Batch process robust optimization quality improvement method based on adaptive correction

Abstract

The invention provides a batch process robust optimization quality improvement method based on adaptive correction, and aims at solving the problem that a robust model is difficult to establish due to insufficient data in a new batch process, and constructing a JYPLS migration model by utilizing sufficient data in a similar process; uncertain factors caused by a complex operation environment, frequent disturbance and the like of the intermittent process are analyzed, and an intermittent process inter-batch robust optimization mathematical model under model uncertainty is established by using a robust optimization method so as to process the uncertain problem; a robust optimization method is used to solve uncertainty factors caused by complex operation environment and process disturbance of the intermittent process, and an adaptive correction method is introduced at the same time; according to the problem that optimal necessary conditions of different operation optimization stages are not matched, a migration model and an uncertain set dual update mechanism for data update and elimination guidance are formulated; and finally, the model is solved, and an optimal operation variable is found. The method can effectively improve the final quality of products and the economic benefits of enterprises.

Description

Technical Field

[0001] The present invention belongs to the technical field of operation optimization of intermittent production processes, and specifically is an intermittent process robust optimization quality improvement method based on adaptive correction. Background Art

[0002] The intermittent production process has the characteristics of small batches, multiple varieties and high added value. It can produce high-quality, personalized and diversified products. It is a key production method in the process industry. The intermittent process is also often called a batch process. It is defined as: according to a specific process flow and processing sequence, a certain ratio of raw materials is put into one or more production equipment, and after a certain period of time, through physical or chemical reactions, products that meet the quantity and quality requirements are produced. Since the raw materials in the intermittent process often change, the production conditions and environment also fluctuate greatly, and it involves complex physical and chemical reactions, there are many process steps, and there is no stable operating point. Therefore, this process is particularly suitable for the production of products with high added value, small-scale production, and multi-stage operation characteristics, and is widely used in mineral beneficiation, fine chemicals, pharmaceuticals and foods, polymers, and microelectronics.

[0003] In the intermittent production process, factors such as raw material composition, equipment status, process parameters and product quality are often difficult to measure in real time. Coupled with the disturbances in the operating environment and the uncertainty of raw materials, it is particularly important to optimize the operation of the intermittent production process to improve the quality and intelligence level of the end product.

[0004] Establishing a reliable process model is the basis for quality prediction and operation optimization control. With the rapid changes in the market and the increasing demand for product quality, diversification and personalization, modern process industries are gradually developing in the direction of scale, intensiveness and intelligence. The internal production processes of process industries and the physical and chemical principles involved have become more complex and diverse, making it difficult to fully grasp them, making it difficult to effectively implement model methods based on process mechanism drive. However, with the widespread application of distributed control systems, fieldbus control systems and advanced sensor technologies, a large amount of historical operation data and process knowledge have been accumulated in industrial processes, providing a reliable foundation for data-driven modeling methods. Data-driven modeling methods do not rely on the internal mechanisms of the production process, but instead mine, analyze and extract features from the process information contained in historical data to construct the target process model.

[0005] However, in industrial scenarios where production data is insufficient or the data quality is poor, it is difficult for data-driven modeling methods to establish accurate quality prediction models. This may cause the optimization control scheme derived from the model to be suboptimal for the actual production process, or even impossible to implement. In modern process industries, there are usually multiple production lines producing the same or similar products. Since they involve the same or similar production processes and physical and chemical principles, these process data often have similar or identical characteristics. Transfer learning can effectively use similar information from other production processes to establish prediction models. However, due to the inevitable differences between different processes, there may be a mismatch between the transfer model and the actual production process, resulting in the result of operation optimization often being a suboptimal solution, or even not meeting the actual operating conditions. In addition, uncertain factors such as complex operating environment and frequent process disturbances further increase the difficulty of quality prediction and operation optimization in intermittent production processes. In order to effectively solve the above problems, it is urgent to provide a robust optimization quality improvement method for intermittent processes based on adaptive correction. Summary of the invention

[0006] In view of the problems existing in the above-mentioned prior art, the present invention provides a robust optimization quality improvement method for intermittent processes based on adaptive correction. The implementation process of the method is simple and the implementation cost is low. It can realize quality prediction and operation optimization of the production process under insufficient data and uncertain environment, thereby effectively improving the final quality of the product and the economic benefits of the enterprise.

