A NOx emission prediction method based on physical neural network ensemble learning

Abstract

This invention discloses a NOx emission prediction method based on ensemble learning of physical neural networks, comprising the following steps: Step 1, establishing a physical prediction model based on the physical laws governing NOx generation from diesel engines; Step 2, collecting test data using a diesel engine test bench; normalizing the collected data; training a feedforward neural network using the backpropagation method with the normalized data to obtain a neural network prediction model; Step 3, fusing the physical prediction model from Step 1 and the neural network prediction model from Step 2 by constructing a fusion loss function to build a physical neural network prediction model, and training the physical neural network prediction model using the backpropagation method; Step 4, fusing the models from Steps 1 to 3 using an ensemble learning strategy to obtain an ensemble learning model, and using the ensemble learning model to predict NOx emissions. This invention has high prediction accuracy and reduces the cost and difficulty of data collection.

Description

Technical Field

[0001] This invention relates to the field of diesel engine NOx emission prediction technology, and in particular to a NOx emission prediction method based on physical neural network ensemble learning. Background Technology

[0002] Nitrogen oxides (NOx) are one of the main air pollutants emitted by diesel engines during operation. They contribute to environmental pollution such as acid rain and photochemical smog, and damage the human respiratory system, causing numerous adverse effects. Therefore, many countries and regions have established stringent vehicle emission standards. In July 2021, China fully implemented the China VI emission standard for heavy-duty diesel vehicles. In March 2024, the European Union adopted the Euro 7 emission standard, which will be implemented in July 2025. Both domestic and international standards have imposed stricter requirements on diesel engine emission control. Selective catalytic reduction (SCR) technology, as an effective method to reduce NOx emissions, is widely used in diesel engine aftertreatment systems. Improving the accuracy of SCR system control strategies requires accurate measurement or estimation of raw NOx emission data from diesel engines. However, using NOx sensors to measure raw NOx emissions is costly; therefore, using accurate NOx emission prediction models to predict raw NOx emissions is a more convenient and cost-effective method.

[0003] NOx formation is controlled by complex chemical kinetics, involving numerous reaction steps. The extended Zeldovich mechanism is generally considered to be the main reaction controlling the formation of NOx. Since NOx is generated in the environment produced during combustion, and diesel engine combustion is complex, involving turbulence, mixing and diffusion, combustion exothermics, and chemical reactions, it is difficult to model accurately. Furthermore, NOx formation is a dynamic process; changes in the external gas environment and operating conditions can lead to variations in intake air temperature, pressure, engine speed, torque, and fuel injection, thus affecting the in-cylinder combustion process and ultimately NOx formation. Therefore, establishing an accurate NOx prediction model for diesel engines is a complex and challenging problem.

[0004] Currently, NOx prediction models are mainly based on physical mechanisms and data-driven models.

[0005] In research on physical mechanism-based modeling methods, Jonas Asprion et al. combined the advantages of phenomenological and empirical models. They extracted physical relationships by identifying the physical phenomena most relevant to NOx formation, forming the basis of the model, and combined it with setpoint relative formulas to form a simple model structure. Wonah Park et al., based on the analysis of computational fluid dynamics results, established a NO formation model by combining it with a physical model, using in-cylinder pressure to predict NO formation 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, the accuracy of NOx emission prediction depends on the accuracy of input parameters; measurement errors and changes in operating conditions can affect the accuracy of NOx emission predictions.

[0006] In research on data-driven modeling methods, Ivan Arsie et al. used recurrent neural networks (RNNs) as the core and updated the RNN model parameters online to establish a virtual sensor for NOx emissions from automotive diesel engines. XiaoHang (Leo) Fang used neural network methods to predict NOx emissions from high-speed direct-injection diesel engines under various operating conditions and compared the application of Levenberg-Marquardt and Bayesian regularization backpropagation algorithms 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 predicting NOx emissions from diesel engines. Qianqiao Shen et al. and Youlin Guo et al. used LSTM networks to predict NOx emissions. Zhihong et al. used GWO-BP neural networks for NOx emission prediction. Although these models showed certain NOx emission prediction capabilities within the calibration range of the training data, their application in other situations was limited, lacking good generalization ability.

[0007] In summary, existing physical models and neural network models each have their own advantages and disadvantages, and neither can solve the problems of accuracy and generalization ability in NOx emission prediction on its own. Therefore, a method that combines the advantages of physical models and neural network models is needed to improve the accuracy and reliability of NOx emission prediction for diesel engines. Summary of the Invention

[0008] The purpose of this invention is to address the technical deficiencies in the existing technology by providing a NOx emission prediction method based on physical neural network ensemble learning.

