CN106908132B - A method of strain gauge load cell failure is detected based on improved Petri net - Google Patents
A method of strain gauge load cell failure is detected based on improved Petri net Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01G—WEIGHING
- G01G23/00—Auxiliary devices for weighing apparatus
- G01G23/01—Testing or calibrating of weighing apparatus
Abstract
The invention discloses a kind of methods based on improved Petri net detection strain gauge load cell failure, belong to detection technique field.The fault detection method includes being counted according to the physical structure and event of failure of sensor itself, forms the fault logic system of sensor；Above-mentioned fault logic system is combined using follow-on Petri network, establishes fault model；Comprehensive fuzzy statistics, fault statistics data, expertise and neural network adjust algorithm, determine initial library institute confidence level, weight and transition threshold value；Whole library institute confidence levels in model are obtained by reasoning and calculation, by these as a result, carrying out failure predication and diagnosis to sensor.The reliability and accuracy of strain gauge load cell fault detection are improved by the above method.
Description
Technical field
The present invention relates to detection technique fields, and in particular to one kind is based on improved Petri net detection strain weighing sensing
The method of device failure.
Background technique
Strain gauge load cell be mainly used in it is various under the conditions of weighing and dynamometry, and be widely used in our live
In every field, the superiority and inferiority of production technology quality and circuit design directly affects the accuracy of sensor.Currently, increasingly
More industries and field be unable to do without the support of weighing sensor, wherein being no lack of the weighing sensor of many large-tonnages, just to guarantee
The operation and use of its normal table, it is necessary to there are a set of effective failure predication and diagnostic system, it is significant.
Petri network is the mathematical notation to discrete parallel system, since Petri network is a kind of good parallel computation and row
For analysis method, existing stringent mathematical formulae also has intuitive figure to describe.It is examined currently based on the major failure of Petri network
Survey method has: fuzzy technology being combined with Petri network, proposes the modeling of Fuzzy Petri Net (Fuzzy Petri Net, FPN)
Method efficiently solves library institute token value uncertain problem, but does not provide the Dynamic Inference method of FPN.The side MYCIN
Method carries out confidence level reasoning and calculation, but MYCIN method haves the defects that weight computing.Application matrix reasoning Fuzzy Petri Net
Solve the matrix reasoning problems of fuzzy fault Petri network, but its correlation model parameters, such as weight etc., have very big
It is uncertain.Idea about modeling based on directionality reduces the dimension of incidence matrix, simplifies calculating, but not to weight into
The excessive description of row.In conjunction with BP algorithm, so that Petri network has self-learning capability, weight is becomed more clear, but not to model
It is correspondingly improved.BP neural network is combined with traditional fuzzy fault Petri network, proposes adaptive fuzzy Petri
Net solves the learning ability of traditional fuzzy Fault Petri Net, but does not explicitly point out the determination of transition confidence level, so that being
System has more uncertainty.
Summary of the invention
The object of the present invention is to provide a kind of based on improved Petri net in the fault detection side of strain gauge load cell
Method improves the reliability and essence of Transducer fault detection using the failure of improved Petri net detection strain gauge load cell
Parasexuality.
