Particle size measurement method and particle size measurement system

Abstract

The object of this invention is to provide a particle size measurement method and a particle size measurement system that can be applied even to high-concentration dispersions with unknown solid content. [Solution] Based on fundamental data such as the representative particle size obtained by a particle size distribution analyzer, the R, G, and B values ​​of the particle dispersion obtained by a color sensor, and the turbidity of the particle dispersion, a regression model is created in advance. The representative particle size is then obtained using this regression model from the R, G, B, and turbidity values ​​obtained by measuring the dispersion of the target particles.

Description

[Technical Field]

[0001] This invention relates to a method for obtaining particle size and a particle size measurement system. [Background technology]

[0002] A method has been proposed that enables low-cost and efficient particle size measurement (Patent Document 1). The disclosed method involves the steps of: mixing a predetermined amount of suspended solids having known average particle sizes with water according to their average particle size to create suspensions according to their average particle size; measuring the turbidity of the suspensions according to their average particle size to identify the correspondence between average particle size and turbidity; and measuring the turbidity of a target suspension containing the suspended solids to be measured, and comparing the measured turbidity with the aforementioned correspondence to identify the average particle size of the suspended solids contained in the target suspension. Specifically, a graph of turbidity and particle size is created for each amount (concentration) of suspended solids, and the turbidity of the target suspension is compared with the turbidity-average particle size relationship graph. Furthermore, Patent Document 1 discloses a method for creating graphs of suspended substances by color and concentration, such as kaolin (white), slate (gray), and basic volcanic rocks (brown), and then comparing the turbidity of the target suspension with the corresponding color graph in the turbidity-average particle size relationship graph to identify the average particle size of the suspended substances contained in the target suspension that has one of the following color tones: white, gray, or brown.

[0003] Patent Document 2 proposes a method for calculating the particle size of fine particles contained in a liquid to be measured by irradiating a flow of a liquid containing a suspension with light, converting the transmitted light into an electrical signal using a photoelectric conversion means, and using the average value and standard deviation of the absorbance.

[0004] On the other hand, in crystallization operations, which precipitate crystals from a liquid phase, it is necessary to produce crystals with a predetermined representative particle size and particle size distribution. Applications of crystallization include the manufacture of lithium-ion battery cathode material precursors, various inorganic materials, and cosmetic materials. In these applications, the representative particle size and particle size distribution are important physical properties for performance. Therefore, obtaining information on the particle size of the generated particles is important for ensuring their performance. However, methods for measuring the particle size of micron and submicron-order particles include dynamic light scattering, laser diffraction / scattering, centrifugal sedimentation, and image analysis, but all of these methods require expensive measuring equipment or are time-consuming. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2008-191057 [Patent Document 2] Japanese Patent Application Publication No. 4-366750 [Overview of the Initiative] [Problems that the invention aims to solve]

[0006] The invention disclosed in Patent Document 1 utilizes turbidity-average particle size relationship graphs created for different concentrations of the suspended material, or turbidity-average particle size relationship graphs created for different concentrations and three different colors of the suspended material. Therefore, it could not be applied when the concentration of the target suspension was unknown. Furthermore, if the suspended material was colored, it was necessary to use a turbidity-average particle size relationship graph for that color. The invention disclosed in Patent Document 2 uses transmitted light for measurement, and therefore cannot be applied to high-concentration dispersions that do not transmit light.

[0007] This invention provides a particle size measurement method and a particle size measurement system that utilize a color sensor that uses reflected light and can be applied even to high-concentration dispersions with unknown solid content. [Means for solving the problem]

[0008] The aspects of the means for solving the above problems are as follows.

[0009] (First aspect) A method for obtaining a representative particle diameter of particles, including the step of obtaining basic data of the R value, G value, and B value of the dispersion of the particles using the representative particle diameter of the particles and a color sensor, the step of obtaining a regression model for predicting the representative particle diameter from at least one or more values of the R value, the G value, and the B value, the step of obtaining the R value, G value, and B value of the dispersion of the particles to be measured, the step of obtaining the representative particle diameter of the particles to be measured from the regression model based on the R value, G value, and B value of the dispersion of the particles to be measured, A method for obtaining a representative particle diameter of particles, characterized by comprising the above.

