Method, information processing device, and program for predicting addition polymerization reactions

Abstract

The present invention improves prediction related to addition polymerization reaction.　Provided is a method for making a prediction related to addition polymerization reaction, the method being executed by an information processing device 10 and involving a step for training a prediction model on the basis of actual data including a plurality of explanatory factors and an objective factor related to addition polymerization reaction, and a step for predicting, by the prediction model, an objective factor in the addition polymerization reaction on the basis of a plurality of explanatory factors related to the addition polymerization reaction, wherein the plurality of explanatory factors include a plurality of feature amounts obtained by clustering analysis of time-series data of a plurality of instruments in a temperature rising step and a dropping step; and the objective factor includes at least one of the NV and solution viscosity.

Description

[Technical Field]

[0001] The present disclosure relates to a method for predicting addition polymerization reactions, an information processing device, and a program. This application claims priority to Japanese Patent Application No. 2023-048922, filed on March 24, 2023, the contents of which are incorporated herein by reference. [Background technology]

[0002] Conventionally, methods for making predictions related to chemical reactions have been proposed (for example, Patent Document 1). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] International Publication No. 2003 / 026791 Summary of the Invention [Problem to be solved by the invention]

[0004] The technology described in Patent Document 1 discloses that modeling techniques such as neural networks, partial least squares, and principal component regression are used to optimize the control of a reactor system. However, no consideration is given to specific design methods and optimizations when making predictions related to addition polymerization reactions, and there is room for improvement in prediction techniques related to addition polymerization reactions.

[0005] In view of the above circumstances, an object of the present disclosure is to improve prediction techniques relating to addition polymerization reactions. [Means for solving the problem]

[0006] (1) In one embodiment of the present disclosure, a method includes: A method for making predictions regarding an addition polymerization reaction, executed by an information processing device, comprising: training a prediction model based on performance data including a plurality of explanatory factors and a target factor related to the addition polymerization reaction; predicting the target factor during the addition polymerization reaction based on a plurality of explanatory factors related to the addition polymerization reaction using the prediction model; Including, the plurality of explanatory factors include a plurality of feature quantities obtained by clustering analysis of time-series data of a plurality of measuring instruments in the temperature-raising process and the dropping process, The objective factors include at least one of NV and solution viscosity.

[0007] (2) In one embodiment of the present disclosure, the method is the method described in (1), The plurality of explanatory factors includes theoretical values ​​in a reaction physics model.

[0008] (3) In one embodiment of the present disclosure, the method is the method described in (1) or (2), wherein the addition polymerization reaction is an acrylic addition polymerization reaction.

[0009] (4) In one embodiment of the present disclosure, the method is a method according to any one of (1) to (6), The prediction model is a neural network model including an input layer, an intermediate layer, and an output layer, and the coefficient of the activation function related to the intermediate layer is larger than the coefficient of the activation function related to the output layer.

[0010] (5) An information processing device according to an embodiment of the present disclosure is an information processing device that includes a control unit and performs predictions related to an addition polymerization reaction, The control unit training a prediction model based on performance data including a plurality of explanatory factors and a target factor related to the addition polymerization reaction; predicting the target factor during the addition polymerization reaction based on a plurality of explanatory factors related to the addition polymerization reaction using the prediction model; the plurality of explanatory factors include a plurality of feature quantities obtained by clustering analysis of time-series data of a plurality of measuring instruments in the temperature-raising process and the dropping process, The objective factors include at least one of NV and solution viscosity.

[0011] (6) In one embodiment of the present disclosure, a non-transitory computer-readable recording medium includes: A non-transitory computer-readable storage medium having stored thereon instructions that, when executed by a processor, cause the processor to: training a predictive model based on performance data including a plurality of explanatory factors and a target factor related to the addition polymerization reaction; predicting the target factor during the addition polymerization reaction based on a plurality of explanatory factors related to the addition polymerization reaction using the prediction model; Execute the plurality of explanatory factors include a plurality of feature quantities obtained by clustering analysis of time-series data of a plurality of measuring instruments in the temperature-raising process and the dropping process, The objective factors include at least one of NV and solution viscosity. [Effects of the Invention]