[0007] In order to achieve the above-mentioned object, the present invention provides a batch process robust optimization quality improvement method based on adaptive correction, comprising two similar batch production processes A and B; production process A is an old production process that has been produced for a long time in the factory, which has a large amount of batch production data, and production process B is a new production process that has just been put into production in the factory, which has a small amount of batch production data;

[0008] The robust optimization quality improvement method for intermittent processes based on adaptive correction includes the following steps:

[0009] Step 1: Collect the three-dimensional data matrix (X A ,Y A ) and sends it to the controller, and collects the three-dimensional data matrix (X) of production process B through sensor group B installed in the production system where production process B is located. B ,Y B ) and sent to the data processor; wherein, is the input data matrix of production process A, is the output data matrix of production process A, Input data matrix for production process B, is the output data matrix of production process B, I represents the production batch, J represents the sampling interval, K represents the operating variable, and M represents the number of output variables;

[0010] Step 2: Use the data processor to expand the three-dimensional data matrices of production processes A and B into two-dimensional data matrices according to the batch dimension, and obtain and

[0011] Step 3: Use the data processor to establish the JYPLS process migration model;

[0012] A1: and Defined in the same score space, and Distributed in the same latent variable space;

[0013] A2: Define Q J ∈R N×G is the joint load matrix of production processes A and B, representing the load space jointly defined by their joint output matrices, where G represents the number of latent variables;

[0014] A3: Establish the JYPLS model according to formula (1), formula (2) and formula (3);

[0015]

[0016] Where, T A =X A W A , T B =X B W B , E A 、E B and E YJ Represent the corresponding deviations respectively; P A , P B is the load matrix;

[0017] A4: A new input variable x based on a batch in production process B B,new , based on the JYPLS model, the predicted value y of the end product quality is obtained according to formula (4);

[0018]

[0019] In the formula, B J is the regression coefficient,

[0020] Step 4: Initialize the uncertainty set;

[0021] Step 5: Use the data processor to construct the objective function and constraints of the robust optimization model;

[0022] B1: By solving the consistency of the first-order approximation term to compensate for the NCO mismatch problem in the optimization problem, the modified JYPLS model of the kth batch is obtained according to formula (5);

[0023]

[0024] In the formula, represents the modified JYPLS model quality prediction, Represents the prediction output of the JYPLS model. and have the same meaning; σ is the standard deviation, ε k is the zero-order correction term of the k-th batch, λ k is the first-order correction term for the kth batch, in, pass Calculated, pass, Calculated, represents the Kronecker product;

[0025] B2: After the JYPLS model is modified according to formula (5), the batch process optimization problem based on the JYPLS model is expressed as formula (6);

[0026]

[0027] B3: Considering the uncertainty of the model, the auxiliary parameter F is introduced to convert the optimization problem based on the JYPLS model into the form in formula (7);

[0028]

[0029] B4: Select the box uncertainty set and express the model parameter uncertainty in the form of formula (8);

[0030] B=B * +ξ(8);

[0031] In the formula, U={ξe T ξ=0,ξ min ≤ξ≤ξ max};

[0032] B5: According to the robust optimization method, formula (7) is equivalently transformed into solving two optimization problems: formula (9) and formula (10);

[0033]

[0034] B6: The actual process output value and the JYPLS model prediction value are expressed as formula (11) using the first-order adaptive correction method;

[0035]

[0036] In the formula, represents the revised JYPLS model prediction value;

[0037] B7: for y p (x) and Perform univariate and bivariate Taylor expansion respectively, and obtain formula (12), formula (13), formula (14) and formula (15) respectively;

[0038] y p (x) = y p (x k )+y p '(x k )(xx k )(12);

[0039]

[0040] B8: Solving the maximization problem Equivalent to solving Will Expand into the form in formula (16);

[0041]

[0042] In the formula,

[0043] B9: For uncertain Construct the Lagrangian function according to formula (17);

[0044]

[0045] B10: Order Among them, α, l, γ are Lagrange coefficients respectively, and formula (18) is obtained according to the optimization duality theory;

[0046]

[0047] B11: According to formula (18), formula (19) is obtained;

[0048]

[0049] B12: Transform formula (10) to obtain the new robust optimization problem in formula (20);

[0050]

[0051] Step 6: Use the data processor to perform inter-batch optimization on the kth batch;

[0052] C1: Combine the uncertainty set constructed in step 4 to solve the robust optimization model constructed in step 5 and obtain the initial operation variable trajectory

[0053] C2: Calculate the current initial operation variable trajectory The operation variable trajectory of the previous batch difference

