CN115840419A - Complex industrial process monitoring method and system based on cloud edge collaborative dictionary learning - Google Patents
Complex industrial process monitoring method and system based on cloud edge collaborative dictionary learning Download PDFInfo
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Abstract
The invention discloses a complex industrial process monitoring method and a system based on cloud edge collaborative dictionary learning, wherein the method comprises the following steps: the cloud end establishes a monitoring model for the industrial process by using a label consistent dictionary learning method, simplifies the established monitoring model, and sends the simplified monitoring model to the edge end; the edge terminal uses the simplified monitoring model to perform online monitoring on the industrial process, including fault detection and working condition identification, and judges whether the simplified monitoring model has model mismatch or not; and when the simplified monitoring models are mismatched, triggering the cloud to update the monitoring models and the corresponding simplified monitoring models. According to the method, the industrial process monitoring model is kept to be always matched with the process data through cloud edge cooperation, so that the industrial process is accurately and efficiently monitored, and the stable and healthy operation of the industrial process is guaranteed.
Description
Technical Field
The invention belongs to the technical field of process monitoring, and particularly relates to a complex industrial process monitoring method and system based on cloud edge collaborative dictionary learning, which can be applied to monitoring a multi-working-condition time-varying industrial process.
Background
With the development of industrial production technology, modern industrial processes are more and more complex, and the production scale is continuously increased. This results in any minor failure in the industrial process causing immeasurable losses to the overall system. In addition, there are frequent duty shifts in industrial systems due to variations in raw materials, settings of parameters, and market demands. These variations in conditions cause industrial processes to typically operate in different modes of operation. The strategy of adjustment is different for different modes, and the wrong way may reduce the performance of the system and even cause great economic loss. Therefore, it is very important to provide advanced process monitoring methods for fault detection and condition identification of complex industrial processes.
The data-driven process monitoring method uses data acquired in an industrial process to establish a mathematical model, and the model is simple and strong in universality, so that the method is widely researched and applied. Typical data-driven process monitoring methods are Multivariate Statistical Process Monitoring (MSPM) methods such as PCA and PLS. With the development of artificial intelligence, some machine learning methods are also applied to process monitoring, such as SVM-based methods and bayesian analysis methods.
Dictionary learning is a powerful machine learning method. The goal of dictionary learning is to train out a dictionary with data representation capabilities. Dictionaries are composed of atoms, and a small number of atoms are used to linearly represent a piece of data. However, the traditional dictionary learning can not be applied to multi-modal data, namely, the learned dictionary has no discriminability. To address this problem, jiang et al propose an LC-KSVD method that can jointly learn a single overcomplete dictionary and an optimal linear classifier. This provides an effective reference for fault detection and condition identification of an industrial process using a model.
Conventional process monitoring methods tend to include two phases, offline learning and online monitoring. And training a corresponding model by using the collected historical data of the industrial process in an off-line learning stage. The model is deployed into an edge device near the industrial site. In the on-line monitoring stage, the edge device collects real-time data of the industrial process and monitors the industrial process based on the deployed model. However, complex industrial processes often have a time-varying phenomenon, that is, the distribution, characteristics, and the like of data change as the process progresses. This can result in a model trained based on historical data not always matching the current real-time data, resulting in monitoring failures. The most effective way to solve model mismatch is to update the model using real-time data, but most edge devices currently do not have the capability to update the model. The development of the cloud edge cooperation technology provides a new idea for solving the problem. And the edge end monitors the acquired real-time data and uploads the data to the cloud. The cloud stores a large amount of data of the industrial process, and when the model is mismatched, the cloud updates the training model by using the powerful computing capacity of the training model and sends the model to the edge end, so that the model of the edge end can be matched with the current data all the time.
