A method for optimizing and calibrating engine transient performance based on response surface design

Abstract

This invention relates to the field of engine performance calibration technology, and provides a method for optimizing and calibrating engine transient performance based on response surface design. The method includes the following steps: setting decision variables and target variables to construct an experimental matrix; conducting experimental tests based on the test matrix; fitting and evaluating a quadratic model; simplifying and selecting the fitted model; performing predictive optimization calculations and experimental verification; and performing full-condition Map calibration over a speed range. This method can be practically applied to transient performance optimization during engine R&D testing, optimizing engine performance during real-vehicle operation, and intuitively demonstrating the validity of test data through mathematical models, without requiring excessive testing resources.

Description

Technical Field

[0001] This invention belongs to the field of engine performance calibration technology, and in particular relates to an engine transient performance optimization calibration method based on response surface design. Background Technology

[0002] Transient operating conditions of automotive engines are increasingly considered key to understanding engine performance and emissions. During environmental regulation testing and real-world vehicle operation, most operating conditions are transient—that is, constantly changing conditions, such as acceleration, deceleration, or load changes. Due to the delay in intake response, these conditions significantly affect engine performance, as well as particulate matter and nitrogen oxides (NOx). x The formation of emissions such as [missing information]. A major focus of diesel engine transient operating condition research is the transition in performance from steady-state to transient conditions, particularly in fuel economy and emission control. Various test results indicate that boundary parameters of transient conditions, such as injection timing and injection pressure, influence combustion parameters, thus establishing a relationship between them and changes in emission concentration. During actual engine operation, all parameters are based on pre-calibrated maps; therefore, actual engine performance is directly related to the calibrated maps. Traditional engine map calibration is performed under steady-state conditions, where all input parameters are constant, and the optimal points of each parameter are found to derive an optimal map under steady-state conditions. However, real-world vehicle operation often involves varying parameters and operating conditions, which can lead to significant deterioration in fuel consumption and emissions under severe conditions. Furthermore, the calibration of these traditional maps requires testing at all operating points, which is time-consuming and labor-intensive.

[0003] Response surface methodology (RSM) is a set of statistical and mathematical techniques for developing, improving, and optimizing processes. It significantly reduces the number of experiments required to evaluate combinations of variables and creates predictive models that effectively capture the interactions between variables. In the context of diesel engines, this approach explores the relationship between input factors, such as injection timing and injection pressure, and engine performance indicators. Therefore, by combining defined transient calibration parameters, a set of optimization maps based on transient calibration can be developed, which can be better applied to actual engine operation. Summary of the Invention

[0004] The purpose of this invention is to provide a method for optimizing and calibrating the transient performance of an engine based on response surface design, aiming to solve the problems mentioned in the background art.

[0005] The present invention is implemented as follows: a method for optimizing and calibrating the transient performance of an engine based on response surface design, comprising the following steps:

[0006] Step 1: Set decision variables and target variables to construct the experimental matrix;

[0007] Step 2: Conduct experimental tests based on the test matrix;

[0008] Step 3: Fit and evaluate the quadratic model;

[0009] Step 4: Simplify and select the fitting model;

[0010] Step 5: Perform prediction optimization calculations and experimental verification;

[0011] Step 6: Perform full-condition Map calibration within the speed range.

[0012] In a further technical solution, step 1 includes the following specific steps:

[0013] Engine developers determine the engine's input and output parameters based on the transient operating conditions they are studying, defining them as decision variables and target variables, respectively.

[0014] The experimental matrix is ​​designed using an orthogonal approach. Assuming three parameters A, B, and C, the experimental matrix design is based on the following:

[0015] ;

[0016] ;

[0017] ;

[0018] ;

[0019] Where c is the center point, i.e., the point where all parameters are at level 0; the center point is typically repeated 3-5 times. k One decision variable, number of experiments n Then it is:

[0020] ;

[0021] Based on the above rules, an experimental scheme was designed, and the test order was randomly shuffled to construct an experimental matrix.