The following technical solution is employed by the present invention:
A method of strain gauge load cell failure is detected based on improved Petri net, comprising the following steps:
Step 1: being counted according to the physical structure of strain gauge load cell itself and event of failure, form the event of sensor
Hinder flogic system, fault logic system is the relationship of other failures that causes by one or more failures；
Step 2: above-mentioned fault logic system being combined according to Petri network, establishes fault model；Fuzzy fault Petri network
It is defined as 9 tuples: Sp=(P, T, I, O, K, ω, α, f, λ)；Wherein,
(1) P={ p1,p2,...,pnLibrary institute failure collection, represent the various failures of sensor generation, including " output
Adjust the disconnected grid of resistance ", " weighing overload ", " sensitivity that diaphragm shunts is bigger than normal "；
(2) T={ t1,t2,...,tnIndicate transition set, the t when there are transition to triggeri=1, otherwise ti=0；
(3) K=(k1,k2,...,kn)TLibrary representation institute mark vector, when the event represented by the library breaks down, ki=1, it is no
Then, ki=0；
(4) ω=(ω1,ω2,...,ωn)TFor library institute weight n-dimensional vector, satisfaction is worked asPkWhen ∈ I (t),
(5) α=(α1,α2,...,αn)TFor library institute confidence level n-dimensional vector, the confidence level that event of failure really occurs is indicated；
(6) f=(f1,f2,...,fn)TFor library institute event fuzzy probability set, fiLibrary representation institute event piWhat is occurred is general
Rate size；
(7) λ=(λ1,λ2,...,λn)TTo change threshold values vector；
Step 3: comprehensive fuzzy statistics, fault statistics data, expertise and neural network adjust algorithm, determine initial library
Institute's confidence level, weight and transition threshold value；Initial library institute confidence level is by fuzzy statistical method, in conjunction with historical data and expertise
It obtains；The determination of weight is to be adjusted to obtain by neural network algorithm:
Define diFor the due output (desired output) of i-th of unit；
Define yiFor the reality output of i-th of unit, the error signal e of the uniti=di-yi, wherein yi=vi(∑
αi·ωi), vi(x)=1/ (exp (x)+1)；
The adjusting of weight is embodied in error-duration model, wherein square-errorAnti-pass is carried out as adjustment signal；
Modification amount gradient is
The correction amount of weight isWherein η is learning rate；Obtain a new weightBy its back substitution into above-mentioned formula, through iterating calculate, until square-error E allowed band it
Interior, weight adjusting terminates；
Step 4: whole library institute confidence levels in model being obtained by reasoning and calculation, by these as a result, carrying out to sensor
Failure predication and diagnosis；Reasoning and calculation includes forward reasoning and backward inference, and forward reasoning is based on FPN model, and forward direction pushes away
Reason reflects the characteristic of fault propagation, according to the failure symptom information that the detection of working environment and element or professional obtain,
To predict the possible situation occurred, the flowing of the discrimination matrix lighted a fire by transition and malfunction mark, to possible generation
Failure is assessed, and takes corresponding counter-measure；Backward inference is when faulty generation, to derive the original of failure generation
Cause；
Forward reasoning for clarity, compactly indicates each matrix reasoning operation, describes concurrent system using Petri network
Ability and Fuzzy Petri Net mathematical theory derive basis, define 5 Special operators:
(1) ◇: C=A ◇ B, A, B and C of comparison operator are m * n matrix, work as aij> bijWhen, Cij=1；Work as aij< bij
When, Cij=0, i=1,2 ..., m；J=1,2 ..., n；
(2) taking small operator ∧: C=A ∧ B, A, B and C is m * n matrix, cij=min (aij,bij), i=1,2 ..., m；
J=1,2 ..., n；
(3) taking big operator ∨: C=A ∨ B, A, B and C is m * n matrix cij=max (aij,bij), i=1,2 ..., m；j
=1,2 ..., n；
(4) directly multiply operator *: C=A*b, A and C are respectively m × n, and n × m matrix, b is n-dimensional vector, then cij=aij·bi, i
=1,2 ..., m；J=1,2 ..., n；
