Training method and system for multi-stage heat release rate prediction model of low-carbon engine

Abstract

The present invention belongs to the technical field of heat release rate prediction of low-carbon engines. In order to solve the problem that the existing model is not suitable for the changes in combustion characteristics under various working conditions, a method and system for training a multi-stage heat release rate prediction model for a low-carbon engine are provided. Among them, the method for training a multi-stage heat release rate prediction model for a low-carbon engine includes obtaining the engine operating parameters and combustion characteristic parameters of the set dimension; using the active subspace sensitivity analysis method to calculate the normalized activity score of each dimension of the engine operating parameter to the combustion characteristic parameter and use it as the weight of the corresponding dimension of the engine operating parameter; weighting the engine operating parameters of each dimension according to their corresponding weights, and then combining the combustion heat release rate fitted by the three-Weibull function to form a data set; using the data set to fine-tune the heat release rate prediction model preliminarily trained, and obtain a multi-stage heat release rate prediction model for a low-carbon engine. It can fully capture the characteristics of the engine combustion process and improve the prediction accuracy and generalization ability of the model in virtual test applications.

Description

Technical Field

[0001] The invention belongs to the technical field of heat release rate prediction of low-carbon engines, and in particular relates to a training method and system for a multi-stage heat release rate prediction model of a low-carbon engine. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] High-pressure direct injection engines use coaxial injectors to inject different fuels (high-activity fuel and low-carbon fuel) into the cylinders separately. The combustion process of dual-fuel engines is affected by many factors, such as the fuel mixing ratio, the control of injection parameters, and changes in intake conditions. The complexity and variability of these factors make it very challenging to study the combustion process of dual-fuel engines. Traditional test methods usually require a lot of resources and time to carry out, and it is difficult to cover all possible working conditions, making data acquisition and analysis difficult and expensive. Existing technologies apply machine learning to the modeling and performance evaluation of engine combustion models, but since the combustion process of dual-fuel engines has obvious multi-stage combustion characteristics and involves more complex physical and chemical processes, including dual-fuel mixing, ignition control, and changes in combustion dynamics, the application of machine learning in the combustion model of dual-fuel low-carbon engines faces huge challenges. In addition, on the one hand, bench tests require a lot of resources and equipment, which is costly, limiting the frequency and scale of tests; on the other hand, it is difficult to simulate or obtain all the working conditions of the engine in actual operation, so the collected data cannot cover all possible working conditions, which limits the comprehensiveness of the data.

[0004] In summary, due to the influence of many factors, the amount of data collected in the actual engine bench test is limited, which cannot cover sufficient changes and complexity, resulting in limited model generalization ability and prone to overfitting. This leads to poor model generalization ability and inability to adapt to changes in combustion characteristics under different working conditions. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides a low-carbon engine multi-stage heat release rate prediction model training method and system, which can comprehensively capture the characteristics of the engine combustion process and further improve the prediction accuracy and generalization ability of the model in virtual test applications.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] A first aspect of the present invention provides a method for training a multi-stage heat release rate prediction model for a low-carbon engine.

[0008] In one or more embodiments, a method for training a multi-stage heat release rate prediction model for a low-carbon engine is provided, comprising:

[0009] Obtaining engine operating parameters and combustion characteristic parameters of set dimensions;

[0010] Active subspace sensitivity analysis method is used to calculate the normalized activity score of each dimension of engine operating parameters on combustion characteristic parameters, and used as the weight of the corresponding dimension of engine operating parameters;

[0011] The engine operating parameters of each dimension are weighted according to their corresponding weights, and then combined with the combustion heat release rate fitted by the three-Weibull function to form a data set;

[0012] The data set is used to fine-tune the heat release rate prediction model that was initially trained, and a multi-stage heat release rate prediction model for a dual-fuel low-carbon engine is obtained;

[0013] In the initial training process of the heat release rate prediction model, the natural gas data in the training samples are pseudo natural gas data formed by converting the calorific value of the secondary injection in the diesel engine test data into equivalent natural gas mass.

[0014] As an implementation method, the normalized activity score of each dimension of engine operating condition parameter on the combustion characteristic parameter is:

[0015]

[0016] in, It represents the normalized activity score of each dimension of engine operating condition parameter on the combustion characteristic parameter; Indicates the first dimensions; m is the dimension of the input parameter; n is the number of eigenvalues; Indicates the activity score of each dimension of engine operating condition parameter on combustion characteristic parameter; is the characteristic value; represents the eigenvector matrix Line Column elements.

[0017] As an implementation method, the combustion heat release rate is fitted by three Weibull functions:

[0018]

[0019] The superscript Pick They represent the premixed combustion stage, the main combustion stage and the tail combustion stage respectively; is the combustion efficiency index; Indicates the starting point of combustion; Indicates the duration of combustion; represents the shape factor; Indicates the combustion ratio; is the normalized combustion heat release rate expressed using the three-Weibull function; Indicates the crankshaft angle.

[0020] As an implementation method, in optimizing the three-Weibull function parameters , , and In the process, the objective function is constructed to minimize the gap between the heat release rate predicted by the model and the actual heat release rate data; the expression of the objective function is for:

[0021]

[0022] In the formula, is the total loss; , , , is a weight parameter used to adjust the balance between the overall error and the feature point error; , , In the corresponding fitted heat release rate curve, the crankshaft angle positions where the cumulative heat release rates reach 10%, 50%, and 90% respectively; , , is the test value of the combustion characteristic point; is the predicted value vector calculated according to the model, is the parameter vector to be optimized, The model is Input data, is the test data, is the number of data points; is the function that minimizes the residual sum of squares.

