CN112650063A - Self-adaptive soft measurement method based on semi-supervised incremental Gaussian mixture regression - Google Patents
Self-adaptive soft measurement method based on semi-supervised incremental Gaussian mixture regression Download PDFInfo
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Abstract
The invention discloses a self-adaptive soft measurement method based on semi-supervised incremental Gaussian mixed regression, which comprises the steps of firstly using an incremental Gaussian mixed regression model, and carrying out prediction estimation on quality variables which are difficult to measure in real time in a time-varying industrial process by selecting a group of process variables which have relatively large correlation with key quality variables and are easy to measure as input of the model. In order to solve the influence of rare phenomena of labeled samples on the prediction accuracy of the model, which widely exist in the industrial process, the incremental Gaussian mixture regression model is expanded to a semi-supervised incremental Gaussian mixture regression model. The method can effectively face the nonlinear, non-Gaussian and time-varying characteristics in the actual industrial process, can also effectively solve the problem of inaccurate model parameter learning caused by rare labeled samples in the industrial process, relieves overfitting of the model to a certain extent, improves the model updating efficiency and achieves the aim of self-adaptive soft measurement for the key variable.
Description
Technical Field
The invention belongs to the field of prediction and control of industrial processes, and particularly relates to a self-adaptive soft measurement method based on semi-supervised incremental Gaussian mixed regression.
Background
In the actual industrial production process, more or less key process variables often cannot be detected on line, and in order to solve the problem, a mathematical model which takes the variables as input and the key process variables as output is constructed by acquiring the variables which are easy to detect in the process and according to a certain optimal standard side, so that the online estimation of the key process variables is realized, which is the common soft measurement modeling in the industrial process.
The development of the statistical process soft measurement modeling method has remarkable requirements on large-scale industrial data, wherein the Gaussian mixture regression model can well solve the nonlinear and non-Gaussian characteristics in the industrial process, and is widely applied to prediction of industrial quality variables. However, there are some problems with soft measurement modeling today. In most industrial processes, the physical and chemical characteristics of the process are constantly changed due to various factors such as change of process environment, aging of platform instruments and equipment, change of raw material feeding, degradation of catalyst activity and the like, so that the operation condition of the process is constantly changed. In order to correctly track the process state, the soft measurement model needs to be adaptively updated and corrected in time. Meanwhile, a large amount of industrial data is needed in the data-driven soft measurement modeling method, and the soft measurement modeling process always assumes that the acquired input samples and the acquired output samples are in one-to-one correspondence. However, in the actual industrial production process, due to the limitation of production environment and technical means, some key product quality variables can not be directly measured on site. Therefore, the data actually collected only has a small amount of labeled data, and most samples are unlabeled samples containing only auxiliary variables. The traditional soft measurement modeling method can only use the small part of labeled samples to model, and abandons a large amount of unlabeled samples. When a small amount of labeled samples are used for training a model, results of inaccurate model parameter training and poor model generalization capability can be caused, so that the prediction effect is difficult to guarantee, and meanwhile, a large amount of useful information contained in unlabeled samples can be wasted.
Therefore, the method aims to solve the defects of the soft measurement model in the analysis, namely, the method is used for solving the time-varying characteristic in the industrial process and fully utilizing the mass non-label data information in the production process. The method of the invention
Disclosure of Invention
Aiming at the problems in the prior art, the invention provides a self-adaptive soft measurement method based on a semi-supervised incremental Gaussian mixture regression model, which is expanded into the semi-supervised incremental Gaussian mixture regression model on the basis of the incremental Gaussian mixture regression model, so that the model can continuously learn new knowledge from new sample data mixed with labels and without labels, the previously learned knowledge can be stored, statistically equivalent components are fused into one component when the semi-supervised incremental Gaussian mixture regression model is updated, the compactness of the model is kept, and overfitting is avoided. Assuming that a linear relation exists between a process variable and a quality variable, learning probability density functions, regression relation coefficients and mixing coefficients of all components through an expectation-maximization (EM) algorithm, and selecting a model by using a Bayesian Information Criterion (BIC) effectively solves the problem of inaccurate model parameter learning caused by rare labeled samples in an industrial process.
