CN104950875A - Fault diagnosis method by combining correlation analysis and data fusion - Google Patents

Abstract

The invention discloses a fault diagnosis method by combining correlation analysis and data fusion, and is used for solving the technical problem of low fault diagnosis result precision of the existing fault diagnosis method. The fault diagnosis method has the technical scheme that equipment information from different measuring sources is extracted; multi-source information and same-source information corresponding to the existing fault mode are subjected to correlation analysis; the obtained correlation degree is used as a correlation coefficient between the existing fault mode and the multi-source data measured in a fault to be diagnosed; the information of a plurality of sources is synthesized by a data fusion method; the reliability, belonging to the existing fault mode, of the fault to be diagnosed is calculated; the fault mode corresponding to the maximum reliability is selected from the reliability. The method of replacing the correlation coefficient in the multi-source data fusion process by the grey correlation degree between the single physical quantity in the process of the fault to be diagnosed and the same physical quantity in the existing fault type is adopted, so that the single physical quantity and the multi-information fusion processes are effectively linked, and the precision of the fault diagnosis result is improved.

Description

In conjunction with the method for diagnosing faults of association analysis and data fusion

Technical field

The present invention relates to a kind of method for diagnosing faults, particularly relate to a kind of method for diagnosing faults in conjunction with association analysis and data fusion.

Background technology

Document " based on the motor fault diagnosis of neural network and D-S evidence theory, the 5th national Vibration Using Engineering academic conference and the 4th national Ultrasonic Motor Techniques Conference Papers collection, 2012 " discloses a kind of method for diagnosing faults.The method tests diagnosed object by multisensor, obtains each sensor and is subordinate to angle value to all kinds of fault under certain symptom; The fault of all the sensors is subordinate to the input of angle value vector as neural network, what after network exports and is fusion, this symptom belonged to all kinds of fault is subordinate to angle value vector; Rule-based decision principle is finally utilized to carry out fault decision-making.The degree of membership that neural metwork training obtains by method described in document is as the Basic Probability As-signment of data fusion, be short of the consideration to observing relevance power between the failure symptom that obtains and known all kinds of fault, and the determination of degree of membership is with subjectivity, the accuracy of causing trouble diagnostic result reduces.

Summary of the invention

In order to overcome the low deficiency of existing method for diagnosing faults fault diagnosis result degree of accuracy, the invention provides a kind of method for diagnosing faults in conjunction with association analysis and data fusion.The facility information of originating from different measuring extracts by the method, the homologous information corresponding with known fault pattern to multi-source information carries out correlation analysis, the degree of association obtained is as the related coefficient between the multi-source data treating to record in tracing trouble and known fault pattern, carry out comprehensively by the method for data fusion to the information in multiple source, calculate and treat that tracing trouble belongs to the reliability of each known fault pattern, therefrom select the fault mode that maximum reliability is corresponding.Because the grey relational grade between adopting the same physical quantities waiting to diagnose in failure process in single one physical amount and known fault type replaces the method for the related coefficient in multisource data fusion process, the effective process being connected single one physical amount and multivariate information fusion, eliminate the inaccuracy of self-defined degree of membership foundation subjective judgement in background technology method, effectively make use of the reliability of multiple measuring values, improve the degree of accuracy of fault diagnosis result.

The technical solution adopted for the present invention to solve the technical problems is: a kind of method for diagnosing faults in conjunction with association analysis and data fusion, is characterized in adopting following steps:

Step one, for equipment to be detected, extract the time series of voltage, temperature and deflection angle that each system of equipment exports when q class fault known in history run process occurs.

$\left[\begin{array}{c}{s}_{11}^1\left(t\right),s_{12}^1\left(t\right),\mathrm{...},s_{1n}^1\left(t\right),s_{21}^1\left(t\right),\mathrm{...},s_{2m}^1\left(t\right),\mathrm{...},s_{k1}^1\left(t\right),\mathrm{...},s_{kp}^1\left(t\right)\\ s_{11}^2\left(t\right),s_{12}^2\left(t\right),\mathrm{...},s_{1n}^2\left(t\right),s_{21}^2\left(t\right),\mathrm{...},s_{2m}^2\left(t\right),\mathrm{...},s_{k1}^2\left(t\right),\mathrm{...},s_{kp}^2\left(t\right)\\ .\\ .\\ .\\ s_{11}^q\left(t\right),s_{12}^q\left(t\right),\mathrm{...},s_{1n}^q\left(t\right),s_{21}^q\left(t\right),\mathrm{...},s_{2m}^q\left(t\right),\mathrm{...},s_{k1}^q\left(t\right),\mathrm{...},s_{kp}^q\left(t\right)\end{array}\right]---\left(1\right)$

