Fuel centrifugal pump multi-objective optimization method based on improved point adding criterion

Abstract

The invention discloses a fuel centrifugal pump multi-objective optimization method based on an improved adding point criterion, and belongs to the field of fuel centrifugal pump optimization design, and the method comprises the steps of selecting an initial sample point and establishing an initial database, establishing a Kriging model, collecting a new adding point, calculating a current Pareto solution set, updating the database and a Pareto leading solution, judging a termination condition and the like. According to the method, the improved point adding criterion is introduced and applied to optimization construction of the Kriging model, so that the prediction precision of the model near the optimal solution of the optimization problem is improved, and the optimal solution of the target problem is found more accurately and efficiently. Compared with an existing method, the classical point adding criterion is improved and popularized to the field of parallel and multi-target calculation, the purposes of improving the optimization efficiency and optimizing multiple parameters at the same time are achieved, the classical point adding criterion is applied to optimization design of the centrifugal pump, the external characteristic performance of the centrifugal pump is improved, and the method is suitable for popularization and application. And a reliable theoretical support is provided for optimization of rotary machinery such as a centrifugal pump.

Description

Technical Field

[0001] The invention belongs to the field of optimization design of fuel centrifugal pumps, and in particular relates to a multi-objective optimization method for fuel centrifugal pumps based on an improved addition point criterion. Background Art

[0002] The centrifugal fuel pump plays a vital role in the fuel system of aircraft engines. Its performance affects the stability of the fuel system and determines whether it can provide sufficient power for the engine. Therefore, in the design of the fuel system, the optimization design of the centrifugal pump is an extremely important part. By improving and optimizing its performance, the efficiency of fuel supply can be improved, and the reliability and stability of the engine can be improved.

[0003] In actual design, the performance of centrifugal pumps is affected by multiple parameters. If the traditional empirical method is used to design the parameters of centrifugal pumps, it will lead to problems such as long design cycle, high resource consumption and low performance of design results. With the development of computer computational fluid dynamics methods, the use of mathematical models to simulate the working process of pumps has become the mainstream method of pump design. However, the structure and working parameters of centrifugal pumps are too complex, and modeling, simulation and optimization of pumps require a large number of iterative processes. At present, the geometric parameters and performance parameters of the pumps have not been effectively analyzed. Therefore, it will cause problems such as long optimization time, cumbersome steps and easy to fall into local optimal solutions, which will eventually lead to large errors in the optimization results.

[0004] The Kriging model is an efficient interpolation model that fits the entire data set through a limited number of sample points to construct an approximate model. The model can use the response values ​​of known points to infer and estimate unknown points, so it is widely used in optimization design. After extracting the initial sample points, in order to improve the accuracy of the optimization results, an effective method is to use the information provided by the model (such as predicted values ​​and prediction errors) to construct a point-adding criterion function and search in the optimization space.

[0005] There are many function forms of the point adding criterion, and its purpose is to select the corresponding function to continuously generate new sampling points and add them to the initial data set according to the characteristics of the required points. However, several commonly used point adding criteria are currently aimed at single-objective optimization problems, and multi-objective point adding criteria are still rarely involved. In addition, existing research often involves complex parameter iteration processes, which makes the point adding criterion difficult to implement in parallel computing, and the application of the improved algorithm in centrifugal pumps is also very limited.

[0006] Therefore, in view of the above technical problems, how to improve the deficiencies of the existing technology and improve the performance, actual design accuracy and efficiency of the fuel centrifugal pump has become a technical challenge in this field. Summary of the invention

[0007] In response to the above technical problems, the present invention provides a multi-objective optimization method for a fuel centrifugal pump based on an improved adding-point criterion. The method introduces the improved adding-point criterion and applies it to the optimization construction of the Kriging model, thereby improving the prediction accuracy of the model near the optimal solution of the optimization problem, and thus finding the optimal solution of the target problem more accurately and efficiently.

