Prediction model

Abstract

To provide a prediction model that enables more probable prediction.SOLUTION: The prediction model of the present invention is constituted through machine learning using information representing catalyst compositions of an exhaust gas purification catalyst as explanatory variables and information representing purification performance as objective variables. The information representing the catalyst composition includes data of synthesized XRD spectra of support powder for each type of at least one type of catalytic metal. The synthesized XRD spectrum is obtained by: calculate the number equal to the number of types of the support powder, of data of intensities at respective diffraction angles of the standard XRD spectra of respective types of support powder reflected with an amount of each of types of catalyst metals, by multiplying the intensity at each diffraction angle of the standard XRD spectrum of each type of support powder alone of at least one type of support powder carrying each type of catalyst metal of at least one type of catalytic metal, by an amount of each catalytic metal supported on each type of the support powder; and summing up the number equal to the number of types, of the calculated data.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a prediction model for predicting the purification performance of an exhaust gas purification catalyst. [Background technology]

[0002] Various prediction models for predicting the purification performance of exhaust gas purification catalysts have been known in the past, including a prediction model that is trained in advance using teacher data based on the ratio of elements contained on the surface of multiple types of catalysts and the specific surface area of ​​the catalyst surface (Patent Document 1). [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2022-185940 Summary of the Invention [Problem to be solved by the invention]

[0004] The purification performance of an exhaust gas purification catalyst is determined by, for example, the catalyst configuration, the test conditions of a purification performance evaluation test, the durability history, etc. Conventionally, in a prediction model that predicts purification performance using machine learning, data on the catalytic metals contained in each layer of the catalyst layer, among the information expressing the catalyst configuration used as explanatory variables for machine learning, has sometimes been used in a matrix format in which the amount of each type of catalytic metal supported on each type of support powder is used as a column name. In this case, the amounts of a predetermined type of catalytic metal supported on multiple similar types of support powder are expressed by multiple different explanatory variables displayed with different column names, and multiple explanatory variables that vary separately along multiple orthogonal axes. Therefore, these explanatory variables do not express the similarity between the multiple types of support powder. As a result, in an original exhaust gas purification catalyst, simply changing the support powder that supports a specified type of catalytic metal to a similar support powder that has the same or similar elemental composition but slightly different physical properties results in almost no change in purification performance.However, in conventional prediction models, over-learning occurs, and when predicting the purification performance of an exhaust gas purification catalyst that has been changed to a similar support powder, the model is sensitive to the changes in the support powder, which can lead to inaccurate prediction results.

[0005] The present invention has been made in view of the above points, and an object of the present invention is to provide a prediction model that can make more accurate predictions. [Means for solving the problem]

[0006] In order to solve the above-mentioned problems, the prediction model of the present invention is a prediction model for predicting the purification performance of an exhaust gas purification catalyst, wherein the exhaust gas purification catalyst comprises a catalyst layer having a layer containing at least one type of support powder and at least one type of catalytic metal supported on the at least one type of support powder, and the prediction model is constructed by performing machine learning using information having information representing the catalyst configuration of the exhaust gas purification catalyst as an explanatory variable and information representing the purification performance as a target variable, the information representing the catalyst configuration includes data of a synthetic XRD spectrum of supported powder for each type of the at least one catalytic metal, and The synthetic XRD spectrum of the supported powder for each type of catalytic metal is characterized in that it is a synthetic XRD spectrum obtained by multiplying the intensity at each diffraction angle of the standard XRD spectrum of each type of support powder alone of the at least one type of support powder supporting each type of catalytic metal of the at least one type of catalytic metal by the amount of each type of catalytic metal supported on each type of support powder, calculating the intensity data at each diffraction angle of the standard XRD spectrum of each type of support powder that reflects the amount of each type of catalytic metal, for the number of types of support powder, and adding up the data calculated for the number of types. [Effects of the Invention]

[0007] According to the present invention, more reliable predictions can be made. [Brief explanation of the drawings]

