Intermittent process quality prediction method based on self-correction batch-related Gaussian regression

Abstract

The invention discloses an intermittent process quality prediction method fusing batch associated information and dynamic data correction. The method comprises the following steps: 1) acquiring and integrating multiple batches of data in the batch process, mining the relevance between batches by adopting canonical correlation analysis, constructing a batch relevance matrix, improving a kernel function by combining Gaussian process regression, and improving the capture capability of a model on the batch data relevance; 2) introducing a dynamic data correction method, dynamically adjusting a prediction error through Bayesian reasoning, optimizing a prediction result in combination with measurement data, and further reducing the influence of noise on the model; and (3) carrying out modeling training and testing by utilizing the improved model, and verifying the effectiveness of the model in the intermittent crystallization process. Through a contrast experiment on a plurality of models, a result shows that the batch process quality prediction method fusing batch association information and dynamic data correction shows higher prediction precision and stability when processing batch process data with high noise and small samples.

Description

Technical Field

[0001] The present invention belongs to the technical field of batch process quality prediction modeling, and in particular relates to a batch process quality prediction method based on self-correcting batch-related Gaussian regression. Background Art

[0002] In modern manufacturing, batch processes are a key production method widely used in food processing, fine chemicals, and biopharmaceuticals. Therefore, developing reliable quality prediction models is crucial. Compared to continuous processes, batch processes, due to their complex and varied product formulations and production methods, make it difficult to fully understand the mechanistic characteristics of all reaction processes, making it difficult to establish accurate soft-sensing mechanism models to control production quality.

[0003] Data-driven methods, another popular soft sensing approach, effectively estimate difficult-to-measure variables by analyzing the relationship between them. This approach, independent of process mechanisms and empirical knowledge, offers unique advantages in batch process quality prediction. Commonly used data-driven methods include those based on multivariate statistics, such as partial least squares (PLS), and artificial intelligence-based approaches, such as machine learning and deep learning models. However, PLS has limited ability to capture the nonlinear relationships and temporal characteristics of batch processes, and the performance of deep learning models depends largely on the quantity and quality of training samples. Actual batch processes are characterized by small sample sizes and strong noise, which reduces the predictive performance of deep learning models.

[0004] Gaussian Process Regression (GPR) has significant advantages in dealing with regression problems such as nonlinearity and small sample sizes, and is gradually gaining attention in quality prediction research for batch processes. However, existing GPR methods do not consider the potential connections between batches in batch processes and fail to fully explore the characteristic information contained in these connections. At the same time, current GPR models are unable to adjust parameters in real time, and the accuracy of their prediction results will be affected when faced with noise and data uncertainty. Among related technologies, Canonical Correlation Analysis (CCA) can effectively capture the potential correlations between batches by analyzing typical process variables, thereby revealing hidden relevant characteristic information. To address the characteristics of strong sample noise, Dynamic Data Reconciliation (DDR) effectively combines prior knowledge and optimized estimation of observed data, with excellent integration and real-time performance.

[0005] To address these challenges, we designed a batch process quality prediction method based on self-correcting batch-correlated Gaussian regression. This model incorporates CCA (Computational Correlation Analysis) into the modeling process to exploit potential correlations between batches and refines the kernel function to adapt to the data structure. Considering that noise from offline hardware measurements can significantly impact the model's prediction accuracy, we further introduced DDR (Reference Time Domain Regression) to suppress measurement noise. Finally, we proposed a batch-wise self-reconciled Gaussian process regression (BSGPR) model to achieve quality prediction for complex, dynamic batch processes. Summary of the Invention

[0006] In response to the problems of small samples, strong noise and insufficient exploration of potential correlations between batches in intermittent processes, the present invention provides a process quality prediction model based on BSGPR. According to the batch repetitive characteristics of the intermittent process, the key variables in the process are selected as learning variables, and CCA analysis is performed on any two batches at the same timestamp. The correlation matrix between batches is used to improve GPR. The improved re-predicted mean and variance are regarded as the output signals of the soft sensor, and DDR is applied to dynamically adjust the prediction variance in combination with the measurement data to reduce the influence of Gaussian noise. Finally, the effectiveness of this method is verified in the case of crystal size distribution (CSD) prediction in combination with the proposed BSGPR model.