Disclosure of Invention
The invention provides a complex industrial process monitoring method and system based on cloud-edge collaborative dictionary learning, which can be used for keeping an industrial process monitoring model to be matched with process data all the time through cloud-edge collaboration, realizing accurate and efficient monitoring on an industrial process and ensuring stable and healthy operation of the industrial process.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a complex industrial process monitoring method based on cloud edge collaborative dictionary learning comprises the following steps:
the cloud establishes a monitoring model for the industrial process by using a label consistent dictionary learning method, simplifies the established monitoring model, and issues the simplified monitoring model to an edge terminal;
the edge terminal uses the simplified monitoring model to perform online monitoring on the industrial process, including fault detection and working condition identification, and judges whether the simplified monitoring model has model mismatch or not; and when the simplified monitoring models are mismatched, triggering the cloud to update the monitoring models and the corresponding simplified monitoring models.
In a more preferred technical scheme, the method for establishing the monitoring model for the industrial process by using the label consistent dictionary learning method comprises the following steps:
step a1, acquiring historical monitoring data Y = [ Y ] of industrial process 1 ,y 2 ,…,y M ]∈R m×M And the corresponding label matrix H = [ H ] 1 ,h 2 ,…,h M ]∈R n×M M represents the number of monitoring data samples, and M represents the dimension of each monitoring data sample; n represents n working conditions of the monitored data samples, namely the label of each monitored data sample is a column vector with n dimensionality, if the monitored data sample belongs to the j working condition, the j element of the label of the monitored data sample is 1, and the other elements are 0;
step a2, constructing the following dictionary learning model:
wherein D = [ D ] 1 ,d 2 ,…d K ]∈R m×K To be a complete dictionary for learning, d 1 ,d 2 ,…d K K atoms in a complete dictionary D;
Q＝[q 1 ,q 2 ,…,q M ]∈R K×M is a discrimination matrix in which column vectors
Denotes q i The discrimination matrix is determined by the class label of the monitored data sample and the class label of the atom in the dictionary, when the monitored data sample y i And dictionary atom d k When the two-dimensional images belong to the same category,
otherwise->
A∈R K×K Representing a linear transformation matrix by linear transformation Ax to encode the original sparse codex to feature space R with discriminant K ；
W∈R n×K Representing a linear classifier, and reconstructing a class label h of the data through Wx;
X＝[x 1 ,x 2 ,…x M ]∈R K×M is a sparse coding matrix, x i Is a monitoring data sample y i Sparse coding using a complete dictionary representation, i =1,2, ·, M;
Step a3, setting intermediate variables
And &>
The dictionary learning model of equation (0-1) is simplified to the following equation:
step a4, solving the dictionary learning optimization function shown in the formula (0-2) by using a K-SVD method to obtain an intermediate variable D c Decomposition of D c And for obtaining D and W respectively 2 Normalizing the norm to obtain a final complete dictionary D and a classifier W for identifying the working condition;
and a5, storing the complete dictionary D and the classifier W as high-precision industrial process monitoring models in a cloud.
In a more preferred technical scheme, the method for simplifying the established monitoring model comprises the following steps:
step b1, counting the using times of each atom in the complete dictionary D in the historical monitoring data Y, and recording the kth atom D k Is used for a number of times of
Step b2, judging whether the using times of each dictionary atom is less than a preset threshold value tau: if yes, deleting the dictionary atom from the complete dictionary D, and deleting the column corresponding to the dictionary atom in the classifier W from the classifier W; processing all dictionary atoms according to the step b2 to obtain a simplified dictionary D sim And a classifier W sim ；
Step b3, using the simplified dictionary D sim Representing historical monitoring data to obtain a sparse coding matrix X sim Comprises the following steps:
step b4, according to the simplified dictionary D sim Calculating the reconstruction error of each monitoring data sample, and calculating the control limit R of fault detection by adopting a nuclear density estimation method tr ；
Step b5, simplifying the dictionary D sim Sorter W sim And a control limit D sim The model is stored at the edge as a simplified high-speed industrial process monitoring model.
In a more preferred technical solution, the method for presetting the threshold τ is as follows:
in the formula, ω represents a weight coefficient, M represents the number of samples of the historical monitoring data, sparsity represents the sparsity when sparsely representing the monitoring data, and K represents the number of atoms in the complete dictionary.