[0008] The present invention solves the above problems by the following technical means:

[0009] A multi-objective optimization method for a fuel centrifugal pump based on an improved fuel point criterion, characterized in that it comprises the following steps:

[0010] Step 1) Select the initial sample points and establish the initial database, where: n initial sample points [x 1 ,x 2 ,...,x n ], and analyze the true response value to obtain the initial sample library [y 1 ,y 2 ,...,y n ];

[0011] Step 2) Establish a Kriging model, where: the initial database [x 1 ,x 2 ,...,x n ] and its corresponding response value [y 1 ,y 2 ,...,y n ], Kriging models are established for m optimization objectives respectively, and a total of m models are constructed;

[0012] Step 3) Calculate the current Pareto solution set, where: Analyze and compare the current database [y 1 ,y 2 ,...,y n ] and calculate the current Pareto solution set;

[0013] Step 4) Collect new points, where: obtain the new points x by solving the sub-optimization problem of the PAM / PPAM criterion new , x new Calculated by the following two formulas:

[0014] When the PAM criterion is used for iteration, x new Calculated by the following formula: When the PPAM criterion is used for iteration, the qth new point is calculated by the following formula:

[0015] In the formula, U(x) is the improved point addition criterion function, n is the dimension of the optimization problem, k is the number of points in the current Pareto solution set, and θ m The θ value corresponding to the Kriging model of the mth optimization target;

[0016] Step 5) Update the database and Pareto frontier solution, analyze the true response value of the newly added sample points, update and reconstruct m Kriging models, compare the dominance relationship between the newly added points and the current Pareto frontier solution, and update the current Pareto solution set;

[0017] Step 6) Determine the termination condition, where: when computing resources are insufficient, the stopping criterion is set to the number of model iterations or the number of true value evaluations of the newly added points; when computing resources are sufficient, the overall accuracy of the model is used as the stopping condition; if the termination condition is currently met, the iteration is stopped and the current Pareto solution set is output; otherwise, go to step 4 and continue to iterate the model.

[0018] Preferably, in the process of selecting initial sample points and establishing an initial database, Latin hypercube sampling is implemented through the lhsdesign function built into the Matlab software, and the number of sample points in the initial sample library is set to 8 to 12 times the dimension of the optimization problem; if the target problem is a conventional mathematical example, the corresponding mathematical function is directly called to obtain the corresponding; if the target problem is an engineering problem, the true response value is obtained through finite element software.

[0019] Preferably, in the process of establishing the Kriging model, modeling is performed based on the DACE toolbox in Matlab software.

[0020] Preferably, in the process of calculating the current Pareto solution set, a non-dominated sorting algorithm is used for calculation.

[0021] Preferably, in the process of collecting new points, the value of the number of new points q is 2 to 5.

[0022] Preferably, in the process of collecting the newly added points, when the number of the newly added points q=1, the PPAM criterion becomes the original PAM criterion.

[0023] The multi-objective optimization method of the fuel centrifugal pump based on the improved addition point criterion of the present invention has the following beneficial effects:

[0024] 1) This paper proposes a variety of improved point addition criteria. By optimizing and improving several classic point addition criteria, it successfully extends them to the field of multi-objective optimization and parallel computing. The improved point addition criteria can search more effectively in the optimization space, significantly improving the optimization ability of the model. In the actual centrifugal pump optimization design, the performance of the optimized pump is also significantly improved.

[0025] 2) By comparing characteristic indicators such as hypervolume, the performance of different addition criteria in multi-objective optimization problems is evaluated, and the addition criteria that are most suitable for the engineering environment are selected. This process not only verifies the advantages of the improved addition criteria in optimization efficiency and optimization ability, but also provides certain theoretical support for the optimization application of the addition criteria in actual engineering.

[0026] 3) By applying the improved point-adding criterion to the optimal design of centrifugal pumps, the results show that the pump head and efficiency have been improved to a certain extent. This result not only verifies the effectiveness of the improved point-adding criterion in actual engineering, but also provides a certain theoretical basis and practical application examples for the field of optimal design of centrifugal pumps.

