Intermittent process soft measurement modeling method based on FDTE-RVM

Abstract

The invention discloses an intermittent process soft measurement modeling method based on FDTE-RVM, and belongs to the technical field of intermittent production process monitoring. The method comprises the following steps: standardizing intermittent production process data by using a normal cumulative distribution function, and symbolizing the process data through fuzzy dispersion transformation to obtain an intermittent production process symbolized data set; then calculating transfer entropy between the soft measurement dominant variable and the auxiliary variable to obtain a causal effect index between the variables, selecting a causal auxiliary variable of the intermittent process according to the causal effect index, and constructing a causal auxiliary variable set; and finally, establishing a batch process soft measurement model based on the RVM, and realizing prediction of batch process dominant variables. According to the method, the causal effect between the dominant variable and the auxiliary variable of the batch process soft measurement is quantified through the fuzzy dispersion transfer entropy, the causal auxiliary variable set is constructed, the batch process soft measurement model is established, and the stability and the prediction accuracy of the batch process soft measurement model are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of intermittent production process monitoring, and in particular relates to an intermittent process soft measurement modeling method based on FDTE-RVM (Fuzzy Dispersion Transfer Entropy-Relevant Vector Machine). Background Art

[0002] As an important production method in modern industry, intermittent process is widely used in fine chemicals, semiconductor processing, biomedicine and other fields. Real-time measurement of quality variables in intermittent production process is the key to achieve safe and efficient operation of production process. Soft measurement realizes online prediction of leading variables by constructing mathematical models between difficult-to-measure leading variables and easy-to-measure auxiliary variables, and has been applied to online measurement of quality variables in intermittent production process.

[0003] In the existing soft measurement modeling of intermittent processes, the soft measurement modeling based on mechanism analysis establishes a soft measurement mechanism model according to the process mechanism. However, the mechanism of the intermittent process is complex and it is difficult to establish an accurate soft measurement mechanism model. Soft measurement modeling based on process data drive has become an important way of soft measurement modeling of intermittent processes. Affected by the changes in operating conditions of intermittent production processes and the attenuation of sensor performance, there are large differences in the distribution of process data between batches, and the data-driven soft measurement modeling method usually uses empirical analysis or correlation analysis to select auxiliary variables and dominant variables, so that there is a false correlation between the dominant variable and the auxiliary variable, which directly affects the stability of the intermittent process soft measurement model and the accuracy of prediction. Therefore, a soft measurement modeling method for intermittent processes based on FDTE-RVM is invented, which uses fuzzy scattered transfer entropy to quantify the causal effect between the auxiliary variable and the dominant variable, constructs a soft measurement causal auxiliary variable set, and establishes a relevant vector machine (RVM) soft measurement model for intermittent production processes, which can effectively improve the stability of the soft measurement model for intermittent production processes and the accuracy of prediction. Summary of the invention

[0004] The present invention aims to improve the stability of the soft sensor model of the intermittent process and the accuracy of prediction, and invents an intermittent process soft sensor modeling method based on FDTE-RVM, comprising the following steps:

[0005] Step 1: Collect multiple batches of intermittent production process data, standardize the process data using the normal cumulative distribution function, symbolize the process data through fuzzy scatter transformation, and obtain the symbolized data set of the intermittent production process;

[0006] Step 2: Estimate the probability density of fuzzy scattered symbolic data of intermittent production process, quantify the causal effect between variables by using the transfer entropy between soft-sensing dominant variables and auxiliary variables, calculate the causal effect index between variables, and select the causal auxiliary variables of intermittent process according to the causal effect index, and construct the causal auxiliary variable set of intermittent process soft-sensing;

[0007] Step 3: Based on the set of causal auxiliary variables, the RVM soft sensor model is established to predict the dominant variables of the intermittent production process.

