Predictive model

Abstract

Provided is a prediction model for predicting the purification performance of an exhaust gas purification catalyst, the prediction model being capable of achieving generalization ability and obtaining a reliable prediction value. The prediction model is composed of a neural network having an input layer, a plurality of intermediate layers, and an output layer. The prediction model takes three groups of information as explanatory variables, wherein the three groups of information are composed of a group of information displayed, a group of information displayed with a durable historical record and a group of information displayed with a purification performance evaluation test. A set of information showing purification performance is used as a target variable, and three sets of information of an explanation variable and information of the target variable are used as teaching data to be respectively given to an input layer and an output layer to carry out machine learning to construct a model. The prediction model is a local coupling-type model in which only nodes showing the same set of information among three sets of information of explanatory variables are coupled among all nodes of the input layer and the intermediate layer adjacent to the input layer among the plurality of intermediate layers.

Description

Technical Field

[0001] This invention relates to a predictive model for predicting the performance of catalysts for waste gas purification. Background Technology

[0002] Previously, various predictive models were known to predict the purification performance of catalysts for waste gas purification. Specifically, for example, patent document 1 describes a predictive model obtained by learning in advance using the proportion of elements contained on the surface of multiple types of catalysts and the specific surface area of ​​the catalyst surface as teaching data.

[0003] Patent Document 1: Japanese Patent Application Publication No. 2022-185940

[0004] The purification performance of exhaust gas purification catalysts is determined by factors such as catalyst composition, test conditions for purification performance evaluation, and the catalyst's durability history. Therefore, in predictive methods using machine learning to predict the purification performance of exhaust gas purification catalysts, when using deep learning to construct a predictive model consisting of a neural network with an input layer, multiple intermediate layers, and an output layer, sometimes the predictive model is constructed by using three sets of information—one representing catalyst composition, one representing durability history, and one representing purification performance evaluation—as explanatory variables, and one set of information representing purification performance as the target variable. This is achieved by assigning the three sets of explanatory variable information and the target variable information as teaching data to the input and output layers respectively, and then learning from them. In this case, a fully coupled model has been constructed where all nodes from the input layer through multiple intermediate layers to the adjacent layers of the output layer are coupled. While fully coupled predictive models can exhibit nonlinearity and interactions between explanatory variables, achieving high predictive accuracy, there are concerns about overlearning and decreased generalization ability. This is because excessive nonlinearity is used to represent the sensitivity of normally linearly related explanatory variables or to represent interactions between explanatory variables that do not actually exist. Summary of the Invention

[0005] The present invention is proposed in view of this situation, and its purpose is to provide a prediction model that can achieve high generalization ability and obtain reliable prediction values.

[0006] To address the aforementioned issues, the prediction model of this invention is a prediction model for predicting the purification performance of exhaust gas purification catalysts. The prediction model is characterized by being a neural network comprising an input layer, multiple intermediate layers, and an output layer. This model is constructed by using three sets of information—one representing the catalyst composition, one representing durability history, and one representing purification performance evaluation tests—as explanatory variables, and one set of information demonstrating the purification performance of the exhaust gas purification catalyst as the objective variable. The three sets of information representing the explanatory variables and the information representing the objective variable are respectively assigned as teaching data to the input layer and the output layer for machine learning. This prediction model is a locally coupled model where all nodes in the input layer and the intermediate layers adjacent to the input layer only display the same set of information from the three sets of information representing the explanatory variables.

[0007] According to the present invention, high generalization ability can be achieved, and reliable prediction values ​​can be obtained. Attached Figure Description

[0008] Figure 1 (a) is a simplified cross-sectional view showing the partition walls of the substrate and the catalyst layer in each sample of the catalyst. Figure 1 (b) is a diagram that briefly explains how a set of information showing the durability history is obtained. Figure 1 Figure (c) is a brief illustration of the method for obtaining the NOx 50% purification time.

[0009] Figure 2 (a) is a diagram that briefly illustrates the main parts of a method for obtaining a set of information about the catalyst composition involved in Comparative Examples and Examples 1 and 2. Figure 2 (b) is a diagram schematically representing the fully coupled predictive model used as a comparative example. Figure 2 (c) is a diagram schematically representing a locally coupled model as the prediction model in Example 1. Figure 2 (d) is a diagram schematically representing a locally coupled model as the prediction model of Example 2.