The purpose of the invention is realized by the following technical scheme: a self-adaptive soft measurement method based on semi-supervised incremental Gaussian mixture regression specifically comprises the following steps:
(1) tagged data set of historical operating conditions in industrial processes
And unlabeled datasets
Forming an initial training data set, wherein l represents a label of the label, i represents an index of the labeled data set, and xiDenotes the ith sample, y, in the labeled datasetiRepresents a label, nlDenotes the number of samples of the tagged dataset, j denotes the index of the untagged dataset, u denotes the tag of the untagged, xjDenotes the jth sample, n, in the unlabeled datasetuRepresenting the number of samples of the unlabeled dataset;
(2) standardizing the initial training data set collected in the step (1) with the mean value of 0 and the variance of 1 to obtain a standardized data set
(3) Learning semi-supervised Gaussian mixture regression model parameters theta by adopting an EM algorithm in an iterative mode, wherein the semi-supervised Gaussian mixture regression model parameters theta comprise: prior probability alpha of kth component in semi-supervised Gaussian mixture regression modelkMean vector mu of kth component in semi-supervised Gaussian mixture regression modelkCovariance matrix sigma of kth component in semi-supervised Gaussian mixed regression modelkRegression coefficient omega of kth component in semi-supervised Gaussian mixture regression modelkRegression coefficient of kth component label in semi-supervised Gaussian mixture regression model
Measuring noise variance
The method specifically comprises the following substeps:
(3.1) obtaining the posterior probability distribution of the hidden variables of the labeled samples respectively by using linear Gaussian operation
And the hidden variable posterior probability distribution of unlabeled samples
Wherein z isiIs the hidden variable of the ith labeled sample, zjHidden variable for jth unlabeled sample, RikRepresenting a semi-supervised Gaussian mixture regression modelThe k component in the generation of the posterior probability, R, of the ith labeled samplejkRepresenting the posterior probability of the kth component in the semi-supervised Gaussian mixed regression model in generating the jth unlabeled sample; p represents the probability of the kth component from 0 to 1 in the semi-supervised gaussian mixture regression model,
represents the mean vector of the labeled samples in the kth component in the semi-supervised gaussian mixture regression model,
representing a covariance matrix of labeled samples in the kth component of the semi-supervised gaussian mixture regression model,
represents the mean vector of the k component without label in the semi-supervised Gaussian mixture regression model,
represents the unlabeled covariance matrix in the kth component of the semi-supervised gaussian mixture regression model,
representing a kth gaussian distribution based on the mean vector and the covariance matrix;
(3.2) posterior probability distribution of hidden variables obtained by the step (3.1)
And
to calculate a corresponding log-likelihood function, said log-likelihood function
Comprises the following steps:
wherein z represents an implicit variable of the sample,
maximizing log-likelihood functions for each semi-supervised Gaussian mixture regression model parameter
Wherein β is a lagrange multiplier;
estimating the updated value of the parameters of the semi-supervised Gaussian mixed regression model:
wherein the content of the first and second substances,
in order to be a set of regression coefficients,
is a set of hidden variable posterior probability distributions for labeled exemplars,
in the form of a matrix of tagged data sets,
i is 1 and dimension is nlThe vector of (a) is determined,
(3.3) calculating a normalized data set based on the updated values of the parameters of the semi-supervised Gaussian mixture regression model estimated in step (3.2)
Log likelihood function of
Repeating steps (3.1) - (3.2) until the log-likelihood function
When convergence occurs, the parameters of the semi-supervised Gaussian mixture regression model at the moment are the parameters of the final semi-supervised Gaussian mixture regression model;
(4) and (3) predicting quality variables by using the final semi-supervised Gaussian mixture regression model parameters:
wherein the content of the first and second substances,
predicting the expected value of data x for a given band, y being a quality variable, RxkRepresenting the probability value of the data to be predicted belonging to each component of the semi-supervised Gaussian mixture regression model,
representing the probability mean value of each component of the semi-supervised Gaussian mixture regression model belonging to the data x to be predicted,
(5) collecting new labeled and unlabeled mixed data in the same proportion as training data, training the mixed data into a semi-supervised incremental Gaussian mixed regression model according to the processes of the steps (2) to (3), and storing parameters of the semi-supervised incremental Gaussian mixed regression model and the number of the training data into a historical database;
(6) calculating each component in the semi-supervised Gaussian mixture regression model in the step (3) and each component in the semi-supervised incremental Gaussian mixture regression model in the step (5) pairwise to obtain a symmetrical Kullback-Leibler divergence SKLD, judging whether the SKLD value exceeds 10, keeping the original mean vector and covariance unchanged when the SKLD value exceeds 10, and updating the mixture weight of the components; when the SKLD value is less than 10, fusing; the calculation process of the SKLD value is as follows:
wherein phi is1Parameter set of a certain component in semi-supervised Gaussian mixture regression model, phi2Is a parameter set, mu, of a corresponding component in a semi-supervised incremental Gaussian mixture regression model1Is a mean vector of a certain component in a semi-supervised Gaussian mixed regression model2Is a semi-supervisorMean vectors, sigma, of corresponding components in the Du-delta Gaussian mixture regression model1Is a covariance matrix, sigma, of a certain component in a semi-supervised Gaussian mixed regression model2The covariance matrix of corresponding components in the semi-supervised incremental Gaussian mixed regression model is obtained, and KLD is relative entropy;
(7) and (5) continuously repeating the steps (5) to (6) along with the inflow of the data to be measured, so that the self-adaptive quality prediction of the industrial process can be realized.
