CN108416106B - Water feeding pump fault detection method based on multi-scale principal component analysis - Google Patents
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Abstract
The invention discloses a water feeding pump fault detection method based on multi-scale principal component analysis, which decomposes collected variable data by using discrete wavelet transform, determines wavelet coefficients in each scale by using a principal component analysis method, and selects coefficients larger than a specific threshold value to generate a multi-scale model; modeling the new statistic by principal component analysis method, and respectively calculating T2Statistics and Q statistics, and a fault alarm is raised when one of the statistics exceeds a threshold. The process data of the water feeding pump is multiscale in nature, and has difference in different time domains and frequency domains, and the traditional statistical method based on a single scale cannot accurately separate main variables for expressing the system running state; therefore, the sensitivity of detection can be improved by selecting a multi-scale principal component analysis method for feature extraction.
Description
Technical Field
The invention relates to a water feeding pump fault detection method based on multi-scale principal component analysis, and belongs to the technical field of thermal process state detection and fault diagnosis.
Background
With the increase of the capacity of a single machine, the influence and economic loss caused by equipment failure are increased, so that extremely high requirements are put on the working reliability and safety of each equipment in the power plant. The feed water pump is one of important auxiliary machines in the power plant, and the failure of the feed water pump is also one of important reasons for causing the unplanned shutdown of the power plant. Therefore, fault early warning is carried out on the water feeding pump, so that faults can be found in time and can be eliminated, and the reliability of the unit is improved.
People have not paid enough attention to important auxiliary machines such as a water feeding pump of a thermal power plant for a long time, and the fault detection technology and detection equipment of the auxiliary machines are rarely researched, so that the auxiliary machines only stay at the low-level stage of long-term itinerant detection, shutdown maintenance and post-accident analysis. The water feeding pump is used as high-speed rotating and high-voltage equipment, the state variable data are non-Gaussian, the measurement noise is high, the state variable data have high correlation, and the difficulty of fault detection of the water feeding pump is improved.
Compared with a mechanism modeling method and an empirical knowledge-based method, the data-driven fault detection method has better generalization capability, and can be directly applied to feed water pumps of different models or be slightly modified. At present, a real-time database covering the operation data of key equipment of all large thermal power units in the whole province is basically built in Jiangsu province and other provinces, fault detection of a water feed pump is carried out by adopting a data driving method, and the state monitoring of the water feed pump can be carried out on the thermal power units in the whole province by depending on the database.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a water feeding pump fault detection method based on multi-scale principal component analysis, and compared with the traditional statistical method based on a single scale, the method can improve the detection sensitivity by selecting a multi-scale principal component analysis method to extract features.
The invention discloses a water feeding pump fault detection method based on multi-scale principal component analysis, which comprises the following steps:
step 1: collecting running state parameter data of a power plant water supply pump in a normal running state, standardizing the collected data to form a training data sample set X belonging to Rm×nWherein m is the number of state variables, and n is the number of training samples;
step 2: by dispersionThe wavelet transformation decomposes each state variable in m state variables to obtain a wavelet coefficient d1,d2…dLAnd approximation coefficient aLObtaining a coefficient matrix Y, wherein L is a selected scale;
step 3: for each selected dimension (d)1,d2,d3,d4,a4) Applying principal component analysis to the coefficient matrix Y; selecting the number l of the principal elements, and reserving the principal component loading vectors with corresponding number, so that the wavelet coefficient is reconstructed in each selected scale;
step 4: the coefficients of the coefficient matrix Y with the statistical indexes larger than the set threshold are reserved to obtain a new coefficient matrix Ynew；
Step 5: from the new coefficient matrix Y by inverse discrete wavelet transformnewIn the method, a variable data array containing deterministic components is reconstructed
Step 6: variable data for wavelet reconstruction by multi-scale principal component analysis method
Modeling is carried out, PCA loading matrix P of the extracted deterministic components is calculated, and T is obtained through calculation2Statistics and Q statistics and corresponding thresholds;
step 7: collecting the sample data value of the water feeding pump running state at the current moment, and calculating to obtain the corresponding T by adopting a multi-scale principal component analysis method2And comparing the statistic and the Q statistic with a threshold value, and sending a fault alarm if the threshold value is exceeded.
In Step1, the normalized mean data value is 0 and the standard deviation is 1.