[0010] Figure 3 The left-hand graph in (a) shows the relationship between the predicted and measured NOx 50% purification time calculated using the prediction models of Comparative Examples and Examples 1 and 2 for the case where the catalyst durability time is within the learning range of 50 hours for the seven samples used for catalyst prediction. Figure 3 The chart to the right of (a) is a chart showing the average error of these predicted and measured values. Figure 3The graph in (b) is a graph showing the sensitivity of the predicted NOx 50% purification time calculated from 5 out of 7 samples for the catalyst prediction to the catalyst durability time [h]. Detailed Implementation

[0011] The prediction model used in this embodiment is the same as the prediction model used in the prediction device according to one embodiment of Japanese Patent Application 2023-007974, and predicts the same exhaust gas purification catalyst (e.g., described later) as the prediction model of the prediction device according to one embodiment of Japanese Patent Application 2023-007974. Figure 1 The purification performance of the catalyst shown in (a). As a prediction model involved in the implementation, it is not particularly limited as long as it is a locally coupled model in which only the same set of information from the three sets of information of the explanatory variables is displayed among all nodes of the intermediate layer adjacent to the input layer and among the multiple intermediate layers. It can also be a model in which all nodes of the intermediate layers adjacent to each other are coupled, or a model in which only the same set of information from the three sets of information of the explanatory variables is displayed among all nodes.

[0012] The following comparative examples and embodiments are provided to illustrate the prediction model involved in the implementation in more detail.

[0013] [Comparative Example]

[0014] An example of a predictive model that has been made into a comparative example.

[0015] 1. Obtaining the datasets for the explanatory and objective variables used in constructing the predictive model.

[0016] (1) Preparation of samples of waste gas purification catalyst

[0017] First, similar to the embodiment in Japanese Patent Application No. 2023-007974, 800 samples of the exhaust gas purification catalyst (catalyst) were prepared for study purposes. For example... Figure 1As shown in (a), each sample CS is a straight-flow type catalyst, comprising: a honeycomb substrate (substrate) 10, integrally formed with a frame portion (not shown) and partition walls 14 dividing the space inside the substrate into a honeycomb pattern to divide multiple units 12; and a catalyst layer 20 having at least a first layer to a fifth layer 20e of a first layer 20a to a fifth layer 20e stacked on the surface 14c of the unit 12 side of the partition walls 14. Each layer of the catalyst layer 20 contains a mixed powder containing powders P1 to Px (x is a specified integer of 2 or more) as a carrier powder, and contains a catalyst metal supported by at least one of the powders P1 to Px. The catalyst metal is at least one of the catalyst metals M1 to My (y is a specified integer of 2 or more).

[0018] (2) Explanation of variables and acquisition of target variables for each sample of catalyst

[0019] Next, three sets of information were obtained from each catalyst sample: one set of information demonstrating the catalyst composition, one set of information demonstrating the durability history, and one set of information demonstrating the purification performance evaluation test. These were used as explanatory variables, and a set of information demonstrating the purification performance was obtained as the objective variable. In obtaining the set of information demonstrating the catalyst composition, information related to each layer of the catalyst layer before dimensional compression and information related to the substrate were first obtained from each catalyst sample as information before dimensional compression. As shown in Table 1 below, the following information, which relates to each layer of the catalyst layer before dimensional compression, includes, similar to the example in Japanese Patent Application No. 2023-007974, N data points of intensity [au] at each diffraction angle (N (4250) diffraction angles at 0.02° intervals in the range of 2θ = 5° to 90°) of the synthesized XRD spectra of each layer, which were synthesized according to the composition ratio of the XRD spectra of powders P1 to Px; the amount [g] of each type of catalyst metal M1 to My supported by each type of P1 to Px; and coating information (data related to the coating area of ​​each layer, data indicating the width and position of the coating of each layer). As information related to the substrate, the weight, unit shape, and wall thickness were obtained.

