A Multi-objective Performance Optimization Method for Diesel Engines Based on Gaussian Process

Abstract

The present invention provides a multi-objective performance optimization method for a diesel engine based on Gaussian process, which relates to the field of diesel engine performance optimization. First, by collecting the input and output data of the diesel engine air path system, the Gaussian process modeling method is used to model two performance indicators, namely the exhaust gas recirculation rate and the pumping loss, and the Gaussian process models of the two obtained indicators are used as the objective functions for solving the multi-objective optimization problem. The NSGA-II is adopted to obtain the current non-dominated solutions, and the acquisition function in the Bayesian optimization idea is used to select the next point to be observed and add it to the current training set, and the Gaussian process is repeatedly trained, and iterative solution is carried out in this way to finally approximate the global optimal solution. Finally, the optimal performance of the diesel engine air path system and the optimal control values of the corresponding actuators are obtained, achieving the effect of performance improvement, reducing the generation of harmful exhaust gases, and improving the fuel economic performance.

Description

Technical Field

[0001] The present invention belongs to the technical field of diesel engine performance optimization, and particularly relates to a multi-objective performance optimization method for diesel engines based on Gaussian process. Background Art

[0002] A turbocharged diesel engine mainly consists of six parts: a cylinder, an exhaust manifold, exhaust gas recirculation (EGR), a turbine, a compressor, and an intake manifold. A part of the exhaust gas discharged from the engine passes through the exhaust manifold and the EGR valve, and then flows back into the cylinder to participate in combustion. Another part of the exhaust gas passes through a variable geometry exhaust bypass valve (VGT) and flows towards the turbine, driving the intake compressor to rotate rapidly, so that more fresh air enters the intake passage. Under the condition of the same cylinder working volume, the intake pressure is increased, thereby improving the output power of the engine. The gas path optimization and control technology of turbocharged diesel engines can effectively improve the power performance, fuel economy, and emission performance of the engine. Most of the existing control algorithms use a look-up table method calibrated by static experiments to control actuators such as the EGR valve and VGT to obtain satisfactory engine performance. However, this control method ignores the optimal performance under transient operating conditions, and in the process of optimizing the diesel engine gas path system, there are often more than one optimization objective and they are in a competing relationship. The performance optimization method based on single-objective optimization has certain limitations. Optimizing a single specific index in the diesel engine gas path system usually causes a decline in other performance indexes. For example, obtaining a lower pumping loss will cause an inappropriate exhaust gas recirculation rate.

[0003] Most of the existing diesel engine performance optimization methods optimize a single performance index of the diesel engine and cannot optimize multiple optimization objectives simultaneously. Therefore, the comprehensive optimization of diesel engine performance cannot be achieved. In view of the above problems, the present invention proposes and designs a multi-objective performance optimization method for diesel engines based on Gaussian process, effectively improving the performance of diesel engines and achieving the comprehensive optimization of diesel engine performance. Summary of the Invention

[0004] Based on the above problems, in order to improve the performance of the engine, a multi-objective performance optimization method is adopted to optimize the performance of two indicators, namely the exhaust gas recirculation rate and the pumping loss. The Gaussian process is used to fit the objective function to construct a surrogate model, reducing the computational cost. As a non-parametric probability model, the Gaussian process model can not only give the predicted value but also its uncertainty, and can effectively handle the non-linearity and high-dimensional mapping between input and output. At the same time, the Bayesian idea is adopted, and the acquisition function is used to update the Gaussian process, making the final result approach the optimal value. Under this method, by optimizing the two performance indicators of the exhaust gas recirculation rate and the pumping loss, the execution values of the EGR valve and the VGT under the optimal performance are obtained, effectively reducing the emissions of nitrogen oxides and fuel consumption.

