CN114528939B - Micro fault detection method based on Kolmogorov-Smirnov test - Google Patents
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Abstract
The invention discloses a method for detecting micro faults based on Kolmogorov-Smirnov test, which comprises the following steps: after standardized pretreatment is carried out on the training samples, a PCA model is established, a load matrix P is obtained, then sample data are collected online in real time, a principal component space of online data is calculated by utilizing the PCA model established in an offline process, K-S test is carried out on the training data and the principal component space of the online data, and the value of the obtained K-S test statistic D n is compared with a control limit, so that online monitoring is realized. The invention solves the problem that the traditional PCA fault detection method has poor fault detection performance on the micro faults because of smaller amplitude of the micro faults, and has higher detection rate on the micro faults.
Description
Technical Field
The invention relates to the technical field of micro fault detection, in particular to a micro fault detection method based on Kolmogorov-Smirnov test.
Background
With rapid development of modern economy and continuous improvement of the technological level, industrial processes or equipment are increasingly complicated and large-sized. This presents a serious challenge to engineers responsible for ensuring reliable operation of the process. Once the production process or equipment has tiny faults, if the faults cannot be found and properly handled in time, the faults gradually develop into serious faults or even cause serious accidents over time, so that casualties and huge economic losses are caused.
A fault is an undesirable feature or any anomaly exhibited by the system. Thus, in modern industry, fault detection is critical to improve system reliability, prevent serious system performance degradation, and ensure optimal process operation.
Fault detection and diagnosis are of great importance in ensuring safe and reliable operation of modern industrial processes. Most existing fault detection methods are only effective for sudden or significant faults with large magnitudes. In recent years, the detection and diagnosis of micro-faults have become one of the hot spots of interest in the scientific and engineering fields, with the aim of identifying micro-faults at an early stage in time. Patent CN110244692a discloses a method for detecting micro faults in chemical process, which introduces Kullback-Leibler divergence (english: kullback-Leibler Divergence, abbreviated as KLD) into a traditional local-global principal component analysis method, based on a model of principal component analysis training offline data, calculates principal component spatial statistics T 2 and residual spatial statistics SPE by using KLD components of online data, monitors the principal component spatial statistics T 2 and residual spatial statistics SPE by a control limit calculated by a kernel density method, and improves the micro fault detection rate.
The traditional fault diagnosis method based on knowledge and analysis models is excessively dependent on establishing an accurate mathematical model, and knowledge experience is difficult to acquire. For complex industrial processes with different data characteristics, model and knowledge based fault detection methods are poorly effective. The highly automated and complex industrial process accumulates massive data containing effective information, and fault detection and diagnosis based on a data driving method are generated. The method does not need an accurate mathematical model of a known industrial process, directly applies sensor data acquired in the process, establishes a model by utilizing a multivariate statistical theory, and realizes fault detection and diagnosis of the process.
Disclosure of Invention
In view of the above, the present invention aims to provide a micro-fault detection method based on Kolmogorov-Smirnov test, which is used for solving the problems that the traditional fault detection method based on data driving is insensitive to micro-faults and has low fault detection rate, and the method has high fault detection rate and low fault false alarm rate when used for micro-fault detection. The K-S test is widely used in statistics to determine whether the probability distribution of one set of data is the same as the probability distribution of a known data, or whether the probability distributions of two sets of data are similar. The invention deeply digs the probability distribution situation of the data caused by the micro faults in the industrial process and effectively detects the faults.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
A micro-fault detection method based on Kolmogorov-Smirnov test, the micro-fault detection method comprising an offline modeling process and an online monitoring process, wherein the offline modeling process comprises:
Step S1, collecting CSTH historical normal data X in the process, dividing the data into a training sample set X tr and a test sample set X te according to a certain proportion, and carrying out normalization processing;
Step S2, a principal component analysis is used for the training sample set X tr obtained in the step S1 to obtain a PCA model of the training sample set X tr, and then a load matrix P of the training sample set X tr is obtained;
Step S3, according to the load matrix P obtained in the step S2, a principal element subspace T tr of a training sample set X tr and a principal element subspace T te of a test sample set X te are calculated;
Step S4, performing K-S test, which comprises the following steps: firstly, setting a sliding window, and calculating the empirical distribution function EDF of the ith principal element t tri of the training sample and the ith principal element t tei of the test sample in the window; then K-S test is carried out to obtain the value of K-S statistic D n; then, sliding the sliding window backwards, repeating the steps until the window slides to the last data in the pivot;
Step S5, given a significant level alpha, calculating a control limit D n (alpha);
The online monitoring process specifically comprises the following steps:
s6, acquiring real-time online data X on in CSTH process, and carrying out normalization processing on the data;
step S7, calculating a principal component space T on of the online data X on by using the load matrix P of the training sample set X tr obtained in the step S2;
Step S8, performing K-S test, which comprises the following steps: given the width of a sliding window, calculating the empirical distribution function EDF of the ith principal element t tri of the training sample in the window and the ith principal element t oni of the online sample, and further solving the value of the K-S test statistic D n;
s9, comparing the statistic D n with the value of the control limit D n (alpha), and judging whether a fault occurs at the current moment of the system;
step S10, repeating the steps S7-S9 when the online data at the next moment is collected, and sliding the window backwards.