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

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

[0011] Step 1: Establish a physical prediction model based on the physical laws governing NOx generation in diesel engines;

[0012] Step 2: Collect test data using a diesel engine test bench; normalize the collected data; use the normalized data to train a feedforward neural network using the backpropagation method to obtain a neural network prediction model;

[0013] Step 3: By constructing a fusion loss function, the physical prediction model from Step 1 and the neural network prediction model from Step 2 are fused to construct a physical neural network prediction model, and the physical neural network prediction model is trained using the backpropagation method.

[0014] Step 4: The physical prediction model from Step 1, the neural network prediction model from Step 2, and the physical neural network prediction model obtained in Step 3 are fused using an ensemble learning strategy to obtain an ensemble learning model. The ensemble learning model is then used 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] In the formula, X egr T represents the EGR rate. coolant This indicates the coolant temperature, and SOI indicates the start time of the main injection. Indicates the fuel injection mass flow rate. Indicates air mass flow rate, Indicates EGR mass flow rate. E represents the oxygen mass flow rate. a T represents the activation energy of the reaction, R represents the molar gas constant, and T represents the activation energy of the reaction. comb The values ​​represent the in-cylinder combustion temperature, and c1, c2, c3, c4, c5, and c6 represent the parameters to be identified.

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

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

[0020]

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

[0022] In the above technical solution, step 2, the specific steps of training the feedforward neural network using the backpropagation method, include:

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

[0024] Step S2.2: Train the neural network prediction model using the error backpropagation method;

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

[0026] Step S2.4: Select the mean squared error (MSE) as the loss function for 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] In the formula, x represents the input parameters of the neural network.

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

[0031]

[0032] In the formula, MSE is the mean squared error, n is the total number of test samples, and y i This represents the actual value of the i-th data point. This represents the predicted value for the i-th data point.

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

[0034] Loss=(1-λ)·L data +λ·L physics

[0035] In the formula, L data L represents the mean square error calculated between the predicted NOx emissions output by the physical neural network prediction model and the actual NOx emissions; physicsThe mean square error is calculated between the predicted NOx emissions obtained by the physical neural network prediction model and the predicted NOx emissions output by the physical prediction model in step 1. λ represents the weighting factor, with a value ranging from 0 to 1.

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

[0037]

[0038] In the formula, y final ω represents the prediction result of the ensemble learning model, k represents the number of sub-models, and ω represents the prediction result of the ensemble learning model. j y represents the weight of submodel j. j The sub-model represents the prediction result of the sub-model, which 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 This represents the mean absolute error between the sub-model's predictions and the actual values. It represents the sum of the inverse values ​​of the mean absolute errors between the predictions of all sub-models and the true values.

[0042] Compared with the prior art, the beneficial effects of the present invention are:

[0043] 1. The physical neural network ensemble learning model proposed in this invention combines a physical model and a neural network model to construct a physical neural network model, and uses the 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 problems of 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 low dependence on a large amount of data during training because the physical model provides prior knowledge. This means that even with limited data, the ensemble learning model can still maintain high prediction accuracy, thereby reducing the cost and difficulty of data collection. Attached Figure Description

[0046] Figure 1 The diagram shows a flowchart of the diesel engine NOx emission prediction method of the present invention.

[0047] Figure 2 The figure shown is a prediction result of the diesel engine NOx emission prediction method of the present invention.

[0048] Figure 3 The figure shows the correlation coefficient (R0) between the predicted results and measured values ​​of the diesel engine NOx emission prediction method of this invention. 2 )picture.

[0049] Figure 4 The figure shown is a residual distribution diagram of the prediction results of the diesel engine NOx emission prediction method of the present invention. Detailed Implementation

[0050] The present invention will be further described in detail below with reference to specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the 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: Establish a physical prediction model based on the physical laws governing NOx generation in diesel engines;

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

[0054]

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

[0056] Step 2: Collect test data using a diesel engine test bench; normalize the collected data; use the normalized data to train a feedforward neural network using the backpropagation method to obtain a neural network prediction model;

[0057] When collecting data for experiments, it is important to cover a wide range of operating conditions to ensure the model's generalization ability.

[0058] The normalization formula is as follows:

[0059]

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

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

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

[0063] Step S2.2: Train the neural network prediction model using the error backpropagation method;

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

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

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

[0067] In the formula, x represents the input parameters of the neural network.

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

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

[0070]

[0071] In the formula, MSE is the mean squared error, n is the total number of test samples, and y i This represents the actual value of the i-th data point. This represents the predicted value for the i-th data point.

[0072] Step 3: By constructing a fusion loss function, the physical prediction model from Step 1 and the neural network prediction model from Step 2 are fused to construct a physical neural network prediction model, and the physical neural network prediction model is trained using the backpropagation method.

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

[0074] Loss=(1-λ)·L data +λ·L physics

[0075] In the formula, L dataL represents the mean square error calculated between the predicted NOx emissions output by the physical neural network prediction model and the actual NOx emissions; physics The mean squared error is calculated between the predicted NOx emissions obtained by the physical neural network prediction model and the predicted NOx emissions output by the physical prediction model in step 1. λ represents a weighting factor, ranging from 0 to 1, used to balance the relative contributions of data loss and physical loss. When λ is large, the weight of physical loss increases; when λ is small, the weight of physical loss decreases.