[0005] A multi-objective performance optimization method for a diesel engine based on Gaussian process provided by the present invention includes:

[0006] Step 1: Establish a mechanism model of the diesel engine air path system;

[0007] Step 2: Based on the mechanism model of the diesel engine air path system, construct a multi-objective performance optimization problem of the diesel engine air path system;

[0008] Step 3: Construct a Gaussian process of the optimization objective function;

[0009] Step 4: Use the non-dominated sorting genetic algorithm NSGA-II to obtain the current non-dominated solutions, use the EHVI acquisition function to select the data points to be observed, update the data set and re-model the Gaussian process;

[0010] Step 5: According to the set value of the EGR rate, obtain the execution values of the EGR valve and the VGT valve that meet the current working conditions from the obtained Pareto front. Use the obtained execution values of the EGR valve and the VGT valve as the control inputs of the system to obtain the optimal performance under the current working conditions.

[0011] The specific description of Step 1 is as follows:

[0012] For the cylinder, exhaust manifold, and exhaust gas recirculation rate in the diesel engine air path system, three dynamic equations are obtained respectively according to the ideal gas equation and the law of conservation of energy:

[0013]

[0014]

[0015]

[0016] In the formula, are the change rates of the intake manifold pressure and the exhaust manifold pressure respectively, P t 、P c are the powers of the turbine and the compressor; Tim , T em , V im , V em , and R are the intake air temperature, exhaust gas temperature, intake manifold volume, exhaust manifold volume, and ideal gas constant, respectively. W c , W egr , W ei , W eo , W t are the air mass flow rate through the compressor, the gas flow rate of EGR (exhaust gas recirculation), the air mass flow rate into the cylinder, the air mass flow rate out of the cylinder, and the exhaust gas mass flow rate through the turbine, respectively; τ is the turbine inertia coefficient; η m is the turbine efficiency coefficient.

[0017] The mechanism model of the diesel engine air path system is simplified to:

[0018]

[0019] x s = [p em , p im , P c , u = [u egr , u wg (5)

[0020] In the formula, X egr represents the EGR rate, P loss = p em - p im represents the pumping loss; u egr and u wg represent the opening degrees of the EGR valve and the exhaust bypass valve. u = 0 means fully closed, and u = 1 means fully open.

[0021] The multi-objective performance optimization problem of the diesel engine air path system in step 2 is expressed as:

[0022] min{X egr (u), P loss (u)} (5)

[0023] s.t. u ∈ Ω (6)

[0024] where, u = [u egr , u wg , u egr and u wg are used as decision variables, Ω is the feasible region of the decision variables, X egr and P loss represent the EGR rate and the pumping loss.

[0025] Step 3 is specifically described as:

[0026] Given a training sample set (X, Y), where X = [x 1 , …, x t , …, x K , Y = [y 1 , …, y t , …, y K . Here, x t = [u egr , u wg represents the opening degrees of the exhaust gas recirculation valve and the exhaust bypass valve at the t-th sampling point in the training sample set, and y t = [X egr , P loss represents the exhaust gas recirculation rate and the pumping loss value at the t-th sampling point in the training sample set. Using the collected (X, Y) as the training set of the Gaussian process, the general form of the Gaussian process is:

[0027] y = f(x) + ε (7)

[0028] where f is the form of an unknown function, and ε is Gaussian noise with a mean of 0 and a variance of σ 2 . For a new input X * , the corresponding probability prediction output y * also follows a Gaussian distribution, and its mean and variance are shown in equations (8) and (9):

[0029] f * = c(X * , X)[c(X, X) + σ 2 I] -1 Y (8)

[0030] cov(f * ) = c(X * , X * ) - c(X * , X)[c(X, X) + σ 2 I]c(X, X * ) (9)

[0031] In the equations, c(X * , X) is the covariance matrix between the training data and the test data, c(X, X) is the covariance matrix between the training data, I is the K×K dimensional identity matrix, and c(X * , X * ) is the autocovariance of the test data.

[0032] The covariance matrix can be generated by the covariance function c(x i , x j ), and the form of the kernel function used is:

[0033]

[0034] In the formula, θ n represents the hyperparameter of the Gaussian process. For the unknown hyperparameter θ in the above formula n , it is generally obtained by maximum likelihood estimation.

