NOx emission prediction method based on physical neural network ensemble learning

Abstract

The invention discloses a NOx emission prediction method based on physical neural network ensemble learning. The NOx emission prediction method comprises the following steps: step 1, establishing a physical prediction model according to a physical rule of NOx generation of a diesel engine; step 2, acquiring test data by using a diesel engine rack; data normalization is carried out on the collected data; using the normalized data to train a feedforward neural network by adopting a back propagation method to obtain a neural network prediction model; 3, fusing the physical prediction model in the step 1 and the neural network prediction model in the step 2 through a method of constructing a fusion loss function, constructing a physical neural network prediction model, and training the physical neural network prediction model by adopting a back propagation method; and step 4, fusing the models from the step 1 to the step 3 by adopting an integrated learning combination strategy to obtain an integrated learning model, and predicting the NOx emission by utilizing the integrated learning model. The method has high prediction accuracy, and reduces the cost and difficulty of data collection.

Description

Technical Field

[0001] The invention relates to the technical field of NOx emission prediction of diesel engines, and in particular to a NOx emission prediction method based on physical neural network ensemble learning. Background Art

[0002] Nitrogen oxides (NOx) are one of the main air pollutants emitted by diesel engines during operation. They form environmental pollution such as acid rain and photochemical smog in the atmosphere, and damage the human respiratory system, causing many adverse effects. To this end, many countries and regions have formulated strict automobile emission standards. In July 2021, China will fully implement the National VI emission standard for heavy-duty diesel vehicles. In March 2024, the European Union passed the Euro 7 emission standard, which will be implemented in July 2025. Both domestic and foreign standards have put forward stricter requirements for diesel engine emission control. Selective catalytic reduction (SCR) technology is widely used in diesel engine aftertreatment systems as an effective method to reduce NOx emissions. Improving the accuracy of the SCR system control strategy requires accurate measurement or estimation of the original NOx emission data of the diesel engine. However, the cost of nitrogen oxide sensors for measuring NOx original emissions is relatively high. Therefore, using an accurate NOx emission prediction model to predict NOx original emissions is a more convenient and cost-effective method.

[0003] The formation of NOx is controlled by complex chemical kinetics and contains many reaction steps. It is generally believed that the main reaction that controls the product is the extended Zeldovich mechanism. Since NOx is generated in the environment produced by the combustion process, and the diesel engine combustion process is complex, involving many processes such as turbulence, mixing and diffusion, combustion heat release and chemical reactions, it is difficult to accurately model. In addition, the generation of NOx is a dynamic process. Changes in the external gas environment and operating conditions will lead to changes in factors such as intake temperature, pressure, engine speed, torque and fuel injection, thereby affecting the combustion process in the cylinder and ultimately affecting the formation of NOx. Therefore, establishing an accurate diesel engine NOx prediction model is a complex and challenging problem.

[0004] At present, the modeling methods of NOx prediction models mainly include modeling based on physical mechanisms and modeling based on data-driven.

[0005] In the study of modeling methods based on physical mechanisms, Jonas Asprion et al. combined the advantages of phenomenological models and empirical models to model. They extracted physical relationships by identifying the physical phenomena most relevant to NOx formation, formed the basis of the model, and combined with the set point relative formula to form a simple model structure. Wonah Park et al. established a NO generation model based on the analysis of computational fluid dynamics results and combined with physical models, using in-cylinder pressure to predict the amount of NO generated under different engine operating conditions. Varun Rao et al. coupled the Mellor NOx model and the extended Zeldvich NOx model into a multi-zone quasi-dimensional diesel engine model, which can simulate processes such as spray evolution, fuel evaporation, air entrainment, ignition delay, ignition, combustion and product formation, and predict NOx emissions in direct injection naturally aspirated diesel engines. Although physical models can effectively estimate NOx emissions, they rely on the accuracy of input parameters, measurement errors and changes in operating conditions to affect the prediction accuracy of NOx emissions.

[0006] In the research on data-driven modeling methods, Ivan Arsie et al. used recurrent neural network (RNN) as the core and updated the RNN model parameters online to establish a virtual sensor for NOx emissions of automotive diesel engines. XiaoHang (Leo) Fang used a neural network method to predict NOx emissions under various working conditions of high-speed direct injection diesel engines, and compared the application of two back-propagation algorithms, Levenberg-Marquardt and Bayesian regularization, in this method. Seunghyup Shin et al. and Wen Zeng et al. studied the application of Bayesian hyperparameter optimization methods in training deep neural network models and machine learning models for diesel engine NOx emission prediction. Qianqiao Shen et al. and Youlin Guo et al. used LSTM networks to predict NOx emissions. Zhihong et al. used GWO-BP neural networks to predict NOx emissions. Although these models showed certain NOx emission prediction capabilities within the calibration range of the data used for training, their applications in other situations were limited and lacked good generalization capabilities.

