CN109675935B - Online fault diagnosis method for IPCA rolling process with variable control limit - Google Patents

Online fault diagnosis method for IPCA rolling process with variable control limit Download PDF

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CN109675935B
CN109675935B CN201910166635.1A CN201910166635A CN109675935B CN 109675935 B CN109675935 B CN 109675935B CN 201910166635 A CN201910166635 A CN 201910166635A CN 109675935 B CN109675935 B CN 109675935B
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CN109675935A (en
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张飞
王超超
肖雄
王健翔
任晓怀
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University of Science and Technology Beijing USTB
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    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
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Abstract

The invention belongs to the field of fault diagnosis in a rolling process, and particularly relates to an IPCA rolling process on-line fault diagnosis method with variable control limits. The online fault diagnosis method identifies and diagnoses the faults in the rolling process on line through real-time data, thereby meeting the requirements of production continuity and stability, reducing the overhaul time and improving the yield and quality of products in the steel rolling process; and updating the diagnostic model and the statistic control limit of the normal historical training data on line by an Incremental Principal Component Analysis (IPCA) method, and expanding the diagnosed online data without faults into the diagnostic model to adapt to the current production state in the rolling process and improve the fault diagnosis accuracy.

Description

Online fault diagnosis method for IPCA rolling process with variable control limit
Technical Field
The invention belongs to the technical field of rolling process fault diagnosis, and particularly relates to an IPCA rolling process online fault diagnosis method with variable control limits.
Background
With the automation and higher informatization degree of the rolling process, the control level of the rolling process is greatly improved. But the fault occurrence rate of the rolling process is high due to the high temperature, high pressure and high speed of the rolling process and the abnormal and complicated production environment, and meanwhile, the rolling process is one of the production processes with the highest requirement on production continuity, so that the online fault diagnosis of the rolling process is of great significance.
In recent years, researchers at home and abroad research on how to carry out fault diagnosis on a rolling process, and the researchers seek to establish a more accurate system model and try to research the fault diagnosis problem of the rolling process from the aspect of control. In "apparatus and method for diagnosing faults in finish rolling of strip steel" of POSCO corporation and toshiba mitsubishi electric machine industry co, etc., in patent (CN 1502424a) "fault diagnosis apparatus and method in finish rolling of strip steel" preset data and real-time data related to rolling process and control conditions, equation models representing control and physical phenomena, and a database constructed based on operation experience are used to diagnose thickness defects in finish rolling of strip steel. Because the thickness defect of the hot strip mill is caused by various factors, the model and the operation experience of the rolling process are accurate within a certain error range, and the method is improved subsequently, but still is the diagnosis result of model estimation and manual experience. Due to the fact that the modeling process of the rolling process is still inaccurate due to the nonlinearity, the multi-coupling and the environmental complexity of the rolling process, and the same accuracy of different systems is difficult to guarantee, fault diagnosis of the rolling process according to the model is extremely dependent on the accuracy of the model, and the accuracy of the model is difficult to guarantee. The manual experience fault diagnosis depends on the experience of human observation on the fault of the past equipment, but the experience cannot be accurate every time. Meanwhile, the system has the condition that manual experience is not contacted at present.
Danhui et al established a cold rolling mill hydraulic AGC fault diagnosis expert system in the patent (CN 106607461 a) "rolling mill hydraulic AGC fault diagnosis expert system", fully utilized the software and hardware technology and network advantages developed at high speed, and sent the data collected on site or through network to the cloud expert server after analyzing and processing, so as to better exert the advantages of the expert system, thereby improving the reliability of the cold rolling mill hydraulic AGC system. The technology mainly depends on strong software and hardware support, and the fault diagnosis of the hydraulic AGC of the rolling mill is realized through an expert system. However, strong hardware and software support means higher cost, and the high cost has a weak effect even if the accuracy is improved.
The fault diagnosis method comprises the steps of designing a three-level information fusion fault diagnosis system according to the fault characteristics of a rolling process in a paper P L S of the Zhang feather, an application research of an improved method of the P L S in the fault diagnosis of the rolling process, applying the P L S and the improved method to the fault diagnosis of the rolling process, and designing a three-level information fusion fault diagnosis system according to the fault characteristics of the rolling process in the paper N, N.