[0007] The specific technical solutions of the present invention for solving the technical problems are as follows:

[0008] A batch process quality prediction method based on self-correcting batch-dependent Gaussian regression includes the following steps:

[0009] (1) Gaussian process regression integrates batch correlation information

[0010] Step 1.1: Extract multiple batch process data samples D from batch process production = {(x i ,y i )|i=1,...,n}=(X,y),x i ∈R m is an m-dimensional input vector, X∈R m×n It is an m×n matrix composed of n input vectors, and the noise in the regression model y=f(X)+ε is a Gaussian vector, is the noise variance of the normal distribution. Expand each batch into a two-dimensional matrix with the same time length, perform zero mean processing on the data, and obtain any batch X i The mean vector μ of (i=1,...,n) is:

[0011]

[0012] Among them, N i is the total number of samples in the i-th batch of data, and the zero-mean data is obtained The zero-mean data is divided into a training set and a test set in a 1:1 ratio.

[0013] Step 1.2: Use CCA method to analyze any two batches X i and X j The zero-mean data of (j=1,...,n) is time-sliced and projected, the correlation coefficients between batches at different time points are calculated, and the direction of maximum correlation is found. The resulting projection vector is W i and W j , the correlation matrix Σ is obtained by singular value decomposition b , the correlation matrix Σ b The element r ij Represents the correlation between batches, given by the formula definition;

[0014] Step 1.3: Convert the batch correlation matrix Σ b The kernel function k(x i ,x j ), so that it takes into account both the potential correlation between batches and the similarity between input variables, the improved kernel function expression is as follows:

[0015]

[0016] Among them, σ f is the signal variance, l is the length scale, z i and z j are the process variables corresponding to the i-th and j-th batches at the same time point, and ζ is the length scale of the similarity of the process variables.

[0017] (2) BSGPR modeling and training

[0018] Step 2.1: GPR model combined with CCA for any input data X i , predicted mean μ i and the prediction variance (σ i ) 2 It is given by the following formula:

[0019]

[0020] Where K(·,·) is the covariance matrix between the elements in the brackets, I n For units;

[0021] Step 2.2: Based on the μ calculated in the above steps iand (σ i ) 2 As a priori estimate, the measurement noise generated by offline hardware measurement during production is The model prediction error is Σ ε Reflects the uncertainty in the measurement process, Σ δ Used to measure the uncertainty of the predicted output. Assume that the true output is y t , the predicted output of the system is y, and the probability density function (PDF) of the measurement noise is expressed as:

[0022]

[0023] The predicted output of the system Under the influence of process model uncertainty, it can be expressed as The best true output y estimated by combining the measured and predicted values t The PDF is:

[0024]

[0025]

[0026] Among them, p(y t |y)=p(yy t )=p(ε) is the given true output y t The PDF of the measured value y, is the given predicted output The true output y t Likelihood function of .

[0027] By maximizing the posterior probability distribution, we get an estimate of the true output. Introducing the time step k and batch index i, we get the estimated output of the DDR in the form of real-time prediction-correction.

[0028]

[0029] Among them, W d =Σ δ (Σ ε +Σ δ ) -1 is the actual value and predicted value The weight matrix between

[0030] Step 2.3: Update the prediction variance matrix Σ by DDR method d , whose expression is:

[0031]

[0032] The kernel function of GPR is improved based on the updated prediction variance matrix. The improved kernel function The expression is:

[0033]

[0034] Among them, the signal variance is adjusted to The length scale is adjusted to Using the corrected prediction variance matrix Σ d and kernel function parameters, and retrain the Gaussian process regression model to obtain the BSGPR prediction results.