Further, in the step S1, the training sample set is denoted as X tr＝[Xtr(1) Xtr(2) … Xtr(n)]T∈Rn×m, the test sample set is denoted as X te＝[Xte(1) Xte(2) … Xte(n)]T∈Rn×m, where n is denoted as the number of samples, and m is denoted as a variable involved in the CSTH process.
Further, the step S2 specifically includes:
Step S201, aiming at a training sample set X tr, solving a covariance matrix according to a formula (1), and decomposing the covariance matrix to obtain a characteristic value matrix of the training sample set and a corresponding characteristic vector thereof;
Step S202, determining the number l of principal components of a training sample set according to a criterion that the accumulated contribution rate of the eigenvalues reaches 90%, and calculating a load matrix P according to a formula (1) and a first l column of eigenvectors corresponding to the eigenvalue matrix, wherein the formula (1) specifically represents:
in the formula (1), S is a covariance matrix, Λ= [ λ 1,λ2,...,λm ] is a eigenvalue matrix and λ 1≥λ2≥...≥λm, V is an eigenvector corresponding to the eigenvalue, P is a load matrix, M-l columns of y;
The criterion that the cumulative contribution rate of the characteristic values reaches 90 percent is specifically expressed as follows:
Further, the step S4 specifically includes:
Step S401, a sliding window width W is given as 20, and a formula (3) is utilized to calculate EDFF 1 (x) of a first principal element t tr1 in a principal element subspace of a training sample in the window and EDFF 2 (x) of a first principal element t te1 in a principal element subspace of a test sample;
in equation (3), y k is the kth observation of a random variable;
Step S402, calculating the value of the statistic D n of K-S (t tr1,tte1) according to the formula (4), wherein the formula (4) specifically comprises:
In equation (4), n 1,n2 is the number of samples in the sliding window, A maximum value of a vertical distance between the empirical distribution function images of the two samples;
Step S403, setting the step pitch of the sliding window to be 1, and calculating the value of the statistic D n in the second window by the backward sliding window until the window slides to the last data in the first principal element, thereby obtaining the value of n-W+1 statistic of the first principal element;
and S404, repeating the steps, and calculating the values of n-W+1 statistic values of all the l principal elements.
Further, in the step S5, the significant level α=0.05, and the value of the control limit D n (α) is obtained by the formula (5), expressed as:
further, in the step S9, it is determined whether a fault occurs according to the formula (6), which specifically includes:
Further, the variable m is involved in CSTH, which specifically includes: the liquid level of the reaction kettle, the flow of cold water, the valve position of cold water, the temperature of the reaction kettle, the flow of hot water and the valve position of hot water.
The beneficial effects of the invention are as follows:
The invention provides a K-S-based micro fault detection method for the first time, which can effectively monitor the occurrence of micro faults in an industrial process, thereby reducing serious harm caused by the micro faults; secondly, the invention has lower false alarm rate and missing report rate for detecting the micro faults, and can effectively avoid economic loss caused by high false alarm rate and the like; finally, the invention solves the problem that the traditional PCA fault detection method has poor fault detection performance on the micro faults due to smaller amplitude of the micro faults, and has higher detection rate on the micro faults.
