CN104361238A - Fault sensitive characteristic extraction method based on information entropy improved PCA (Principal Component Analysis) - Google Patents

Abstract

The invention relates to a fault sensitive characteristic extraction method based on information entropy improved PCA (Principal Component Analysis). The method comprises the following steps of acquiring a plurality of items of operating state parameters of a reciprocating compressor; calculating a fault sensitive value, and constructing a fault sensitive characteristic matrix; calculating a fault sensitive covariance matrix; decomposing the fault sensitive characteristic covariance matrix to obtain characteristic values of the fault sensitive characteristic covariance matrix and a unitization characteristic vector corresponding to each characteristic value; calculating the contribution p_i of an i-th principal component and the accumulated contribution rate p_lj of first j principal components, and combining the characteristic vectors corresponding to the first k characteristic values to form a mapping matrix; performing mapping conversion on the fault sensitive characteristic matrix to obtain a reconfigurable main fault characteristic matrix; calculating fault information quantity carried by the main fault characteristic matrix and each main characteristic information entropy weighting fusion weight coefficient to obtain an information entropy weighting coefficient matrix; performing information entropy weighting fusion on each main fault characteristic by utilizing the information entropy weighting coefficient matrix to obtain fused fault sensitive characteristics.

Description

A kind of Fault-Sensitive feature extracting method improving PCA based on information entropy

Technical field

The present invention relates to the fault signature extracting method in a kind of mechanical fault diagnosis field, particularly about a kind of Fault-Sensitive feature extracting method improving PCA (principal component analysis (PCA)) based on information entropy for reciprocating compressor fault diagnosis.

Background technology

Reciprocating compressor is widely used in the industrial circle such as oil, chemical industry, carries the tasks such as important Power output, energy conversion, belongs to key equipment aborning.In reciprocating compressor fault diagnosis, Fault-Sensitive feature extraction is an important step of fault diagnosis, and it directly has influence on the accuracy of fault diagnosis result.

Existing reciprocating mechanical failure diagnostic method utilizes vibration signal or pressure signal etc. to extract Fault-Sensitive feature, if only carry out feature extraction according to single parameter to equipment, can bring limitation to equipment fault diagnosis.And in reciprocating compressor fault diagnosis, there is certain correlationship between multiple monitored parameters, if direct multivariate is extracted, calculated amount can be caused excessive; And it is inaccurate to adopt single argument to extract fault signature causing trouble diagnostic result, and the problem such as not comprehensive.Therefore, how to adopt multiple monitored parameters to carry out diagnosis to equipment failure and become problem demanding prompt solution.

Summary of the invention

For the problems referred to above, the object of this invention is to provide and a kind ofly improve the Fault-Sensitive feature extracting method of PCA based on information entropy, the method effectively reduce fault signature correlativity, provide reliable basis for reciprocating compressor fault diagnosis.

For achieving the above object, the present invention takes following technical scheme: a kind of Fault-Sensitive feature extracting method improving PCA based on information entropy, and it comprises the following steps: 1) utilize available data acquisition system to gather the multinomial running state parameter of reciprocating compressor; 2) calculate Fault-Sensitive value according to the multinomial running state parameter of reciprocating compressor, and construct Fault-Sensitive eigenmatrix X _{m × n}, n represents running status number, m representation feature number; 3) Fault-Sensitive eigenmatrix X is utilized _{m × n}calculate Fault-Sensitive covariance matrix C, by Fault-Sensitive eigenmatrix X _{m × n}be abbreviated as X:

$C=\frac{1}{n-1}{\mathrm{XX}}^T;$

4) utilize eig function or SVD decomposition method to decompose Fault-Sensitive Eigen Covariance Matrix C, obtain the eigenwert of Fault-Sensitive Eigen Covariance matrix, and descending sort is carried out to eigenwert, obtain the unitization proper vector that each eigenwert is corresponding; 5) according to step 4) in the eigenwert that obtains, calculate contribution p_i and front j the major component accumulation contribution rate p_lj of i-th major component, and be limited with accumulation contribution rate, choose front k eigenwert characteristic of correspondence vector and carry out being combined to form mapping matrix P:P=[u ₁, u ₂..., u _k]; u _kfor a kth eigenwert characteristic of correspondence vector; 6) utilize mapping matrix P to carry out mapping transformation to Fault-Sensitive eigenmatrix X, obtain reconstruct major error eigenmatrix Y:Y=P ^tx; 7) the fault information volume E that major error eigenmatrix Y carries is calculated _iand each main characteristic information entropy Weighted Fusion weight coefficient w _i, and then obtain information entropy weighting coefficient matrix W; Wherein each column vector of major error eigenmatrix Y is each major error feature; 8) utilize information entropy weighting coefficient matrix W to carry out information entropy Weighted Fusion to each major error feature, obtaining fusion Fault-Sensitive characteristic Y _ F is: Y_F=Y ^t* W, by merging Fault-Sensitive characteristic Y _ F concentrated expression reciprocating compressor operation conditions.

In described step (5), the contribution p_i of described i-th major component and front j major component accumulation contribution rate p_lj is respectively:

$p\_i-\frac{{\mathrm{\λ}}_i}{{\mathrm{\Σ}}_{i=1}^m{\mathrm{\λ}}_i},$

$p\_\mathrm{lj}=\frac{{\mathrm{\Σ}}_{i=1}^j{\mathrm{\λ}}_i}{{\mathrm{\Σ}}_{i=1}^m{\mathrm{\λ}}_i},$

In formula, λ _ifor the eigenwert of Fault-Sensitive covariance matrix C.

In described step (5), described accumulation contribution rate is 85% or 90%.

In described step (7), described fault information volume E _ifor:

$E_i=\frac{{\mathrm{\λ}}_i}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_i},i=\mathrm{1,2},...,k,$

According to described fault information volume E _iobtain described main characteristic information entropy Weighted Fusion weight coefficient w _ifor:

$w_i=\frac{E_i}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{E}_i},i=\mathrm{1,2},...,k,$

According to each described main characteristic information entropy Weighted Fusion weight coefficient w _iobtaining described information entropy weighting coefficient matrix W is: W=diag [w ₁, w ₂..., w _k].

The present invention is owing to taking above technical scheme, it has the following advantages: 1, the present invention is owing to improving PCA based on information entropy, the fault information volume carried with major error feature is tolerance, the fault contribution rate calculating major error feature is carried out tax power to major error feature thus carries out fault signature fusion, obtain merging fault signature effectively objective, reduce the correlativity of fault signature, provide reliable basis for reciprocating compressor fault diagnosis.2, the present invention due to adopt Fault-Sensitive feature extraction be from Monitoring Data extraction fault signature, simple and practical, effectively can reduce the correlativity of fault signature.3, the present invention due to the fusion Fault-Sensitive feature extracted can concentrated expression equipment operation condition, reliable basis can be provided for reciprocating compressor fault.The present invention can extensively apply in mechanical fault diagnosis feature extraction field.

Accompanying drawing explanation

Fig. 1 is overall flow schematic diagram of the present invention.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in detail.

As shown in Figure 1, the invention provides a kind of Fault-Sensitive feature extracting method improving PCA based on information entropy, certain correlationship is there is between the multiple running state data of reciprocating compressor that the method obtains for actual monitoring, for extracting the sensitive features of reflection equipment failure comprehensively, realize the advantage of Data Dimensionality Reduction fusion and the advantage of information entropy quantitative evaluation Fault-Sensitive signature contributions rate in conjunction with PCA (principal component analysis (PCA)) analytical approach, extract the fusion sensitive features of reflection equipment failure comprehensively.It comprises the following steps:

1) available data acquisition system is utilized to gather the multinomial running state parameter such as pressure, temperature, flow of reciprocating compressor;

2) Fault-Sensitive value is calculated (as Pressure maximum value, minimum value according to the multinomial running state parameter of reciprocating compressor; Temperature maximum, minimum value; Flow equilibrium, load etc.), structure Fault-Sensitive eigenmatrix X _{m × n}, n represents running status number, m representation feature number;

$X_{m\×n}=\left[\begin{array}{cccc}{x}_{11}& x_{12}& ...& x_{1n}\\ x_{21}& x_{22}& ...& x_{2n}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ x_{m1}& x_{m2}& ...& x_{\mathrm{mn}}\end{array}\right]$

In formula, x _mnit is the Fault-Sensitive value of the n-th running status of m feature.