[0035] According to formulas (7)-(10), Gaussian processes f 1 (x) and f 2 (x) for the two optimization objective functions of exhaust gas recirculation rate and pumping loss are obtained as the models for subsequent optimization and solution.

[0036] In step 4, the non-dominated sorting genetic algorithm NSGA-II is used to obtain the current non-dominated solutions, which are specifically described as follows:

[0037] Step 4.1: Set the maximum number of iterations to M, and initialize to obtain the population P 0 , and use the Gaussian processes f 1 (x) and f 2 (x) to evaluate the population and assign fitness values.

[0038] Step 4.2: Perform non-dominated sorting to generate the population P t ;

[0039] Step 4.3: Select, crossover, and mutate to generate the offspring population Q t ;

[0040] Step 4.4: Combine P t and Q t of the two populations and perform fast non-dominated sorting;

[0041] Step 4.5: Calculate the crowding degree for each individual in the non-dominated layer, and select appropriate individuals according to the non-dominated relationship and the crowding degree of the individuals to form a new parent population P T ;

[0042] Step 4.6: If the maximum number of iterations M is not reached, return to step 4.3; if the maximum number of iterations is reached, end. At this time, the output P T is the current Pareto optimal solution.

[0043] In step 4, the EHVI acquisition function is used to select the data points to be observed, update the data set, and re-model the Gaussian process, which is specifically described as follows:

[0044] Step S1: Determine the expression of EHVI:

[0045]

[0046] Among them, PDF x(y) is the probability density function of the objective function; A is the currently dominated region, and x is P in step 4 T , that is, the Pareto optimal solution generated by the current iteration; R is the integration region composed of A; y = [f 1 (x), f 2 (x)] represents the value of the optimization objective function corresponding to x;

[0047] In the expression of EHVI, I(x, A) is:

[0048] I(x, A) = H(x ∪ A) - H(A) (12)

[0049] Among them,

[0050] H(A) = Vol(x ∈ R|x ∈ A, x < r) (13)

[0051] Among them, Vol is the volume formula, < represents Pareto domination, and r is the reference point (a point dominated by each point in region A).

[0052] Step S2: Determine the next point x to be observed by maximizing EHVI next :

[0053] x next = arg max EHVI(x, A) (14)

[0054] Evaluate x using the diesel engine mechanism model formulas (1)-(3) obtained in step 1, and add it to the training set of the Gaussian process to retrain the Gaussian process; next

[0055] Step S3: Determine whether the current Pareto optimal solution meets the conditions. If it meets, execute step 5; otherwise, go to step S2.

[0056] The beneficial effects of the present invention are:

[0057] The present invention provides a multi-objective performance optimization method for a diesel engine based on a Gaussian process, selects the exhaust gas recirculation rate and pumping loss as optimization objectives, realizes the comprehensive optimization of the two optimization objectives, solves the conflicting relationship between the two optimization objectives, and effectively improves the emission performance and fuel economy performance of the diesel engine. In addition, due to a large number of function evaluations in the optimization process, the Gaussian process is used to replace the real optimization objective function as the model in the optimization, reducing the calculation cost. Finally, the values of the actuators under the optimal performance are obtained, and the optimal performance of the diesel engine air path system is realized during the control process. Description of the Drawings

[0058] Figure 1Schematic diagram of the diesel engine air path system described in the present invention;

[0059] Figure 2 Flowchart of the multi-objective performance optimization method based on Gaussian process in the present invention;

[0060] Figure 3 Relationship diagram between the two optimization objectives of the exhaust gas recirculation rate and the pumping loss in the present invention;

[0061] Figure 4 Schematic diagram of the Pareto front obtained by solving the multi-objective algorithm in the present invention and its update with the number of evaluations;

[0062] Figure 5 Curve graph of the hypervolume index (HV) value of the Pareto front with the increase in the number of evaluations in the present invention. Detailed implementation manners