[0054] C3: Judgment Is it less than the preset threshold θ? If so, let x k =x k-1 Otherwise, the initial operation variable trajectory of the current batch is filtered by the first-order exponential filter shown in formula (21) Filter and obtain the final operating variable trajectory x k ;

[0055]

[0056] Step 7: Use the final manipulated variable trajectory x obtained in step 6 through the data processor k Carry out the production of the current batch and measure the process output y after the batch is completed k ;

[0057] Step 8: Output the latest acquired process y through the data processor k Add to modeling data set and uncertainty set and perform data removal;

[0058] D1: After the kth batch is produced and data is filled, the end-point product quality deviation between the current batch and the adjacent batch is calculated according to formula (22), and the data set F is constructed according to formula (23);

[0059]

[0060] D2: Setting the stability threshold γ s and the trust threshold γ t As a judgment indicator for the timing of data removal; if the quality deviation of t consecutive endpoint products collected by the data set F is less than the trust threshold γ t And at least s (s≤t) endpoint product quality deviations are less than the stability threshold γ s, it is believed that the model mismatch caused by the difference between the new and old processes hinders the further improvement of model performance, and data elimination begins. At this time, the second stage of the dual update mechanism of the model and the uncertainty set is entered;

[0061] D3: Use formula (24) and formula (25) respectively to select the modeling dataset and dataset D in the order of similarity from small to large. m Eliminate several groups of data respectively;

[0062]

[0063] Step 9: Use the data processor to update the uncertainty set;

[0064] E1: Determine the worst-case uncertainty range of the process output using formula (26) The allowable range of process output under model uncertainty is determined by formula (27):

[0065]

[0066] In the formula, and are the upper and lower bounds of the uncertainty range, respectively, which are based on the data set D m The n groups of data with high similarity or the q groups of data closest to the current batch are obtained, and y is the output of the current batch process model;

[0067] E2: According to The uncertainty range of the model can be inferred by the current batch operation variables;

[0068] Step 10: Set k=k+1 and return to step 3 until all production batches are completed.

[0069] The present invention provides a method for improving the quality of batch process robust optimization based on adaptive correction. In the method, firstly, for the problem that it is difficult to establish a robust model for a new batch process due to insufficient data, a joint output partial least squares (JYPLS) migration model is constructed using sufficient data of similar processes, which can improve model performance and data utilization. Then, the uncertainty factors caused by the complex operating environment and frequent disturbances of the batch process are analyzed, and a robust optimization method is used to establish a robust optimization mathematical model between batches of batches of batches under model uncertainty to deal with the uncertainty problem. In view of the complex and diverse uncertainties of the batch process, and the problem that the robust optimization method is more conservative than the actual production process due to the satisfaction of conditions in all cases within the uncertainty set, an adaptive correction method is introduced while using the robust optimization method to solve the uncertainty factors caused by the complex operating environment and process disturbances of the batch process. On the one hand, the adaptive method compensates for the mismatch between the migration model and the actual process, and on the other hand, it compensates for the problem that the optimization results of the robust optimization method are more conservative due to the complex and changeable uncertainties and the consideration of all possible situations within the uncertainty set. While dealing with model uncertainty, process information can be used as much as possible to further improve product quality and optimization efficiency. In addition, according to the NCO mismatch problem in different stages of operation optimization, a data updating and elimination-guided migration model and uncertainty set dual updating mechanism are formulated to continuously improve the accuracy of the process model and uncertainty set, which can ensure the performance of the proposed method in the entire production operation of the new intermittent process. Finally, the model is solved to find the optimal operating variables.

[0070] The method has a simple implementation process and low implementation cost. It can realize quality prediction and operation optimization of the production process under insufficient data and uncertain environment, thereby effectively improving the final quality of the product and the economic benefits of the enterprise. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 This is a schematic diagram of the production process of cobalt oxalate crystals;

[0072] Figure 2 To optimize the effect comparison;

[0073] Figure 3 is the confidence interval comparison;

[0074] Figure 4 Comparison of standard deviation trends;

[0075] Figure 5 It is a comparison of standard deviation box plot;

[0076] Figure 6 Feeding trajectories for different batches;

[0077] Figure 7 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0078] The present invention will be further described below in conjunction with the accompanying drawings.