[0008] [Figure 1] FIG. 1A is a diagram for explaining a prediction device, and FIG. 1B is a diagram for showing a configuration of a computer that realizes the prediction device. [Figure 2] (a) is a schematic cross-sectional view showing an enlarged view of the partition walls and catalyst layer of the substrate in each sample of the exhaust gas purification catalyst. (b) to (d) are diagrams explaining a method for acquiring information representing the catalyst configuration, a method for acquiring information representing the durability history, and a method for acquiring information representing the purification performance evaluation test and information representing the purification performance, respectively. [Figure 3]FIG. 1 is a diagram illustrating a method for acquiring n pieces of data on the intensity at each diffraction angle of the synthetic XRD spectrum of the powder supporting each type of catalytic metal M1 to My. [Figure 4] Graph (a) is a graph plotting on an XY coordinate the combinations of the "amount of Pd [g] supported on support powder A" (X) and the "amount of Pd [g] supported on support powder A'" (Y), which are used as explanatory variables in the prediction model of the comparative example, when the "amount of Pd [g] supported on support powder A" is changed in the range of 0.0 to 2.0 and when the "amount of Pd [g] supported on support powder A'" is changed in the range of 0.0 to 2.0 for the specification data of a given sample of catalyst. (b) is a graph plotting on the XY coordinate the combination of "intensity [au] at a diffraction angle of 40° in the synthetic XRD spectrum of the Pd-supported powder" (X) and "intensity [au] at a diffraction angle of 50° in the synthetic XRD spectrum of the Pd-supported powder" (Y), which are used as explanatory variables in the prediction model of the example, when the "amount of Pd [g] supported on support powder A" in the specification data is similarly varied within the range of 0.0 to 2.0, and when the "amount of Pd [g] supported on support powder A'" in the specification data is similarly varied within the range of 0.0 to 2.0. [Figure 5] Graph (a) shows the results of calculations of the NOx 50% conversion temperature (predicted value) according to the amount of a predetermined type of catalytic metal supported on the powder of the predetermined type of catalytic metal contained in a predetermined layer of the catalyst layer, using the prediction model of the comparative example and the specification data of a predetermined sample of the catalyst. Graph (b) shows the results of calculations of the NOx 50% conversion temperature (predicted value) according to the amount of a predetermined type of catalytic metal supported on the powder of the predetermined type of catalytic metal contained in a predetermined layer of the catalyst layer, using the prediction model of the example and the specification data of a predetermined sample of the catalyst. DETAILED DESCRIPTION OF THE INVENTION

[0009] The prediction model according to the embodiment will be described with reference to a prediction device that predicts the purification performance of an exhaust gas purification catalyst (hereinafter, sometimes abbreviated as "catalyst") using the prediction model according to the embodiment. As shown in FIG. 1(a), the prediction device 1 includes a memory unit 4 that stores a prediction model 4a according to the embodiment and other data 4b, a processing unit 6 that includes a prediction unit 6a and a calculation unit 6b, an input unit 2, and an output unit 8. The prediction device 1 is realized, for example, by a computer 100 shown in FIG. 1(b). The computer 100 includes a processing unit (calculator) 110, a storage device 120, an input device 130, an output device 140, an input / output interface (I / F) 150, and the like. The prediction model 4a in the memory unit 4 predicts the purification performance of a catalyst having a catalyst layer that includes at least one type of support powder and at least one type of catalytic metal supported on the at least one type of support powder. The prediction model 4a is constructed by performing machine learning using a dataset consisting of multiple sets of explanatory variables (information having information representing the catalyst configuration of the catalyst to be predicted) and objective variables (information representing the purification performance) obtained from multiple learning samples of the catalyst. The prediction unit 6a of the processing unit 6 uses the prediction model 4a to obtain information representing the purification performance (objective variable) from information having information representing the catalyst configuration of the catalyst to be predicted (explanatory variables), thereby predicting the purification performance. The calculation unit 6b of the processing unit 6 calculates the NOx 50% purification temperature from the information representing the purification performance. The input unit 2 inputs information having information representing the catalyst configuration of the catalyst to be predicted (explanatory variables). The output unit 8 outputs the prediction results and calculation results.

[0010] The information expressing the catalyst configuration in the explanatory variables includes data on synthetic XRD spectra of the supported powders for each type of the at least one catalytic metal. The synthetic XRD spectra of the supported powders for each type of the at least one catalytic metal are synthetic XRD spectra obtained by multiplying the intensity at each diffraction angle of the standard XRD spectrum of each type of support powder alone of the at least one support powder supporting each type of catalytic metal by the amount of each type of catalytic metal supported on each type of support powder, calculating the number of types of support powder, and adding up the data for the calculated number of types. The synthetic XRD spectrum data of the supported powders for each type of the at least one catalytic metal included in the information expressing the catalyst configuration is not particularly limited, and may be data on the intensity at each diffraction angle of the synthetic XRD spectrum, or data after dimensional compression of the intensity at each diffraction angle of the synthetic XRD spectrum.

[0011] According to the prediction model of the embodiment, the data of the composite XRD spectrum of the support powder for each type of at least one catalytic metal is used as information representing the amount of each type of catalytic metal supported on each type of support powder in the explanatory variables, thereby making it possible to express the similarity between the support powders, thereby enabling more accurate predictions. [Example]

[0012] The prediction model according to the embodiment will be described in more detail below with reference to comparative examples and examples.

[0013] [Comparative Example] A prediction model of the comparative example was constructed. The procedure for constructing the prediction model of the comparative example will be described below.