Disclosure of Invention
Aiming at the technical problem, the invention provides an IPCA rolling process online fault diagnosis method with variable control limits. The diagnosis method is based on real-time data, effectively utilizes a large amount of data which exist and can be collected in the rolling process, carries out online fault diagnosis on the rolling process through the real-time data, meets the continuity of the rolling production process, shortens the overhaul time and improves the product quality; in addition, the diagnosis method does not need to establish an accurate model of the rolling process, and only needs to screen quality normal data and other data within a certain range to establish a training diagnosis model. During on-line diagnosis, the fault diagnosis of the rolling process can be finished by inputting corresponding real-time data, and the contribution rate of each variable to the fault is output.
The invention is realized by the following technical scheme:
an online fault diagnosis method for a variable control limit IPCA rolling process comprises a model training and diagnosis stage and an online diagnosis stage, and specifically comprises the following steps:
training a diagnosis model: screening historical data under normal working conditions according to product quality factors, taking the historical data under the normal working conditions as training data, establishing a principal component diagnosis model of the training data under the normal working conditions, and calculating a control limit of the principal component diagnosis model;
an online diagnosis stage: processing sampling point data in each sampling period, substituting the processed sampling point data into the principal component diagnosis model, and respectively calculating Hotelling T2Statistics and SPE statistics; during online fault diagnosis, the HotellingT is used2Comparing the statistic and the SPE statistic with the control limit of the principal component diagnosis model obtained by calculation in the stage of training the diagnosis model; judging whether a fault occurs according to the comparison result, and if the fault occurs, performing fault alarm; and if the fault does not occur, updating the load transformation matrix, the control limit and the mean value and the variance of the training data of the principal component diagnosis model by an incremental principal component analysis method.
Further, the historical data under the normal working condition refers to data collected by each sensor under the normal running state in the rolling process of the strip steel. The normal working condition refers to that when the system normally operates, data related to product quality, such as various indexes of strip steel thickness difference, convexity, plate type and the like, fluctuate within an error allowable range. Besides the data related to the product quality, the system state data including rolling speed, roll gap, current, rolling force, roll bending force, rolling force difference and the like or other parameters need to be screened out.
Further, in the stage of training a diagnostic model, establishing a principal component diagnostic model and calculating a control limit of the principal component diagnostic model, specifically comprising:
(1) collecting and selecting historical data under normal working conditions as training data;
(2) carrying out centralization processing on the training data, and then calculating a quadratic matrix C of the data after the centralization processing;
wherein, the centralized processing formula is as follows:
Figure BDA0001986545370000041
Figure BDA0001986545370000042
is the sample data at the central post-processing; xi( i 1, 2.. n) is sample data at the ith sampling time, and the total number of samples is n; the number of the observation variables, namely the dimension is m; mu is the average value of the corresponding classification of the training data, and sigma is the variance of the corresponding classification of the training data;
and (3) performing quadratic matrix processing on the data after the centralization processing, wherein the calculation formula is as follows:
Figure BDA0001986545370000043
decomposing the eigenvalue of quadratic matrix to obtain principal component model, calculating m eigenvalues, and arranging λ according to the order from large to small1,λ2,...,λmThe corresponding unit feature vector is P1,P2,...,PmThe characteristic matrix U ═ P1,P2,...,Pm]；
(3) Performing principal component analysis modeling process on the quadratic matrix C, according to a variance contribution rate method, because the principal component corresponding to the maximum characteristic value also contains the maximum information in proportion, when the sum of the current l characteristic values exceeds a certain threshold of the sum of the characteristic values, considering that the influence of the subsequent characteristic values on a principal component model can be ignored, and reducing the original data matrix to l dimension at the moment, thereby determining the number l of the principal components, wherein the calculation formula of the principal component contribution rate percentage is as follows:
Figure BDA0001986545370000051
after the percentage of the cumulative contribution rate of the current l principal elements exceeds a threshold value, the corresponding l value is the number of the principal elements, and the threshold value is selected to be 85% -95%;
load matrix at this time
Figure BDA0001986545370000052
Score matrix, i.e. principal component matrix
Figure BDA0001986545370000053
(4) Principal component diagnosis model for establishing training data under normal working condition
Figure BDA0001986545370000054
Classifying and storing the score matrix, the load matrix and the eigenvector corresponding to the eigenvalue of the principal component diagnosis model for a principal component matrix or called the score matrix;
(5) using Hotelling T2And the SPE statistics amount to calculate respective Hotelling T of different types of principal component diagnosis models2Control limit L imT at confidence level α for statistics and SPE statistics2And L imQ, and storing by classification.
Further, Hotelling's T2The control limit for the statistic at significance level α is calculated by:
Figure BDA0001986545370000055
wherein Fα(l, n-l) means the α critical point on the F distribution with degrees of freedom l and (n-l).
