Method for optimizing crystallization process parameters of monohydrate citric acid based on dynamic experiment design

Abstract

The application discloses a monohydrate citric acid crystallization process parameter optimization method based on dynamic experiment design, relates to the technical field of chemical crystallization, and utilizes dynamic sub-factors to parameterize a time-varying curve of cooling, adopts D-optimal design to construct a plurality of experimental parameter combinations, and combines a dynamic experiment design method to obtain a crystal size proportion and a crystallization yield corresponding to each experimental parameter combination, and finally, multi-objective optimization is carried out based on experimental data to obtain an optimal process parameter combination, so that the crystal size proportion and the crystallization yield can be double-target cooperatively optimized, the product quality of monohydrate citric acid crystallization is improved, and compared with a traditional experience method, the number of experiments is greatly reduced, and optimization efficiency is improved.

Description

Technical Field

[0001] This application relates to the field of chemical crystallization technology, and in particular to a method for optimizing process parameters of citric acid monohydrate crystallization based on dynamic experimental design. Background Technology

[0002] Citric acid monohydrate, as an important organic acid, is widely used in food, medicine, chemical industry, cosmetics and other fields. The size ratio (particle size distribution) of its crystal products directly affects the storage stability, flowability and subsequent processing performance of the products. The crystallization yield is directly related to the original loss rate and production economic benefits. Therefore, the crystal size ratio and crystallization yield are the core evaluation indicators of the citric acid monohydrate crystallization process.

[0003] Currently, the crystallization process of citric acid monohydrate in industry and laboratories mostly relies on traditional empirical methods or static experimental design to determine the combination of process parameters. The main approach involves setting several fixed parameter values ​​for experiments and then adjusting them based on operator experience. The shortcomings of this technique are mainly reflected in the following: First, traditional empirical methods lack systematic dynamic design guidance, often requiring extensive trial and error to adjust to a feasible combination of process parameters. This not only results in low experimental efficiency but also makes it difficult to accurately capture the interactions between various process parameters, making it difficult to find a truly suitable combination of process parameters for the crystallization process. Second, traditional static experimental design treats each process parameter as a fixed object for optimization, failing to effectively handle time-varying input trajectories such as temperature during crystallization. This causes the optimization results to deviate from the dynamic needs of actual production, making the determined process parameters unsuitable for the real crystallization environment. Third, it fails to achieve the dual objective of synergistic optimization of crystal size uniformity and crystallization yield. Often, one indicator must be sacrificed to ensure the other meets the target, failing to simultaneously satisfy the dual requirements of industrial production for product quality stability and economic efficiency. Summary of the Invention

[0004] This application addresses the aforementioned problems and technical needs by proposing a method for optimizing the crystallization process parameters of citric acid monohydrate based on dynamic experimental design. The technical solution of this application is as follows: A method for optimizing the crystallization process parameters of citric acid monohydrate based on dynamic experimental design, comprising: The time-varying cooling curve is parameterized using dynamic sub-factors, and the constraints on the values ​​of dynamic sub-factors are determined based on the range of cooling parameters. Under the constraints of dynamic sub-factor values, stirring rate range, cooling time range, and seed addition amount range, multiple experimental parameter combinations were constructed using D-optimal design. Each experimental parameter combination included the values ​​of dynamic sub-factor, stirring rate, cooling time, and seed addition amount. Citric acid monohydrate was selected as the raw material to prepare the initial crystallization solution. Crystallization experiments were carried out on the initial crystallization solution according to the process parameter combination corresponding to each experimental parameter combination. After the experiment, the crystal size ratio and crystallization yield were measured as the response values ​​corresponding to the current experimental parameter combination. Each process parameter combination included the cooling time-varying curve, stirring rate, cooling time, and seed crystal addition amount. Based on the response values ​​corresponding to different combinations of experimental parameters, combined with a multi-objective optimization algorithm, a combination of process parameters is obtained that enables both the crystal size ratio and crystallization yield to reach the preset optimization targets.

[0005] A further technical solution involves using dynamic sub-factors to parameterize the time-varying cooling curve as follows:

[0006] in, and For two dynamic sub-factors, Represents a dimensionless time parameter and , Indicates time, It's the cooling time; It is a dimensionless temperature parameter and , Indicates temperature. The initial temperature, This is the final temperature.