[0010] (Function and effect) According to this method, without the need for expensive equipment such as a particle size distribution measuring device, it is possible to easily and quickly obtain the representative particle diameter of particles from the R value, G value, and B value measured using a color sensor for the dispersion of the particles. In addition, since it uses reflected light, it is applicable to high-concentration dispersions. Furthermore, it is applicable to dispersions with unknown particle concentrations.

[0011] (Second aspect) The regression model is a linear regression model, The method for obtaining the representative particle diameter of particles according to the first aspect.

[0012] (Function and effect) When using a linear regression model, the calculation formula is simple, and the influence of the measured values on the representative particle diameter is easy to understand.

[0013] (Third aspect) When the regression model sets the representative particle diameter of the particles as Y μm, the R value as X1, the G value as X2, the B value as X3, X4 = (X1 + X2), X5 = (X1 + X3), X6 = (X2 + X3), and X7 = (X1 + X2 + X3), [Number] Here, [Number] (n is an integer greater than or equal to 1, and X ij represents any one of X1, X2, X3, X4, X5, X6, X7, and they may be different from each other) and g ij (X) is a function (which may be different from each other) representing any one of X, X 2 , X 3 , X i , ln(X), exp(X), and h i1 (g i2 (X), g i1 (X)) is a function (which may be different from each other) representing either (g i2 (X) + g i1 (X)) or (g i2 (X) × g n (X)), and here, at least one of A1 to A ij is a non - zero real number, and the others are set to 0, the non - zero real number and A0 are determined by a linear regression model from the basic data. The method for obtaining the representative particle diameter according to the second aspect.

[0014] (Function and effect) By using the above linear regression model, the representative particle diameter of the generated particles can be accurately obtained. Furthermore, the computational load can also be reduced.

[0015] (Fourth aspect) Furthermore, it includes the step of obtaining the basic data of the turbidity of the dispersion liquid, The step of obtaining the regression model involves predicting the representative particle size from at least one of the R value, G value, and B value, and turbidity. The step of obtaining the representative particle size of the particles involves obtaining the representative particle size of the particles to be measured from the regression model based on the R value, G value, B value, and turbidity of the dispersion of the particles to be measured. A method for obtaining the representative particle size described in the first embodiment.

[0016] (Effects and Benefits) By obtaining a regression model using turbidity data in addition to R, G, and B values ​​measured using a color sensor, it may be possible to obtain representative particle sizes with greater accuracy than with regression models using only R, G, and B values.

[0017] (Fifth aspect) The regression model is a linear regression model. A method for obtaining a representative particle size of the particle described in claim 4.

[0018] (Effects and Benefits) When using a linear regression model, the calculation formula is simple, and the influence of the measured values ​​on the representative particle size is easy to understand.

[0019] (Sixth aspect) The regression model assumes that the representative particle diameter of the particle is Y μm, the R value is X1, the G value is X2, the B value is X3, X4 = (X1 + X2), X5 = (X1 + X3), X6 = (X2 + X3), X7 = (X1 + X2 + X3), and the turbidity measured at different light source wavelengths is X8 and X9.

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[0020] (Effects and Benefits) By using the multiple regression model described above, the representative particle size of the generated particles can be obtained with high accuracy. Furthermore, the computational load can be reduced.

[0021] (Seventh aspect) A Gaussian process regression model, trained using machine learning based on the representative particle size of the aforementioned particles and at least one of the basic data points of the R value, G value, and B value of the dispersion of the aforementioned particles obtained using a color sensor, is used. A method for obtaining the representative particle size described in the first embodiment.

[0022] (Effects and Benefits) A representative particle size prediction model trained using a Gaussian process regression method can accurately predict particle sizes without the need for a specific function. Furthermore, it allows for the evaluation of the variability of the predicted values.

[0023] (Eighth aspect) A Gaussian process regression model, trained using machine learning based on the representative particle size of the aforementioned particles, at least one of the R value, G value, and B value of the dispersion of the aforementioned particles obtained using a color sensor, and the basic data of the turbidity, is used. A method for obtaining the representative particle size described in claim 4.

[0024] (Effects and Benefits) A representative particle size prediction model trained using a Gaussian process regression method can accurately predict particle sizes without the need for a specific function. Furthermore, it allows for the evaluation of the variability of the predicted values.