[0035] (3) Model testing and performance evaluation

[0036] Step 3.1: Validate the BSGPR model in a numerical case of a batch crystallization process (CSD). Use the processed test data set to validate the GPR model with batch association and the BSGPR model with dynamic data correction. Compare the predicted output of the model with the actual observations of the test data set and use the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and coefficient of determination (R) to evaluate the predicted output. 2 ) Several evaluation indicators are used to evaluate the performance of the model. The specific expression is:

[0037]

[0038] y i is the actual observed value, is the model prediction value, is the mean of the actual observations, and n is the number of samples in the test data set. Based on the results of the above evaluation indicators, the optimal model structure and parameter configuration are determined;

[0039] Step 3.2: Compare the test results of the BSGPR model with those of other quality prediction models. Compare the model's predictions on the test dataset with the actual observed data. Use visualization tools such as 3D surface mesh plots and residual plots to display the prediction distribution of each model and analyze its adaptability and stability under different operating conditions.

[0040] The beneficial effects of the present invention are mainly manifested in:

[0041] The present invention proposes a batch process quality prediction method based on self-correcting batch-correlated Gaussian regression. By combining canonical correlation analysis and dynamic data correction, the model can not only better capture the potential correlation between batch data, but also adapt to measurement uncertainty and prediction error through dynamic data correction, thereby significantly improving the prediction performance and stability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a flow chart of the method of the present invention;

[0043] Figure 2 Schematic diagram of an intermittent cooling crystallizer of the present invention;

[0044] Figure 3 3a is the distribution of CSD and each model in batch 1 and batch 5 in the embodiment of the present invention; 3b is the distribution of CSD and each model in batch 5;

[0045] Figure 4 4a is the distribution of BSGPR and each model in batch 1 and batch 5 in the embodiment of the present invention; 4b is the distribution of BSGPR and each model in batch 5;

[0046] Figure 5 In the embodiment of the present invention, the true values in batches 1 and 5 are compared with the predicted outputs of each model; 5a is the comparison between the true values in batch 1 and the predicted outputs of each model, and 5b is the comparison between the true values in batch 5 and the predicted outputs of each model. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0048] On the contrary, the present invention covers any alternatives, modifications, equivalents, and solutions that fall within the spirit and scope of the present invention as defined by the claims. Furthermore, to facilitate a better understanding of the present invention, certain specific details are described in detail below in the detailed description of the present invention. Those skilled in the art will be able to fully understand the present invention without these details.

[0049] Reference Figure 1 A batch process quality prediction method based on self-correcting batch-dependent Gaussian regression is proposed. Taking CSD prediction in batch crystallization process as an example, the method includes the following steps:

[0050] (1) Gaussian process regression fusion batch association information step

[0051] Step 1.1: Simulate the intermittent cooling crystallization (CSD) process and generate data for two different operating conditions, with five data sets for each condition. These data sets simulate cooling processes from 25°C-15°C to 21°C-11°C, and from 35°C-25°C to 31°C-21°C. Gaussian noise was added to the 280 sampling points in each data set. The number of CSD data points for each time period was 14, and the total sample data was zero-meaned.

[0052] First, perform singular value decomposition (SVD) on the input feature variables (temperature, seed width, time) of each batch to construct the projection vector of each batch. Then, use the following formula to calculate the correlation coefficient between each batch of data:

[0053]

[0054] in, and are the input variable matrices after zero mean processing for the i-th and j-th batches, W i and W j is the batch projection vector extracted by singular value decomposition, r ij is the correlation coefficient between batch i and batch j. Calculate r for all batches ij To construct the batch correlation matrix Σ b By performing correlation analysis on the batch data at different cooling crystallization temperatures, the average Pearson correlation coefficient was calculated to be 0.423.

[0055] Step 1.2: Based on the batch correlation matrix Σ constructed in step 1.1 b This matrix was applied to the kernel function of the GPR to improve the model's ability to capture inter-batch correlations. Subsequently, the improved GPR model was trained using five sets of data with cooling crystallization temperatures ranging from 25°C to 15°C, and the predicted mean and variance were obtained. The model's prediction output was normalized CSD data, which was then denormalized to restore the actual data values.