(5) multiplication operatorIt is respectively m × q with C, q × n, m * n matrix,J=1,2 ..., n；
Based on the confidence level of MYCIN, related algorithm is improved, can be obtained after reasoning whole libraries
Confidence value, the successively foundation as assessment of fault and diagnosis.It improves as follows:
Defining one: weight matrix P is m * n matrix, and works as weight ωjIt is library institute αiWeight when, pij=1, otherwise
pij=0, i=1,2 ..., m；J=1,2 ..., n；
Defining two: transition matrix Q is m * n matrix, and works as weight ωiConnection transition tjWhen, qij=1, otherwise qij=
0, i=1,2 ..., m；J=1,2 ..., n；
MYCIN rational formula after improvement: αi+1=αi∨(1+exp[ORT])-1.Wherein, R=[(αTP) * ω] Q, it indicates
In several transition library institute's confidence level and weight product equivalent and n dimensional vector, and if only if αi+1=αiWhen, reasoning terminates,
Otherwise continue reasoning；
Transition igniting discrimination matrix and malfunction mark inference mode are as follows:
(1) transition differentiate, define three:T is referred to as that potential transition are enabled
's；Define four: if transition T can trigger igniting, in output library institute POjOne new confidence level of upper generation；If being unable to trigger point
Fire, then 0 carried out by output library；
Igniting matrix is changed to calculate, then with obtained vector R calculated above, obtains transition igniting by comparing formula
Discrimination matrix, Y=R ◇ λ, wherein Y=(y1,y2,...,yn)TTo change discrimination matrix of lighting a fire, if meeting ignition condition yi=1,
Otherwise yi=0, according to firing rule, obtain the library containing token the corresponding enabled igniting matrix rational formula changed:
In formula: Ki-1-Ki-2Indicate (i-1)-th new igniting mark vector；
(2) malfunction mark vector brings the above results into inference understanding formula:
Backward inference introduces minimal cut set rate of breakdown, defines three: if minimal cut set G={ p1,p2,...,pn,
Minimal cut set rate of breakdown are as follows:
F (G)=(α1+α2+…+αn)/n n > 0；
The input of backward inference, output library are respectively positive output, input magazine institute, i.e. I-=O, O-=I, are inversely pushed away
Manage Matrix Formula are as follows:In formula:When igniting reverse for kth time
Inverse net enable transition sequence.
The invention has the advantages that:
The present invention provides a kind of method based on improved Petri net detection strain gauge load cell failure, designs one
Kind modified Petri network replaces uncertain stronger transition confidence level with sigmoid function.The modified Petri network benefit
It is adjusted to obtain determining weight with neural network algorithm, designs completely new MYCIN method, reasoning and calculation obtains whole library institutes
Confidence value；Forward reasoning and backward inference give the Dynamic Inference method of FPN, can predict the situation that may occur,
And corresponding counter-measure is taken, when faulty mode, derive the reason of occurring of being out of order.The fault detection method passes through shape
At the fault logic system of sensor；Above-mentioned fault logic system is combined using follow-on Petri network, establishes failure mould
Type；Comprehensive fuzzy statistics, fault statistics data, expertise and neural network adjust algorithm, determine initial library institute confidence level, power
Value and transition threshold value；Whole library institute confidence levels in model are obtained by reasoning and calculation, by these as a result, carrying out event to sensor
Barrier prediction improves the reliability and accuracy of strain gauge load cell fault detection with the process of diagnosis.
Detailed description of the invention
Fig. 1 show the basic unit of modified Petri network in the present invention.
Fig. 2 show the fault model of strain gauge load cell.
Fig. 3 show the part Petri net model of specific fault reasoning of the invention.
Fig. 4 show all libraries after forward reasoning failure distribution map.
Fig. 5 show all libraries after backward inference failure distribution map.
Fig. 6 show error curve diagram when weight is adjusted.
Fig. 7 show the curve graph of weight adjusting.