[0007] In summary, the physical model and neural network model in the prior art each have their own advantages and disadvantages, and cannot solve the accuracy and generalization problem of NOx emission prediction alone. Therefore, a method that can combine the advantages of physical models and neural network models is needed to improve the accuracy and reliability of diesel engine NOx emission prediction. Summary of the invention

[0008] The purpose of the present invention is to provide a NOx emission prediction method based on physical neural network ensemble learning in order to address the technical defects in the prior art.

[0009] The technical solution adopted to achieve the purpose of the present invention is:

[0010] A NOx emission prediction method based on physical neural network ensemble learning includes the following steps:

[0011] Step 1, establishing a physical prediction model based on the physical laws of NOx generation in diesel engines;

[0012] Step 2, using a diesel engine bench to collect test data; normalizing the collected data; using the normalized data to train a feedforward neural network using a back propagation method to obtain a neural network prediction model;

[0013] Step 3, fusing the physical prediction model of step 1 and the neural network prediction model of step 2 by constructing a fusion loss function, constructing a physical neural network prediction model, and training the physical neural network prediction model by using a back propagation method;

[0014] Step 4, using an integrated learning combination strategy to fuse the physical prediction model of step 1, the neural network prediction model of step 2 and the physical neural network prediction model obtained in step 3 to obtain an integrated learning model, and use the integrated learning model to predict NOx emissions.

[0015] In the above technical solution, in step 1, the expression of the physical prediction model is as follows:

[0016]

[0017] Where, X egr Indicates the EGR rate, T coolant Indicates the coolant temperature, SOI indicates the start time of main injection, represents the injection mass flow rate, represents the air mass flow rate, represents the EGR mass flow rate, represents the oxygen mass flow rate, E a represents the reaction activation energy, R represents the molar gas constant, T comb represents the combustion temperature in the cylinder, and c1, c2, c3, c4, c5, and c6 represent the parameters to be identified.

[0018] In the above technical solution, in step 2, a wide range of operating conditions are covered when collecting experimental data.

[0019] In the above technical solution, in step 2, the normalization method formula is as follows:

[0020]

[0021] In the formula, x represents the measured data value, x norm Represents the normalized data value, x max Indicates the maximum value in the measured data, x min Indicates the minimum value in the measured data.

[0022] In the above technical solution, in step 2, the specific steps of using the back propagation method to train the feedforward neural network include:

[0023] Step S2.1: Select a feedforward neural network as the network structure of the neural network prediction model;

[0024] Step S2.2: using the error back propagation method to train the neural network prediction model;

[0025] Step S2.3: Select the ReLU function as the activation function of the neural network prediction model;

[0026] Step S2.4: Select mean square error (MSE) as the loss function when training the neural network prediction model.

[0027] In the above technical solution, in step S2.3, the expression of the ReLU activation function is as follows:

[0028] f(x)=max(0,x)

[0029] Where x represents the neural network input parameter.

[0030] In the above technical solution, in step S2.4, the expression of the loss function is as follows:

[0031]

[0032] Where MSE is the mean square error, n is the total number of test samples, and y i represents the actual value of the ith data point, Represents the predicted value of the ith data point.

[0033] In the above technical solution, in step 3, the expression of the fusion loss function is as follows:

[0034] Loss = (1-λ)·L data +λ·L physics

[0035] Where, L data represents the mean square error calculated between the NOx emission prediction value output by the physical neural network prediction model and the actual NOx emission value; L physicsrepresents the mean square error calculated between the NOx emission prediction value obtained by the physical neural network prediction model and the NOx emission prediction value output by the physical prediction model in step 1, and λ represents the weight factor, with a value range of 0 to 1.

[0036] In the above technical solution, in step 4, the expression of the combination strategy of the ensemble learning is:

[0037]

[0038] In the formula, y final represents the prediction result of the integrated learning model, k represents the number of sub-models, ω j represents the weight of sub-model j, y j Represents the prediction result of the sub-model, wherein the sub-model includes the physical prediction model of step 1, the neural network prediction model of step 2 and the physical neural network prediction model obtained in step 3.

[0039] In the above technical solution, ω j The calculation formula is as follows:

[0040]

[0041] In the formula, a j It represents the mean absolute error between the sub-model prediction result and the true value. It represents the sum of the inverse values ​​of the mean absolute errors between the prediction results of all sub-models and the true values.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] 1. The physical neural network ensemble learning model proposed in the present invention combines the physical model and the neural network model to construct a physical neural network model, and uses an ensemble learning method to achieve higher prediction accuracy and generalization ability.

