Method and system for predicting NOx emissions of hybrid electric vehicles based on dictionary learning

Abstract

The present invention proposes a method and system for predicting NOx emissions of hybrid electric vehicles based on dictionary learning, which belongs to the field of vehicle emission prediction. Emission-related parameters, an initial high-dimensional driving emission data set, and incremental test data are obtained; the initial high-dimensional driving emission data set is mapped to an initial low-dimensional embedding through t-SNE; based on the initial low-dimensional embedding, a high-dimensional dictionary and a low-dimensional dictionary are constructed through dictionary learning and iterative optimization is performed; a sparse coding matrix of the incremental test data on the high-dimensional dictionary is calculated, and an incremental low-dimensional embedding is generated by coupling with the low-dimensional dictionary; the incremental low-dimensional embedding is input into a pre-trained SuperLearner regression model to obtain an incremental NOx emission factor correction coefficient; NOx emissions are calculated based on the emission-related parameters and the incremental NOx emission factor correction coefficient. The present invention utilizes t-SNE and dictionary learning dimensionality reduction, combined with the SuperLearner regression model, to improve the prediction accuracy of NOx emissions of hybrid electric vehicles and efficiently process incremental data.

Description

Technical Field

[0001] The present invention relates to the technical field of vehicle emission prediction, and in particular to a method and system for predicting NOx emissions of a hybrid electric vehicle based on dictionary learning. Background Art

[0002] As transportation demand grows and vehicle ownership increases, mobile sources have become a major source of air pollution. Among these, NOx emissions from road vehicles account for a significant portion. Hybrid vehicles, as a new energy solution, have attracted considerable attention. However, due to their poor NOx control, accurately predicting their NOx emissions has become a key issue.

[0003] In the field of vehicle emission prediction, correction coefficients are crucial to improving prediction accuracy, and the selection or extraction of key parameters is also critical. Currently, research mainly focuses on two directions: using advanced algorithms for modeling and using correction coefficients to calibrate emission data. However, existing technologies have many defects. On the one hand, in terms of dimensionality reduction, traditional methods cannot efficiently process incremental data. For example, some dimensionality reduction technologies require recalculation when processing new data, which has high computational costs and low efficiency, and it is difficult to quickly obtain a low-dimensional representation of incremental data. On the other hand, the accuracy of the prediction model needs to be improved. When faced with complex vehicle emission data, some algorithms cannot fully explore the potential nonlinear correlation between variables, resulting in insufficient accuracy of the prediction model and a large deviation between the predicted NOx emission values ​​and the measured values, which is difficult to meet actual needs. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a method and system for predicting NOx emissions of hybrid vehicles based on dictionary learning. By combining t-SNE and dictionary learning for dimensionality reduction, t-SNE processes the nonlinear relationship of high-dimensional data and retains local and global structures, while dictionary learning extracts key features and efficiently processes incremental data, thereby avoiding the computational complexity and information redundancy problems of traditional methods. In addition, the SuperLearner regression model is adopted to integrate the advantages of multiple algorithms, accurately learn the nonlinear correlation of variables, and improve the accuracy of the NOx emission factor correction coefficient, thereby improving the accuracy of NOx emissions prediction.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] In a first aspect, the present invention provides a method for predicting NOx emissions of a hybrid electric vehicle based on dictionary learning, comprising:

[0007] Obtain emission-related parameters, initial driving emission high-dimensional datasets, and incremental test data;

[0008] Mapping the initial driving emission high-dimensional dataset into an initial low-dimensional embedding via t-SNE;

[0009] Based on the initial low-dimensional embedding, a high-dimensional dictionary and a low-dimensional dictionary are constructed through dictionary learning, and iterative optimization is performed; a sparse coding matrix of incremental test data on the high-dimensional dictionary is calculated, and coupled with the low-dimensional dictionary to generate an incremental low-dimensional embedding;

[0010] Inputting the incremental low-dimensional embedding into a pre-trained SuperLearner regression model to obtain an incremental NOx emission factor correction coefficient;

[0011] NOx emissions are calculated based on emission-related parameters and the incremental NOx emission factor correction factor.

[0012] In a second aspect, the present invention provides a hybrid vehicle NOx emission prediction system based on dictionary learning, comprising:

[0013] Data acquisition module, used to obtain emission-related parameters, initial driving emission high-dimensional data set and incremental test data;

[0014] A data dimensionality reduction module is used to map the initial driving emission high-dimensional dataset into an initial low-dimensional embedding via t-SNE;

[0015] A dictionary construction and optimization module is used to construct a high-dimensional dictionary and a low-dimensional dictionary through dictionary learning based on the initial low-dimensional embedding, and perform iterative optimization; calculate the sparse coding matrix of the incremental test data on the high-dimensional dictionary, and couple it with the low-dimensional dictionary to generate an incremental low-dimensional embedding;

[0016] A correction coefficient acquisition module is used to input the incremental low-dimensional embedding into a pre-trained SuperLearner regression model to obtain an incremental NOx emission factor correction coefficient;

[0017] The emission calculation module is used to calculate NOx emissions based on emission-related parameters and an incremental NOx emission factor correction coefficient.