In Step2, selecting a dimension L which is 4;
solving wavelet coefficient d1,d2,d3,d4And approximation coefficient a4The steps are as follows:
a4＝H4X,di＝GiX,i＝1,2,3,4 (1)
in the formula, H4Representing 4 projections on a scaling function, GiRepresents the projection (i-1) times on the scaling function and the projection once on the wavelet; h and G are low-pass and high-pass filters, respectively, derived from the basis functions, and X is the raw measurement data matrix.
Carrying out discrete wavelet transform on the original data matrix to obtain a new wavelet coefficient matrix Y
Wherein W is an n × n-dimensional orthogonal matrix containing orthogonal wavelet transform operators of filter coefficients, H4Is a 1 Xn-dimensional low-pass filter coefficient matrix, GiIs composed of
A dimensional high-pass filter coefficient matrix.
In Step 3, the specific steps for reconstructing the wavelet coefficients are as follows:
s3.1: calculating the covariance matrix Φ of Y:
s3.2: performing singular value decomposition on phi:
Φ＝PYΛYPYT(5)
in the formula, PY＝[P1Y...PmY]∈Rm×mBeing a load matrix, ΛY＝diag(α1α2…αm)，α1≥α2≥…≥αm，αuIs the eigenvalue of covariance matrix, u is more than or equal to 1 and less than or equal to m;
s3.3: using the Cumulative Percentage (CPV) method, the l principal elements are retained with the sum of the eigenvalues of the l principal elements being a percentage component (e.g., 85%) greater than the sum of the total eigenvalues
After selecting the number of principal elements l, P is addedYAnd Λ Y decomposition:
in the formula, Ppc∈Rm×l，Pres∈Rm×(m-l)，Λpc∈Rl×l，Λres∈R(m-l)×(m-l)。
In Step 4, the specific steps are as follows:
s4.1: corresponding to the statistic index Y, T in Yy 2The computational expression of the statistics is:
s4.2: selecting confidence degree alpha, Ty 2The threshold for the statistics is:
in the formula, Fα(l, n-l) is the F distribution obeying the degrees of freedom l and n-l;
when in use
Statistical exceedance
When the threshold value of the statistic is set, the corresponding statistic index y is retained, and when the threshold value of the statistic is set
If the statistic does not exceed the threshold, it is set to 0, so obtaining a new coefficient matrix Ynew
In the formula (I), the compound is shown in the specification,
are the reconstructed new wavelet coefficients and approximation coefficients.
In Step5, a new data matrix is obtained through inverse wavelet discrete transform
The method comprises the following specific steps:
in the formula, WTIs a transposed matrix of W, YnewIs a new coefficient matrix.
In Step 6, T is calculated2The specific steps of statistics and Q statistics and corresponding thresholds are as follows:
s6.1 for wavelet reconstructed variable data matrix
The following linear transformation is done:
in which S is
Covariance matrix of
S6.2 decomposition by singular values
S＝PΛPT,PPT＝PTP＝Im (13)
Wherein P ═ P1...Pm]∈Rm×mIs a loading matrix, PjIs an eigenvalue λ of a covariance matrixjThe associated jth orthogonal eigenvector, and Λ ═ diag (λ)1λ2…λm) Is a matrix of diagonal eigenvalues with decreasing order, ImIs an identity matrix of order m;
wherein T ═ T1…Tm]Is a principal component matrix;
s6.3 retains the l principal component components, and the different matrices are decomposed into the following forms:
in the formula (I), the compound is shown in the specification,
is the eigenvector corresponding to the first one eigenvalue,
is the remaining feature vector;
in the formula (I), the compound is shown in the specification,
is the first l principal component vectors,
are the remaining vectors;
in the formula (I), the compound is shown in the specification,
is the first one diagonal eigenvalue matrix,
is the remaining diagonal eigenvalue matrix;
s6.4 calculating T of sample data2And Q statistics and corresponding thresholds:
T2statistic as
Wherein x is an observation vector of the data set;
selecting significance level alpha, and calculating T2Threshold value T of statisticaIs composed of
In the formula, Fa(l, n-l) is the F distribution subject to degrees of freedom l and n-l, l and (n-l) are degrees of freedom, α is the significance level;
the Q statistic is:
Q＝eTe＝||e||2 (20)
the threshold value of the Q statistic is Qα：
In the formula, cαIs the value of a normal distribution, and alpha is the level of significance，
The process data of the water feeding pump is multiscale in nature, and has difference in different time domains and frequency domains, and the traditional statistical method based on a single scale cannot accurately separate main variables for expressing the system running state; therefore, the sensitivity of detection can be improved by selecting a multi-scale principal component analysis method for feature extraction.
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FIG. 1 is a flow chart of the operation of an embodiment of the present invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further described with the specific embodiments.