[0044] 2. The diesel engine NOx prediction method of the present invention can avoid the high cost and easy damage of traditional physical sensors, reduce maintenance costs, and improve the reliability and stability of the system.

[0045] 3. The diesel engine NOx emission prediction method based on physical neural network ensemble learning of the present invention has a low reliance on a large amount of data during the training process because the physical model provides prior knowledge. This means that in the case of limited data, the ensemble learning model can still maintain a high prediction accuracy, thereby reducing the cost and difficulty of data collection. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Shown is a flow chart of the diesel engine NOx emission prediction method of the present invention.

[0047] Figure 2 Shown is a diagram showing prediction results of the diesel engine NOx emission prediction method of the present invention.

[0048] Figure 3 The figure shows the correlation coefficient (R 2 )picture.

[0049] Figure 4 Shown is a residual distribution diagram of the prediction results of the diesel engine NOx emission prediction method of the present invention. DETAILED DESCRIPTION

[0050] The present invention is further described in detail below in conjunction with specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0051] like Figure 1 As shown, a NOx emission prediction method based on physical neural network ensemble learning includes the following steps:

[0052] Step 1, establishing a physical prediction model based on the physical laws of NOx generation in diesel engines;

[0053] The expression of the physical prediction model is as follows:

[0054]

[0055] Where, X egr Indicates the EGR rate, T coolant Indicates the coolant temperature, SOI indicates the start time of main injection, represents the injection mass flow rate, represents the air mass flow rate, represents the EGR mass flow rate, represents the oxygen mass flow rate, E a represents the reaction activation energy, R represents the molar gas constant, T comb represents the combustion temperature in the cylinder, and c1, c2, c3, c4, c5, and c6 represent the parameters to be identified.

[0056] Step 2, using a diesel engine bench to collect test data; normalizing the collected data; using the normalized data to train a feedforward neural network using a back propagation method to obtain a neural network prediction model;

[0057] Experimental data collection should cover a wide range of operating conditions to ensure the generalization ability of the model.

[0058] The normalization method formula is as follows:

[0059]

[0060] In the formula, x represents the measured data value, x norm Represents the normalized data value, x max Indicates the maximum value in the measured data, x min Indicates the minimum value in the measured data.

[0061] The specific steps of training a feedforward neural network using the backpropagation method include:

[0062] Step S2.1: Select a feedforward neural network as the network structure of the neural network prediction model;

[0063] Step S2.2: using the error back propagation method to train the neural network prediction model;

[0064] Step S2.3: Select the ReLU function as the activation function of the neural network prediction model;

[0065] The expression of the ReLU activation function is as follows:

[0066] f(x)=max(0,x)

[0067] Where x represents the neural network input parameter.

[0068] Step S2.4: Select mean square error (MSE) as the loss function when training the neural network prediction model.

[0069] The expression of the loss function is as follows:

[0070]

[0071] Where MSE is the mean square error, n is the total number of test samples, and y i represents the actual value of the ith data point, Represents the predicted value of the ith data point.

[0072] Step 3, fusing the physical prediction model of step 1 and the neural network prediction model of step 2 by constructing a fusion loss function, constructing a physical neural network prediction model, and training the physical neural network prediction model by using a back propagation method;

[0073] The expression of the fusion loss function is as follows:

[0074] Loss = (1-λ)·L data +λ·L physics

[0075] Where, L datarepresents the mean square error calculated between the NOx emission prediction value output by the physical neural network prediction model and the actual NOx emission value; L physics Represents the mean square error calculated between the NOx emission prediction value predicted by the physical neural network prediction model and the NOx emission prediction value output by the physical prediction model in step 1. λ represents a weight factor, ranging from 0 to 1, which is used to balance the relative contribution of data loss and physical loss, wherein when λ is larger, the physical loss weight increases; when λ is smaller, the physical loss weight decreases.

[0076] Step 4, using an integrated learning combination strategy to fuse the physical prediction model of step 1, the neural network prediction model of step 2 and the physical neural network prediction model obtained in step 3 to obtain an integrated learning model, and use the integrated learning model to predict NOx emissions.

[0077] The expression of the combination strategy of the ensemble learning is:

[0078]

[0079] In the formula, y final represents the prediction result of the integrated learning model, k represents the number of sub-models, ω j represents the weight of sub-model j, y j Represents the prediction result of the sub-model, wherein the sub-model includes the physical prediction model of step 1, the neural network prediction model of step 2 and the physical neural network prediction model obtained in step 3.