[0018] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for predicting NOx emissions of a hybrid vehicle based on dictionary learning described in the first aspect.

[0019] In a fourth aspect, the present invention provides a computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the method for predicting NOx emissions of a hybrid vehicle based on dictionary learning described in the first aspect are implemented.

[0020] Compared with the prior art, the present invention has the following beneficial effects:

[0021] (1) After acquiring multiple types of test data, the present invention uses t-SNE and dictionary learning to reduce dimensionality, effectively solving the computational complexity and information redundancy problems brought about by high-dimensional data, extracting key features and reducing computational costs. By iteratively optimizing the mapping relationship between dictionaries, incremental data can be efficiently processed, improving the timeliness of predictions. The SuperLearner regression model combines dimensionality-reduced data to accurately learn the variable relationship and obtain a high-precision NOx emission factor correction coefficient. Finally, NOx emissions are calculated based on the correction coefficient and emission-related parameters, significantly improving prediction accuracy. Compared with traditional methods, the present invention takes into account both data processing efficiency and prediction accuracy, providing strong support for the effective management and control of NOx emissions from hybrid vehicles.

[0022] (2) To better predict the NOx emission factor of hybrid electric vehicles, this paper applies an incremental dimensionality reduction method based on dictionary learning to the problem of processing multivariate variables that affect NOx emissions. The high-dimensional data obtained from the RDE test is embedded into a low-dimensional space using t-SNE. Based on these low-dimensional embeddings, high-dimensional and low-dimensional dictionaries are then constructed using dictionary learning. For the incremental data, the sparse encoding matrix of the incremental data is calculated on the high-dimensional dictionary and coupled with the pre-constructed low-dimensional dictionary to quickly obtain the low-dimensional embedding corresponding to the incremental data, achieving efficient dimensionality reduction through simple matrix operations.

[0023] (3) After dimensionality reduction, the present invention uses the low-dimensional data obtained through t-SNE dimensionality reduction to train a SuperLearner regression model to further construct an accurate NOx emission correction factor prediction model. The incremental low-dimensional embeddings obtained through the incremental dimensionality reduction method based on dictionary learning are input into the SuperLearner prediction model, and the corresponding correction coefficients can be directly obtained, thereby further improving the accuracy of NOx emission prediction.

[0024] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their description are used to explain the present invention but do not constitute a limitation of the present invention.

[0026] Figure 1 A main flow chart of a method for predicting NOx emissions of hybrid electric vehicles based on dictionary learning provided by an embodiment of the present invention;

[0027] Figure 2 A schematic flow chart of a method for predicting NOx emissions of a hybrid electric vehicle based on dictionary learning provided by an embodiment of the present invention;

[0028] Figure 3 A schematic diagram of an RDE test driving condition provided by an embodiment of the present invention;

[0029] Figure 4 Flowchart of the incremental dimensionality reduction method based on dictionary learning provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0030] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0031] Example 1

[0032] like Figure 1 As shown, this embodiment discloses a method for predicting NOx emissions of a hybrid vehicle based on dictionary learning, comprising the following steps:

[0033] S1: Acquire emission-related parameters, initial driving emission high-dimensional dataset, and incremental test data;

[0034] S2: Mapping the initial driving emission high-dimensional dataset into an initial low-dimensional embedding via t-SNE;

[0035] S3: Based on the initial low-dimensional embedding, a high-dimensional dictionary and a low-dimensional dictionary are constructed through dictionary learning, and iterative optimization is performed; a sparse coding matrix of the incremental test data on the high-dimensional dictionary is calculated, and coupled with the low-dimensional dictionary to generate an incremental low-dimensional embedding;

[0036] S4: Inputting the incremental low-dimensional embedding into a pre-trained SuperLearner regression model to obtain an incremental NOx emission factor correction coefficient;

[0037] S5: Calculate NOx emissions based on emission-related parameters and the incremental NOx emission factor correction coefficient.

[0038] Next, combine Figure 2 , a hybrid vehicle NOx emission prediction method based on dictionary learning disclosed in this embodiment is described in detail.

[0039] At present, the existing technology has proposed a method for calculating the instantaneous NOx emission factor. This method is based on the emission-related parameters in the actual driving emission test data, namely, the NOx volume concentration in the exhaust gas, the engine exhaust rate, the engine fuel rate, and the fuel flow rate data collected second by second to calculate the instantaneous NOx emission factor, as shown in formula (1):

[0040]

[0041] Where, The instantaneous NOx emission factor of the vehicle (g / s), which is used to characterize the amount of NOx emitted by the vehicle per unit time at a certain moment; is the NOx concentration downstream of SCR (selective catalytic reduction) (ppm); is the engine exhaust rate (kg / h); is the engine fuel rate (kg / h); is the engine fuel flow rate (L / h); is the density of gasoline, which is set to 0.73 kg / L; M is the molecular weight of NOx, because a high percentage of NO is converted to , so its molecular weight is considered to be Same as 46g; 1-losses represents the correction factor, obtained by validating the calculation results using RDE data; is the exhaust density, which is assumed to be approximately the same as the density of air at 29 g / mol.