[0027] In summary, the present invention proposes an innovative solution to the multi-objective optimization problem of fuel centrifugal pumps by improving the classic point-adding criterion, and successfully generalizes the classic point-adding criterion to multi-objective and parallelization. This improvement effectively solves the common problems in the optimization design of centrifugal pumps, such as long optimization cycle and easy to fall into local optimal solution, and significantly improves the optimization efficiency and optimization ability. This solution provides strong technical support for the optimization design of centrifugal pumps, and fully demonstrates the advantages of the present invention in performance and application prospects through example verification and application in actual design. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] In order to more clearly illustrate the technical solution of the present invention, the drawings required for use in the implementation mode will be briefly introduced below. Obviously, the drawings described below are only some implementation modes of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0029] Figure 1 It is a Pareto frontier diagram of two optimization objectives;

[0030] Figure 2 It is an iterative flow chart based on the optimization of PAM criteria;

[0031] Figure 3 It is a schematic diagram of the hypervolume iteration of each criterion on the DTLZ2 example;

[0032] Figure 4 It is a schematic diagram of the hypervolume iteration of each criterion on the DTLZ2 example when the number of true value evaluations is the same;

[0033] Figure 5 is the box plot of each serial criterion hypervolume index;

[0034] Figure 6It is a comparison diagram of the Paerto solution set with the lowest hypervolume index and the true solution set of MPM and EIM on the DTLZ2 example;

[0035] Figure 7 It is the X-type fuel centrifugal pump impeller model and 3D model schematic diagram;

[0036] Figure 8 It is a schematic diagram of the cross section of the meridian flow channel of a centrifugal pump;

[0037] Fig. 9 It is a schematic diagram of the accuracy test results of the head model and the efficiency model;

[0038] Fig.10 It is a schematic diagram of the Pareto frontier;

[0039] Fig.11 It is the pressure distribution cloud diagram of the middle section of the centrifugal pump before and after optimization under different working conditions;

[0040] Fig.12 It is the distribution cloud diagram of turbulent kinetic energy in the middle section of the centrifugal pump before and after optimization under different working conditions; DETAILED DESCRIPTION

[0041] In the description of the present invention, it should be understood that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. The terms "first" and "second" are used for descriptive purposes only, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0042] The present invention will be described in detail below with reference to the accompanying drawings.

[0043] Embodiment 1

[0044] This embodiment describes in detail the optimization method of the Kriging model. In order to expand the effective multi-objective point addition criteria, the idea of ​​the point addition matrix is ​​introduced, and the original several classic point addition criteria are improved and extended to the multi-objective field. In order to improve the optimization efficiency, the improved multiple point addition criteria are extended to parallel computing. First, the classic point addition criteria are extended to the multi-objective field. In the multi-objective optimization problem, the Pareto frontier solution replaces the concept of the optimal solution in the single-objective optimization problem. Figure 1 It gives a schematic diagram of the Pareto front with two optimization objectives.

[0045] Among the Pareto front solutions, none of the solutions completely outperforms the others. In space, if the response values (f 1 1 , f 2 1 ) corresponding to point A completely outperform the response values (f 1 2 , f 2 2 ) corresponding to point B, that is, f 1 1 < f 1 2 and f 2 1 < f 2 2 , it is said that point A dominates point B, denoted as A < B. Thus, the entire design space is divided by the Pareto front into a dominated region and a non-dominated region, and any point in the dominated region is dominated by the points in the non-dominated region. The Pareto front solution is a vector that contains all the current non-dominated solutions and can be expressed as:

[0046]

[0047] where m is the number of optimization objectives and k is the number of points in the current Pareto front solution.

[0048] The Pareto front can be regarded as an extension of the optimal value f min in a single-objective optimization problem. It is considered that there is not just one optimal value but k optimal values for one optimization objective. Then, theoretically, the values of k addition criterion functions can be calculated. When there are m Kriging models, for a sample point in the defined space, k × m addition criterion function values can be obtained. Combining these addition criterion function values forms an addition matrix (Point adding matrix, PAM):

[0049]

[0050] In the formula, represents the value of the addition criterion function obtained for the sample point x on the m-th surrogate model for the k-th optimal value. To quantify the improvement of different points on the current Pareto front solution, the improvement amount of the m-th objective value y m (x) relative to the function value of the k-th point in the m-th optimization objective in the current Pareto front solution is defined as:

[0051]

[0052] Then the improvement matrix (IM) expression is as follows:

[0053]

[0054] Combining IM with the Euler distance improvement criterion can obtain the multi-objective Euler distance criterion based on improvement expectation, as shown in the following formula:

[0055]

[0056] According to this idea, the size of the PAM value can also clearly show the improvement of the sample point on the optimal value. The IM value in the above formula can be changed to the PAM value to form the PAM criterion based on the Euler distance. Therefore, several point addition criteria for single-objective optimization problems can be extended to the field of multi-objective optimization.