Drawings
FIG. 1 is a graph of the empirical distribution function of two samples provided in example 1;
FIG. 2 is a process schematic of CSTH processes provided in example 1;
FIG. 3 is a flow chart of fault detection based on the K-S test provided in example 1;
fig. 4 is a graph showing the detection effect of the zero drift fault provided in embodiment 1;
fig. 5 is a graph showing the detection effect of the deviation fault provided in example 1;
FIG. 6 is a graph comparing the failure detection rates of the T 2 statistic, SPE statistic, and D n statistic provided in example 1;
Fig. 7 is a graph comparing failure false alarm rates of T 2 statistic, SPE statistic, and D n statistic provided in example 1.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1
Referring to fig. 1-7, the present embodiment provides a method for detecting micro-faults based on Kolmogorov-Smirnov test, which faces CSTH process, CSTH is an experimental platform developed by university of alberta laboratory in canada. The stirring kettle has the functions of mixing cold water and hot water together, heating the mixture by steam, and finally flowing out the heated mixed water from the bottom of the heating kettle. The process flow diagram is shown in figure 2. The cross section of the stirring kettle is circular, the volume is 8 liters, the height is 0.5 meter, and although the model of CSTH process is small and no actual reaction process exists, all sensors, valves and heat exchangers of the process have complete characteristics, so that the process of releasing heat of chemical reaction is simulated.
In the embodiment, MATLAB is adopted as a simulation platform, a simulation model is built in a Simulink, three general interferences, namely deterministic oscillation interference of a cold water flow control transmission link, random interference of a liquid level control transmission link and noise interference of a temperature control transmission link, are added, the actual chemical process is simulated to the maximum extent, and the test result is ensured to have higher authenticity. Process data information is collected from the 6 variables of the CSTH system, see in particular table one. The fault type refers to two types of sensor micro faults commonly seen in chemical processes: zero drift and offset faults. The first 200 sampling points of each sample are data when the system normally operates, a tiny fault is introduced at the 201 st sampling point, the amplitude of the fault is set to be a tiny amplitude, the amplitude of the zero drift fault is set to be 0.001mA, the amplitude of the deviation fault is set to be 0.1mA, and 500 sampling points are set in total. The initial modal parameters of the simulation are set as follows: the liquid level is 12mA, the temperature is 10.5mA, and the hot water valve is 0mA.
List one
| Variable(s) | Variable description |
| Level | Liquid level of reaction kettle |
| CW flow | Cold water flow rate |
| CW valve | Cold water valve position |
| Temperature | Reaction kettle temperature |
| HW flow | Flow rate of hot water |
| HW valve | Hot water valve position |
The method for detecting the micro fault based on the Kolmogorov-Smirnov test mainly comprises an offline modeling process and an online monitoring process, wherein the offline modeling process mainly comprises the following steps of:
Step S1: collecting CSTH historical normal data of the process, and dividing the historical normal data into a training sample set X tr＝[Xtr(1) Xtr(2) … Xtr(n)]T∈Rn×m and a test sample set X te＝[Xte(1) Xte(2) … Xte(n)]T∈Rn×m; wherein n is the number of samples 500, m is the number of variables 6 shown in Table one, the training sample mean mu and standard deviation sigma are calculated, and the training data and the test data are normalized by using formula (1).
Step S2: the PCA model is obtained by using a training sample set, and the specific steps are as follows:
The covariance matrix is obtained by the formula (2) And decomposing the covariance matrix to obtain training
A eigenvalue matrix of the sample and corresponding eigenvectors, wherein Λ= [ λ 1,λ2,...,λm ] is the eigenvalue matrix and λ 1≥λ2≥...≥λm, V is the eigenvector corresponding to the eigenvalue;
adopting a formula (3), determining the number l of principal elements of the training sample set by using a criterion that the cumulative contribution rate of the characteristic values reaches 90%, taking the front l column of V to calculate a load matrix P, For the remaining m-l columns. Calculating a principal component subspace T tr＝XtrP＝[ttr1 ttr2 … ttrl]∈Rn×l of the training sample;
step S3: calculating a principal component subspace T te＝XteP＝[tte1 tte2 … ttel]∈Rn×l of the test sample by using the load matrix P calculated in the step S2;
Step S4: the K-S test is carried out, and the specific steps are as follows:
Given a sliding window width W of 20, calculating EDFF 1 (x) of a first principal element t tr1 in a principal element subspace of the training sample and EDFF 2 (x) of a first principal element t te1 in a principal element subspace of the test sample in the window by using a formula (4);
Calculating the value of statistic D n of K-S (t tr1,tte1) by using formula (5), wherein n 1,n2 is the number of samples in the sliding window, Is the maximum of the vertical distance between the empirical distribution function images of the two samples. As shown in fig. 1;
Setting the step distance of the sliding window to be 1, and calculating the value of statistic D n in the second window by the backward sliding window until the window slides to the last data in the first principal element, thereby obtaining the value of n-W+1 statistic of the first principal element;
Repeating the steps to calculate the values of n-W+1 statistic of all the principal elements;
Step S5: given a significant level α=0.05, the value of the control limit D n (α) is obtained by formula (6); and judging whether a fault occurs or not through the logic of the formula (7).