[0023] As an implementation mode, the engine operating parameters include eight parameters, namely, engine speed, excess air coefficient, intake pressure, intake temperature, fuel injection amount, natural gas injection amount, fuel injection timing and natural gas injection timing.

[0024] As an embodiment, the combustion characteristic parameters include crankshaft angles corresponding to 10%, 50% and 90% fuel combustion.

[0025] As an implementation method, during the initial training of the heat release rate prediction model, training samples are enhanced based on CTGAN (Conditional Tabular Generative Adversarial Network).

[0026] A second aspect of the present invention provides a low-carbon engine multi-stage heat release rate prediction model training system.

[0027] In one or more embodiments, a low-carbon engine multi-stage heat release rate prediction model training system includes:

[0028] A parameter acquisition module, which is used to obtain engine operating parameters and combustion characteristic parameters of a set dimension;

[0029] A weight calculation module, which is used to calculate the normalized activity score of each dimension of the engine operating condition parameter to the combustion characteristic parameter by using the active subspace sensitivity analysis method, and use it as the weight of the corresponding dimension of the engine operating condition parameter;

[0030] A data set construction module, which is used to weight the engine operating parameters of each dimension according to their corresponding weights, and then combine them with the combustion heat release rate fitted by the three-Weibull function to form a data set;

[0031] A model training module, which uses the data set to fine-tune the preliminarily trained heat release rate prediction model to obtain a multi-stage heat release rate prediction model for a low-carbon engine;

[0032] In the initial training process of the heat release rate prediction model, the natural gas data in the training samples are pseudo natural gas data formed by converting the calorific value of the secondary injection in the diesel engine test data into equivalent natural gas mass.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] (1) The low-carbon engine multi-stage heat release rate prediction model training method of the present invention combines the sensitivity analysis results to perform weighted optimization on the input parameters, and reduces the interference of redundant features by highlighting important parameters and weakening secondary parameters, thereby improving the recognition and learning capabilities of the model and obtaining more stable prediction results; in addition, weighted optimization can help the model more accurately capture the pattern of dominant features, thereby more effectively generalizing to unseen data. This is especially important for low-carbon engine test data with relatively limited data volume.

[0035] (2) The present invention also uses the sensitivity analysis weighted method and the three-Weber combustion model results to determine the engine operating parameters that affect the combustion process and to parameterize the combustion process; at the same time, a machine learning algorithm is introduced to establish a complex nonlinear relationship between the operating parameters and the combustion parameters.

[0036] (3) The present invention reduces the reliance on a large amount of dual-fuel engine data, shortens the model training time, and improves the prediction accuracy of the model by transferring the knowledge learned from the diesel engine model to the dual-fuel low-carbon engine. In addition, transfer learning can utilize the detailed information in the diesel engine data to make up for the shortcomings of the dual-fuel engine in data collection, thereby improving the reliability of the heat release rate prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings in the specification, 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 descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0038] Figure 1 It is a flow chart of a method for training a multi-stage heat release rate prediction model for a low-carbon engine according to an embodiment of the present invention;

[0039] Figure 2 2 is a schematic diagram of the structure of a low-carbon engine multi-stage heat release rate prediction model training system according to an embodiment of the present invention;

[0040] Figure 3 This is a framework diagram of a multi-stage heat release rate prediction model according to an embodiment of the present invention;

[0041] Figure 4 is a schematic diagram of a transfer learning model of a multi-stage heat release rate prediction model according to an embodiment of the present invention;

[0042] Figure 5 is an example of a multi-stage combustion distribution according to an embodiment of the present invention;

[0043] Figure 6 is a schematic diagram of a linear model sequence according to an embodiment of the present invention;

[0044] Figure 7 is a data enhancement method according to an embodiment of the present invention;

[0045] Figure 8 is an activity variable weight map of CA10 for 8-dimensional parameters according to an embodiment of the present invention;

[0046] Fig. 9 is an activity variable weight diagram of CA50 for 8-dimensional parameters according to an embodiment of the present invention;

[0047] Fig.10 is an activity variable weight diagram of CA90 for 8-dimensional parameters according to an embodiment of the present invention;

[0048] Fig.11 It is a response surface model diagram of CA10 to 8-dimensional parameters according to an embodiment of the present invention;

[0049] Fig.12 It is a response surface model diagram of CA50 to 8-dimensional parameters according to an embodiment of the present invention;

[0050] Fig.13 It is a response surface model diagram of CA90 to 8-dimensional parameters according to an embodiment of the present invention;

[0051] Fig.14 is 900 rpm of the embodiment of the present invention, and the three-Weibull function fits the heat release rate effect;

[0052] Fig.15 It is 1200 rpm of the embodiment of the present invention, and the three-Weibull function fits the heat release rate effect;

[0053] Fig.16 It is 1500 rpm of the embodiment of the present invention, and the three-Weibull function fits the heat release rate effect;

[0054] Fig.17 It is 1800 rpm of the embodiment of the present invention, and the three-Weibull function fits the heat release rate effect;

[0055] Fig.18 It is 1700 rpm of the embodiment of the present invention, and the heat release rate prediction model predicts the effect;

[0056] Fig.19 It is 1400 rpm of the embodiment of the present invention, and the heat release rate prediction model predicts the effect;

[0057] Fig. 20 It is 1100 rpm of the embodiment of the present invention, and the heat release rate prediction model predicts the effect;

[0058] Fig.21 It is 800 rpm of the embodiment of the present invention, and the heat release rate prediction model predicts the effect;

[0059] Fig. 22 It is a distribution diagram of absolute errors between CA10 predicted values ​​and test values ​​at 205 operating points of an embodiment of the present invention;

[0060] Fig.23 It is a distribution diagram of absolute errors between CA50 predicted values ​​and test values ​​at 205 operating points of an embodiment of the present invention;

[0061] Fig.24 It is a distribution diagram of the absolute errors between the CA90 predicted values ​​and the test values ​​at 205 operating points in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0063] It should be noted that the following detailed descriptions are all illustrative and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0064] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0065] Figure 1 FIG. 1 is a flow chart of a method for training a multi-stage heat release rate prediction model for a low-carbon engine according to an embodiment of the present invention. Figure 1 The low-carbon engine multi-stage heat release rate prediction model training method in the present embodiment shown may include steps S101 to S104.