[0063] The present invention will be further described below in conjunction with the accompanying drawings and specific implementation examples. First, by collecting the input and output data of the diesel engine air path system, the Gaussian process modeling method is used to model the two performance indicators of the exhaust gas recirculation rate and the pumping loss, and the Gaussian process models of the two obtained indicators are used as the objective functions for solving the multi-objective optimization problem; the NSGA-II is used to obtain the current non-dominated solutions, and the acquisition function in the Bayesian optimization idea is used to select the next point to be observed and add it to the current training set, and the Gaussian process is repeatedly trained, and the iteration is solved in this way to finally approach the global optimal solution; finally, the optimal performance of the diesel engine air path system and the optimal control values of the corresponding actuators are obtained, achieving the effect of performance improvement, reducing the generation of harmful exhaust gases, and improving the fuel economy performance.

[0064] As Figure 2 shown, a multi-objective performance optimization method for diesel engines based on Gaussian process includes:

[0065] Step 1: Establish a mechanism model of the diesel engine air path system; specifically described as:

[0066] Figure 1 is a schematic diagram of the diesel engine air path system. For the cylinder, exhaust manifold, and exhaust gas recirculation rate in the diesel engine air path system, three dynamic equations are obtained respectively according to the ideal gas equation and the law of conservation of energy:

[0067]

[0068]

[0069]

[0070] In the formula, are respectively the change rates of the intake manifold pressure and the exhaust manifold pressure, Pt , P c is the power of the turbine and compressor; T im , T em , V im , V em , and R are the intake air temperature, exhaust gas temperature, intake manifold volume, exhaust manifold volume, and ideal gas constant respectively. W c , W egr , W ei , W eo , W t are respectively the air mass flow rate through the compressor, the gas flow rate of EGR (exhaust gas recirculation), the air mass flow rate into the cylinder, the air mass flow rate out of the cylinder, and the exhaust gas mass flow rate through the turbine; τ is the turbine inertia coefficient; η m is the turbine efficiency coefficient.

[0071] The mechanism model of the diesel engine air path system is simplified to:

[0072]

[0073] x s = [p em , p im , P c , u = [u egr , u wg (5)

[0074] In the formula, X egr represents the exhaust gas recirculation rate, P loss = p em - p im represents the pumping loss; u egr and u wg represent the opening degrees of the exhaust gas recirculation valve and the exhaust bypass valve. u = 0 means fully closed, and u = 1 means fully open.

[0075] Step 2: Construct the multi-objective performance optimization problem of the diesel engine air path system. The two optimization objectives of the present invention are to minimize the exhaust gas recirculation rate and the pumping loss. Since u egr and u wg have a very important impact on the EGR rate and the pumping loss, so u egr and u wg are selected as the decision variables. The multi-objective performance optimization problem of the diesel engine air path system is expressed as:

[0076] min{X egr (u), P loss (u)} (5)

[0077] s.t. u ∈ Ω (6)

[0078] where u = [uegr , u wg , u egr and u wg As decision variables, Ω is the feasible region of the decision variables, X egr and P loss represent the exhaust gas recirculation rate and the pumping loss.

[0079] Step 3: Construct the Gaussian process of the optimization objective function; specifically expressed as:

[0080] Collect u egr and u wg , as well as the corresponding X egr and P loss during the actual production process, and collect 60 groups of data; represent the training sample set as (X, Y), X = [x 1 , …, x t , …, x K , Y = [y 1 , …, y t , …, y K , where x t = [u egr , u wg represents the opening degrees of the exhaust gas recirculation valve and the exhaust bypass valve at the t-th sampling point in the training sample set, and y t = [X egr , P loss represents the exhaust gas recirculation rate and the pumping loss value at the t-th sampling point in the training sample set;

[0081] Use the collected (X, Y) as the training set of the Gaussian process. The general form of the Gaussian process is:

[0082] y = f(x) + ε (7)