Further, the fusion process of step (6) is:
wherein mu is a mean vector of the components in the fusion semi-supervised increment Gaussian mixed regression model, and sigma is a covariance of the components in the fusion semi-supervised increment Gaussian mixed regression model,
the method is characterized in that the mixed weight of components in a post-half-supervision incremental Gaussian mixed regression model is fused, N represents the total number of original sample data, mujThe mean vector of the jth component in the semi-supervised Gaussian mixture regression model of the initial training data is shown,
represents the mixing weight, sigma of the jth component in the semi-supervised Gaussian mixed regression model of the initial training data samplejRepresents the covariance, M, of the jth component in the semi-supervised Gaussian mixture regression model of the initial training data samplekSemi-supervised incremental gaussians representing new sample trainingNumber of samples, μ, of the kth component in the mixed regression modelkSum ΣkRespectively, the mean vector and the covariance matrix of the kth component in the corresponding semi-supervised incremental gaussian mixture regression model.
Further, the step (6) of updating the mixing weights of the components comprises the following steps:
when the remaining components belong to a new sample:
when the remaining components belong to the initial training data sample:
compared with the prior art, the invention has the beneficial effects that: in order to fully utilize a large amount of non-label data information in the industrial production process, the invention provides semi-supervised incremental Gaussian mixed regression on the basis of the incremental Gaussian mixed regression. In semi-supervised incremental gaussian mixture regression, it is assumed that process variables and quality variables have a linear relationship, while model learning is engaged with labeled and unlabeled data. The probability density function, the regression relation coefficient and the mixing coefficient of each component are learned through an EM (effective memory) algorithm, and model selection is performed by utilizing a Bayesian information criterion, so that the problems of model overfitting and inaccurate parameter learning caused by rare labeled data are effectively solved, and the prediction accuracy of the model is improved. On the basis of the incremental Gaussian mixture regression model, the problem of inaccurate model parameter learning caused by rare labeled samples in the industrial process is solved. Compared with other traditional self-adaptive soft measurement models, the method has the advantages that overfitting is relieved, prediction errors are reduced, and model updating efficiency is improved.
Drawings
FIG. 1 is a diagram of an adaptive soft-sensing method of a semi-supervised incremental Gaussian mixture regression model of the present invention;
FIG. 2 is a process block diagram of a primary reformer;
FIG. 3 is a graph of the predicted effect of the method of the present invention on a segment of a furnace industrial process.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
Fig. 1 is a diagram of an adaptive soft measurement method of a semi-supervised incremental gaussian mixture regression model according to the present invention, and the adaptive soft measurement method specifically includes the following steps:
(1) tagged data set of historical operating conditions in industrial processes
And unlabeled datasets
Forming an initial training data set, wherein l represents a label of the label, i represents an index of the labeled data set, and xiDenotes the ith sample, y, in the labeled datasetiRepresents a label, nlDenotes the number of samples of the tagged dataset, j denotes the index of the untagged dataset, u denotes the tag of the untagged, xjDenotes the jth sample, n, in the unlabeled datasetuRepresenting the number of samples of the unlabeled dataset;
(2) standardizing the initial training data set collected in the step (1) with the mean value of 0 and the variance of 1 to obtain a standardized data set
(3) Assuming that there are K gaussian components in the semi-supervised gaussian mixture regression model, the Probability Density Function (PDF) of the K gaussian component for x and the functional dependence of y on x are defined as:
wherein P isk(x) Represented as a Probability Density Function (PDF) of the auxiliary variable x,
represented as mean-based vectors
Sum covariance matrix
A gaussian distribution of (a). OmegakAnd
representing the regression coefficient between the auxiliary variable x and the quality variable y,
representing the measurement noise of the mass variable y in the kth gaussian component.
