CN106094749B - Based on the nonlinear fault detection method and application for improving nuclear entropy constituent analysis - Google Patents
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Abstract
The invention discloses a kind of based on the nonlinear fault detection method and its application of improving nuclear entropy constituent analysis.This method judges the whether faulty generation of production process by combining integrated study and Bayesian inference realization to be monitored industrial generating process using nuclear entropy constituent analysis side.Nonlinear problem of the present invention for data in actual production process, using nuclear entropy constituent analysis using the actual distribution situation (Gaussian Profile, non-gaussian distribution etc.) for effectively avoiding considering data the characteristics of comentropy, and the problem of multiple models are blindly chosen so as to avoid nuclear entropy constituent analysis Kernel Function parameter is introduced by integrated study.Effectively improve the detection effect of failure in industrial generating process.
Description
Technical Field
The invention belongs to industrial production process detection, and particularly relates to a nonlinear fault detection method based on improved nuclear entropy component analysis.
Background
With the increasing production scale, modern industries are more concerned about the safety of the production process, and fault diagnosis is used for monitoring the production process, which can detect abnormal working conditions of the production process and judge the root cause of the abnormal working conditions. Therefore, multivariate statistical process monitoring as a fault diagnosis method is being studied in large quantities.
Principal Component Analysis (PCA) is a typical multivariate statistical process monitoring method that is extensively applied to pattern recognition, image processing, and process monitoring. The method achieves the purpose of reducing dimension by extracting main components in the process, and the main components are reflected by the size of variance. The principal component analysis method can be effectively applied to the process with the characteristics of high dimension, high correlation and the like. However, this method also has the obvious disadvantage that it is a linear method, which makes the method less effective in dealing with non-linear processes.
In order to overcome the situation that the effect of the principal component analysis method is rapidly deteriorated when dealing with the nonlinear condition, many people have made many researches and improvements in the past decades, wherein Kernel Principal Component Analysis (KPCA) is the most influential method. In kernel principal component analysis, the mapping of data from non-linear to linear is achieved by projecting the original data into a space of high or infinite dimensions. To better apply this method to process monitoring, Lee et al propose a method of calculating the Squared Prediction Error (SPE), whereby two statistical indicators, T ^2 and SPE, are used in KPCA to detect the process. However, both statistical indicators of confidence limit calculation methods assume that the input data follows a gaussian distribution, but this assumption, which takes into account process non-linearities, is not well satisfied in the actual production process. Ge et al introduces the statistical local method into KPCA, has reconstructed two detection indexes through the hypothesis test with the statistical local method, and the newly constructed detection index can better satisfy the Gaussian distribution, thus makes the detection rate of trouble improve. Samuel et al, based on certain assumptions, calculate the control limit of the monitoring index by using a Kernel Density Estimation (KDE) method, which also improves the monitoring quality to some extent.
Disclosure of Invention
The invention aims to provide a nonlinear fault detection method based on improved nuclear entropy component analysis and application thereof aiming at the defects of the prior art, and the method is used for monitoring an industrial generation process by utilizing a nuclear entropy component analysis party in combination with ensemble learning and Bayesian inference and judging whether a fault occurs in a production process. Aiming at the problem of data nonlinearity in the actual production process, the invention adopts the characteristic of the information entropy for analyzing the nuclear entropy components to effectively avoid considering the actual distribution condition (Gaussian distribution, non-Gaussian distribution and the like) of the data, and introduces a plurality of models through integrated learning so as to avoid the problem of blind selection of the kernel function parameters in the nuclear entropy component analysis. The detection effect of faults in the industrial generation process is effectively improved.