[0076] Step 4: The physical prediction model from Step 1, the neural network prediction model from Step 2, and the physical neural network prediction model obtained in Step 3 are fused using an ensemble learning strategy to obtain an ensemble learning model. The ensemble learning model is then used to predict NOx emissions.

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

[0078]

[0079] In the formula, y final ω represents the prediction result of the ensemble learning model, k represents the number of sub-models, and ω represents the prediction result of the ensemble learning model. j y represents the weight of submodel j. j The sub-model represents the prediction result of the sub-model, which 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 This represents the mean absolute error between the sub-model's predictions and the actual values. It represents the sum of the inverse values ​​of the mean absolute errors between the predictions of all sub-models and the true values.

[0083] The NOx emissions output by the ensemble learning model were compared with the actual values, and the results are as follows: Figures 2-4 As shown, by Figure 2 It is evident that the predictions of the ensemble learning model match the measured values ​​well across the entire dataset. Figure 3 It can be seen that the correlation coefficient R between the model's predicted values ​​and the actual values ​​is... 2 The value is 0.984, from Figure 4 It is evident that the error distribution of the prediction results is relatively concentrated.

[0084] The above description is only a preferred embodiment of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within 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, Includes the following steps: Step 1: Establish a physical prediction model based on the physical laws governing NOx generation in diesel engines; Step 2: Collect test data using a diesel engine test bench; The collected data is normalized; the normalized data is used to train a feedforward neural network using the backpropagation method to obtain a neural network prediction model; Step 3: By constructing a fusion loss function, the physical prediction model from Step 1 and the neural network prediction model from Step 2 are fused to construct a physical neural network prediction model, and the physical neural network prediction model is trained using the backpropagation method. Step 4: The physical prediction model from Step 1, the neural network prediction model from Step 2, and the physical neural network prediction model obtained in Step 3 are fused using an ensemble learning strategy to obtain an ensemble learning model. The ensemble learning model is then used to predict NOx emissions. In step 1, the expression of the physical prediction model is as follows: In the formula, X egr T represents the EGR rate. coolant This indicates the coolant temperature, and SOI indicates the start time of the main injection. Indicates the fuel injection mass flow rate. Indicates air mass flow rate, Indicates EGR mass flow rate. E represents the oxygen mass flow rate. a T represents the activation energy of the reaction, R represents the molar gas constant, and T represents the activation energy of the reaction. comb This indicates the in-cylinder combustion temperature, and c1, c2, c3, c4, c5, and c6 represent the parameters to be identified. In step 3, the expression for the fusion loss function is as follows: Loss=(1-λ)·L data +λ·L physics Where, L data L represents the mean square error calculated between the predicted NOx emissions output by the physical neural network prediction model and the actual NOx emissions; physics The mean square error is calculated between the predicted NOx emissions obtained by the physical neural network prediction model and the predicted NOx emissions output by the physical prediction model in step 1. λ represents the weighting factor, with a value ranging from 0 to 1.

2. The NOx emission prediction method as described in 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 x represents the normalized data value. max x represents the maximum value in the measured data. min This represents the minimum value in the measured data.

3. The NOx emission prediction method as described in claim 1, characterized in that, In step 2, the specific steps for training the feedforward neural network using the backpropagation method include: Step S2.1: Select a feedforward neural network as the network structure for the neural network prediction model; Step S2.2: Train the neural network prediction model using the error backpropagation method; Step S2.3: Select the ReLU function as the activation function for the neural network prediction model; Step S2.4: Select the mean squared error (MSE) as the loss function for training the neural network prediction model.

4. The NOx emission prediction method as described in claim 3, characterized in that, In step S2.3, the expression for the ReLU function is as follows: f(x) = max(0,x) In the formula, x represents the input parameters of the neural network.

5. The NOx emission prediction method as described in claim 3, characterized in that, In step S2.4, the expression for the loss function is as follows: In the formula, MSE is the mean squared error, n is the total number of test samples, and y i This represents the actual value of the i-th data point. This represents the predicted value for the i-th data point.

6. The NOx emission prediction method as described in claim 1, characterized in that, In step 4, the expression for the ensemble learning combination strategy is: In the formula, y final ω represents the prediction result of the ensemble learning model, k represents the number of sub-models, and ω represents the prediction result of the ensemble learning model. j y represents the weight of submodel j. j The sub-model represents the prediction result of the sub-model, which 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.

7. The NOx emission prediction method as described in claim 6, characterized in that, ω j The calculation formula is as follows: In the formula, a j This represents the mean absolute error between the sub-model's predictions and the actual values. It represents the sum of the inverse values ​​of the mean absolute errors between the predictions of all sub-models and the true values.

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