[0025] (Ninth aspect) The aforementioned particles are produced by supplying aqueous solutions containing multiple types of metal salts to a crystallization apparatus and bringing them into contact. A method for obtaining a representative particle size described in any one of the first to eighth embodiments.

[0026] (Effects and Benefits) The methods for obtaining representative particle sizes according to the first to eighth embodiments are applicable when obtaining representative particle sizes of particles generated in a crystallization apparatus. By installing a color sensor and a turbidimeter in the flow path of the particle dispersion, it becomes possible to quickly measure the particle size of the generated particles regardless of the particle concentration.

[0027] (Tenth aspect) A system for obtaining a representative particle size of a particle, A color sensor that acquires the R, G, and B values ​​of the dispersion of the aforementioned particles, A regression model creation unit that obtains a regression model for predicting the representative particle size of the particles obtained by a particle size distribution measuring device from at least one of the R value, G value, and B value. A representative particle diameter calculation unit obtains the representative particle diameter of the particles to be measured from the regression model based on the R, G, and B values ​​of the dispersion of the particles to be measured. A representative particle size acquisition system characterized by having the following features.

[0028] (Effects and Benefits) This system eliminates the need for expensive equipment such as particle size distribution analyzers, and allows for the simple and rapid acquisition of representative particle sizes from R, G, and B values ​​measured using a color sensor of the particle dispersion. Furthermore, because it utilizes reflected light, it can be applied to high-concentration dispersions. It can also be applied to dispersions where the particle concentration is unknown.

[0029] (The 11th aspect) Furthermore, it is equipped with a turbidity acquisition unit that acquires the turbidity of the dispersion of the particles, The regression model creation unit obtains a regression model that predicts the representative particle size of the particles obtained by a particle size distribution measuring device from at least one of the R value, the G value, and the B value, and turbidity. The representative particle size calculation unit obtains the representative particle size of the particles to be measured from the regression model based on the R value, G value, B value, and turbidity of the dispersion of the particles to be measured. A representative particle size acquisition system according to the tenth aspect.

[0030] (Effects and Benefits) In addition to the tenth embodiment, the system is equipped with a turbidity acquisition unit, and by acquiring a regression model using turbidity data in addition to R-values, G-values, and B-values, it may be possible to obtain representative particle sizes with even greater accuracy than with a regression model using only R-values, G-values, and B-values.

[0031] (The 12th aspect) The aforementioned particles are produced by supplying aqueous solutions containing multiple types of metal salts to a crystallization apparatus and bringing them into contact. A representative particle size acquisition system according to claim 10 or 11.

[0032] (Effects and Benefits) By installing a color sensor and a turbidimeter in the flow path of a particle dispersion crystallization apparatus, it becomes possible to quickly and in-line measure the particle size of the generated particles, regardless of the particle concentration. [Effects of the Invention]

[0033] According to the present invention, it is possible to obtain a representative particle size regardless of the particle concentration of the dispersion by using a regression model based on data from a color sensor or a color sensor and turbidimeter. Furthermore, when generated particles are produced by the reaction of raw material substances, it is possible to obtain the representative particle size of the generated particles in the crystallization apparatus using a regression model based on data from a color sensor or a color sensor and turbidimeter measured in-line. [Brief explanation of the drawing]

[0034] [Figure 1] This is the flow for obtaining representative particle size. [Figure 2] This is the system configuration. [Figure 3] This is a schematic diagram of the entire crystallization apparatus. [Figure 4] This graph shows the calculated and measured representative particle size values ​​using the method of Example 1. [Figure 5] This graph shows the calculated and measured representative particle size values ​​using the method of Example 4. [Modes for carrying out the invention]

[0035] Next, embodiments for carrying out the present invention will be described. An example of an apparatus and a method for obtaining the particle size will be explained.

[0036] (Representative particle size acquisition method) The following describes a method for obtaining particle diameter data from R-value, G-value, B-value, and turbidity data obtained from the color sensor 6, without directly measuring the particle size distribution with a particle size distribution analyzer. Figure 1 shows the flow for obtaining the representative particle diameter of the particles. As basic data, the representative particle diameter of the particle dispersion, the R-value, G-value, and B-value obtained from the color sensor 6, and the response value of the turbidimeter 7 are obtained (S1). Representative particle size can be measured using a particle size distribution analyzer. For example, dynamic light scattering, laser diffraction / scattering, centrifugal sedimentation, and image analysis methods can be used. When using laser diffraction / scattering, the volume-average particle size can be obtained, but weight-average particle size, number-average particle size, etc., can also be used. In addition, sometimes the particle size is expressed as d50, which is the particle size at which 50% of the volume is calculated by accumulating the particle sizes from smallest to largest. In this case, the particle size at which 10% of the volume is calculated by accumulating the particle sizes from smallest to largest is expressed as d10, and the particle size at which 90% of the volume is expressed as d90. The volume-average particle diameter can also be expressed by the following formula.