Learning semi-supervised Gaussian mixture regression model parameters theta by adopting an EM algorithm in an iterative mode, wherein the semi-supervised Gaussian mixture regression model parameters theta comprise: prior probability alpha of kth component in semi-supervised Gaussian mixture regression modelkMean vector mu of kth component in semi-supervised Gaussian mixture regression modelkCovariance matrix sigma of kth component in semi-supervised Gaussian mixed regression modelkRegression coefficient omega of kth component in semi-supervised Gaussian mixture regression modelkRegression coefficient of kth component label in semi-supervised Gaussian mixture regression model
Measuring noise variance
The method specifically comprises the following substeps:
(3.1) obtaining the posterior probability distribution of the hidden variables of the labeled samples respectively by using linear Gaussian operation
And the hidden variable posterior probability distribution of unlabeled samples
Wherein z isiIs the hidden variable of the ith labeled sample, zjHidden variable for jth unlabeled sample, RikRepresenting the posterior probability, R, of the kth component in the semi-supervised Gaussian mixture regression model in generating the ith labeled samplejkRepresenting the posterior probability of the kth component in the semi-supervised Gaussian mixed regression model in generating the jth unlabeled sample; p represents the probability of the kth component from 0 to 1 in the semi-supervised gaussian mixture regression model,
represents the mean vector of the labeled samples in the kth component in the semi-supervised gaussian mixture regression model,
representing a covariance matrix of labeled samples in the kth component of the semi-supervised gaussian mixture regression model,
represents the mean vector of the k component without label in the semi-supervised Gaussian mixture regression model,
represents the unlabeled covariance matrix in the kth component of the semi-supervised gaussian mixture regression model,
representing the kth gaussian distribution based on the mean vector and covariance matrix.
(3.2) posterior probability distribution of hidden variables obtained by the step (3.1)
And
to calculate a corresponding log-likelihood function, said log-likelihood function
Comprises the following steps:
z represents an implicit variable of the sample,
maximizing log-likelihood functions for each semi-supervised Gaussian mixture regression model parameter
Wherein β is a lagrange multiplier;
estimating the updated value of the parameters of the semi-supervised Gaussian mixed regression model:
wherein the content of the first and second substances,
in order to be a set of regression coefficients,
is a set of hidden variable posterior probability distributions for labeled exemplars,
in the form of a matrix of tagged data sets,
i is 1 and dimension is nlThe vector of (a) is determined,
(3.3) calculating a normalized data set based on the updated values of the parameters of the semi-supervised Gaussian mixture regression model estimated in step (3.2)
Log likelihood function of
Repeating steps (3.1) - (3.2) until the log-likelihood function
When convergence occurs, the parameters of the semi-supervised Gaussian mixture regression model at the moment are the parameters of the final semi-supervised Gaussian mixture regression model;
(4) to achieve the prediction of the quality variables, semi-supervised Gaussian mixture regression model parameters are utilized
To calculate the joint probability density function of the auxiliary variable x and the quality variable y:
wherein
In each gaussian component, the conditional distribution of y after a given x is:
wherein the mean vector
Covariance matrix
The final conditional probability distribution of y can be expressed as:
wherein
Thus, given the auxiliary variable x, we can predict the quality variable y as:
wherein the content of the first and second substances,
predicting the expected value of data x for a given band, y being a quality variable, RxkRepresenting the probability value R of each component of the semi-supervised Gaussian mixture regression model belonging to the data to be predictedxkRepresenting the probability that the data x to be predicted belongs to each component of the semi-supervised gaussian mixed regression model,
represents the mean value of the corresponding components;
(5) after the collected real-time data are standardized, the quality of the new sample is predicted by using the steps (3) to (4) and the result is output
Obtaining a true output Y of the quality variable YnewThereafter, sample data was collected into the new data set Z, while quantitative evaluation of the predicted performance was performed using Root Mean Square Error (RMSE), as shown below:
where i 1, 2, N represents the total length of the test set, YiAnd
respectively representing the true value and the predicted value of the output quality variable. Will collect new labels in the same proportionTaking the label and non-label mixed data as training data, training the training data into a semi-supervised incremental Gaussian mixed regression model according to the processes in the steps (2) to (3), and storing parameters of the semi-supervised incremental Gaussian mixed regression model and the number of the training data into a historical database;
(6) calculating each component in the semi-supervised Gaussian mixture regression model in the step (3) and each component in the semi-supervised incremental Gaussian mixture regression model in the step (5) pairwise to obtain a symmetrical Kullback-Leibler divergence SKLD, judging whether the SKLD value exceeds 10, keeping the original mean vector and covariance unchanged when the SKLD value exceeds 10, and updating the mixture weight of the components; when the SKLD value is less than 10, fusing; the calculation process of the SKLD value is as follows:
wherein phi is1Parameter set of a certain component in semi-supervised Gaussian mixture regression model, phi2Is a parameter set, mu, of a corresponding component in a semi-supervised incremental Gaussian mixture regression model1Is a mean vector of a certain component in a semi-supervised Gaussian mixed regression model2Is the mean vector, sigma, of the corresponding component in the semi-supervised incremental Gaussian mixture regression model1Is a covariance matrix, sigma, of a certain component in a semi-supervised Gaussian mixed regression model2The covariance matrix of corresponding components in the semi-supervised incremental Gaussian mixed regression model is obtained, and KLD is relative entropy;
and when the calculated SKLD value is less than 10, judging that the original GMR component j and the new GMR component k are equivalent statistically and can be fused. The following is a parameter update formula fused into a new component:
wherein mu is a mean vector of the components in the fusion semi-supervised increment Gaussian mixed regression model, and sigma is a covariance of the components in the fusion semi-supervised increment Gaussian mixed regression model,
the method is characterized in that the mixed weight of components in a post-half-supervision incremental Gaussian mixed regression model is fused, N represents the total number of original sample data, mujThe mean vector of the jth component in the semi-supervised Gaussian mixture regression model of the initial training data is shown,
represents the mixing weight, sigma of the jth component in the semi-supervised Gaussian mixed regression model of the initial training data samplejRepresents the covariance, M, of the jth component in the semi-supervised Gaussian mixture regression model of the initial training data samplekRepresents the number of samples, mu, of the k component in the semi-supervised incremental Gaussian mixture regression model of the newly-come sample trainingkSum ΣkRespectively, the mean vector and the covariance matrix of the kth component in the corresponding semi-supervised incremental gaussian mixture regression model.
When the calculated SKLD value is larger than 10, the two components can not be fused and become residual components, the original mean vector mu and covariance matrix sigma are kept unchanged, and the mixed weight of the components is updated
That is, the following are the mixing weights
The update formula of (2):
when the remaining components belong to a new sample:
when the remaining components belong to the initial training data sample:
(7) and (5) continuously repeating the step (5) and the step (6) along with the inflow of the data to be measured, on one hand, predicting the quality variable of the new data by using a semi-supervised Gaussian mixture regression model, on the other hand, collecting new data mixed with labels and without labels for modeling, updating the semi-supervised Gaussian mixture regression model in an incremental mode, and realizing the self-adaptive quality prediction of the industrial process. In short, historical data are discarded in the updating process, and only the number of the historical data and the model parameters need to be stored, so that the occupation of storage space is greatly reduced; on the other hand, model parameters established by historical data are used for updating, so that the time of subsequent training is remarkably shortened; and finally, parameter learning is carried out by using the data of the labeled samples and the data of the unlabeled samples, so that the accuracy of model parameter learning is improved.
Examples
The performance of the semi-supervised incremental gaussian mixed regression model is described below in conjunction with a specific primary reformer example for a hydrogen production unit process for an ammonia synthesis process. The main raw material NH3 of the hydrogen production unit of the ammonia synthesis process is usually the main raw material in the urea synthesis process, and the primary reformer is the main place for carrying out the conversion reaction according to the process flow design, and the process flow diagram is shown in figure 2. According to the reaction mechanism, the reaction temperature is a key factor for ensuring the hydrogen production in the first-stage converter, in order to stabilize the temperature at a certain level, the combustion state needs to be monitored in real time, and the control of the oxygen content at the top in the converter within a set range is one of effective means. In a practical industrial process, the cost of measuring oxygen concentration using a mass spectrometer is very expensive. Therefore, in order to improve the control quality of the primary reformer and reduce the measurement cost, an adaptive soft measurement model needs to be established for the oxygen content in the primary reformer. Table 1 summarizes the detailed description of the 13 auxiliary variables and the 1 quality variable.
Table 1: sample variable description
| Label (R) | Name (R) |
| U1 | Fuel natural gas flow |
| U2 | Fuel exhaust gas flow |
| U3 | E3 outlet fuel natural gas pressure |
| U4 | PR outlet hearth flue gas pressure |
| U5 | T E3 temperature of tail gas of outlet fuel |
| U6 | PH outlet fuel natural gas temperature |
| U7 | PR inlet process gas temperature |
| U8 | Flue gas temperature of PR top left side hearth |
| U9 | Flue gas temperature of PR top right hearth |
| U10 | Flue gas temperature of PR top mixed hearth |
| U11 | PR outlet transition air temperature |
| U12 | PR right side outlet switching air temperature |
| U13 | PR outlet transition air temperature |
| Y | Top oxygen content in the furnace |
First, a total of 7000 samples of industrial process data were collected. The first 1500 samples are taken as original sample training models by taking time as a sequence, and new data prediction and model updating are carried out by different updating step lengths. Using root mean square error RMSE as index to measure the proposed S2Measurement accuracy of IGMR and IGMR soft measurement models.