[0014] 1. Obtaining a data set of explanatory variables and target variables to be used in building a predictive model First, a data set of explanatory variables and objective variables to be used in building a prediction model was obtained from a learning sample of exhaust gas purification catalysts. The method of obtaining this data is explained below.

[0015] (1) Preparation of a sample for studying exhaust gas purification catalysts First, 800 samples of exhaust gas purification catalysts were prepared for study. As shown in FIG. 2(a), each catalyst sample CS was a straight-flow type catalyst and included a honeycomb substrate 10 and a catalyst layer 20. The honeycomb substrate 10 is a substrate integrally formed with a cylindrical frame (not shown) and partition walls 14 that divide the inner space into a honeycomb shape. The partition walls 14 are porous bodies that define a plurality of cells 12 extending from the inlet-side end face to the outlet-side end face of the substrate 10. The catalyst layer 20 includes at least the first layer 20a and the second layer 20b of the first layer 20a to the fifth layer 20e that are stacked in the order of n-th layer to first layer (n is an integer between 2 and 5) on the cell-side surface 14c of the partition walls 14. Each layer of the catalyst layer 20 contains at least one type of support powder P1 to Px (x is an integer of 1 or more) and at least one type of catalytic metal M1 to My (y is an integer of 1 or more) supported on the support powder P1 to Px. Examples of the support powder include powders belonging to AZ (alumina-zirconia binary composite oxide) and powders belonging to alumina, and examples of the catalytic metal include Pd (palladium), Rh (rhodium), and Pt (platinum).

[0016] (2) Obtaining explanatory variables and target variables for each catalyst sample Next, for each catalyst sample, three categories of information were obtained as explanatory variables: information representing the catalyst configuration, information representing the durability history, and information representing the purification performance evaluation test, and information representing the purification performance was obtained as the objective variable.

[0017] (2-1) Acquisition of information that describes the catalyst structure In obtaining information expressing the catalyst configuration, first, specification data for each catalyst sample was prepared. As shown in Table 1 below, the specification data for each catalyst sample included specification data for each layer of the catalyst layer and specification data for the honeycomb substrate. Then, as the specification data for each layer of the catalyst layer, data including the amount [g] of each type of support powder P1 to Px and the amount [g] of each type of catalytic metal M1 to My supported on each type, and data regarding the coating region were obtained. As the data regarding the coating region, data including the coating width and coating position of each layer of the catalyst layer was obtained. As the specification data for the honeycomb substrate, data regarding the weight, cell shape, and wall thickness (partition wall thickness) were obtained.

[0018] [Table 1]

[0019] Next, pre-dimensionality reduced information representing the catalyst configuration was obtained from the specification data of each catalyst sample. As shown in Table 2 below, the pre-dimensionality reduced information representing the catalyst configuration included pre-dimensionality reduced information for each layer of the catalyst layer and pre-dimensionality reduced information for the honeycomb substrate. The pre-dimensionality reduced information for each layer of the catalyst layer included n pieces of data on the intensity [au] at each diffraction angle of the synthetic XRD spectrum of the support powders P1 to Px (each of n (4250) diffraction angles at 0.02° intervals in the range of 2θ = 5° to 90°), the amount [g] of each type of catalytic metal M1 to My supported on each type of support powder P1 to Px, and data on the coating region. The data on the coating region was the same as the data on the coating region included in the specification data for each layer of the catalyst layer. The pre-dimensionality reduced information for the honeycomb substrate was the same as the specification data for the honeycomb substrate.

[0020] [Table 2]

[0021] When obtaining n pieces of intensity data at each diffraction angle of the composite XRD spectrum of the support powders P1 to Px, as shown in FIG. 2(b), first, for each type of support powder P1 to Px, n pieces of intensity data [au] were obtained at each diffraction angle (each of n diffraction angles at 0.02° intervals in the range of 2θ = 5° to 90°) of the standard XRD spectrum of each type of support powder alone. Next, the intensity at each diffraction angle of the standard XRD spectrum of each type of support powder P1 to Px was multiplied by the composition ratio (weight ratio) of each type of support powder P1 to Px to calculate n pieces of intensity data at each diffraction angle of the standard XRD spectrum of each type of support powder reflecting the composition ratio, for the number (x) of types of support powder P1 to Px. Then, the calculated data for each type was added together to obtain the composite XRD spectrum of the support powders P1 to Px, and n pieces of intensity data at each diffraction angle of the synthetic XRD spectrum were obtained. It should be noted that R1 to Rx shown in FIG. 2(b) indicate the composition ratios of the carrier powders P1 to Px, respectively.