[0012] According to the method, information processing device, and program for making predictions regarding addition polymerization reactions in one embodiment of the present disclosure, it is possible to improve prediction techniques regarding addition polymerization reactions. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a block diagram showing a schematic configuration of an information processing device according to an embodiment of the present invention; [Figure 2] 4 is a flowchart illustrating an operation of the information processing device according to the present embodiment. [Figure 3] 1 is a conceptual diagram illustrating the steps of an addition polymerization reaction according to the present embodiment. [Figure 4A] FIG. 10 is a diagram showing time progression of data related to a temperature increase process and a dropping process. [Figure 4B] The graph shows the time transition of categories related to the temperature increase process and the dropping process. [Figure 5] 10 shows an example of a result of verifying the accuracy of the prediction model according to this embodiment. [Figure 6] 10 shows an example of a result of verifying the accuracy of the prediction model according to this embodiment. [Figure 7] FIG. 2 is a conceptual diagram illustrating an example of a prediction model according to the present embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0014] A method, an information processing device, and a program for making predictions related to addition polymerization reactions according to embodiments of the present disclosure will be described below with reference to the drawings. Prediction targets according to embodiments of the present disclosure include both batch reactions and continuous reactions. Major polymer materials synthesized by addition polymerization reactions according to this embodiment include acrylic, poly(meth)acrylic acid ester, polyethylene, polypropylene, polystyrene, polyvinyl chloride, polyvinyl acetate, polyvinylidene chloride, polyacrylonitrile, polytetrafluoroethylene, and the like. For example, the addition polymerization reaction according to this embodiment includes an acrylic addition polymerization reaction.

[0015] In each drawing, the same or corresponding parts are denoted by the same reference numerals. In the description of this embodiment, the description of the same or corresponding parts will be omitted or simplified as appropriate.

[0016] First, an overview of this embodiment will be described. The method for predicting an addition polymerization reaction according to this embodiment is executed by an information processing device 10. The information processing device 10 trains a prediction model based on performance data including multiple explanatory factors and an objective factor related to the addition polymerization reaction. Furthermore, the information processing device 10 predicts the objective factor during the addition polymerization reaction based on the multiple explanatory factors related to the addition polymerization reaction using the trained prediction model. Here, the multiple explanatory factors include multiple feature quantities obtained by clustering analysis of time-series data from multiple measuring instruments during the temperature-raising process and the dropping process. Furthermore, the objective factor is characterized by including at least one of NV and solution viscosity. NV stands for nonvolatile content or non-volatile matter content and represents the nonvolatile content in the resin solution. Addition polymerization reactions are typically performed in a solvent. Polymerized polymers are considered nonvolatile content, and unpolymerized monomers are considered volatile content. As the addition polymerization reaction progresses and the monomers are consumed, the volatile content decreases and the nonvolatile content increases. The reaction rate is estimated by confirming that the nonvolatile content has increased to a certain value.

[0017] As described above, according to this embodiment, the multiple explanatory factors include multiple feature quantities obtained by clustering analysis of time-series data from multiple measuring instruments in the heating step and the dropping step. The target factor is also characterized by including either NV or solution viscosity. When predicting such a target factor in an addition polymerization reaction, prediction accuracy can be improved by including multiple feature quantities obtained by clustering analysis of time-series data from multiple measuring instruments in the heating step and the dropping step, as described below, in the explanatory factors. Therefore, this embodiment can improve prediction technology related to addition polymerization reactions.

[0018] (Configuration of information processing device) Next, each component of the information processing device 10 will be described in detail with reference to Fig. 1. The information processing device 10 is any device used by a user. For example, a personal computer, a server computer, a general-purpose electronic device, or a dedicated electronic device can be employed as the information processing device 10.

[0019] As shown in FIG. 1, the information processing device 10 includes a control unit 11, a storage unit 12, an input unit 13, and an output unit .

[0020] The control unit 11 includes at least one processor, at least one dedicated circuit, or a combination thereof. The processor is a general-purpose processor such as a central processing unit (CPU) or a graphics processing unit (GPU), or a dedicated processor specialized for a specific process. The dedicated circuit is, for example, a field-programmable gate array (FPGA) or an application specific integrated circuit (ASIC). The control unit 11 executes processes related to the operation of the information processing device 10 while controlling each unit of the information processing device 10.