[0007] A further technical solution involves determining the dynamic sub-factor value constraints based on the range of cooling parameter values, including: Based on the initial temperature The range of values, the final temperature The range of values, and the cooling rate The range of values ​​for which the dynamic sub-factor is determined. and The value constraints.

[0008] A further technical solution involves obtaining a combination of process parameters that achieves both the crystal size ratio and crystallization yield meeting preset optimization targets, including: Response surface optimization models for crystal size ratio and crystallization yield were established based on the response values ​​corresponding to each combination of experimental parameters. A multi-objective optimization algorithm was used to perform multi-objective optimization based on the response surface optimization models of crystal size ratio and crystallization yield, so as to obtain the experimental parameter combination that makes both crystal size ratio and crystallization yield reach the preset optimization objectives and determine the corresponding process parameter combination.

[0009] Further technical solutions include: the optimization method for citric acid monohydrate crystallization process parameters also includes: When using a multi-objective optimization algorithm to perform multi-objective optimization based on the response surface optimization models of crystal size ratio and crystallization yield, if it is impossible to obtain a combination of experimental parameters that makes both crystal size ratio and crystallization yield reach the preset optimization objectives, the range of values ​​for at least one experimental parameter should be adjusted and the response surface optimization models of crystal size ratio and crystallization yield should be reconstructed.

[0010] Further technical solutions include: the optimization method for citric acid monohydrate crystallization process parameters also includes: A multi-objective optimization algorithm is used to perform multi-objective optimization based on the response surface optimization models of crystal size ratio and crystallization yield. When the current optimal response value still cannot reach the preset optimization target, the value boundary of the experimental parameter that reaches the value boundary in the experimental parameter combination that reaches the current optimal response value is shifted outward to expand the value range.

[0011] A further technical solution involves establishing a response surface optimization model for crystal size distribution and crystallization yield based on the response values ​​corresponding to various combinations of experimental parameters, including: The effects of dynamic sub-factor, stirring rate, cooling time, and seed addition amount on the response value were analyzed to determine the experimental parameters that have a significant impact on the crystal size ratio and the experimental parameters that have a significant impact on the crystallization yield. Based on the experimental parameters that have a significant impact on the crystal size ratio, the response surface optimization model of the crystal size ratio is obtained by fitting the response values ​​corresponding to the combinations of experimental parameters. Based on the experimental parameters that have a significant impact on the crystallization yield, the response surface optimization model for the crystallization yield is obtained by fitting the response values ​​corresponding to the combinations of experimental parameters.

[0012] A further technical solution involves obtaining an experimental parameter combination that achieves both the crystal size ratio and crystallization yield meeting preset optimization targets, and determining the corresponding process parameter combination, which also includes: By using various multi-objective optimization algorithms, multiple candidate experimental parameter combinations were obtained that enable both the crystal size ratio and crystallization yield to achieve the preset optimization objectives. For each candidate experimental parameter combination, multiple crystallization experiments are conducted on the initial crystallization solution according to the process parameter combination corresponding to the current candidate experimental parameter combination. After the experiment, the crystal size ratio and crystallization yield are measured as the measured response values, and the average value of the measured response values ​​under multiple crystallization experiments is calculated. The current candidate experimental parameter combination is substituted into the response surface optimization model of the crystal size ratio and crystallization yield respectively to obtain the predicted response value, and the deviation between the predicted response value and the average value of the measured response value under the current candidate experimental parameter combination is calculated. The candidate experimental parameter combination with the smallest deviation between the predicted response value and the average measured response value is selected, and the corresponding process parameter combination is determined.

[0013] The further technical solution is that the multi-objective optimization algorithm used includes the expectation function method and NSGA-II.

[0014] A further technical solution is that the method for optimizing the crystallization process parameters of citric acid monohydrate also includes: The initial cooling parameter settings range includes the initial temperature. Final temperature The range of values ​​for the cooling rate is: Corresponding to the determined dynamic sub-factor and The value constraints include as well as ; The initial setting range for the stirring rate is: ; The initial setting for the cooling time ranges from [value to value]. ; The initial setting for the seed crystal addition amount is within the range of the mass of the citric acid monohydrate raw material. .