[0022] Next, the information representing the catalyst configuration of each catalyst sample before dimensional compression was dimensionally compressed to obtain information representing the catalyst configuration (dimensionally compressed information). As shown in Table 3 below, the information representing the catalyst configuration was obtained by dimensionally compressing information on each layer of the catalyst layer after dimensional compression and information on the honeycomb substrate after dimensional compression. When obtaining the dimensionally compressed information on each layer of the catalyst layer, a predetermined autoencoder was used to dimensionally compress n pieces of data on the intensity at each diffraction angle of the composite XRD spectrum of the support powders P1 to Px in the dimensionally compressed information on each layer of the catalyst layer. Separately, a predetermined autoencoder was used to dimensionally compress the amount of each type of catalytic metal M1 to My supported on each type of support powder P1 to Px in the dimensionally compressed information on each layer of the catalyst layer. As a result, dimensionally compressed information for each layer of the catalyst layer was obtained, including dimensionally compressed data for the intensity at each diffraction angle of the composite XRD spectrum of the support powders P1 to Px, dimensionally compressed data for the amount of each type of catalytic metal M1 to My supported on each type of support powder P1 to Px, and data for the coated region. Note that the data for the coated region was used as is without dimensional compression. Furthermore, dimensionally compressed information for the honeycomb substrate was obtained by dimensionally compressing the information for the honeycomb substrate before dimensional compression, thereby obtaining dimensionally compressed data for the weight, cell shape, and wall thickness.

[0023] [Table 3]

[0024] (2-2) Acquisition of information representing durability history First, a durability test was performed on each catalyst sample in the same manner as in the examples of Japanese Patent Application No. 2023-007974. Next, as shown in FIG. 2(c), the catalyst bed temperature (endurance temperature) and the air-fuel ratio (A / F sensor value) containing the catalyst were measured throughout each durability test and saved as data for each durability test. Next, as in the examples of Japanese Patent Application No. 2023-007974, durability history 2D histogram data (30 pixel x 30 pixel image data where pixel values ​​represent the frequency of combinations of air-fuel ratio and catalyst bed temperature) representing the durability history of each catalyst sample was created from the data of each durability test. Next, the durability history 2D histogram data was subjected to dimensional compression using a convolutional autoencoder in the same manner as in Japanese Patent Application No. 2023-081090, thereby obtaining 16-dimensional latent variable data representing the durability history as information representing the durability history.

[0025] (2-3) Acquisition of information that expresses purification performance evaluation tests and information that expresses purification performance First, a purification performance evaluation test (temperature characteristic test) was conducted on each sample of catalyst deteriorated in each durability test, similar to the example of Patent Application No. 2023-007974. Test condition data (exhaust gas flow rate, catalyst inlet temperature, CO concentration at catalyst inlet, NOx concentration at catalyst inlet, HC concentration at catalyst inlet, and air-fuel ratio (A / F sensor value) per second) was obtained as information representing the purification performance evaluation test. As information representing the purification performance (temperature characteristic), data was obtained per second of the catalyst inlet temperature, NOx concentration at catalyst inlet, and NOx concentration at catalyst outlet in the purification performance evaluation test. Note that the NOx 50% purification temperature can be calculated from the information representing the purification performance, as shown in Figure 2(d).

[0026] (3) Obtaining a data set of explanatory variables and target variables For the 800 learning samples of exhaust gas purification catalysts, the explanatory variables and response variables of each catalyst sample were obtained as described above, thereby obtaining a dataset consisting of 800 sets of data for the explanatory variables and response variables.

[0027] 2. Building a predictive model Next, a predictive model was constructed by machine learning using the datasets of explanatory variables and objective variables. First, the dataset was randomly divided into three: a training dataset, a test dataset, and a validation dataset. Next, a multilayer perceptron model with two hidden layers was constructed. Random values ​​were assigned to the hyperparameters (the number of dimensions of the latent variables in the first hidden layer, the number of dimensions of the latent variables in the second hidden layer, the learning rate, dropout, and epsilon) to construct the model. Next, the multilayer perceptron model was trained on the training dataset while verifying the accuracy of the model on the test dataset. The model was trained to minimize the root mean squared error (RMSE) for both the training and test datasets. The iteration count was 1000. Next, predictions were made on the validation dataset using the trained model, and the RMSE was calculated relative to the actual measurements. This series of steps—model construction, training, and calculation of the RMSE for the validation dataset using the trained model—was repeated 100 times, changing the values ​​assigned to the hyperparameters. This resulted in a dataset consisting of 100 sets of hyperparameters (explanatory variables) and RMSE (objective variable). Next, the hyperparameter values ​​that minimized the RMSE were selected from the dataset. Next, a multilayer perceptron model was constructed with the selected values ​​assigned to the hyperparameters, and this was used as the prediction model.

[0028] [Example] A prediction model according to an embodiment of the present invention was created. The procedure for constructing the prediction model according to the embodiment will be described below.