In formula, k is the quantity of subsystem, and n, m, p are respectively the sequence number of the output quantity of the 1st, 2, k subsystem, and the physical quantity that each subsystem exports is different, might not represent same physical quantities, and all kinds of fault all might not can cause the change of identical subsystem, the physical quantity do not changed is represented with 0.Meanwhile, the same physical amount that when needing the fault of diagnosis to occur, each system exports is obtained.

[s ₁₁(t),s ₁₂(t),…,s _1n(t),s ₂₁(t),…,s _2m(t),…,s _k1(t),…,s _kp(t)] (2)

Step 2, the angle going out physical quantity from single rice delivery treat the fault data of diagnosis and known fault mode carries out correlation analysis.The power of relevance is using grey relational grade as quantizating index.Measure the military discrete value of the output physical quantity obtained, according to formula

${\mathrm{\ξ}}_{ab}^i\left(k\right)=\frac{\underset{k}{min}|s_{ab}\left(k\right)-s_{ab}^i\left(k\right)|+\mathrm{\ρ}\underset{k}{max}|s_{ab}\left(k\right)-s_{ab}^i\left(k\right)|}{|s_{ab}\left(k\right)-s_{ab}^i\left(k\right)|+\mathrm{\ρ}\underset{k}{max}|s_{ab}\left(k\right)-s_{ab}^i\left(k\right)|}$

Calculate at moment k, the time series s of a certain physical quantity in fault data to be diagnosed _abthe time series of same physical quantities in (t) and the i-th known class fault mode between correlation coefficient.In formula, s _abk () represents the value of time series at moment k of b the physical quantity exported in a subsystem.

Then the grey relational grade of single one physical amount is calculated according to this result.Grey relational grade is averaged at not correlation coefficient in the same time, and its computing formula is

$C_{ab}^i=\frac{1}{N_t}\underset{k=1}{\overset{N_t}{\Σ}}{\mathrm{\ξ}}_{ab}^i\left(k\right)$

In formula, N _tfor seasonal effect in time series length.

In calculating formula (2), physical quantity and formula (1) neutralize the grey relational grade of the identical physical quantity of its lower footnote, i.e. s ₁₁(t) with with until with grey relational grade, obtain grey relational grade matrix.

$\left[\begin{array}{c}{C}_{11}^1\left(t\right),C_{12}^1\left(t\right),\mathrm{...},C_{1n}^1\left(t\right),C_{21}^1\left(t\right),\mathrm{...},C_{2m}^1\left(t\right),\mathrm{...},C_{k1}^1\left(t\right),\mathrm{...},C_{kp}^1\left(t\right)\\ C_{11}^2\left(t\right),C_{12}^2\left(t\right),\mathrm{...},C_{1n}^2\left(t\right),C_{21}^2\left(t\right),\mathrm{...},C_{2m}^2\left(t\right),\mathrm{...},C_{k1}^2\left(t\right),\mathrm{...},C_{kp}^2\left(t\right)\\ .\\ .\\ .\\ C_{11}^q\left(t\right),C_{12}^q\left(t\right),\mathrm{...},C_{1n}^q\left(t\right),C_{21}^q\left(t\right),\mathrm{...},C_{2m}^q\left(t\right),\mathrm{...},C_{k1}^q\left(t\right),\mathrm{...},C_{kp}^q\left(t\right)\end{array}\right]$

Step 3, calculate its belief function belonging to each known fault pattern by each single one physical gauge.In formula (3), W _j, R _jbe actually and measure the intrinsic weight correlation of the sensor of this physical quantity and reliability coefficient, K is also experience value as correction factor, as long as can determine C _j(A _i), then physical quantity j is to fault mode A _ibelief function m _j(A _i) can be calculated by formula (3).With what obtain in step 2 replace C _j(A _i), with the degree of association replace related coefficient, then by this both represent the amount of correlativity by correlation analysis and information fusion united.Calculate single rice delivery and go out the belief function of physical quantity to several fault type that it may belong to.According to formula