The control limit for the SPE statistic at significance level α is calculated as:
Figure BDA0001986545370000056
in the formula:
Figure BDA0001986545370000061
i＝1,2,3，λjis the jth eigenvalue, C, of a quadratic matrix CαThe standard deviations corresponding to quantiles 1- α.
Further, the online diagnosis stage specifically includes:
(1) collecting real-time data to be diagnosed, wherein the sample data of the ith sampling point is yi；
(2) Sample data y of sampling pointiCarrying out centralization treatment to obtain centralization treatment:
Figure BDA0001986545370000062
yiis the sample data after centralization, mu is the average value of the corresponding classification of the training data, and sigma is the variance of the corresponding classification of the training data;
(3) centering the sample data yiSubstituting into corresponding principal component diagnosis model to calculate Hotelling T2Statistics and SPE statistics;
hotelling T for ith sample point2The statistic calculation formula is as follows:
Figure BDA0001986545370000063
Λ is a diagonal matrix composed of eigenvalues corresponding to the principal elements, Λ∈ Rl×l；
The formula for calculating SPE statistic of ith sampling point is as follows:
Figure BDA0001986545370000064
i is a unit matrix of l × l;
(4) hotelling's T of ith sample point2And SPE two statistics and control limits L imT2And L imQ comparison;
if T isi 2＞LimT2Or Qi> L imQ, and N successive points are overrun, Ti 2，Ti+1 2，...,Ti+N-1 2＞LimT2Or Qi，Qi+1，...，Qi+N-1If the sampling point is more than L imQ, the ith sampling point is failed, and a failure alarm is carried out, wherein the size of N can be adjusted according to the system requirement;
otherwise, the ith sampling point is not in fault, and no alarm is given, the data in the sampling period system is normal, the data in the sampling period is added into the training principal component diagnosis model, and the load transformation matrix, the control limit, the training data mean value and the variance of the principal component diagnosis model are updated by adopting an incremental principal component analysis method.
Further, when a fault occurs, besides performing fault alarm, determining the cause of the fault according to the contribution of each variable to the statistic, and further positioning the subsequent fault, specifically comprising:
if T isi 2，Ti+1 2，...,Ti+N-1 2＞LimT2When fault alarm is carried out, the contribution degree of each variable to the fault is determined according to a contribution graph method, and the jth observation variable to Hotelling T2The calculation formula of the contribution degree of the statistic is as follows:
Figure BDA0001986545370000071
wherein
Figure BDA0001986545370000072
As a load matrix
Figure BDA0001986545370000073
The value of row i and column j;
if Q isi，Qi+1，...，Qi+N-1When the fault alarm is carried out, determining the contribution degree of each variable to the fault according to a contribution graph method, and calculating the contribution of the jth observation variable to the SPE statistic according to a formula:
Figure BDA0001986545370000074
wherein the content of the first and second substances,
Figure BDA0001986545370000076
is that
Figure BDA0001986545370000075
Is the unit matrix of l × l.
The invention has the beneficial technical effects that:
the invention provides an IPCA rolling process online fault diagnosis method with variable control limits, which has the advantages of online fault diagnosis: normal data after on-line diagnosis is added into a training data set, and the accuracy of on-line fault diagnosis in the rolling process is improved by adapting to the recent rolling state and expanding the training set.
In addition, the method of the invention starts from the data driving angle, does not need to establish an accurate mathematical physical model of the rolling process, and can carry out state monitoring and fault diagnosis on the running state of the rolling process only through actual production data. And the historical data principal component model is continuously processed by an increment principal component method, so that the data volume and accuracy of the training diagnosis data are improved, and the adaptability to the real-time production state is enhanced. Compared with the traditional mechanism model and the empirical diagnosis method, the modeling difficulty is small, the realization difficulty is low, and the accuracy is high. Compared with the traditional offline fault diagnosis method based on data, the method meets the real-time performance of online diagnosis and meets the requirement of the rolling process on production continuity; the method improves the training data quantity, updates the training data principal component model, and simultaneously improves the accuracy of fault diagnosis.
