CN113935124B - Multi-target performance optimization method for biodiesel for diesel engine - Google Patents

Multi-target performance optimization method for biodiesel for diesel engine Download PDF

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CN113935124B
CN113935124B CN202111056687.7A CN202111056687A CN113935124B CN 113935124 B CN113935124 B CN 113935124B CN 202111056687 A CN202111056687 A CN 202111056687A CN 113935124 B CN113935124 B CN 113935124B
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潘锁柱
蔡敏
杜晨搏
蔡凯
方嘉
何国太
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Abstract

The invention relates to the technical field of diesel engine fuel, and relates to a multi-target performance optimization method for biodiesel for diesel engine combustion, which comprises the following steps: firstly, establishing a PSO-SVM emission prediction model; secondly, respectively predicting the emission of nitrogen oxides NOx and particulate matters emitted by the diesel engine by utilizing a PSO-SVM prediction model to construct a nonlinear function z1、z2(ii) a Performing multi-objective optimization on the two decision equations by using an NSGA-II algorithm to obtain Pareto optimal solutions of NOx and particulate matters; fourthly, calculating the optimization degree of pareto optimal solution of NOx and particulate matter emission obtained through an optimization algorithm; the invention realizes the simultaneous optimization of the emission of NOx and particulate matters, and the emission of NOx and particulate matters can be simultaneously reduced.

Description

Multi-target performance optimization method for biodiesel for diesel engine
Technical Field
The invention relates to the technical field of diesel engine fuel, in particular to a multi-target performance optimization method for biodiesel for diesel engine combustion.
Background
Diesel engines have been widely used in the fields of transportation, ships, engineering machinery, generator sets, etc. due to their advantages of high thermal efficiency, low oil consumption, high reliability, long service life, etc. The diesel engine is used as a power output device, and fossil fuel is a power source of the diesel engine, so that the consumption of the fossil fuel is increased along with the wide application of the diesel engine, and besides, the fossil fuel also releases a large amount of substances harmful to the atmospheric environment and human bodies in the combustion process, thereby bringing serious challenges to energy safety and environmental protection.
Biodiesel is a clean renewable carbon neutral energy source, and is the optimal choice for replacing petroleum diesel due to high similarity of physicochemical properties with the petroleum diesel. Meanwhile, the great popularization of the application of the biodiesel to the diesel engine is one of powerful means for realizing the aims of carbon peak reaching and carbon neutralization in the field of internal combustion engines. Biodiesel is prepared from various natural vegetable oils, animal oils, waste oils of food industry, engineering microalgae, etc. by transesterification with alcohols, and is a mixture of various fatty acid methyl esters or ethyl esters (FAE). The molecular formula of the fatty acid methyl ester or ethyl ester can be abbreviated as R1-COO-R2, wherein R1 represents a hydrocarbon group, and R2 represents a methyl group or an ethyl group (short for alcohol chain). The carbon chain length, the number and position of double bonds, and the type of R2 of R1 are closely related to physicochemical properties of the fuel, such as viscosity, cetane number, calorific value, and density. Therefore, the change of the basic physicochemical properties of the biodiesel caused by the change of the components has to influence the formation of the mixed gas of the diesel engine and the combustion process, and further influence the emission. Therefore, a large amount of basic research work has been carried out by domestic and foreign scholars on the subject of the emission performance of biodiesel for diesel combustion. In the process of diesel engine research, with the continuous development of science and technology, methods for establishing numerical simulation models (most models are thermodynamic models and statistical methods based on physics and chemistry) based on computer software have been gradually applied to diesel engine combustion and emission performance research, and although numerical simulation models have certain advantages compared with the prior traditional experimental methods, the numerical simulation models established based on computer software still have limitations when more complex engineering problems are involved. In recent years, with the continuous application of machine learning in the engineering field, the performance response prediction in the internal combustion engine field becomes possible. Machine learning is the core of artificial intelligence, is an important knowledge discovery method, and can extract an abstract mapping relation hidden in data by training known data samples, so that unknown data can be accurately predicted. At present, scholars at home and abroad develop a great deal of research work on the aspect of diesel engine performance prediction aiming at machine learning, and a feasible way is provided for the application and development of machine learning in the field of diesel engine performance prediction. Biodiesel serves as a high-quality alternative fuel of a diesel engine, can realize 'net zero' greenhouse gas emission in a full life cycle, and becomes one of powerful means for realizing the 'carbon peak reaching and carbon neutralization' targets in the field of diesel engines. Also, with the increasing public concern over environmental safety and health and the tightening of emissions regulations, effective control of diesel emissions has received great attention. Because the influences of the physical and chemical properties of the biodiesel on the emission of nitrogen oxides (NOx) and particulate matters of the diesel engine are not independent of each other and have a certain internal relationship, the physical and chemical properties of the biodiesel need to be optimized in a multi-objective manner, and the influence of the physical and chemical properties on the emission of the diesel engine needs to be researched.