$\begin{array}{c}{\mathrm{\α}}_j=\max \left\{C_j\left(A_i\right)\right\}i=1,2,\mathrm{...},q\\ {\mathrm{\β}}_j=\{\[{\mathrm{qW}}_j/\underset{i=1}{\overset{q}{\Σ}}{C}_j\left(A_i\right)-1\]/(q-1)\}q\≥2\\ R_j=\left(W_j{\mathrm{\α}}_j{\mathrm{\β}}_j\right)/\left(\underset{j=1}{\overset{N}{\Σ}}{W}_j{\mathrm{\α}}_j{\mathrm{\β}}_j\right)j=1,2,\mathrm{...},N\\ m_j\left(A_j\right)=C_j\left(A_i\right)/\left(\underset{i=1}{\overset{q}{\Σ}}{C}_j\right(A_i)+N\×K(1-R_j)(1-W_j{\mathrm{\α}}_j{\mathrm{\β}}_j))\end{array}---\left(3\right)$

In formula, C _j(A _i) be that single one physical amount j is to known fault Mode A _irelated coefficient; According to step one, target pattern quantity is q; N is physical quantity sum, i.e. the columns of formula (2); W _jbe the weight correlation of physical quantity j, its codomain is [0,1]; α _jit is physical quantity j maximum correlation coefficient; β _jit is the relevant apportioning cost of physical quantity j; R _jit is the reliability coefficient of physical quantity j; m _j(A _i) be that physical quantity j is to fault mode A _ibelief function, K is correction factor.Wherein, with in step 2 replace C _j(A _i), i=1,2 ..., q.

Step 4, according to D-S information fusion criterion, the belief function of multiple physical quantity comprehensively to be considered, show which kind of known fault is fault to be diagnosed most possibly belong to.Owing to waiting to diagnose the multiple physical quantitys in fault mode all to characterize unified fault mode, there is not the situation of conflicting completely, therefore C=0 in formula (4), draws formula (5).Calculate and treat that tracing trouble is under the jurisdiction of fault mode A _iconfidence level be m (A _i), corresponding A _iit is the result of fault diagnosis.In formula, i=1,2 ..., q.

According to D-S rule of combination, many physical quantitys are merged the result obtaining fault diagnosis.According to formula

$\begin{array}{c}m\left(B\right)=\left\{\begin{array}{cc}\frac{\underset{B_1\∩B_2\∩...\∩B_n=B}{\Σ}{m}_1\left(B_1\right)m_2\left(B_2\right)...m_n\left(B_n\right)}{1-C}& B\≠\mathrm{\φ}\\ 0& B=\mathrm{\φ}\end{array}\right.\\ C=\underset{B_1\∩B_2\∩...\∩B_n=B}{\Σ}{m}_1\left(B_1\right)m_2\left(B_2\right)...m_n\left(B_n\right)\end{array}---\left(4\right)$

Then have

$m\left(A_i\right)=\underset{j=1}{\overset{N}{\Σ}}{m}_j\left(A_i\right),A_i\≠\mathrm{\φ},i=1,2,...,q---\left(5\right)$

Obtaining the confidence level that fault to be diagnosed belongs to different faults type, is namely diagnostic result.

The invention has the beneficial effects as follows: the facility information of originating from different measuring extracts by the method, the homologous information corresponding with known fault pattern to multi-source information carries out correlation analysis, the degree of association obtained is as the related coefficient between the multi-source data treating to record in tracing trouble and known fault pattern, carry out comprehensively by the method for data fusion to the information in multiple source, calculate and treat that tracing trouble belongs to the reliability of each known fault pattern, therefrom select the fault mode that maximum reliability is corresponding.Because the grey relational grade between adopting the same physical quantities waiting to diagnose in failure process in single one physical amount and known fault type replaces the method for the related coefficient in multisource data fusion process, the effective process being connected single one physical amount and multivariate information fusion, eliminate the inaccuracy of self-defined degree of membership foundation subjective judgement in background technology method, effectively make use of the reliability of multiple measuring values, improve the degree of accuracy of fault diagnosis result.

Below in conjunction with the drawings and specific embodiments, the present invention is elaborated.

Accompanying drawing explanation

Fig. 1 is the present invention in conjunction with the process flow diagram of the method for diagnosing faults of association analysis and data fusion.