[0021] The storage unit 12 includes at least one semiconductor memory, at least one magnetic memory, at least one optical memory, or a combination of at least two of these. The semiconductor memory is, for example, a random access memory (RAM) or a read only memory (ROM). The RAM is, for example, a static random access memory (SRAM) or a dynamic random access memory (DRAM). The ROM is, for example, an electrically erasable programmable read only memory (EEPROM). The storage unit 12 functions as, for example, a main storage device, an auxiliary storage device, or a cache memory. The storage unit 12 stores data used in the operation of the information processing device 10 and data obtained by the operation of the information processing device 10.

[0022] The input unit 13 includes at least one input interface. The input interface may be, for example, a physical key, a capacitance key, a pointing device, or a touch screen integrated with a display. The input interface may also be, for example, a microphone that accepts voice input, or a camera that accepts gesture input. The input unit 13 accepts an operation to input data used in the operation of the information processing device 10. The input unit 13 may be connected to the information processing device 10 as an external input device instead of being provided in the information processing device 10. Any connection method may be used, for example, a Universal Serial Bus (USB), a High-Definition Multimedia Interface (HDMI) (registered trademark), or Bluetooth (registered trademark).

[0023] The output unit 14 includes at least one output interface. The output interface is, for example, a display that outputs information as a video. The display is, for example, an LCD (liquid crystal display) or an organic EL (electro luminescence) display. The output unit 14 displays and outputs data obtained by the operation of the information processing device 10. The output unit 14 may be connected to the information processing device 10 as an external output device instead of being provided in the information processing device 10. Any connection method may be used, for example, USB, HDMI (registered trademark), or Bluetooth (registered trademark).

[0024] The functions of the information processing device 10 are realized by executing a program according to this embodiment on a processor corresponding to the information processing device 10. That is, the functions of the information processing device 10 are realized by software. The program causes a computer to execute the operations of the information processing device 10, thereby causing the computer to function as the information processing device 10. That is, the computer functions as the information processing device 10 by executing the operations of the information processing device 10 in accordance with the program.

[0025] In this embodiment, the program can be recorded on a computer-readable recording medium. The computer-readable recording medium includes non-transitory computer-readable media, such as a magnetic recording device, an optical disc, a magneto-optical recording medium, or a semiconductor memory. The program can be distributed, for example, by selling, transferring, or lending a portable recording medium, such as a DVD (digital versatile disc) or a CD-ROM (compact disc read only memory), on which the program is recorded. The program can also be distributed by storing the program in the storage of an external server and transmitting the program from the external server to another computer. The program can also be provided as a program product.

[0026] Some or all of the functions of the information processing device 10 may be implemented by a dedicated circuit equivalent to the control unit 11. In other words, some or all of the functions of the information processing device 10 may be implemented by hardware.

[0027] In this embodiment, the storage unit 12 stores, for example, performance data and a prediction model. The performance data and the prediction model may be stored in an external device separate from the information processing device 10. In this case, the information processing device 10 may be provided with an external communication interface. The communication interface may be either a wired or wireless communication interface. In the case of wired communication, the communication interface is, for example, a LAN interface or a USB. In the case of wireless communication, the communication interface is, for example, an interface compatible with a mobile communication standard such as LTE, 4G, or 5G, or an interface compatible with short-range wireless communication such as Bluetooth (registered trademark). The communication interface is capable of receiving data used in the operation of the information processing device 10 and transmitting data obtained by the operation of the information processing device 10.

[0028] (Operation of information processing device) Next, the operation of the information processing device 10 according to this embodiment will be described with reference to FIG.

[0029] Step S101: The control unit 11 of the information processing device 10 trains a prediction model based on performance data related to the addition polymerization reaction. The performance data includes explanatory factors and objective factors related to the addition polymerization reaction. The explanatory factors include multiple feature quantities obtained by clustering analysis of time-series data from multiple measuring instruments in the temperature-raising process and the dropping process. The objective factors include at least one of NV and solution viscosity. In other words, the control unit 11 trains a prediction model using these explanatory factors and objective factors included in the performance data as learning data.

[0030] Any method can be used to acquire the performance data. For example, the control unit 11 acquires the performance data from the storage unit 12. The control unit 11 may also acquire the performance data by receiving an input of the performance data from a user via the input unit 13. Alternatively, the control unit 11 may acquire the performance data from an external device that stores the performance data via a communication interface.