[0066] Specifically, S101, obtaining engine operating parameters and combustion characteristic parameters of a set dimension.

[0067] As an implementation mode, the engine operating parameters include eight parameters, namely, engine speed, excess air coefficient, intake pressure, intake temperature, fuel injection amount, natural gas injection amount, fuel injection timing and natural gas injection timing.

[0068] As an embodiment, the combustion characteristic parameters include crankshaft angles corresponding to 10%, 50% and 90% fuel combustion.

[0069] CA10, CA50, and CA90 represent the crankshaft angles corresponding to 10%, 50%, and 90% fuel combustion, and they are important characteristic parameters that reflect the combustion process. Among them, CA10 can reflect the trend of ignition delay, CA50 represents the combustion phase, and CA90 can reflect the characteristics of the final stage of combustion.

[0070] S102, using an active subspace sensitivity analysis method to calculate the normalized activity score of each dimension of the engine operating parameter to the combustion characteristic parameter, and use it as the weight of the corresponding dimension of the engine operating parameter.

[0071] Active subspace is a method for sensitivity analysis of model parameters. The method separates the direction of relative change from the direction of relative flatness by performing a linear spatial transformation in the space of all input parameters. The method projects the input space into a low-dimensional subspace that reflects variability through the direction of change in the high-dimensional space for sensitivity analysis and dimensionality reduction. The separation directions are a set of orthogonal directions, and the low-dimensional subspace obtained by projection is defined as the active subspace.

[0072] Assume f is a continuous differentiable function and the input variable is recorded as , then its gradient can be expressed as a column vector , m is the dimension of the input parameter, defining the uncentered covariance matrix C of the gradient:

[0073] (1)

[0074] In the formula, , represents the orthogonal matrix composed of the eigenvectors of C, , which represents a diagonal matrix with eigenvalues ​​arranged in descending order.

[0075] Separate the components of the rotated coordinate system into a set corresponding to a larger average change and a set corresponding to a smaller average change, and partition the eigenvalues ​​and eigenvectors, and we have

[0076] (2)

[0077] In the formula, is a diagonal matrix consisting of the first n largest eigenvalues, , is the corresponding eigenvector matrix, and the subspace it defines is called the active subspace, which represents the important directions in which the perturbations in the input have the greatest impact on the output.

[0078] The active subspace uses the obtained eigenvalues ​​and eigenvectors to calculate the score As a sensitivity measure of the i-th parameter, it is defined as the activity score:

[0079] (3)

[0080] For a clearer comparative analysis, the activity scores are normalized:

[0081] (4)

[0082] in, It represents the normalized activity score of each dimension of engine operating condition parameter on the combustion characteristic parameter; Indicates the first dimensions; m is the dimension of the input parameter; n is the number of eigenvalues; Indicates the activity score of each dimension of engine operating condition parameter on combustion characteristic parameter; is the characteristic value; represents the eigenvector matrix i Line j Column elements.

[0083] This embodiment uses the global linear model (OLS) in the Python library to calculate the approximate gradient to estimate the one-dimensional active subspace.

[0084] This embodiment combines the sensitivity analysis results to perform weighted optimization on the input parameters:

[0085] The combustion process of a dual-fuel engine involves a variety of input parameters, and there may be certain correlations or redundancies between these parameters. Directly using the original input features will cause the model to be interfered with by unnecessary noise during the training process, resulting in unsatisfactory training results. Weighted optimization can reduce the interference of redundant features by highlighting important parameters and weakening secondary parameters, thereby improving the recognition and learning capabilities of the model and obtaining more stable prediction results. In addition, weighted optimization can help the model capture the patterns of dominant features more accurately, thereby generalizing to unseen data more effectively. This is especially important for dual-fuel engine test data with relatively limited data volume.

[0086] This embodiment uses the active subspace sensitivity analysis method to calculate the active variable weight corresponding to each dimension of the engine operating parameters. The engine operating parameters are weighted according to the weights to generate a weighted feature set. The weighted features are used as input data for model training, thereby helping the model to more accurately identify the variables that have the greatest impact on the heat release rate prediction and improve the overall prediction performance. This weighted optimization method enables the model to enhance its focus on key features, helps reduce input noise, optimizes model performance, and improves the accuracy and reliability of heat release rate prediction.

[0087] S103, weighting the engine operating parameters of each dimension according to their corresponding weights, and then combining them with the combustion heat release rate fitted by the three-Weibull function to form a data set.

[0088] As shown in formula (5), the original input variables are weighted according to the corresponding activity variable weights to generate weighted new features as the input data of the algorithm model. Compared with the original features, the weighted features can help the model capture more representative and highly influential input parameters, thereby improving training efficiency.