Table 2: the method of the invention compares the parameters of the prediction results of the incremental Gaussian mixture regression model
As shown in FIG. 3, which is a diagram of the predicted effect of a section of the industrial process of the furnace, it can be seen that the method can better capture the dynamic curve of the top oxygen content in the furnace. From table 2, we can see that when the new data update step size is changed from 60 to 200, the overall prediction accuracy RMSE shows a trend of decreasing first and then increasing. The reason for the change is that when the sample update step is too small, the model trained by the new sample is difficult to better fit data, so that the prediction accuracy is reduced; when the step length reaches a proper number, the precision also reaches the best; with the continuous increase of the sample updating step length, the model is not updated timely, and when the working condition is changed, the model is difficult to adapt to new data, so that the prediction precision is poor. With the reduction of the proportion of the labeled samples in the data set, the prediction effect of the incremental Gaussian mixture regression model begins to deteriorate, and particularly when the proportion of the labeled samples reaches 10%, compared with the situation that the performance of the incremental Gaussian mixture regression model is relatively slowly reduced, a better prediction effect can still be achieved. Therefore, the method is considered to be an effective method for predicting the oxygen content on line, and is beneficial to better controlling the reaction temperature, thereby ensuring continuous and stable hydrogen production.
Claims (3)
1. A self-adaptive soft measurement method based on semi-supervised incremental Gaussian mixture regression is characterized by comprising the following steps:
(1) tagged data set of historical operating conditions in industrial processes
And unlabeled datasets
Forming an initial training data set, wherein l represents a label of the label, i represents an index of the labeled data set, and xiDenotes the ith sample, y, in the labeled datasetiRepresents a label, nlRepresenting the number of samples of the tagged data setItem, j denotes the index of the unlabeled dataset, u denotes the unlabeled label, xjDenotes the jth sample, n, in the unlabeled datasetuRepresenting the number of samples of the unlabeled dataset;
(2) standardizing the initial training data set collected in the step (1) with the mean value of 0 and the variance of 1 to obtain a standardized data set
(3) Learning semi-supervised Gaussian mixture regression model parameters theta by adopting an EM algorithm in an iterative mode, wherein the semi-supervised Gaussian mixture regression model parameters theta comprise: prior probability alpha of kth component in semi-supervised Gaussian mixture regression modelkMean vector mu of kth component in semi-supervised Gaussian mixture regression modelkCovariance matrix sigma of kth component in semi-supervised Gaussian mixed regression modelkRegression coefficient omega of kth component in semi-supervised Gaussian mixture regression modelkRegression coefficient of kth component label in semi-supervised Gaussian mixture regression model
Measuring noise variance
The method specifically comprises the following substeps:
(3.1) obtaining the posterior probability distribution of the hidden variables of the labeled samples respectively by using linear Gaussian operation
And the hidden variable posterior probability distribution of unlabeled samples
Wherein z isiIs the hidden variable of the ith labeled sample, zjHidden variable for jth unlabeled sample, RikRepresenting the posterior probability, R, of the kth component in the semi-supervised Gaussian mixture regression model in generating the ith labeled samplejkRepresenting the posterior probability of the kth component in the semi-supervised Gaussian mixed regression model in generating the jth unlabeled sample; p represents the probability of the kth component from 0 to 1 in the semi-supervised gaussian mixture regression model,
represents the mean vector of the labeled samples in the kth component in the semi-supervised gaussian mixture regression model,
representing a covariance matrix of labeled samples in the kth component of the semi-supervised gaussian mixture regression model,
represents the mean vector of the k component without label in the semi-supervised Gaussian mixture regression model,
represents the unlabeled covariance matrix in the kth component of the semi-supervised gaussian mixture regression model,
representing a kth gaussian distribution based on the mean vector and the covariance matrix;
(3.2) posterior probability distribution of hidden variables obtained by the step (3.1)
And
to calculate a corresponding log-likelihood function, said log-likelihood function