[0080] ω j The calculation formula is as follows:

[0081]

[0082] In the formula, a j It represents the mean absolute error between the sub-model prediction result and the true value. It represents the sum of the inverse values ​​of the mean absolute errors between the prediction results of all sub-models and the true values.

[0083] The NOx emissions output by the ensemble learning model are compared with the true value. Figure 2-Figure 4 As shown by Figure 2 It can be seen that the prediction results of the integrated learning model are in good agreement with the measured values ​​on the entire data set. Figure 3 It can be seen that the correlation coefficient R between the model prediction value and the true value 2 The value is 0.984, Figure 4 It can be seen that the error distribution of the prediction results is relatively concentrated.

[0084] The above is only a preferred embodiment of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A NOx emission prediction method based on physical neural network ensemble learning, characterized in that: The following steps are involved: Step 1, establishing a physical prediction model based on the physical laws of NOx generation in diesel engines; Step 2, collecting test data using a diesel engine bench; Normalize the collected data; use the normalized data to train the feedforward neural network using the back propagation method to obtain a neural network prediction model; Step 3, fusing the physical prediction model of step 1 and the neural network prediction model of step 2 by constructing a fusion loss function, constructing a physical neural network prediction model, and training the physical neural network prediction model by using a back propagation method; Step 4, using an integrated learning combination strategy to fuse the physical prediction model of step 1, the neural network prediction model of step 2 and the physical neural network prediction model obtained in step 3 to obtain an integrated learning model, and use the integrated learning model to predict NOx emissions.

2. The NOx emission prediction method according to claim 1, characterized in that: In step 1, the expression of the physical prediction model is as follows: Where, X egr Indicates the EGR rate, T coolant Indicates the coolant temperature, SOI indicates the start time of main injection, represents the injection mass flow rate, represents the air mass flow rate, represents the EGR mass flow rate, represents the oxygen mass flow rate, E a represents the reaction activation energy, R represents the molar gas constant, T comb represents the combustion temperature in the cylinder, and c1, c2, c3, c4, c5, and c6 represent the parameters to be identified.

3. The NOx emission prediction method according to claim 1, characterized in that: In step 2, the experiments cover a wide range of operating conditions when collecting data.

4. The NOx emission prediction method according to claim 1, characterized in that: In step 2, the normalization method formula is as follows: In the formula, x represents the measured data value, x norm Represents the normalized data value, x max Indicates the maximum value in the measured data, x min Indicates the minimum value in the measured data.

5. The NOx emission prediction method according to claim 1, characterized in that: In step 2, the specific steps of using the back propagation method to train the feedforward neural network include: Step S2.1: Select a feedforward neural network as the network structure of the neural network prediction model; Step S2.2: using the error back propagation method to train the neural network prediction model; Step S2.3: Select the ReLU function as the activation function of the neural network prediction model; Step S2.4: Select mean square error (MSE) as the loss function when training the neural network prediction model.

6. The NOx emission prediction method according to claim 5, characterized in that: In step S2.3, the expression of the ReLU activation function is as follows: f(x)=max(0,x) Where x represents the neural network input parameter.

7. The NOx emission prediction method according to claim 5, characterized in that: In step S2.4, the loss function is expressed as follows: Where MSE is the mean square error, n is the total number of test samples, and y i represents the actual value of the ith data point, Represents the predicted value of the ith data point.

8. The NOx emission prediction method according to claim 1, characterized in that: In step 3, the expression of the fusion loss function is as follows: Loss=(1-λ)·L data +λ·L physics Where, L data represents the mean square error calculated between the NOx emission prediction value output by the physical neural network prediction model and the actual NOx emission value; L physics represents the mean square error calculated between the NOx emission prediction value obtained by the physical neural network prediction model and the NOx emission prediction value output by the physical prediction model in step 1, and λ represents the weight factor, with a value range of 0 to 1.

9. The NOx emission prediction method according to claim 1, characterized in that: In step 4, the expression of the combination strategy of the ensemble learning is: In the formula, y final represents the prediction result of the integrated learning model, k represents the number of sub-models, ω j represents the weight of sub-model j, y j Represents the prediction result of the sub-model, wherein the sub-model includes the physical prediction model of step 1, the neural network prediction model of step 2 and the physical neural network prediction model obtained in step 3.

10. The NOx emission prediction method according to claim 9, characterized in that: ω j The calculation formula is as follows: In the formula, a j It represents the mean absolute error between the sub-model prediction result and the true value. It represents the sum of the inverse values ​​of the mean absolute errors between the prediction results of all sub-models and the true values.

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