[0020] Table 1

[0021]

[0022] Next, as in Figure 2 As illustrated in (a), which describes a sample of catalyst with layers one through four, information about each sample of catalyst before dimensional compression was obtained by dimensional compression of N data points representing the intensity at each diffraction angle of the synthetic XRD spectra of each layer, thus revealing a set of information about the catalyst composition of each sample. At this point, as... Figure 2 As illustrated in (a), firstly, for each layer of the catalyst layer, N data points of intensity at each diffraction angle of the synthetic XRD spectrum of each layer were prepared, representing each layer by N blocks of an assembly of N blocks arranged in the depth direction. Next, by using an autoencoder to dimensionally compress the N data points of intensity at each diffraction angle of the synthetic XRD spectrum of each layer, four latent variables representing each layer by four blocks were obtained. Thus, multiple layers of the catalyst (in...) were obtained. Figure 2 In example (a), there are four latent variables for the first to fourth layers. Next, by combining the four latent variables of each layer with information other than N data points of intensity at each diffraction angle of the synthetic XRD spectra of each layer in the information before dimensionality compression, a set of information (information after dimensionality compression) showing the catalyst composition of each sample of the catalyst is obtained.

[0023] In obtaining a set of information showcasing the durability history, durability tests were first conducted on each sample of the catalyst, in the same manner as in the example described in Japanese Patent Application No. 2023-007974. Next, as... Figure 1As shown in (b), the catalyst bed temperature (durability temperature) and the air-fuel ratio at the catalyst inlet (A / F sensor value) were measured for all time during each durability test and saved as data for each durability test. Next, similar to the embodiment in Japanese Patent Application No. 2023-007974, a 2D histogram of durability history data (30-pixel × 30-pixel image data representing the frequency of the combination of air-fuel ratio and catalyst bed temperature) was created based on the data from each durability test, showing the durability history of each sample of the catalyst. Next, similar to Japanese Patent Application No. 2023-081090, the data of the 2D histogram of durability history was dimensionally compressed using a convolutional autoencoder, thereby obtaining data on 16-dimensional latent variables showing the durability history as a set of information showing the durability history. In obtaining a set of information showing the purification performance evaluation test (heating characteristic test) and a set of information showing the purification performance (heating characteristics), a heating characteristic test was first performed on each sample of the catalyst that deteriorated in each durability test. In the heating characteristic test, a degraded catalyst was installed in the main exhaust system of a 2000cc gasoline engine, with a branch to the bypass line installed on the engine side at the catalyst mounting location. The engine output was then set to constant, with exhaust gas initially flowing to the bypass line while the catalyst reached room temperature. Next, the exhaust gas flow was switched, directing it towards the main line. Data under these test conditions (exhaust gas flow rate, catalyst inlet temperature, CO concentration at the catalyst inlet, NOx concentration at the catalyst inlet, HC concentration at the catalyst inlet, and air-fuel ratio (A / F sensor value) at the catalyst inlet, measured per second) were collected as a set of information demonstrating the heating characteristic test. Additionally, data per second of the catalyst inlet temperature, NOx concentration at the catalyst inlet, and NOx concentration at the catalyst outlet were collected as a set of information demonstrating the heating characteristics. Furthermore, based on this set of information demonstrating the heating characteristics, such as... Figure 1 As shown in (c), the time when the NOx purification amount (NOx concentration at the catalyst inlet - NOx concentration at the catalyst outlet) reaches half of the NOx concentration at the catalyst inlet can be calculated as the NOx 50% purification time.

[0024] (3) Explain how the data sets for the variables and the target variable were obtained.

[0025] By obtaining the explanatory and target variables for each of the 800 samples of the exhaust gas purification catalyst as described above, a dataset consisting of 800 sets of data for the explanatory and target variables was obtained.