[0008] The step 1 specifically includes:

[0009] Collect multiple batches of intermittent production process data X (I × N × J), where I is the number of batches, N is the number of process data sampling points, and J is the number of measurable variables in the process. Use the normal cumulative distribution function to standardize the process variable x to

[0010]

[0011] In the formula, is the standardized measurement data of the intermittent production process; σ and γ are the standard deviation and mean of x respectively; t is the sampling time of the measurement data of the intermittent production process; e is a natural constant.

[0012] Then Mapping to time series z c for

[0013]

[0014] In the formula, is the process time series z c The i-th element; c is z c the number of categories; Standardizing measurement data for intermittent production processes The ith element.

[0015] Then construct the intermittent process m-dimensional sequence for

[0016]

[0017] In the formula, Represents the process time series z c The i+m-1th element.

[0018] Each sequence Can be mapped to a fuzzy scattered pattern in

[0019]

[0020] sequence The dispersion pattern Fuzzy membership The calculation method is

[0021]

[0022] In the formula, Represents the process time series z c The i+jth element The fuzzy membership of .

[0023] Considering the nonlinearity of intermittent production process data, the constructed fuzzy scatter membership function is:

[0024]

[0025]

[0026] Where, k = 2, 3, ..., c-1 is the symbolic category of process fuzzy dispersion; Represents the i-th element of the process time series The fuzzy membership degree of the k-th class.

[0027] According to equations (1) to (8), the measurable variables of the intermittent production process are fuzzy-scattered and symbolized to obtain the symbolized soft-sensing dominant variables. and the auxiliary variables to be selected for

[0028]

[0029] In the formula, It represents the Jth candidate auxiliary variable of the process soft sensor model after fuzzy dispersion symbolization.

[0030] The step 2 specifically includes:

[0031] Obtaining a symbolic batch process data set After that, the probability density p of the estimated process fuzzy scattered symbolic measurable variable is

[0032]

[0033] Select one of the K measurable variables in the process as the dominant variable y, and the remaining K-1 variables as the auxiliary variables to be selected. Calculate the fuzzy spread transfer entropy FDT of the soft sensor auxiliary variable x and the dominant variable y. xy for

[0034]

[0035] Where p(·) is the probability density estimation function of the process symbolic variable; Symbolize dominant variables for soft sensors The value is taken at the i+hth moment; Symbolize the auxiliary variables to be selected for the process The value is taken at the i-th moment, log(·) is a logarithmic function with the natural constant e as the base.

[0036] According to the definition of conditional probability and entropy, equation (11) can be rewritten as

[0037]

[0038] In the formula, It represents the joint entropy of the soft sensor symbolized dominant variable and the candidate auxiliary variable.

[0039] In order to facilitate the quantification of the causal effect between variables, the causal effect index calculation formula is constructed as follows:

[0040]

[0041] In the formula, FDT yx It represents the fuzzy spread transfer entropy of the soft sensor dominant variable y and the candidate auxiliary variable x.

[0042] If 1≥FDTE(x,y)>0, the information flows from x to y, and x is the direct cause of y. If 0≥FDTE(x,y)≥-1, there is no direct causal relationship between the soft sensor auxiliary variable x and the dominant variable y.

[0043] According to formulas (10) to (13), the causal effect index between the auxiliary variables x and the dominant variable y of each batch of soft measurement is calculated, and the average causal effect index is obtained by averaging the calculation results. The soft measurement causal auxiliary variable set is selected according to the average causal effect index. Where L is the number of causal auxiliary variables.

[0044] The step three specifically includes:

[0045] Using the causal auxiliary variable set of the intermittent production process obtained in step 2, the RVM soft sensor model is established. The RVM soft sensor model can be expressed as

[0046]

[0047] In the formula, y i is the output of the soft sensor model at the i-th moment; is the input of the soft sensor model at the i-th moment, where K(·) is the kernel function of the soft sensor model, and x i is the value of the soft sensor auxiliary variable x at the i-th moment, R is the process data sampling moment; W is the soft sensor model parameter matrix; T is the matrix transpose; ∈ i is the noise at the i-th moment of the process, and its mean is 0 and its variance is σ2 The normal distribution of .