[0042] While conventional techniques involve introducing correction factors to calibrate NOx emissions, calculating these correction factors remains problematic. For one thing, traditional methods often rely on a small number of characteristic variables, overlooking numerous potential factors related to exhaust emissions, such as subtle differences in engine operation under different operating conditions. This can lead to inaccurate correction factors. Furthermore, with the continuous accumulation of test data, the volume of data continues to grow, and the feature dimensionality increases. Existing calculation methods, when processing high-dimensional data, are extremely computationally complex and inefficient, making it difficult to meet real-time and accuracy requirements.

[0043] Therefore, this embodiment extracts a high-dimensional dataset from actual driving emission test data, encompassing a wealth of multi-dimensional data such as vehicle information and speed. However, if this were used directly to calculate the correction coefficient, not only would it consume enormous computing resources, but the reliability of the results would also be affected by the curse of dimensionality. However, t-SNE, a nonlinear dimensionality reduction technique, can better handle the nonlinear characteristics of the data, balancing the local and global structures of the data, and dictionary learning can effectively retain key information. Therefore, this embodiment proposes a dimensionality reduction method that combines t-SNE and dictionary learning to provide a more efficient and reliable data processing foundation for accurately calculating the correction coefficient.

[0044] First, the initial high-dimensional driving emission dataset described in this embodiment is obtained based on the RDE test dataset of 10 hybrid vehicles. This high-dimensional data is first used for dimensionality reduction to obtain an initial low-dimensional embedding, and then the initial low-dimensional embedding is used to assist in dimensionality reduction of subsequent incremental data.

[0045] The data of the high-dimensional dataset includes engine characteristics, driving characteristics, and external characteristic data under different test conditions. The test conditions are divided into three types: urban (v ≤ 60 km / h), suburban (60 km / h < v ≤ 90 km / h), and highway (v > 90 km / h), as Figure 3 shown.

[0046] A parameter database related to NOx emissions is established. Specifically, the engine characteristics include four items: coolant temperature, exhaust temperature, engine speed, and intake temperature; the driving characteristics cover vehicle specific power (VSP), vehicle speed, and acceleration; the external characteristics include ambient temperature, ambient pressure, and road slope. The above variables are all collected in real time at a frequency of once per second during the RDE test, and the parameter information is summarized in Table 1.

[0047] Table 1 Parameter information;

[0048]

[0049] Upon preliminary processing of the data, it is found that some key parameters are invalid. Therefore, preprocessing and quality control are performed on the dataset to check the validity of the real-time measurement data and ensure that all values are non-negative to guarantee the reliability and usability of the dataset.

[0050] It should be understood that the preprocessing methods include missing value processing, outlier processing, data transformation, non-numeric data encoding processing, and numeric data normalization processing, etc. These methods can be selected by those skilled in the art according to the actual situation and are not limited in this embodiment.

[0051] Furthermore, since the RDE test dataset used in this embodiment contains many feature variables, directly using the original data for analysis not only has a high computational complexity and low efficiency, but may also affect the accuracy and reliability of the analysis results due to problems such as multicollinearity between features. Therefore, a suitable dimensionality reduction technique must be adopted to extract representative feature information. According to the non-linear characteristics of the data, t-SNE is selected as the main dimensionality reduction method in this embodiment.

[0052] t-SNE is a typical nonlinear dimensionality reduction technique that can map high-dimensional data to low-dimensional space while better maintaining local structure and revealing the global structure of the data. t-SNE converts the Euclidean distance between data points in high-dimensional space into a probability distribution, giving similar points a higher probability, and then constructs another set of probability distributions in low-dimensional space, achieving dimensionality reduction by minimizing the Kullback-Leibler divergence between the high- and low-dimensional probability distributions. To improve the robustness to outliers, t-SNE uses a symmetric joint probability distribution, which not only simplifies the gradient calculation but also speeds up the optimization process. At the same time, in low-dimensional space, t-SNE no longer uses the traditional Gaussian distribution, but instead uses the Student-t distribution with a degree of freedom of 1. This distribution can effectively alleviate the "crowding problem" in high-dimensional to low-dimensional mapping, thereby better revealing the global structure of the data. Given that the RDE test data set of this embodiment has nonlinear characteristics, and t-SNE can effectively balance the local and global structures of the data, t-SNE is used as the main dimensionality reduction method.

[0053] This example uses t-SNE to map a high-dimensional dataset into a low-dimensional dataset, achieving low-dimensional embedding for extracting key features. As a typical nonlinear dimensionality reduction technique, t-SNE effectively handles the complex nonlinear relationship between parameters and NOx emissions. Its t-distribution also mitigates the effects of noise in RDE test data.

[0054] In actual hybrid vehicle research scenarios, new real driving emissions (RDE) test data is constantly generated over time, as test conditions change, or to obtain more comprehensive data to improve model accuracy and generalization. For example, driving tests at different time periods and locations, and tests after different mileages, can all generate new data. In this embodiment, this newly input test data is referred to as incremental data.