Comprises the following steps:
wherein z represents an implicit variable of the sample,
maximizing log-likelihood functions for each semi-supervised Gaussian mixture regression model parameter
Wherein β is a lagrange multiplier;
estimating the updated value of the parameters of the semi-supervised Gaussian mixed regression model:
wherein the content of the first and second substances,
in order to be a set of regression coefficients,
is a set of hidden variable posterior probability distributions for labeled exemplars,
in the form of a matrix of tagged data sets,
i is 1 and dimension is nlThe vector of (a) is determined,
(3.3) calculating a normalized data set based on the updated values of the parameters of the semi-supervised Gaussian mixture regression model estimated in step (3.2)
Log likelihood function of
Repeating steps (3.1) - (3.2) until the log-likelihood function
When convergence occurs, the parameters of the semi-supervised Gaussian mixture regression model at the moment are the parameters of the final semi-supervised Gaussian mixture regression model;
(4) and (3) predicting quality variables by using the final semi-supervised Gaussian mixture regression model parameters:
wherein the content of the first and second substances,
predicting the expected value of data x for a given band, y being a quality variable, RxkRepresenting the probability value of the data to be predicted belonging to each component of the semi-supervised Gaussian mixture regression model,
representing the probability mean value of each component of the semi-supervised Gaussian mixture regression model belonging to the data x to be predicted,
(5) collecting new labeled and unlabeled mixed data in the same proportion as training data, training the mixed data into a semi-supervised incremental Gaussian mixed regression model according to the processes of the steps (2) to (3), and storing parameters of the semi-supervised incremental Gaussian mixed regression model and the number of the training data into a historical database;
(6) calculating each component in the semi-supervised Gaussian mixture regression model in the step (3) and each component in the semi-supervised incremental Gaussian mixture regression model in the step (5) pairwise to obtain a symmetrical Kullback-Leibler divergence SKLD, judging whether the SKLD value exceeds 10, keeping the original mean vector and covariance unchanged when the SKLD value exceeds 10, and updating the mixture weight of the components; when the SKLD value is less than 10, fusing; the calculation process of the SKLD value is as follows:
wherein phi is1Parameter set of a certain component in semi-supervised Gaussian mixture regression model, phi2Is a parameter set, mu, of a corresponding component in a semi-supervised incremental Gaussian mixture regression model1Is a mean vector of a certain component in a semi-supervised Gaussian mixed regression model2Is the mean vector, sigma, of the corresponding component in the semi-supervised incremental Gaussian mixture regression model1Is a covariance matrix, sigma, of a certain component in a semi-supervised Gaussian mixed regression model2The covariance matrix of corresponding components in the semi-supervised incremental Gaussian mixed regression model is obtained, and KLD is relative entropy;
(7) and (5) continuously repeating the steps (5) to (6) along with the inflow of the data to be measured, so that the self-adaptive quality prediction of the industrial process can be realized.
2. The adaptive soft measurement method based on semi-supervised incremental Gaussian mixture regression as claimed in claim 1, wherein the fusion process of the step (6) is as follows:
wherein u is a mean vector of the components in the fusion semi-supervised increment Gaussian mixed regression model, and Σ is a covariance of the components in the fusion semi-supervised increment Gaussian mixed regression model,
the method is characterized in that the mixed weight of components in a post-half-supervision incremental Gaussian mixed regression model is fused, N represents the total number of original sample data, mujThe mean vector of the jth component in the semi-supervised Gaussian mixture regression model of the initial training data is shown,
represents the mixing weight, sigma of the jth component in the semi-supervised Gaussian mixed regression model of the initial training data samplejRepresents the covariance, M, of the jth component in the semi-supervised Gaussian mixture regression model of the initial training data samplekRepresents the number of samples, mu, of the k component in the semi-supervised incremental Gaussian mixture regression model of the newly-come sample trainingkSum ΣkRespectively, the mean vector and the covariance matrix of the kth component in the corresponding semi-supervised incremental gaussian mixture regression model.