Drawings
FIG. 1 is a flow chart of an online fault diagnosis method for an IPCA rolling process with variable control limits according to an embodiment of the present invention;
FIG. 2 is a Hotelling T for diagnosing online faults in the IPCA rolling process with variable control limits in the embodiment of the invention2A statistics control chart;
FIG. 3 is a control diagram of online fault diagnosis Q statistics of an IPCA rolling process with variable control limits according to an embodiment of the present invention;
FIG. 4 is a Hotelling T for diagnosing online faults in the IPCA rolling process with variable control limits in the embodiment of the invention2A statistics contribution graph;
FIG. 5 is a graph of contribution of online fault diagnosis Q statistics for an IPCA rolling process with varying control limits in an embodiment of the present invention;
FIG. 6 is a schematic diagram of the prior art in which the hot rolling T is used for online fault diagnosis in the PCA rolling process2A statistics control chart;
FIG. 7 is a control diagram of online fault diagnosis Q statistic of PCA rolling process in the prior art.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
On the contrary, the invention is intended to cover alternatives, modifications, equivalents and alternatives which may be included within the spirit and scope of the invention as defined by the appended claims. Furthermore, in the following detailed description of the present invention, certain specific details are set forth in order to provide a better understanding of the present invention. It will be apparent to one skilled in the art that the present invention may be practiced without these specific details.
The embodiment provides an online fault diagnosis method for an IPCA rolling process with variable control limits, as shown in fig. 1, including a training diagnosis model stage and an online diagnosis stage, specifically:
training a diagnosis model: screening historical data under normal working conditions according to product quality factors, taking the historical data under the normal working conditions as training data, establishing a principal component diagnosis model of the training data under the normal working conditions, and calculating a control limit of the principal component diagnosis model;
an online diagnosis stage: processing sampling point data in each sampling period, substituting the processed sampling point data into the principal component diagnosis model, and respectively calculating Hotelling T2Statistics and SPE statistics; during online fault diagnosis, the HotellingT is used2Comparing the statistic and the SPE statistic with the control limit of the principal component diagnosis model obtained by calculation in the stage of training the diagnosis model; judging whether a fault occurs according to the comparison result, and if the fault occurs, performing fault alarm; and if the fault does not occur, updating the load transformation matrix, the control limit and the mean value and the variance of the training data of the principal component diagnosis model by an incremental principal component analysis method.
The method provided by the embodiment is used for researching the online fault diagnosis method in the rolling process from the perspective of real-time data driving. Taking a finishing mill group of a hot continuous rolling production line of a certain steel mill as an example, the finishing mill group consists of 6 frames, namely F1, F2, … and F6. This example was studied on the rolling process of the outlet of the finish rolling end stand, i.e., the F6 stand. And selecting outlet thickness difference as a quality evaluation standard in the training principal component diagnosis model stage, selecting 1270 groups of normal working condition data as training data according to the actual thickness difference +/-10 um, wherein the example data variables comprise rolling speed, roll gap, current, rolling force, roll bending force and rolling force difference, and the variable number, namely the dimension n is 6.
The centralized processing formula for the data is as follows:
Figure BDA0001986545370000101
Figure BDA0001986545370000102
is the sample data at the central post-processing; xi( i 1, 2.. n) is sample data at the ith sampling time, and the total number of samples is n; the number of the observation variables, namely the dimension is m;mu is the average value of the corresponding classification of the training data, and sigma is the variance of the corresponding classification of the training data;
and (3) performing quadratic matrix processing on the data after the centralization processing, wherein the calculation formula is as follows:
Figure BDA0001986545370000103
decomposing the eigenvalue of quadratic matrix to obtain principal component model, calculating m eigenvalues, and arranging λ according to the order from large to small1,λ2,...,λmThe corresponding unit feature vector is P1,P2,...,PmThe characteristic matrix U ═ P1,P2,...,Pm]；
Next, the number of the pivot is determined, and since the number of the pivot obtained by different methods is almost the same, one of the most common methods, the method of variance Contribution (CPV), is used herein. The method is to judge according to the ratio of the characteristic value corresponding to each principal element to the total characteristic value, according to the variance contribution ratio method, because the principal element corresponding to the maximum characteristic value also contains the maximum information in proportion, when the sum of the current l characteristic values exceeds a certain threshold value of the sum of the characteristic values, the influence of the subsequent characteristic values on a principal element model is considered to be negligible, at the moment, the original data matrix is reduced to l dimension, so that the number l of the principal elements is determined, and the calculation formula for determining the percentage of the principal element contribution ratio is as follows:
Figure BDA0001986545370000111
after the percentage of the cumulative contribution rate of the current l principal elements exceeds a threshold value, when the percentage is generally selected to be 85% -95%, the corresponding value l is the number of the principal elements;
load matrix at this time
Figure BDA0001986545370000112
Score matrix, i.e. principal component matrix
Figure BDA0001986545370000113
Principal component diagnosis model for establishing training data under normal working condition
Figure BDA0001986545370000114
Classifying and storing the score matrix, the load matrix and the feature vector corresponding to the feature value of the principal component diagnosis model;
meanwhile, solving Hotelling T2The control limit for the statistic at significance level α was calculated as:
Figure BDA0001986545370000115
wherein Fα(l, n-l) means the α critical point on the F distribution with degrees of freedom l and (n-l).