In a more preferred embodiment, the calculation formula of the reconstruction error of each historical monitoring data sample in step b4 is:
the probability density of the reconstruction error is calculated according to the following formula:
in the formula, M represents the number of training samples, f (R) is a probability density function taking a reconstruction error as an independent variable R, and h is a bandwidth; k (x) is a kernel function which requires nonnegative and has an integral of 1,R i Representing a reconstruction error of an ith historical monitoring data sample;
and after the probability density function of the reconstruction error is obtained, calculating the control limit of the reconstruction error according to a preset confidence coefficient alpha.
In a more preferred technical scheme, the method for the edge terminal to perform online monitoring on the industrial process by using the simplified monitoring model comprises the following steps:
step c1, when on-line monitoring data y is received, using simplified dictionary D sim Sparse coding x to compute y new ：
Step c2, calculating a reconstruction value of the simplified dictionary to the online data:
step c3, according to the reconstructed value of the online data
Calculating the reconstruction error RE new ：
Step c4, solving the obtained reconstruction error RE new And a control limit R tr Comparison, if RE new Greater than R tr Judging that the on-line monitoring data y is fault data, namely that the current industrial process has a fault; otherwise, the online monitoring data y is normal data;
step c5, if the line monitoring data y is normal data, according to the simplified classifier W sim And sparse coding x new Calculating a label vector of the online monitoring data y:
label＝W sim x new (0-10)
and c6, selecting the maximum element value in the label vector label vector calculated by the edge end, and determining the position of the element as the current working condition of the industrial process.
In a more preferred technical scheme, after the label vector label of the online monitoring data is obtained in step c5, the main body of the working condition identification is determined by calculating the label quality, and then the determined main body of the working condition identification is used for the working condition identification, specifically:
step c6.1, sorting all elements in the label vector label in descending order, l 1 Representing the element ordering first, i.e. the largest element in label,/ 2 Representing the element ordering the second bit, the label quality q is calculated as:
q＝||l 1 |-|l 2 || (0-11)
step c6.2, judging whether the quality of the label is greater than a preset threshold value sigma, if so, determining that the quality of the label is qualified, otherwise, determining that the quality of the label is unqualified;
step c6.3, if the label quality is judged to be qualified in the step c6.2, directly using the maximum element value in the label vector calculated by the edge end at the edge end, and determining the position of the element as the current working condition of the industrial process; if the label quality is judged to be unqualified in the step c6.2, uploading the online monitoring data y to a cloud end, and executing: and calculating sparse coding of y by using a complete dictionary D, calculating a tag vector by using a classifier W, selecting a maximum element value in the tag vector calculated by the cloud, and determining the position of the element as the current working condition of the industrial process.
In a more preferred technical scheme, the simplified method for judging whether the model mismatch occurs in the monitoring model is as follows: and judging whether the number of the unqualified labels is greater than a preset unqualified label number threshold value mu, and if so, determining that the monitoring model with the simplified edge end is mismatched.
A complex industrial process monitoring system based on cloud edge collaborative dictionary learning comprises a cloud end and an edge end;
the cloud establishes a monitoring model for the industrial process by using a label consistent dictionary learning method, simplifies the established monitoring model, and issues the simplified monitoring model to an edge terminal;
the edge terminal uses a simplified monitoring model to perform online monitoring on the industrial process, including fault detection and working condition identification, and judges whether the simplified monitoring model has model mismatch or not; and when the simplified monitoring models are mismatched, triggering the cloud to update the monitoring models and the corresponding simplified monitoring models.