[0055] Incremental data also requires dimensionality reduction, but conventional technologies have some limitations. Traditional dimensionality reduction methods, such as linear dimensionality reduction techniques such as principal component analysis (PCA), do not work well for complex nonlinear data structures, and it is difficult to fully retain the key features of the data. In addition, the calculation process is relatively complex and inefficient. When faced with a large amount of incremental data, these methods may cause information loss, which in turn affects the accuracy of subsequent model predictions. Therefore, this embodiment introduces dictionary learning, which can extract a set of representative basic elements or features from the original data to encapsulate data features and achieve a low-dimensional representation of the entire data set. For incremental data, it is only necessary to use the pre-learned dictionary to calculate its sparse coding matrix, without the need to rebuild the complete dictionary each time, which significantly shortens the calculation time and reduces the overall computing cost, providing an efficient solution for dimensionality reduction of incremental data.

[0056] Specifically, the goal of dictionary learning is to reconstruct the original data into a linear combination of a small number of dictionary atoms, effectively eliminating redundant information in the data. Imagine the original data as a complex puzzle, with each data point as a piece. Dictionary atoms are like basic puzzle pieces. By combining these basic pieces in different proportions (corresponding to the coefficients in the sparse coefficient matrix), an approximate representation of the original data can be reconstructed. The goal is to replace a large number of complex data points with a small number of basic pieces (dictionary atoms). Through linear combinations of these feature pieces, the image is reconstructed and key features are extracted, thereby simplifying the data and eliminating redundant information.

[0057] The incremental dimensionality reduction method based on dictionary learning used in this embodiment combines an efficient iterative algorithm with a dynamic dictionary atom update strategy to accelerate the training process while maintaining accuracy. It is mainly divided into the following parts:

[0058] (1) Initialization phase

[0059] The general model of dictionary learning can be expressed as follows:

[0060]

[0061] Where X represents a high-dimensional dataset; is a high-dimensional dictionary; C represents a sparse coefficient matrix, which is used to describe the high-dimensional dictionary The weights (coefficients) of the dictionary atoms in are combined to reconstruct the high-dimensional dataset X; ε is the relative error.

[0062] Assumptions is the low-dimensional dataset obtained by dimensionality reduction of X, is the corresponding low-dimensional data dictionary. For a given data point ,make Indicates that it is in a high-dimensional dictionary The encoding in corresponds to the i-th column of the encoding matrix. Apply t-SNE to X to obtain a low-dimensional dataset , and randomly select K samples from X to initialize the high-dimensional dictionary .

[0063] (2) Sparse coding stage

[0064] At this stage the high-dimensional dictionary Keep it fixed and apply the principle of iterative reduction FISTA (IR-FISTA) algorithm to solve the sparse coding matrix C. The core of IR-FISTA algorithm is to introduce the concept of working set, which only processes two types of indexes (in matrix C, each element The corresponding unique index ) performs the accelerated iterative threshold shrinkage (FISTA) operation on the corresponding sparse coefficients:

[0065] ① The current non-zero sparse index;

[0066] ② The coefficient index is currently zero but has a large gradient and may become non-zero in the next iteration.

[0067] This process avoids unnecessary computation of large, stable zero portions of the sparse code.

[0068] Specifically, the variables in the working set are solved as follows:

[0069]

[0070] in, Represents the intermediate value of the sparse coding matrix C at the kth iteration; Represents the value of the sparse coding matrix C at the kth iteration; 、 Respectively represent the kth and k-1th iteration step parameters, , ; is the soft threshold operator, Indicates the step length; represents the regularization parameter; Represents the independent variable parameter in the soft threshold operator; represents the symbolic function, Indicates transpose.

[0071] During the sparse coding phase, this embodiment uses the IR-FISTA algorithm to efficiently solve the sparse coding matrix C. Iterative operations are performed only on the current non-zero coefficient index and the zero coefficient index with a large gradient, avoiding redundant calculations for a large number of stable zero-valued coefficients. This allows for rapid generation of the sparse coding matrix when processing high-dimensional incremental data, shortening the dimensionality reduction process.

[0072] (3) Dictionary update phase

[0073] In this stage, the sparse coding matrix C is fixed, and the high-dimensional dictionary is calculated by combining the learning rate decay and the dynamic update strategy based on the importance of atoms. The dynamic update strategy counts the sum of the absolute values ​​of the corresponding dictionary atoms in the sparse matrix C as the "importance" of the dictionary atom. The jth atom of , its importance Defined as:

[0074]

[0075] Where N is the total number of data samples, is the sparse coefficient corresponding to the jth dictionary atom when representing the i-th data sample.

[0076] At the same time, the learning rate attenuation mechanism is introduced on this basis, and the basic learning rate is reduced in the form of exponential decay. The exponential decay decays with the increase of the number of dictionary learning training iterations, avoiding the significant oscillation of the optimization process caused by excessive parameter updates in the late iterative training, which would hinder the model from converging stably to the optimal solution. The mathematical expression of exponential decay is shown in the following formula:

[0077]

[0078] in, is the initial base learning rate, is the attenuation coefficient, represents the exponential decay factor.