Embodiment

With reference to Fig. 1.The present invention is as follows in conjunction with the method for diagnosing faults concrete steps of association analysis and data fusion:

Step one, acquisition data and data prediction.Known fault data to be diagnosed, comprises the physical quantity of the N number of output of equipment, and these physical quantitys are distributed in k subsystem of equipment, and the physical quantity that each subsystem exports is not quite similar.In the history run process of equipment, the known fault type of appearance has q class.The fault mode known to this q class, obtains and waits to diagnose fault data type to export physical quantity one to one.For equipment to be detected, extract the physical quantity that when q class fault known in history run process occurs, each Major Systems of equipment exports, as the time series of voltage, temperature, deflection angle.

$\left[\begin{array}{c}{s}_{11}^1\left(t\right),s_{12}^1\left(t\right),\mathrm{...},s_{1n}^1\left(t\right),s_{21}^1\left(t\right),\mathrm{...},s_{2m}^1\left(t\right),\mathrm{...},s_{k1}^1\left(t\right),\mathrm{...},s_{kp}^1\left(t\right)\\ s_{11}^2\left(t\right),s_{12}^2\left(t\right),\mathrm{...},s_{1n}^2\left(t\right),s_{21}^2\left(t\right),\mathrm{...},s_{2m}^2\left(t\right),\mathrm{...},s_{k1}^2\left(t\right),\mathrm{...},s_{kp}^2\left(t\right)\\ .\\ .\\ .\\ s_{11}^q\left(t\right),s_{12}^q\left(t\right),\mathrm{...},s_{1n}^q\left(t\right),s_{21}^q\left(t\right),\mathrm{...},s_{2m}^q\left(t\right),\mathrm{...},s_{k1}^q\left(t\right),\mathrm{...},s_{kp}^q\left(t\right)\end{array}\right]---\left(1\right)$

In formula, k is the quantity of subsystem, and n, m, p are respectively the sequence number of the output quantity of the 1st, 2, k subsystem, and the physical quantity that each subsystem exports is different, such as, might not represent same physical quantities, and all kinds of fault all might not can cause the change of identical subsystem, the physical quantity do not changed is represented with 0.Meanwhile, the same physical amount that when needing the fault of diagnosis to occur, each system exports is obtained.

[s ₁₁(t),s ₁₂(t),…,s _1n(t),s ₂₁(t),…,s _2m(t),…,s _k1(t),…,s _kp(t)] (2)

Step 2, the angle going out physical quantity from single rice delivery treat the fault data of diagnosis and known fault mode carries out correlation analysis.The power of relevance is using grey relational grade as quantizating index.Measure the military discrete value of the output physical quantity obtained, according to formula

${\mathrm{\ξ}}_{ab}^i\left(k\right)=\frac{\underset{k}{min}|s_{ab}\left(k\right)-s_{ab}^i\left(k\right)|+\mathrm{\ρ}\underset{k}{max}|s_{ab}\left(k\right)-s_{ab}^i\left(k\right)|}{|s_{ab}\left(k\right)-s_{ab}^i\left(k\right)|+\mathrm{\ρ}\underset{k}{max}|s_{ab}\left(k\right)-s_{ab}^i\left(k\right)|}$

Calculate at moment k, the time series s of a certain physical quantity in fault data to be diagnosed _abthe time series of same physical quantities in (t) and the i-th known class fault mode between correlation coefficient.In formula, s _abk () represents the value of time series at moment k of b the physical quantity exported in a subsystem.

Then the grey relational grade of single one physical amount is calculated according to this result.Grey relational grade is averaged at not correlation coefficient in the same time, and its computing formula is

$C_{ab}^i=\frac{1}{N_t}\underset{k=1}{\overset{N_t}{\Σ}}{\mathrm{\ξ}}_{ab}^i\left(k\right)$

In formula, N _tfor seasonal effect in time series length.

Calculate grey relational grade.In calculating formula (2), physical quantity and formula (1) neutralize the grey relational grade of the identical physical quantity of its lower footnote, as s ₁₁(t) with with until with grey relational grade, obtain grey relational grade matrix.