Disclosure of Invention
The invention provides a multi-objective performance optimization method for biodiesel for diesel combustion, which can overcome certain defects or some defects in the prior art.
The multi-target performance optimization method of the biodiesel for the diesel engine comprises the following steps of:
firstly, establishing a PSO-SVM emission prediction model;
secondly, respectively predicting the emission of NOx and particulate matters by utilizing a PSO-SVM prediction model to construct a nonlinear function z1、z2Both of these functions are non-linear relationships of the design variables to the optimization objectives, thus yielding two objective functions for the design variables:
f1(NOx)＝z1(x1，x2，x3)
f2(particulate matter) ═ z2(x1，x2，x3)
Constraint conditions are as follows:
49.8≤x1≤ 64.64
2.56≤x2≤ 3.321
26.7≤x3≤ 34.12
in the formula: z is a radical of1、z2For using PSO-A nonlinear function of NOx and particulate matter emission constructed by the SVM prediction model; f. of1(NOx)、f2(particulate matter) is NOx and the emission amount of the particulate matter; x is a radical of a fluorine atom1、x2、x3Cetane number, viscosity and surface tension of the biodiesel respectively;
performing multi-objective optimization on the two decision equations by using an NSGA-II algorithm to obtain Pareto optimal solutions of NOx and particulate matters;
fourthly, calculating the optimization degree of pareto optimal solution of NOx and particulate matter emission obtained through an optimization algorithm, and solving the optimization degree of NOx and particulate matter values through the following formula:
Figure BDA0003254932920000031
in the formula: eta is the optimization percentage, P is the Pareto optimal solution, S is the experimental value, P is the optimal solutionmaxIs the maximum value, P, in the Pareto optimal solutionminIs the minimum value in the Pareto optimal solution.
Preferably, the PSO-SVM emission prediction model establishing method comprises the following steps:
a. establishing a support vector machine prediction model, namely an SVM prediction model;
b. using a grid search algorithm to perform preliminary optimization on the penalty factor (C) and the kernel function parameter (g); meanwhile, a K-fold cross validation method is used for further optimization;
c. performing further precise optimization on C and g by using a Particle Swarm Optimization (PSO);
d. and obtaining an optimized SVM prediction model, namely a PSO-SVM emission prediction model.
Preferably, the method for establishing the SVM prediction model comprises the following steps:
first, a data set T { (x) of dimension m × (n +1) is given1，y1)，(x2，y2)，...，(xm，ym) Is equal to (X multiplied by Y), wherein X is equal to RnAnd for an n-dimensional input vector, y belongs to R and is the output of the system, and the optimal hyperplane established based on the SVM model is as follows:
g(x)＝wxi+b
in the formula: w is a hyperplane normal vector; b is a hyperplane constant;
then, the problem of establishing the linear support vector machine is converted into the problem of solving a quadratic convex programming, and the following results are obtained:
Figure BDA0003254932920000041
in the formula: zetaiIs a relaxation variable; c is a penalty factor;
and finally, converting the quadratic convex programming problem into a dual problem, namely obtaining:
Figure BDA0003254932920000042
in the formula: a isiFor Lagrange coefficients, applicable only to SVM models, aiIs not equal to 0; k (x)i，xj) Is a kernel function;
by carrying out mathematical theory analysis on the problems, the regression function of the support vector machine is obtained as follows:
Figure BDA0003254932920000043
0＜ai＜C。
preferably, the K-fold cross validation method comprises the following steps:
firstly, taking a training sample as an object, dividing the training sample into k equal parts, enabling data of each equal part to be a verification set in sequence, and using the rest data for model establishment; performing k times according to the steps, and solving the mean square error of each training model; and finally, dividing the sum of the obtained mean square errors by K to obtain a model error of K-fold cross validation, wherein the error is used as an index for evaluating the precision of the model.