[0057] For the MP criterion, there is no current optimal value term in its calculation expression. After being extended to the MPM criterion, for an optimization objective, the improvement (MP value) of any unknown point to the current optimal value is the same, so it is necessary to improve it first so that it can give corresponding improvement values ​​for different optimal value points of the same optimization objective. The improved expression is as follows:

[0058]

[0059] In the formula, Indicates the first k The mth element of the row, Indicates the response value corresponding to the kth point in the mth optimization objective in the current Pareto frontier solution, is the predicted value given by the Kriging model of the mth optimization objective for the sample point x. For the convenience of description, the modified point addition criterion function is uniformly named U(x). In the MPM criterion,

[0060]

[0061] The MPM criterion based on the Euler distance criterion can be expressed as follows:

[0062]

[0063] Similarly, rewrite the LCB function as follows:

[0064]

[0065] in, The prediction variance given by the Kriging model for the mth optimization objective for the sample point x is given in the LCBM criterion:

[0066]

[0067] The corresponding LCBM criterion is expressed as:

[0068]

[0069] The expressions of EI and PI criteria contain the current optimal value terms, so there is no need to rewrite them. The corresponding EIM and PIM criteria expressions U(x) are the original EI and PI function expressions. When using the PPA criterion iteration, select the point with the largest PPA value in the design space as the new point. The PPA criterion calculates the new point x. new The expression is:

[0070]

[0071] After extending the classic point adding criterion to the multi-objective field, the present invention further applies the improved point adding criterion to parallel computing. By multiplying the element value in the PAM criterion with the influence function, the resulting matrix is ​​called PPAM (Paralleled point adding matrix, PPAM), and its expression is as follows:

[0072]

[0073] in, Calculated by the following formula:

[0074]

[0075] Among them, x (1) For the first new point, IF m is the influence function constructed according to the mth agent model. Thus, PMPM, PEIM, PPIM and PLCBM criteria can be obtained. Taking PMPM criterion as an example, in one cycle, the expression of the qth sample point that PMPM criterion needs to obtain is:

[0076]

[0077] in, is the kth element in the mth row of the current Pareto solution set, n is the dimension of the optimization problem, θ mis the predicted value of the Kriging model at x for the mth optimization target and the corresponding θ value. When q=1, the PMPM criterion becomes the original MPM criterion. Replacing U(x) in the above formula with the U(x) corresponding to each criterion in the PAM criterion can obtain the expression of other criteria to obtain the qth sample point. When calling the PPAM criterion iteration, each newly added point is the point with the largest PPAM value in the corresponding formula. The qth newly added point is calculated by the following formula:

[0078]

[0079] Embodiment 2

[0080] The flowchart of solving multi-objective optimization problems based on improved PAM and PPAM criteria is as follows Figure 2 As shown, the specific iteration includes the following steps:

[0081] (1) Selection of initial sample points and establishment of initial database. Using the Latin hypercube sampling method, n initial sample points [x 1 ,x 2 ,...,x n ], and analyze the true response value to obtain the initial sample library. The Latin hypercube sampling is implemented by the lhsdesign function built into the Matlab software. The number of sample points n in the initial sample library is generally set to 10 times the dimension d of the optimization problem. If the target problem is a conventional mathematical example, directly call the corresponding mathematical function to obtain the corresponding [y 1 ,y 2 ,...,y n ] If the target problem is an engineering problem, the true response value is obtained through finite element software such as Ansys.

[0082] (2) Establishment of Kriging model. The initial database [x 1 ,x 2 ,...,x n ] and its corresponding response value [y 1 ,y 2 ,...,y n ], based on the DACE toolbox in Matlab software, Kriging models were established for m optimization objectives respectively, and a total of m models were constructed.

[0083] (3) Calculate the current Pareto solution set. Analyze and compare the current database [y 1 ,y 2 ,...,y n ] to calculate the dominance relationship between them, and calculate the current Pareto solution set, which is generally calculated using a non-dominated sorting algorithm.