[0083] where f is the form of the unknown function, and ε is Gaussian noise with a mean of 0 and a variance of σ 2 . For a new input X * , the corresponding probabilistic prediction output y * also follows a Gaussian distribution, and its mean and variance are shown in Eqs. (8) and (9):

[0084] f * = c(X * , X)[c(X, X) + σ 2 I] -1 Y (8)

[0085] cov(f * ) = c(X * , X * ) - c(X * , X)[c(X, X) + σ2 I]c(X,X * ) (9)

[0086] Where c(X * ,X) is the covariance matrix between the training data and the test data, c(X,X) is the covariance matrix between the training data, I is the K×K dimensional identity matrix, and c(X * ,X * ) is the autocovariance of the test data.

[0087] The covariance matrix can be generated by the covariance function c(x i ,x j ), and the form of the kernel function adopted is:

[0088]

[0089] Where θ n represents the hyperparameters of the Gaussian process; for the unknown hyperparameters θ n in the above formula, they are generally obtained by maximum likelihood estimation.

[0090] According to formulas (7)-(10), the Gaussian processes f 1 (x) and f 2 (x) of the two optimization objective functions of the exhaust gas recirculation rate and the pumping loss are obtained as the models for subsequent optimization and solution.

[0091] Step 4: Use the non-dominated sorting genetic algorithm NSGA-II to obtain the current non-dominated solutions, which are specifically described as:

[0092] Step 4.1: Set the maximum number of iterations to M, initialize to obtain the population P 0 , and use the Gaussian processes f 1 (x) and f 2 (x) to evaluate the population and assign fitness values.

[0093] Step 4.2: Perform non-dominated sorting to generate the population P t ;

[0094] Step 4.3: Select, crossover, and mutate to generate the offspring population Q t ;

[0095] Step 4.4: Combine the two populations P t and Q t and perform fast non-dominated sorting;

[0096] Step 4.5: Calculate the crowding degree for each individual in the non-dominated layer, and select appropriate individuals according to the non-dominated relationship and the crowding degree of the individuals to form a new parent population P T ;

[0097] Step 4.6: If the maximum number of iterations M is not reached, return to Step 4.3; if the maximum number of iterations is reached, end, and the output P at this time T is the current Pareto optimal solution; as Figure 3 shown Figure 4 is the corresponding HV value. As the number of evaluations increases, the HV value increases and finally stabilizes, reaching convergence. The curve graph of the hypervolume indicator (HV) value of the Pareto front with the increase in the number of evaluations is as Figure 5 shown

[0098] Calculate the hypervolume expected improvement EHVI of the Bayesian acquisition function, use the EHVI acquisition function to select the next point x to be evaluated, find the true objective function value y corresponding to x, add (x, y) to the dataset, and re - model the Gaussian process after updating the dataset. Using the updated Gaussian process as the optimization model, use Step 4 to obtain the current Pareto optimal solution.

[0099] The hypervolume expected improvement (EHVI) is an acquisition function in Bayesian multi - objective optimization for selecting the points to be observed. The acquisition function reflects the benefit brought by the new observation points to the optimization. By maximizing the hypervolume expected improvement, the next point to be observed is selected. After evaluating with the true performance index function, it is added to the training set of the Gaussian process to re - train the Gaussian process and make the model more accurate.

[0100] Use the EHVI acquisition function to select the data points to be observed, update the dataset and re - model the Gaussian process; specifically described as:

[0101] Step S1: Determine the expression of EHVI:

[0102]

[0103] where, PDF x (y) is the probability density function (Probability Distribution Function, PDF) of the objective function; A is the currently dominated region, x is the P in Step 4 T , that is, the Pareto optimal solution generated by the current iteration; R is the integration region composed of A; y = [f 1 (x), f 2 (x)] represents the value of the optimization objective function corresponding to x;

[0104] In the expression of EHVI, I(x, A) is:

[0105] I(x, A)=H(x∪A)-H(A) (12)

[0106] where

[0107] H(A) = Vol(x ∈ R|x ∈ A, x < r) (13)

[0108] Where Vol represents the volume formula, < represents Pareto domination, and r is the reference point (a point dominated by each point in region A).