The control limits of the SPE statistic at significance level α are approximated by Jackson and Mudholkard as follows:
Figure BDA0001986545370000116
in the formula:
Figure BDA0001986545370000121
i＝1,2,3，λjis the jth eigenvalue, C, of a quadratic matrix CαThe standard deviations corresponding to quantiles 1- α.
In the real-time diagnosis stage, a group of data y is collected according to the sampling time of 40m, the observation variables of the sampled data still comprise rolling speed, roll gap, current, rolling force, roll bending force and rolling force difference, firstly, the required data is still centralized, and the calculation formula is as follows:
Figure BDA0001986545370000122
wherein the content of the first and second substances,
Figure BDA0001986545370000123
is the centered sample data, mu is the training data pairThe mean value of the corresponding class, σ is the variance of the corresponding class of the training data.
Then, will
Figure BDA0001986545370000126
Substituting into the principal component diagnosis model to obtain two statistic values, i-th sampling point Hotelling T2The statistic calculation formula is as follows:
Figure BDA0001986545370000124
Λ is a diagonal matrix composed of eigenvalues corresponding to the principal elements, Λ∈ Rl×l。
The formula for calculating SPE statistic of ith sampling point is as follows:
Figure BDA0001986545370000125
i is a unit matrix of l × l.
Hotelling's T of ith sample point2And SPE two statistics and control limits L imT2And L imQ comparison;
if T isi 2＞LimT2Or Qi> L imQ, and N successive points are overrun, Ti 2，Ti+1 2，...,Ti+N-1 2＞LimT2Or Qi，Qi+1，...，Qi+N-1If the sampling point is more than L imQ, the ith sampling point is failed, and a failure alarm is carried out, wherein the size of N can be adjusted according to the system requirement;
otherwise, the ith sampling point is not in fault, and no alarm is given, the data in the sampling period system is normal, the data in the sampling period is added into the training principal component diagnosis model, and the load transformation matrix, the control limit, the training data mean value and the variance of the principal component diagnosis model are updated by adopting an incremental principal component analysis method.
When a fault occurs, besides fault alarming, the method also comprises the step of determining the reason of the fault according to the contribution of each variable to the statistic, and further positioning the subsequent fault, and specifically comprises the following steps:
if T isi 2，Ti+1 2，...,Ti+N-1 2＞LimT2When fault alarm is carried out, the contribution degree of each variable to the fault is determined according to a contribution graph method, and the jth observation variable to Hotelling T2The calculation formula of the contribution degree of the statistic is as follows:
Figure BDA0001986545370000131
wherein
Figure BDA0001986545370000132
As a load matrix
Figure BDA0001986545370000133
The value of row i and column j;
if Q isi，Qi+1，...，Qi+N-1When the fault alarm is carried out, determining the contribution degree of each variable to the fault according to a contribution graph method, and calculating the contribution of the jth observation variable to the SPE statistic according to a formula:
Figure BDA0001986545370000134
wherein the content of the first and second substances,
Figure BDA0001986545370000136
is that
Figure BDA0001986545370000135
Is the unit matrix of l × l.
Otherwise, the ith sampling point fails, no alarm is given, and the working condition is considered to be normal at the moment. And (3) the data in the sampling period system is normal, the data in the sampling period is added into a training principal component diagnosis model, and a load transformation matrix, a control limit, a training data mean value and a variance of the principal component diagnosis model are updated by adopting an incremental principal component analysis method. The method comprises the following steps:
to be incorporated into a training pivot diagnostic modelCentering the new data sample y
Figure BDA0001986545370000141
Updating the mean value:
Figure BDA0001986545370000142
wherein the content of the first and second substances,
Figure BDA0001986545370000143
for the updated mean, n is Xi( i 1, 2.. times.n) is the total number of samples at the ith sampling time plus the number of samples that have already been diagnosed by the online fault diagnosis.
Quadratic form of the update sample:
Figure BDA0001986545370000144
wherein, C'nnIs a quadratic form of the updated sample.