[0029] 1. Obtaining a data set of explanatory variables and target variables to be used in building a predictive model First, a data set of explanatory variables and objective variables used to build a prediction model was obtained from 800 learning samples of the same catalyst as in the comparative example. In this case, first, for each catalyst sample, three types of information consisting of information representing the catalyst configuration, information representing durability history, and information representing a purification performance evaluation test were obtained as explanatory variables, and information representing purification performance was obtained as the objective variable. In this case, the information representing the durability history and information representing the purification performance evaluation test in the explanatory variables, and the information representing purification performance in the objective variable were obtained in the same way as in the comparative example. On the other hand, the information representing the catalyst configuration in the explanatory variables was obtained by a method different from that in the comparative example.

[0030] In obtaining information expressing the catalyst configuration, first, the data shown in Table 1 above was prepared as specification data for each catalyst sample, as in the comparative example. Next, pre-dimensionally reduced information expressing the catalyst configuration was obtained from the specification data for each catalyst sample. As shown in Table 4 below, the pre-dimensionally reduced information expressing the catalyst configuration included pre-dimensionally reduced information for each layer of the catalyst layer and pre-dimensionally reduced information for the honeycomb substrate. Then, as the pre-dimensionally reduced information for each layer of the catalyst layer, information including n pieces of data on the intensity at each diffraction angle of the synthetic XRD spectrum of the support powders P1 to Px, n pieces of data on the intensity [au] at each diffraction angle (n pieces (4250) of diffraction angles at 0.02° intervals in the range of 2θ = 5° to 90°) of the synthetic XRD spectrum of the supported powder for each type of catalyst metal M1 to My, and data on the coated region was obtained. The n pieces of data on the intensity at each diffraction angle of the synthetic XRD spectrum of the support powders P1 to Px and the data on the coated region were the same as those in the comparative example. The information regarding the honeycomb substrate before dimensional compression is the same as that of the comparative example.

[0031] [Table 4]

[0032] When n pieces of intensity data at each diffraction angle of the synthetic XRD spectrum of the supported powder for each type of catalytic metal M1 to My were obtained, as shown in Figure 3, the intensity at each diffraction angle of the standard XRD spectrum of each type of support powder P1 to Px supporting each type of catalytic metal M1 to My was multiplied by the amount (weight) [g] of each type of catalytic metal supported on each type of support powder to calculate n pieces of intensity data at each diffraction angle of the standard XRD spectrum of each type of support powder reflecting the amount of each type of catalytic metal.The calculated data for each type of support powder was then added together to obtain synthetic XRD spectra of the supported powders supporting each type of catalytic metal, and n pieces of intensity data at each diffraction angle of the synthetic XRD spectrum were obtained.In this way, n pieces of intensity data at each diffraction angle of the synthetic XRD spectrum of the supported powder for each type of catalytic metal M1 to My were obtained. It should be noted that W11 to Wyx shown in FIG. 3 indicate the amounts of each type of catalytic metal M1 to My supported on the support powders P1 to Px, respectively.

[0033] Next, the information representing the catalyst configuration of each catalyst sample before dimensional compression was dimensionally compressed to obtain information representing the catalyst configuration (dimensionally compressed information). As shown in Table 5 below, the information representing the catalyst configuration includes dimensionally compressed information for each layer of the catalyst layer and dimensionally compressed information for the honeycomb substrate. When obtaining the dimensionally compressed information for each layer of the catalyst layer, a predetermined autoencoder was used to dimensionally compress n pieces of data on the intensity at each diffraction angle of the synthetic XRD spectrum of the support powders P1 to Px in the dimensionally compressed information for each layer of the catalyst layer. Separately, a predetermined autoencoder was used to dimensionally compress n pieces of data on the intensity at each diffraction angle of the synthetic XRD spectrum of the supported powder for each type of catalyst metal M1 to My in the dimensionally compressed information for each layer of the catalyst layer. As a result, dimensionally compressed information for each layer of the catalyst layer was obtained, including dimensionally compressed data for the intensity at each diffraction angle of the synthetic XRD spectrum of the support powders P1 to Px, dimensionally compressed data for the intensity at each diffraction angle of the synthetic XRD spectrum of the supported powder for each type of catalytic metal M1 to My, and data for the coated region. Note that the data for the coated region was used as is without dimensional compression. Furthermore, dimensionally compressed information for the honeycomb substrate was obtained by dimensionally compressing the information for the honeycomb substrate before dimensional compression, thereby obtaining dimensionally compressed data for the weight, cell shape, and wall thickness.

[0034] [Table 5]

[0035] By obtaining the explanatory variables and response variables for each of the 800 learning samples of catalysts as described above, a dataset consisting of 800 sets of data for the explanatory variables and response variables was obtained.

[0036] 2. Building a predictive model Next, a prediction model was constructed by machine learning using the data sets of explanatory variables and response variables. In this case, the prediction model was constructed in the same manner as in the comparative example, except that the data sets of explanatory variables and response variables obtained in the examples were used.