Specific embodiment
The present invention is specifically described with reference to the accompanying drawing:
In conjunction with Fig. 1 to Fig. 7, a method of strain gauge load cell failure is detected based on improved Petri net, including with
Lower step:
Step 1: being counted according to the physical structure of strain gauge load cell itself and event of failure, form the event of sensor
Hinder flogic system, fault logic system is the relationship of other failures that causes, such as " supply voltage by one or more failures
It is excessively high " or " supply voltage is unstable and generates ' surge voltage ' " initiation " strain ga(u)ge is burnt out " etc.；
Step 2: above-mentioned fault logic system being combined according to Petri network, establishes fault model；Fuzzy fault Petri network
It is defined as 9 tuples: Sp=(P, T, I, O, K, ω, α, f, λ)；Wherein,
(1) P={ p1,p2,...,pnLibrary institute failure collection, represent the various failures of sensor generation, including " output
Adjust the disconnected grid of resistance ", " weighing overload ", " sensitivity that diaphragm shunts is bigger than normal " etc.；
(2) T={ t1,t2,...,tnIndicate transition set, the t when there are transition to triggeri=1, otherwise ti=0；
(3) K=(k1,k2,...,kn)TLibrary representation institute mark vector, when the event represented by the library breaks down, ki=1, it is no
Then, ki=0；
(4) ω=(ω1,ω2,...,ωn)TFor library institute weight n-dimensional vector, satisfaction is worked asPkWhen ∈ I (t),
(5) α=(α1,α2,…,αn)TFor library institute confidence level n-dimensional vector, the confidence level that event of failure really occurs is indicated；
(6) f=(f1,f2,...,fn)TFor library institute event fuzzy probability set, fiLibrary representation institute event piWhat is occurred is general
Rate size；
(7) λ=(λ1,λ2,...,λn)TTo change threshold values vector；
Step 3: comprehensive fuzzy statistics, fault statistics data, expertise and neural network adjust algorithm, determine initial library
Institute's confidence level, weight and transition threshold value；When making inferences with Fuzzy Petri Net, need extraneous input is initial library institute
The confidence level of (bottom library institute), middle database in one's power conclusion library confidence level generally obtained by reasoning.So confidence level determines
Problem is mainly for initial library institute.Initial library institute confidence level is to be obtained by fuzzy statistical method in conjunction with historical data and expertise
?.
The determination of weight is to be adjusted to obtain by neural network algorithm:
Define diFor the due output (desired output) of i-th of unit；
Define yiFor the reality output of i-th of unit, the error signal e of the uniti=di-yi, wherein yi=vi(∑
αi·ωi), vi(x)=1/ (exp (x)+1)；
The adjusting of weight is embodied in error-duration model, wherein square-errorAnti-pass is carried out as adjustment signal；
Modification amount gradient is
The correction amount of weight isWherein η is learning rate；Obtain a new weightBy its back substitution into above-mentioned formula, through iterating calculate, until square-error E allowed band it
Interior, weight adjusting terminates.
Step 4: whole library institute confidence levels in model being obtained by reasoning and calculation, by these as a result, carrying out to sensor
Failure predication and diagnosis；Reasoning and calculation includes forward reasoning and backward inference, and forward reasoning is based on FPN model, and forward direction pushes away
Reason reflects the characteristic of fault propagation, according to the failure symptom information that the detection of working environment and element or professional obtain,
To predict the possible situation occurred, the flowing of the discrimination matrix lighted a fire by transition and malfunction mark, to possible generation
Failure is assessed, and takes corresponding counter-measure；Backward inference is when faulty generation, to derive the original of failure generation
Cause.To avoid blindness when overhauling and improving the efficiency of the tracking source of trouble, we introduce the method for minimal cut set as event
Barrier derives and diagnosis basis.
Forward reasoning for clarity, compactly indicates each matrix reasoning operation, describes concurrent system using Petri network
Ability and Fuzzy Petri Net mathematical theory derive basis, define 5 Special operators:
(1) ◇: C=A ◇ B, A, B and C of comparison operator are m * n matrix, work as aij> bijWhen, Cij=1；Work as aij< bij
When, Cij=0, i=1,2 ..., m；J=1,2 ..., n；
(2) taking small operator ∧: C=A ∧ B, A, B and C is m * n matrix, cij=min (aij,bij), i=1,2 ..., m；
J=1,2 ..., n；
(3) taking big operator ∨: C=A ∨ B, A, B and C is m * n matrix cij=max (aij,bij), i=1,2 ..., m；j
=1,2 ..., n；
(4) directly multiply operator *: C=A*b, A and C are respectively m × n, and n × m matrix, b is n-dimensional vector, then cij=aij·bi, i
=1,2 ..., m；J=1,2 ..., n；
(5) multiplication operatorIt is respectively m × q with C, q × n, m * n matrix,J=1,2 ..., n；
Based on the confidence level of MYCIN, related algorithm is improved, can be obtained after reasoning whole libraries
Confidence value, the successively foundation as assessment of fault and diagnosis.It improves as follows:
Defining one: weight matrix P is m * n matrix, and works as weight ωjIt is library institute αiWeight when, pij=1, otherwise
pij=0, i=1,2 ..., m；J=1,2 ..., n；
Defining two: transition matrix Q is m * n matrix, and works as weight ωiConnection transition tjWhen, qij=1, otherwise qij=
0, i=1,2 ..., m；J=1,2 ..., n；
MYCIN rational formula after improvement: αi+1=αi∨(1+exp[ORT])-1.Wherein, R=[(αTP) * ω] Q, it indicates
In several transition library institute's confidence level and weight product equivalent and n dimensional vector, and if only if αi+1=αiWhen, reasoning terminates,
Otherwise continue reasoning.