3. The adaptive soft measurement method based on semi-supervised incremental gaussian mixture regression as recited in claim 1, wherein the step (6) of updating the mixture weights of the components comprises the following steps:
when the remaining components belong to a new sample:
when the remaining components belong to the initial training data sample:
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113158473A (en) * | 2021-04-27 | 2021-07-23 | 昆明理工大学 | Semi-supervised integrated instant learning industrial rubber compound Mooney viscosity soft measurement method |
| CN113707240A (en) * | 2021-07-30 | 2021-11-26 | 浙江大学 | Component parameter robust soft measurement method based on semi-supervised nonlinear variational Bayes mixed model |
| CN114239400A (en) * | 2021-12-16 | 2022-03-25 | 浙江大学 | Multi-working-condition process self-adaptive soft measurement modeling method based on local double-weighted probability hidden variable regression model |
| CN114662620A (en) * | 2022-05-24 | 2022-06-24 | 岚图汽车科技有限公司 | Automobile endurance load data processing method and device for market users |
Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102542126A (en) * | 2011-10-10 | 2012-07-04 | 上海交通大学 | Soft measurement method based on half supervision learning |
| CN102693452A (en) * | 2012-05-11 | 2012-09-26 | 上海交通大学 | Multiple-model soft-measuring method based on semi-supervised regression learning |
| CN102708294A (en) * | 2012-05-11 | 2012-10-03 | 上海交通大学 | Self-adaptive parameter soft measuring method on basis of semi-supervised local linear regression |
| CN103927412A (en) * | 2014-04-01 | 2014-07-16 | 浙江大学 | Real-time learning debutanizer soft measurement modeling method on basis of Gaussian mixture models |
| CN104462850A (en) * | 2014-12-25 | 2015-03-25 | 江南大学 | Multi-stage batch process soft measurement method based on fuzzy gauss hybrid model |
| CN107451101A (en) * | 2017-07-21 | 2017-12-08 | 江南大学 | It is a kind of to be layered integrated Gaussian process recurrence soft-measuring modeling method |
| CN108171002A (en) * | 2017-11-30 | 2018-06-15 | 浙江大学 | A kind of polypropylene melt index Forecasting Methodology based on semi-supervised mixed model |
| CN108764295A (en) * | 2018-04-28 | 2018-11-06 | 江南大学 | A kind of soft-measuring modeling method based on semi-supervised integrated study |
| US10678196B1 (en) * | 2020-01-27 | 2020-06-09 | King Abdulaziz University | Soft sensing of a nonlinear and multimode processes based on semi-supervised weighted Gaussian regression |
-
2020
- 2020-12-30 CN CN202011614387.1A patent/CN112650063B/en active Active
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102542126A (en) * | 2011-10-10 | 2012-07-04 | 上海交通大学 | Soft measurement method based on half supervision learning |
| CN102693452A (en) * | 2012-05-11 | 2012-09-26 | 上海交通大学 | Multiple-model soft-measuring method based on semi-supervised regression learning |
| CN102708294A (en) * | 2012-05-11 | 2012-10-03 | 上海交通大学 | Self-adaptive parameter soft measuring method on basis of semi-supervised local linear regression |
| CN103927412A (en) * | 2014-04-01 | 2014-07-16 | 浙江大学 | Real-time learning debutanizer soft measurement modeling method on basis of Gaussian mixture models |
| CN104462850A (en) * | 2014-12-25 | 2015-03-25 | 江南大学 | Multi-stage batch process soft measurement method based on fuzzy gauss hybrid model |
| CN107451101A (en) * | 2017-07-21 | 2017-12-08 | 江南大学 | It is a kind of to be layered integrated Gaussian process recurrence soft-measuring modeling method |
| CN108171002A (en) * | 2017-11-30 | 2018-06-15 | 浙江大学 | A kind of polypropylene melt index Forecasting Methodology based on semi-supervised mixed model |
| CN108764295A (en) * | 2018-04-28 | 2018-11-06 | 江南大学 | A kind of soft-measuring modeling method based on semi-supervised integrated study |
| US10678196B1 (en) * | 2020-01-27 | 2020-06-09 | King Abdulaziz University | Soft sensing of a nonlinear and multimode processes based on semi-supervised weighted Gaussian regression |
Non-Patent Citations (4)
| Title |
|---|
| JINGBO WANG等: ""Bayesian Regularized Gaussian Mixture Regression with Application to Soft Sensor Modeling for Multi-Mode Industrial Processes"", 《2018 IEEE 7TH DATA DRIVEN CONTROL AND LEARNING SYSTEMS CONFERENCE (DDCLS)》 * |
| WEIMING SHAO等: ""Soft-Sensor Development for Processes With Multiple Operating Modes Based on Semisupervised Gaussian Mixture Regression"", 《IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY》 * |
| 邵伟明等: ""基于循环神经网络的半监督动态软测量建模方法"", 《电子测量与仪器学报》 * |
| 邵伟明等: ""基于集成学习的多产品化工过程软测量建模方法"", 《化工学报》 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113158473A (en) * | 2021-04-27 | 2021-07-23 | 昆明理工大学 | Semi-supervised integrated instant learning industrial rubber compound Mooney viscosity soft measurement method |
| CN113707240A (en) * | 2021-07-30 | 2021-11-26 | 浙江大学 | Component parameter robust soft measurement method based on semi-supervised nonlinear variational Bayes mixed model |
| CN113707240B (en) * | 2021-07-30 | 2023-11-07 | 浙江大学 | Component parameter robust soft measurement method based on semi-supervised nonlinear variation Bayesian hybrid model |
| CN114239400A (en) * | 2021-12-16 | 2022-03-25 | 浙江大学 | Multi-working-condition process self-adaptive soft measurement modeling method based on local double-weighted probability hidden variable regression model |
| CN114662620A (en) * | 2022-05-24 | 2022-06-24 | 岚图汽车科技有限公司 | Automobile endurance load data processing method and device for market users |
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