[0089] (5)

[0090] Compared with the single-Weibull function and the double-Weibull function, the three-Weibull function model can better represent the combustion process in the cylinder of a diesel / natural gas dual-fuel engine. This is because at the end of combustion, due to the incomplete combustion of the fuel and the complexity of the later oxidation process, there is a long tail of energy release. The single-Weibull and double-Weibull functions are difficult to capture the tail combustion stage, resulting in a large difference between the experiment and the model. The three-Weibull curve can simulate three heat release stages: premixed combustion, diffusion combustion, and tail combustion. By following the three Weibull curves Figure 5 The superposition of the displayed methods can make the simulation results closer to the actual situation of the combustion heat release rate.

[0091] The calculation formula of the apparent heat release rate AHRR of a diesel / natural gas dual-fuel engine is:

[0092] (6)

[0093] In the formula, is the normalized combustion heat release rate expressed by the three-Weibull function, expressed by equation (7), Indicates the fuel quality, Indicates the lower heating value of the fuel. Indicates combustion efficiency.

[0094] Combustion heat release rate fitted by three Weibull functions:

[0095] (7)

[0096] The superscript Pick They represent the premixed combustion stage, the main combustion stage and the tail combustion stage respectively; is the combustion efficiency index, and the calculation formula is shown in formula (8); Indicates the starting point of combustion; Indicates the duration of combustion; represents the shape factor; Indicates the combustion ratio; is the normalized combustion heat release rate expressed using the three-Weibull function; Indicates the crankshaft angle.

[0097] (8)

[0098] In the formula, Indicates the percentage of fuel burned when the combustion reaction in the cylinder ends. In numerical simulation, it is usually considered that the combustion process ends when the combustion reaches 99.9%. The efficiency coefficient is calculated accordingly. =6.908.

[0099] The sum of each stage should equal the total heat release:

[0100] (9)

[0101] According to the form of three-Weibull function, it is necessary to find the starting point of combustion , 3 burning durations , 3 combustion qualities and 2 combustion ratios There are 9 parameters in total. The number of parameters to be fitted is large, the calculation process is complicated, and it is easy to produce multiple solutions. In order to ensure the rationality of the fitting results, first of all, the crankshaft angle corresponding to the start of continuous heat release rate is taken as the combustion start point. , reducing the number of parameters to be fitted to reduce the difficulty of calibrating the three-Weibull function. Secondly, considering the physical meaning of each parameter, the following value constraints are added:

[0102] (10)

[0103] This embodiment uses the fmincon function in Matlab to perform multivariate nonlinear fitting, and fits the experimental heat release rate curve through the three-Weibull function. For nonlinear fitting problems, the most common objective function is to minimize the residual sum of squares, and the goal is to minimize the gap between the model prediction value and the experimental data. Its mathematical expression is as follows:

[0104] (11)

[0105] In the formula, is the predicted value vector calculated according to the model, is the parameter vector to be optimized, is the input data of the model, is the test data, is the number of data points.

[0106] In this example, the goal of the fmincon function is to adjust the parameters of the three-Weibull function , , and , so that the gap between the heat release rate predicted by the model and the actual heat release rate data is minimized.

[0107] Characteristic points in the combustion process, such as CA10, CA50, and CA90, reflect the speed of combustion, combustion stability, and power performance. They are important parameters for describing the combustion process, and it is crucial to accurately predict these characteristic points. However, the conventional objective function only optimizes the model by minimizing the overall error, which makes it difficult to fully consider these key characteristic points. To this end, this embodiment uses a customized objective function to introduce error terms of characteristic points such as CA10, CA50, and CA90 into the objective function, so that the fitting results can not only match the overall heat release rate curve, but also accurately reflect the key turning points in the combustion process. The improved objective function expression is as follows:

[0108] (12)

[0109] In the formula, is the total loss; , , , is a weight parameter used to adjust the balance between the overall error and the feature point error; , , In the corresponding fitted heat release rate curve, the crankshaft angle positions where the cumulative heat release rates reach 10%, 50%, and 90% respectively; , , is the test value of the combustion characteristic point; is the predicted value vector calculated according to the model, is the parameter vector to be optimized, The model is Input data, is the test data, is the number of data points; is the function that minimizes the residual sum of squares.

[0110] S104, fine-tuning the preliminarily trained heat release rate prediction model using the data set to obtain a multi-stage heat release rate prediction model for the dual-fuel engine.

[0111] In the initial training process of the heat release rate prediction model, the natural gas data in the training sample is pseudo natural gas data formed by converting the calorific value of the secondary injection in the diesel engine test data into equivalent natural gas mass, such as Figure 3 and Figure 4 shown.

[0112] This embodiment performs transfer learning to reduce the reliance on a large amount of dual-fuel engine data: since the dual-fuel engine bench test requires a large amount of resources and equipment, the cost is high, which limits the frequency and scale of the test; on the other hand, it is difficult to simulate or obtain all the working conditions of the engine in actual operation, so the collected data cannot cover all possible working conditions, thereby limiting the comprehensiveness of the data. In summary, due to the influence of many factors, the amount of data collected by the actual engine bench test is limited, which cannot cover enough changes and complexity, resulting in limited model generalization ability and prone to overfitting. Transfer learning can effectively utilize the existing diesel engine test data set, by corresponding the secondary injection characteristics of the diesel engine with the heat release characteristics of natural gas, thereby providing a valuable prediction starting point for the dual-fuel engine. By transferring the knowledge learned from the diesel engine model to the dual-fuel engine, the reliance on a large amount of dual-fuel engine data is reduced, the model training time is shortened, and the prediction accuracy of the model is improved. In addition, transfer learning can use the detailed information in the diesel engine data to make up for the shortcomings of the dual-fuel engine in data collection, thereby improving the reliability of the heat release rate prediction.