A nonlinear fault detection method based on improved kernel entropy component analysis comprises the following steps:
the method comprises the following steps: the method comprises the following steps of establishing a model in an off-line mode, establishing off-line models of different nuclear parameters by using data under normal working conditions through a nuclear entropy analysis method, and the specific process comprises the following steps:
1) collecting data in industrial production process, preprocessing related variables, normalizing sample data, and expressing the collected data as X ═ X1,x2,…,xN]T∈RN×mWhere m represents the number of process variables, N represents the number of samples, xi∈RmI is 1, …, N corresponds to the ith sample, and then the data is de-dimensioned and processed into 0-mean data with variance of 1; the normalization method of the sample data comprises the following steps: x is the number ofi *＝(xi-minxi)/(maxxi-minxi) Wherein x isiAnd xi *Respectively representing the values before and after normalization, maxxiAnd minxiRespectively representing the maximum and minimum values in the sample data;
2) preprocessing data under normal working conditions and establishing offline models of different nuclear parameters by a nuclear entropy analysis method; the entropy estimate can be expressed as:
wherein,representing the entropy estimation, K is the kernel matrix, 1 is the column vector with elements 1, K (x)iAnd x) is a kernel function, the present invention employs a Gaussian kernel function, which is defined as follows:
the kernel matrix is subjected to eigen decomposition, in which case the entropy estimate is expressed as:
wherein λ represents the decomposed feature value, e represents the corresponding feature vector, then the feature vector corresponding to the value with the maximum entropy is the projection vector thereof, and the projected nonlinear part can be represented as:
T＝KE；
wherein T is the projected nonlinear part, and E is a projection matrix;
3) and determining the control limit corresponding to each submodel.
Step two: online detection, namely projecting online data to the kernel direction with the maximum entropy of each model by using an offline established model; then converting the models into a probability form by using Bayesian inference; and finally, combining a plurality of models in the probability forms by utilizing ensemble learning, detecting data in the actual production process by utilizing the first step, and judging whether a fault occurs. The specific process comprises the following steps:
1) the data to be subjected to online detection is processed into data with a mean value of 0 and a variance of 1 by adopting a data preprocessing method which is the same as that in an offline modeling stage, and the normalization method comprises the following steps: x is the number ofi *＝(xi-minxi)/(maxxi-minxi) Wherein x isiAnd xi *Respectively representing the values before and after normalization, maxxiAnd minxiRespectively representing the maximum and minimum values in the sample data;
2) and projecting the online data to the direction of each kernel with the maximum model entropy by using the model established offline, wherein the projection of the ith model can be represented as:
T(i)＝K(i)E(i)
respectively projecting different models, and respectively extracting principal component parts of the models;
3) after online data is projected by using a model of a nuclear entropy component analysis method, the obtained projection part is converted into a probability form by using Bayesian inference, and the probability form is as follows:
and the probability in the denominator can be calculated by the following two equations:
n, F respectively indicate normal and fault conditions, p (N), p (F) indicate their corresponding probability values, which can be calculated from a given confidence level, and other probability forms can be calculated exponentially from the ratio of its control limit to its actual value.
4) The multiple models in these probability forms are combined by weights using ensemble learning, and the statistical indexes after ensemble are as follows:
5) and 4) comparing the calculated statistical index with the confidence level to judge whether a fault occurs, if the statistical index is greater than the confidence level, the fault occurs, otherwise, the working condition is normal, and the fault is not detected.
The invention has the beneficial effects that:
the invention discloses a fault detection method based on improved nuclear entropy component analysis and application thereof. Aiming at the problem of data nonlinearity in the actual production process, the invention adopts the characteristic of the information entropy for analyzing the nuclear entropy components to effectively avoid considering the actual distribution condition (Gaussian distribution, non-Gaussian distribution and the like) of the data, and introduces a plurality of models through integrated learning so as to avoid the problem of blind selection of the kernel function parameters in the nuclear entropy component analysis. The method is found to have better fault detection rate aiming at the actual verification of the industrial process, and the fault detection effect in the industrial generation process is effectively improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
Aiming at the non-linear problem of industrial production process data, the invention applies the nuclear entropy component analysis algorithm to the fault detection process and establishes an off-line model based on the nuclear entropy component analysis. And the method introduces the ensemble learning and Bayesian inference, effectively avoids the blindness of kernel function parameter selection, and is suitable for different types of fault diagnosis. The flow chart of the invention is shown in figure 1.