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[0037] Because a color sensor 6 that measures reflected light is used, the method can be applied even at high particle concentrations, but typically the particle concentration is 1 to 50% by mass, preferably 3 to 30% by mass. Within this range, accurate prediction of particle size is possible regardless of concentration.

[0038] Next, a regression model to obtain representative particle size is created using machine learning based on the obtained basic data (S2). Linear regression models (simple regression models, multiple regression models), Gaussian process regression models, etc., can be applied as regression models. In creating the regression model, one or more of the basic data obtained from the color sensor 6 (R, G, and B values) can be used. In addition, turbidity can also be used.

[0039] Next, the R, G, and B values, and turbidity data as needed, are acquired from the particle dispersion liquid to be measured using the color sensor 6 (S3). The acquired data is applied to the regression model created in S2 to determine the representative particle size of the particles to be measured (S4).

[0040] (Linear regression model) For example, a linear regression model can be used as the regression model. Possible methods include using a single-variable or multi-variable polynomial, exponential function, or logarithmic function as the basis function. If the polynomial is up to the third degree, then, with the representative particle diameter being Y μm, the R value being X1, the G value being X2, the B value being X3, and X4=(X1+X2), X5=(X1+X3), X6=(X2+X3), X7=(X1+X2+X3), then the linear regression model would be:

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[0041] When using a linear regression model, the coefficients can be determined and the linear regression model created using the method described above.

[0042] (Gaussian process regression model) Gaussian process regression does not assume a specific functional form; instead, the distribution of the function is obtained from the underlying data through machine learning, and the output value of the function follows a Gaussian distribution, allowing for the acquisition of information about the reliability of the predicted values. Kernel functions used in Gaussian process regression models include Gaussian kernels, linear kernels, exponential kernels, and periodic kernels, but in Gaussian process regression models, the Gaussian kernel is primarily used, often in combination with other kernels. For example, a Gaussian process regression model can be created by using a Gaussian kernel and performing machine learning based on the underlying data (S2). Next, R values, G values, B values, and turbidity data, if necessary, are acquired from the particle dispersion liquid to be measured using the color sensor 6 (S3). The acquired data can be applied to the regression model created in S2 to determine the representative particle size of the particles to be measured (S4).

[0043] (Representative particle size acquisition system) The following describes a representative particle size acquisition system that obtains the particle size from R, G, and B values ​​obtained from a color sensor 6, and turbidity data if necessary, without directly measuring the particle size distribution with a particle size distribution analyzer. An overview of the representative particle size acquisition system is shown in Figure 2. The representative particle size acquisition system consists of a color sensor 110 that acquires the R, G, and B values ​​of a particle dispersion, a turbidity acquisition unit 120 that acquires turbidity, a regression model creation unit 130 that creates a regression model representing the relationship between the representative particle size of the particles acquired by the particle size distribution measuring device, the R, G, and B values ​​of the particle dispersion, and the turbidity of the particle dispersion, and a representative particle size calculation unit 140.

[0044] The turbidity acquisition unit 120 acquires the turbidity of the particle dispersion. The turbidimeter 7, which measures the turbidity of the particle dispersion, can use any of the following methods: backscattering method, side scattering method, light transmission / scattering comparison method (integrating sphere method), or light beam transmission method. However, when the concentration of generated particles in the dispersion is high, the backscattering method is preferred. This is because, at high concentrations, scattering to the back becomes dominant.

[0045] The color sensor 6 emits light from its light-emitting section and detects the light reflected by the detected object with its light-receiving section, allowing it to detect the amount of red (R value), green (G value), and blue (B value) light received.