[0026] 2. Construction of the prediction model

[0027] Next, a predictive model was built by using the dataset containing the explanatory and target variables for machine learning. First, the dataset was randomly split into three sets: a training dataset, a test dataset, and a validation dataset. Then, as follows... Figure 2 As shown in (b), a fully coupled multilayer perceptron model (a model composed of neural networks) was constructed, which includes a first intermediate layer and a second intermediate layer in addition to the input layer (descriptive variables) and the output layer (target variable). Specifically, three sets of information on the descriptive variables (one set showing the catalyst composition, one set showing the durability history, and one set showing the purification performance evaluation test) and the information on the target variable were used as teaching data and assigned to the input and output layers respectively for machine learning. This constructed a fully coupled model where all nodes from the input layer through the first and second intermediate layers to the adjacent layers of the output layer were coupled. At this time, a model was constructed with randomly assigned values ​​for the hyperparameters (dimensionality of the latent variables in the first intermediate layer, dimension of the latent variables in the second intermediate layer, learning rate, dropout, and epsilon). Next, the multilayer perceptron model was tested to verify its accuracy using a test dataset while simultaneously learning using a training dataset. At this time, the model was trained to minimize the RMSE (Root Mean Squared Error) for both the training and test datasets. Furthermore, the number of iterations was set to 1000. Next, the learned model is used to predict on the validation dataset, and the RMSE (Real-Time Sequence) is calculated against the measured values. This process of building the model, learning it, and calculating the RMSE on the validation dataset using the learned model is repeated 100 times by changing the values ​​assigned to the hyperparameters. This yields a dataset of 100 sets of data consisting of hyperparameters (explanatory variables) and RMSE (target variable). Next, the hyperparameter value with the smallest RMSE is selected from this dataset. Finally, a multilayer perceptron model is constructed with the selected values ​​assigned to the hyperparameters and used as the prediction model.

[0028] [Example 1]

[0029] An example of a predictive model involved in the implementation method was created. First, a dataset of explanatory and target variables, identical to that of the comparative example, was obtained for each sample of the same catalyst. Then, a predictive model was constructed by performing machine learning on the dataset of explanatory and target variables using the same method as in the comparative example, except for the method used to construct the multilayer perceptron model. When constructing the multilayer perceptron model, as follows... Figure 2As shown in (c), a locally coupled model is constructed that has a first intermediate layer and a second intermediate layer in addition to the input layer (descriptive variables) and the output layer (target variables). Specifically, the following locally coupled model is constructed: nodes that display only the same set of information from the three sets of information of the descriptive variables are coupled between all nodes in the input layer and the first intermediate layer (an intermediate layer adjacent to the input layer among multiple intermediate layers); all nodes in the first intermediate layer and the second intermediate layer (intermediate layers that are adjacent to each other) are coupled; and all nodes in the second intermediate layer (an intermediate layer adjacent to the output layer among multiple intermediate layers) and the output layer are coupled.

[0030] [Example 2]

[0031] An example of a predictive model involved in the implementation method is provided. First, for each sample of the same catalyst as in the comparative example, the same dataset of explanatory and target variables as in the comparative example is obtained. Next, except for the method of constructing the multilayer perceptron model, machine learning is performed using the dataset of explanatory and target variables in the same way as in the comparative example to construct a predictive model. When constructing the multilayer perceptron model, as follows... Figure 2 As shown in (d), a locally coupled model is constructed that has a first and a second intermediate layer in addition to the input layer (description variable) and the output layer (target variable). Specifically, the locally coupled model is constructed as follows: there is coupling between all nodes in the input layer and the first intermediate layer (the intermediate layer adjacent to the input layer among multiple intermediate layers), and between all nodes in the first and second intermediate layers (intermediate layers that are adjacent to each other) that represent only the same set of information from the three sets of information of the descriptive variable; and there is coupling between all nodes in the second intermediate layer (the intermediate layer adjacent to the output layer among multiple intermediate layers) and the output layer.

[0032] [Evaluation of Prediction Accuracy]