The invention uses the incremental principal component analysis method, does not directly carry out singular value decomposition on a new quadratic form, and calculates a new load vector by calculating the variable quantity R of the load
Figure BDA0001986545370000145
Wherein the content of the first and second substances,
Figure BDA00019865453700001412
the residual error is calculated by the following method;
in that
Figure BDA0001986545370000146
Before calculating (2) a new data sample is calculated first
Figure BDA00019865453700001413
Score g of (a):
Figure BDA0001986545370000147
predicted value is
Figure BDA0001986545370000148
So the predicted value residual h is
Figure BDA0001986545370000149
Unitizing the residual error to obtain:
Figure BDA00019865453700001410
due to the fact that
Figure BDA00019865453700001411
Λ 'is a diagonal matrix formed by eigenvalues corresponding to the I principal elements of the updated principal element model, Λ' ∈ R(l+1)×(l+1)。
And substituting the updated quadratic form and the load vector to obtain:
Figure BDA0001986545370000151
wherein:
Figure BDA0001986545370000152
the subscripts to the matrix representation symbols are the dimensions of the matrix.
Consider that
Figure BDA0001986545370000153
So as to obtain:
Figure BDA0001986545370000154
can obtain the product
Figure BDA0001986545370000155
For the same reason have
Figure BDA0001986545370000156
Order to
Figure BDA0001986545370000157
Obtaining:
Figure BDA0001986545370000158
finally, the following is obtained:
Figure BDA0001986545370000159
therefore, R is
Figure BDA0001986545370000161
The decomposed eigenvectors of the eigenvalues of (a) are used to update the load matrix.
To this end, the state monitoring of the rolling process data for one cycle is completed. If the fault alarm does not occur in the period, the principal component model for judging the statistic and the control limit thereof is updated and changed according to the incremental principal component calculation method in the next period. Meanwhile, the number n of updated latest principal component training data is increased by 1 unit on the original basis, the mean value, the variance and the quadratic form of the training set data are updated according to the current online data, and the principal component load matrix is updated
Figure BDA0001986545370000162
And the characteristic value of the quadratic form is convenient for using the latest principal component model in the next period. As the total number of the principal component model and the training set samples is changed, the calculation formula of the control limit can find that the statistic of the training principal component diagnosis model in a new period, particularly the control limit of the SPE statistic is also changed correspondingly, namely the new principal component model takes the interference of the upper period system and the external change factors into consideration, and the Hotelling T model takes the interference of the upper period system and the external change factors into account2The control limits of the statistics do not change much because of the Hotelling's T2Statistics profilingThe change of the pivot space is described, the main state of the system is not changed, and therefore the control limit of the system is almost unchanged.
In the embodiment, the data of the above 6 variables of the finish rolling strip steel are collected, the sampling time is 40ms, the sampling number is 1270, and the post online fault diagnosis and verification are carried out. In advance we find that there is a depression data failure at point 901-1000. FIG. 2 is a Hotelling T method for IPCA online fault diagnosis with variable control limits2The statistic control chart is shown in FIG. 3, and the Hotelling T at 910 th sampling point is shown in FIG. 42Statistic contribution graph, FIG. 5 is the SPE statistic contribution graph at the 910 th sampling point. Fig. 6 and 7 are control charts of two statistics of the same data for online (offline) fault diagnosis by the PCA method. From Hotelling T2The statistics and the SPE statistics control chart can show that the false alarm phenomenon exists at the head part and the tail part in the rolling process.
The head point of the Hotelling T2 statistic is overrun at the 1 st to 6 th, 9 th and 10 th sampling points; the tail part exceeds the limit at the sampling points of 1231-; the other part is overrun at the 873, 880, 881, 901-1000 sampling point. Predicting faults by overrun at three consecutive points, Hotelling T2The number of the head error report points is 6, the error report rate is about 0.51%, the number of the tail error report points is 38, the error report rate is about 3.25%, the number of the other part excess report points is reduced to 0, the error report rate is about 0%, and the missing report rate is 0%. The SPE statistic headers overrun at sample points 1-6, 9, 12, 18, 24-27, 30, 32-34, 37-42, 48, 49; and the tail is overrun at the 1249-; the other part is overrun at the 901 < th > and 1000 < th > sampling points. And (3) over-limit forecasting faults according to three continuous points, wherein the number of error reporting points at the head part of the SPE statistic is 19, the error reporting rate is about 1.62%, the number of error reporting points at the tail part is 22, the error reporting rate is about 1.88%, the number of the over-limit points at other parts is 0, the error reporting rate is about 0%, and the missing reporting rate is 0%.