[0079] like Figures 1 to 7 As shown, the present invention provides a robust optimization quality improvement method for intermittent processes based on adaptive correction, including two similar intermittent production processes A and B; production process A is an old production process that has been produced for a long time in the factory, and has a large amount of batch production data, and production process B is a new production process that has just been put into production in the factory, and has a small amount of batch production data;

[0080] The robust optimization quality improvement method for intermittent processes based on adaptive correction includes the following steps:

[0081] Step 1: Collect the three-dimensional data matrix (X A ,Y A ) and sends it to the controller, and collects the three-dimensional data matrix (X) of production process B through sensor group B installed in the production system where production process B is located. B ,Y B ) and sent to the data processor; wherein, is the input data matrix of production process A, is the output data matrix of production process A, Input data matrix for production process B, is the output data matrix of production process B, I represents the production batch, J represents the sampling interval, K represents the operating variable, and M represents the number of output variables;

[0082] Step 2: Use the data processor to expand the three-dimensional data matrices of production processes A and B into two-dimensional data matrices according to the batch dimension, and obtain and

[0083] Step 3: Use the data processor to establish the JYPLS process migration model;

[0084] A1: and Defined in the same score space, and Distributed in the same latent variable space;

[0085] A2: Define Q J ∈R N×Gis the joint load matrix of production processes A and B, representing the load space jointly defined by their joint output matrices, where G represents the number of latent variables;

[0086] A3: Establish the JYPLS model according to formula (1), formula (2) and formula (3);

[0087]

[0088]

[0089] Where, T A =X A W A , T B =X B W B , E A 、E B and Represent the corresponding deviations respectively; P A , P B is the load matrix;

[0090] A4: A new input variable x based on a batch in production process B B,new , based on the JYPLS model, the predicted value y of the end product quality is obtained according to formula (4);

[0091]

[0092] In the formula, B J is the regression coefficient,

[0093] Step 4: Initialize the uncertainty set;

[0094] Step 5: Use the data processor to construct the objective function and constraints of the robust optimization model;

[0095] B1: By solving the consistency of the first-order approximation term to compensate for the NCO mismatch problem in the optimization problem, the modified JYPLS model of the kth batch is obtained according to formula (5);

[0096]

[0097] In the formula, represents the modified JYPLS model quality prediction, Represents the prediction output of the JYPLS model. and have the same meaning; σ is the standard deviation, ε k is the zero-order correction term of the k-th batch, λ k is the first-order correction term for the kth batch, in, pass Calculated, pass, Calculated, represents the Kronecker product;

[0098] B2: After the JYPLS model is modified according to formula (5), the batch process optimization problem based on the JYPLS model is expressed as formula (6);

[0099]

[0100] B3: Considering the uncertainty of the model, the auxiliary parameter F is introduced to convert the optimization problem based on the JYPLS model into the form in formula (7);

[0101]

[0102] B4: Select the box uncertainty set and express the model parameter uncertainty in the form of formula (8);

[0103] B=B * +ξ(8);

[0104] In the formula, U={ξe T ξ=0,ξ min ≤ξ≤ξ max};

[0105] B5: According to the robust optimization method, formula (7) is equivalently transformed into solving two optimization problems: formula (9) and formula (10);

[0106]

[0107] B6: The actual process output value and the JYPLS model prediction value are expressed as formula (11) using the first-order adaptive correction method;

[0108]

[0109] In the formula, represents the revised JYPLS model prediction value;

[0110] B7: for y p (x) and Perform univariate and bivariate Taylor expansion respectively, and obtain formula (12), formula (13), formula (14) and formula (15) respectively;

[0111] y p (x) = y p (x k )+yp '(x k )(xx k )(12);

[0112]

[0113]

[0114] B8: Solving the maximization problem Equivalent to solving because There are uncertain parameters in the model, and the model is nonlinear and difficult to solve directly. Therefore, Expand into the form in formula (16);

[0115]

[0116] In the formula,

[0117] B9: For uncertain Construct the Lagrangian function according to formula (17);

[0118]

[0119] B10: Order Among them, α, l, γ are Lagrange coefficients respectively, and formula (18) is obtained according to the optimization duality theory;

[0120]

[0121] B11: According to formula (18), formula (19) is obtained;

[0122]

[0123] B12: Transform formula (10) to obtain the new robust optimization problem in formula (20);

[0124]

[0125] Step 6: Use the data processor to perform inter-batch optimization on the kth batch;

[0126] C1: Combine the uncertainty set constructed in step 4 to solve the robust optimization model constructed in step 5 and obtain the initial operation variable trajectory

[0127] C2: Calculate the current initial operation variable trajectory The operation variable trajectory of the previous batch difference

[0128] C3: Judgment Is it less than the preset threshold θ? If so, let x k =x k-1 Otherwise, the initial operation variable trajectory of the current batch is filtered by the first-order exponential filter shown in formula (21) Filter and obtain the final operating variable trajectory x k ;

