Prediction model

Abstract

To provide a prediction model which can realize generalization performance, can acquire a probable prediction value and predicts purification performance of an exhaust gas purification catalyst.SOLUTION: A prediction model is constructed of a neural network having an input layer, a plurality of intermediate layers, and an output layer. The prediction model is a model constructed by respectively giving information of three groups of explanatory variables and information of an objective variable to the input layer and the output layer as teacher data to perform machine learning with information of three groups composed of information of one group representing a configuration, information of one group representing a durability history, and information of one group representing a purification performance evaluation test as an explanatory variable and with information of one group representing purification performance as an objective variable. The prediction model is a locally connected model obtained by making a connection only among nodes representing information of the same groups in the information of three groups of explanatory variables among all nodes of intermediate layers adjacent to the input layer in the input layer and the plurality of intermediate layers.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a prediction model for predicting the 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. Specifically, for example, Patent Document 1 describes a prediction model that is trained in advance using teacher data of the ratios of elements contained on the surfaces of multiple types of catalysts and the specific surface area values ​​on the catalyst surfaces. [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 for the purification performance evaluation test, the catalyst's durability history, etc. Therefore, in a prediction method for predicting the purification performance of an exhaust gas purification catalyst using machine learning, a prediction model consisting of a neural network with an input layer, multiple intermediate layers, and an output layer is constructed using deep learning. Three sets of information, consisting of one set of information representing the catalyst configuration, one set of information representing the durability history, and one set of information representing the purification performance evaluation test, are used as explanatory variables, and one set of information representing the purification performance is used as the objective variable. The three sets of explanatory variable information and the objective variable information are then provided as training data to the input layer and output layer, respectively, to construct the prediction model. In this case, a fully connected model was previously constructed, in which all nodes in adjacent layers are connected, from the input layer through multiple intermediate layers to the output layer. While a fully connected prediction model can represent nonlinearities and interactions between explanatory variables, resulting in highly accurate predictions, it is prone to overfitting and may have poor generalization performance. This is because the sensitivity of explanatory variables that are actually linearly correlated is expressed with excessive nonlinearity, or interactions between explanatory variables that do not actually exist are expressed.

[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 achieve high generalization performance and obtain reliable predicted values. [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 that predicts the purification performance of an exhaust gas purification catalyst, the prediction model being a model consisting of a neural network having an input layer, multiple intermediate layers, and an output layer, the prediction model using three groups of information consisting of one group of information that represents the catalyst configuration of the exhaust gas purification catalyst, one group of information that represents a durability history, and one group of information that represents a purification performance evaluation test as explanatory variables, and one group of information that represents the purification performance of the exhaust gas purification catalyst as a response variable, and is constructed by performing machine learning by providing the three groups of information of the explanatory variables and the information of the response variable to the input layer and the output layer, respectively, and the prediction model is characterized in that, among all nodes of the input layer and an intermediate layer adjacent to the input layer among the multiple intermediate layers, only nodes that represent the same group of information in the three groups of information of the explanatory variables are connected. [Effects of the Invention]

[0007] According to the present invention, high generalization performance can be achieved and reliable predicted values ​​can be obtained. [Brief explanation of the drawings]

[0008] [Figure 1] (a) is a schematic enlarged cross-sectional view of the partition walls and catalyst layer of the substrate in each catalyst sample. (b) is a diagram illustrating a method for obtaining a group of information representing durability history. (c) is a diagram illustrating a method for obtaining the NOx 50% conversion time. [Figure 2] (a) is a diagram illustrating a schematic example of a main part of a method for acquiring a group of information representing a catalyst configuration according to a comparative example and examples 1 and 2. (b) is a diagram illustrating a fully coupled model, which is a prediction model according to the comparative example, (c) is a diagram illustrating a locally coupled model, which is a prediction model according to example 1, and (d) is a diagram illustrating a locally coupled model, which is a prediction model according to example 2. [Figure 3]The left graph in (a) shows the relationship between the predicted values ​​of the NOx 50% purification time calculated by the prediction models of the Comparative Example and Examples 1 and 2 and the actual measured values ​​for the case where the catalyst endurance time is 50 hours (hours) for seven samples used for catalyst prediction, while the right graph in (a) shows the average error between the predicted values ​​and the actual measured values. The graph in (b) shows the sensitivity of the predicted values ​​of the NOx 50% purification time calculated for five of the seven samples used for catalyst prediction to the catalyst endurance time [h]. DETAILED DESCRIPTION OF THE INVENTION