[0015] The beneficial technical effects of this application are: This application discloses a method for optimizing the crystallization process parameters of citric acid monohydrate based on dynamic experimental design. This method uses the D-optimal design method to construct multiple combinations of experimental parameters, and then combines the dynamic experimental design method to obtain the crystal size ratio and crystallization yield corresponding to each combination of experimental parameters. Finally, based on the experimental data, multi-objective optimization is performed to obtain the optimal combination of process parameters. This method can achieve dual-objective synergistic optimization of crystal size ratio and crystallization yield, which is beneficial to improving the product quality of citric acid monohydrate crystallization. Compared with the traditional empirical method, the number of experiments is greatly reduced, thus improving optimization efficiency.

[0016] This method accurately characterizes the time-varying parameter of the cooling curve through dynamic sub-factors, which solves the problem that traditional static experimental design cannot handle time-varying trajectories. At the same time, it does not require the establishment of complex mechanism models, thus greatly improving optimization efficiency. Attached Figure Description

[0017] Figure 1 This is a flowchart of a method according to an embodiment of this application.

[0018] Figure 2 This is a schematic diagram of the residual normal distribution of the response surface optimization model for the crystal size ratio obtained in an example of this application.

[0019] Figure 3 for Figure 2 The example uses a response surface optimization model based on crystal size ratio to compare the predicted and measured values ​​of crystal size ratio for 35 experimental parameter combinations.

[0020] Figure 4 for Figure 2 The residuals and experimental sequence distribution of the predicted crystal size ratio values ​​for 35 experimental parameter combinations obtained by using the response surface optimization model based on crystal size ratio in the example are shown in the figure.

[0021] Figure 5 This is a schematic diagram of the residual normal distribution of the response surface optimization model for crystallization yield obtained in an example of this application.

[0022] Figure 6 for Figure 5 The example uses a response surface optimization model for crystallization yield to compare the predicted and measured values ​​of crystallization yield for 35 experimental parameter combinations.

[0023] Figure 7 for Figure 5 The residuals and experimental sequence distribution of the crystallization yield predictions for 35 experimental parameter combinations obtained using the response surface optimization model for crystallization yield in the example are shown in the figure.

[0024] Figure 8 This is a comparison of cooling curves obtained by using the expectation function method and the NSGA-II response surface optimization model for multi-objective optimization in an example of this application. Detailed Implementation

[0025] The specific embodiments of this application will be further described below with reference to the accompanying drawings.

[0026] This application discloses a method for optimizing the crystallization process parameters of citric acid monohydrate based on dynamic experimental design. Please refer to [link / reference]. Figure 1 The flowchart illustrates the optimization method for citric acid monohydrate crystallization process parameters, which includes the following steps: Step 1: Initialize and set the value range of various process parameters. The main process parameters for citric acid monohydrate crystallization include seed crystal addition amount, stirring rate, and cooling time. The time-varying curves of cooling, including the amount of seed crystals added, stirring rate, and cooling time. All parameters are static and customized; the cooling time-varying curve is based on temperature. As time goes by A decreasing time-varying curve.

[0027] The value ranges of these four process parameters are initialized and set respectively. In one embodiment: Initialize and set the stirring rate The range of values ​​is .

[0028] Initialize and set the cooling time The range of values ​​is , Indicates hours.

[0029] Initialize the seed crystal addition amount The value range is the mass of citric acid monohydrate raw material. .

[0030] The range of values ​​for the cooling parameters in the initial cooling time-varying curve includes: initial temperature. Final temperature The range of values ​​for the cooling rate is: .

[0031] Step 2: Parameterize the cooling time-varying curve using dynamic sub-factors, and determine the dynamic sub-factor value constraints based on the range of cooling parameter values.

[0032] Constructing dimensionless time parameters and dimensionless temperature parameters , The initial temperature, The final temperature is then determined based on the dimensionless time parameter. and dimensionless temperature parameters The expression for establishing the time-varying cooling curve is as follows:

[0033] In the above formula, and These are two dynamic sub-factors.

[0034] Therefore, the expression for the cooling rate can be determined as follows:

[0035] Then, using the above expression, combined with the initial temperature... The range of values, the final temperature The range of values, and the cooling rate The range of values ​​for which the dynamic sub-factor can be determined. and The value constraints.

[0036] Initialize and set the initial temperature. Final temperature The range of values ​​for the cooling rate is: In this case, the dynamic sub-factor is calculated. and The value constraints include as well as .