The method comprises the following steps: and (3) establishing a model in an off-line mode, and establishing off-line models of different nuclear parameters by using data under normal working conditions through a nuclear entropy analysis method.
1) Collecting data in industrial production process, preprocessing related variables, normalizing sample data, collecting dataExpressed as X ═ X1,x2,…,xN]T∈RN×mWhere m represents the number of process variables, N represents the number of samples, xi∈RmI is 1, …, N corresponds to the ith sample, and then the data is de-dimensioned and processed into 0-mean data with variance of 1; the normalization method of the sample data comprises the following steps: x is the number ofi *＝(xi-minxi)/(maxxi-minxi) Wherein x isiAnd xi *Respectively representing the values before and after normalization, maxxiAnd minxiRespectively representing the maximum and minimum values in the sample data;
2) preprocessing data under normal working conditions and establishing offline models of different nuclear parameters by a nuclear entropy analysis method; the entropy estimate can be expressed as:
wherein,representing the entropy estimation, K is the kernel matrix, 1 is the column vector with elements 1, K (x)iAnd x) is a kernel function, the present invention employs a Gaussian kernel function, which is defined as follows:
the kernel matrix is subjected to eigen decomposition, in which case the entropy estimate is expressed as:
wherein λ represents the decomposed feature value, e represents the corresponding feature vector, then the feature vector corresponding to the value with the maximum entropy is the projection vector thereof, and the projected nonlinear part can be represented as:
T＝KE；
wherein T is the projected nonlinear part, and E is a projection matrix;
3) and determining the control limit corresponding to each submodel.
Step two: online detection, namely projecting online data to the kernel direction with the maximum entropy of each model by using an offline established model; then converting the models into a probability form by using Bayesian inference; and finally, combining a plurality of models in the probability forms by utilizing ensemble learning, detecting data in the actual production process by utilizing the first step, and judging whether a fault occurs. The specific process comprises the following steps:
1) the data to be subjected to online detection is processed into data with a mean value of 0 and a variance of 1 by adopting a data preprocessing method which is the same as that in an offline modeling stage, and the normalization method comprises the following steps: x is the number ofi *＝(xi-minxi)/(maxxi-minxi) Wherein x isiAnd xi *Respectively representing the values before and after normalization, maxxiAnd minxiRespectively representing the maximum and minimum values in the sample data;
2) and projecting the online data to the direction of each kernel with the maximum model entropy by using the model established offline, wherein the projection of the ith model can be represented as:
T(i)＝K(i)E(i)
respectively projecting different models, and respectively extracting principal component parts of the models;
3) after online data is projected by using a model of a nuclear entropy component analysis method, the obtained projection part is converted into a probability form by using Bayesian inference, and the probability form is as follows:
and the probability in the denominator can be calculated by the following two equations:
n, F respectively indicate normal and fault conditions, p (N), p (F) indicate their corresponding probability values, which can be calculated from a given confidence level, and other probability forms can be calculated exponentially from the ratio of its control limit to its actual value.
4) The multiple models in these probability forms are combined by weights using ensemble learning, and the statistical indexes after ensemble are as follows:
5) and 4) comparing the calculated statistical index with the confidence level to judge whether a fault occurs, if the statistical index is greater than the confidence level, the fault occurs, otherwise, the working condition is normal, and the fault is not detected.
Examples
China is a country with shortage of resources and energy, and the dependence of the paper making industry on imported fiber raw materials is as high as more than 40%. For chemi-mechanical pulping, the pulping process is the main process of fiber formation. The pulping refiner is a closed reflecting environment, and pulping is realized through a series of complex physical and chemical processes in the pulping refiner. The data generated in the pulping process has the characteristics of nonlinearity and the like. Based on the method, the fault detection method provided by the invention has adaptability to diagnosis of faults in the pulping process. The effectiveness of the invention is described below in connection with the paper industry of the kingdom (Jiangsu) GmbH (short for the paper industry of the kingdom east).