[0009] The prediction model according to the embodiment is a prediction model used in place of a prediction model in a prediction device according to an embodiment of Japanese Patent Application No. 2023-007974, and predicts the purification performance of an exhaust gas purification catalyst (for example, the catalyst shown in FIG. 1(a) described below) similar to the prediction model in the prediction device according to an embodiment of Japanese Patent Application No. 2023-007974. The prediction model according to the embodiment is not particularly limited as long as it is a locally coupled model in which only nodes that represent the same group of information in three groups of explanatory variables are coupled between all nodes in the input layer and one of the multiple intermediate layers adjacent to the input layer, and may be a model in which all nodes in adjacent intermediate layers are coupled between each other, or a model in which only nodes that represent the same group of information in three groups of explanatory variables are coupled between all nodes. [Example]

[0010] The prediction model according to the embodiment will be described in more detail below with reference to comparative examples and examples.

[0011] [Comparative Example] An example of a prediction model for a comparative example was created.

[0012] 1. Obtaining a data set of explanatory variables and target variables to be used in building a predictive model (1) Preparation of exhaust gas purification catalyst samples First, 800 samples of exhaust gas purification catalysts (catalysts) for study were prepared in the same manner as in the examples of Japanese Patent Application No. 2023-007974. As shown in FIG. 1(a), each sample CS was a straight-flow type catalyst and included a honeycomb substrate (substrate) 10 integrally formed with a frame (not shown) and partition walls 14 that partition the inner space into a honeycomb shape to define multiple cells 12, and a catalyst layer 20 including at least a first layer and a second layer among first layers 20a to fifth layers 20e stacked on the cell-12-side surface 14c of the partition walls 14. Each layer of the catalyst layer 20 contained a mixed powder containing powders P1 to Px (x is a predetermined integer of 2 or greater) as a support powder, and a catalytic metal supported on at least one of the powders P1 to Px. The catalytic metal was at least one of catalytic metals M1 to My (y is a predetermined integer of 2 or greater).

[0013] (2) Obtaining explanatory variables and target variables for each catalyst sample Next, from each catalyst sample, three groups of information consisting of one group of information expressing the catalyst configuration, one group of information expressing the durability history, and one group of information expressing the purification performance evaluation test were obtained as explanatory variables, and one group of information expressing the purification performance was obtained as the objective variable. In obtaining the group of information expressing the catalyst configuration, first, from each catalyst sample, information before dimensionality reduction regarding each layer of the catalyst layer and information regarding the substrate were obtained as information before dimensionality reduction. As shown in Table 1 below, the information before dimension reduction for each layer of the catalyst layer was obtained by synthesizing the XRD spectra of powders P1 to Px at the composition ratio ratio. N data points were obtained for the intensity [au] at each diffraction angle (N (4250) diffraction angles at 0.02° intervals in the range of 2θ = 5° to 90°) of the composite XRD spectrum of each layer, as in the example of Japanese Patent Application No. 2023-007974. The amounts [g] of each type of P1 to Px, the amounts [g] of each type of catalytic metal M1 to My supported on each type of P1 to Px, and coating information (data regarding the coating area of ​​each layer, data representing the width and position of the coating of each layer). Information regarding the substrate was obtained, including weight, cell shape, and wall thickness.

[0014] [Table 1]

[0015] Next, as illustrated in Figure 2(a) for a catalyst layer having four layers for one catalyst sample, we obtained a set of information representing the catalyst structure of each catalyst sample by performing dimensionality compression on N pieces of data representing the intensities at each diffraction angle of the composite XRD spectrum of each layer for the pre-dimensionality compression information for each catalyst sample. To do this, as illustrated in Figure 2(a), we first prepared N pieces of data representing the intensities at each diffraction angle of the composite XRD spectrum of each layer, each represented by N blocks in a block assembly with N blocks arranged in the depth direction. Next, we used an autoencoder to perform dimensionality compression on the N pieces of data representing the intensities at each diffraction angle of the composite XRD spectrum of each layer, obtaining four latent variables for each layer, each represented by four blocks. This resulted in four latent variables for the multiple layers of the catalyst (layers 1 to 4 in the example of Figure 2(a)). Next, by combining the four latent variables of each layer with information other than the N data points of the intensity at each diffraction angle of the synthetic XRD spectrum of each layer in the information before dimensionality reduction, a group of information (information after dimensionality reduction) representing the catalyst composition of each catalyst sample was obtained.