[0048] Define the prior probability distribution of the soft sensor model parameter W to satisfy the Gaussian distribution with a mean of 0

[0049]

[0050] In the formula, α=[α1,α2,…,α R ] is the hyperparameter of the soft sensor model; α r Represents the rth element in α.

[0051] The optimization goal of the RVM soft sensor model is to minimize the prior probability distribution function P(W,α,σ 2 |y), in order to maximize the marginal likelihood of this distribution, let β = σ 2 , then the update formula of α and β is

[0052]

[0053] In the formula, represents the rth element after the hyperparameter α of the soft sensor model is updated; β new represents the updated value of the process data noise variance β; A is the diagonal matrix composed of all elements of the hyperparameter α, and diag(·) represents the diagonalization of the matrix; Represents the kernel function matrix of all causal auxiliary variables of the intermittent process; m and Δ are the intermediate variables constructed in RVM soft sensor modeling, m r represents the rth element of m, Δ rr represents the rth element on the diagonal of Δ; T is the matrix transpose.

[0054] By continuously iterating equations (16) to (20), the optimal parameter values ​​α and β of the soft sensor model are obtained. Then the online measurement data x of the intermittent production process is online The soft sensor model predicts the value y online and the soft sensor model prediction variance β online for

[0055]

[0056]

[0057] Advantages of the present invention: The present invention fully considers the distribution differences of data between batches of intermittent production processes, uses fuzzy scattered transfer entropy to quantify the causal effect strength between soft-sensing auxiliary variables and dominant variables in intermittent processes, obtains the causal relationship between variables, selects soft-sensing causal auxiliary variables based on the causal relationship between variables, establishes an intermittent process soft-sensing model based on FDTE-RVM, realizes online prediction of dominant variables, and improves the stability of the soft-sensing model and the accuracy of prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a flow chart of the soft sensor modeling method for intermittent production process based on FDTE-RVM of the present invention;

[0059] Figure 2 It is the calculation result of the causal effect index between the auxiliary variables and the dominant variables in the soft measurement of penicillin fermentation production process;

[0060] Figure 3 This is a diagram of the prediction results of the soft measurement model established by the method of the present invention on batch 1 of the penicillin fermentation production process. DETAILED DESCRIPTION

[0061] The present invention is further described below in conjunction with examples and drawings. It should be noted that the embodiments do not limit the scope of protection claimed by the present invention.

[0062] Example

[0063] Penicillin fermentation production process is a typical intermittent production process. Using the Pensim simulation platform, 15 batches of data were generated under different initial conditions, of which 10 batches of data were used as training sets and 5 batches of data were used as test sets. The sampling time was 400 hours and the sampling interval was 1 hour. Table 1 shows the variables of penicillin fermentation production process, and penicillin concentration is used as the dominant variable of the soft sensor model.

[0064] Table 1 Candidate auxiliary variables for soft measurement in penicillin fermentation process

[0065]

[0066] The implementation flow chart of the present invention is as follows Figure 1 As shown, the specific steps are as follows:

[0067] Step 1: Use the normal cumulative distribution function to standardize the 10 batches of training data X (10 × 400 × 14) of the penicillin fermentation process, and obtain the symbolic candidate auxiliary variables through fuzzy scatter transformation and dominant variables

[0068] Step 2: Estimate symbolic candidate auxiliary variables and dominant variables The probability density function of , and calculate the causal effect index, the calculation results are as follows Figure 2 As shown in the figure, the soft sensor auxiliary variable set of penicillin fermentation process is obtained according to the causal effect index.

[0069] Step 3: Use the causal auxiliary variables obtained in step 2 to establish a soft sensor model for the penicillin fermentation process, and use the Bayesian parameter optimization algorithm to optimize the model hyperparameters to predict the penicillin concentration.