[0109] Step S2: Determine the next point x to be observed by maximizing EHVI next :

[0110] x next = argmax EHVI(x, A) (14)

[0111] Evaluate x using the diesel engine mechanism model formulas (1)-(3) obtained in step 1, and add it to the training set of the Gaussian process to retrain the Gaussian process; next Perform the evaluation on x using the diesel engine mechanism model formulas (1)-(3) obtained in step 1, and add it to the training set of the Gaussian process to retrain the Gaussian process;

[0112] Step S3: Determine whether the current Pareto optimal solution satisfies the condition. If it does, execute step 5; otherwise, go to step S2;

[0113] Step 5: According to the set value of the EGR rate, obtain the actuator values of the EGR valve and VGT valve that satisfy the current operating condition from the obtained Pareto front. Use the obtained actuator values of the EGR valve and VGT valve as the control input of the system to obtain the optimal performance under the current operating condition.

Claims

1. A multi-objective performance optimization method for diesel engines based on Gaussian processes, characterized in that, it includes: Step 1: Establish a mechanism model of the diesel engine air path system; Step 2: Based on the mechanism model of the diesel engine air path system, construct a multi-objective performance optimization problem for the diesel engine air path system; Step 3: Construct a Gaussian process for the optimization objective function; Step 4: Use the non-dominated sorting genetic algorithm NSGA-II to obtain the current non-dominated solutions, use the EHVI acquisition function to select the data points to be observed, update the data set and re-model the Gaussian process; Step 5: According to the set value of the EGR rate, obtain the execution values of the EGR valve and VGT valve that meet the current working conditions from the obtained Pareto front; Take the obtained execution values of the EGR valve and VGT valve as the control input of the system to obtain the optimal performance under the current working conditions; The said Step 1 includes: For the cylinder, exhaust manifold, and exhaust gas recirculation rate in the diesel engine air path system, respectively obtain three dynamic equations according to the ideal gas equation and the law of conservation of energy: Wherein, are the change rates of the intake manifold pressure and the exhaust manifold pressure respectively, P t , P c are the powers of the turbine and the compressor; T im , T em , V im , V em , R are the intake temperature, the exhaust temperature, the intake manifold volume, the exhaust manifold volume and the ideal gas constant respectively, W c , W egr , W ei , W eo , W t are the air mass flow rate through the compressor, the gas flow rate of EGR (Exhaust Gas Recirculation), the air mass flow rate into the cylinder, the air mass flow rate out of the cylinder and the exhaust gas mass flow rate through the turbine respectively; τ is the turbine inertia coefficient; η m is the turbine efficiency coefficient; Simplify the mechanism model of the diesel engine air path system to: x s = [p em , p im , P c , u = [u egr , u wg (5) In the formula, X egr represents the exhaust gas recirculation rate, and P loss = p em - p im represents the pumping loss; u egr and u wg represent the opening degrees of the exhaust gas recirculation valve and the exhaust bypass valve. u = 0 means fully closed, and u = 1 means fully open.

2. A multi-objective performance optimization method for diesel engines based on Gaussian processes according to claim 1, characterized in that, The multi-objective performance optimization problem of the diesel engine air path system in the said Step 2 is expressed as: min{X egr (u),P loss (u)} (5) s.t.u∈Ω (6) where \(u = [u egr , u wg \), \(u egr and \(u wg are decision variables, \(\Omega\) is the feasible region of the decision variables, \(X egr and \(P loss represent the exhaust gas recirculation rate and the pumping loss.