[0022] A further technical solution involves 3-6 decision variables, which are divided into 3 levels according to the research scope using the Box-Behnken method: -1, 0, and 1. The decision variables include engine speed and load rate, providing a basis for quickly developing a transient map. The engine speed is set with upper and lower limits based on the research speed range, and the load rate is the rate at which the engine loads from 0% to 100% at a constant speed, set in terms of torque per second, load ratio per second, or process loading time.

[0023] A further technical solution, for the target variable, provides the following defined parameters:

[0024] The effective fuel consumption rate and indicated thermal efficiency when the load reaches 50% during the transient process, along with their corresponding variable coefficients under steady-state conditions, are used as performance indicators; the time when the loaded load reaches 99% is used as the settling time, and the CO and NO values ​​during the settling time are used as the settling time. x The average emission concentration of Soot during the process is used as the emission index;

[0025] Effective fuel consumption rate variable coefficient The calculation formula is as follows:

[0026] ;

[0027] in, The effective fuel consumption rate under transient operating conditions at 50% load is expressed in g / kWh. The effective fuel consumption rate under 50% load in steady-state operating conditions is expressed in g / kWh.

[0028] Indicator coefficients for thermal efficiency:

[0029] ;

[0030] Average CO emission concentration during the process:

[0031] ;

[0032] NO x Process average emission concentration:

[0033] ;

[0034] Average emission concentration during the Soot process:

[0035] ;

[0036] in, Real-time emission concentrations of CO, NOx, and Soot; The time at 99% load; This is the start time of loading.

[0037] A further technical solution involves, in step 2, testing based on the experimental matrix, matching the recorded target variables with the decision variables in the test matrix, and rearranging them according to the order of change of the decision variables to prepare for fitting.

[0038] In a further technical solution, step 3 includes the following specific steps:

[0039] The general form of the quadratic form model is:

[0040] ;

[0041] in, and For the parameters to be estimated, and For the first i and j One decision variable, For random errors; written in matrix form:

[0042] ;

[0043] in, y for The target vector, X is The design matrix , for The parameter vector, for The error vector satisfies ;

[0044] Minimize the sum of squared residuals using least squares estimation:

[0045] ;

[0046] Solve for parameter estimation:

[0047] right Taking the derivative and setting it to zero, we obtain the normal equation:

[0048] ;

[0049] ;

[0050] like If it is invertible, then the parameter estimate is:

[0051] ;

[0052] Then, for each objective variable, the quadratic model is:

[0053] ;

[0054] Model evaluation index calculation:

[0055] Decompose and calculate the sum of squares of the data:

[0056] ;

[0057] in, The sum of squares is denoted as , and the fluctuation of the response value around the mean is denoted as . is the regression sum of squares, and is the difference between the fitted value and the mean; The sum of squared residuals is the deviation between the predicted and actual values; the standard deviation of the residuals is:

[0058] ;

[0059] So the determination coefficient :

[0060] ;

[0061] To avoid overfitting, insignificant variables in the model are penalized by introducing an adjustment coefficient. :

[0062] ;

[0063] Then the prediction coefficient value for:

[0064] ;

[0065] ;

[0066] in, To predict the sum of squared residuals, To remove the first i The predicted value after refitting after one sample;

[0067] Perform the following assumptions test:

[0068] Null hypothesis: The model parameters are not significant;

[0069] Alternative hypothesis: The model parameters are significant;

[0070] calculate value:

[0071] ;

[0072] The calculated The corresponding P-value is obtained by looking up the value in the table. If the P-value is less than the significance level, the null hypothesis can be rejected.

[0073] Introducing the coefficient of variation Value, quantifying the magnitude of prediction error:

[0074] ;

[0075] Introducing Adaptation Precision This measures the balance between the predictive power and complexity of a model.

[0076] ;

[0077] For each target variable, the parameter evaluation is summarized. If the evaluation parameters show good results, the next calculation is performed. Otherwise, the data is checked for errors. If the data is incorrect, a correction test is performed. If the data is correct but the performance evaluation is poor, it indicates that the decision variable is not correlated with the target variable.

[0078] Further technical solutions, A value above 0.8 indicates a well-fitting model. A value not exceeding 10% is considered to indicate that the model's dispersion is within an acceptable range. A value greater than 4 indicates that the model is considered ideal.