[0056] Attachment Figure 3The 3D surface mesh plots show the true distribution of CSD crystals, the GPR-predicted distribution, and the GPR-predicted distribution combined with CCA for the first and fifth batches, respectively, with a noise variance of 0.004. It can be seen that the GPR model combined with CCA better captures the main trends in the CSD distribution than the traditional GPR model, especially when the data fluctuates significantly, where the model predictions are closer to the actual values. This demonstrates that the GPR model, which incorporates inter-batch correlations, achieves higher prediction accuracy when processing dynamic data.

[0057] (2) BSGPR modeling and training steps

[0058] Step 2.1: Use the GPR model combined with the batch correlation matrix to perform preliminary training on the test data set and calculate the predicted mean μ of each sample i and the prediction variance (σ i ) 2 for:

[0059]

[0060] Where K(·,·) is the covariance matrix between the elements in the brackets, is the variance of the noise, I n is the unit matrix, X is the training dataset, and y is the observed output of the training dataset. These results provide a priori estimates for the subsequent dynamic data correction (DDR).

[0061] Step 2.2: In the CSD prediction process, the measurement data contains a certain amount of noise ε, and the prediction output contains the prediction error δ. Both are assumed to obey the normal distribution, and their covariance matrices are ∑ ε and ∑ δ .

[0062] Based on Bayesian inference, the posterior probability distribution is Among them, the likelihood function Reflects the given prediction output When the real output y t By maximizing the posterior probability distribution, we can get the corrected true output y t , introducing the time step t and batch index i, the final correction result can be obtained through the DDR gain matrix W d To express:

[0063]

[0064] Among them, W d =Σ δ (Σ ε +Σ δ ) -1The weight matrix used to combine the measured data and the model's predicted data.

[0065] Step 2.3: After fusing the covariance matrix of measurement noise and prediction error, update the prediction variance matrix Σ d :

[0066]

[0067] Using the updated prediction variance matrix Σ d , redefine the kernel function of the Gaussian process regression model The signal variance is adjusted to The length scale is adjusted to The kernel function further takes into account the similarity between data points, batch correlation and uncertainty.

[0068] Step 2.4: Use the updated BSGPR model based on the improved kernel function and prediction variance matrix to re-predict the validation data. Predictions are made using the normalized data and then denormalized. The final model output is the corrected CSD prediction data. Every sample point in the validation dataset is generated using the updated model, significantly improving prediction accuracy and stability.

[0069] (3) Model testing and performance evaluation steps

[0070] Step 3.1: After completing the construction and re-forecasting of the BSGPR model, the model is tested and its performance is evaluated. The model testing mainly focuses on evaluating the prediction accuracy of the model using the validation dataset. The core indicators of the test include root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and coefficient of determination (R 2 Table 1 shows the average RMSE values, average R 2 Comparison of the average MAE value and the average MAPE value:

[0071] Table 1 Average RMSE and R of different models under 3% and 5% noise 2 , MAE and MAPE value comparison

[0072]

[0073] Table 1 compares the prediction performance of different models under 3% and 5% noise conditions. The results show that as the noise level increases, the BSGPR model always maintains the lowest RMSE and MAE values, and R 2Values close to 1 demonstrate optimal prediction accuracy and stability. In contrast, the performance of other models significantly degrades under high-noise conditions. In summary, the BSGPR model has significant advantages when processing batch process data with high noise and small sample sizes.

[0074] Step 3.2: Compare the distribution results of BSGPR model, other GPR prediction models and CSD, Figure 4 The prediction performance of three GPR models was compared across different batches. The results showed that the BSGPR model achieved the best prediction accuracy across all batches. Compared to the GPR model combined with CCA, the BSGPR model was able to better correct prediction bias, maintaining high stability and accuracy, especially in the presence of high-noise data.

[0075] Attachment Figure 5 Comparisons of the CSD outputs of three GPR models across two batches are shown. The predictions of the GPR model combined with CCA and the BSGPR model are closer to the actual distribution. In particular, in batch 5, which exhibits significant dynamic changes, the BSGPR model further reduces prediction error, significantly outperforming the other models. This demonstrates the model's effectiveness in handling complex dynamic processes.