[0113] The equivalent natural gas mass is calculated from the calorific value of the secondary injection in the diesel engine test data to form "pseudo natural gas data". The model is initially trained using this data to capture key patterns in the heat release characteristics. Through transfer learning, the model is transferred to the dual-fuel engine data for fine-tuning to adapt to the dual-fuel heat release characteristics of natural gas and diesel. Transfer learning effectively utilizes diesel engine test data to help the model acquire more knowledge of the combustion process and reduce dependence on a large amount of dual-fuel engine data.

[0114] The engine operating parameters that have an important impact on the combustion performance obtained through analysis are used as the input data of the combustion prediction model, and the three-Weibull function parameters obtained through fitting are used as the output data of the combustion prediction model. They are combined to construct the data set of the combustion prediction algorithm model. In order to make the distribution of the test set as wide as possible, the data set is divided into a training set and a test set by an equidistant sampling method, in which the test set accounts for 20% of the total data set. Targeting small samples, multi-dimensional input and output, and complex nonlinear regression problems, based on the complexity of the problem, in the initial stage of this embodiment, a variety of machine learning algorithms such as support vector regression (SVR), K nearest neighbor (KNN), fully connected neural network (FCNN), random forest (RF), and decision tree (DT) are trained for subsequent evaluation and selection of the algorithm that best suits the characteristics of the research problem. Among them, it should be noted that the traditional SVR algorithm is a single-output regression model, and the output data has multi-dimensional characteristics. For this reason, this embodiment creates a linear model sequence for SVR for multi-output regression. The principle of the created linear model sequence is as follows Figure 6As shown in the figure, the first model in the sequence uses the input and predicts an output; the second model uses the input and output of the first model to make predictions; the third model uses the input and output of the first two models to make predictions, and so on. In this method, the output of the previous model is passed to the next model so that the next model can better utilize the prediction information of the previous model and capture the correlation between the outputs, so that the entire model sequence can more comprehensively learn complex multi-output relationships, thereby improving the overall prediction performance.

[0115] In order to further improve the performance of the initially determined combustion prediction algorithm, the GridSearchCV method can be used to automatically seek the optimal hyperparameters of the model. GridSearchCV is a combination of grid search and cross-validation techniques. Grid search uses exhaustive methods to traverse all combinations in a given parameter space, and cross-validation is used to evaluate the performance of each combination, so as to find the best hyperparameter combination to optimize model performance. Since the number of samples in the data set involved is small, the leave-one-out cross-validation method is used. In the leave-one-out cross-validation method, each sample is used as a validation set separately, and the remaining N-1 samples are used as training sets, which can maximize the use of each sample for validation. Therefore, the proposed multi-level heat release rate prediction model is highlighted with the best hyperparameters based on a complete and comprehensive training of the target data set.

[0116] In one or more embodiments, when the amount of data is limited, machine learning is difficult to fully learn complex patterns and may face the risk of overfitting; in addition, due to the limitation of training samples, the model may be difficult to adapt to changes in different fields or application scenarios and show greater uncertainty when facing new data. The standard solution for the limited number of samples is to artificially enhance the data set. In order to enrich the training data, this embodiment adopts a data enhancement method based on the CTGAN network.

[0117] During the initial training of the heat release rate prediction model, the training samples are enhanced based on the Conditional Tabular Generative Adversarial Network (CTGAN) network. CTGAN is a framework consisting of a generator network and a discriminator network. The task of the generator is to generate new samples similar to real data from random noise, while the discriminator is responsible for distinguishing whether the generated samples are real. The two networks compete and cooperate with each other. Through continuous iterative training, the samples generated by the generator become more and more realistic, which is difficult for the discriminator to distinguish. CTGAN invented a mode-specific normalization method based on Original GAN ​​to handle columns with non-Gaussian distribution and multi-modal distribution in tabular data, and designed a method of combining conditional generator with sampling training, which can effectively deal with the problem of data imbalance. CTGAN needs to integrate the conditional generator into the architecture of GAN. To this end, Xu et al. proposed a solution with three key elements, namely: conditional vector, generator loss and sampling training method.

[0118] The conditional vector refers to the conditional vector whose input contains both random noise and related discrete information, so that the generator can generate samples according to the specified conditions.

[0119] CTGAN introduces a generator loss by adding the cross entropy between the conditional vector and the synthetic sample in the loss term, which is used to force the generator to generate samples under specified conditions.

[0120] The sampling training method of CTGAN involves randomly selecting a discrete column when generating samples, and generating discrete values ​​based on the categorical distribution of the discrete column. Then, the corresponding conditional vector is constructed based on the generated discrete values. At the same time, samples that match the values ​​of the discrete column are randomly selected from the real samples as input samples of the discriminator. This processing method helps the generator to better learn and generate samples with discrete variable distributions similar to the training data.

[0121] It should be noted that CTGAN requires a large amount of real tabular data to train the model and generate synthetic data with similar statistical properties to the real data. For this reason, the data enhancement method proposed in this embodiment is: first, the test set data in the original data set is separated without any changes to facilitate the subsequent comparison of the prediction effect, and Gaussian noise is added to the training set in the original data set to enhance the basic training set; then, the training set after preliminary enhancement is used to train GTGAN; next, the trained GTGAN is used to generate new data; finally, the new data is combined with the preliminary enhanced training set for training the combustion prediction model. The proposed data enhancement method is as follows: Figure 7 shown.

[0122] In this embodiment, the inline four-stroke turbocharged WP14TDI engine bench test data provided includes data of 205 steady-state operating points, of which transient cylinder pressure data and transient heat release rate data are only tested and recorded at some engine operating points, and the remaining operating points only record CA10, CA50, and CA90 data to characterize combustion heat release. The basic parameters of the test engine are shown in Table 1. The test environment temperature is 23.9°C, the pressure is 105.6KPa, and the relative humidity is 42.62%.