[0031] The prediction model trained based on the learning data is subjected to cross-validation, and if the accuracy is within a practical range as a result of the cross-validation, the prediction model is used to make predictions regarding addition polymerization reactions.

[0032] Step S102: The control unit 11 predicts the objective factor related to the addition polymerization reaction based on the multiple explanatory factors related to the addition polymerization reaction. For example, the control unit 11 may acquire the explanatory factors by receiving an input of the explanatory factors from a user via the input unit 13.

[0033] Step S103: The control unit 11 outputs the objective factor predicted in step S102 as a prediction result from the output unit 14.

[0034] In this embodiment, the explanatory factors include multiple feature quantities obtained by clustering analysis of time-series data from multiple measuring instruments in the heating process and the dropping process. FIG. 3 shows a conceptual diagram illustrating the steps of an addition polymerization reaction. As shown in FIG. 3, the addition polymerization reaction includes a feeding process 410, a heating process 420, a dropping process 430, a holding process 440, a cooling process 450, and a post-cooling process 460. Graph 401 shows the temperature transition of the materials to be synthesized. In the heating process 420, the temperature of the materials to be synthesized increases. In the holding process 440, the temperature of the materials to be synthesized is kept constant. In the final stage 461 of the post-cooling process 460, the quality value of the materials is analyzed.

[0035] The analytical values ​​for the addition polymerization reaction correspond to the objective factors in this embodiment. Furthermore, these analytical values ​​depend on the temperature-raising and dropping processes. On the other hand, the temperature-raising and dropping processes involve a wide variety of time-series data, making it unrealistic to use all of this time-series data as explanatory variables. The time-series data includes measurements at intervals of one second to one minute. Therefore, this embodiment is characterized by using multiple feature quantities obtained by clustering analysis of time-series data from multiple measuring instruments in the temperature-raising and dropping processes as explanatory factors. Specifically, clustering analysis is performed after the dropping process 430 in FIG. 3 is completed. From this point (the end point of the dropping process 431) when all explanatory factors are available, reaction prediction is performed for approximately five hours (the time of the holding process 440) until the cooling timing of the cooling process 450 is determined.

[0036] 4A and 4B show a method for calculating multiple feature quantities for a certain lot (lot number D001). Item 501 in FIG. 4A shows the time progression of each piece of data related to the temperature increase process and the dripping process for that lot. This data includes data related to the reactor temperature, condenser temperature (air temperature difference), reactor jacket temperature, monomer dripping flow rate, and catalyst dripping flow rate. Each piece of data in item 501 is normalized. Item 502 in FIG. 4B shows the time progression of categories related to the temperature increase process and the dripping process. In this embodiment, the categories are 0 ~ There are five levels: 1, 2, 3, 4. Specifically, the categories are determined by clustering analysis of time-series data from multiple measuring instruments for the heating process and the dripping process. Based on the categories, feature quantities for the heating process and the dripping process are determined. For example, the feature quantities are determined based on the time proportion of the category. The time proportion of the category is the value obtained by dividing the cumulative time spent in each category by the total time. In this way, in this embodiment, the heating process and the dripping process are characterized by clustering analysis.

[0037] As described above, according to this embodiment, the multiple explanatory factors include multiple feature quantities obtained by clustering analysis of time-series data from multiple measuring instruments in the heating process and the dropping process. The objective factor is also characterized by including either NV or solution viscosity. When predicting an addition polymerization reaction, the accuracy of the prediction model can be improved by including multiple feature quantities obtained by clustering analysis of the heating process and the dropping process in the explanatory factors. Therefore, this embodiment can improve prediction techniques for addition polymerization reactions.

[0038] 5 and 6 show an example of the results of verifying the accuracy of the prediction model according to this embodiment. FIG. 5 is a graph showing the NV of a certain acrylic lot (lot number D001) predicted by the prediction model and the actual measured value. As shown in FIG. 5, the NV predicted by the prediction model and the actual measured value generally match. FIG. 6 is a graph showing the solution viscosity of the above acrylic lot predicted by the prediction model and the actual measured value. As shown in FIG. 6, the solution viscosity predicted by the prediction model and the actual measured value generally match. This shows that the accuracy of the prediction model is sufficiently high.