3) Fault-Sensitive eigenmatrix X is utilized _{m × n}calculate Fault-Sensitive covariance matrix C, covariance matrix reflects the relation between multivariate to a certain extent, by Fault-Sensitive eigenmatrix X _{m × n}be abbreviated as X.

$C=\frac{1}{n-1}{\mathrm{XX}}^T---\left(1\right)$

4) utilize eig function or SVD to decompose (svd) method to decompose Fault-Sensitive Eigen Covariance Matrix C, obtain the eigenwert of Fault-Sensitive Eigen Covariance matrix, and descending sort is carried out to eigenwert, obtain the unitization proper vector that each eigenwert is corresponding:

λ _iu _i＝Cu _i，i＝1，2，…，m (2)

The eigenvalue λ of Fault-Sensitive covariance matrix is calculated according to formula (2) ₁, λ ₂..., λ _m; Corresponding unitization proper vector is u ₁, u ₂..., u _m.Wherein, m is natural number.

5) according to step 4) in the eigenwert that obtains, calculate contribution p_i and front j the major component accumulation contribution rate p_lj of i-th major component, and be limited with accumulation contribution rate, choose front k eigenwert characteristic of correspondence vector and carry out being combined to form mapping matrix P:P=[u ₁, u ₂..., u _k]; Accumulation contribution rate in the present invention gets 85% or 90%.

$p\_i-\frac{{\mathrm{\λ}}_i}{{\mathrm{\Σ}}_{i=1}^m{\mathrm{\λ}}_i}---\left(3\right)$

$p\_\mathrm{lj}=\frac{{\mathrm{\Σ}}_{i=1}^j{\mathrm{\λ}}_i}{{\mathrm{\Σ}}_{i=1}^m{\mathrm{\λ}}_i}---\left(4\right)$

Contribution rate represents that the major significance that selected feature is born in whole Fault-Sensitive eigenmatrix accounts for great proportion, when getting a front k major component and replacing original all variablees, the size of contribution rate of accumulative total has reacted the reliability of this replacement, and contribution rate of accumulative total is larger, and reliability is larger; Otherwise then reliability is less.

6) utilize mapping matrix P to carry out mapping transformation to Fault-Sensitive eigenmatrix X, obtain reconstruct major error eigenmatrix Y.

Y＝P ^TX (5)

7) the fault information volume E that major error eigenmatrix Y carries is calculated _iand each main characteristic information entropy Weighted Fusion weight coefficient w _i, and then obtain information entropy weighting coefficient matrix W.

Fault information volume E _ifor each major error feature provides the probability of failure message, major error eigenmatrix characteristic of correspondence value is utilized to carry out calculating fault information volume E _i, wherein eigenvalue of maximum λ ₁corresponding maximal eigenvector u ₁what mapping obtained is exactly the first major error characteristic Y ₁, namely Second Largest Eigenvalue λ ₂characteristic of correspondence vector u ₂mapping obtains the second major error characteristic Y ₂, namely each column vector of major error eigenmatrix Y is each major error feature.Fault information volume E _ifor:

$E_i=\frac{{\mathrm{\λ}}_i}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_i},(i=\mathrm{1,2},...,k)---\left(6\right)$

According to fault information volume E _iobtain main characteristic information entropy Weighted Fusion weight coefficient w _ifor:

$w_i=\frac{E_i}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{E}_i},(i=\mathrm{1,2},...,k)---\left(7\right)$

According to each main characteristic information entropy Weighted Fusion weight coefficient w _iobtaining information entropy weighting coefficient matrix W is:

W＝diag[w ₁,w ₂,…,w _k] (8)

8) utilize information entropy weighting coefficient matrix W to carry out information entropy Weighted Fusion to each major error feature, can obtain fusion Fault-Sensitive characteristic Y _ F is:

Y_F＝Y ^T*W， (9)

Merge Fault-Sensitive characteristic Y _ F energy concentrated expression reciprocating compressor operation conditions, reliable foundation can be provided for fault diagnosis.