[0079] In a further technical solution, step 4 includes the following steps:

[0080] Following Occam's razor principle, which states that unnecessary items should not be added, the model is simplified to avoid overfitting. Insignificant terms in the model are removed to obtain a simplified model. By comparing the above evaluation parameters, the simplified model is selected first if the performance does not deteriorate; otherwise, the original model is maintained.

[0081] In a further technical solution, step 5 includes the following steps:

[0082] For the target variable that needs optimization, its fitted model is transformed into the expected value. Perform multi-objective optimization; for a single-objective expectation function, define the optimization objective and constraints, and maximize the objective:

[0083] ;

[0084] When minimizing the objective:

[0085] ;

[0086] in s For shape parameters, when s When = 1, the expected function changes linearly; when s When >1, the expected function is a convex function; when s When <1, the expected function is concave. The overall expected function is:

[0087] ;

[0088] in, Assign importance, and set the importance of the target variable according to the requirements;

[0089] Maximize using gradient descent :

[0090] Set an initial point , where is the value of the decision variable at the start of the iteration, and is denoted as during the iteration. Randomly select or specify any point and set the learning rate. Maximum number of iterations, set convergence threshold When the parameter change is less than the threshold, convergence is considered achieved, and iteration stops.

[0091] During the iteration process, the overall expected function of the target variable is calculated and its gradient is determined at each iteration point. For each decision variable Calculate its partial derivatives:

[0092] ;

[0093] Update variables:

[0094] ;

[0095] when Stop iterating when the time comes;

[0096] List the operating points under the maximum overall expectation function, i.e. the optimal operating points predicted by the model; proceed according to the decision variables of the optimal operating points or other predicted operating points.

[0097] A further technical solution involves, in step 6, formulating the transient operating condition optimization map by performing full-condition optimization under constant speed and constant load rate. During optimization, the importance is set according to the required target performance, and the engine speed is set to a fixed speed starting from the lower limit of the research range, while the optimization prediction begins with a variable load rate. Then, the speed is gradually increased at 100 r / min intervals, and the engine load rate gradually changes according to the requirements to perform optimization prediction and establish the transient operating condition optimization map.

[0098] This invention provides an engine transient performance optimization and calibration method based on response surface design. This method can be practically applied to the performance calibration during engine R&D testing. It can optimize the engine performance during actual vehicle operation and intuitively display the validity of test data with a mathematical model without requiring excessive testing resources. Attached Figure Description

[0099] Figure 1 A flowchart of an engine transient performance optimization and calibration method based on response surface design is provided for an embodiment of the present invention;

[0100] Figure 2 Maps are retrieved for actual application conditions. Detailed Implementation

[0101] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0102] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.

[0103] like Figure 1 As shown, an embodiment of the present invention provides a method for optimizing and calibrating the transient performance of an engine based on response surface design, comprising the following steps:

[0104] Step 1: Set decision variables and target variables to construct the experimental matrix;

[0105] Step 2: Conduct experimental tests based on the test matrix;

[0106] Step 3: Fit and evaluate the quadratic model;

[0107] Step 4: Simplify and select the fitting model;

[0108] Step 5: Perform prediction optimization calculations and experimental verification;

[0109] Step 6: Perform full-condition Map calibration within the speed range.

[0110] In a preferred embodiment of the present invention, step 1 includes the following specific steps:

[0111] Engine developers determine the engine's input and output parameters based on the transient operating conditions they are studying, defining them as decision variables and target variables, respectively.

[0112] The experimental matrix is ​​designed using an orthogonal approach. For example, with three parameters A, B, and C, the experimental matrix design is based on the following:

[0113] ;

[0114] ;

[0115] ;

[0116] ;

[0117] Where c is the center point, i.e., the point where all parameters are at level 0; the center point is typically repeated 3-5 times. k One decision variable, number of experiments n Then it is:

[0118] ;

[0119] Based on the above rules, an experimental scheme was designed, and the test order was randomly shuffled to construct an experimental matrix.

[0120] In this embodiment of the invention, the decision variables are generally 3-6 parameters, which are divided into 3 levels according to the research scope using the Box-Behnken method: -1, 0, and 1. It is recommended to include engine speed and load rate as decision variables to provide a basis for quickly developing transient maps. The engine speed is set with upper and lower limits based on the research speed range, generally within the range of 800 r / min to 2200 r / min. The load rate is the rate at which the engine loads from 0% to 100% at a constant speed, and is set in terms of loading torque per second (Nm / s), load ratio per second (% / s), or process loading time (s).

