A multi-objective optimization method for fuel centrifugal pump based on improved point adding criterion

Abstract

This invention discloses a multi-objective optimization method for fuel centrifugal pumps based on an improved point-addition criterion, belonging to the field of fuel centrifugal pump optimization design. The method includes steps such as selecting initial sample points and establishing an initial database, building a Kriging model, collecting newly added points, calculating the current Pareto solution set, updating the database and Pareto front solutions, and determining termination conditions. This method introduces an improved point-addition criterion and applies it to the optimization construction of the Kriging model, thereby improving the model's prediction accuracy near the optimal solution of the optimization problem, and thus finding the optimal solution of the target problem more accurately and efficiently. Compared with existing methods, this method improves the classical point-addition criterion and extends it to the field of parallel and multi-objective computation, achieving the goal of improving optimization efficiency and simultaneously optimizing multiple parameters. Its application in the optimization design of centrifugal pumps improves their external performance characteristics, providing reliable theoretical support for the optimization of centrifugal pumps and other rotating machinery.

Description

Technical Field

[0001] This invention belongs to the field of fuel centrifugal pump optimization design, and particularly relates to a multi-objective optimization method for fuel centrifugal pumps based on an improved addition criterion. Background Technology

[0002] Centrifugal pumps play a crucial role in aircraft engine fuel systems, and their performance directly impacts the stability of the fuel system, ultimately determining whether sufficient power can be provided to the engine. Therefore, optimizing the design of centrifugal pumps is an extremely important aspect of fuel system design. By improving and optimizing their performance, fuel supply efficiency can be increased, enhancing engine reliability and stability.

[0003] In practical design, the performance of centrifugal pumps is affected by multiple parameters. Using traditional empirical methods to design these parameters leads to long design cycles, high resource consumption, and low performance. With the development of computational fluid dynamics (CFD), simulating the pump's operation using mathematical models has become the mainstream method for pump design. However, the structure and operating parameters of centrifugal pumps are extremely complex. Modeling, simulating, and optimizing pumps require numerous iterations, and currently, there is no effective analytical method for analyzing the pump's geometric and performance parameters. This results in long optimization times, cumbersome steps, and a tendency to get trapped in local optima, ultimately leading to significant errors in the optimization results.

[0004] The Kriging model is an efficient interpolation model that fits the entire dataset to a finite number of sample points to construct an approximate model. This model can infer and estimate unknown points using the response values ​​of known points, and is therefore widely used in optimization design. After extracting initial sample points, an effective method to improve the accuracy of the optimization results is to construct an addition criterion function using information provided by the model (such as predicted values ​​and prediction errors) and search within the optimization space.

[0005] The point addition criterion has various functional forms. Its purpose is to continuously generate new sampling points and add them to the initial dataset based on the characteristics of the required points and the corresponding function. However, the commonly used point addition criteria are all aimed at single-objective optimization problems. Multi-objective point addition criteria are still rarely involved. Moreover, existing studies often involve complex parameter iteration processes, making point addition criteria difficult to implement in parallel computing. The application of improved algorithms in centrifugal pumps is also very limited.

[0006] Therefore, addressing the aforementioned technical issues, how to improve the shortcomings of existing technologies and enhance the performance, actual design accuracy, and efficiency of fuel centrifugal pumps has become a key technical challenge in this field. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a multi-objective optimization method for fuel centrifugal pumps based on an improved addition criterion. This method introduces an improved addition criterion and applies it to the optimization construction of the Kriging model, thereby improving the model's prediction accuracy 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 through the following technical means:

[0009] A multi-objective optimization method for a fuel centrifugal pump based on an improved addition criterion, characterized by the following steps:

[0010] Step 1) Select initial sample points and establish an initial database, wherein: n initial sample points [x1, x2, ..., xn] are extracted according to the dimension d of the optimization problem using the Latin hypercube sampling method. n ], and perform real response value analysis on them to obtain the initial sample library [y1, y2, ..., y n ];

[0011] Step 2) Establish the Kriging model, where: the initial database [x1, x2, ..., x] obtained in Step 1 is used. n ] and their corresponding response values ​​[y1, y2, ..., y n For each of the m optimization objectives, a Kriging model is established, resulting in a total of m models.

[0012] Step 3) Calculate the current Pareto solution set, where: analyze and compare [y1, y2, ..., y] in the current database. n ] , calculate the current Pareto solution set based on the dominance relationship between them;

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

[0014] When using the PAM criterion for iteration, x new Calculated using the following formula When using the PPAM criterion for iteration, the qth newly added point is calculated using 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 Let θ be the value of the Kriging model corresponding to the m-th optimization objective;

[0015] Step 5) Update the database and Pareto front solutions, perform true response value analysis on the newly added sample points, update and reconstruct m Kriging models, compare the dominance relationship between the newly added points and the current Pareto front solutions, and update the current Pareto solution set;

[0016] Step 6) Determine the termination condition, where: when computing resources are insufficient, the stopping criterion is set to the number of iterations of the model or the number of times the true value of the newly added point is evaluated; when computing resources are sufficient, the overall accuracy of the model is used as the stopping condition; if the current termination condition is met, the iteration stops and the current Pareto solution set is output; otherwise, go to step 4 and continue iterating the model.