[0079] In each dictionary update iteration, the learning rate allocation strategy is optimized based on the learning rate decay mechanism and the importance of dictionary atoms, and a specific learning rate is assigned to each atom. :

[0080]

[0081] in, is the maximum value of the atomic importance, is a small positive number used to ensure that the denominator in the formula is not zero.

[0082] Through the above learning rate distribution strategy, atoms with higher "importance" receive larger learning rates to adjust to the optimal state faster; atoms with lower importance use smaller learning rates to avoid unnecessary calculations. This dynamic update strategy enables the dictionary update process to take into account the needs of rapid exploration and stable and accurate convergence, thereby optimizing the high-dimensional dictionary. learning efficiency.

[0083] Repeat the sparse coding phase and dictionary update phase until the reconstruction error is lower than the preset threshold or the maximum number of iterations is reached. Figure 4 shown.

[0084] In this embodiment, the learning efficiency and adaptability of the high-dimensional dictionary are optimized through the learning rate decay and atom importance dynamic strategy. The atom importance statistics are the sum of the absolute values ​​of the corresponding coefficients of each atom in the sparse matrix, so that the key atoms that contribute most to data reconstruction are given priority to obtain a larger learning rate, accelerating the convergence to the optimal state; and the learning rate decay mechanism reduces the update step size in the late iteration in an exponential form, avoiding oscillation of the optimization process and ensuring stable convergence of the dictionary. This dynamic update strategy enables the dictionary to adaptively capture the key features in the RDE test data, and the generated dictionary atoms are more representative. Therefore, there is no need to rebuild the dictionary during incremental dimensionality reduction. New data can be quickly processed only by coupling the pre-learned dictionary with sparse coding, reducing computational costs while improving the model's ability to represent complex data.

[0085] (4) Incremental dimensionality reduction stage

[0086] Iterative optimization process based on dictionary learning, low-dimensional data dictionary The solution can be expressed as:

[0087]

[0088] In the formula, the sparse coefficient matrix C plays the role of connecting high-dimensional data with low-dimensional data dictionary, through which the result after dimensionality reduction of high-dimensional data is obtained. To calculate the low-dimensional data dictionary.

[0089] When new data is acquired, the encoding matrix corresponding to it on the high-dimensional dictionary is first calculated; then the encoding matrix is ​​coupled with the low-dimensional dictionary to achieve rapid dimensionality reduction of the new data and obtain the low-dimensional embedding of the incremental data. The incremental dimensionality reduction calculation formula is shown in formula (4):

[0090]

[0091] in, Represents incremental test data in its high-dimensional dictionary The encoding matrix on .

[0092] Dictionary learning extracts a set of representative "atoms" from raw data to encapsulate data features, thereby achieving a low-dimensional representation of the entire dataset. For incremental data, only the sparse encoding matrix needs to be calculated using a pre-learned dictionary, eliminating the need to rebuild the entire dictionary each time. This method significantly shortens computation time and reduces overall computational cost, providing an efficient solution for dimensionality reduction of incremental data.

[0093] As an implementation method, dictionary learning can learn each column of dictionary atoms from the initial dataset. These learned dictionary atoms can fully extract the characteristic information in the data. Therefore, dictionary learning-based methods can generate dictionaries with strong adaptability and data feature representation capabilities. Dimensionality reduction methods based on dictionary learning can be simply described as using high-dimensional data and its corresponding low-dimensional data as training samples, establishing a mapping relationship between the two, and applying this mapping to subsequent new data to quickly obtain its corresponding low-dimensional representation.

[0094] t-SNE excels at revealing the nonlinear structure of data, while dictionary learning can extract sparse representations from data. This embodiment combines the two to more comprehensively capture emission patterns, remove noise and redundant information, and retain the features most relevant to NOx emissions.

[0095] This embodiment uses t-SNE to reduce the dimensionality of the original high-dimensional data set. The obtained low-dimensional embedding is not only used to construct a low-dimensional dictionary through dictionary learning, but also serves as the input of the regression prediction model to predict the correction coefficient of the NOx emission factor.

[0096] In predictive modeling problems, selecting the right machine learning algorithm and choosing the optimal parameters for a specific dataset is crucial. The SuperLearner regression algorithm avoids the dilemma of selecting a single optimal model by integrating multiple base machine learning algorithms. First, SuperLearner performs k-fold cross-validation on the data, evaluating the performance of each algorithm on the same data partition and retaining the predictions of all base models. These predictions are then used to train a meta-learner, which synthesizes the outputs of each model to determine the final optimal model.

[0097] To evaluate the performance of the SuperLearner regression method, this example randomly generated a test dataset consisting of 1000 samples (rows) and 100 features (columns) for comparison with various models, including the SuperLearner algorithm. The results in Table 2 demonstrate that SuperLearner performs comparable to the best baseline model and may even outperform all individual baseline models. Therefore, this example selected SuperLearner as the method for constructing the NOx correction coefficient model.