[0016] To obtain a group of information representing the durability history, a durability test was first performed on each catalyst sample in the same manner as in the examples of Japanese Patent Application No. 2023-007974. Next, as shown in Figure 1(b), 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 in which 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 for 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 a group of information representing the durability history. To obtain a set of data representing the purification performance evaluation test (warm-up characteristics test) and a set of data representing purification performance (warm-up characteristics), a warm-up characteristics test was first conducted on each catalyst sample degraded in each durability test. For the warm-up characteristics test, a degraded catalyst was installed in the main exhaust system of a 2000cc gasoline engine, and a bypass line was attached to the engine side of the catalyst. The engine output was maintained constant, and exhaust gas was first diverted into the bypass line to allow the catalyst to reach room temperature. Next, the exhaust gas flow was switched to the main line. The test condition data (exhaust gas flow rate, catalyst inlet temperature, catalyst inlet CO concentration, catalyst inlet NOx concentration, catalyst inlet HC concentration, and catalyst inlet air-fuel ratio (A / F sensor value) per second) were collected as a set of data representing the warm-up characteristics test. Second-by-second data on the catalyst inlet temperature, catalyst inlet NOx concentration, and catalyst outlet NOx concentration were also collected as a set of data representing the warm-up characteristics. From a group of information representing the warm-air characteristics, the time when the NOx purification amount (NOx concentration at the catalyst entrance - NOx concentration at the catalyst exit) reaches half the NOx concentration at the catalyst entrance can be calculated as the NOx 50% purification time, as shown in Figure 1(c).

[0017] (3) Obtaining a data set of explanatory variables and target variables For the 800 samples of exhaust gas purification catalysts, by obtaining the explanatory variables and response variables for each sample of catalyst as described above, a data set consisting of 800 sets of data for the explanatory variables and response variables was obtained.

[0018] 2. Building a predictive model Next, a predictive model was constructed by machine learning using the data sets of explanatory variables and objective variables. First, the data set was randomly divided into three: a training data set, a test data set, and a validation data set. Next, as shown in Figure 2(b), a fully connected multilayer perceptron model (a model consisting of a neural network) was constructed, which had an input layer (explanatory variables) and an output layer (objective variable) as well as first and second hidden layers. Specifically, machine learning was performed by providing three groups of explanatory variables (one group representing catalyst configuration, one group representing durability history, and one group representing purification performance evaluation tests) and objective variable information to the input and output layers, respectively, as training data. A fully connected model was constructed in which all nodes in adjacent layers were connected from the input layer through the first and second hidden layers to the output layer. In this case, 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) were randomly assigned values. Next, the multilayer perceptron model was trained on the training data set while verifying the model's accuracy with the test data set. The model was trained to minimize the root mean squared error (RMSE) for both the training and test data sets. The iterations were 1,000. The trained model was then used to make predictions on the validation data set, 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 data set 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 data for hyperparameters (explanatory variables) and RMSE (objective variable). The hyperparameter values ​​that minimized the RMSE were then selected from the dataset. A multilayer perceptron model was then constructed with the selected values ​​assigned to the hyperparameters, and this was used as the prediction model.

[0019] [Example 1] An example of a predictive model according to the embodiment was created. First, a data set of explanatory variables and response variables similar to those in the comparative example was obtained for each sample of the same catalyst as in the comparative example. Next, a predictive model was constructed by performing machine learning using the data set of explanatory variables and response variables using the same method as in the comparative example, except for the construction method of the multilayer perceptron model. When constructing the multilayer perceptron model, a locally coupled model having an input layer (explanatory variables) and an output layer (response variable) as well as first and second hidden layers was constructed, as shown in FIG. 2(c). Specifically, a locally coupled model was constructed in which only nodes representing the same group of information in the three groups of explanatory variables were connected between all nodes in the input layer and the first hidden layer (the hidden layer adjacent to the input layer among multiple hidden layers), and all nodes in the first and second hidden layers (the hidden layers adjacent to each other) and the second hidden layer (the hidden layer adjacent to the output layer among multiple hidden layers) were connected.