Preferably, the step of optimizing the parameters by the grid search method comprises:
(1) setting a search range and a search step length according to experience, and drawing a two-dimensional grid;
(2) taking node parameter combinations in the grids, substituting the node parameter combinations into a target function to verify the performance of the nodes;
(3) and selecting a parameter combination with the lowest mean square error in the grid according to the performance evaluation, and if a plurality of groups of parameters have the same mean square error, selecting the group with the lowest parameter C as the optimal parameter.
Preferably, the particle swarm algorithm comprises the following steps:
step 1: initializing particle parameters; comprises the following steps: setting population size N, determining maximum iteration number tmaxSelecting an inertia weight value omega, setting values of learning constants c1 and c2, and setting an initial position x of each particlei＝(xi1，xi2，...，xid) And an initial velocity vi＝(vi1，vi2，...，vid) And particle flight range;
step 2: calculating the fitness f (p) of any particle; solving the fitness of any particle according to the fitness function;
and step 3: optimal particle fitness pbestUpdating; the current generation fitness f (p) of any particle and the optimal particle fitness p obtained beforebestBy comparison, if f (p) is better than pbestReplacing p with f (p)bestAs the optimal particle fitness, otherwise, the original optimal particle fitness pbestAnd is not changed.
And 4, step 4: optimal population fitness gbestUpdating; matching the fitness f (p) of all the particle generations with the optimal population fitness g obtained beforebestFor comparison, if f (p) is better than gbestReplacing g with f (p)bestAs the optimal population fitness, otherwise, the original optimal population fitness gbestAnd is not changed.
And 5: particle position and velocity updates; according to the optimal particle fitness pbestAnd an optimal population fitness gbestUpdating the position and the speed of the particles by adopting a standard particle swarm algorithm to generate a new generation of population;
and 6: judging a termination condition; if the termination condition is satisfied (outputting the optimal solution or reaching the maximum iteration number t)max) Then terminate no longerIteration is carried out; otherwise, returning to the step 2 to continue the iteration.
Preferably, the NSGA-II algorithm is a modified non-dominated sorting genetic algorithm comprising the steps of:
1) randomly generating an initialization population with the population scale of N, and carrying out non-dominated sorting on the initialization population;
2) calculating the initialized population by flexibly combining several algorithms of selection, crossing and variation to obtain a first generation sub population; in the process of establishing the second generation sub-population, the parent population and the child population are not discussed separately, but the non-dominated sorting and individual crowding degree evaluation are carried out by adhering to a rule of high-out and low-out, and excellent individuals are selected from the excellent individuals to form a new parent population;
3) step 2) is infinitely circulated until the practical requirement is met.
The invention adopts a mode of combining a PSO-SVM emission prediction model and an NSGA-II algorithm to establish a multi-objective optimization model of pollutant emission of the biodiesel for diesel combustion, and obtains a Pareto optimal solution of NOx and particulate matter emission. The simultaneous optimization of the emission of NOx and particulate matters is realized, and the emission of NOx and the emission of particulate matters can be simultaneously reduced.
Drawings
FIG. 1 is a flow chart of the multi-objective performance optimization method for biodiesel for diesel fuel in example 1;
FIG. 2 is a schematic diagram of a Pareto optimal solution for NOx and particulate matter emissions for the diesel engine of example 1 at 1500r/min, 50% load conditions;
FIG. 3 is a Pareto optimal solution diagram of NOx and particulate matter emissions of the diesel engine of example 1 at 1800r/min, 50% load
FIG. 4 is a schematic diagram of the percentage of optimization of the Pareto optimal solution of the diesel engine in example 1 under the working condition of 1500r/min and 50% load;
FIG. 5 is a schematic diagram of the percentage of optimization of the Pareto optimal solution of the diesel engine in example 1 at 1800r/min and 50% load condition.
Detailed Description
For a further understanding of the present invention, reference is made to the following detailed description taken in conjunction with the accompanying drawings and examples. It is to be understood that the examples are illustrative of the invention and not limiting.