The various embodiments described above are only for illustration of the present invention; wherein the structure of each parts, connected mode and manufacture craft etc. all can change to some extent; every equivalents of carrying out on the basis of technical solution of the present invention and improvement, all should not get rid of outside protection scope of the present invention.

Claims (5)

1. improve a Fault-Sensitive feature extracting method of PCA based on information entropy, it comprises the following steps:

1) available data acquisition system is utilized to gather the multinomial running state parameter of reciprocating compressor;

2) calculate Fault-Sensitive value according to the multinomial running state parameter of reciprocating compressor, and construct Fault-Sensitive eigenmatrix X _{m × n}, n represents running status number, m representation feature number;

3) Fault-Sensitive eigenmatrix X is utilized _{m × n}calculate Fault-Sensitive covariance matrix C, by Fault-Sensitive eigenmatrix X _{m × n}be abbreviated as X:

$C=\frac{1}{n-1}{\mathrm{XX}}^T;$

4) utilize eig function or SVD decomposition method to decompose Fault-Sensitive Eigen Covariance Matrix C, obtain the eigenwert of Fault-Sensitive Eigen Covariance matrix, and descending sort is carried out to eigenwert, obtain the unitization proper vector that each eigenwert is corresponding;

5) according to step 4) in the eigenwert that obtains, calculate contribution p_i and front j the major component accumulation contribution rate p_lj of i-th major component, and be limited with accumulation contribution rate, choose front k eigenwert characteristic of correspondence vector and carry out being combined to form mapping matrix P:P=[u ₁, u ₂..., u _k]; u _kfor a kth eigenwert characteristic of correspondence vector;

6) utilize mapping matrix P to carry out mapping transformation to Fault-Sensitive eigenmatrix X, obtain reconstruct major error eigenmatrix Y:

Y＝P ^TX；

7) the fault information volume E that major error eigenmatrix Y carries is calculated _iand each main characteristic information entropy Weighted Fusion weight coefficient w _i, and then obtain information entropy weighting coefficient matrix W; Wherein each column vector of major error eigenmatrix Y is each major error feature;

8) utilize information entropy weighting coefficient matrix W to carry out information entropy Weighted Fusion to each major error feature, obtaining fusion Fault-Sensitive characteristic Y _ F is:

Y_F＝Y ^T*W，

By merging Fault-Sensitive characteristic Y _ F concentrated expression reciprocating compressor operation conditions.

2. a kind ofly as claimed in claim 1 improve the Fault-Sensitive feature extracting method of PCA based on information entropy, it is characterized in that: in described step (5), the contribution p_i of described i-th major component and front j major component accumulation contribution rate p_lj is respectively:

$p\_i=\frac{{\mathrm{\λ}}_i}{{\mathrm{\Σ}}_{i=1}^m{\mathrm{\λ}}_i},$

$p\_\mathrm{lj}=\frac{{\mathrm{\Σ}}_{i=1}^j{\mathrm{\λ}}_i}{{\mathrm{\Σ}}_{i=1}^m{\mathrm{\λ}}_i},$

In formula, λ _ifor the eigenwert of Fault-Sensitive covariance matrix C.

3. a kind ofly as claimed in claim 1 improve the Fault-Sensitive feature extracting method of PCA based on information entropy, it is characterized in that: in described step (5), described accumulation contribution rate is 85% or 90%.

4. a kind ofly as claimed in claim 2 improve the Fault-Sensitive feature extracting method of PCA based on information entropy, it is characterized in that: in described step (5), described accumulation contribution rate is 85% or 90%.

5. as claimed in claim 1 or 2 or 3 or 4 a kind of improves the Fault-Sensitive feature extracting method of PCA based on information entropy, it is characterized in that: in described step (7), described fault information volume E _ifor:

$E_i=\frac{{\mathrm{\λ}}_i}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_i},i=\mathrm{1,2},...,k,$

According to described fault information volume E _iobtain described main characteristic information entropy Weighted Fusion weight coefficient w _ifor:

$w_i=\frac{E_i}{\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{E}_i},i=\mathrm{1,2},...,k,$

Obtaining described information entropy weighting coefficient matrix W according to each described main characteristic information entropy Weighted Fusion weight coefficient wi is:

W＝diag[w ₁,w ₂,…,w _k]。