Transition igniting discrimination matrix and malfunction mark inference mode are as follows:
(1) transition differentiate, define three:T is referred to as that potential transition are enabled
's；Define four: if transition T can trigger igniting, in output library institute POjOne new confidence level of upper generation；If being unable to trigger point
Fire, then 0 carried out by output library；
Igniting matrix is changed to calculate, then with obtained vector R calculated above, obtains transition igniting by comparing formula
Discrimination matrix, Y=R ◇ λ, wherein Y=(y1,y2,...,yn)TTo change discrimination matrix of lighting a fire, if meeting ignition condition yi=1,
Otherwise yi=0, according to firing rule, obtain the library containing token the corresponding enabled igniting matrix rational formula changed:
In formula: Ki-1-Ki-2Indicate (i-1)-th new igniting mark vector；
(2) malfunction mark vector brings result obtained above into inference understanding formula:
Backward inference introduces minimal cut set rate of breakdown, defines three: if minimal cut set G={ p1,p2,...,pn,
Minimal cut set rate of breakdown are as follows:
F (G)=(α1+α2+...+αn)/n n > 0；
The input of backward inference, output library are respectively positive output, input magazine institute, i.e. I-=O, O-=I, inversely pushes away
Manage Matrix Formula are as follows:In formula:When igniting reverse for kth time
Inverse net enable transition sequence.
It is as shown in the table that Fig. 2 corresponds to library institute meaning:
Event of failure corresponding to 1 library of table
Since model built is larger, the writing of input and output matrix is excessively cumbersome, and the present invention is with " bridge circuit failure "
It is calculated to make inferences, FPN fault model is as shown in Figure 3.It is calculated according to step 3.
(1) method according to step 3 obtains bottom library institute confidence level vector form are as follows: α0=(0.89,0.87,
0.84,0.71,0.88,0.93,0.89,0.8,0.87,0,0,0.69,0,0.88,0.9,0,0,0,0)T。
(2) method according to step 3 is adjusted the weight of P4, P5, P6 for changing T5.Pass through system
It is 0.6937, η=0.3 that P30 desired output, which is calculated, and maximum study step number is set as 1000, square error 0.001.Instruction
It is as shown in Figure 6 and Figure 7 to practice result.
After the interative computation of 931 steps, square error is within the allowable range.P4, the weight difference of P5, P6 are obtained at this time
It is 0.3864,0.5071,0.1065.
(3) it according to the calculating of this model and analysis, changes threshold value and is set as 0.5.
By α0, O, U, I bring into improve MYCIN rational formula calculated.Until α4=α3, reasoning terminates, α3=(0.89,
0.87,0.84,0.71,0.88,0.93,0.89,0.8,0.87,0.7089,0.72,0.69,0.7,0.88,0.9,0.84,
0.67,0.71,0.71).As a result, we obtain each library confidence level, thus be used as positive and negative reasoning foundation.
Below by taking department pattern as an example, calculating is made inferences.
(1) forward reasoning: sensor operates normally, and does not have failure, but pass through detection discovery failure symptom, it is assumed that hair
Raw following sign: " supply voltage is excessively high ", " output lead disconnection ", " cable rosin joint ", " humid environment ", " output adjustment electricity
Block grid ".Obtain initial marking vector M0=(1,0,0,1,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0)T, by α3It brings into
It changes in discrimination formula, obtains potential change and enable matrix y=(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)T。
By M0, y brings the enabled igniting matrix rational formula of transition into, makes inferences calculating.It finally obtains: M3=(1,0,0,1,1,0,0,
0,1,1,1,0,0,0,1,1,1,1,1)T, Y3=Y4Reasoning terminates, Y3=(0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
0,1)T, final mark vector is M3, fault propagation path is as shown in Figure 4, it may be clearly seen that the failure that will occur.By
This can be used as the foundation of trouble shooting, maintenance the job stability that improves sensor.