The following detailed description of the implementation steps of the present invention is provided in conjunction with the specific process:
the method comprises the following steps: and (3) establishing a model in an off-line mode, and establishing off-line models of different nuclear parameters by using data under normal working conditions through a nuclear entropy analysis method.
1) Process data are collected for data affecting fiber morphology distribution during papermaking, including 59 variables, such as pulp feed concentration, pulp exit freeness, mill power, dilution water volume, and model pressure. Preprocessing the related variable, normalizing the sample data, and expressing the acquired data as X ═ X1,x2,…,xN]T∈RN×mWhere m represents the number of process variables, N represents the number of samples, xi∈RmI-1, …, N corresponding to the ith sample, and then de-dimensionalizing the data to 0-mean, variance 1 data. The normalization method comprises the following steps: x is the number ofi *＝(xi-minxi)/(maxxi-minxi) Wherein x isiAnd xi *Respectively representing the values before and after normalization, maxxiAnd minxiRespectively representing the maximum and minimum values in the sample data;
2) preprocessing data under normal production conditions in a section of pulping process, and establishing offline models with different nuclear parameters by a nuclear entropy analysis method; the entropy estimation can be expressed as
Wherein,representing the entropy estimation, K is the kernel matrix, 1 is the column vector with elements 1, K (x)iAnd x) is a kernel function, the present invention employs a Gaussian kernel function, which is defined as follows:
the kernel matrix is subjected to eigen decomposition, in which case the entropy estimate is expressed as:
wherein λ represents the decomposed feature value, e represents the corresponding feature vector, then the feature vector corresponding to the value with the maximum entropy is the projection vector thereof, and the projected nonlinear part can be represented as:
T＝KE；
wherein T is the projected nonlinear part, and E is a projection matrix;
3) and determining the control limit corresponding to each submodel.
Step two: online detection, namely projecting online data of the pulping process to the kernel direction with the maximum entropy of each model by using the model established offline; then converting the models into a probability form by using Bayesian inference; and finally, combining a plurality of models in the probability forms by utilizing ensemble learning, detecting data in the actual production process by utilizing the first step, and judging whether a fault occurs. The specific implementation process comprises the following steps:
1) and processing the data to be subjected to online detection into data with a mean value of 0 and a variance of 1 by adopting the same data preprocessing method as the offline modeling stage. The normalization method comprises the following steps: x is the number ofi *＝(xi-minxi)/(maxxi-minxi) Wherein x isiAnd xi *Respectively representing the values before and after normalization, maxxiAnd minxiRespectively representing the maximum and minimum values in the sample data;
2) and projecting the online data to the kernel direction with the maximum entropy of each model by using the model established offline: wherein the projection of the ith model can be represented as:
T(i)＝K(i)E(i)
and respectively projecting different models, and respectively extracting principal component parts of the models.
3) After online data is projected by using a model of a nuclear entropy component analysis method, the obtained projection part is converted into a probability form by using Bayesian inference, and the probability form is as follows:
and the probability in the denominator can be calculated by the following two equations:
n, F respectively indicate normal and fault conditions, p (N), p (F) indicate their corresponding probability values, which can be calculated from a given confidence level, and other probability forms can be calculated exponentially from the ratio of its control limit to its actual value.
4) The multiple models in these probability forms are combined by weights using ensemble learning, and the statistical indexes after ensemble are as follows:
5) and 4) comparing the calculated statistical index with the confidence level to judge whether a fault occurs, if the statistical index is greater than the confidence level, the fault occurs, otherwise, the working condition is normal, and the fault is not detected.
The above embodiments are provided to illustrate the effectiveness of the present invention, and the use of the present invention is not limited to the above examples, and any modifications and changes made within the spirit of the present invention and the scope of the claims fall within the scope of the present invention.