[0123] Table 1 Basic parameters of WP14TDI engine

[0124]

[0125] Based on the active subspace method, the sensitivity of CA10, CA50 and CA90 to the eight-dimensional parameters of engine speed, intake pressure, intake temperature, excess air coefficient, natural gas injection timing, fuel injection timing, natural gas injection amount and fuel injection amount were analyzed respectively. The active variable weight diagram of the eight-dimensional parameters was drawn as shown in Figure 8 , Fig. 9 , Fig.10 As shown in the figure, it can be seen that the selected engine operating parameters have a certain degree of influence on CA10, CA50, and CA90 in the direction with higher sensitivity in the high-dimensional space. In order to further prove the rationality of the selected 8-dimensional parameters, a response surface model was established using the polynomial approximation method. Fig.11 , Fig.12 , Fig.13 The response surface model diagram shows the relationship between CA10, CA50, CA90 and activity variables. The orange area shows the maximum uncertainty at the 95% confidence level and the determination coefficient R 2 All of them are greater than 0.85, indicating that the selected 8-dimensional parameters can better predict the values ​​of CA10, CA50 and CA90 through the active subspace dimensionality reduction method combined with the response surface model construction method. This further proves that the selected 8-dimensional parameters have an important influence on the combustion process of the diesel / natural gas dual-fuel engine and can be used as input data for constructing a combustion prediction model.

[0126] The test apparent heat release rate data Substituting into equation (6) we can obtain the standardized experimental heat release rate: , using the multivariate nonlinear fitting fmincon function in Matlab Fitting is performed according to equation (7), while considering the constraints expressed by equations (9) and (10), and the values ​​of the parameters of the three-Weibull function are obtained. Figure 14-17The fitting effects of the heat release rate at speeds of 900rpm, 1200rpm, 1500rpm and 1800rpm are shown respectively. The curves represented by the three dotted lines describe the three combustion stages of premixed combustion, diffusion combustion and tail combustion respectively. The black solid line curve represents the total heat release rate curve obtained by superimposing the three dotted line curves. Its shape is basically consistent with the experimental heat release rate curve, indicating that the combustion heat release rate of the diesel / natural gas dual-fuel engine can be well described by the three-Weibull function.

[0127] Table 2 records the errors between the apparent heat release rate data obtained by fitting the three-Weibull function and the experimental heat release rate data at different speeds. The root mean square error RMSE is smaller than the average value of the experimental heat release rate data, and the determination coefficient R 2 The values ​​of are all greater than 0.98, which shows that the overall fitting effect of the three-Weibull function on the combustion heat release rate of the diesel / natural gas dual-fuel engine is good. The parameters of the three-Weibull function at different speeds can be used as output data for combustion prediction model training and testing.

[0128] Table 2 Error between apparent heat release rate data obtained by fitting three Weibull functions and experimental heat release rate data

[0129]

[0130] The combustion prediction model was built based on Python. The data set relied on by the model building consisted of engine operating parameters closely related to combustion and the parameters of the three-Weibull function obtained by fitting. The data set was divided into a training set and a test set by equidistant sampling, and the ratio of the training set to the test set was 4:1. K nearest neighbor regressor, random forest regressor, decision tree regressor, fully connected layer neural network, and support vector regressor were created in Python respectively, and the default hyperparameter values ​​of each algorithm model were used for preliminary training and prediction.

[0131] In order to evaluate the prediction performance of the model for the apparent combustion heat release rate, the error between the predicted three-Weibull function parameters and the three-Weibull parameters in the test set is not directly calculated, but the apparent combustion heat release rate is solved according to the predicted three-Weibull parameters, and finally the error between the heat release rate data and the experimental heat release rate is calculated, and this error is used as the evaluation index of the model prediction effect. Table 3 records the predicted heat release rate errors of each machine learning algorithm corresponding to some speeds in the test set. The speed distribution is selected from near idle speed to near rated speed. The verification range has good representativeness. Finally, the support vector regression (SVR) algorithm with the best comprehensive performance in prediction effect is selected for subsequent optimization and construction of the final combustion prediction model.

[0132] Table 3 Prediction heat release rate errors of each machine learning algorithm corresponding to some speeds in the test set

[0133]

[0134] SVR: Support Vector Regression, support vector regression is a regression method based on support vector machines. Its core idea is to build a regression model that can minimize errors and maximize intervals by finding support vectors. SVR uses kernel functions to map input features to high-dimensional feature space, so that it can handle nonlinear regression problems. Since kernel functions are used for feature mapping, SVR can handle high-dimensional data, avoid the dimensionality disaster problem, have good generalization ability for small sample data, and have high accuracy and stability. It is suitable for the characteristics of small samples, multi-dimensional input and output, and complex nonlinear regression of the target data set in this embodiment.

[0135] KNN: K-NearestNeighbor, K nearest neighbor, that is, each sample can be represented by its closest K neighboring values.

[0136] FCNN: Fully Connected Neural Network, fully convolutional neural network.

[0137] DT: Decision Tree. The decision tree algorithm is a commonly used machine learning model for classification and regression. It represents the data decision process in a tree structure.