(2) backward inference: backward inference is carried out by taking " non-output signal or output signal very little after load " as an example.Initial mark
Know vectorThere is forward direction
It is potential obtained in reasoning to change enabled matrix y-=(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1)T。
It willy-,I-,O-It brings into backward inference Matrix Formula, by reasoning and calculation, whenWhen, reasoning knot
Beam obtains mark vector and reverse transition matrix Library is distributed such as Fig. 5 institute
Show.Cause P49Minimal cut set G1={ p1, G2={ p2, G3={ p3, G4={ p4, G5={ p4·p5, G6={ p5, G7=
{p5·p6, G8={ p4·p5·p6, G9={ p7}.It is calculated according to above-mentioned formula: f (G1)=0.89, f (G2)=0.87, f
(G3)=0.84, f (G4)=0.88, f (G5)=0.795, f (G6)=0.71, f (G7)=0.93, f (G8)=0.89.Thus may be used
To obtain, diagnostic sequence should be first G7, then successively detect G1, G9, G6, G2, G3, G5, G5, G4Thus as fault diagnosis
Data foundation improves diagnosis speed.
Certainly, the above description is not a limitation of the present invention, and the present invention is also not limited to the example above, this technology neck
The variations, modifications, additions or substitutions that the technical staff in domain is made within the essential scope of the present invention also should belong to of the invention
Protection scope.
Claims (1)
1. a kind of method based on improved Petri net detection strain gauge load cell failure, which is characterized in that including following step
It is rapid:
Step 1: being counted according to the physical structure of strain gauge load cell itself and event of failure, the failure for forming sensor is patrolled
The system of collecting；
Step 2: above-mentioned fault logic system being combined according to Petri network, establishes fault model；The definition of fuzzy fault Petri network
For 9 tuples: Sp=(P, T, I, O, K, ω, α, f, λ)；Wherein,
(1) P={ p1,p2,...,pnLibrary institute failure collection, represent the various failures of sensor generation, including " output adjustment
Resistance breaks grid ", " weighing overload ", " sensitivity that diaphragm shunts is bigger than normal "；
(2) T={ t1,t2,...,tnIndicate transition set, the t when there are transition to triggeri=1, otherwise ti=0；
(3) K=(k1,k2,...,kn)TLibrary representation institute mark vector, when the event represented by the library breaks down, ki=1, otherwise,
ki=0；
(4) ω=(ω1,ω2,...,ωn)TFor library institute weight n-dimensional vector, satisfaction is worked asPkWhen ∈ I (t),
(5) α=(α1,α2,...,αn)TFor library institute confidence level n-dimensional vector, the confidence level that event of failure really occurs is indicated；
(6) f=(f1,f2,...,fn)TFor library institute event fuzzy probability set, fiLibrary representation institute event piThe probability occurred is big
It is small；
(7) λ=(λ1,λ2,...,λn)TTo change threshold values vector；
Step 3: comprehensive fuzzy statistics, fault statistics data, expertise and neural network adjust algorithm, determine that initial library is set
Reliability, weight and transition threshold value；Initial library institute confidence level is to be obtained by fuzzy statistical method in conjunction with historical data and expertise
?；The determination of weight is to be adjusted to obtain by neural network algorithm:
Define diFor the due output (desired output) of i-th of unit；
Define yiFor the reality output of i-th of unit, the error signal e of the uniti=di-yi, wherein yi=vi(∑αi·
ωi), vi(x)=1/ (exp (x)+1)；
The adjusting of weight is embodied in error-duration model, wherein square-errorAnti-pass is carried out as adjustment signal；
Modification amount gradient is
The correction amount of weight isWherein η is learning rate；Obtain a new weight ωi (1)=Δ ωi+
ωi, by its back substitution into above-mentioned formula, calculated by iterating, until square-error E is within allowed band, weight is adjusted
Terminate；