$\left[\begin{array}{c}{C}_{11}^1\left(t\right),C_{12}^1\left(t\right),\mathrm{...},C_{1n}^1\left(t\right),C_{21}^1\left(t\right),\mathrm{...},C_{2m}^1\left(t\right),\mathrm{...},C_{k1}^1\left(t\right),\mathrm{...},C_{kp}^1\left(t\right)\\ C_{11}^2\left(t\right),C_{12}^2\left(t\right),\mathrm{...},C_{1n}^2\left(t\right),C_{21}^2\left(t\right),\mathrm{...},C_{2m}^2\left(t\right),\mathrm{...},C_{k1}^2\left(t\right),\mathrm{...},C_{kp}^2\left(t\right)\\ .\\ .\\ .\\ C_{11}^q\left(t\right),C_{12}^q\left(t\right),\mathrm{...},C_{1n}^q\left(t\right),C_{21}^q\left(t\right),\mathrm{...},C_{2m}^q\left(t\right),\mathrm{...},C_{k1}^q\left(t\right),\mathrm{...},C_{kp}^q\left(t\right)\end{array}\right]$

Step 3, calculate its belief function belonging to each known fault pattern by each single one physical gauge.In formula (3), W _j, R _jbe actually and measure the intrinsic weight correlation of the sensor of this physical quantity and reliability coefficient, K is also experience value as correction factor, as long as can determine C _j(A _i), then physical quantity j is to fault mode A _ibelief function m _j(A _i) can be calculated by formula (3).With what obtain in step 2 replace C _j(A _i), with the degree of association replace related coefficient, then by this both represent the amount of correlativity by correlation analysis and information fusion united.Calculate single rice delivery and go out the belief function of physical quantity to several fault type that it may belong to.According to formula

$\begin{array}{c}{\mathrm{\α}}_j=\max \left\{C_j\left(A_i\right)\right\}i=1,2,\mathrm{...},q\\ {\mathrm{\β}}_j=\{\[{\mathrm{qW}}_j/\underset{i=1}{\overset{q}{\Σ}}{C}_j\left(A_i\right)-1\]/(q-1)\}q\≥2\\ R_j=\left(W_j{\mathrm{\α}}_j{\mathrm{\β}}_j\right)/\left(\underset{j=1}{\overset{N}{\Σ}}{W}_j{\mathrm{\α}}_j{\mathrm{\β}}_j\right)j=1,2,\mathrm{...},N\\ m_j\left(A_j\right)=C_j\left(A_i\right)/\left(\underset{i=1}{\overset{q}{\Σ}}{C}_j\right(A_i)+N\×K(1-R_j)(1-W_j{\mathrm{\α}}_j{\mathrm{\β}}_j))\end{array}---\left(3\right)$

In formula, C _j(A _i) be that single one physical amount j is to known fault Mode A _irelated coefficient; According to step one, target pattern quantity is q; N is physical quantity sum, i.e. the columns of formula (2); W _jbe the weight correlation of physical quantity j, its codomain is [0,1]; α _jit is physical quantity j maximum correlation coefficient; β _jit is the relevant apportioning cost of physical quantity j; R _jit is the reliability coefficient of physical quantity j; m _j(A _i) be that physical quantity j is to fault mode A _ibelief function, K is correction factor.Wherein, with in step 2 replace C _j(A _i).

Step 4, according to D-S information fusion criterion, the belief function of multiple physical quantity comprehensively to be considered, show which kind of known fault is fault to be diagnosed most possibly belong to.Owing to waiting to diagnose the multiple physical quantitys in fault mode all to characterize unified fault mode, there is not the situation of conflicting completely, therefore C=0 in formula (4), can draw formula (5).Calculate and treat that tracing trouble is under the jurisdiction of fault mode A _iconfidence level be m (A _i), corresponding A _iit is the result of fault diagnosis.In formula, i=1,2 ..., q.

According to D-S rule of combination, many physical quantitys are merged the result obtaining fault diagnosis.According to formula

$\begin{array}{c}m\left(B\right)=\left\{\begin{array}{cc}\frac{\underset{B_1\∩B_2\∩...\∩B_n=B}{\Σ}{m}_1\left(B_1\right)m_2\left(B_2\right)...m_n\left(B_n\right)}{1-C}& B\≠\mathrm{\φ}\\ 0& B=\mathrm{\φ}\end{array}\right.\\ C=\underset{B_1\∩B_2\∩...\∩B_n=B}{\Σ}{m}_1\left(B_1\right)m_2\left(B_2\right)...m_n\left(B_n\right)\end{array}---\left(4\right)$

Then have

$m\left(A_i\right)=\underset{j=1}{\overset{N}{\Σ}}{m}_j\left(A_i\right),A_i\≠\mathrm{\φ},i=1,2,...,q---\left(5\right)$

Obtaining the confidence level that fault to be diagnosed belongs to different faults type, is namely diagnostic result.