[0046] As basic data, the representative particle size of the particle dispersion, R-value, G-value, and B-value obtained from the color sensor 6, and the response value from the turbidimeter 7 (if necessary) are acquired, and a regression model is acquired in the regression model creation unit 130. As the regression model, linear regression models (simple regression models, multiple regression models), Gaussian process regression models, etc., can be applied.

[0047] According to the representative particle size acquisition system consisting of these components, the representative particle size of the generated particles can be obtained from at least one data point of the R, G, and B values ​​of the particle dispersion, and optionally from the turbidity data of the particle dispersion, without using a particle size distribution measuring device, by using the regression model created in the regression model creation unit 130.

[0048] (Application to crystallization apparatus) The particle size measurement method and particle size measurement system according to the present invention are applicable to crystallization apparatus. A typical example of a crystallization apparatus is a reaction crystallization apparatus for obtaining metal particles. One specific example is one that is intended for producing particles using transition metals such as Ni, Co, and Mn. However, since the method for carrying out reaction crystallization is broadly applicable, it may also be used for metals other than the aforementioned transition metals or for other substances.

[0049] Figure 3 shows an example of a crystallization apparatus equipped with the data acquisition device according to the present invention. An injection liquid containing the substance constituting the generated particles is injected into the reactor 1, and the reaction process is carried out. The injection liquid containing the metal salt to be injected may be, for example, three liquids A, B, and C, or only A and B. Reaction crystallization occurs when the injection liquid comes into contact with the substance, and particles are generated. The dispersion of generated particles is led to a retention tank 2, where the dispersion of generated particles is stabilized, and then returned to the reactor 1 through the flow path 11 by the circulation pump 4. In addition, a portion of the dispersion is sent from the retention tank 2 through the flow path 12 to the UF membrane device 3, concentrated, and then returned to the reactor 1 by the circulation pump 4. As shown in Figure 3, the color sensor 6 and turbidimeter 7 may be installed in the flow path 12.

[0050] An in-line turbidimeter 7 can be used to measure the turbidity of the dispersion of generated particles. Any of the turbidimeters 7 can be used: backscattering, side scattering, light transmission / scattering comparison (integrating sphere method), or light beam transmission. However, when the concentration of generated particles in the dispersion is high, the backscattering method is preferred. This is because at high concentrations, scattering mainly occurs backward.

[0051] The representative particle size acquisition method of the present invention is applicable to continuous, batch, and semi-continuous crystallization apparatuses. In the case of a batch system, in order to maintain operational balance, the dispersion of generated particles cannot be collected from the crystallization apparatus until the crystallization process is completed. Therefore, this representative particle size acquisition method, which uses a color sensor 6 and an in-line turbidimeter 7 that can acquire the representative particle size during operation, is particularly effective in batch systems.

[0052] (Example 1) Four types of NCM (nickel cobalt manganese) hydroxide powder samples were prepared with water to solid content concentrations of 1%, 3%, 10%, and 30%, and placed in 50 mL bottles. The R, G, and B values ​​measured by the color sensor 6, and the intensities of the turbidimeter 7 at 850 nm and 380 nm light sources were measured for each sample. The particle size distribution of the powder samples was analyzed using a laser diffraction / scattering particle size distribution analyzer. The SALD-2300 (Shimadzu Corporation) was used for this analysis. The measurement conditions involved using a flow cell, confirming dispersion with ultrasonic irradiation, and measuring at a refractive index appropriate for the sample. In this case, the representative particle size obtained is the volume-based particle size.

[0053] A color sensor 6, model LR-W500C (Keyence Corporation), was used. The color sensor 6 was configured to measure the amount of R, G, and B light received. The color sensor 6 was positioned so that the distance to the object being measured remained constant, and the focus was adjusted so that the illumination surface of the light source was located on the surface of the object being measured. After thoroughly shaking and stirring the sample prepared with water, the light from the color sensor 6 was shone on it, and the measured values ​​were recorded.

[0054] The turbidity of the particle dispersion was analyzed using a backscattering turbidimeter 7. The turbidimeter 7 used was the NBP007 (KEMTRAK). The measurement conditions used light source wavelengths of 850 nm and 380 nm.

[0055] Table 1 shows d50 (μm), particle concentration (mass%), B value obtained from color sensor 6, and D50 predicted value from a linear regression model. As the regression model, we used a simple linear regression model represented by the following equation.

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[0056] (Example 2) In Example 1, the following multiple regression model was used instead of the simple regression model.