[0039] Here, the explanatory factors may include theoretical values ​​in a reaction physics model (reaction physics model theoretical values). In this way, the reaction physics model may be used as an explanatory factor to serve as a baseline for reaction characteristics. Similarly, the explanatory factors may include the amount of monomer raw material charged, the amount of solvent raw material charged, the amount of initiator charged, the reactor temperature, the condenser temperature, the reactor jacket temperature, etc.

[0040] The prediction model according to this embodiment may be, for example, a neural network model. When the prediction model is a neural network model, the coefficients of the activation function of the neural network model may be different between the intermediate layer and the output layer. For example, the coefficients of the activation function for the intermediate layer are larger than the coefficients of the activation function for the output layer.

[0041] FIG. 7 shows a conceptual diagram of a neural network model according to this embodiment. The neural network model includes an input layer 100, a middle layer 200, and an output layer 300. The neural network model according to this embodiment is fully connected. In this embodiment, the number of layers in the neural network model is, for example, two. This number of layers is the number of layers excluding the input layer. By setting the number of layers in the neural network model to two, it is possible to prevent a model shape that is incompatible with the physical phenomena in an addition polymerization reaction. In other words, by minimizing the number of layers in the neural network model, it is possible to realize a model shape that is suitable for the physical phenomena in an addition polymerization reaction. The number of layers in the neural network model according to this embodiment is not limited to three layers, and may be three or more. When the number of layers in the neural network model is three or more, the activation function coefficient may be set to be larger in the earlier layers of the neural network model.

[0042] The input layer 100 includes a plurality of elements 101-104 (also referred to as input elements 101-104). In the neural network model shown in FIG. 7, the number of input elements is four. The input elements 101-104 are also referred to as the first to fourth elements, respectively. Explanatory factors are input to each of the input elements 101-104. Note that the number of input elements is not limited to this, and may be less than four or five or more.

[0043] The hidden layer 200 includes multiple elements 201-214 (also referred to as middle elements 201-214). In the neural network model shown in FIG. 7, there are 14 middle elements. The middle elements 201-214 are also referred to as the 1st to 14th elements, respectively. Note that the number of middle elements is not limited to this, and may be less than 14 or 15 or more.

[0044] The output layer 300 includes an element 301 (output element 301). In the neural network model shown in Fig. 7, the number of output elements is one. The output element 301 is also called the first element. Note that the number of output elements is not limited to this, and may be two or more.

[0045] The values ​​input from the input elements 101-104 of the input layer 100 to the intermediate elements 201-214 of the intermediate layer 200 are transformed in the intermediate layer 200 based on the activation function of the intermediate layer 200. The transformed values ​​are output to the element 301 of the output layer 300. The activation function of the intermediate layer 200 is, for example, a sigmoid function. The values ​​input from the intermediate elements 201-214 of the intermediate layer 200 to the output element 301 of the output layer 300 are transformed in the output layer 300 based on the activation function of the output layer 300 and output. The activation function of the output layer 300 is, for example, a sigmoid function. Specifically, the activation functions of the intermediate layer and the output layer are, for example, sigmoid functions defined by the following mathematical expressions (1) and (2), respectively.

[0046]

number

[0047] In the neural network model according to this embodiment, the coefficients of the activation function for the intermediate layer are larger than the coefficients of the activation function for the output layer. This allows the configuration of the neural network model to be optimized when making predictions related to addition polymerization reactions. Specifically, in a neural network model that makes predictions related to addition polymerization reactions, it is desirable that changes in the explanatory factors be perceived as clear changes. Therefore, by making the coefficients of the activation function for the intermediate layer larger than the coefficients of the activation function for the output layer, changes in the input values ​​to the intermediate layer can be transmitted to the output layer as clear changes. On the other hand, in the output layer of a neural network model that makes predictions related to addition polymerization reactions, it is necessary to converge the values ​​of the training data and the objective factor. Therefore, the coefficients of the activation function for the output layer are set smaller than the coefficients of the activation function for the intermediate layer. This allows fine adjustment of the value of the objective factor output from the output layer.

[0048] Furthermore, by making the coefficients of the activation function different between the intermediate layer and the output layer, the learning process of the neural network model can be optimized. Specifically, by changing the coefficients of the activation function, it is possible to adjust the amount of update of the weight variables in the output layer and intermediate layer during the learning process. Furthermore, updating the weight variables has a significant impact on the learning process. Therefore, the learning process can be optimized based on adjusting the amount of update.