[0070] In order to verify the effectiveness of the present invention, auxiliary variables were selected by empirical and mutual information (MI), and soft sensor models of penicillin fermentation process based on RVM were established respectively. The results of auxiliary variables selected by each method are shown in Table 2. The root mean square error (RMSE) and determination coefficient (R 2 ) is used as the accuracy evaluation index of the model, and the stable error (SE) and stable factor (SF) are used as the evaluation index of the model stability. The calculation formula of stable error and stable factor is:

[0071]

[0072] In the formula, RMSE b and R 2b They are the root mean square error and determination coefficient of the prediction results of the soft sensor model for batch b in the penicillin fermentation production process, respectively.

[0073] Table 2 Results of auxiliary variable selection by different methods

[0074]

[0075]

[0076] Figure 3 The predicted results of penicillin concentration of test batch 5 under different soft sensor modeling methods. Figure 3 It can be seen that the soft measurement modeling method based on empirical auxiliary variable selection takes all measurable variables of the process as auxiliary variables, and the correlation between some selected auxiliary variables and the dominant variables is low, which reduces the accuracy of soft measurement model prediction; the soft measurement modeling method based on correlation auxiliary variable selection selects auxiliary variables according to the correlation between variables, ignores the influence of the change of correlation between variables on the soft measurement model, and makes the prediction result of the soft measurement model poor at certain moments; the method of the present invention starts from the causal effect analysis between process variables, and the selected auxiliary variables have a stable causal relationship with the dominant variables, and the constructed soft measurement model has high stability and prediction accuracy.

[0077] Table 3 shows the RMSE, R 2 , SE and SF evaluation indicators.

[0078] Table 3 Evaluation indicators of penicillin concentration prediction results under different modeling methods

[0079]

[0080] As shown in Table 3, compared with the other two methods, the method of the present invention has the lowest RMSE and the highest R in all five test batches. 2 , and has the lowest stability error and the highest stability coefficient, which effectively improves the stability and prediction accuracy of the soft sensor model of the intermittent production process.

Claims

1. A soft sensor modeling method for intermittent processes based on FDTE-RVM, characterized by: The method comprises the following steps: Step 1: Collect multiple batches of intermittent production process data, standardize the process data using the normal cumulative distribution function, symbolize the process data through fuzzy scatter transformation, and obtain the symbolized data set of the intermittent production process; Step 2: Estimate the probability density of fuzzy scattered symbolic data of intermittent production process, quantify the causal effect between variables by using the transfer entropy between soft-sensing dominant variables and auxiliary variables, calculate the causal effect index between variables, and select the causal auxiliary variables of intermittent process according to the causal effect index, and construct the causal auxiliary variable set of intermittent process soft-sensing; Step 3: Based on the set of causal auxiliary variables, the RVM soft sensor model is established to predict the dominant variables of the intermittent production process.

2. The intermittent process soft sensor modeling method based on FDTE-RVM according to claim 1, characterized in that: The step 1 specifically includes: Collect multiple batches of intermittent production process data X (I × N × J), where I is the number of batches, N is the number of process data sampling points, and J is the number of measurable variables in the process; use the normal cumulative distribution function to standardize the process variable x to In the formula, is the intermittent production process measurement data after standardization; σ and γ are the standard deviation and mean of x respectively; t is the sampling time of the intermittent production process measurement data; e is a natural constant; Then Mapping to time series z c for: In the formula, is the process time series z c The i-th element; c is z c the number of categories; Standardizing measurement data for intermittent production processes The i-th element; Then construct the intermittent process m-dimensional sequence for: In the formula, Represents the process time series z c The i+m-1th element; Each sequence Mapped to a fuzzy scattered pattern in sequence The dispersion pattern Fuzzy membership The calculation method is: In the formula, Represents the process time series z c The i+jth element The fuzzy membership of Considering the nonlinearity of intermittent production process data, the constructed fuzzy scatter membership function is: Where, k = 2, 3, ..., c-1 is the symbolic category of process fuzzy dispersion; Represents the i-th element of the process time series Fuzzy membership of the kth class; According to equations (1) to (8), the measurable variables of the intermittent production process are fuzzy-scattered and symbolized to obtain the symbolized soft-sensing dominant variables. and the auxiliary variables to be selected for In the formula, It represents the Jth candidate auxiliary variable of the process soft sensor model after fuzzy dispersion symbolization.