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[0057] (Example 3) A Gaussian regression model was created using machine learning with the R-values, G-values, B-values, and turbidity shown in Table 2. Turbidity values ​​were obtained at 850 nm and 380 nm. The predicted values ​​for d10, d50, and d90 based on the Gaussian regression model are also shown. (R of d10) 2 The value is 0.86, d50 R 2 The value is 0.93, d90 R 2 The value was 0.95, which is a good result, indicating that predictions are possible with high accuracy not only for d50 but also for d10 and d90. The kernel function used was a combination of a constant kernel, a Gaussian kernel, and a white kernel, and the hyperparameters were optimized using maximum likelihood estimation. [Table 2]

[0058] (Example 4) Using the apparatus shown in Figure 3, demineralized water was first added to the apparatus, followed by the addition of cobalt sulfate aqueous solution, manganese sulfate aqueous solution, and nickel sulfate aqueous solution to reactor 1 simultaneously with caustic soda solution and ammonia solution, allowing the generated particles to grow. The particle size of the generated particles increased over time. The sum of the R, G, and B values ​​of the generated particles, as well as the turbidity at wavelengths of 850 nm and 380 nm, were measured using a color sensor 6. In addition, the particle size distribution of the generated particles was measured separately using a laser diffraction / scattering particle size distribution analyzer. This crystallization operation was performed twice. The measurement results are shown in Table 3. [Table 3]

[0059] As the regression model, we used a simple linear regression model represented by the following equation.

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[0060] (Example 5) In Example 4, a linear regression model represented by the following equation was used as the regression model.

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[0061] (Example 6) A Gaussian regression model was created using machine learning with the R-value, G-value, B-value, and turbidity shown in Table 3. Turbidity values ​​were obtained at 850 nm and 380 nm. Table 4 shows the predicted values ​​for d10, d50, and d90 based on the Gaussian regression model. The R-value for d10 is shown below. 2 The value is 0.94, d50 R 2 The value is 0.94, d90 R 2 The value was 0.95, which was a good result. The kernel function used was a combination of a constant kernel, a Gaussian kernel, and a white kernel, and the hyperparameters were optimized using maximum likelihood estimation. [Table 4] [Industrial applicability]

[0062] This invention creates a regression model from R-values, G-values, B-values, and optionally turbidity obtained from a color sensor for a particle dispersion. Based on this regression model, it is possible to easily and quickly predict the representative particle size from the R-values, G-values, B-values, and optionally turbidity measured for the target particles, without using expensive particle size distribution analyzers. Furthermore, in the crystallization process, it becomes possible to obtain the particle size of the generated particles in the crystallization apparatus using a regression model based on R, G, and B values ​​measured in-line by a color sensor, and turbidity if necessary. This allows for simple and rapid prediction of representative particle size without the need for expensive particle size distribution analyzers. [Explanation of symbols]

[0063] 1…Reactor, 2…Retention tank, 3…UF membrane device, 4…Circulation pump, 5…Diaphragm pump, 6…Color sensor, 7…Turbidimeter, 11, 12…Flow channels

Claims

1. A method for obtaining a representative particle size of a particle, A step of acquiring basic data on the representative particle size of the aforementioned particles and the R, G, and B values ​​of the dispersion of the aforementioned particles using a color sensor. A step of obtaining a regression model that predicts the representative particle size from at least one of the R value, G value, and B value. A step to obtain the R value, G value, and B value of the dispersion of particles to be measured. A step of obtaining the representative particle size of the particles to be measured from the regression model based on the R value, G value, and B value of the dispersion of the particles to be measured. A method for obtaining a representative particle size of a particle, characterized by comprising the following:

2. The regression model is a linear regression model. A method for obtaining a representative particle size of the particle described in claim 1.