[0076] The proposed batch process quality prediction method based on self-corrected batch-correlated Gaussian regression has been fully validated on CSD data from batch crystallization processes. By introducing a batch correlation matrix, the GPR kernel function is improved, taking into account not only the similarity of input data points but also the correlation between batches, thereby improving the model's predictive performance. Furthermore, a batch self-corrected Gaussian process regression model (BSGPR) is proposed by integrating the dynamic data correction (DDR) method. This model can effectively correct prediction results and update variances using actual measurements. This model has significant advantages when dealing with complex dynamic processes and high-noise environments, reducing prediction errors and improving goodness of fit.

[0077] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The scope of protection of the present invention should not be regarded as limited to the specific forms described in the embodiments. The scope of protection of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A batch process quality prediction method based on self-correcting batch-dependent Gaussian regression, characterized in that: The steps include: Step (1): Acquire and integrate multiple batch data of the batch process, use canonical correlation analysis (CCA) to analyze the correlation between batches, construct a batch correlation matrix, and use the batch correlation matrix to improve the kernel function of the Gaussian process regression (GPR) model; Step (2): Introduce a dynamic data correction method, dynamically adjust the prediction error through Bayesian reasoning, optimize the prediction results based on the measured data, update the prediction variance matrix and obtain the batch self-correcting Gaussian process regression (BSGPR) model; Step (3): Use the BSGPR model for modeling training and testing to verify its effectiveness in the batch crystallization process.

2. The batch process quality prediction method based on self-correcting batch-dependent Gaussian regression according to claim 1, characterized in that: The specific process of step (1) is as follows: Step 1.1: Extract multiple batches of process data samples from batch production, expand each batch of data into a two-dimensional matrix of the same time length, perform zero-mean processing on the data, and divide the zero-mean data into a training set and a test set; Step 1.2: Use canonical correlation analysis (CCA) to analyze any two batches X i and X j The zero-mean data is time-sliced and projected, the correlation coefficients between batches at different time points are calculated, the direction of maximum correlation is found, and the projection vector W is obtained. i and W j , and obtain the correlation matrix Σ by singular value decomposition b , the correlation matrix Σ b The element r ij Indicates the correlation between batches; Step 1.2: Convert the correlation matrix Σ b The kernel function k(x i ,x j ), so that it can simultaneously consider the potential correlation between batches and the similarity between input variables, and obtain the improved kernel function.

3. The batch process quality prediction method based on self-correcting batch-dependent Gaussian regression according to claim 1, characterized in that: The specific process of step (2) is as follows: Step 2.1: GPR model combined with CCA for any input data X i , calculate the predicted mean μ i and the prediction variance (σ i ) 2 ; Step 2.2: Set μ i and (σ i ) 2 Treated as a priori estimation, the estimated value of the true output is obtained by maximizing the posterior probability distribution; the time step k and batch index i are introduced to obtain the estimated output of the dynamic data correction DDR in the form of real-time prediction-correction Step 2.3: Update the prediction variance matrix Σ by DDR method d , based on the updated prediction variance matrix Σ d Improve the kernel function of GPR and use the corrected prediction variance matrix Σ d and kernel function parameters, and retrain the Gaussian process regression model to obtain the BSGPR prediction results.

4. The batch process quality prediction method based on self-correcting batch-dependent Gaussian regression according to claim 1, characterized in that: The specific process of step (3) is as follows: Step 3.1: Use the test dataset to verify the GPR model with batch association and the BSGPR model with dynamic data correction; the details are as follows: Step 3.1: Compare the predicted output of the model with the actual observations of the test dataset using the root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), and coefficient of determination (R). 2 Evaluate the performance of the model; Step 3.2: Compare the test results of the BSGPR model with those of other quality prediction models: Compare the prediction results of the model on the test dataset with the actual observation data, use visualization tools to display the prediction distribution of each model, and analyze its adaptability and stability under different working conditions.

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