[0084] (4) Collection of new points. The new points x are obtained by solving the sub-optimization problem of the PAM / PPAM criterion mentioned above. new , taking the MPM criterion and the PMPM criterion as examples, when calling the MPM criterion, the new point is obtained by finding the maximum value of formula (22), that is, When the PMPM criterion is called, the calculation formula for the qth new point is The maximum value in the formula is calculated, that is, The necessary parameter descriptions have been given in the previous article. In one iteration cycle, the number of new points q is specified by the designer. In the subsequent examples, the values ​​of q are 2 and 4 respectively.

[0085] (5) Update of database and Pareto frontier solution. Perform true response value analysis on the newly added sample points obtained in (4), update and reconstruct m Kriging models, compare the dominance relationship between the newly added points and the current Pareto frontier solution, and update the current Pareto solution set.

[0086] (6) Termination condition. Determine whether to stop the iteration at this time. When the computing resources are insufficient, the stopping criterion is set to the number of model iterations or the number of true value evaluations of the newly added points. When the computing resources are sufficient, the overall accuracy of the model is used as the stopping condition. If the termination condition is currently met, the iteration is stopped and the current Pareto solution set is output. Otherwise, go to step (4) and continue to iterate the model.

[0087] Embodiment 3

[0088] This embodiment describes in detail the multi-objective optimization method example test process. In order to verify the multi-objective optimization capabilities of several serial criteria and parallel criteria, the verification and comparison between the criteria are carried out on the classic DTLZ2 example. The example has six optimization parameters and three optimization objectives. The number of initial sample points is determined according to the dimension of the test example and is set to 60. The convergence condition is k≤k max , where parameter k is the current number of iterations, k max The maximum number of iterations allowed is set to 120. The hypervolume index is used to measure the multi-objective optimization ability of different algorithms, and the reference point for calculating the hypervolume value is set to [2.5, 2.5, 2.5]. 20 repeated tests were performed on the test case using different criteria to reduce the experimental error. The iteration of the hypervolume of each criterion on the DTLZ2 test function is shown in Figure 3 The results show that in the early iteration process, as the q value increases, the optimization speed is significantly accelerated, and the optimization efficiency of the parallel criterion is higher than that of the serial criterion.

[0089] Also note Figure 3The q value increases, but the final hypervolume index does not increase. The reason is that after a small number of search iterations, an approximate frontier solution set has been obtained. When the number of sample points in the sample library reaches a certain level, the fitted Pareto frontier is already very close to the real Pareto frontier of the example, and the hypervolume value will not change much when iterated again. Therefore, considering the computational cost factor, when selecting the parallel criterion for optimization, it is more inclined to select the parallel criterion of q=2. In summary, the four parallel point-adding criteria proposed in the present invention are superior to the original serial criteria in terms of optimization ability and efficiency in most cases, among which the improvement is particularly significant when q=2. In actual engineering optimization problems, since the number of true value evaluations is usually limited, it is necessary to compare the optimization capabilities of serial criteria and parallel criteria when the same number of true value evaluations is used. The maximum number of true value evaluations is set to 120, and the other settings remain unchanged. The hypervolume iteration process of the DTLZ2 example can be seen in Figure 4 The results show that the sample point utilization of the parallel criterion is not as good as that of the serial criterion, and as the q value increases, the sample point utilization shows a downward trend.

[0090] Therefore, in the subsequent multi-objective optimization of centrifugal pumps, the serial criterion with higher sample point utilization is more suitable for the actual application environment. The performance of the four serial criteria on the test problem is compared. Figure 5 The hypervolume box plots of each criterion on the test problem in 20 repeated experiments are given. The results show that in the DTLZ2 example, the MPM criterion is superior in median and mean, and the EIM criterion is superior in standard deviation.

[0091] Further comparison of these two criteria, Figure 6 The comparison between the fitted Pareto front and the true Pareto front is shown when the final hypervolume index is minimized in 20 iterations.

[0092] The results show that the approximate Pareto frontier collected by the EIM criterion has more discrete points on the plane, but the overall difference with the MPM criterion is small, and there is no obvious difference between the two methods. Therefore, we compare the robustness of the criterion. Table 1 gives the comparison of parameter indicators of the two methods on the DTLZ2 example.