[0138] The GridSearchCV method is used to optimize the SVR model. In the SVR model, the most important parameters are the penalty coefficient C of the error term, the kernel function type (kernel) and the kernel function coefficient gamma. The penalty coefficient C represents the tolerance for errors. The larger its value, the higher the fitting accuracy of the training set, but the weaker the generalization ability. In this embodiment, the penalty coefficient C is set to a value range of 10 in the grid search. -3 to 10 5 , with a step size of 10. The kernel function types suitable for nonlinear data mainly include poly, RBF, sigmoid, etc. The kernel function coefficient gamma controls the width of the kernel function. When training a smaller data set, selecting a larger gamma value can improve the model's fitting ability. In this embodiment, the value range of gamma is set to 10 -3 to 10 3 , with a step size of 10. Based on leave-one-out cross validation, the value R that minimizes the loss function 2 As the goal, automatically seek the optimal combination of C, kernel and gamma. Table 4 shows the configuration of the optimal hyperparameter combination.

[0139] Table 4 SVR optimal hyperparameter combination configuration

[0140]

[0141] Call the saved optimized SVR model, provide the engine operating parameters in the test set as input data to the model, and the model outputs the predicted three-Weibull function parameters, further obtain the predicted apparent heat release rate curve, and calculate the determination coefficient R of the test apparent heat release rate curve 2 . 2 A value greater than 0.95 is used as the evaluation standard for the qualified prediction accuracy of the model. If the model fails, it is retrained on the training set until the model meets the accuracy requirements.

[0142] Figure 18-Figure 21 The prediction effect of the optimized SVR model at some speeds in the test set is demonstrated. It can be seen that the prediction accuracy of the trained and optimized SVR combustion prediction model remains at a high level in the speed range from near idle speed to near rated speed of the dual-fuel engine.

[0143] Table 5 shows the prediction error of the optimized SVR model at some speeds in the test set. Compared with the results in Table 4, the prediction error RMSE is reduced overall, and the determination coefficient R 2 There is a certain improvement, indicating that the GridSearchCV method can effectively optimize the prediction performance of the model.

[0144] Table 5 Prediction error of the optimized SVR model at some speeds in the test set

[0145]

[0146] Since the target data set is small and the samples are not diverse enough, the model may not be able to fully learn the real features behind the data, resulting in poor generalization of the model. To this end, this embodiment uses the proposed data enhancement method in Python to expand the sample of the original data set. First, by adding Gaussian noise to the original training set, the number of training set samples is doubled to obtain a preliminary enhanced data set. Then, a CTGAN object is created, the fit method is called, and the preliminary enhanced data set is input for training the CTGAN model; the number of training rounds is set to 100,000 rounds. In each round of training, the model updates the parameters to approximate the distribution of the real data; the sample method is called, and the target number of samples generated is set to 1000 to generate a synthetic data set containing 1000 samples. The data sets obtained in the two steps are merged to finally obtain an enhanced data set for optimizing the training of the combustion prediction model. Using the enhanced training set, the optimization and training process of the combustion prediction model is repeated.

[0147] Table 6 shows the error of the heat release rate prediction of the SVR combustion prediction model after data enhancement at four operating points in the original test set. It can be seen that after data enhancement, the SVR combustion prediction model still shows a high prediction accuracy on the original test set, indicating that the samples synthesized by the proposed data enhancement method effectively learn the distribution characteristics of the original samples.

[0148] Table 6 Prediction error of the SVR combustion prediction model at some operating points in the original test set after data enhancement

[0149]

[0150] The data-enhanced SVR combustion prediction model was verified on 205 test operating points, and the apparent heat release rate data of the 205 operating points were predicted and calculated. Since some operating points only recorded CA10, CA50, and CA90 data to characterize combustion heat release, after obtaining the predicted apparent heat release rate data of 205 operating points, the predicted CA10, CA50, and CA90 values ​​were further calculated for comparison with the test data. Figure 22-Figure 24 The distribution of absolute errors between the predicted values ​​and the experimental values ​​of CA10, CA50 and CA90 is shown. It can be seen that except for a few operating points where the deviation between the predicted value of CA10 and the experimental value is less than 3°, the predicted values ​​of CA10, CA50 and CA90 at most operating points have a deviation of less than 1° from the experimental value, which is consistent with the prediction error accuracy of CA10, CA50 and CA90 by Jiancun Hu, Seokwon Cho, Qifan Wang and others, indicating that the SVR combustion prediction model after data enhancement has good generalization ability and can be simulated within the entire engine operating range.

[0151] Figure 2 Schematic diagram of a low-carbon engine multi-stage heat release rate prediction model training system in an embodiment of the present invention. Figure 1 The low-carbon engine multi-stage heat release rate prediction model training method corresponds to Figure 2 As shown, the low-carbon engine multi-stage heat release rate prediction model training system in this embodiment may include:

[0152] A parameter acquisition module 201 is used to acquire engine operating parameters and combustion characteristic parameters of a set dimension;

[0153] A weight calculation module 202, which is used to calculate the normalized activity score of each dimension of the engine operating condition parameter to the combustion characteristic parameter by using the active subspace sensitivity analysis method, and use it as the weight of the corresponding dimension of the engine operating condition parameter;

[0154] A data set construction module 203 is used to weight each dimension of the engine operating condition parameter according to its corresponding weight, and then combine it with the combustion heat release rate fitted by the three-Weibull function to form a data set;

[0155] A model training module 204, which uses the data set to fine-tune the preliminarily trained heat release rate prediction model to obtain a multi-stage heat release rate prediction model for a low-carbon engine;

[0156] In the initial training process of the heat release rate prediction model, the natural gas data in the training samples are pseudo natural gas data formed by converting the calorific value of the secondary injection in the diesel engine test data into equivalent natural gas mass.