[0129]

[0130] Step 7: Use the final manipulated variable trajectory x obtained in step 6 through the data processor k Carry out the production of the current batch and measure the process output y after the batch is completed k ;

[0131] Step 8: Output the latest acquired process y through the data processor k Add to modeling data set and uncertainty set and perform data removal;

[0132] D1: After the kth batch is produced and data is filled, the end-point product quality deviation between the current batch and the adjacent batch is calculated according to formula (22), and the data set F is constructed according to formula (23);

[0133]

[0134] D2: Setting the stability threshold γ s and the trust threshold γ t As a judgment indicator for the timing of data removal; if the quality deviation of t consecutive endpoint products collected by the data set F is less than the trust threshold γ t And at least s (s≤t) endpoint product quality deviations are less than the stability threshold γ s , it is believed that the model mismatch caused by the difference between the new and old processes hinders the further improvement of model performance, and data elimination begins. At this time, the second stage of the dual update mechanism of the model and the uncertainty set is entered;

[0135] D3: Use formula (24) and formula (25) respectively to select the modeling dataset and dataset D in the order of similarity from small to large. m Eliminate several groups of data respectively;

[0136]

[0137] Step 9: Use the data processor to update the uncertainty set;

[0138] E1: Determine the worst-case uncertainty range of the process output using formula (26) The allowable range of process output under model uncertainty is determined by formula (27):

[0139]

[0140] In the formula, and are the upper and lower bounds of the uncertainty range, respectively, which are based on the data set D m The n groups of data with high similarity or the q groups of data closest to the current batch are obtained, and y is the output of the current batch process model;

[0141] E2: According to The uncertainty range of the model can be inferred by the current batch operation variables;

[0142] Step 10: Set k=k+1 and return to step 3 until all production batches are completed.

[0143] The present invention is further described below in conjunction with embodiments, and its feasibility is verified.

[0144] The synthesis process of cobalt oxalate is a typical intermittent process and a representative example of the mineral processing industry. As one of the raw materials for preparing metallic cobalt, the synthesis process of cobalt oxalate is a key link in the hydrometallurgical production of metallic cobalt. Cobalt oxalate crystals are obtained mainly through the liquid phase reaction of cobalt chloride solution and ammonium oxalate solution as shown in formula (28).

[0145]

[0146] The synthesis process of cobalt oxalate is mainly in the form of solution. Figure 1 The reaction device shown in the figure mainly includes the steps of preparing oxalic acid solution, synthesizing ammonium oxalate solution, synthesizing cobalt oxalate precipitate, and filtering, washing, drying, etc.:

[0147] (a) dissolving solid oxalic acid and water in a certain proportion and filtering to obtain an oxalic acid solution of appropriate concentration;

[0148] (b) pouring the prepared oxalic acid solution into an ammonium oxalate synthesis reactor and passing ammonia gas of a certain concentration, and reacting at a certain temperature to obtain an ammonium oxalate solution;

[0149] (c) adding the ammonium oxalate solution into the cobalt oxalate synthesis reactor at a certain feed rate, and reacting with a cobalt chloride solution of a certain concentration at a suitable temperature to obtain a cobalt oxalate precipitate;

[0150] (d) After filtration, washing, drying and other operations, the finished cobalt oxalate product can be obtained.

[0151] The average particle size of cobalt oxalate is a key indicator for measuring the synthesis process of cobalt oxalate. In the synthesis process of cobalt oxalate, the average particle size of cobalt oxalate is affected by factors such as the temperature of the reaction process, the stirring rate, and the feed rate of the ammonium oxalate solution. In the actual production process, the reaction temperature and stirring rate are set at constant values, and the average particle size of the cobalt oxalate product is adjusted by adjusting the feed rate of the ammonium oxalate solution. Single-input-single-output process with the average particle size of the cobalt oxalate product as the output variable

[0152] (1) Data generation and parameter setting

[0153] By setting different initial raw material volumes / concentrations, stirring rates, or different rate coefficients k of the nucleation and growth processes in the established cobalt oxalate synthesis process mechanism model, b and k g , crystal density ρ c , shape factor Kv and other parameters to achieve differences in working environment and process level; by adding 2%-5% random noise to parameters such as stirring rate and initial volume / concentration of raw materials, the many uncertain factors in intermittent process production such as complex operating environment and process disturbance are simulated. Production process A represents an old process that has been completed and has accumulated a certain amount of process data, and production process B represents a new process that has just been put into production and is also the target process that needs to be optimized. Based on actual production experience and prior knowledge, the parameters of similar process A and target process B are set as shown in Table 1:

[0154] Table 1 Mechanism model parameters

[0155] Mechanistic model parameters Process A Process B <![CDATA[Concentration of cobalt chloride solution (mol / m 3 )]]> 1064.3～1182.6 811.9～1253.2 <![CDATA[Concentration of ammonium oxalate solution (mol / m 3 )]]> 1674.8～1842.2 1682.8～1858.7 <![CDATA[Initial volume of cobalt chloride (m 3 )]]> 1.38±1％ 1.4±1％ Temperature (K) 298 298.5 Stirring speed (rpm) 0.7 0.72 <![CDATA[K b (k)]]> <![CDATA[1.366×10 4 ]]> <![CDATA[1.3623×10 4 ]]> <![CDATA[K g (k)]]> <![CDATA[1.584×10 4 ]]> <![CDATA[1.5823×10 4 ]]> <![CDATA[k b (s -1 μm -3 )]]> <![CDATA[6.31×10 31 ]]> <![CDATA[6.3×10 31 ]]> <![CDATA[k g (s -1 μm)]]> <![CDATA[2.68×10 14 ]]> <![CDATA[2.7×10 14 ]]>

[0156] 40 batches of process data are randomly generated in the old process A to simulate a production scenario where a similar old process already has a large amount of process data. 5 batches of process data are randomly generated in the new process B to simulate a production scenario where the new process data is insufficient.

[0157] The feed rate of ammonium oxalate solution was selected as the operating variable, and the average particle size of cobalt oxalate was selected as the indicator of the end product quality. The filter gain coefficient K was set to 0.25, the production time of a single batch was 660 seconds, and it was evenly discretized into 11 segments to control the feed rate of ammonium oxalate solution. In addition, an amplitude of ±0.0005m 3 A random Gaussian signal of 100 Hz / s is used to simulate the dynamic characteristics of the actual production process, and 0.5% white noise is added to the acquired process output to simulate sampling noise.

[0158] (2) Adaptive correction strategy based on JYPLS

[0159] There are inevitable differences in raw materials, production equipment, production environment, initial conditions, etc. between similar processes. In addition, the uncertainty factors caused by the complex operating environment and frequent disturbances in the intermittent production process lead to the mismatch between the data-driven model and the actual process, which in turn leads to the NCO mismatch of the optimization problem. The adaptive correction method compensates for the NCO mismatch problem in the optimization problem by pursuing the consistency of the first-order approximation terms. According to the knowledge of Taylor expansion, formula (10) performs a first-order Taylor expansion approximation on the actual output value of the process and the predicted value of the JYPLS model, and then makes a difference, thereby compensating for the difference between the two in the zero-order term and the first-order term, and realizing the equivalent substitution between model optimization and actual optimization. The key to the first-order adaptive correction method is to achieve accurate gradient estimation of the JYPLS model and the actual process. However, in actual production, due to the existence of parameter uncertainty or model error, accurate gradient correction of the objective function and constraints cannot be guaranteed. Therefore, while using the MA method to correct the gradient of the objective function and constraints, the model uncertainty must also be processed. The model is expanded, and the Lagrangian function is constructed for the objective function with uncertainty. According to the optimization duality theory, the robust optimization model of the end-point product quality of the batch process is transformed into a general linear programming model for easy solution.

[0160] (3) Robust optimization strategy for product quality between batches based on adaptive correction