Advantageous effects
The method is based on a cloud-edge cooperative framework, the cloud end is responsible for training, updating and simplifying a dictionary learning model and storing process data, the edge end is responsible for monitoring real-time process data including fault detection and working condition recognition, and whether the model is matched with the current data or not is judged according to the quality of a label given by the model. And when the model is mismatched, triggering the cloud end to update the model, and sending the updated model to the edge end. The method and the device realize the on-line inference of the edge end and the updating of the cloud model, solve the problem that the model cannot be updated due to model mismatching caused by time change of the industrial process, improve the monitoring accuracy of the operation state of the industrial process and ensure the safe and stable operation of the industrial production process.
Drawings
FIG. 1 is an overall block diagram of the method and system described in embodiments of the present application.
Detailed Description
The following describes embodiments of the present invention in detail, which are developed based on the technical solutions of the present invention, and give detailed implementation manners and specific operation procedures to further explain the technical solutions of the present invention.
The complex industrial process monitoring method and system based on cloud edge collaborative dictionary learning comprise two parts of establishment of a dictionary learning model and online monitoring. In the first part, the cloud establishes a monitoring model for the industrial process by using a label consistent dictionary learning method, simplifies the established monitoring model, and issues the simplified monitoring model to the edge terminal. In the second part, the edge terminal continuously uploads the online monitoring data of the industrial process to the cloud, and uses the simplified monitoring model to perform online monitoring on the industrial process, including fault detection and working condition identification, and judges whether the simplified monitoring model has model mismatch or not; and when the simplified monitoring models are mismatched, triggering the cloud to update the monitoring models and the corresponding simplified monitoring models. The overall framework is shown in fig. 1.
1. Cloud model training and simplification
1. The cloud uses a label-consistent dictionary learning model to model the industrial process.
Step a1, acquiring historical monitoring data Y = [ Y ] of industrial process 1 ,y 2 ,…,y M ]∈R m×M And the corresponding label matrix H = [ H ] 1 ,h 2 ,…,h M ]∈R n×M M represents the number of monitoring data samples, and M represents the dimension of each monitoring data sample; n represents n working conditions of the monitored data samples, namely the label of each monitored data sample is a column vector with n dimensionality, if the monitored data sample belongs to the j working condition, the j element of the label of the monitored data sample is 1, and the other elements are 0;
step a2, constructing a dictionary learning model:
the basic principle of dictionary learning is to represent data linearly sparsely using a small number of dictionary atoms. Dictionary learning can learn a dictionary D = [ D = 1 ,d 2 ,…d K ]∈R m×K Where K represents the number of atoms in the dictionary. For ease of calculation, units are made for each atomThe chemical treatment is carried out on the mixture,
to achieve dictionary representation of data, there is Y ≈ DX where X = [ X ] 1 ,x 2 ,…x M ]∈R K×M Is a sparse coding matrix, X is sparse since only a few atoms are used in the data representation. In order to train out a dictionary and a sparse coding matrix in a dataset, dictionary learning can be transformed into the following optimization problem:
in order to make the dictionary have discriminability, an optimization term is added on the basis of the formula (1), and the following optimization function is obtained:
wherein Q = [ Q ] 1 ,q 2 ,…,q M ]∈R K×M Known as discriminant sparse coding. This puts requirements on the class characteristics of the dictionary atoms. I.e. when dictionary atoms and data y i When belonging to the same class, q i Is 1, whereas if the atom is associated with data y i Not belonging to the same class, q i The corresponding element is 0. This allows the dictionary to try to use the same class of atoms to represent this class of data.
In order to make dictionary learning have classification effect while data is represented, a linear classifier is used to reconstruct class labels of data, and the following optimization function is obtained:
the optimization function model of the label-consistent dictionary learning is shown as formula (3). The method enables the model to have the capability of data representation and classification at the same time, so that the method is very suitable for solving the problems of fault detection and working condition identification of the industrial process.
After obtaining the optimization function, variables such as a dictionary and a classifier need to be optimized, and therefore, equation (3) can be rewritten as:
the above formula (4) is the dictionary learning model established by the invention.