Example 1
As shown in fig. 1, the embodiment provides a multi-objective performance optimization method for biodiesel for diesel combustion, which includes the following steps:
firstly, establishing a PSO-SVM emission prediction model; PSO refers to a particle group algorithm, and SVM refers to a support vector machine;
secondly, respectively predicting the emission of nitrogen oxides (NOx) and particulate matters by utilizing a PSO-SVM prediction model to construct a nonlinear function z1、z2Both of these functions are non-linear relationships of the design variables to the optimization objective, thus yielding two objective functions for the design variables:
f1(NOx)＝z1(x1，x2，x3)
f2(particulate matter) ═ z2(x1，x2，x3)
Constraint conditions are as follows:
49.8≤x1≤ 64.64
2.56≤x2≤ 3.321
26.7≤x3≤ 34.12
in the formula: z is a radical of1、z2The non-linear function of the NOx and particulate matter emission is constructed by utilizing a PSO-SVM prediction model; f. of1(NOx)、f2(particulate matter) is NOx and the emission amount of the particulate matter; x is the number of1、x2、x3Cetane number, viscosity and surface tension of the biodiesel respectively;
performing multi-objective optimization on the two decision equations by using an NSGA-II algorithm to obtain Pareto (Pareto) optimal solutions of NOx and particulate matters;
fourthly, calculating the optimization degree of pareto optimal solution of NOx and particulate matter emission obtained through an optimization algorithm, and solving the optimization degree of NOx and particulate matter values through the following formula:
Figure BDA0003254932920000071
in the formula: eta is the optimization percentage, P is the Pareto optimal solution, S is the experimental value, P is the optimal solutionmaxIs the maximum value, P, in the Pareto optimal solutionminIs the minimum value in the Pareto optimal solution.
The method for establishing the PSO-SVM emission prediction model comprises the following steps:
a. establishing a support vector machine prediction model, namely an SVM prediction model;
b. using a grid search algorithm to perform preliminary optimization on the penalty factor (C) and the kernel function parameter (g); meanwhile, a K-fold cross validation method is used for further optimization;
c. performing further precise optimization on C and g by using a Particle Swarm Optimization (PSO);
d. and obtaining an optimized SVM prediction model, namely a PSO-SVM emission prediction model.
The method for establishing the SVM prediction model comprises the following steps:
first, a data set T { (x) of m × (n +1) dimensions is given1，y1)，(x2，y2)，...，(xm，ym) Is equal to (X multiplied by Y), wherein X is equal to RnAnd for an n-dimensional input vector, y belongs to R and is the output of the system, and the optimal hyperplane established based on the SVM model is as follows:
g(x)＝wxi+b
in the formula: w is a hyperplane normal vector; b is a hyperplane constant;
then, the problem of establishing the linear support vector machine is converted into the problem of solving a quadratic convex programming, and the following results are obtained:
Figure BDA0003254932920000072
in the formula: zetaiAs a relaxation variable, if 0. ltoreq. ζiIf the sample is less than or equal to 1, the sample x is determinediIs well-known; c is a penalty factor;
and finally, converting the quadratic convex programming problem into a dual problem, namely obtaining:
Figure BDA0003254932920000081
in the formula: a isiFor Lagrange coefficients, applicable only to SVM models, aiIs not equal to 0; k (x)i，xj) Is a kernel function;
by carrying out mathematical theory analysis on the problems, the regression function of the support vector machine is obtained as follows:
Figure BDA0003254932920000082
0＜ai＜C。
the K-fold cross validation method comprises the following steps:
firstly, taking a training sample as an object, dividing the training sample into k equal parts, enabling data of each equal part to be a verification set in sequence, and using the rest data for model establishment; performing k times according to the steps, and solving the mean square error of each training model; and finally, dividing the sum of the obtained mean square errors by K to obtain a model error of K-fold cross validation, wherein the error is used as an index for evaluating the precision of the model.
The method for optimizing parameters by the grid search method comprises the following steps:
(1) setting a search range and a search step length according to experience, and drawing a two-dimensional grid;
(2) taking node parameter combinations in the grids, substituting the node parameter combinations into a target function to verify the performance of the nodes;
(3) and selecting a parameter combination with the lowest mean square error in the grid according to the performance evaluation, and if a plurality of groups of parameters have the same mean square error, selecting the group with the lowest parameter C as the optimal parameter.