Claims (1)

1., in conjunction with a method for diagnosing faults for association analysis and data fusion, it is characterized in that comprising the following steps:

Step one, for equipment to be detected, extract the time series of voltage, temperature and deflection angle that each system of equipment exports when q class fault known in history run process occurs;

$\left[\begin{array}{c}{s}_{11}^1\left(t\right),s_{12}^1\left(t\right),\mathrm{...},s_{1n}^1\left(t\right),s_{21}^1\left(t\right),\mathrm{...},s_{2m}^1\left(t\right),\mathrm{...},s_{k1}^1\left(t\right),\mathrm{...},s_{kp}^1\left(t\right)\\ s_{11}^2\left(t\right),s_{12}^2\left(t\right),\mathrm{...},s_{1n}^2\left(t\right),s_{21}^2\left(t\right),\mathrm{...},s_{2m}^2\left(t\right),\mathrm{...},s_{k1}^2\left(t\right),\mathrm{...},s_{kp}^2\left(t\right)\\ .\\ .\\ .\\ s_{11}^q\left(t\right),s_{12}^q\left(t\right),\mathrm{...},s_{1n}^q\left(t\right),s_{21}^q\left(t\right),\mathrm{...},s_{2m}^q\left(t\right),\mathrm{...},s_{k1}^q\left(t\right),\mathrm{...},s_{kp}^q\left(t\right)\end{array}\right]---\left(1\right)$

In formula, k is the quantity of subsystem, and n, m, p are respectively the sequence number of the output quantity of the 1st, 2, k subsystem, and the physical quantity that each subsystem exports is different, might not represent same physical quantities, and all kinds of fault all might not can cause the change of identical subsystem, the physical quantity do not changed is represented with 0; Meanwhile, the same physical amount that when needing the fault of diagnosis to occur, each system exports is obtained;

[s ₁₁(t),s ₁₂(t),…,s _1n(t),s ₂₁(t),…,s _2m(t),…,s _k1(t),…,s _kp(t)] (2)

Step 2, the angle going out physical quantity from single rice delivery treat the fault data of diagnosis and known fault mode carries out correlation analysis; The power of relevance is using grey relational grade as quantizating index; Measure the military discrete value of the output physical quantity obtained, according to formula

${\mathrm{\ξ}}_{ab}^i\left(k\right)=\frac{\underset{k}{min}|s_{ab}\left(k\right)-s_{ab}^i\left(k\right)|+\mathrm{\ρ}\underset{k}{max}|s_{ab}\left(k\right)-s_{ab}^i\left(k\right)|}{|s_{ab}\left(k\right)-s_{ab}^i\left(k\right)|+\mathrm{\ρ}\underset{k}{max}|s_{ab}\left(k\right)-s_{ab}^i\left(k\right)|}$

Calculate at moment k, the time series s of a certain physical quantity in fault data to be diagnosed _abthe time series of same physical quantities in (t) and the i-th known class fault mode between correlation coefficient; In formula, s _abk () represents the value of time series at moment k of b the physical quantity exported in a subsystem;

Then the grey relational grade of single one physical amount is calculated according to this result; Grey relational grade is averaged at not correlation coefficient in the same time, and its computing formula is

$C_{ab}^i=\frac{1}{N_t}\underset{k=1}{\overset{N_t}{\Σ}}{\mathrm{\ξ}}_{ab}^i\left(k\right)$

In formula, N _tfor seasonal effect in time series length;

In calculating formula (2), physical quantity and formula (1) neutralize the grey relational grade of the identical physical quantity of its lower footnote, i.e. s ₁₁(t) with with until with grey relational grade, obtain grey relational grade matrix;