Step a3, simplifying a dictionary learning model: in order to optimize variables such as dictionaries, classifiers and the like, intermediate variables are set
And &>
The dictionary learning model of equation (4) is simplified to the following equation:
in the step a4, the formula (5) is a basic dictionary learning optimization function, and a K-SVD method can be used for solving. After the optimization, D is obtained c D is c After decomposition D and W can be obtained. But since the joint is used in the K-SVD algorithm 2 Norm normalization, i.e.
Therefore, l is required for D and W respectively after decomposition 2 Norm normalization, which is:
and a5, storing the complete dictionary D and the classifier W which are obtained by standardization in the step a4 as high-precision industrial process monitoring models in a cloud.
2. And simplifying the established high-precision industrial process monitoring model.
Since the computation power and computation resources of the edge are often limited, the model of the edge is usually as simple as possible to enhance the real-time performance of the edge inference. But simple models may reduce the accuracy of edge-end inference. Therefore, a dictionary D and a classifier W are trained at the cloud end and are simplified to obtain a simplified model D sim And W sim And the original model is reserved at the cloud end, and the simplified model is issued to the edge end. When the edge end infers inaccuracy, the high-precision model of the cloud end is used for inferring, and the accuracy of inference is guaranteed through cooperation of the two sides.
B1, training D by using the training data Y, counting the use times of each atom in the complete dictionary D in the historical monitoring data Y, and recording the kth atom D k The number of uses of
Step b2, judging whether the using times of each dictionary atom is less than a preset threshold value tau: if yes, deleting the dictionary atom from the complete dictionary D, and deleting the column corresponding to the dictionary atom in the classifier W from the classifier W; processing all dictionary atoms according to the step b2 to obtain a simplified dictionary D sim And a classifier W sim ；
The preset method of the preset threshold tau comprises the following steps:
in the formula, omega represents a weight coefficient, M represents the number of samples of historical monitoring data, sparsity represents the sparsity when the monitoring data are sparsely represented, the sparsity is set in a K-SVD algorithm used when a model is trained, and K represents the number of atoms in a complete dictionary;
the threshold τ in equation (7) has an influence on the size of the simplified model. If τ is larger, more atoms are deleted, D sim Will be smaller, otherwise D sim May be relatively large. D sim The magnitude of (a) has a certain influence on the monitoring effect of the edge end, so that an appropriate τ needs to be found by adjusting ω, so that the edge end has a reliable monitoring effect while the calculation time is saved by using a simplified model.
Step b3, obtaining a simplified dictionary D sim Thereafter, the simplified dictionary D is used sim Representing historical monitoring data to obtain a sparse coding matrix X sim Comprises the following steps:
specifically, the sparse coding matrix of equation (8) can be solved by using a commonly used OMP method.
Step b4, obtaining a sparse coding matrix X sim Then, according to the simplified dictionary D sim Calculating the reconstruction error of each monitoring data sample, and calculating the control limit R of fault detection by adopting a kernel density estimation method tr ；
The calculation formula of the reconstruction error of each historical monitoring data sample is as follows:
R i denotes the reconstruction error of the ith data, y i Indicating the ith data in the historical monitoring data Y,
represents X sim I.e. sparse coding of the ith data.
After the reconstruction errors of all the monitoring data samples in the Y are calculated, a Kernel Density Estimation (KDE) method is used for calculating a control limit R of the reconstruction errors tr . The present invention uses a univariate kernel estimator, which is defined as follows:
in the formula, M represents the number of training samples, f (R) is a probability density function taking a reconstruction error as an independent variable R, and h is a bandwidth; k (x) is a kernel function which requires non-negative and has an integral of 1,R i Representing a reconstruction error of an ith historical monitoring data sample;
after the probability density function of the reconstruction error is obtained, the control limit of the reconstruction error is calculated according to the preset confidence coefficient alpha, namely, the value of the probability density function under the preset confidence coefficient is used as the control limit.
Step b5, simplifying the dictionary D sim Classifier W sim And a control limit D sim The model is stored at the edge as a simplified high-speed industrial process monitoring model.