[0033] Regarding the seven samples used for prediction of catalysts different from those used in the construction of the prediction model, for the case where the catalyst durability time is 50 hours (within the learning range), based on the explanatory variables obtained in the same manner as in Comparative Examples and Examples 1 and 2, a set of information (target variable) demonstrating purification performance (heating characteristics) was obtained using the prediction models of each example in Comparative Examples and Examples 1 and 2, according to the obtained explanatory variables. Then, the predicted value of the NOx 50% purification time was calculated based on the set of information demonstrating the heating characteristics. Figure 3As shown in (a), regarding the average error between the predicted and measured values ​​of the NOx 50% purification time for the seven samples, Example 1 had the lowest average error, while the average errors of the Comparative Examples and Example 2 were higher than that of Example 1. The prediction model of Example 1 demonstrated high generalization ability. In the prediction model of the Comparative Examples, unnecessary interactions and nonlinearities were exhibited due to the complex coupling structure between the nodes, resulting in what was presumed to be overlearning and a decrease in generalization ability. On the other hand, the prediction model of Example 2 was presumed to be unable to exhibit necessary interactions due to the overly simple coupling structure between the nodes, indicating a lack of high-precision learning. Furthermore, the sensitivity of the catalyst relative to durability time [h] was evaluated using the prediction models of the Comparative Examples and Examples 1 and 2 for the predicted NOx 50% purification time calculated for five of the seven samples used for prediction. Figure 3 As shown in (b), the sensitivity of the predicted NOx 50% purification time of the catalyst for the prediction sample relative to the durability time [h] in the comparative example predictions does not reflect the degradation trend of the catalyst for the prediction sample in cases where the durability time exceeds 150h. That is, although the learning sample was also trained for the case where the durability time exceeds 150h, the prediction accuracy is poor in the case where the durability time exceeds 150h if the sensitivity of the prediction for the durability time of the prediction sample with a catalyst composition that was not trained for the case where the durability time exceeds 150h is poor. In the prediction model of the comparative example, it is speculated that due to overlearning, a set of information showing the catalyst composition and a set of information showing the durability history interact excessively in the complex coupling structure between nodes. On the other hand, in the predictions of Examples 1 and 2, even in cases where the durability time exceeds 150h, the degradation trend of the catalyst for the prediction sample can be accurately reflected, and the original physical trend of the catalyst can be predicted. In the prediction models of Examples 1 and 2, regarding the coupling structure between nodes, it is speculated that unnecessary interactions that reveal a set of information about the catalyst composition and a set of information about the durability history are removed, without causing any unnecessary effects other than those that reveal the original deterioration trend of the catalyst.

Claims

1. A prediction model that is a prediction model that predicts purification performance of an exhaust gas purification catalyst, characterized in that, the prediction model is a model constituted by a neural network having an input layer, a plurality of intermediate layers, and an output layer, the prediction model is a model constructed by performing machine learning by giving, as explanatory variables, three sets of information constituted by a set of information exhibiting a catalyst constituting the exhaust gas purification catalyst, a set of information exhibiting a durability history record, and a set of information exhibiting a purification performance evaluation test, and, as a target variable, a set of information exhibiting purification performance of the exhaust gas purification catalyst, to the input layer and the output layer, respectively, the prediction model is a locally coupled model in which nodes exhibiting only the same set of information among the three sets of information of the explanatory variables are coupled between the input layer and all nodes of an intermediate layer adjacent to the input layer among the plurality of intermediate layers.

2. The prediction model according to claim 1, wherein the locally coupled model is a model in which the nodes exhibiting only the same set of information among the three sets of information of the explanatory variables are coupled between the input layer and all nodes of the intermediate layer adjacent to the input layer among the plurality of intermediate layers.

3. The prediction model according to claim 1 or 2, wherein the locally coupled model is a model in which the nodes exhibiting only the same set of information among the three sets of information of the explanatory variables are coupled between the input layer and all nodes of the intermediate layer adjacent to the input layer among the plurality of intermediate layers.

4. The prediction model according to any one of claims 1 to 3, wherein the locally coupled model is a model in which the nodes exhibiting only the same set of information among the three sets of information of the explanatory variables are coupled between the input layer and all nodes of the intermediate layer adjacent to the input layer among the plurality of intermediate layers.

5. The prediction model according to any one of claims 1 to 4, wherein the locally coupled model is a model in which the nodes exhibiting only the same set of information among the three sets of information of the explanatory variables are coupled between the input layer and all nodes of the intermediate layer adjacent to the input layer among the plurality of intermediate layers.

6. The prediction model according to any one of claims 1 to 5, wherein the locally coupled model is a model in which the nodes exhibiting only the same set of information among the three sets of information of the explanatory variables are coupled between the input layer and all nodes of the intermediate layer adjacent to

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