Specifically, the on-line monitoring process specifically includes:
Step S1: collecting real-time data of CSTH processes, and carrying out normalization treatment to obtain an online sample set X on＝[Xon(1) Xon(2) … Xon(q)]T∈Rq×m, wherein q is more than or equal to W;
Step S2: calculating a principal component subspace T on＝XonP＝[ton1 ton2 … tonl]∈Rq×l of an online process data sample by utilizing a load matrix P obtained by offline process training data;
Step S3: performing on-line K-S test, wherein the specific steps are as follows:
Given a sliding window width W of 20, calculating EDFF 1 (x) of a first principal element t tr1 in a training sample principal element subspace and EDFF on (x) of a first principal element t on1 in an online sample principal element subspace in the window by using a formula (4);
Calculating the value of statistic D n of K-S (t tr1,ton) by using formula (5);
step S4: judging whether a fault occurs at the current sampling moment by utilizing the logic of the formula (7);
step S5: the above steps S1-S4 are repeated when the online data at the next moment is collected, while the window slides backward.
After the method is adopted to detect the micro faults, the fault detection results of different methods are compared through the fault detection rate FDR and the fault false alarm rate FAR indexes in order to evaluate the fault detection performance of different fault detection methods. The failure detection rate FDR is defined as the ratio of the number of detected failure data to the actual total number of failure data. It is obvious that the larger the value of FDR, the better the fault detection effect of the industrial process fault detection method; conversely, the poorer the fault detection effect of the industrial process fault detection method. The false alarm rate FAR is defined as the ratio of the number of normal samples falsely reported as a fault to the total number of normal samples, and obviously, the lower the false alarm rate is, the better the detection effect is.
Fig. 6 and 7 show graphs of the effect comparison of the statistics of T 2 and SPE calculated by the conventional PCA method with the FDR and FAR for detecting the micro fault by the statistics of the K-Stest method D n adopted by the present invention, and as can be observed from the graphs, the method of the present invention is more stable, has a higher fault detection rate, and the fault false alarm rate is close to 0;
In summary, the fault detection method provided by the invention generally obtains a better fault detection effect and has higher stability.
In summary, after the training sample is subjected to standardized pretreatment, a PCA model is established to obtain a load matrix P, then sample data is collected online in real time, a principal component space of online data is calculated by using the PCA model established in an offline process, and the training data and the principal component space of the online data are subjected to K-S test to obtain a value of K-S test statistic D n and a control limit to realize online monitoring. In order to verify the feasibility of the invention, principal component space statistic T 2 and residual space statistic SPE statistic calculated by the traditional PCA fault detection model are compared with the monitoring effect of K-S test statistic D n. According to the fault detection method, the change condition of the micro fault characteristics of the industrial process can be more accurately found by comparing the micro differences of the probability distribution of the data of the training sample and the probability distribution of the data of the test sample, so that the fault detection rate can be improved, and the fault false alarm rate can be reduced.
The present invention is not described in detail in the present application, and is well known to those skilled in the art.
The foregoing describes in detail preferred embodiments of the present invention. It should be understood that numerous modifications and variations can be made in accordance with the concepts of the invention by one of ordinary skill in the art without undue burden. Therefore, all technical solutions which can be obtained by logic analysis, reasoning or limited experiments based on the prior art by the person skilled in the art according to the inventive concept shall be within the scope of protection defined by the claims.