2. Edge terminal on-line monitoring and model mismatch judgment
After the edge terminal is deployed with the simplified high-speed industrial process monitoring model, a simplified dictionary D is obtained sim Simplified classifier W sim And a control limit D sim . Then, when the edge terminal receives the online monitoring data of the industrial process, the invention carries out fault detection and working condition identification on the monitoring data, and judges whether the model mismatch occurs according to the label quality.
1. The edge terminal uses the simplified model to perform online monitoring on the industrial process.
Step c1, when the online monitoring data y is received, using a simplified dictionary D sim Sparse coding x to compute y new ：
Step c2, calculating a reconstruction value of the simplified dictionary to the online data:
step c3, according to the reconstructed value of the online data
Calculating the reconstruction error RE new ：
Step c4, solving the obtained reconstruction error RE new And a control limit R tr Comparison, if RE new Greater than R tr Judging that the on-line monitoring data y is fault data, namely that the current industrial process has a fault; otherwise, the online monitoring data y is normal data;
step c5, if the line monitoring data y is normal data, according to the simplified classifier W sim And sparse coding x new Calculating a label vector of the online monitoring data y:
label＝W sim x new (15)
and c6, selecting the maximum element value in the label vector label vector calculated by the edge end, and determining the position of the element as the current working condition of the industrial process.
In a more preferred technical solution, the step c6 is replaced by determining a main body for identifying the working condition by calculating the label quality, and then identifying the working condition by the determined main body for identifying the working condition, specifically:
step c6.1, sorting all elements in the label vector label in descending order, l 1 Indicating the element that is first in the order, i.e. the largest element in the label,/ 2 Representing the element ordering the second bit, the label quality q is calculated as:
q＝||l 1 |-|l 2 || (16)
if the label is normal, the value of q is large, and when the quality of the label is poor, l is large 1 And l 2 Will be relatively close, resulting in a smaller value of q.
Step c6.2, setting a threshold sigma of the quality q of the label, wherein the quality of the label is qualified when q is larger than sigma, and the quality of the label is unqualified otherwise;
step c6.3, if the label quality is judged to be qualified in the step c6.2, directly using the maximum element value in the label vector calculated by the edge end at the edge end, and determining the position of the element as the current working condition of the industrial process; if the label quality is judged to be unqualified in the step c6.2, uploading the online monitoring data y to a cloud end, and executing in the cloud end: and calculating sparse coding of y by using a complete dictionary D, calculating a tag vector by using a classifier W, selecting a maximum element value in the tag vector calculated by the cloud, and determining the position of the element as the current working condition of the industrial process.
2. Simplified monitoring model mismatch determination
When the label consistent dictionary learning is optimized, the dictionary and the classifier are jointly optimized, and the joint optimization ensures that the characteristics extracted by the model meet the requirements of data representation and working condition identification. When the quality of the label is poor to cause failure of the working condition identification, the data representation capability reflecting the model is also poor, namely, model mismatch occurs. It is reasonable to judge whether model mismatch occurs by label quality.
Therefore, the tag quality judgment in the step c6.2 can be counted, if the number of the unqualified tags is greater than the preset unqualified tag number threshold value mu, the simplified industrial process monitoring model at the edge end is considered to be mismatched, and the edge end triggers the cloud to update the monitoring model and the corresponding simplified monitoring model, namely the cloud is triggered to reestablish, simplify and issue the monitoring model according to the process by utilizing a plurality of current recent historical monitoring data.
The invention also provides a complex industrial process monitoring system based on cloud-edge collaborative dictionary learning, which corresponds to the complex industrial process monitoring method and comprises a cloud end and an edge end;
the cloud establishes a monitoring model for the industrial process by using a label consistent dictionary learning method, simplifies the established monitoring model, and issues the simplified monitoring model to an edge terminal;
the edge terminal uses a simplified monitoring model to perform online monitoring on the industrial process, including fault detection and working condition identification, and judges whether the simplified monitoring model has model mismatch or not; and when the simplified monitoring models are mismatched, triggering the cloud to update the monitoring models and the corresponding simplified monitoring models.