[0037] Step 3: Under the constraints of dynamic sub-factor values, stirring rate range, cooling time range, and seed crystal addition range, multiple experimental parameter combinations are constructed using D-optimal design. Each experimental parameter combination includes a set of values ​​for dynamic sub-factor, stirring rate, cooling time, and seed crystal addition.

[0038] Step 4: Select citric acid monohydrate raw material to prepare the initial crystallization solution. This includes placing the citric acid monohydrate raw material and deionized water in a reactor, setting the temperature, and turning on the magnetic stirrer to stir continuously until the citric acid monohydrate raw material is completely dissolved. Use a hydrometer to measure the specific gravity of the solution to ensure that the specific gravity of the solution is within the error range of 1.345, so as to obtain a uniform initial crystallization solution. All subsequent crystallization experiments are carried out using the same initial crystallization solution.

[0039] In one example, 980g of citric acid monohydrate and 260g of deionized water were weighed and placed in a reactor. The temperature was set to 63℃, and a magnetic stirrer was turned on. The stirring speed was adjusted to 150r / min, and stirring was continued for 25min until the seed crystals were completely dissolved. 300mL of the initial crystallization solution was measured from each bottle, and each subsequent crystallization experiment was carried out based on a single bottle of 300mL of the initial crystallization solution.

[0040] Step 5: Conduct crystallization experiments on the initial crystallization solution according to the process parameter combination corresponding to each experimental parameter combination, and measure the crystal size ratio and crystallization yield after the experiment as the response value corresponding to the current experimental parameter combination.

[0041] Each experimental parameter combination corresponds to a process parameter combination including a cooling time-varying curve, stirring rate, cooling time, and seed addition amount. The cooling time-varying curve is obtained by substituting the values ​​of the dynamic sub-factors in the experimental parameter combination into the expression of the cooling time-varying curve. The stirring rate, cooling time, and seed addition amount directly use the values ​​in the experimental parameter combination.

[0042] When conducting crystallization experiments on the initial crystallization solution according to each combination of process parameters, this includes adding citric acid monohydrate seed crystals to the initial crystallization solution according to the seed crystal addition amount specified in the combination of process parameters, continuously stirring according to the stirring rate specified in the combination of process parameters, and following the cooling time-varying curve and cooling time specified in the combination of process parameters. From the initial temperature Cool down to the final temperature Conduct crystallization experiments.

[0043] After each crystallization experiment, the mixture of crystals and the initial crystallization solution was centrifuged for solid-liquid separation. The separated crystals were then placed in a hot air drying device and dried for 30 minutes. After cooling to room temperature, the mass of the obtained crystals was weighed, and the crystallization yield was calculated. Then, sieving was performed using sieves of different mesh sizes and a bottom collection device. The mass of crystals collected from each sieve and the bottom was weighed, and the proportion of crystal sizes for a specific crystal size was calculated. This specific crystal size is set according to actual needs. In one example, 8-mesh, 16-mesh, 30-mesh, 40-mesh, and 60-mesh sieves and a bottom collection device were used for sieving. The mass of crystals collected from each sieve and the bottom was weighed, and the proportion of crystal sizes in the 8-30 mesh range was calculated. Subsequent examples will use this proportion of crystal sizes as illustrations.

[0044] By conducting crystallization experiments according to the above process under each combination of experimental parameters and combining all experimental data, the response values ​​for each combination of experimental parameters can be obtained. In one example, step 3 uses a D-optimal design to construct 29 combinations of experimental parameters. The values ​​of each parameter in each combination and the corresponding measured response values ​​are shown in the table below: Table 1 Initial Experimental Results

[0045] Step 6: Based on the response values ​​corresponding to different combinations of experimental parameters, and combined with a multi-objective optimization algorithm, obtain the combination of process parameters that makes both the crystal size ratio and the crystallization yield reach the preset optimization target.

[0046] First, response surface optimization models for crystal size ratio and crystallization yield are established based on the response values ​​corresponding to each combination of experimental parameters. Then, a multi-objective optimization algorithm is used to perform multi-objective optimization based on the respective response surface optimization models for crystal size ratio and crystallization yield. The multi-objective optimization algorithm used in this application is a mature existing method, including any one of the expectation function method and NSGA-II.