3. The intermittent process soft sensor modeling method based on FDTE-RVM according to claim 1, characterized in that: The step 2 specifically includes: Obtaining a symbolic batch process data set After that, the probability density p of the estimated process fuzzy scattered symbolic measurable variable is: Select one of the K measurable variables in the process as the dominant variable y, and the remaining K-1 variables as the auxiliary variables to be selected. Calculate the fuzzy spread transfer entropy FDT of the soft sensor auxiliary variable x and the dominant variable y. xy for: Where p(·) is the probability density estimation function of the process symbolic variable; Symbolize dominant variables for soft sensors The value is taken at the i+hth moment; Symbolize the auxiliary variables to be selected for the process The value is taken at the i-th moment, log(·) is a logarithmic function with the natural constant e as the base; According to the definition of conditional probability and entropy, equation (11) can be rewritten as: In the formula, It represents the joint entropy of the soft-sensing symbolic dominant variable and the candidate auxiliary variable; In order to facilitate the quantification of the causal effect between variables, the causal effect index calculation formula is constructed as follows: In the formula, FDT yx It represents the fuzzy spread transfer entropy of the soft sensor dominant variable y and the auxiliary variable x to be selected; If 1≥FDTE(x,y)>0, the information flows from x to y, and x is the direct cause of y. If 0≥FDTE(x,y)≥-1, there is no direct causal relationship between the soft sensor auxiliary variable x and the dominant variable y. According to formulas (10) to (13), the causal effect index between the auxiliary variables x and the dominant variable y of each batch of soft measurement is calculated, and the average causal effect index is obtained by averaging the calculation results. The soft measurement causal auxiliary variable set is selected according to the average causal effect index. Where L is the number of causal auxiliary variables.

4. The FDTE-RVM-based soft sensor modeling method for intermittent processes according to claim 1, characterized in that: The step three specifically includes: Using the causal auxiliary variable set of the intermittent production process obtained in step 2, the RVM soft sensor model is established. The RVM soft sensor model is expressed as: In the formula, y i is the output of the soft sensor model at the i-th moment; is the input of the soft sensor model at the i-th moment, where K(·) is the kernel function of the soft sensor model, and x i is the value of the soft sensor auxiliary variable x at the i-th moment, R is the process data sampling moment; W is the soft sensor model parameter matrix; T is the matrix transpose; ∈ i is the noise at the i-th moment of the process, and its mean is 0 and its variance is σ 2 Normal distribution of The prior probability distribution of the soft sensor model parameter W is defined to satisfy a Gaussian distribution with a mean of 0: In the formula, α=[α1,α2,…,α R ] is the hyperparameter of the soft sensor model; α r represents the rth element in α; The optimization goal of the RVM soft sensor model is to minimize the prior probability distribution function P(W,α,σ 2 |y), in order to maximize the marginal likelihood of this distribution, let β = σ 2 , then the update calculation formula of α and β is: In the formula, represents the rth element after the hyperparameter α of the soft sensor model is updated; β new represents the updated value of the process data noise variance β; A is the diagonal matrix composed of all elements of the hyperparameter α, and diag(·) represents the diagonalization of the matrix; Represents the kernel function matrix of all causal auxiliary variables of the intermittent process; m and Δ are the intermediate variables constructed in RVM soft sensor modeling, m r represents the rth element of m, Δ rr represents the rth element on the diagonal of Δ; T is the matrix transpose symbol; By iterating equations (16) to (20), we can obtain the optimal parameter values ​​α and β of the soft sensor model. Then the online measurement data x of the intermittent production process is online The soft sensor model predicts the value y online and the soft-sensing model prediction variance β online for:

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