The invention relates to a water feeding pump fault detection method based on a multi-scale principal component analysis Method (MSPCA). The method comprises the steps of decomposing collected variable data by utilizing discrete wavelet transform, determining wavelet coefficients in each scale by utilizing a principal component analysis method, and selecting the coefficients larger than a specific threshold value to generate a multi-scale model; modeling the new statistic by principal component analysis method, and respectively calculating T2Statistics and Q statistics, and a fault alarm is raised when one of the statistics exceeds a threshold. Compared with the traditional statistical method based on a single scale, the method extracts more state information from the time domain and the frequency domain through multi-scale analysis by multi-scale principal component analysis, and can obtain better detection effect.
Referring to fig. 1, the method for detecting the fault of the feed pump based on the multi-scale principal component analysis (MSPCA) specifically comprises the following steps:
step 1: collecting main operation state parameter data of a power plant water supply pump in a normal operation state, standardizing the collected data to form a training data sample set X belonging to Rm×nWherein m is the number of state variables, and n is the number of training samples;
step 2: for m state variables by discrete wavelet transformEach state variable of (a) is decomposed to obtain a wavelet coefficient d1,d2…dLAnd approximation coefficient aLI.e. obtaining a coefficient matrix Y, where the chosen scale is 4, i.e. L-4;
step 3: for each selected dimension (d)1,d2,d3,d4,a4) Applying principal component analysis to the coefficient matrix Y; selecting the number l of the principal elements, and reserving the principal component loading vectors with corresponding number, so that the wavelet coefficient is reconstructed in each selected scale;
step 4: the coefficient of the statistic index larger than the set threshold value in the coefficient matrix Y is reserved, and a new coefficient matrix Y is obtainednew；
Step 5: from the new coefficient matrix Y by inverse discrete wavelet transformnewIn the method, a variable data array containing deterministic components is reconstructed
Step 6: variable data for wavelet reconstruction by multi-scale principal component analysis method
Modeling is carried out, PCA loading matrix P of the extracted deterministic components is calculated, and T is obtained through calculation2Statistics and Q statistics and corresponding thresholds;
step 7: collecting the sample data value of the main operation state of the water-feeding pump at the current moment, and calculating to obtain the corresponding T by adopting a multi-scale principal component analysis method2And comparing the statistic and the Q statistic with a threshold value, and sending a fault alarm if the threshold value is exceeded.
In Step1, the normalized mean data value is 0 and the standard deviation is 1.
In Step2, solving wavelet coefficient d1,d2,d3,d4And approximation coefficient a4The steps are as follows:
a4＝H4X,di＝GiX,i＝1,2,3,4 (1)
in the formula, H4Representing 4 projections on a scaling function, GiRepresenting the projection (i-1) times on the scaling function and the projection once on the wavelet. H and G are low-pass and high-pass filters, respectively, derived from the basis functions, and X is the raw measurement data matrix.
Carrying out discrete wavelet transform on the original data matrix to obtain a new wavelet coefficient matrix Y
Wherein W is an n × n-dimensional orthogonal matrix containing orthogonal wavelet transform operators of filter coefficients, H4Is a 1 Xn-dimensional low-pass filter coefficient matrix, GiIs composed of
A dimensional high-pass filter coefficient matrix;
in Step 3, the specific steps for reconstructing the wavelet coefficients are as follows:
s3.1: calculating the covariance matrix Φ of Y:
s3.2: performing singular value decomposition on phi:
Φ＝PYΛYPYT (5)
in the formula, PY＝[P1Y...PmY]∈Rm×mBeing a load matrix, ΛY＝diag(α1α2…αm)，α1≥α2≥…≥αm，αuIs the eigenvalue of covariance matrix, u is more than or equal to 1 and less than or equal to m;
s3.3: using the Cumulative Percentage (CPV) method, the l principal elements are retained with the sum of the eigenvalues of the l principal elements being a percentage component (e.g., 85%) greater than the sum of the total eigenvalues
After selecting the number of principal elements l, P is addedYAnd ΛYAnd (3) decomposition:
in the formula, Ppc∈Rm×l，Pres∈Rm×(m-l)，Λpc∈Rl×l，Λres∈R(m-l)×(m-l)；
In Step 4, the specific steps are as follows:
s4.1: corresponding to the statistic index Y, T in Yy 2The computational expression of the statistics is:
s4.2: selecting confidence degree alpha, Ty 2The threshold for the statistics is:
in the formula, Fα(l, n-l) is the F distribution obeying the degrees of freedom l and n-l.