While the basic PCA method Hotelling T2Overrun at the header at sample points 1-24; the tail part exceeds the limit at the sampling points 1231-; the other part is overrun at the sampling points 871 and 891, 894, 895, 897 and 899. According to the continuous over-limit forecasting of the faults of 3 points, 24 error reporting points are arranged at the head part, the error reporting rate is 2.05 percent, 40 error reporting points are arranged at the tail part, the error reporting rate is 3.41 percent,the other parts exceed the limit points by 21 and have the false alarm rate of about 1.80 percent. 4 sampling points in the overrun of the 901 th and 100 th sampling points are lower than the control limit, and the missing report rate is 4%. And the sample point of 901 plus 1000 has abnormal pressing quantity failure, and the missing report rate is 4%. SPE counts overrun at 1 st to 18 th sampling points; overrun is generated at sampling points 1068, 1231-; the other portion exceeds the control limit in the vicinity of sample points 602, 732, 830, 861, 869-. According to continuous 3 points, the fault is over-forecast, the number of the head error report points is 18, the error report rate is 1.54%, the number of the tail error report points is 21, the error report rate is 1.81%, the number of other part error report points is 13, the error report rate is 1.11%, and the missing report rate is 0%.
The accuracy rates of the PCA method and the IPCA method in online fault diagnosis in the same rolling process are shown in the table 1, and the table shows that compared with the PCA method, the accuracy rate of the IPCA method in online fault diagnosis in the rolling process is greatly improved.
TABLE 1 accuracy of PCA and IPCA methods in online fault diagnosis in the same rolling process
Figure BDA0001986545370000181
The invention realizes fault diagnosis in the rolling process by analyzing the increment principal element. By adding the sampling data which is subjected to online diagnosis and has no fault into the training set principal component diagnosis model, the applicability of the diagnosis model to the current working condition and the accuracy of online fault diagnosis are improved, and the online fault diagnosis method has a specific practical guiding significance for online fault diagnosis in the actual rolling process.

Claims (4)

1. The online fault diagnosis method for the variable control limit IPCA rolling process is characterized by comprising a model training and diagnosis stage and an online diagnosis stage, and specifically comprises the following steps:
training a diagnosis model: screening historical data under normal working conditions according to product quality factors, taking the historical data under the normal working conditions as training data, establishing a principal component diagnosis model of the training data under the normal working conditions, and calculating a control limit of the principal component diagnosis model;
an online diagnosis stage: processing sampling point data in each sampling period, substituting the processed sampling point data into the principal component diagnosis model, and respectively calculating Hotelling T2Statistics and SPE statistics; during online fault diagnosis, the Hotelling T is used2Comparing the statistic and the SPE statistic with the control limit of the principal component diagnosis model obtained by calculation in the stage of training the diagnosis model; judging whether a fault occurs according to the comparison result, and if the fault occurs, performing fault alarm; if the fault does not occur, updating a load transformation matrix, a control limit and a mean value and a variance of training data of the principal component diagnosis model by an incremental principal component analysis method,
the historical data under the normal working condition refers to data collected by each sensor under the normal running state in the strip steel rolling process;
in the stage of training a diagnostic model, establishing a principal component diagnostic model and calculating a control limit of the principal component diagnostic model, specifically comprising:
(1) collecting and selecting historical data under normal working conditions as training data;
(2) carrying out centralization processing on the training data, and then calculating a quadratic matrix C of the data after the centralization processing;
wherein, the centralized processing formula is as follows:
Figure FDA0002506886280000011
Figure FDA0002506886280000021
is the sample data after the centralization processing; xi(i 1, 2.. n) is sample data at the ith sampling time, and the total number of samples is n; the number of the observation variables, namely the dimension is m; mu is the average value of the corresponding classification of the training data, and sigma is the variance of the corresponding classification of the training data;
and (3) performing quadratic matrix processing on the data after the centralization processing, wherein the calculation formula is as follows:
Figure FDA0002506886280000022
decomposing the eigenvalue of quadratic matrix to obtain principal component model, calculating m eigenvalues, and arranging λ according to the order from large to small1,λ2,...,λmThe corresponding unit feature vector is P1,P2,...,PmThe characteristic matrix U ═ P1,P2,...,Pm]；
(3) Performing principal component analysis modeling process on the quadratic matrix C, according to a variance contribution rate method, because the principal component corresponding to the maximum characteristic value also contains the maximum information in proportion, when the sum of the current l characteristic values exceeds a certain threshold of the sum of the characteristic values, considering that the influence of the subsequent characteristic values on a principal component model can be ignored, and reducing the original data matrix to l dimension at the moment, thereby determining the number l of the principal components, wherein the calculation formula of the principal component contribution rate percentage is as follows:
Figure FDA0002506886280000023
when the percentage of the cumulative contribution rate of the current l principal elements exceeds a threshold value, the corresponding l value is the number of the principal elements, and l is more than or equal to 1 and less than or equal to m; the threshold is selected to be 85% -95%;
load matrix at this time
Figure FDA0002506886280000024
Score matrix, i.e. principal component matrix
Figure FDA0002506886280000025
(4) Principal component diagnosis model for establishing training data under normal working condition
Figure FDA0002506886280000026
Figure FDA0002506886280000027
Storing the principal component diagnosis model for classification for principal component matrix or called score matrixThe score matrix, the load matrix and the eigenvector corresponding to the eigenvalue of the model;
(5) using Hotelling T2And the SPE statistics amount to calculate respective Hotelling T of different types of principal component diagnosis models2Control limit L imT at confidence level α for statistics and SPE statistics2And L imQ, and storing by classification.