[0098] Table 2 Evaluation of SuperLearner regression results;

[0099]

[0100] Therefore, this embodiment uses the initial low-dimensional embedding based on t-SNE dimensionality reduction to train the SuperLearner regression model. Figure 2 As shown, represents the low-dimensional dataset obtained by applying t-SNE to the high-dimensional dataset. and Represents the elements corresponding to different dimensions in the low-dimensional dataset; represents the SuperLearner regression model, Corresponding to the model training stage, it represents the prediction relationship between learning low-dimensional features and NOx emission factor correction coefficients.

[0101] The training process of the SuperLearner regression model specifically includes:

[0102] 1. Data preparation: Collect historical real driving emissions (RDE) test data of hybrid vehicles, including emission-related parameters, a high-dimensional dataset of historical driving emissions, and measured NOx emissions.

[0103] Based on the emission-related parameters in the actual driving emission test data, the theoretical NOx emission factor is calculated according to formula (1);

[0104] Then, based on the historical measured NOx emissions and the theoretical NOx emission factor, the correction factor label is derived based on the ratio.

[0105] Using the theoretical NOx emission factor correction coefficient as the label, the low-dimensional embedding of the historical high-dimensional dataset after t-SNE dimensionality reduction is divided into a training set and a test set according to a certain ratio. The training set is used for model training, and the test set is used to evaluate model performance.

[0106] 2. Basic model selection and training: Select an appropriate algorithm from a variety of basic machine learning algorithms, such as linear regression, decision tree regression, support vector regression, etc. Use the training set data to train each basic model separately to obtain the trained basic model.

[0107] 3. k-fold cross-validation: Using the k-fold cross-validation method, the training set data is divided into k mutually exclusive subsets. For each basic model, k-1 subsets are used as training data, and the remaining subset is used as validation data for training and validation. This is repeated k times, and the prediction results of each validation are recorded.

[0108] 4. Meta-learner training: The prediction results of all base models in k-fold cross-validation are combined as input data for the meta-learner. This data is used to train the meta-learner. The optimization algorithm adjusts the meta-learner parameters so that it can integrate the prediction results of each base model to obtain the final SuperLearner regression model.

[0109] 5. Model evaluation and optimization: Use the test set data to evaluate the performance of the trained SuperLearner regression model by calculating RMSE, If the model performance does not meet expectations, adjust the base model, the number of k-fold cross-validation folds, or the parameters of the meta-learner, and retrain and evaluate until the model performance meets the requirements.

[0110] The low-dimensional embedding of the incremental data is input into the trained SuperLearner regression model to obtain the corresponding incremental NOx emission factor correction coefficient. Figure 2 As shown, Represents the low-dimensional dataset obtained by incremental high-dimensional dataset based on dictionary learning, and Represents the elements corresponding to different dimensions in the low-dimensional dataset. In the application stage after the corresponding model training is completed, the incremental NOx emission factor correction coefficient is obtained based on the low-dimensional embedding of the incremental data.

[0111] Furthermore, in order to verify the accuracy and effectiveness of the NOx emission calculation model, this embodiment uses the EF calculated by formula (1) NOx (g / s) and the instantaneous measured EF collected from ten HEVs during the RDE test NOx (g / s) for comparison. At this time, the coefficient (1-losses) in formula (1) is taken as 1, that is, no correction is made. The least squares method is used for fitting, and the coefficient of determination is used respectively. The overall correlation between the calculated and measured NOx emission values ​​was evaluated by two indicators: the slope of the fitting curve equation.

[0112] Table 3 lists the correlation between the calculated and measured NOx emission values ​​without considering the correction factor, and the correlation between the calculated and measured NOx emission values ​​is shown in Table 3. And RMSE calculated by formula (g / s) and measured The parameter K is defined as the calculated value of the NOx emission rate of a single HEV in the RDE test. and measured values The slope of the fitting curve obtained by least square fitting is specifically expressed as follows:

[0113]

[0114] As shown in Table 3, there is a significant deviation between the calculated and measured NOx emissions of the ten HEVs. The lowest is only 0.879.

[0115] Table 3 Evaluation indicators of ten hybrid vehicles;

[0116]

[0117] Therefore, it is necessary to further calibrate by optimizing the correction coefficient in formula (1) and determine its specific value based on the multivariate variables in the RDE test data so that the parameters K and The value of approaches the ideal value of 1. The advantages of the dimensionality reduction and correction process proposed in this embodiment are reflected in two aspects: first, it avoids the complex processing process in traditional dimensionality reduction methods and obtains the corresponding low-dimensional data through simple matrix calculations, significantly reducing the calculation time; second, the excellent modeling ability of the SuperLearner regression method makes the correction coefficient prediction model more accurate, effectively correcting the NOx emission prediction value corresponding to the incremental data.

[0118] Based on formula (1), “1-losses” is replaced by the incremental NOx emission factor correction coefficient to calculate more accurate NOx emissions.