[0047] In one scenario, a multi-objective optimization algorithm can be used to perform multi-objective optimization based on two response surface optimization models. This can directly yield the experimental parameter combination that enables both the crystal size ratio and crystallization yield to reach the preset optimization objectives. Then, the corresponding process parameter combination can be determined to complete the process parameter optimization.

[0048] In another scenario, when using a multi-objective optimization algorithm to perform multi-objective optimization based on the response surface optimization models of crystal size ratio and crystallization yield, the obtained optimal response value may still fail to meet the preset optimization objective. In other words, the current situation does not allow for the experimental parameter combination that enables both crystal size ratio and crystallization yield to meet the preset optimization objective.

[0049] For example, in one instance, the preset optimization objective is to achieve a crystal size ratio of no less than 90% and a maximum crystallization yield. Based on the initial experimental results in Table 1, a response surface optimization model for crystal size ratio and crystallization yield is established. A multi-objective optimization algorithm is then used to perform multi-objective optimization based on the established response surface optimization model to determine the optimal response values ​​(including predicted crystal size ratio and predicted crystallization yield) and the corresponding experimental parameter values. Furthermore, multiple crystallization experiments are conducted on the initial crystallization solution according to the process parameter combinations corresponding to the experimental parameter combinations at this time, and the measured values ​​of crystal size ratio and crystallization yield are measured after the experiments. The results of multi-objective optimization using the expectation function method and NSGA-II are shown in Table 2 below. Table 2 Initial Multi-Objective Optimal Solution

[0050] As can be seen from the results in Table 2, under both multi-objective optimization algorithms, neither the predicted crystal size ratio determined by the response surface optimization model nor the measured crystal size ratio obtained after the crystallization experiment reached 90%, indicating that the optimal response value could not reach the preset optimization objective.

[0051] The failure to achieve the preset optimization target for the optimal response value is often due to an unreasonable range of values ​​for the various process parameters set during initialization. Therefore, the range of at least one experimental parameter needs to be adjusted. When adjusting the range of at least one experimental parameter, the adjustment direction is determined based on the values ​​of each experimental parameter in the experimental parameter combination corresponding to the current optimal response value. When the value of an experimental parameter in the experimental parameter combination corresponding to the optimal response value has reached its corresponding value boundary, it indicates that the value range of that experimental parameter may be set unreasonably, resulting in the experimental parameter not reaching its most reasonable value. Therefore, the value boundary of the experimental parameter that has reached the value boundary is moved outward to expand the value range of that experimental parameter.

[0052] For example, in example 2, it can be seen that in the experimental parameter combination corresponding to the optimal response value, the stirring rate has reached its upper boundary of 450 r / min, and the seed addition amount has also reached its upper boundary of 3%. Therefore, the upper boundaries of the stirring rate and the seed addition amount should be moved outward, for example, by expanding the range of the stirring rate to 250 r / min to 650 r / min, and expanding the range of the seed addition amount to 1% to 4%.

[0053] After adjusting the range of at least one experimental parameter, the experimental parameter combination can be directly reconstructed using D-optimal design based on the design space formed by the new range. Alternatively, to improve efficiency, the original experimental parameter combination can be kept unchanged, and multiple additional experimental parameter combinations can be constructed using D-optimal design only within the design space formed by the changed range. Crystallization experiments can then be conducted on the initial crystallization solution according to each additional constructed experimental parameter combination, and the crystal size ratio and crystallization yield can be measured as response values ​​after the experiment.

[0054] For example, by expanding the range of stirring rate to 250 r / min to 650 r / min and the range of seed crystal addition to 1% to 4%, the 29 experimental parameter combinations in Table 1 can be kept unchanged. Within the design space formed by the newly added ranges, 6 additional experimental parameter combinations can be constructed using D-optimal design. The values ​​of each parameter in these 6 experimental parameter combinations and the corresponding measured response values ​​are shown in Table 3 below: Table 3 Supplementary Experimental Results

[0055] After adjusting the range of values ​​for at least one experimental parameter and obtaining the combinations of experimental parameters and their response values, the response surface optimization models for crystal size ratio and crystallization yield are reconstructed. Multi-objective optimization is then performed again using a multi-objective optimization algorithm until the experimental parameter combination that makes both crystal size ratio and crystallization yield reach the preset optimization objectives is obtained.