[0161] Due to the inherent conservatism of robust optimization methods, their optimization effects need to be further improved. At the same time, for production enterprises with high production costs and high requirements for batch consistency of end product quality, such as the cobalt oxalate production process and penicillin fermentation process, it is necessary to ensure safe production while making use of production process information as much as possible to improve production efficiency and ensure batch consistency of product quality. Based on the analysis of uncertainty factors in the synthesis process of cobalt oxalate, the JYPLS process migration model is first used to solve the problems of poor model performance and unsatisfactory operation optimization in the scenario of insufficient new process data. Then, a batch-to-batch robust optimization method under model uncertainty is proposed in combination with the idea of ​​adaptive correction. This aims to use robust optimization methods to handle uncertainty while making use of process information as much as possible, so as to obtain better optimization effects and batch consistency of product quality under uncertain production conditions. Figure 2 It can be seen that the robust optimization method for the end-point product quality based on adaptive correction stabilizes the average particle size of cobalt oxalate after about 20 production batches, and reduces the end-point product quality from 1.91×10 -6 m increased to 2.286×10 -6 m; its optimization effect and optimization efficiency are most ideal. When multiple production lines produce the same product at the same time, 10 groups of experiments are carried out continuously under the same experimental conditions. Figure 3The product quality confidence interval diagram shown in the figure shows that compared with the adaptive correction optimization strategy, the endpoint product quality robust optimization method based on adaptive correction can take into account the adverse effects of uncertainty factors on operation optimization while utilizing more first-order process information. Therefore, it has a more ideal endpoint product quality and a smaller standard deviation of the average particle size of cobalt oxalate in the first and second stages of the dual update mechanism of the model and uncertainty set. After 40 production batches, under the action of data elimination and data update, the modeling data set data can already fit the target new process well. At this time, it enters the third stage of the dual update mechanism of the model and uncertainty set and can establish a more accurate migration model. The adverse effects of insufficient data and model uncertainty are gradually reduced. The uncertainty set update mechanism of the robust optimization method is greatly affected by the quality of process data. The established uncertainty set cannot accurately reflect the size and form of the uncertainty of the target process model. The optimization results are conservative to a certain extent. The endpoint product quality robust optimization method based on adaptive correction can also utilize more process information, thereby improving the optimization efficiency. The endpoint product quality robust optimization method based on adaptive correction has a larger average particle size of cobalt oxalate, the highest optimization efficiency, and the smallest standard deviation, with better product quality batch consistency.

[0162] The present invention provides a method for improving the quality of batch process robust optimization based on adaptive correction. In the method, firstly, for the problem that it is difficult to establish a robust model for a new batch process due to insufficient data, a joint output partial least squares (JYPLS) migration model is constructed using sufficient data of similar processes, which can improve model performance and data utilization. Then, the uncertainty factors caused by the complex operating environment and frequent disturbances of the batch process are analyzed, and a robust optimization method is used to establish a robust optimization mathematical model between batches of batches of batches under model uncertainty to deal with the uncertainty problem. In view of the complex and diverse uncertainties of the batch process, and the problem that the robust optimization method is more conservative than the actual production process due to the satisfaction of conditions in all cases within the uncertainty set, an adaptive correction method is introduced while using the robust optimization method to solve the uncertainty factors caused by the complex operating environment and process disturbances of the batch process. On the one hand, the adaptive method compensates for the mismatch between the migration model and the actual process, and on the other hand, it compensates for the problem that the optimization results of the robust optimization method are more conservative due to the complex and changeable uncertainties and the consideration of all possible situations within the uncertainty set. While dealing with model uncertainty, process information can be used as much as possible to further improve product quality and optimization efficiency. In addition, according to the NCO mismatch problem in different stages of operation optimization, a data updating and elimination-guided migration model and uncertainty set dual updating mechanism are formulated to continuously improve the accuracy of the process model and uncertainty set, which can ensure the performance of the proposed method in the entire production operation of the new intermittent process. Finally, the model is solved to find the optimal operating variables.

[0163] The method has a simple implementation process and low implementation cost. It can realize quality prediction and operation optimization of the production process under insufficient data and uncertain environment, thereby effectively improving the final quality of the product and the economic benefits of the enterprise.