[0119] As an implementation method, this example uses three independent RDE test datasets to evaluate the performance of the proposed method that combines incremental dimensionality reduction based on dictionary learning with a prediction model based on SuperLearner. The evaluation indicators include parameters K, and RMSE to comprehensively evaluate the performance of the method from multiple dimensions.

[0120] Table 4 shows the correlation between the calculated and measured NOx emissions from the three HEV test data sets without introducing any correction factors, while Table 5 shows the accuracy of the corrected NOx emissions using the proposed system approach. The results show that the application of this system approach can significantly improve the evaluation index of the correlation between the predicted and measured NOx emissions. Specifically, the parameter K is generally improved from approximately 0.8-0.9 to the range of 1±0.05. It increased from a minimum of 0.956 to above 0.995. In addition, RMSE also showed significant improvement.

[0121] Table 4 Evaluation index values ​​of the test dataset before correction;

[0122]

[0123] Table 5 Evaluation index values ​​after correction of test dataset;

[0124]

[0125] These results show that the method described in this embodiment combines the incremental dimensionality reduction technology based on dictionary learning with the SuperLearner prediction model. It not only achieves rapid dimensionality reduction of incremental data through simple matrix operations and simplifies the calculation process, but also can accurately predict the correction coefficient and obtain more accurate NOx emission estimates compared with the uncorrected method.

[0126] In view of the deviation between the calculated value and the measured value of NOx emissions, this specific embodiment proposes an optimization method based on correction coefficients. Since the number of characteristic variables obtained from the RDE test is large, this embodiment uses t-SNE to reduce the dimensionality of high-dimensional features, and constructs a high- and low-dimensional dictionary mapping through dictionary learning, and uses simple matrix operations to quickly map incremental data to low-dimensional space. At the same time, the SuperLearner regression model is trained based on the t-SNE low-dimensional embedding to achieve accurate prediction of low-dimensional parameters to correction coefficients. For incremental data, the low-dimensional embedding obtained by the incremental dimensionality reduction method based on dictionary learning is directly input into the correction coefficient model, and the corresponding NOx emission factor correction coefficient can be quickly generated, thereby effectively ensuring the speed and accuracy of emission prediction.

[0127] Example 2

[0128] This embodiment provides a hybrid vehicle NOx emission prediction system based on dictionary learning, including:

[0129] Data acquisition module, used to obtain emission-related parameters, initial driving emission high-dimensional data set and incremental test data;

[0130] A data dimensionality reduction module is used to map the initial driving emission high-dimensional dataset into an initial low-dimensional embedding via t-SNE;

[0131] A dictionary construction and optimization module is used to construct a high-dimensional dictionary and a low-dimensional dictionary through dictionary learning based on the initial low-dimensional embedding, and perform iterative optimization; calculate the sparse coding matrix of the incremental test data on the high-dimensional dictionary, and couple it with the low-dimensional dictionary to generate an incremental low-dimensional embedding;

[0132] A correction coefficient acquisition module is used to input the incremental low-dimensional embedding into a pre-trained SuperLearner regression model to obtain an incremental NOx emission factor correction coefficient;

[0133] The emission calculation module is used to calculate NOx emissions based on emission-related parameters and an incremental NOx emission factor correction coefficient.

[0134] Example 3

[0135] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps of the method for predicting NOx emissions of a hybrid electric vehicle based on dictionary learning as described in the first embodiment above are implemented.

[0136] Example 4

[0137] This embodiment provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the method for predicting NOx emissions of a hybrid electric vehicle based on dictionary learning as described in the first embodiment above are implemented.

[0138] The steps or modules involved in Examples 2 to 4 above correspond to those in Example 1. For detailed implementations, please refer to the relevant description of Example 1. The term "computer-readable storage medium" should be understood to mean a single medium or multiple media that includes one or more instruction sets; it should also be understood to include any medium that can store, encode, or carry an instruction set for execution by a processor and cause the processor to perform any method of the present invention.

[0139] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A method for predicting NOx emissions from hybrid electric vehicles based on dictionary learning, characterized in that: include: Obtain emission-related parameters, initial driving emission high-dimensional datasets, and incremental test data; Mapping the initial driving emission high-dimensional dataset into an initial low-dimensional embedding via t-SNE; Based on the initial low-dimensional embedding, construct a high-dimensional dictionary and a low-dimensional dictionary through dictionary learning, and perform iterative optimization; Calculate the sparse encoding matrix of the incremental test data on the high-dimensional dictionary, and couple it with the low-dimensional dictionary to generate incremental low-dimensional embedding; Inputting the incremental low-dimensional embedding into a pre-trained SuperLearner regression model to obtain an incremental NOx emission factor correction coefficient; NOx emissions are calculated based on emission-related parameters and the incremental NOx emission factor correction factor, specifically: ； in, The instantaneous NOx emission factor of the vehicle is used to characterize the amount of NOx emitted by the vehicle per unit time at a certain moment; The concentration of NOx downstream of the selective catalytic reduction; is the engine exhaust velocity; is the engine fuel rate; is the engine fuel flow rate; is the density of gasoline; M is the molecular weight of NOx; 1-losses is the correction factor; is the exhaust density.