2. The method for diagnosing the online fault of the variable control limit IPCA rolling process according to claim 1,
Hotelling T2the control limit for the statistic at significance level α is calculated by:
Figure FDA0002506886280000031
wherein, Fα(l, n-l) refers to the α critical point on the F distribution with degrees of freedom l and (n-l);
the control limit for the SPE statistic at significance level α is calculated as:
Figure FDA0002506886280000032
in the formula:
Figure FDA0002506886280000033
λjis the jth eigenvalue, C, of a quadratic matrix CαThe standard deviations corresponding to quantiles 1- α.
3. The method for diagnosing the online fault of the variable control limit IPCA rolling process according to claim 2, wherein the online diagnosis stage specifically comprises the following steps:
(1) collecting real-time data to be diagnosed, wherein the sample data of the ith sampling point is yi；
(2) Sample data y of sampling pointiCarrying out centralization treatment to obtain centralization treatment:
Figure FDA0002506886280000034
Figure FDA0002506886280000035
is the sample data after centralization, mu is the average value of the corresponding classification of the training data, and sigma is the variance of the corresponding classification of the training data;
(3) centering the sample data
Figure FDA0002506886280000036
Substituting into corresponding principal component diagnosis model to calculate Hotelling T2Statistics and SPE statistics;
hotelling T for ith sample point2The statistic calculation formula is as follows:
Figure FDA0002506886280000041
Λ is a diagonal matrix composed of eigenvalues corresponding to the principal elements, Λ∈ Rl×l；
The formula for calculating SPE statistic of ith sampling point is as follows:
Figure FDA0002506886280000042
i is a unit matrix of l × l;
(4) hotelling's T of ith sample point2And SPE two statistics and control limits L imT2And L imQ comparison;
if T isi 2＞LimT2Or Qi> L imQ, and N successive points are overrun, Ti 2，Ti+1 2，...,Ti+N-1 2＞LimT2Or Qi，Qi+1，...，Qi+N-1If the sampling point is more than L imQ, the ith sampling point is failed, and a failure alarm is carried out, wherein the size of N can be adjusted according to the system requirement;
otherwise, the ith sampling point is not in fault, and no alarm is given, the data in the sampling period system is normal, the data in the sampling period is added into the training principal component diagnosis model, and the load transformation matrix, the control limit, the training data mean value and the variance of the principal component diagnosis model are updated by adopting an incremental principal component analysis method.
4. The method for diagnosing the online fault of the variable control limit IPCA rolling process according to claim 3, wherein when the fault occurs, in addition to performing fault alarm, the method further comprises the step of determining the cause of the fault according to the contribution of each variable to the statistic so as to locate the subsequent fault, and specifically comprises the following steps:
if T isi 2，Ti+1 2，...,Ti+N-1 2＞LimT2When fault alarm is carried out, the contribution degree of each variable to the fault is determined according to a contribution graph method, and the jth observation variable to Hotelling T2The calculation formula of the contribution degree of the statistic is as follows:
Figure FDA0002506886280000051
wherein
Figure FDA0002506886280000052
As a load matrix
Figure FDA0002506886280000053
The value of row i and column j;
if Q isi，Qi+1，...，Qi+N-1When the fault alarm is carried out, determining the contribution degree of each variable to the fault according to a contribution graph method, and calculating the contribution of the jth observation variable to the SPE statistic according to a formula:
Figure FDA0002506886280000054
wherein the content of the first and second substances,
Figure FDA0002506886280000055
is that
Figure FDA0002506886280000056
Is the unit matrix of l × l.
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