The particle swarm algorithm comprises the following steps:
step 1: initializing particle parameters; comprises the following steps: setting population size N, determining maximum iteration number tmaxSelecting an inertia weight value omega, setting values of learning constants c1 and c2, and setting an initial position x of each particlei＝ (xi1，xi2，...，xid) And an initial velocity vi＝(vi1，vi2，...，vid) And particle flight range;
step 2: calculating the fitness f (p) of any particle; solving the fitness of any particle according to the fitness function;
and step 3: optimal particle fitness pbestUpdating; the current generation fitness f (p) of any particle and the optimal particle fitness p obtained beforebestComparing if f (p) is better than pbestReplacing p with f (p)bestAs the optimal particle fitness, otherwise, the original optimal particle fitness pbestThe change is not changed;
and 4, step 4: optimal population fitness gbestUpdating; matching the fitness f (p) of all the particle generations with the optimal population fitness g obtained beforebestFor comparison, if f (p) is better than gbestReplacing g with f (p)bestAs the optimal population fitness, otherwise, the original optimal population fitness gbestThe change is not changed;
and 5: particle position and velocity updates; according to the optimal particle fitness pbestAnd the optimal population fitness gbestUpdating the position and the speed of the particles by adopting a standard particle swarm algorithm to generate a new generation of population;
step 6: judging a termination condition; if the termination condition is satisfied (outputting the optimal solution or reaching the maximum iteration number t)max) If yes, stopping not to perform iteration; otherwise, returning to the step 2 to continue the iteration.
The NSGA-II algorithm is a modified non-dominated sorting genetic algorithm, comprising the following steps:
1) randomly generating an initialization population with the population scale of N, and carrying out non-dominated sorting on the initialization population;
2) calculating the initialized population by flexibly combining several algorithms of selection, crossing and variation to obtain a first generation sub population; in the process of establishing the second generation sub-population, the parent population and the child population are not discussed separately, but the non-dominated sorting and individual crowding degree evaluation are carried out by adhering to a rule of high-out and low-out, and excellent individuals are selected from the excellent individuals to form a new parent population;
3) step 2) is infinitely circulated until the practical requirement is met.
The NSGA-II algorithm is mainly divided into two steps when solving the actual engineering problem: firstly, sequencing each individual in a population by using a quick sequencing algorithm, removing solutions obviously not meeting engineering requirements in a solution set, and carrying out population division on all the remaining solutions to enable a calculation result to be continuously close to a Pareto solution set; secondly, randomly arranging individuals in the same non-dominant order based on a congestion degree evaluation method in combination with an engineering setting data arrangement method, and determining the category of the population in an adjacent range according to the distance between the target functions of two adjacent individuals; and finally, integrating the evaluation results to obtain a fitness function value of each individual, and finishing the fitness distribution according to the fitness function value.
When solving practical problems using the NSGA-II algorithm, the whole multi-objective optimization is already half done if the choice of parameters is reasonable enough. The basic parameters that have an influence on the accuracy of the NSGA-II algorithm are: the size Pop of the population, the maximum iterative evolution algebra maxGen, the cross probability Pc, the variation probability Pv and the like. However, when the NSGA-II algorithm is applied to solve the actual engineering problem, the parameter setting needs to be performed by combining the complexity, the solving precision, and the like of the actual problem, and multiple tests or according to an empirical method, and the basic parameter setting of the NSGA-II algorithm is as follows:
A. population size Pop
The size of the population is mainly determined by the number of internal parameters of the population, and the individual parameters in the population play a decisive role in the calculation time of the NSGA-II algorithm and the capability of seeking an optimal solution; if the individual parameters in the population are excessive, the sample size needing to be processed by the NSGA-II algorithm is too large, so that the optimal solution searching capability is reduced; however, if the individual parameters in the population are too small, the optimization time is greatly shortened, but the local optimal solution cannot be converted into the global optimal solution because the sample size is too small. Therefore, when the NSGA-II algorithm is adopted to carry out multi-objective optimization on the actual engineering problem, the population size should be in a proper range, the value of the Pop is generally not lower than 20 at the lowest and not higher than 200 at the highest according to the experience, and the Pop value is 50 in the embodiment.