[0056] To construct response surface optimization models for crystal size ratio and crystallization yield, the effects of dynamic sub-factor, stirring rate, cooling time, and seed crystal addition amount on the response values ​​were first analyzed to determine the experimental parameters that significantly affect crystal size ratio and crystallization yield. Then, based on the experimental parameters that significantly affect crystal size ratio, a response surface optimization model for crystal size ratio was obtained by fitting the response values ​​corresponding to various combinations of experimental parameters; similarly, a response surface optimization model for crystallization yield was obtained by fitting the response values ​​corresponding to various combinations of experimental parameters. The experimental parameters that significantly affect the response values ​​include the dynamic sub-factor. Dynamic sub-factors Stirring rate Seed crystal addition amount and cooling time And other terms with p-values ​​less than 0.05.

[0057] Taking the case of adjusting the range of stirring rate and seed addition amount and obtaining the supplementary experimental results in Table 3, and then using the initial experimental results in Table 1 and the supplementary experimental results in Table 3, a total of 35 sets of experimental results are used to construct response surface optimization models for crystal size ratio and crystallization yield, respectively.

[0058] The variance analysis results of the response surface optimization model for crystal size ratio are shown in Table 4 below, including the dynamic sub-factor. Dynamic sub-factors Stirring rate Seed crystal addition amount and cooling time All of these were directly retained as experimental parameters that have a significant impact on the crystal size ratio. In addition, other terms with p values ​​less than 0.05 also made significant contributions to the crystal size ratio and were also retained as experimental parameters that have a significant impact on the crystal size ratio.

[0059] Table 4. Analysis of variance results of the response surface optimization model for crystal size ratio

[0060] The data in Table 4 show that the experimental parameters that significantly affect the crystal size ratio include the first-order term. , , , , and quadratic terms , , , , , , , , , , , Based on these experimental parameters that significantly affect the crystal size ratio, the crystal size ratio is obtained by fitting the response values ​​corresponding to each combination of experimental parameters. The response surface optimization model is as follows:

[0061] In this example, the obtained crystal size ratio The residual normal distribution plot of the response surface optimization model is as follows: Figure 2 As shown, using crystal size ratio The comparison between the predicted and measured values ​​of crystal size percentage under 35 experimental parameter combinations obtained from the response surface optimization model is shown in the figure below. Figure 3 As shown, the residual distribution of crystal size proportions for 35 experimental parameter combinations is as follows: Figure 4 As shown.

[0062] The results of the analysis of variance for the response surface optimization model of crystallization yield are shown in Table 5 below, with dynamic sub-factors. Dynamic sub-factors Stirring rate Seed crystal addition amount and cooling time All of these were directly retained as experimental parameters that significantly affected the crystallization yield. In addition, other terms with p values ​​less than 0.05 also made significant contributions to the crystal size ratio and were also retained as experimental parameters that significantly affected the crystallization yield.

[0063] Table 5. Analysis of variance results of the response surface optimization model for crystallization yield.

[0064] The data in Table 5 show that the experimental parameters that significantly affect the crystallization yield include the first-order term. , , , , and quadratic terms , , , , , , , , Based on these experimental parameters that significantly affect the crystal size ratio, the crystallization yield was obtained by fitting the response values ​​corresponding to each combination of experimental parameters. The response surface optimization model is as follows:

[0065] In this example, the obtained crystallization yield The residual normal distribution plot of the response surface optimization model is as follows: Figure 5 As shown, using crystallization yield The comparison between the predicted and measured crystallization yield values ​​under 35 experimental parameter combinations obtained from the response surface optimization model is shown in the figure below. Figure 6 As shown, the residual distribution of crystallization yield for 35 combinations of experimental parameters is as follows: Figure 7 As shown.

[0066] The crystal size ratio obtained above The coefficient of determination of the response surface optimization model 0.9915, adjusted The yield was 0.9818. The coefficient of determination of the response surface optimization model 0.9849, adjusted The coefficient of determination for the response surface optimization model is 0.9699. All values ​​were greater than 0.95, indicating that the response surface optimization model had a good fit and could accurately reflect the relationship between each parameter and the response value. Then, a multi-objective optimization algorithm was used based on the constructed crystal size ratio. Response surface optimization model and crystallization yield The response surface optimization model can obtain a combination of experimental parameters that takes into account both the crystal size ratio and the crystallization yield.