[0037] [Prediction accuracy evaluation] Using the prediction models of the comparative examples and examples, the sensitivity of the purification performance according to the amount of a predetermined type of catalytic metal supported on the supported powder of a predetermined type of catalytic metal contained in a predetermined layer of the catalytic layer was predicted for the specification data of a predetermined sample of a catalyst having a honeycomb substrate and a catalytic layer, similar to the catalyst learning sample.

[0038] Support powders P1 to Px include support powder A and support powder A', which has the same elemental composition as support powder A but a slightly different standard XRD spectrum; support powder B and support powder B', which has the same elemental composition as support powder B but a slightly different standard XRD spectrum; and support powder C and support powder C', which has the same elemental composition as support powder C but a slightly different standard XRD spectrum. Catalytic metals M1 to My include Pd and Rh. Of the 800 catalyst training samples, there are many samples in which support powder A supports Pd in ​​a given layer of the catalyst layer, whereas there are very few samples in which support powder A' supports Pd in ​​a given layer of the catalyst layer. Furthermore, there are many samples in which support powders B and C each support Rh in a given layer of the catalyst layer, whereas there are very few samples in which support powders B' and C' each support Rh in a given layer of the catalyst layer.

[0039] Here, Figure 4(a) is a graph plotting on XY coordinates combinations of the "amount of Pd [g] supported on support powder A" (X) and the "amount of Pd [g] supported on support powder A'" (Y) contained in the information before dimensional reduction regarding a specified layer of the catalyst layer used as explanatory variables in constructing the prediction model of the comparative example, when the specification data for a specified sample of catalyst is used when the amount of Pd [g] supported on support powders other than support powder A in the specification data for a specified layer of the catalyst layer is set to 0 and the "amount of Pd [g] supported on support powder A'" is varied within the range of 0.0 to 2.0, and when the specification data for a specified layer of the catalyst layer is used when the amount of Pd [g] supported on support powders other than support powder A' is set to 0 and the "amount of Pd [g] supported on support powder A'" is varied within the range of 0.0 to 2.0. Figure 4(b) is a graph plotting on an XY coordinate the combination of "intensity [au] of the synthetic XRD spectrum of the Pd-supported powder at a diffraction angle of 40°" (X) and "intensity [au] of the synthetic XRD spectrum of the Pd-supported powder at a diffraction angle of 50°" (Y), which are included in the information before dimensional reduction for a specific layer of the catalyst layer used as an explanatory variable in constructing the prediction model of the example, when the "amount of Pd supported on support powder A [g]" in the specification data is similarly varied within the range of 0.0 to 2.0, and when the "amount of Pd supported on support powder A' [g]" in the specification data is similarly varied within the range of 0.0 to 2.0. 4(a), the coordinates of the combination of the "amount of Pd [g] supported on support powder A" and the "amount of Pd [g] supported on support powder A'" included in the pre-dimensionality reduced information for a given layer of the catalyst layer used as explanatory variables for constructing the predictive model of the comparative example are plotted on the X-axis when the "amount of Pd [g] supported on support powder A" is varied in the specification data, and plotted on the Y-axis perpendicular to the X-axis when the "amount of Pd [g] supported on support powder A'" is varied in the specification data. Therefore, it is considered that the combination does not express the similarity between the effects of these two cases. In other words, it is considered that the explanatory variables used to construct the predictive model of the comparative example do not express the similarity between support powder A and support powder A'.4(b), the coordinates of the combination of "intensity [au] at a diffraction angle of 40° in the synthetic XRD spectrum of the Pd-supported powder" and "intensity [au] at a diffraction angle of 50° in the synthetic XRD spectrum of the Pd-supported powder," which are included in the information before dimensionality reduction for a specific layer of the catalyst layer used as explanatory variables in constructing the predictive model of the example, are plotted on closely spaced coordinates in the two cases where the "amount of Pd [g] supported on support powder A" in the specification data is varied and the "amount of Pd [g] supported on support powder A'" in the specification data is varied. This combination is therefore considered to represent the similarity between the effects of these two cases. In other words, the explanatory variables used in constructing the predictive model of the example are considered to represent the similarity between support powder A and support powder A'.