Claims

1. A robust optimization quality improvement method for intermittent processes based on adaptive correction, including two similar intermittent production processes A and B; production process A is an old production process that has been produced for a long time in the factory, which has a large amount of batch production data, and production process B is a new production process that has just been put into production in the factory, which has a small amount of batch production data; It is characterized in that The following steps are involved: Step 1: Collect the three-dimensional data matrix (X A ,Y A ) and sends it to the controller, and collects the three-dimensional data matrix (X) of production process B through sensor group B installed in the production system where production process B is located. B ,Y B ) and sent to the data processor; wherein, is the input data matrix of production process A, is the output data matrix of production process A, Input data matrix for production process B, is the output data matrix of production process B, I represents the production batch, J represents the sampling interval, K represents the operating variable, and M represents the number of output variables; Step 2: Use the data processor to expand the three-dimensional data matrices of production processes A and B into two-dimensional data matrices according to the batch dimension, and obtain and Step 3: Use the data processor to establish the JYPLS process migration model; A1: and Defined in the same score space, and Distributed in the same latent variable space; A2: Define Q J ∈R N×G is the joint load matrix of production processes A and B, representing the load space jointly defined by their joint output matrices, where G represents the number of latent variables; A3: Establish the JYPLS model according to formula (1), formula (2) and formula (3); Where, T A =X A W A , T B =X B W B , E A 、E B and Represent the corresponding deviations respectively; P A , P B is the load matrix; A4: A new input variable x based on a batch in production process B B,new , based on the JYPLS model, the predicted value y of the end product quality is obtained according to formula (4); In the formula, B J is the regression coefficient, Step 4: Initialize the uncertainty set; Step 5: Use the data processor to construct the objective function and constraints of the robust optimization model; B1: By solving the consistency of the first-order approximation term to compensate for the NCO mismatch problem in the optimization problem, the modified JYPLS model of the kth batch is obtained according to formula (5); In the formula, represents the quality prediction of the modified JYPLS model, Represents the prediction output of the JYPLS model. and have the same meaning; σ is the standard deviation, ε k is the zero-order correction term of the k-th batch, λ k is the first-order correction term for the kth batch, in, pass Calculated, pass, Calculated, represents the Kronecker product; B2: After the JYPLS model is modified according to formula (5), the batch process optimization problem based on the JYPLS model is expressed as formula (6); B3: Considering the uncertainty of the model, the auxiliary parameter F is introduced to convert the optimization problem based on the JYPLS model into the form in formula (7); B4: Select the box uncertainty set and express the model parameter uncertainty in the form of formula (8); B=B * +ξ(8); in the form i=1,2,···,m,U={ξe T ξ=0,ξ min ≤ξ≤ξ max }; B5: According to the robust optimization method, formula (7) is equivalently transformed into solving two optimization problems: formula (9) and formula (10); B6: The actual process output value and the JYPLS model prediction value are expressed as formula (11) using the first-order adaptive correction method; In the formula, represents the revised JYPLS model prediction value; B7: for y p (x) and Perform univariate and bivariate Taylor expansion respectively, and obtain formula (12), formula (13), formula (14) and formula (15) respectively; and p (x)=y p (x k )+y p '(x k )(xx k )(12); B8: Solving the maximization problem Equivalent to solving because There are uncertain parameters in the model, and the model is nonlinear and difficult to solve directly, so we can Expand into the form in formula (16); In the formula, B9: For uncertain Construct the Lagrangian function according to formula (17); B10: Order Among them, α, l, γ are Lagrange coefficients respectively, and formula (18) is obtained according to the optimization duality theory; B11: According to formula (18), formula (19) is obtained; B12: Transform formula (10) to obtain the new robust optimization problem in formula (20); Step 6: Use the data processor to perform inter-batch optimization on the kth batch; C1: Combine the uncertainty set constructed in step 4 to solve the robust optimization model constructed in step 5 and obtain the initial operation variable trajectory C2: Calculate the current initial operation variable trajectory The operation variable trajectory of the previous batch difference C3: Judgment Is it less than the preset threshold θ? If so, let x k =x k-1 Otherwise, the initial operation variable trajectory of the current batch is filtered by the first-order exponential filter shown in formula (21) Filter and obtain the final operating variable trajectory x k ; Step 7: Use the final manipulated variable trajectory x obtained in step 6 through the data processor k Carry out the production of the current batch and measure the process output y after the batch is completed k ; Step 8: Output the latest acquired process y through the data processor k Add to modeling data set and uncertainty set and perform data removal; D1: After the kth batch is produced and data is filled, the end-point product quality deviation between the current batch and the adjacent batch is calculated according to formula (22), and the data set F is constructed according to formula (23); D2: Setting the stability threshold γ s and the trust threshold γ t As a judgment indicator for the timing of data removal; if the quality deviation of t consecutive endpoint products collected by the data set F is less than the trust threshold γ t And at least s (s≤t) endpoint product quality deviations are less than the stability threshold γ s , it is believed that the model mismatch caused by the difference between the new and old processes hinders the further improvement of model performance, and data elimination begins. At this time, the second stage of the dual update mechanism of the model and the uncertainty set is entered; D3: Use formula (24) and formula (25) respectively to select the modeling dataset and dataset D in the order of similarity from small to large. m Eliminate several groups of data respectively; Step 9: Use the data processor to update the uncertainty set; E1: Determine the worst-case uncertainty range of the process output using formula (26) The allowable range of process output under model uncertainty is determined by formula (27): In the formula, and are the upper and lower bounds of the uncertainty range, respectively, which are based on the data set D m The n groups of data with high similarity or the q groups of data closest to the current batch are obtained, and y is the output of the current batch process model; E2: According to The uncertainty range of the model can be inferred by the current batch operation variables; Step 10: Set k=k+1 and return to step 3 until all production batches are completed.

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