The above embodiments are preferred embodiments of the present application, and those skilled in the art can make various changes or modifications without departing from the general concept of the present application, and such changes or modifications should fall within the scope of the claims of the present application.
Claims (9)
1. A complex industrial process monitoring method based on cloud edge collaborative dictionary learning is characterized by comprising the following steps:
the cloud establishes a monitoring model for the industrial process by using a label consistent dictionary learning method, simplifies the established monitoring model, and issues the simplified monitoring model to an edge terminal;
the edge terminal uses the simplified monitoring model to perform online monitoring on the industrial process, including fault detection and working condition identification, and judges whether the simplified monitoring model has model mismatch or not; and when the simplified monitoring models are mismatched, triggering the cloud to update the monitoring models and the corresponding simplified monitoring models.
2. The method of claim 1, wherein the method of building a monitoring model for an industrial process using a label-consistent dictionary learning method is:
step a1, acquiring historical monitoring data Y = [ Y ] of industrial process 1 ,y 2 ,…,y M ]∈R m×M And the corresponding label matrix H = [ H ] 1 ,h 2 ,…,h M ]∈R n×M M represents the number of monitoring data samples, and M represents the dimension of each monitoring data sample; n represents n working conditions of the monitoring data samples, namely the label of each monitoring data sample is a column vector with n dimensionality, if the monitoring data sample belongs to the j working condition, the j element of the label of the monitoring data sample is 1, and the other elements are 0;
step a2, constructing the following dictionary learning model:
wherein D = [ D ] 1 ,d 2 ,…d K ]∈R m×K To be a complete dictionary for learning, d 1 ,d 2 ,…d K K atoms in a complete dictionary D;
Q＝[q 1 ,q 2 ,…,q M ]∈R K×M is a discrimination matrix in which column vectors
Denotes q i The discrimination matrix is determined by the class label of the monitored data sample and the class label of the atom in the dictionary, when the monitored data sample y i And dictionary atom d k When the two-dimensional images belong to the same category,
otherwise
A∈R K×K Representing a linear transformation matrix by linear transformation Ax transforming the original sparse code x into a discriminative eigenspace R K ；
W∈R n×K Representing a linear classifier, and reconstructing a class label h of the data through Wx;
X＝[x 1 ,x 2 ,…x M ]∈R K×M is a sparse coding matrix, x i Is monitoring a data sample y i Sparse coding using a perfect dictionary representation, i =1,2, · M;
step a3, setting intermediate variables
And
the dictionary learning model of equation (0-1) is simplified to the following equation:
step a4, solving the dictionary learning optimization function shown in the formula (0-2) by using a K-SVD method to obtain an intermediate variable D c Decomposition of D c And for obtaining D and W respectively 2 Normalizing the norm to obtain a final complete dictionary D and a classifier W for identifying the working condition;
and a5, storing the complete dictionary D and the classifier W as high-precision industrial process monitoring models in a cloud.
3. The method of claim 2, wherein the method for simplifying the established monitoring model comprises:
step b1, counting the using times of each atom in the complete dictionary D in the historical monitoring data Y, and recording the kth atom D k The number of uses of
Step b2, judging whether the using times of each dictionary atom is less than a preset threshold value tau: if yes, deleting the dictionary atom from the complete dictionary D, and classifying the dictionary atom in the classifier WThe corresponding column is deleted from the classifier W; processing all dictionary atoms according to the step b2 to obtain a simplified dictionary D sim And a classifier W sim ；
Step b3, using the simplified dictionary D sim Representing historical monitoring data to obtain a sparse coding matrix X sim Comprises the following steps:
step b4, according to the simplified dictionary D sim Calculating the reconstruction error of each monitoring data sample, and calculating the control limit R of fault detection by adopting a nuclear density estimation method tr ；
Step b5, simplified dictionary D sim Sorter W sim And a control limit D sim The model is stored at the edge as a simplified high-speed industrial process monitoring model.