B. Maximum iterative evolution algebra maxGen
When the NSGA-II algorithm is adopted for multi-objective optimization, the whole optimization process cannot become a dead loop, and an iteration termination condition, namely the maximum iterative evolution algebra maxGen, is required. In the process of selecting the maximum iterative evolutionary algebra, attention is paid to: the size of the parameter value and the optimization efficiency have a negative correlation relationship, if the value is too large, the optimization time is increased, and if the value is too small, the optimization effect is poor. According to the experience, in general engineering application, the maxGen value is not more than 2000 at the maximum and is not less than 50 at the minimum. In this embodiment, the maximum iterative evolution algebra maxGen is taken as 100.
C. Cross probability Pc
The crossover probability represents the likelihood that an individual of the population will get a new individual based on a crossover genetic operator. In practical application, the selection of the value of Pc is also noticed, and if the value is too large, crossing between individuals in parent population and children population can be caused; if the value is too small, the time of population iteration is greatly increased, generally, the maximum value of the Pc value is not more than 1, and the minimum value is not less than 0.5; in this example, the Pc value is 0.9.
D. Probability of variation Pv
Pv refers to the probability that a new individual will be formed by the mutation operator. In practical application, a proper Pv value should be selected, the reasonable value range of the value is between 0.001 and 0.2, when an improper Pv value is selected, if the value is too large, good individuals in a parent can enter a child population, and if the value is too small, an optimal solution in a global range cannot be obtained. In this example, the value of Pv was 0.1.
Optimizing results and analysis
The pareto optimal solution of NOx and particulate matter emission under the working conditions that the rotating speed of the diesel engine is 1500r/min and 1800r/min and the load is 50% is obtained through NSGA-II optimization, as shown in figures 2 and 3.
The abscissa in the Pareto optimal solution graph is the NOx emission optimal value, and the ordinate is the particulate matter emission optimal value. The square points in the graph are experimental data points; the circle points in the graph are Pareto optimal solutions; the curve formed by the gathering of the circular points is called Pareto front surface. Each data point in the Pareto optimal solution map corresponds to the physicochemical characteristic parameters (cetane number, viscosity, surface tension) of biodiesel. It can be seen from the figure that under the same rotating speed and load, the discharge amount of NOx and particulate matters is always in a mutually restricted state along with the change of the physical and chemical properties of the biodiesel, and the reduction of the NOx discharge is accompanied by the increase of the particulate matters, and vice versa. The cetane number, viscosity and surface tension values corresponding to each data point in the Pareto optimal solution chart under different working conditions are shown in tables 1 and 2.
Table 11500 r/min, Pareto optimum solution under 50% load condition and physical and chemical characteristic parameters of biodiesel corresponding to experimental values
Figure BDA0003254932920000111
TABLE 21800 r/min, 50% load Pareto optimal solution and corresponding biodiesel physical and chemical characteristic parameters of experimental value
Figure BDA0003254932920000112
Figure BDA0003254932920000121
And calculating the optimization degree of pareto optimal solution of NOx and particulate matter emission obtained by an optimization algorithm by taking the magnitude of the experimental value as reference, and analyzing and obtaining the influence of the physical and chemical properties of the biodiesel on the NOx and particulate matter emission.
In conjunction with the location of the experimental data points in fig. 2, it can be seen that the experimental data in the upper middle of the search is at a lower NOx emission, but there is some room for optimization. As can be seen from fig. 4, based on the experimental point data, the 1 st to 5 th Pareto optimal solutions, although reducing NOx emissions, reduce NOx emissions by only 7.85% at most, while increasing particulate emissions by 46.04% at most. In the 6 th to 7 th Pareto optimal solutions, the NOx and the particulate matter emission are reduced simultaneously, especially the reduction of the particulate matter emission is relatively obvious, and the particulate matter emission is reduced by 5.72% and 31.74% while the NOx is reduced by 1.97% and 1.53%, respectively. The 8 th Pareto optimal solution reduced particulate emissions by 39.65% based on 0.95% increased NOx emissions. The 9 th to 15 th Pareto optimal solutions, although particulate matter emissions are significantly reduced, NOx emissions begin to gradually deteriorate. Therefore, under the working condition of 1500r/min and 50% load, the emission of the diesel engine can be well reduced by taking the cetane number, the viscosity and the surface tension corresponding to the 6 th to 7 th Pareto optimal solutions as the physical and chemical property indexes of the biodiesel.