3. A multi-objective performance optimization method for diesel engines based on Gaussian processes according to claim 1, characterized in that, The said Step 3 includes: Given a training sample set (X, Y), X = [x 1 , …, x t , …, x K , Y = [y 1 , …, y t , …, y K , where x t = [u egr , u wg represents the opening degrees of the exhaust gas recirculation valve and the exhaust bypass valve at the t-th sampling point in the training sample set, and y t = [X egr , P loss represents the exhaust gas recirculation rate and the pumping loss value at the t-th sampling point in the training sample set; Using the collected (X, Y) as the training set of the Gaussian process, the Gaussian process is expressed as: y=f(x)+ε (7) where f is the form of the unknown function, and ε is Gaussian noise with a mean of 0 and a variance of σ 2 ; for a new input X * , the corresponding probability prediction output y * also follows a Gaussian distribution, and its mean and variance are shown in Equations (8) and (9): f * = c(X * , X)[c(X, X)+σ 2 I] -1 Y (8) cov(f * ) = c(X * , X * ) - c(X * , X)[c(X, X) + σ 2 I]c(X, X * ) (9) where c(X * , X) is the covariance matrix between the training data and the test data, c(X, X) is the covariance matrix between the training data, I is the K×K dimensional identity matrix, and c(X * , X * ) is the autocovariance of the test data; The covariance matrix is generated by the covariance function c(x i , x j ), and the adopted kernel function form is as follows: where θ n represents the hyperparameter of the Gaussian process; According to formulas (7)-(10), the Gaussian processes \(f_{EGR}(x)\) and \(f_{pumping}(x)\) for the two optimization objective functions of exhaust gas recirculation rate and pumping loss are obtained as the models for subsequent optimization and solution. 1 \((x)\) and \(f\) 2 \((x)\) 4. A multi-objective performance optimization method for diesel engines based on Gaussian processes according to claim 1, characterized in that, In the said Step 4, use the non-dominated sorting genetic algorithm NSGA-II to obtain the current non-dominated solutions, and the specific expression is: Step 4.1: Set the maximum number of iterations to M and initialize to obtain the population P 0 , and use the Gaussian processes f 1 (x) and f 2 (x) to evaluate the population and assign fitness values Step 4.2: Perform non-dominated sorting to generate population P t ; Step 4.3: Select, crossover, and mutate to generate the offspring population Q t ; Step 4.4: Merge P t and Q t for the two populations and perform fast non-dominated sorting; Step 4.5: Calculate the crowding degree for each individual in each non-dominated layer, and select appropriate individuals according to the non-dominated relationship and the crowding degree of the individuals to form a new parental population P T ; Step 4.6: If the maximum number of iterations M has not been reached, return to Step 4.3; if the maximum number of iterations has been reached, end, and the output P at this time T is the current Pareto optimal solution.

5. A multi-objective performance optimization method for diesel engines based on Gaussian processes according to claim 1, characterized in that, In the said Step 4, use the EHVI acquisition function to select the data points to be observed, update the data set and re-model the Gaussian process; the specific expression is: Step S1: Determine the expression of EHVI: Among them, PDF x (y) is the probability density function of the objective function; A is the currently dominated region, let x = P T , that is, the Pareto optimal solution generated by the current iteration; R is the integration region composed of A; y = [f 1 (x), f 2 (x)] represents the value of the optimization objective function corresponding to x; Step S2: Determine the next point x to be observed by maximizing the EHVI next : x next = argmax EHVI(x, A) (14) Evaluate x using the mechanism model formulas (1)-(3) of the diesel engine obtained in step 1 next and add it to the training set of the Gaussian process to retrain the Gaussian process; Step S3: Judge whether the current Pareto optimal solutions meet the conditions. If they meet, execute Step 5; otherwise, go to Step S2.

6. A multi-objective performance optimization method for diesel engines based on Gaussian processes according to claim 5, characterized in that, In the expression of the said EHVI, I(x,A) is: I(x,A)=H(xUA)-H(A) (12) where, H(A)=Vol(x∈R|x∈A,x<r) (13) In the formula, Vol is the volume formula, < represents Pareto domination, and r is the reference point.

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