table 2.
Table 2 makes all faults have the optimum measuring point set of detectability
Figure BSA00000737806100081
2. make electric machine assembly fault F mOptimum measuring point set with maximum separability
This joint is with electric machine assembly fault F mBe example, the selection algorithm that makes single fault have the optimum measuring point of maximum separability is elaborated.
With electric machine assembly fault F mCorresponding equality m e(t)=K mI (t)+F mFrom the contiguous matrix of idol, delete, and utilize the DM decomposition technique to obtain restriction relation shown in Figure 6, and then the relation that obtains between surplus variable and the fault is: i (F d/ { F b, F c), m e(/), m d(/ { F b), w (/ { F b), u (F c/ { F b, F d), m f(F b/), the variables set that then makes the residue fault have detectability is combined into: { current i (t) }, { driving voltage u (t) } is because motor output torque m eDirect fault comprise F m, so also need add m in the measuring point set e, obtain making electric machine assembly fault F at last mMinimum measuring point set with maximum separability is { current i (t), motor output torque m eAnd { driving voltage u (t), motor output torque m (t) } e(t) }.
Utilize same steps as to obtain making driving circuit fault F respectively d, bearing assembly fault F bWith control circuit fault F cOptimum measuring point set with maximum separability is as shown in table 3.
Table 3 makes fault f iOptimum measuring point set with maximum separability
Figure BSA00000737806100082
3. make the optimum measuring point set that all faults all have separability among the F
According to the restriction relation of each variable of momenttum wheel shown in Figure 4, the relation that obtains between variable and the fault is i (F d/ { F b, F m, F c), m e(F m/ { F b, F d, F c), m d(/ { F b, F d, F c, F m), w (/ { f b, f d, f c, f m), u (F c/ { F b, F d, F m), m f(F b/).For driving circuit fault F dWith control circuit fault F c, owing to be not 0 to the direct fault of the next variation of dependent variable u (t) and i (t), therefore need with u (t) with i (t) but the adding measuring point is concentrated.And bearing assembly fault F bWith electric machine assembly fault F mThere is not direct fault in next variable to dependent variable, therefore need identify, and the variable set that is identified is respectively I (F m)={ m e(t), m d(t), w (t) } and I (F b)={ m f(t), m d(t), w (t) }.
Owing to search out the fault of suitable measuring point bearing assembly fault F is not arranged bWith electric machine assembly fault F m, the corresponding identification variable is: I (F m)={ m e(t), m d(t), w (t) } and I (F b)={ m f(t), m d(t), w (t) }, then need from I (F m) and I (F b) the middle searching in 2 unduplicated variablees adding Measurable Set, can obtain making all faults all to have the failure collection of separability, concrete outcome is as shown in table 4.
Table 4 makes all faults have the optimum measuring point set of separability
Figure BSA00000737806100091
The present invention not detailed description is a technology as well known to those skilled in the art.

Claims (2)

1. a closed-loop system measuring point that decomposes based on DM is distributed method rationally, it is characterized in that step is following:
(1) set up the quantitative model of closed-loop system, provide the analytic relationship between variable and variable, fault and the variable, the closed-loop system quantitative model adopts following form to represent:
e 1∶x 1＝g 1(x 1，x 2，…，x n)+h 1(f 1，f 2，…，f m)
e 2∶x 2＝g 2(x 1，x 2，…，x n)+h 2(f 1，f 2，…，f m)
. . .
. . .
. . .
e k∶x k＝g k(x 1，x 2，…，x n)+h k(f 1，f 2，…，f m)
E wherein iI equality in the expression closed-loop system quantitative model, g i(x 1, x 2..., x n) expression variable x 1, x 2..., x nWith variable x iBetween relation, h i(f 1, f 2..., f m) expression fault f 1, f 2..., f mWith variable x iBetween relation, i=(1,2 ... k), n is the variable number, and m is the fault number;
(2) with the contiguous matrix representation of analytic relationship utilization idol that obtains in the step (1), the behavior equality E={e of the contiguous matrix of idol 1, e 2..., e k, classify variable X={ x as 1, x 2..., x n, as variable x iBe present in equality e jThe time, x i∈ X, e j∈ E, the then (e in the contiguous matrix of idol j, x i) be 1, otherwise be 0;
(3) utilize the DM decomposition technique that the contiguous matrix of idol that step (2) obtains is decomposed the restriction relation that obtains between the variable;
(4) obtain making failure collection F={f according to variable bound relation in the step (3) 1, f 2..., f mHave detectability the set of optimum measuring point, make single fault f iOptimum measuring point set with maximum separability, and i ∈ (1, m), make fault F={f 1, f 2..., f mOptimum measuring point set with separability.
2. a kind of closed-loop system measuring point that decomposes based on DM according to claim 1 is distributed method rationally; It is characterized in that: the implementation of said step (3) is: the capable and rank transformation of the contiguous matrix of antithesis; Make it become upper triangular matrix; And the variable on the equality left side is positioned over diagonal positions, for variable x i, i=1,2 ..., n is if it is positioned at equality e zDiagonal positions, z=1,2 ... K is positioned at equality e simultaneously qNon-diagonal position, q=1,2 ... K, q ≠ z is then at equality e zIn, other variable can be to variable x iExert an influence, and x iThrough equality e qTo being positioned at e qThe variable of diagonal positions exerts an influence, and finally obtains the restriction relation between the variable.
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CN104571087B (en) * 2014-12-26 2017-08-29 北京控制工程研究所 Spacecraft control diagnosability determination method under a kind of influence of noise
CN104571087A (en) * 2014-12-26 2015-04-29 北京控制工程研究所 Diagnostic determination method for spacecraft control system under influence of noise
CN104571088A (en) * 2014-12-26 2015-04-29 北京控制工程研究所 Satellite control system multi-objective optimization method based on fault diagnosability constraint
CN104571088B (en) * 2014-12-26 2018-01-05 北京控制工程研究所 Satellite control system Multipurpose Optimal Method based on fault diagnosability constraint
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CN105808842B (en) * 2016-03-07 2019-04-05 北京航空航天大学 A kind of measuring point preferred method decomposed based on DM
CN106200629A (en) * 2016-09-30 2016-12-07 山东科技大学 The fault of a kind of UAV Flight Control System degree of detection can analyze method
CN109978059A (en) * 2019-03-28 2019-07-05 南京富岛信息工程有限公司 A kind of crude oil distillation process primary distillation tower rushes tower fault early warning method
CN109978059B (en) * 2019-03-28 2024-02-23 南京富岛信息工程有限公司 Early warning method for tower flushing faults of primary distillation tower in crude oil distillation process
CN111259553A (en) * 2020-01-19 2020-06-09 北京空间飞行器总体设计部 Spacecraft system fault detection obtaining method based on distance similarity
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