[0093] Table 1 Comparison of the results of the two optimization methods on the test problem

[0094]

[0095] The results show that the standard deviation index of the EIM criterion performs better when the differences in other indicators are small. Therefore, considering the frontier performance and characteristic indicators of the two criteria, the EIM criterion is considered to be the best choice.

[0096] Embodiment 4

[0097] The above method is used to optimize the design of the X-type aviation fuel centrifugal pump, and its model is shown in the figure below. Figure 7 As shown. It is required that both pump head and efficiency performance be optimized and improved. The actual head calculation expression of the centrifugal pump is

[0098]

[0099] In the formula, H T is the theoretical infinite head of the pump, h hT is the hydraulic loss of the pump, D 2 is the centrifugal pump impeller outlet diameter, Ψ 2 is the impeller outlet displacement coefficient, b 2 is the impeller outlet width, β 2 Place the blade outlet angle.

[0100] The calculation expression of hydraulic efficiency of centrifugal pump is:

[0101]

[0102] The performance parameters and some main structural parameters of the X-type aviation fuel centrifugal pump are shown in Table 2.

[0103] Table 2X aviation fuel centrifugal pump parameter table

[0104]

[0105] Through the analysis of the sensitivity of each parameter to the head and efficiency, the structural parameters D 2 , b 2 and β 2 , profile parameter k 1 , k 2 The parameter Δz is the optimization parameter. Δz is defined as the axial distance between the impeller middle profile and the impeller inlet. 1 , k 2 The two points are the determining points of the hub profile position of the centrifugal pump meridian flow channel, such as Figure 8 The calculation formula is as follows:

[0106]

[0107] The initial values ​​and variation ranges of each optimization parameter are shown in Table 3.

[0108] Table 3 Initial values ​​and variation ranges of each optimization parameter

[0109]

[0110] Based on the EIM criterion, the multi-objective optimization of the centrifugal pump head and efficiency is completed, and the complex correlation coefficient is used as the iteration stop condition of the model. The calculation formula of the complex correlation coefficient is as follows:

[0111]

[0112] In the formula, y i is the true value of the sample point, is the model prediction value of the corresponding sample point, is the average value of all sample point responses, R 2 The closer the value is to 1, the higher the approximation accuracy of the model. v is the number of sample points in the test set. Due to the large lift value, a certain error in model prediction is allowed. The R of stopping iteration of lift model 2 The value is set to 0.85, and the R 2 After 273 iterations, the accuracy of the model reached the convergence requirement. At this time, the R 2 The values ​​are 0.8753 and 0.9262 respectively. The accuracy test results of the two models are as follows Fig. 9 .

[0113] The converged model is used as the fitness function, and the MOPSO algorithm is called to search for the Pareto frontier solution in the entire optimization space. The initial population size is set to 200, the current Pareto frontier library size is 100, and it is iterated 500 times. The Pareto frontier searched is as follows: Fig.10 .

[0114] The 100 points in the Pareto front are all non-dominated solutions. Theoretically, these 100 points are the optimal solutions to the optimization problem in this section. Compared with the head, we pay more attention to the improvement of the efficiency of the centrifugal pump. Therefore, the following formula is constructed to select the final optimization result from the 100 points in the Pareto front.

[0115]

[0116] Where η ori With H ori represents the efficiency and head of the prototype pump, η P With H P is the efficiency and lift of the midpoint of the Pareto frontier, and the I P The point with the largest value can be used to obtain the point with relatively large efficiency improvement, and the relevant parameters of the extracted optimal point are given in Table 4. After optimization, the head of the pump is relatively increased by 11.11%, and the efficiency is relatively increased by 10.82%.

[0117] Table 4 Comparison of various performances of centrifugal pumps before and after optimization

[0118]

[0119] In order to compare the performance of the centrifugal pump under different working conditions before and after optimization, the d , Q d and 1.2Q d The performance of the centrifugal pump before and after optimization was compared and analyzed under working conditions.