Step 4: whole library institute confidence levels in model being obtained by reasoning and calculation, by these as a result, carrying out failure to sensor
Prediction and diagnosis；Reasoning and calculation includes forward reasoning and backward inference, and forward reasoning is the forward reasoning reflection based on FPN model
The characteristic of fault propagation, according to the failure symptom information that the detection of working environment and element or professional obtain, predicting
May occur situation, by transition igniting discrimination matrix and malfunction mark flowing, to may occur failure into
Row assessment, and take corresponding counter-measure；Backward inference is when faulty generation, to derive the reason of failure occurs；
Forward reasoning for clarity, is compactly indicated each matrix reasoning operation, the ability of concurrent system is described using Petri network
Basis is derived with Fuzzy Petri Net mathematical theory, defines 5 Special operators:
(1) ◇: C=A ◇ B, A, B and C of comparison operator are m * n matrix, work as aij> bijWhen, Cij=1；Work as aij< bijWhen, Cij
=0, i=1,2 ..., m；J=1,2 ..., n；
(2) taking small operator ∧: C=A ∧ B, A, B and C is m * n matrix, cij=min (aij,bij), i=1,2 ..., m；J=
1,2,…,n；
(3) taking big operator ∨: C=A ∨ B, A, B and C is m * n matrix cij=max (aij,bij), i=1,2 ..., m；J=1,
2,…,n；
(4) directly multiply operator *: C=A*b, A and C are respectively m × n, and n × m matrix, b is n-dimensional vector, then cij=aij·bi, i=1,
2,…,m；J=1,2 ..., n；
(5) multiplication operatorIt is respectively m × q with C, q × n, m * n matrix,J=1,2 ..., n；
Based on the confidence level of MYCIN, related algorithm is improved, can be obtained after reasoning whole libraries confidence
Angle value, the successively foundation as assessment of fault and diagnosis；It improves as follows:
Defining one: weight matrix P is m * n matrix, and works as weight ωjIt is library institute αiWeight when, pij=1, otherwise pij=
0, i=1,2 ..., m；J=1,2 ..., n；
Defining two: transition matrix Q is m * n matrix, and works as weight ωiConnection transition tjWhen, qij=1, otherwise qij=0, i
=1,2 ..., m；J=1,2 ..., n；
MYCIN rational formula after improvement: αi+1=αi∨(1+exp[ORT])-1；Wherein, R=[(αTP) * ω] Q, it indicates several
In transition library institute's confidence level and weight product equivalent and n dimensional vector, and if only if αi+1=αiWhen, reasoning terminates, otherwise
Continue reasoning；
Transition igniting discrimination matrix and malfunction mark inference mode are as follows:
(1) transition differentiate, define three:T is referred to as that potential transition are enabled；It is fixed
Justice four: if transition T can trigger igniting, in output library institute POjOne new confidence level of upper generation；If igniting cannot be triggered, that
It exports 0 carried out by library；
Igniting matrix is changed to calculate, then with obtained vector R calculated above, transition igniting is obtained by comparing formula and differentiates
Matrix, Y=R ◇ λ, wherein Y=(y1,y2,...,yn)TTo change discrimination matrix of lighting a fire, if meeting ignition condition yi=1, otherwise
yi=0, according to firing rule, obtain the library containing token the corresponding enabled igniting matrix rational formula changed:
In formula: Ki-1-Ki-2Indicate (i-1)-th new igniting mark vector；
(2) malfunction mark vector brings the above results into inference understanding formula:
Backward inference introduces minimal cut set rate of breakdown, defines three: if minimal cut set G={ p1,p2,...,pn, it is minimum
Cut set rate of breakdown are as follows:
F (G)=(α1+α2+...+αn) n n > 0；
The input of backward inference, output library are respectively positive output, input magazine institute, i.e. I-=O, O-=I, backward inference square
Battle array formula are as follows:In formula:It is inverse when igniting reverse for kth time
Net enabled transition sequence.
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