[0121] For the target variable, the following parameters are defined, which users can extend according to their actual needs:

[0122] The effective fuel consumption rate and indicated thermal efficiency when the load reaches 50% during the transient process, along with their corresponding variable coefficients under steady-state conditions, are used as performance indicators. The time to reach 99% load is defined as the settling time, and the CO and NO values ​​during this settling time are used as the performance indicators. x The average emission concentration of Soot during the process is used as the emission index.

[0123] Effective fuel consumption rate variable coefficient The formula for calculating (%) is as follows:

[0124] ;

[0125] in The effective fuel consumption rate under transient operating conditions at 50% load is expressed in g / kWh. The effective fuel consumption rate under 50% load in steady-state operating conditions is expressed in g / kWh.

[0126] Indicator of thermal efficiency variable coefficient (%):

[0127] ;

[0128] Average CO emission concentration (unit: ppm):

[0129] ;

[0130] NO x Average emission concentration (per ppm):

[0131] ;

[0132] Average emission concentration during the Soot process (unit: 10¹²n / cc):

[0133] ;

[0134] in Real-time emission concentrations of CO, NOx, and Soot; The time at 99% load, in seconds; The start time of loading, in seconds.

[0135] In a preferred embodiment of the present invention, in step 2, the test is performed according to the experimental matrix, and the recorded target variables are matched with the decision variables in the test matrix; the decision variables are rearranged according to the order of change to prepare for fitting.

[0136] In a preferred embodiment of the present invention, step 3 includes the following specific steps:

[0137] Quadratic models can describe the nonlinear relationship between the target variable and multiple decision variables, and their general form is:

[0138] ;

[0139] in, and For the parameters to be estimated, and For the first i and j One decision variable, For random errors; written in matrix form:

[0140] ;

[0141] in, y for The target vector, X is The design matrix , for The parameter vector, for The error vector satisfies .

[0142] Minimize the sum of squared residuals using least squares estimation:

[0143] ;

[0144] Solve for parameter estimation:

[0145] right Taking the derivative and setting it to zero, we obtain the normal equation:

[0146] ;

[0147] ;

[0148] like If it is invertible, then the parameter estimate is:

[0149] ;

[0150] Then, for each objective variable, the quadratic model is:

[0151] ;

[0152] Model evaluation index calculation:

[0153] Decompose and calculate the sum of squares of the data:

[0154] ;

[0155] in, The sum of squares is denoted as , and the fluctuation of the response value around the mean is denoted as . is the regression sum of squares, and is the difference between the fitted value and the mean; Let be the sum of squared residuals, representing the deviation between the predicted and actual values. The standard deviation of the residuals is then:

[0156] ;

[0157] So the determination coefficient :

[0158] ;

[0159] To avoid overfitting, insignificant variables in the model are penalized by introducing an adjustment coefficient. :

[0160] ;

[0161] Then the prediction coefficient value for:

[0162] ;

[0163] ;

[0164] in, To predict the sum of squared residuals, To remove the first i The predicted value after refitting after 100 samples.

[0165] The following assumptions are usually made test:

[0166] Null hypothesis (H0): The model parameters are not significant.

[0167] Alternative hypothesis (H1): The model parameters are significant.

[0168] calculate value:

[0169] ;

[0170] The calculated The corresponding P-value is obtained by looking up the value in the table. If the P-value is less than the significance level (usually 0.05), the null hypothesis can be rejected.

[0171] Introducing the coefficient of variation Value (%), quantifying the magnitude of prediction error:

[0172] ;

[0173] Introducing Adaptation Precision This measures the balance between the predictive power and complexity of a model.

[0174] ;

[0175] For each target variable, the parameter evaluation is summarized. If the evaluation parameters show good results, the next calculation is performed. Otherwise, the data needs to be checked for errors. If the data is incorrect, a correction test is required. If the data is correct but the performance evaluation is poor, it means that the decision variable is not correlated with the target variable.