2. The method for predicting NOx emissions of hybrid electric vehicles based on dictionary learning according to claim 1, characterized in that: The initial driving emission high-dimensional data set includes engine characteristic data, driving characteristic data and external characteristic data collected under different test conditions, and the test conditions include urban, suburban and highway conditions.

3. The method for predicting NOx emissions of hybrid electric vehicles based on dictionary learning according to claim 1, characterized in that: Mapping the initial high-dimensional driving emission dataset into an initial low-dimensional embedding through t-SNE specifically includes: Convert the Euclidean distance between data points in the initial high-dimensional driving emission dataset into a joint probability distribution in a high-dimensional space, so that similar data points are assigned higher joint probabilities; Construct another set of joint probability distributions in the low-dimensional space, where the distances between points in the low-dimensional space are modeled by the Student-t distribution with 1 degree of freedom; A symmetric joint probability distribution is used to represent the relationship between data points in high-dimensional space and low-dimensional space; Minimize the KL divergence between the joint probability distribution in high-dimensional space and low-dimensional space, and iteratively update the point position in low-dimensional space through the gradient optimization algorithm; When the divergence converges or reaches a preset number of iterations, the final low-dimensional embedding representation is output, which retains the local and global structural features of the high-dimensional data.

4. The method for predicting NOx emissions of hybrid electric vehicles based on dictionary learning according to claim 1, characterized in that: Based on the initial low-dimensional embedding, a high-dimensional dictionary and a low-dimensional dictionary are constructed through dictionary learning, and iterative optimization is performed, specifically including: Based on the general model of dictionary learning, samples are randomly extracted from the high-dimensional data set to initialize the high-dimensional dictionary; Optimizing a sparse coding matrix based on iterative reduction, and optimizing a high-dimensional dictionary using a learning rate decay and a dynamic update strategy for atom importance; wherein the iterative reduction is used to iteratively calculate only non-zero coefficient indices in the sparse coding matrix and zero coefficient indices whose gradient exceeds a preset threshold; A low-dimensional dictionary is obtained based on the optimized sparse coding matrix and the initial low-dimensional embedding.

5. The method for predicting NOx emissions of hybrid electric vehicles based on dictionary learning as claimed in claim 4, characterized in that: The optimization of the high-dimensional dictionary by using the learning rate decay and atom importance dynamic update strategy specifically includes: The importance of atoms is measured by summing the absolute values ​​of the corresponding atomic coefficients in the statistical sparse coding matrix; A learning rate decay mechanism is introduced to allow the basic learning rate to decay exponentially as the number of iterations increases, thus avoiding oscillations in the late stages of iterations. At each iteration, a learning rate is assigned to each atom based on the learning rate decay mechanism and the importance of the atom to achieve high-dimensional dictionary optimization.

6. The method for predicting NOx emissions of hybrid electric vehicles based on dictionary learning as claimed in claim 1, characterized in that: The training process of the SuperLearner regression model includes: Calculating an initial NOx emission factor based on emission-related parameters; obtaining an initial NOx emission factor correction factor based on a ratio of measured emission data to the initial NOx emission factor; The SuperLearner regression model is trained based on the initial low-dimensional embedding and the initial NOx emission factor correction coefficient.

7. A hybrid vehicle NOx emission prediction system based on dictionary learning, characterized in that: include: Data acquisition module, used to obtain emission-related parameters, initial driving emission high-dimensional data set and incremental test data; A data dimensionality reduction module is used to map the initial driving emission high-dimensional dataset into an initial low-dimensional embedding via t-SNE; A dictionary construction and optimization module, configured to construct a high-dimensional dictionary and a low-dimensional dictionary through dictionary learning based on the initial low-dimensional embedding, and perform iterative optimization; Calculate the sparse encoding matrix of the incremental test data on the high-dimensional dictionary, and couple it with the low-dimensional dictionary to generate incremental low-dimensional embedding; A correction coefficient acquisition module is used to input the incremental low-dimensional embedding into a pre-trained SuperLearner regression model to obtain an incremental NOx emission factor correction coefficient; An emission calculation module for calculating NOx emissions based on emission-related parameters and an incremental NOx emission factor correction coefficient; Specifically: ； in, The instantaneous NOx emission factor of the vehicle is used to characterize the amount of NOx emitted by the vehicle per unit time at a certain moment; The concentration of NOx downstream of the selective catalytic reduction; is the engine exhaust velocity; is the engine fuel rate; is the engine fuel flow rate; is the density of gasoline; M is the molecular weight of NOx; 1-losses is the correction factor; is the exhaust density.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method for predicting NOx emissions of a hybrid electric vehicle based on dictionary learning as claimed in any one of claims 1 to 6 are implemented.

9. A computer device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method for predicting NOx emissions of a hybrid electric vehicle based on dictionary learning as claimed in any one of claims 1 to 6 are implemented.

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