[0040] When the prediction model of the comparative example was used to predict the sensitivity of the purification performance according to the amount of a predetermined type of catalytic metal supported on a powder of a predetermined type of catalytic metal contained in a predetermined layer of the catalyst layer, for the specification data of a predetermined sample of the catalyst, information expressing the catalyst configuration was obtained in the same manner as in the comparative example from each of the specification data for the predetermined layer of the catalyst, in which the amount of Pd [g] supported on support powders other than support powder A in the specification data for the predetermined layer of the catalyst layer was set to 0 and the ``amount of Pd [g] supported on support powder A'' was varied in the range of 0.0 to 1.0, and from each of the specification data for the predetermined layer of the catalyst layer in which the amount of Pd [g] supported on support powders other than support powder A' was set to 0 and the ``amount of Pd [g] supported on support powder A''' was varied in the range of 0.0 to 1.0.Furthermore, information expressing the durability history and information expressing the purification performance evaluation test were obtained in the same manner as in the comparative example to obtain explanatory variables, and then the prediction model of the comparative example was used to obtain information expressing the purification performance (target variable) from the obtained explanatory variables. Then, the NOx 50% conversion temperature (predicted value) was calculated from the information expressing the conversion performance. Similarly, with respect to the specification data of a predetermined sample of catalyst, information expressing the catalyst configuration was obtained from each specification data in which the amount of Rh [g] supported on support powders other than support powder B in the specification data for a predetermined layer of the catalyst layer was set to 0 and the "amount of Rh [g] supported on support powder B" was varied in the range of 0.0 to 1.0, and each specification data in which the amount of Rh [g] supported on support powders other than support powder B' in the specification data for a predetermined layer of the catalyst layer was set to 0 and the "amount of Rh [g] supported on support powder B'" was varied in the range of 0.0 to 1.0, as in the comparative example. Furthermore, information expressing the durability history and information expressing the conversion performance evaluation test were obtained in the same manner as in the comparative example to obtain explanatory variables, and then, using the prediction model of the comparative example, information expressing conversion performance (objective variable) was obtained from the obtained explanatory variables. Then, the NOx 50% conversion temperature (predicted value) was calculated from the information expressing conversion performance.Similarly, for the specification data of a given sample of catalyst, information representing the catalyst configuration was obtained from each of the specification data for a given layer of the catalyst layer, in which the amount of Rh [g] supported on support powders other than support powder C in the specification data for a given layer of the catalyst layer was set to 0 and the "amount of Rh [g] supported on support powder C" was varied between 0.0 and 1.0, and from each of the specification data for a given layer of the catalyst layer, in which the amount of Rh [g] supported on support powders other than support powder C' in the specification data for a given layer of the catalyst layer was set to 0 and the "amount of Rh [g] supported on support powder C'" was varied between 0.0 and 1.0. Similarly, information representing the catalyst configuration was obtained from each of the specification data for a given layer of the catalyst layer, in which the amount of Rh [g] supported on support powders other than support powder C' in the specification data for a given layer of the catalyst layer was set to 0 and the "amount of Rh [g] supported on support powder C'" was varied between 0.0 and 1.0. Furthermore, information representing the durability history and information representing the purification performance evaluation test were obtained in the same manner as in the comparative example to obtain explanatory variables. Then, using the prediction model of the comparative example, information representing the purification performance (objective variable) was obtained from the obtained explanatory variables. The NOx 50% purification temperature (predicted value) was then calculated from the information representing the purification performance. FIG. 5(a) is a graph showing the results of calculations using a comparative example prediction model for the specification data of a given sample of catalyst, in which the NOx 50% conversion temperature (predicted value) was calculated according to the amount of a given type of catalytic metal (Pd or Rh) supported on a supported powder (support powder A or A', support powder B or B', or support powder C or C') of the given type of catalytic metal contained in a given layer of the catalyst layer.