When T isy 2Statistic exceeds Ty 2When the threshold value of the statistic is set, the corresponding statistic index y is retained, and if T is sety 2If the statistic does not exceed the threshold, it is set to 0, so a new coefficient matrix Y is obtainednew
In the formula (I), the compound is shown in the specification,
are the reconstructed new wavelet coefficients and approximation coefficients.
In Step5, a new data matrix is obtained through inverse wavelet discrete transform
The method comprises the following specific steps:
in the formula, WTIs a transposed matrix of W, YnewAs a new coefficient matrix
In Step 6, T is calculated2The specific steps of statistics and Q statistics and corresponding thresholds are as follows:
s6.1 for wavelet reconstructed variable data matrix
The following linear transformation is done:
in which S is
Covariance matrix of
S6.2 decomposition by singular values
S＝PΛPT,PPT＝PTP＝Im (13)
Wherein P ═ P1...Pm]∈Rm×mIs a loading matrix, PjIs an eigenvalue λ of a covariance matrixjThe associated jth orthogonal eigenvector, and Λ ═ diag (λ)1λ2…λm) Is a matrix of diagonal eigenvalues with decreasing order, ImIs an identity matrix of order m;
wherein T ═ T1…Tm]Is a principal component matrix;
s6.3 retains the l principal component components, and the different matrices are decomposed into the following forms:
in the formula (I), the compound is shown in the specification,
is the eigenvector corresponding to the first one eigenvalue,
is the remaining feature vector;
in the formula (I), the compound is shown in the specification,
is the first l principal component vectors,
are the remaining vectors;
in the formula (I), the compound is shown in the specification,
is the first one diagonal eigenvalue matrix,
is the remaining diagonal eigenvalue matrix;
s6.4 calculation samplesT of data2And Q statistics and corresponding thresholds:
T2statistic as
Where x is the observation vector of the data set.
Selecting significance level alpha, and calculating T2Threshold value T of statisticaIs composed of
In the formula, Fa(l, n-l) is the F distribution subject to degrees of freedom l and n-l, l and (n-l) are degrees of freedom, α is the significance level;
the Q statistic is:
Q＝eTe＝||e||2 (20)
the threshold value of the Q statistic is Qα：
In the formula, cαIs the value of the normal distribution, alpha is the level of significance,
the process data of the water feeding pump is multiscale in nature, difference exists in different time domains and frequency domains, and the traditional statistical method based on single scale cannot accurately separate main variables expressing the system running state(ii) a Therefore, the sensitivity of detection can be improved by selecting a multi-scale principal component analysis method for feature extraction.
The foregoing shows and describes the general principles and broad features of the present invention and advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (4)
1. A water feeding pump fault detection method based on multi-scale principal component analysis is characterized by comprising the following steps: the method comprises the following steps: step 1: collecting running state parameter data of a power plant water supply pump in a normal running state, standardizing the collected data to form a training data sample set X belonging to Rm×nWherein m is the number of state variables, and n is the number of training samples;
step 2: decomposing each state variable in m state variables by discrete wavelet transform to obtain wavelet coefficient d1,d2…dLAnd approximation coefficient aLObtaining a coefficient matrix Y, wherein L is a selected scale;
step 3: the selected dimension L is 4, for each selected dimension d1,d2,d3,d4,a4Applying principal component analysis to the coefficient matrix Y; selecting the number l of the principal elements, and reserving the corresponding number of principal element loading vectors, so that the wavelet coefficient is reconstructed in each selected scale;
in Step 3, the specific steps for reconstructing the wavelet coefficients are as follows:
s3.1: calculating the covariance matrix Φ of Y:
s3.2: performing singular value decomposition on phi:
Φ＝PYΛYPY T (5)
in the formula, PY＝[P1Y…PmY]∈Rm×mBeing a load matrix, ΛY＝diag(α1α2…αm)，α1≥α2≥…≥αm，αuIs the eigenvalue of covariance matrix, u is more than or equal to 1 and less than or equal to m;
s3.3: using a Cumulative Percentage (CPV) method, preserving the l principal elements such that the sum of the eigenvalues of the l principal elements is a percentage component greater than the sum of the total eigenvalues, the percentage component being set to 85%;
after selecting the number of principal elements l, P is addedYAnd ΛYAnd (3) decomposition:
in the formula, Ppc∈Rm×l，Pres∈Rm×(m-l)，Λpc∈Rl×l，Λres∈R(m-l)×(m-l)；
Step 4: the coefficient of the statistic index Y in the coefficient matrix Y which is larger than the set threshold value is reserved to obtain a new coefficient matrix Ynew；