[0020] [Example 2] An example of a predictive model according to the embodiment was created. First, a data set of explanatory variables and response variables similar to those in the comparative example was obtained for each sample of the same catalyst as in the comparative example. Next, a predictive model was constructed by performing machine learning using the data set of explanatory variables and response variables using the same method as in the comparative example, except for the construction method of the multilayer perceptron model. When constructing the multilayer perceptron model, a locally connected model having an input layer (explanatory variables) and an output layer (response variable) as well as first and second hidden layers was constructed, as shown in FIG. 2(d). Specifically, a locally connected model was constructed in which only nodes representing the same group of information in the three groups of explanatory variables were connected between all nodes in the input layer and the first hidden layer (the hidden layer adjacent to the input layer among multiple hidden layers) and between all nodes in the first and second hidden layers (the hidden layers adjacent to each other). Furthermore, a locally connected model was constructed in which all nodes in the second hidden layer (the hidden layer adjacent to the output layer among multiple hidden layers) and the output layer were connected.

[0021] [Prediction accuracy evaluation] For seven prediction samples of catalysts different from the learning samples used to build the prediction model, explanatory variables were acquired in the same manner as in the Comparative Example and Examples 1 and 2 for cases where the catalyst's endurance time was 50 hours (hours) within the learning range. Then, using the prediction models of each of the Comparative Example and Examples 1 and 2, a group of information (objective variables) representing purification performance (warm air characteristics) was acquired from the acquired explanatory variables. Then, a predicted value of the NOx 50% purification time was calculated from the group of information representing the warm air characteristics. As shown in FIG. 3(a), with regard to the average errors 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 Comparative Example and Example 2 were higher than that of Example 1. The prediction model of Example 1 achieved high generalization performance. It is presumed that the prediction model of the Comparative Example had a complex connection structure between model nodes, which resulted in unnecessary interactions and nonlinearities being expressed, resulting in overlearning and reduced generalization performance. On the other hand, in the prediction model of Example 2, the connection structure between nodes was too simple, making it impossible to express the necessary interactions, and it is presumed that high-accuracy learning was not achieved. Furthermore, using the prediction models of the Comparative Example and Examples 1 and 2, the sensitivity of the predicted values ​​of the NOx 50% conversion time calculated for five of the seven prediction samples to the catalyst endurance time [h] was evaluated. As shown in FIG. 3(b), with regard to the sensitivity of the predicted values ​​of the NOx 50% conversion time to the catalyst endurance time [h] of the prediction sample, the prediction value of the Comparative Example did not reflect the catalyst deterioration tendency of the prediction sample in cases where the endurance time exceeded 150 hours. In other words, even though the learning sample had been trained for cases where the endurance time exceeded 150 hours, when the sensitivity of the endurance time was predicted for the prediction sample with a catalyst configuration that had not been trained for cases where the endurance time exceeded 150 hours, the prediction accuracy was poor in cases where the endurance time exceeded 150 hours. In the predictive model of the comparative example, overfitting occurred, and it is presumed that one group of information representing the catalyst configuration and one group of information representing the durability history interacted excessively in a complex interconnection structure between nodes.On the other hand, the predicted values ​​in Examples 1 and 2 accurately reflected the deterioration tendency of the catalyst of the prediction sample, even in cases where the durability time exceeded 150 hours, and the catalyst's true physical tendency could be predicted. In the prediction models of Examples 1 and 2, unnecessary interactions between one group of information representing the catalyst configuration and one group of information representing the durability history were removed in the connection structure between nodes, and it is presumed that no unnecessary effects other than those representing the catalyst's true deterioration tendency occurred.

Claims

[Claim 1] A prediction model for predicting the purification performance of an exhaust gas purification catalyst, the prediction model is a model consisting of 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 using three groups of information, consisting of one group of information expressing a catalyst configuration of the exhaust gas purification catalyst, one group of information expressing a durability history, and one group of information expressing a purification performance evaluation test, as explanatory variables, and one group of information expressing the purification performance of the exhaust gas purification catalyst as a response variable, and providing the three groups of information of the explanatory variables and the information of the response variable to the input layer and the output layer, respectively, as training data; The prediction model is characterized in that it is a locally coupled model in which only nodes that represent the same group of information in the three groups of information of the explanatory variables are coupled between all nodes in the input layer and the intermediate layers adjacent to the input layer among the plurality of intermediate layers.

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