[0041] When the prediction model of the examples was used to predict the sensitivity of the purification performance according to the amount of a predetermined type of catalytic metal supported on a powder of a predetermined type of catalytic metal contained in a predetermined layer of the catalyst layer, with respect to the specification data of a predetermined sample of the catalyst, information expressing the catalyst configuration was obtained in the same manner as in the examples from each of the specification data for the predetermined layer of the catalyst, in which the amount of Pd [g] supported on carrier powders other than carrier powder A in the specification data for the predetermined layer of the catalyst layer was set to 0 and the ``amount of Pd [g] supported on carrier powder A'' was varied in the range of 0.0 to 1.0, and from each of the specification data for the predetermined layer of the catalyst layer in which the amount of Pd [g] supported on carrier powders other than carrier powder A' was set to 0 and the ``amount of Pd [g] supported on carrier powder A''' was varied in the range of 0.0 to 1.0.Furthermore, information expressing the durability history and information expressing the purification performance evaluation test were obtained in the same manner as in the examples to obtain explanatory variables, and then the prediction model of the examples was used to obtain information expressing the purification performance (target variable) from the obtained explanatory variables. Then, the NOx 50% conversion temperature (predicted value) was calculated from the information expressing the conversion performance. Similarly, with respect to the specification data of a predetermined sample of catalyst, the specification data for a predetermined layer of the catalyst layer was obtained from each specification data in which the amount of Rh [g] supported on the support powder other than support powder B was set to 0 and the "amount of Rh [g] supported on support powder B" was varied in the range of 0.0 to 1.0, and the specification data for a predetermined layer of the catalyst layer was obtained from each specification data in which the amount of Rh [g] supported on the support powder other than support powder B' was set to 0 and the "amount of Rh [g] supported on support powder B'" was varied in the range of 0.0 to 1.0. Information expressing the catalyst configuration was obtained in the same manner as in the examples, and information expressing the durability history and information expressing the conversion performance evaluation test were also obtained in the same manner as in the examples to obtain explanatory variables. Then, using the prediction model of the examples, information expressing conversion performance (objective variable) was obtained from the obtained explanatory variables. Then, the NOx 50% conversion temperature (predicted value) was calculated from the information expressing conversion performance.Similarly, for the specification data of a given sample of catalyst, information representing the catalyst configuration was obtained from each of the specification data for a given layer of the catalyst layer, in which the amount of Rh [g] supported on support powders other than support powder C in the specification data for a given layer of the catalyst layer was set to 0 and the "amount of Rh [g] supported on support powder C" was varied between 0.0 and 1.0, and from each of the specification data for a given layer of the catalyst layer, in which the amount of Rh [g] supported on support powders other than support powder C' in the specification data for a given layer of the catalyst layer was set to 0 and the "amount of Rh [g] supported on support powder C'" was varied between 0.0 and 1.0. Similarly to the examples, information representing the catalyst configuration was obtained from each of the specification data. Furthermore, information representing the durability history and information representing the purification performance evaluation test were obtained from the same examples to obtain explanatory variables. Then, using the prediction model of the example, information representing the purification performance (objective variable) was obtained from the obtained explanatory variables. The NOx 50% purification temperature (predicted value) was calculated from the information representing the purification performance. FIG. 5(b) is a graph showing the results of calculations using the prediction model of the embodiment for the specification data of a given sample of catalyst, in which the NOx 50% conversion temperature (predicted value) was calculated according to the amount of a given type of catalytic metal (Pd or Rh) supported on a supported powder (support powder A or A', B or B', or C or C') of the given type of catalytic metal contained in a given layer of the catalyst layer.

[0042] 5(a) and 5(b), the results of calculating the NOx 50% conversion temperature (predicted value) according to the amount of a predetermined type of catalytic metal supported on the support powder using the prediction model of the comparative example and the results of calculating the NOx 50% conversion temperature (predicted value) according to the amount of a predetermined type of catalytic metal supported on the support powder using the prediction model of the example show that the sensitivity of the NOx 50% conversion temperature according to the amount of catalytic metal supported on the support powder A, B, and C can be predicted with confidence, consistent with conventional knowledge. On the other hand, although support powders A', B', and C' are similar to support powders A, B, and C, respectively, the results of using the prediction model of the comparative example show that the sensitivity of the NOx 50% conversion temperature according to the amount of catalytic metal supported on the support powder A', B', and C' cannot be predicted with confidence, because the NOx 50% conversion temperature does not change monotonically with increases or decreases in the amount of catalytic metal. In contrast, in the results obtained using the prediction model of the example, the sensitivity of the NOx 50% conversion temperature according to the amount of catalytic metal supported on the support powders A', B', and C' changed only slightly compared to the sensitivity of the NOx 50% conversion temperature according to the amount of catalytic metal supported on the support powders A, B, and C, and a reliable prediction was made. It is believed that the prediction model of the example was able to suppress overlearning.

[0043] The above describes in detail an embodiment of the predictive model of the present invention, but the present invention is not limited to the above embodiment, and various design modifications can be made within the scope of the spirit of the present invention as set forth in the claims. [Explanation of symbols]

[0044] 1: Prediction device, 4: Storage unit, 4a: Prediction model, 6: Processing unit, 6a: Prediction unit

Claims

[Claim 1] A prediction model for predicting the purification performance of an exhaust gas purification catalyst, the exhaust gas purification catalyst comprises a catalyst layer having a layer containing at least one type of support powder and at least one type of catalytic metal supported on the at least one type of support powder; the prediction model is constructed by performing machine learning using information representing a catalyst configuration of the exhaust gas purification catalyst as an explanatory variable and information representing the purification performance as a target variable; The information representing the catalyst configuration includes data of a synthetic XRD spectrum of a supported powder for each type of the at least one catalytic metal, A prediction model characterized in that the synthetic XRD spectrum of the supported powder for each type of the at least one catalytic metal is a synthetic XRD spectrum obtained by multiplying the intensity at each diffraction angle of the standard XRD spectrum of each type of support powder alone of the at least one support powder supporting each type of catalytic metal of the at least one catalytic metal by the amount of each type of catalytic metal supported on each type of support powder, calculating the number of types of support powder, and adding up the data for the calculated number of types.

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