[0176] In an embodiment of the present invention, A value above 0.8 indicates a well-fitting model. A value not exceeding 10% is considered to indicate that the model's dispersion is within acceptable limits. The larger the value, the better the model's predictive ability at a given complexity. Generally, a value greater than 4 indicates that the model is ideal, which means that the model has a good signal-to-noise ratio and can effectively predict the response variable.

[0177] In a preferred embodiment of the present invention, step 4 includes the following steps:

[0178] Following Occam's Razor principle—that is, not adding unnecessary terms—the model is simplified to avoid overfitting. Insignificant terms are removed to obtain a simplified model. By comparing the evaluation parameters, the simplified model is selected first if performance does not deteriorate; otherwise, the original model is maintained.

[0179] In a preferred embodiment of the present invention, step 5 includes the following steps:

[0180] For the target variable that needs optimization, its fitted model is transformed into the expected value. Perform multi-objective optimization. For a single-objective expectation function, define the optimization objective and constraints, and maximize the objective:

[0181] ;

[0182] When minimizing the objective:

[0183] ;

[0184] in s For shape parameters, when s When = 1, the expected function changes linearly; when s When >1, the expected function is a convex function; when s When <1, the expected function is concave. The overall expected function is:

[0185] ;

[0186] in, Users can set the importance of the target variable according to their needs.

[0187] Maximize using gradient descent :

[0188] Set an initial point , where is the value of the decision variable at the start of the iteration, and is denoted as during the iteration. The learning rate can be set by randomly selecting or specifying any point. For example, 0.01, the maximum number of iterations, such as 1000, sets the convergence threshold. For example, in 1e-6, when the parameter change is less than the threshold, it is considered to have converged and the iteration stops.

[0189] During the iteration process, the overall expected function of the target variable is calculated and its gradient is determined at each iteration point. For each decision variable Calculate its partial derivatives:

[0190] ;

[0191] Update variables:

[0192] ;

[0193] when Stop iterating when the time is right.

[0194] List the operating points under the maximum overall expected value function, i.e., the optimal operating points predicted by the model. Then proceed with the decision variables based on the optimal operating point or other predicted operating points.

[0195] In a preferred embodiment of the present invention, in step 6, the transient operating condition optimization map is formulated by performing full-condition optimization under constant speed and constant load rate. During optimization, the importance of the target performance is set according to the desired performance; for example, the importance of engine thermal efficiency and fuel consumption is set to 5, and other performance parameters are set to 3. Simultaneously, the engine speed is set to a fixed speed starting from the lower limit of the research range, such as 800 r / min, and optimization prediction begins with a variable load rate. Then, the speed is gradually increased at 100 r / min intervals, and the engine load rate gradually changes according to the requirements, performing optimization prediction to establish the transient operating condition optimization map.

[0196] The following is a specific embodiment to verify the effectiveness of this method:

[0197] A 6-cylinder diesel engine was tested under three decision variables: engine speed 900-1300 r / min, loading time 3-7 s, and injection advance angle -2-2°. The experimental design matrix, model evaluation parameters, and significance analysis are shown in Tables 1-3 below.

[0198] Table 1 Experimental Design Matrix

[0199]

[0200] Table 2 Model Evaluation Parameters

[0201]

[0202] Table 3. Significance Analysis of Simplified Model

[0203]

[0204] In Table 3, all target variables fit the model significantly, Co BSFC Although the p-value of the AC interaction term is higher than 0.05, it is not significantly higher and is retained to ensure structural integrity. CO Removing the three interaction terms would affect model performance, so they are retained, mE NOx andmE Soot The interaction coefficients were all significant. Furthermore, Co... BSFC Co BTE andmE Soot The linear and second-order coefficients are significant. For Co BSFC R 2 A value of 0.980, which is close to 1, indicates the accuracy and adequacy of the model. Value (0.965) and The values ​​(0.918) are all relatively large, indicating that the model has good predictive ability. BSFC The fit precision is 24.3, and the coefficient of variation is 6.05. Based on the residuals, standard deviation, and mean, the model is considered effective. Similarly, Co... BTE mE CO mE NOx andmE Soot The model parameter evaluation (Table 2) summarizes the results. The values ​​are all above 0.85, and the fit accuracy is much greater than 4, indicating that each model has appropriate accuracy. Furthermore, the dispersion of residuals, standard deviations, means, and coefficients of variation is within acceptable ranges. The simplified and screened regression equation is as follows:

[0205] ;

[0206] ;

[0207] ;

[0208] ;

[0209] ;

[0210] The model validation analysis is shown in Table 4, with Co set. BSFC With Co ITE The transient performance optimization map, with an importance of 5 and each emission index of 3, is shown in Table 5. Figure 2 'a' is a curve representing a certain actual operating condition. Figure 2 b is the injection advance angle reading curve after converting torque changes into loading time and applying transient performance optimization Map.

[0211] Table 4 Range of Decision Variables

[0212]

[0213] Table 5. Defining the Transient Optimization Map

[0214]

[0215] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing and calibrating the transient performance of an engine based on response surface design, characterized in that, Includes the following steps: Step 1: Set decision variables and target variables to construct the experimental matrix; Step 2: Conduct experimental tests based on the test matrix; Step 3: Fit and evaluate the quadratic model; Step 4: Simplify and select the fitting model; Step 5: Perform prediction optimization calculations and experimental verification; Step 6: Perform full-condition Map calibration within the speed range; For the target variable, the parameters are defined as follows: The effective fuel consumption rate and indicated thermal efficiency when the load reaches 50% during the transient process, along with their corresponding variable coefficients under steady-state conditions, are used as performance indicators; the time it takes for the loaded load to reach 99% is used as the settling time, and the CO and NO values ​​during the settling time are used as the settling time. x The average emission concentration of Soot during the process is used as the emission index; Effective fuel consumption rate variable coefficient Co BSFC The calculation formula is as follows: Co BSFC =((BSFC tr -BSFC st ) / BSFC st Among them, BSFC tr Effective fuel consumption rate under transient operating conditions at 50% load, unit: g / kwh; BSFC st The effective fuel consumption rate under 50% load in steady-state operating conditions is expressed in g / kWh. Indicator coefficients for thermal efficiency: Co ITE =(ITE tr -ITE st ) / ITE st Average CO emission concentration during the process: NO x Process average emission concentration: Average emission concentration during the Soot process: Where t2 is the time at 99% load; t1 is the start time of loading; Step 3 includes the following specific steps: The general form of the quadratic form model is: Among them, β0, β i β ii and β ij Let x be the parameter to be estimated. i and x j Let be the i-th and j-th decision variables, and e be the random error; written in matrix form: y = Xβ + e Where y is the n×1 target vector and X is the n×p design matrix. Let β be a p×1 parameter vector, and e be an n×1 error vector, satisfying ∈ i ~N(0,σ 2 ); Minimize the sum of squared residuals using least squares estimation: RSS=e T e=(y-Xβ) T (y-Xβ) =y T y-2β T X T y+β T X T Xβ Solve for parameter estimation: Taking the derivative with respect to β and setting it to 0, we obtain the normal equation: X T y=X T Xβ If X T If X is invertible, then the parameter estimate is: Then, for each objective variable, its quadratic model is: Model evaluation index calculation Decompose and calculate the sum of squares of the data: Where TSS is the total sum of squares, representing the fluctuation of the response value around the mean; SSR is the regression sum of squares, representing the difference between the fitted value and the mean; SSE is the residual sum of squares, representing the deviation between the predicted value and the actual value; and the residual standard deviation is: Then the determination coefficient R 2 : To avoid overfitting, insignificant variables in the model are penalized by introducing an adjustment coefficient R. 2 adj : Then the prediction coefficient value R 2 pred for: Where PRESS is the sum of squared predicted residuals. The predicted value after refitting after removing the i-th sample; Perform an F-test on the following hypotheses: Null hypothesis: The model parameters are not significant; Alternative hypothesis: The model parameters are significant; Calculate the F-value: Find the corresponding P-value from the table for the calculated F-value. If the P-value is less than the significance level, reject the null hypothesis. Introducing the coefficient of variation (CV) to quantify the magnitude of prediction error: Introducing adaptive accuracy (AP) to measure the balance between the model's predictive power and complexity: For each target variable, the parameter evaluation is summarized. If the evaluation parameters show good results, the next calculation is performed. Otherwise, the data needs to be checked for errors. If the data is incorrect, a correction test is performed. If the data is correct but the performance evaluation is poor, it means that the decision variable is not correlated with the target variable. Step 5 includes the following steps: For the target variable that needs optimization, its fitted model is transformed into the expected value d. i For multi-objective optimization within the range [0,1], and for a single-objective expectation function, define the optimization objective and constraints, maximizing the objective as follows: When minimizing the objective: Where s is the shape parameter, the expectation function is linear when s = 1, convex when s > 1, and concave when s < 1; the overall expectation function is: Where, ω i Assign importance, and set the importance of the target variable according to the requirements; Maximize D using gradient descent: Let an initial point x0 be set, which is the value of the decision variable at the start of the iteration, and denoted as x during the iteration process. t Randomly select or specify any point, set the learning rate α, the maximum number of iterations, and the convergence threshold ε. When the parameter change is less than the threshold, it is considered to have converged and the iteration stops. During the iteration process, the overall expected function of the target variable is calculated and its gradient is determined at each iteration point. For each decision variable x j Calculate its partial derivatives: Update variables: When ||x t+1 -x t Stop iteration when || < ε; List the operating points under the maximum overall expectation function, i.e., the optimal operating points predicted by the model; proceed according to the decision variables of the optimal operating points or other predicted operating points; In step 6, the transient operating condition optimization map is formulated by performing full-condition optimization under constant speed and constant load rate. During optimization, the importance is set according to the required target performance, and the engine speed is set to a fixed speed starting from the lower limit of the research range, and the optimization prediction starts with a variable load rate. Then, the speed is gradually increased at intervals of 100 r / min, and the engine load rate is gradually changed according to the requirements to perform optimization prediction and establish the transient operating condition optimization map. The study incorporates engine speed and load rate as decision variables, providing a basis for rapidly developing transient maps.