[0157] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for training a multi-stage heat release rate prediction model for a low-carbon engine, characterized in that: include: Obtaining engine operating parameters and combustion characteristic parameters of set dimensions; Active subspace sensitivity analysis method is used to calculate the normalized activity score of each dimension of engine operating parameters on combustion characteristic parameters, and used as the weight of the corresponding dimension of engine operating parameters; The normalized activity score of each dimension of the engine operating condition parameter on the combustion characteristic parameter is: in, It represents the normalized activity score of each dimension of engine operating condition parameter on the combustion characteristic parameter; Indicates the first dimensions; m is the dimension of the input parameter; n is the number of eigenvalues; Indicates the activity score of each dimension of engine operating condition parameter on combustion characteristic parameter; is the characteristic value; represents the eigenvector matrix Line List elements; The engine operating parameters of each dimension are weighted according to their corresponding weights, and then combined with the combustion heat release rate fitted by the three-Weibull function to form a data set; The three-Weibull function fits the combustion heat release rate: The superscript Pick They represent the premixed combustion stage, the main combustion stage and the tail combustion stage respectively; is the combustion efficiency index; Indicates the starting point of combustion; Indicates the duration of combustion; represents the shape factor; Indicates the combustion ratio; is the normalized combustion heat release rate expressed using the three-Weibull function; Indicates the crankshaft angle; The data set is used to fine-tune the preliminarily trained heat release rate prediction model to obtain a multi-stage heat release rate prediction model for low-carbon engines. In the initial training process of the heat release rate prediction model, the natural gas data in the training samples are pseudo natural gas data formed by converting the calorific value of the secondary injection in the diesel engine test data into equivalent natural gas mass.

2. The low-carbon engine multi-stage heat release rate prediction model training method according to claim 1, characterized in that: In optimizing the parameters of the three Weibull functions , , and In the process, the objective function is constructed to minimize the gap between the heat release rate predicted by the model and the actual heat release rate data; the expression of the objective function is In the formula, is the total loss; , , , is a weight parameter used to adjust the balance between the overall error and the feature point error; , , In the corresponding fitted heat release rate curve, the crankshaft angle positions where the cumulative heat release rates reach 10%, 50%, and 90% respectively; , , is the test value of the combustion characteristic point; is the predicted value vector calculated according to the model, is the parameter vector to be optimized, The model is Input data, is the test data, is the number of data points; is the function that minimizes the residual sum of squares.

3. The low-carbon engine multi-stage heat release rate prediction model training method according to claim 1, characterized in that: The engine operating parameters include eight parameters: engine speed, excess air coefficient, intake pressure, intake temperature, fuel injection amount, natural gas injection amount, fuel injection timing and natural gas injection timing.

4. The low-carbon engine multi-stage heat release rate prediction model training method according to claim 1, characterized in that: The combustion characteristic parameters include the crankshaft angles corresponding to 10%, 50% and 90% fuel combustion.

5. The low-carbon engine multi-stage heat release rate prediction model training method according to claim 1, characterized in that: During the initial training of the heat release rate prediction model, adversarial network enhanced training samples are generated based on the condition table.

6. A low-carbon engine multi-stage heat release rate prediction model training system, characterized in that: include: A parameter acquisition module, which is used to obtain engine operating parameters and combustion characteristic parameters of a set dimension; A weight calculation module, which is used to calculate the normalized activity score of each dimension of the engine operating condition parameter to the combustion characteristic parameter by using the active subspace sensitivity analysis method, and use it as the weight of the corresponding dimension of the engine operating condition parameter; The normalized activity score of each dimension of the engine operating condition parameter on the combustion characteristic parameter is: in, It represents the normalized activity score of each dimension of engine operating condition parameter on the combustion characteristic parameter; Indicates the first dimensions; m is the dimension of the input parameter; n is the number of eigenvalues; Indicates the activity score of each dimension of engine operating condition parameter on combustion characteristic parameter; is the characteristic value; represents the eigenvector matrix Line List elements; A data set construction module, which is used to weight the engine operating parameters of each dimension according to their corresponding weights, and then combine them with the combustion heat release rate fitted by the three-Weibull function to form a data set; The three-Weibull function fits the combustion heat release rate: The superscript Pick They represent the premixed combustion stage, the main combustion stage and the tail combustion stage respectively; is the combustion efficiency index; Indicates the starting point of combustion; Indicates the duration of combustion; represents the shape factor; Indicates the combustion ratio; is the normalized combustion heat release rate expressed using the three-Weibull function; Indicates the crankshaft angle; A model training module, which uses the data set to fine-tune the preliminarily trained heat release rate prediction model to obtain a multi-stage heat release rate prediction model for a dual-fuel low-carbon engine; In the initial training process of the heat release rate prediction model, the natural gas data in the training samples are pseudo natural gas data formed by converting the calorific value of the secondary injection in the diesel engine test data into equivalent natural gas mass.

7. The low-carbon engine multi-stage heat release rate prediction model training system according to claim 6, characterized in that: In the weight calculation module, the normalized activity score of each dimension of engine operating condition parameter on the combustion characteristic parameter is: in, It represents the normalized activity score of each dimension of engine operating condition parameter on the combustion characteristic parameter; Indicates the first dimensions; m is the dimension of the input parameter; n is the number of eigenvalues; Indicates the activity score of each dimension of engine operating condition parameter on combustion characteristic parameter; is the characteristic value; represents the eigenvector matrix Line Column elements.

8. The low-carbon engine multi-stage heat release rate prediction model training system according to claim 6, characterized in that: In the parameter acquisition module, the engine operating parameters include eight parameters, namely, engine speed, excess air coefficient, intake pressure, intake temperature, fuel injection amount, natural gas injection amount, fuel injection timing and natural gas injection timing.

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