$\left[\begin{array}{c}{C}_{11}^1,C_{12}^1,\mathrm{...},C_{1n}^1,C_{21}^1,\mathrm{...},C_{2m}^1,\mathrm{...},C_{k1}^1,\mathrm{...},C_{kp}^1\\ C_{11}^2,C_{12}^2,\mathrm{...},C_{1n}^2,C_{21}^2,\mathrm{...},C_{2m}^2,\mathrm{...},C_{k1}^2,\mathrm{...},C_{kp}^2\\ .\\ .\\ .\\ C_{11}^q,C_{12}^q,\mathrm{...},C_{1n}^q,C_{21}^q,\mathrm{...},C_{2m}^q,\mathrm{...},C_{k1}^q,\mathrm{...},C_{kp}^q\end{array}\right]$

Step 3, calculate its belief function belonging to each known fault pattern by each single one physical gauge; In formula (3), W _j, R _jbe actually and measure the intrinsic weight correlation of the sensor of this physical quantity and reliability coefficient, K is also experience value as correction factor, as long as can determine C _j(A _i), then physical quantity j is to fault mode A _ibelief function m _j(A _i) can be calculated by formula (3); With what obtain in step 2 replace C _j(A _i), with the degree of association replace related coefficient, then by this both represent the amount of correlativity by correlation analysis and information fusion united; Calculate single rice delivery and go out the belief function of physical quantity to several fault type that it may belong to; According to formula

α _j＝max{C _j(A _i)}i＝1,2,…,q

${\mathrm{\β}}_j=\{\[{\mathrm{qW}}_j/\underset{i=1}{\overset{q}{\Σ}}{C}_j\left(A_i\right)-1\]/(q-1)\},q\≥2$

$R_j=\left(W_j{\mathrm{\α}}_j{\mathrm{\β}}_j\right)/\left(\underset{j=1}{\overset{N}{\Σ}}{W}_j{\mathrm{\α}}_j{\mathrm{\β}}_j\right),j=1,2,...,N---\left(3\right)$

$m_j\left(A_j\right)=C_j\left(A_i\right)/(\underset{i=1}{\overset{q}{\Σ}}{C}_j\left(A_i\right)+N\×K(1-R_j)(1-W_j{\mathrm{\α}}_j{\mathrm{\β}}_j))$

In formula, C _j(A _i) be that single one physical amount j is to known fault Mode A _irelated coefficient; According to step one, target pattern quantity is q; N is physical quantity sum, i.e. the columns of formula (2); W _jbe the weight correlation of physical quantity j, its codomain is [0,1]; α _jit is physical quantity j maximum correlation coefficient; β _jit is the relevant apportioning cost of physical quantity j; R _jit is the reliability coefficient of physical quantity j; m _j(A _i) be that physical quantity j is to fault mode A _ibelief function, K is correction factor; Wherein, with in step 2 replace C _j(A _i), i=1,2 ..., q;

Step 4, according to D-S information fusion criterion, the belief function of multiple physical quantity comprehensively to be considered, show which kind of known fault is fault to be diagnosed most possibly belong to; Owing to waiting to diagnose the multiple physical quantitys in fault mode all to characterize unified fault mode, there is not the situation of conflicting completely, therefore C=0 in formula (4), draws formula (5); Calculate and treat that tracing trouble is under the jurisdiction of fault mode A _iconfidence level be m (A _i), corresponding A _iit is the result of fault diagnosis; In formula, i=1,2 ..., q;

According to D-S rule of combination, many physical quantitys are merged the result obtaining fault diagnosis; According to formula

$m\left(B\right)=\left\{\begin{array}{cc}\frac{\underset{B_1\∩B_2\∩\mathrm{...}\∩B_n=B}{\Σ}{m}_1\left(B_1\right)m_2\left(B_2\right)\mathrm{...}{m}_n\left(B_n\right)}{1-C}& B\≠\mathrm{\φ}\\ 0& B=\mathrm{\φ}\end{array}\right.---\left(4\right)$

$C=\underset{B_1\∩B_2\∩...\∩B_n=\mathrm{\φ}}{\Σ}{m}_1\left(B_1\right)m_2\left(B_2\right)...m_n\left(B_n\right)$

Then have

$m\left(A_i\right)=\underset{j=1}{\overset{N}{\Σ}}{m}_j\left(A_i\right),A_i\≠\mathrm{\φ},i=1,2,...,q---\left(5\right)$

Obtaining the confidence level that fault to be diagnosed belongs to different faults type, is namely diagnostic result.