[0067] In one example, the measured response values ​​of the 35 experimental parameter combinations in Tables 1 and 2 were used for multi-objective optimization using the expectation function method and NSGA-II, respectively. The results are shown in Table 6 below: Table 6. Final multi-objective optimization optimal solution after supplementary experiments

[0068] Comparing the data in Table 6 and Table 2, it can be seen that after the supplementary experiment, under the two multi-objective optimization algorithms, both the predicted value and the measured value of the crystal size ratio reached 90%, indicating that the optimal response value has reached the preset optimization objective.

[0069] To further ensure the optimization effect of process parameters, the crystal size ratio was obtained through fitting. Response surface optimization model and crystallization yield After optimizing the response surface model, various multi-objective optimization algorithms are used to perform multi-objective optimization based on the fitted response surface model, resulting in multiple candidate experimental parameter combinations that achieve the preset optimization objectives for both crystal size ratio and crystallization yield. Then, for each candidate experimental parameter combination, multiple crystallization experiments are conducted on the initial crystallization solution according to the corresponding process parameter combination. After each experiment, the crystal size ratio and crystallization yield are measured as measured response values. The average of the measured response values ​​from multiple crystallization experiments is calculated. Additionally, the current candidate experimental parameter combination is substituted into the crystal size ratio... and crystallization yield The predicted response values ​​are obtained from their respective response surface optimization models, and the deviation between the predicted response values ​​and the average of the measured response values ​​under the current candidate experimental parameter combinations is calculated. When the deviation between the predicted response values ​​and the average of the measured response values ​​is within the error range, it indicates that the prediction effect of the response surface optimization model is reliable. For example, in one instance, multi-objective optimization is performed using the expectation function method and NSGA-II respectively to obtain candidate experimental parameter combinations, and the deviation is then used... and Obtain the cooling curve for example Figure 8 As shown.

[0070] Finally, the results of multiple candidate experimental parameter combinations can be combined to select the candidate experimental parameter combination with the smallest deviation between the predicted response value and the average measured response value, and the corresponding process parameter combination can be determined as the final optimized process parameters.

[0071] The above descriptions are merely preferred embodiments of this application, and this application is not limited to the above embodiments. It is understood that other improvements and variations that can be directly derived or conceived by those skilled in the art without departing from the spirit and concept of this application should be considered to be included within the protection scope of this application.

Claims

1. A method for optimizing process parameters of citric acid monohydrate crystallization based on dynamic experimental design, characterized in that, The method for optimizing the crystallization process parameters of citric acid monohydrate includes: The time-varying cooling curve is parameterized using dynamic sub-factors, and the constraints on the values ​​of dynamic sub-factors are determined based on the range of cooling parameters. Under the constraints of dynamic sub-factor values, stirring rate range, cooling time range, and seed addition amount range, multiple experimental parameter combinations were constructed using D-optimal design. Each experimental parameter combination included the values ​​of dynamic sub-factor, stirring rate, cooling time, and seed addition amount. Citric acid monohydrate was selected as the raw material to prepare an initial crystallization solution. Crystallization experiments were carried out on the initial crystallization solution according to the process parameter combination corresponding to each experimental parameter combination. After the experiment, the crystal size ratio and crystallization yield were measured as the response values ​​corresponding to the current experimental parameter combination. Each process parameter combination included the cooling time-varying curve, stirring rate, cooling time, and seed crystal addition amount. Based on the response values ​​corresponding to different combinations of experimental parameters, combined with a multi-objective optimization algorithm, a combination of process parameters is obtained that enables both the crystal size ratio and crystallization yield to reach the preset optimization targets.

2. The method for optimizing the crystallization process parameters of citric acid monohydrate according to claim 1, characterized in that, The time-varying cooling curve is parameterized using dynamic sub-factors as follows: in, and For two dynamic sub-factors, Represents a dimensionless time parameter and , Indicates time, It's the cooling time; It is a dimensionless temperature parameter and , Indicates temperature. The initial temperature, This is the final temperature.

3. The method for optimizing the crystallization process parameters of citric acid monohydrate according to claim 2, characterized in that, The constraints for determining the values ​​of dynamic sub-factors based on the range of cooling parameters include: Based on the initial temperature The range of values, the final temperature The range of values, and the cooling rate The range of values ​​for which the dynamic sub-factor is determined. and The value constraints.