3. The regression model has the representative particle diameter of the particles as Y μm, the R value as X １ , the G value as X ２ , the B value as X ３ , X ４ = (X １ + X ２ ), X ５ = (X １ + X ３ ), X ６ = (X ２ + X ３ ), X ７ = (X １ + X ２ + X ３ ) when [Math 1] Here, [Math 2] (n is an integer greater than or equal to 1, X ｉｊ is X １ , X ２ , X ３ , X ４ , X ５ , X ６ , X ７ any of (These represent either [something] or [something else], and they may be different.) And, g ｉｊ (X) is X, X ２ , X ３ It is a function that represents either ln(X) or exp(X) (they may be different), h ｉ (g ｉ１ (X), g ｉ２ (X)) is (g ｉ１ (X) + g ｉ２ (X) or (g ｉ１ (X) × g ｉ２ (X)) is a function that represents any of the following (they may be different): Here A １ ~A ｎ At least one of them is a real number other than 0, and the others are set to 0. Real numbers other than 0 and A ０ This is determined by a linear regression model from the aforementioned basic data. A method for obtaining the representative particle size described in claim 2.

4. Furthermore, it includes a step to acquire basic data on the turbidity of the dispersion. The step of obtaining a regression model involves predicting the representative particle size from at least one of the R value, G value, and B value, and the turbidity. The step of obtaining the representative particle size of the particles involves obtaining the representative particle size of the particles to be measured from the regression model based on the R value, G value, B value, and turbidity of the dispersion of the particles to be measured. A method for obtaining the representative particle size described in claim 1.

5. The regression model is a linear regression model. A method for obtaining a representative particle size of the particle described in claim 4.

6. The regression model defines the representative particle diameter as Y μm and the R value as X. １ , the G value is X ２ , the aforementioned B value X ３ , X ４ = (X １ +X ２ ), X ５ = (X １ +X ３ ), X ６ = (X ２ +X ３ ), X ７ = (X １ +X ２ +X ３ ), the turbidity measured at different light source wavelengths X ８、 X ９ In that case, [Math 3] Here, [Math 4] (n is an integer greater than or equal to 1, X ｉｊ is X １ , X ２ , X ３ , X ４ , X ５ , X ６ , X ７ , X ８、 X ９ of (Either represents one of the above, and they may be different.) And, g ｉｊ (X) is X, X ２ , X ３ It is a function that represents either ln(X) or exp(X) (they may be different), h ｉ (g ｉ１ (X), g ｉ２ (X)) is (g ｉ１ (X) + g ｉ２ (X) or (g ｉ１ (X) × g ｉ２ (X)) is a function that represents any of the following (they may be different): Here A １ ~A ｎ At least one of them is a real number other than 0, and the others are set to 0. Real numbers other than 0 and A ０ This is determined by a linear regression model from the aforementioned basic data. A method for obtaining the representative particle size described in claim 5.

7. A Gaussian process regression model, trained using machine learning based on the representative particle size of the aforementioned particles and at least one of the basic data points of the R value, G value, and B value of the dispersion of the aforementioned particles obtained using a color sensor, is used. A method for obtaining the representative particle size described in claim 1.

8. A Gaussian process regression model, trained using machine learning based on the representative particle size of the aforementioned particles, at least one of the R value, G value, and B value of the dispersion of the aforementioned particles obtained using a color sensor, and the basic data of the turbidity, is used. A method for obtaining the representative particle size described in claim 4.

9. The aforementioned particles are produced by supplying aqueous solutions containing multiple types of metal salts to a crystallization apparatus and bringing them into contact. A method for obtaining the representative particle size described in any one of claims 1 to 8.

10. A system for obtaining a representative particle size of a particle, A color sensor that acquires the R, G, and B values ​​of the dispersion of the aforementioned particles, A regression model creation unit that obtains a regression model for predicting the representative particle size of the particles obtained by a particle size distribution measuring device from at least one of the R value, G value, and B value. A representative particle diameter calculation unit obtains the representative particle diameter of the particles to be measured from the regression model based on the R, G, and B values ​​of the dispersion of the particles to be measured. A representative particle size acquisition system characterized by having the following features.

11. Furthermore, it is equipped with a turbidity acquisition unit that acquires the turbidity of the dispersion of the particles, The regression model creation unit obtains a regression model that predicts the representative particle size of the particles obtained by a particle size distribution measuring device from at least one of the R value, the G value, and the B value, and turbidity. The representative particle size calculation unit obtains the representative particle size of the particles to be measured from the regression model based on the R value, G value, B value, and turbidity of the dispersion of the particles to be measured. The representative particle size acquisition system according to claim 10.

12. The aforementioned particles are produced by supplying aqueous solutions containing multiple types of metal salts to a crystallization apparatus and bringing them into contact. A representative particle size acquisition system according to claim 10 or 11.

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