In conjunction with the location of the experimental data points in fig. 3, it can be seen intuitively that the data obtained by the experiment does not differ much from the center location of the optimization space, and that the NOx and particulate matter emissions corresponding to the test points are in a compromise position, but can be further optimized. As can be seen from fig. 5, based on the experimental data points, the 1 st to 6 th Pareto optimal solutions exhibited a significant decrease in NOx emissions and a significant increase in particulate matter emissions. The 7 th to 11 th Pareto optimal solutions simultaneously reduce the NOx and particulate emissions by 23.25%, 18.68%, 16.79%, 13.01% and 2.52%, respectively, and correspondingly reduce the particulate emissions by 8.48%, 15.20%, 15.54%, 20.59% and 29.58%. The 12 th to 18 th Pareto optimal solutions show a significant reduction in particulate matter emissions, but gradually worsen NOx emissions. Therefore, under the working condition of 1800r/min and 50% load, the emission of the diesel engine can be well reduced by taking the cetane number, viscosity and surface tension corresponding to the 7 th to 11 th Pareto optimal solutions as the physical and chemical property indexes of the biodiesel.
By combining the analysis, the optimization method provided by the invention is verified again to well solve the multi-objective optimization problem that the physical and chemical properties of the biodiesel have a trade-off relation with the emission of NOx and particulate matters of the diesel engine, and a relatively comprehensive Pareto optimal solution set can be provided, so that the aim of optimizing the physical and chemical properties of the biodiesel and reducing the emission of the diesel engine is fulfilled.
The present invention and its embodiments have been described above schematically, without limitation, and what is shown in the drawings is only one of the embodiments of the present invention, and the actual structure is not limited thereto. Therefore, if the person skilled in the art receives the teaching, without departing from the spirit of the invention, the person skilled in the art shall not inventively design the similar structural modes and embodiments to the technical solution, but shall fall within the scope of the invention.

Claims (7)

1. The multi-target performance optimization method of the biodiesel for diesel combustion is characterized by comprising the following steps of: the method comprises the following steps:
firstly, establishing a PSO-SVM emission prediction model;
secondly, respectively predicting the emission of NOx and particulate matters by utilizing a PSO-SVM prediction model to construct a nonlinear function z1、z2Both of these functions are non-linear relationships of the design variables to the optimization objectives, thus yielding two objective functions for the design variables:
f1(NOx)＝z1(x1,x2,x3)
f2(particulate matter) ═ z2(x1,x2,x3)
Constraint conditions are as follows:
49.8≤x1≤64.64
2.56≤x2≤3.321
26.7≤x3≤34.12
in the formula: z is a radical of1、z2The non-linear function of the NOx and particulate matter emission is constructed by utilizing a PSO-SVM prediction model; f. of1(NOx)、f2(particulate matter) is NOx and the emission amount of the particulate matter; x is the number of1、x2、x3Cetane number, viscosity and surface tension of the biodiesel respectively;
performing multi-objective optimization on the two decision equations by using an NSGA-II algorithm to obtain Pareto optimal solutions of NOx and particulate matters;
fourthly, calculating the optimization degree of pareto optimal solution of NOx and particulate matter emission obtained through an optimization algorithm, and solving the optimization degree of NOx and particulate matter values through the following formula:
Figure FDA0003598869880000011
in the formula: eta is the optimization percentage, P is the Pareto optimal solution, S is the experimental value, PmaxIs the maximum value, P, in the Pareto optimal solutionminIs the minimum value in the Pareto optimal solution.
2. The multi-objective performance optimization method for biodiesel for combustion of diesel engines as claimed in claim 1, wherein: the method for establishing the PSO-SVM emission prediction model comprises the following steps:
a. establishing a support vector machine prediction model, namely an SVM prediction model;
b. using a grid search algorithm to perform preliminary optimization on the penalty factor C and the kernel function parameter g; meanwhile, a K-fold cross validation method is used for further optimization;
c. further and accurately optimizing C and g by using a Particle Swarm Optimization (PSO);
d. and obtaining an optimized SVM prediction model, namely a PSO-SVM emission prediction model.