Claims (7)
1. A method for detecting a micro-fault based on Kolmogorov-Smirnov test, wherein the method for detecting a micro-fault comprises an offline modeling process and an online monitoring process, wherein the offline modeling process comprises:
Step S1, collecting CSTH historical normal data X in the process, dividing the data into a training sample set X tr and a test sample set X te according to a certain proportion, and carrying out normalization processing;
Step S2, a principal component analysis is used for the training sample set X tr obtained in the step S1 to obtain a PCA model of the training sample set X tr, and then a load matrix P of the training sample set X tr is obtained;
Step S3, according to the load matrix P obtained in the step S2, a principal element subspace T tr of a training sample set X tr and a principal element subspace T te of a test sample set X te are calculated;
Step S4, performing K-S test, which comprises the following steps: firstly, setting a sliding window, and calculating the empirical distribution function EDF of the ith principal element t tri of the training sample and the ith principal element t tei of the test sample in the window; then K-S test is carried out to obtain the value of K-S statistic D n; then, sliding the sliding window backwards, repeating the steps until the window slides to the last data in the pivot;
Step S5, given a significant level alpha, calculating a control limit D n (alpha);
The online monitoring process specifically comprises the following steps:
s6, acquiring real-time online data X on in CSTH process, and carrying out normalization processing on the data;
step S7, calculating a principal component space T on of the online data X on by using the load matrix P of the training sample set X tr obtained in the step S2;
Step S8, performing K-S test, which comprises the following steps: given the width of a sliding window, calculating the empirical distribution function EDF of the ith principal element t tri of the training sample in the window and the ith principal element t oni of the online sample, and further solving the value of the K-S test statistic D n;
s9, comparing the statistic D n with the value of the control limit D n (alpha), and judging whether a fault occurs at the current moment of the system;
step S10, repeating the steps S7-S9 when the online data at the next moment is collected, and sliding the window backwards.
2. The method according to claim 1, wherein in the step S1, the training sample set is denoted as X tr＝[Xtr(1) Xtr(2) … Xtr(n)]T∈Rn×m, the test sample set is denoted as X te＝[Xte(1) Xte(2) … Xte(n)]T∈Rn×m, and n is denoted as the number of samples, and m is denoted as a variable involved in CSTH.
3. The method for detecting micro-faults based on the Kolmogorov-Smirnov test according to claim 2, wherein the step S2 specifically comprises:
Step S201, aiming at a training sample set X tr, solving a covariance matrix according to a formula (1), and decomposing the covariance matrix to obtain a characteristic value matrix of the training sample set and a corresponding characteristic vector thereof;
Step S202, determining the number l of principal components of a training sample set according to a criterion that the accumulated contribution rate of the eigenvalues reaches 90%, and calculating a load matrix P according to a formula (1) and a first l column of eigenvectors corresponding to the eigenvalue matrix, wherein the formula (1) specifically represents:
In the formula (1), S is a covariance matrix, Λ= [ λ 1,λ2,...,λm ] is a eigenvalue matrix and λ 1≥λ2≥…≥λm, V is an eigenvector corresponding to the eigenvalue, P is a load matrix, M-l columns of V;
The criterion that the cumulative contribution rate of the characteristic values reaches 90 percent is specifically expressed as follows:
4. The method for detecting micro-faults based on the Kolmogorov-Smirnov test as claimed in claim 3, wherein the step S4 specifically comprises:
Step S401, a sliding window width W is given as 20, and a formula (3) is utilized to calculate EDFF 1 (x) of a first principal element t tr1 in a principal element subspace of a training sample in the window and EDFF 2 (x) of a first principal element t te1 in a principal element subspace of a test sample;
in equation (3), y k is the kth observation of a random variable;
Step S402, calculating the value of the statistic D n of K-S (t tr1,tte1) according to the formula (4), wherein the formula (4) specifically comprises:
In equation (4), n 1,n2 is the number of samples in the sliding window, A maximum value of a vertical distance between the empirical distribution function images of the two samples;
Step S403, setting the step pitch of the sliding window to be 1, and calculating the value of the statistic D n in the second window by the backward sliding window until the window slides to the last data in the first principal element, thereby obtaining the value of n-W+1 statistic of the first principal element;
and S404, repeating the steps, and calculating the values of n-W+1 statistic values of all the l principal elements.
5. The method for detecting a micro-fault based on the Kolmogorov-Smirnov test according to claim 4, wherein in the step S5, the significant level α=0.05, the value of the control limit D n (α) is obtained by the formula (5), expressed as:
6. the method for detecting a micro-fault based on the Kolmogorov-Smirnov test according to claim 5, wherein in step S9, it is determined whether a fault occurs according to formula (6), specifically:
7. The method for detecting a micro fault based on Kolmogorov-Smirnov test according to claim 6, wherein the process CSTH involves variable m, which specifically includes: the liquid level of the reaction kettle, the flow of cold water, the valve position of cold water, the temperature of the reaction kettle, the flow of hot water and the valve position of hot water.
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| CN110244692A (en) * | 2019-06-20 | 2019-09-17 | 中国石油大学(华东) | Chemical process small fault detection method |
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