In Step 4, the specific steps are as follows:
s4.1: corresponding to the statistic index Y, T in Yy 2The computational expression of the statistics is:
s4.2: selecting confidence degree alpha, Ty 2The threshold for the statistics is:
in the formula, Fα(l, n-l) is the F distribution obeying the degrees of freedom l and n-l;
when T isy 2Statistic exceeds Ty 2When the threshold value of the statistic is set, the corresponding statistic index y is retained, and if T is sety 2If the statistic does not exceed the threshold, it is set to 0, so obtaining a new coefficient matrix Ynew
In the formula (I), the compound is shown in the specification,
new wavelet coefficients and approximation coefficients are reconstructed;
step 5: from the new coefficient matrix Y by inverse discrete wavelet transformnewIn (1), reconstructing a variable data matrix containing deterministic components
Step 6: variable data matrix for wavelet reconstruction by multi-scale principal component analysis method
Modeling is carried out, a principal component analysis loading matrix P of the extracted deterministic components is calculated, and T is obtained through calculation2Statistics and Q statistics and corresponding thresholds;
in Step 6, T is calculated2The specific steps of statistics and Q statistics and corresponding thresholds are as follows:
s6.1 for wavelet reconstructed variable data matrix
The following linear transformation is done:
in which S is
Covariance matrix of
S6.2 decomposition by singular values
S＝PΛPT,PPT＝PTP＝Im (13)
Wherein P ═ P1...Pm]∈Rm×mIs a loading matrix, PjIs an eigenvalue λ of a covariance matrixjThe associated jth orthogonal eigenvector, and Λ ═ diag (λ)1λ2…λm) Is a matrix of diagonal eigenvalues with decreasing order, ImIs an identity matrix of order m;
wherein T ═ T1…Tm]Is a principal component matrix;
s6.3 retains the l principal component components, and the different matrices are decomposed into the following forms:
in the formula (I), the compound is shown in the specification,
is the eigenvector corresponding to the first one eigenvalue,
is the remaining feature vector;
in the formula (I), the compound is shown in the specification,
is the first l principal component vectors,
are the remaining vectors;
in the formula (I), the compound is shown in the specification,
is the first one diagonal eigenvalue matrix,
is the remaining diagonal eigenvalue matrix;
s6.4 calculating T of sample data2And Q statistics and corresponding thresholds:
T2statistic as
Wherein x is an observation vector of the data set;
selecting confidence degree alpha and calculating T2Threshold value T of statisticaIs composed of
In the formula, Fa(l, n-l) are subject to the degrees of freedom l and n-F distribution of l, l and (n-l) degrees of freedom, α is confidence;
the Q statistic is:
Q＝eTe＝||e||2 (20)
the threshold value of the Q statistic is Qα：
In the formula, cαIs the value of the normal distribution, alpha is the level of significance,
step 7: collecting the sample data value of the water feeding pump running state at the current moment, and calculating to obtain the corresponding T by adopting a multi-scale principal component analysis method2And comparing the statistic and the Q statistic with a threshold value, and sending a fault alarm if the threshold value is exceeded.
2. The feedwater pump fault detection method based on multi-scale principal component analysis of claim 1, wherein: in Step1, the normalized mean data value is 0 and the standard deviation is 1.
3. The feedwater pump fault detection method based on multi-scale principal component analysis of claim 1, wherein: in Step2, selecting a dimension L which is 4;
solving wavelet coefficient d1,d2,d3,d4And approximation coefficient a4The steps are as follows:
a4＝H4X,di＝GiX,i＝1,2,3,4 (1)
in the formula, H4Representing 4 projections on a scaling function, GiRepresents the projection i-1 times on the scaling function and once on the wavelet; h and G are low-pass and high-pass filters derived from the basis functions, respectively, and X is a training data sample set;
carrying out discrete wavelet transform on the original data matrix to obtain a new wavelet coefficient matrix Y
Wherein W is an n × n-dimensional orthogonal matrix containing orthogonal wavelet transform operators of filter coefficients, H4Is a 1 Xn-dimensional low-pass filter coefficient matrix, GiIs composed of
A dimensional high-pass filter coefficient matrix.
4. The feedwater pump fault detection method based on multi-scale principal component analysis of claim 1, wherein: in Step5, the new variable data matrix is solved by inverse wavelet discrete transformation
The method comprises the following specific steps:
in the formula, WTIs a transposed matrix of W, YnewIs a new coefficient matrix.
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