4. The method for optimizing the crystallization process parameters of citric acid monohydrate according to claim 1, characterized in that, The combination of process parameters that achieves both the crystal size ratio and crystallization yield meeting the preset optimization targets includes: Response surface optimization models for crystal size ratio and crystallization yield were established based on the response values ​​corresponding to each combination of experimental parameters. A multi-objective optimization algorithm was used to perform multi-objective optimization based on the response surface optimization models of crystal size ratio and crystallization yield, so as to obtain the experimental parameter combination that makes both crystal size ratio and crystallization yield reach the preset optimization objectives and determine the corresponding process parameter combination.

5. The method for optimizing the crystallization process parameters of citric acid monohydrate according to claim 4, characterized in that, The method for optimizing the crystallization process parameters of citric acid monohydrate also includes: When using a multi-objective optimization algorithm to perform multi-objective optimization based on the response surface optimization models of crystal size ratio and crystallization yield, if it is impossible to obtain a combination of experimental parameters that makes both crystal size ratio and crystallization yield reach the preset optimization objectives, the range of values ​​for at least one experimental parameter should be adjusted and the response surface optimization models of crystal size ratio and crystallization yield should be reconstructed.

6. The method for optimizing the crystallization process parameters of citric acid monohydrate according to claim 5, characterized in that, The method for optimizing the crystallization process parameters of citric acid monohydrate also includes: A multi-objective optimization algorithm is used to perform multi-objective optimization based on the response surface optimization models of crystal size ratio and crystallization yield. When the current optimal response value still cannot reach the preset optimization target, the value boundary of the experimental parameter that reaches the value boundary in the experimental parameter combination that reaches the current optimal response value is shifted outward to expand the value range.

7. The method for optimizing the crystallization process parameters of citric acid monohydrate according to claim 4, characterized in that, Response surface optimization models for crystal size ratio and crystallization yield were established based on the response values ​​corresponding to various combinations of experimental parameters, including: The effects of dynamic sub-factor, stirring rate, cooling time, and seed addition amount on the response value were analyzed to determine the experimental parameters that have a significant impact on the crystal size ratio and the experimental parameters that have a significant impact on the crystallization yield. Based on the experimental parameters that have a significant impact on the crystal size ratio, the response surface optimization model of the crystal size ratio is obtained by fitting the response values ​​corresponding to the combinations of experimental parameters. Based on the experimental parameters that have a significant impact on the crystallization yield, the response surface optimization model for the crystallization yield is obtained by fitting the response values ​​corresponding to the combinations of experimental parameters.

8. The method for optimizing the crystallization process parameters of citric acid monohydrate according to claim 4, characterized in that, Obtaining the experimental parameter combination that achieves both the crystal size ratio and crystallization yield meeting the preset optimization targets, and determining the corresponding process parameter combination, also includes: By using various multi-objective optimization algorithms, multiple candidate experimental parameter combinations were obtained that enable both the crystal size ratio and crystallization yield to achieve the preset optimization objectives. For each candidate experimental parameter combination, multiple crystallization experiments are conducted on the initial crystallization solution according to the process parameter combination corresponding to the current candidate experimental parameter combination. After the experiment, the crystal size ratio and crystallization yield are measured as the measured response values, and the average value of the measured response values ​​under multiple crystallization experiments is calculated. The current candidate experimental parameter combination is substituted into the response surface optimization model of the crystal size ratio and crystallization yield respectively to obtain the predicted response value, and the deviation between the predicted response value and the average value of the measured response value under the current candidate experimental parameter combination is calculated. The candidate experimental parameter combination with the smallest deviation between the predicted response value and the average measured response value is selected, and the corresponding process parameter combination is determined.

9. The method for optimizing the crystallization process parameters of citric acid monohydrate according to claim 8, characterized in that, The multi-objective optimization algorithms used include the expectation function method and NSGA-II.

10. The method for optimizing the crystallization process parameters of citric acid monohydrate according to claim 3, characterized in that, The method for optimizing the crystallization process parameters of citric acid monohydrate also includes: The initial cooling parameter settings range includes the initial temperature. Final temperature The range of values ​​for the cooling rate is: Corresponding to the determined dynamic sub-factor and The value constraints include as well as ; The initial setting range for the stirring rate is: ; The initial setting for the cooling time ranges from [value to value]. ; The initial setting for the seed crystal addition amount is within the range of the mass of the citric acid monohydrate raw material. .

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