[0120] Fig.11 The pressure distribution cloud diagram of the middle section of the centrifugal pump before and after optimization is given. The results are shown in Fig.11 Under the three working conditions, the pressure in the optimized pump is higher than that in the original pump. In addition, the low-pressure area of ​​the leading edge of the main blade, the volute tongue and the leading edge of the splitter blade of the optimized pump is reduced, and the overall pressure stratification is more obvious in the optimized pump, and the pressure distribution is more uniform.

[0121] Fig.12 The turbulent kinetic energy distribution cloud diagram of the middle section of the centrifugal pump before and after optimization under different working conditions is given. Fig.12 In the experiment, the multi-objective optimized pump showed higher turbulent kinetic energy under small flow conditions. Under rated conditions, the turbulent kinetic energy of the optimized pump in the volute part was significantly reduced. Under large flow conditions, although the turbulent kinetic energy of the optimized pump in the volute part was slightly higher than that of the prototype pump, the liquid flow in the impeller part was obviously smoother.

[0122] Therefore, under all working conditions, the pressure distribution and the turbulent kinetic energy distribution of the middle section of the multi-objective optimized pump are better than those of the prototype pump, which verifies the feasibility of this method in the actual centrifugal pump optimization problem.

[0123] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective optimization method for a fuel centrifugal pump based on an improved point-adding criterion, characterized in that: The steps include: Step 1) Select the initial sample points and establish the initial database, where: n initial sample points [x1, x2, ..., x n ], and analyze the true response value to obtain the initial sample library [y1,y2,...,y n ]; Step 2) Establish a Kriging model, where: the initial database [x1, x2, ..., x n ] and its corresponding response value [y1,y2,...,y n ], Kriging models are established for m optimization objectives respectively, and a total of m models are constructed; Step 3) Calculate the current Pareto solution set, where: Analyze and compare the current database [y1, y2, ..., y n ] and calculate the current Pareto solution set; Step 4) Collect new points, where: obtain the new points x by solving the sub-optimization problem of the PAM / PPAM criterion new , when the PAM criterion is used for iteration, x new Calculated by the following formula: When the PPAM criterion is used for iteration, the qth new point is calculated by the following formula: In the formula, U(x) is the improved point addition criterion function, n is the dimension of the optimization problem, k is the number of points in the current Pareto solution set, and θ m The θ value corresponding to the Kriging model of the mth optimization target; Step 5) Update the database and Pareto frontier solution, analyze the true response value of the newly added sample points, update and reconstruct m Kriging models, compare the dominance relationship between the newly added points and the current Pareto frontier solution, and update the current Pareto solution set; Step 6) Determine the termination condition, where: when computing resources are insufficient, the stopping criterion is set to the number of model iterations or the number of true value evaluations of the newly added points; when computing resources are sufficient, the overall accuracy of the model is used as the stopping condition; if the termination condition is currently met, the iteration is stopped and the current Pareto solution set is output; otherwise, go to step 4 and continue to iterate the model.

2. The multi-objective optimization method for a fuel centrifugal pump based on an improved point-adding criterion according to claim 1 is characterized in that: In the process of selecting the initial sample points and establishing the initial database, Latin hypercube sampling is implemented through the lhsdesign function built into the Matlab software, and the number of sample points in the initial sample library is set to 8 to 12 times the dimension of the optimization problem; if the target problem is a conventional mathematical example, the corresponding mathematical function is directly called to obtain the corresponding; if the target problem is an engineering problem, the true response value is obtained through finite element software.

3. The multi-objective optimization method for a fuel centrifugal pump based on an improved point-adding criterion according to claim 1 is characterized in that: In the process of establishing the Kriging model, modeling is performed based on the DACE toolbox in Matlab software.

4. The multi-objective optimization method for a fuel centrifugal pump based on an improved point-adding criterion according to claim 1 is characterized in that: In the process of calculating the current Pareto solution set, a non-dominated sorting algorithm is used for calculation.

5. The multi-objective optimization method for a fuel centrifugal pump based on an improved fuel point criterion according to claim 1, characterized in that: In the process of collecting new points, the value of the number of new points q is 2 to 5.

6. The multi-objective optimization method for a fuel centrifugal pump based on an improved point-adding criterion according to claim 1 is characterized in that: In the process of collecting new points, when the number of new points q=1, the PPAM criterion becomes the original PAM criterion.

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