Claims (4)
1. A nonlinear fault detection method based on improved kernel entropy component analysis is characterized by comprising the following steps:
the method comprises the following steps: establishing a model in an off-line mode, namely establishing off-line models of different nuclear parameters by using data under normal working conditions through a nuclear entropy component analysis method;
step two: online detection, namely projecting online data to the core direction with the maximum Renyi entropy of each model by using an offline model; then converting the probability form by Bayesian inference; finally, combining a plurality of models in the probability forms by utilizing ensemble learning, detecting data in the actual production process by utilizing the steps, and judging whether a fault occurs;
the off-line modeling process of the step one is as follows:
1) collecting data in industrial production process, preprocessing related variables, normalizing sample data, and expressing the collected data as X ═ X1,x2,…,xN]T∈RN×mWhere m represents the number of process variables, N represents the number of samples, xi∈RmI is 1, …, N corresponds to the ith sample, and then the data is de-dimensioned and processed into 0-mean data with variance of 1; the normalization method of the sample data comprises the following steps: x is the number ofi *＝(xi-minxi)/(maxxi-minxi) Wherein x isiAnd xi *Respectively representing the values before and after normalization, maxxiAnd minxiRespectively representing the maximum and minimum values in the sample data;
2) preprocessing data under normal working conditions and then establishing offline models of different nuclear parameters by a nuclear entropy component analysis method; the entropy estimate can be expressed as:
wherein,representing the entropy estimation, K is the kernel matrix, 1 is the column vector with elements 1, K (x)iAnd x) is a kernel function, a Gaussian kernel function is adopted, and the definition is as follows:
the kernel matrix is subjected to eigen decomposition, in which case the entropy estimate is expressed as:
wherein λ represents the decomposed feature value, e represents the corresponding feature vector, then the feature vector corresponding to the value with the maximum entropy is the projection vector thereof, and the projected nonlinear part is represented as:
T＝KE；
wherein T is the projected nonlinear part, and E is a projection matrix;
3) determining a control limit corresponding to each sub-model;
the online detection process of the second step is as follows:
1) the data to be subjected to online detection is processed into data with a mean value of 0 and a variance of 1 by adopting a data preprocessing method which is the same as that in an offline modeling stage, and the normalization method comprises the following steps: x is the number ofi *＝(xi-minxi)/(maxxi-minxi) Wherein x isiAnd xi *Respectively representing the values before and after normalization, maxxiAnd minxiRespectively representing the maximum and minimum values in the sample data;
2) and projecting the online data to the direction of each kernel with the maximum model entropy by using the model established offline, wherein the projection of the ith model can be represented as:
T(i)＝K(i)E(i)
respectively projecting different models, and respectively extracting principal component parts of the models;
3) after online data is projected by using a model of a nuclear entropy component analysis method, the obtained projection part is converted into a probability form by using Bayesian inference, and the probability form is as follows:
and the probability in the denominator can be calculated by the following two equations:
n, F respectively representing normal and fault conditions, p (N), p (F) representing their corresponding probability values, which can be calculated by a given confidence level, and other probability forms can be calculated according to the exponential form of the ratio of its control limit to its actual value;
4) the multiple models in these probability forms are combined by weights using ensemble learning, and the statistical indexes after ensemble are as follows:
5) and 4) comparing the calculated statistical index with the confidence level to judge whether a fault occurs, if the statistical index is greater than the confidence level, the fault occurs, otherwise, the working condition is normal, and the fault is not detected.
2. The method of claim 1, wherein the data of the industrial process is characterized by non-linearity.
3. A method according to claim 1, characterized in that the industrial malfunction is a refiner beating process malfunction.
4. A method according to any of claims 1-2 for fault diagnosis in the refining process of refiners.
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| CN109682976B (en) * | 2019-02-28 | 2020-05-22 | 东北大学 | Continuous blood glucose monitoring sensor online fault detection method based on multi-model fusion |
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| CN113688895A (en) * | 2021-08-19 | 2021-11-23 | 广东工业大学 | Method and system for detecting abnormal firing zone of ceramic roller kiln based on simplified KECA |
| CN115758284B (en) * | 2022-11-14 | 2023-05-16 | 南京工业大学 | Photovoltaic hot spot fault detection method and system based on fusion kernel entropy and information gain |
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