4. The method of claim 3, wherein the threshold τ is preset by:
in the formula, ω represents a weight coefficient, M represents the number of samples of the historical monitoring data, sparsity represents the sparsity when sparsely representing the monitoring data, and K represents the number of atoms in the complete dictionary.
5. The method of claim 3, wherein the reconstruction error of each historical monitoring data sample in step b4 is calculated by:
the probability density of the reconstruction error is calculated according to the following formula:
in the formula, M represents the number of training samples, f (R) is a probability density function taking a reconstruction error as an independent variable R, and h is a bandwidth; k (x) is a kernel function which requires non-negative and has an integral of 1,R i Representing a reconstruction error of an ith historical monitoring data sample;
and after the probability density function of the reconstruction error is obtained, calculating the control limit of the reconstruction error according to a preset confidence coefficient alpha.
6. The method of claim 1, wherein the method for the edge terminal to perform online monitoring on the industrial process by using the simplified monitoring model comprises:
step c1, when on-line monitoring data y is received, using simplified dictionary D sim Sparse coding x to compute y new ：
Step c2, calculating a reconstruction value of the simplified dictionary to the online data:
step c3, according to the reconstructed value of the online data
Calculating the reconstruction error RE new ：
Step c4, solving the obtained reconstruction error RE new And controlLimit of R tr Comparison, if RE new Greater than R tr Judging that the online monitoring data y is fault data, namely that a fault occurs in the current industrial process; otherwise, the online monitoring data y is normal data;
step c5, if the line monitoring data y is normal data, according to the simplified classifier W sim And sparse coding x new Calculating a label vector of the online monitoring data y:
label＝W sim x new (0-10)
and c6, selecting the maximum element value in the label vector label vector calculated by the edge end, and determining the position of the element as the current working condition of the industrial process.
7. The method according to claim 6, wherein after the label vector label of the online monitoring data is obtained in step c5, the main body of the working condition identification is determined by calculating the label quality, and then the working condition identification is performed by the determined working condition identification main body, specifically:
step c6.1, sorting all elements in the label vector label in descending order, l 1 Representing the element ordering first, i.e. the largest element in label,/ 2 Representing the element ordering the second bit, the label quality q is calculated as:
q＝||l 1 |-|l 2 || (0-11)
step c6.2, judging whether the quality of the label is greater than a preset threshold value sigma, if so, determining that the quality of the label is qualified, otherwise, determining that the quality of the label is unqualified;
step c6.3, if the label quality is judged to be qualified in the step c6.2, directly using the maximum element value in the label vector calculated by the edge end at the edge end, and determining the position of the element as the current working condition of the industrial process; if the label quality is judged to be unqualified in the step c6.2, uploading the online monitoring data y to a cloud end, and executing: and calculating sparse coding of y by using a complete dictionary D, calculating a tag vector by using a classifier W, selecting a maximum element value in the tag vector calculated by the cloud, and determining the position of the element as the current working condition of the industrial process.
8. The method of claim 7, wherein the simplified monitoring model is determined by: and when the simplified monitoring model is deployed at the edge end and starts to monitor process data, calculating the label quality of each online data and accumulating the number of unqualified labels, judging whether the number of the unqualified labels is greater than a preset unqualified label number threshold value mu, and if so, determining that the simplified monitoring model at the edge end is mismatched.
9. A complex industrial process monitoring system based on cloud edge collaborative dictionary learning is characterized by comprising a cloud end and an edge end;
the cloud establishes a monitoring model for the industrial process by using a label consistent dictionary learning method, simplifies the established monitoring model, and issues the simplified monitoring model to an edge terminal;
the edge terminal uses a simplified monitoring model to perform online monitoring on the industrial process, including fault detection and working condition identification, and judges whether the simplified monitoring model has model mismatch or not; and when the simplified monitoring models are mismatched, triggering the cloud to update the monitoring models and the corresponding simplified monitoring models.
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