3. The multi-objective performance optimization method for biodiesel for combustion of diesel engines as claimed in claim 2, wherein: the method for establishing the SVM prediction model comprises the following steps:
first, a data set T { (x) of m × (n +1) dimensions is given1,y1),(x2,y2),…,(xm,ym) Is equal to (X multiplied by Y), wherein X is equal to RnAnd for an n-dimensional input vector, y belongs to R and is the output of the system, and the optimal hyperplane established based on the SVM model is as follows:
g(x)＝wxi+b
in the formula: w is a hyperplane normal vector; b is a hyperplane constant;
then, the problem of establishing the linear support vector machine is converted into the problem of solving a quadratic convex programming, and the following results are obtained:
Figure FDA0003598869880000021
in the formula: ζ represents a unitiIs a relaxation variable; c is a penalty factor;
and finally, converting the quadratic convex programming problem into a dual problem, namely obtaining:
Figure FDA0003598869880000022
in the formula: a isiFor Lagrange coefficients, applicable only to SVM models, aiIs not equal to 0; k (x)i,xj) Is a kernel function;
by carrying out mathematical theory analysis on the problems, the regression function of the support vector machine is obtained as follows:
Figure FDA0003598869880000023
4. the multi-objective performance optimization method for biodiesel for combustion of diesel engines, according to claim 3, is characterized in that: the K-fold cross validation method comprises the following steps:
firstly, taking a training sample as an object, dividing the training sample into k equal parts, enabling data of each equal part to sequentially become a verification set, and using the rest data for model establishment; performing k times according to the steps, and solving the mean square error of each training model; and finally, dividing the sum of the obtained mean square errors by K to obtain a model error of K-fold cross validation, wherein the error is used as an index for evaluating the precision of the model.
5. The multi-objective performance optimization method for biodiesel for combustion of diesel engines, according to claim 4, is characterized in that: the method for optimizing parameters by the grid search method comprises the following steps:
(1) setting a search range and a search step length according to experience, and drawing a two-dimensional grid;
(2) taking node parameter combinations in the grids, substituting the node parameter combinations into a target function to verify the performance of the nodes;
(3) and selecting a parameter combination with the lowest mean square error in the grid according to the performance evaluation, and if a plurality of groups of parameters have the same mean square error, selecting the group with the lowest parameter C as the optimal parameter.
6. The multi-objective performance optimization method for biodiesel for combustion of diesel engines as claimed in claim 5, wherein: the particle swarm algorithm comprises the following steps:
step 1: initializing particle parameters; comprises the following steps: setting population size N, determining maximum iteration number tmaxSelecting an inertia weight value omega, setting values of learning constants c1 and c2, and setting an initial position x of each particlei＝(xi1,xi2,…,xid) And an initial velocity vi＝(vi1,vi2,…,vid) And particle flight range;
step 2: calculating the fitness f (p) of any particle; solving the fitness of any particle according to the fitness function;
and step 3: optimal particle fitness pbestUpdating; the current generation fitness f (p) of any particle and the optimal particle fitness p obtained beforebestComparing if f (p) is better than pbestReplacing p with f (p)bestAs the optimal particle fitness, otherwise, the original optimal particle fitness pbestThe change is not changed;
and 4, step 4: optimal population fitness gbestUpdating; matching the fitness f (p) of all the particle generations with the optimal population fitness g obtained beforebestFor comparison, if f (p) is better than gbestReplacing g with f (p)bestAs the optimal population fitness, otherwise, the original optimal population fitness gbestKeeping the original shape;
and 5: particle position and velocity updates; according to the optimal particle fitness pbestAnd the optimal population fitness gbestUpdating the position and the speed of the particles by adopting a standard particle swarm algorithm to generate a new generation of population;
step 6: judging a termination condition; if the termination condition is satisfied, the optimal solution is output or the maximum solution is reachedLarge number of iterations tmaxIf yes, stopping not to perform iteration; otherwise, returning to the step 2 to continue the iteration.
7. The diesel combustion biodiesel multi-objective performance optimization method as claimed in claim 6, wherein: the NSGA-II algorithm is a modified non-dominated sorting genetic algorithm, comprising the following steps:
1) randomly generating an initialization population with the population scale of N, and carrying out non-dominated sorting on the initialization population;
2) calculating the initialized population by flexibly combining several algorithms of selection, crossing and variation to obtain a first generation sub population; in the process of establishing the second generation sub-population, the parent population and the child population are not discussed separately, but the non-dominated sorting and individual crowding degree evaluation are carried out by adhering to a rule of high-out and low-out, and excellent individuals are selected from the excellent individuals to form a new parent population;
3) step 2) is infinitely circulated until the practical requirement is met.
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