2. The engine transient performance optimization and calibration method based on response surface design according to claim 1, characterized in that, Step 1 includes the following specific steps: Engine development users determine the engine's input and output parameters based on the transient operating conditions they want to study, defining them as decision variables and target variables, respectively. The experimental matrix is ​​designed using an orthogonal approach. Assuming three parameters A, B, and C, the experimental matrix design is based on the following: A = ±1, B = ±1, C = 0; A = ±1, C = ±1, B = 0; B = ±1, C = ±1, A = 0; c: A = 0, B = 0, C = 0; Where c is the center point, i.e., the point where all parameters are at level 0, and the center point is repeated 3-5 times; for k decision variables, the number of experiments n is: n = 2k(k-1) + c Based on the above rules, an experimental scheme was designed, and the test order was randomly shuffled to construct an experimental matrix.

3. The engine transient performance optimization and calibration method based on response surface design according to claim 2, characterized in that, The decision variables consist of 3-6 parameters, which are divided into 3 levels according to the research scope using the Box-Behnken method: -1, 0, and 1. The engine speed is set with upper and lower limits based on the research speed range, and the loading rate is the rate at which the engine loads from 0% to 100% at a constant speed, which is set in terms of loading torque per second, load loading ratio per second, or process loading time.

4. The engine transient performance optimization and calibration method based on response surface design according to claim 1, characterized in that, In step 2, tests are conducted based on the experimental matrix, and the recorded target variables are matched with the decision variables in the test matrix; the decision variables are then rearranged according to their order of change to prepare for fitting.

5. The engine transient performance optimization and calibration method based on response surface design according to claim 1, characterized in that, R 2 A value above 0.8 indicates a good fit to the model, and a CV value of less than 10% indicates that the model's dispersion is within an acceptable range; an AP value greater than 4 indicates that the model is ideal.

6. The engine transient performance optimization and calibration method based on response surface design according to claim 2, characterized in that, Step 4 includes the following steps: Following Occam's razor principle, which states that unnecessary items should not be added, the model is simplified to avoid overfitting. Insignificant terms in the model are removed to obtain a simplified model. By comparing the above evaluation parameters, the simplified model is selected first if the performance does not deteriorate; otherwise, the original model is maintained.

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