[0049] Specifically, in a neural network model for making predictions related to addition polymerization reactions, it is preferable to make the amount of update of the weight variables related to the intermediate layer relatively large. This allows the weight variables in the intermediate layer to fluctuate more significantly during the learning process, and changes in the input values ​​to the intermediate layer can be transmitted to the output layer as clear changes. On the other hand, it is preferable to make the amount of update of the weight variables related to the output layer relatively small. This allows the weight variables in the output layer to fluctuate less significantly during the learning process, making it easier for the teacher data and the values ​​of the objective factor to converge. In addition, a l >a L By satisfying this condition, it becomes possible to approximate any smooth function with sufficient accuracy, eliminating the need to unnecessarily increase the number of hidden layers. This means that sufficient accuracy can be obtained even with just one hidden layer. Having fewer hidden layers directly leads to suppressing overfitting, which has the secondary effect of improving the stability of the learning process and the robustness of the model.

[0050] In this embodiment, the activation functions of the intermediate and output layers are sigmoid functions, but the activation functions are not limited to sigmoid functions. For example, the activation functions of the intermediate and output layers may be functions such as hyperbolic tangent functions (tanh functions) and ramp functions (ReLU).

[0051] Although the present disclosure has been described based on the drawings and examples, it should be noted that those skilled in the art can easily make various modifications and alterations based on the present disclosure. Therefore, it should be noted that these modifications and alterations are included in the scope of the present disclosure. For example, the functions included in each means or step can be rearranged so as not to be logically inconsistent, and multiple means or steps can be combined or divided into one. [Explanation of symbols]

[0052] 10. Information processing equipment 11 Control section 12 Storage section 13 Input section 14 Output section 100 input layers 200 Middle Class 300 output layers 101-104, 201-214, 301 elements 401 graphs 410 Preparation process 420 Temperature rising process 430 Dripping process 431 At the end of the dripping process 440 Hold Process 450 Cooling process 460 Post-cooling process 461 Final Stage 501, 502 items

Claims

1. A method for making predictions regarding an addition polymerization reaction, executed by an information processing device, comprising: training a prediction model based on performance data including a plurality of explanatory factors and a target factor related to the addition polymerization reaction; predicting the target factor during the addition polymerization reaction based on a plurality of explanatory factors related to the addition polymerization reaction using the prediction model; Including, the plurality of explanatory factors include a plurality of feature quantities determined based on time proportions of categories obtained by clustering analysis of time-series data of a plurality of measuring instruments in a temperature-raising process and a dropping process, The method, wherein the objective factors include at least one of NV and solution viscosity.

2. 10. The method of claim 1, The method, wherein the plurality of explanatory factors include theoretical values ​​in a reaction physics model.

3. 10. The method of claim 1, wherein the addition polymerization reaction is an acrylic addition polymerization reaction.

4. 10. The method of claim 1, The method, wherein the predictive model is a neural network model including an input layer, a hidden layer, and an output layer, and the coefficients of the activation function associated with the hidden layer are greater than the coefficients of the activation function associated with the output layer.

5. An information processing device comprising a control unit and performing predictions related to an addition polymerization reaction, The control unit training a prediction model based on performance data including a plurality of explanatory factors and a target factor related to the addition polymerization reaction; predicting the target factor during the addition polymerization reaction based on a plurality of explanatory factors related to the addition polymerization reaction using the prediction model; the plurality of explanatory factors include a plurality of feature quantities determined based on time proportions of categories obtained by clustering analysis of time-series data of a plurality of measuring instruments in a temperature-raising process and a dropping process, The information processing device, wherein the objective factors include at least one of NV and solution viscosity.

6. A program for making predictions regarding addition polymerization reactions executed by an information processing device, the program comprising: training a predictive model based on performance data including a plurality of explanatory factors and a target factor related to the addition polymerization reaction; predicting the target factor during the addition polymerization reaction based on a plurality of explanatory factors related to the addition polymerization reaction using the prediction model; Execute the plurality of explanatory factors include a plurality of feature quantities determined based on time proportions of categories obtained by clustering analysis of time-series data of a plurality of measuring instruments in a temperature-raising process and a dropping process, The program, wherein the objective factors include at least one of NV and solution viscosity.

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