[0017] Preferably, in the process of selecting initial sample points and establishing the initial database, Latin hypercube sampling is implemented using 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 result. If the target problem is an engineering problem, the actual response value is obtained through finite element software.

[0018] Preferably, the Kriging model is established using the DACE toolbox in Matlab software.

[0019] Preferably, the calculation of the current Pareto solution set is performed using a non-dominated sorting algorithm.

[0020] Preferably, during the process of collecting new data points, the number of new data points q is between 2 and 5.

[0021] Preferably, during the process of collecting new points, when the number of new points q = 1, the PPAM criterion changes to the original PAM criterion.

[0022] The multi-objective optimization method for fuel centrifugal pumps based on the improved addition criterion of the present invention has the following beneficial effects:

[0023] 1) This invention proposes several improved point-addition criteria. By optimizing and improving several classic point-addition criteria, it successfully extends them to the fields of multi-objective optimization and parallel computing. The improved point-addition criteria can search more effectively in the optimization space, significantly improving the model's optimization capability. In actual centrifugal pump optimization design, the performance of the optimized pump is also significantly improved.

[0024] 2) By comparing characteristic indicators such as hypervolume, the performance of different point-addition criteria in multi-objective optimization problems is evaluated, and the most suitable point-addition criterion for the engineering environment is selected. This process not only verifies the advantages of the improved point-addition criterion in optimization efficiency and optimization capability, but also provides certain theoretical support for the optimization application of the point-addition criterion in practical engineering.

[0025] 3) By applying the improved point-addition criterion to the optimization design of centrifugal pumps, the results show that both the pump head and efficiency are improved to a certain extent. This achievement not only verifies the effectiveness of the improved point-addition criterion in practical engineering, but also provides a certain theoretical basis and practical application example for the optimization design of centrifugal pumps.

[0026] In summary, this invention proposes an innovative solution to the multi-objective optimization problem of fuel centrifugal pumps by improving the classic addition criterion, and successfully generalizes the classic addition criterion to multiple objectives and parallel processing. This improvement effectively solves the common problems in centrifugal pump optimization design, such as long optimization cycles and susceptibility to local optima, significantly improving optimization efficiency and optimization capability. This solution provides strong technical support for centrifugal pump optimization design, and through numerical examples and application in practical design, it fully demonstrates the advantages of this invention in terms of performance and application prospects. Attached Figure Description

[0027] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a schematic diagram of a Pareto front with two optimization objectives;

[0029] Figure 2 Iterative flowchart based on PAM criterion for optimization;

[0030] Figure 3 This is a schematic diagram of the hypervolume iteration of each criterion on the DTLZ2 example;

[0031] Figure 4 This 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;

[0032] Figure 5 It is a box plot of the overvolume index of each serial criterion;

[0033] Figure 6 This is a schematic diagram comparing the Paerto solution set with the lowest hypervolume index for MPM and EIM on the DTLZ2 example with the actual solution set.

[0034] Figure 7 This is a schematic diagram of the impeller model and 3D model of an X-type fuel centrifugal pump;

[0035] Figure 8 This is a schematic diagram of the cross-section of the meridional channel of a centrifugal pump;

[0036] Figure 9 This is a schematic diagram showing the accuracy verification results of the head model and efficiency model;

[0037] Figure 10 This is a schematic diagram of the Pareto front;

[0038] Figure 11 These are cloud maps showing the pressure distribution at the mid-section of the centrifugal pump before and after optimization under different operating conditions;

[0039] Figure 12 These are cloud maps showing the turbulent kinetic energy distribution at the mid-section of the centrifugal pump before and after optimization under different operating conditions. Detailed Implementation

[0040] In the description of this invention, it should be understood that the terms "center," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0041] The present invention will now be described in detail with reference to the accompanying drawings.

[0042] Example 1

[0043] This embodiment elaborates on the optimization method of the Kriging model. To expand the effective multi-objective addition criteria, the concept of an addition matrix is ​​introduced, improving and extending several classic addition criteria to the multi-objective domain. To improve optimization efficiency, the improved addition criteria are further extended to parallel computing. First, the classic addition criteria are extended to the multi-objective domain. In multi-objective optimization problems, the Pareto front solution replaces the concept of the optimal solution in single-objective optimization problems. Figure 1 A schematic diagram of the Pareto front with two optimization objectives is given.

[0044] In the Pareto front solutions, no single solution is completely superior to the others. In space, if the response value corresponding to a point A is (f1...) 1 f2 1 It is completely superior to the response value (f1) corresponding to point B. 2 f2 2 ), i.e., f1 1 <f1 2 And f2 1 <f2 2 Point A is said to dominate point B, denoted as A < B. Thus, the entire design space is divided into dominated and non-dominated regions by the Pareto front. Every point in the dominated region is dominated by points in the non-dominated region. The Pareto front solution is a vector containing all current non-dominated solutions, which can be expressed as:

[0045]

[0046] Where m is the number of optimization objectives and k is the number of points in the current Pareto front solution.

[0047] The Pareto front can be viewed as the optimal value f in a single-objective optimization problem. min An extension of this approach. It assumes that there are k optimal values ​​for an optimization objective, not just one. Theoretically, k point-adding criterion functions can be calculated. When there are m Kriging models, for a sample point in the defined space, k×m point-adding criterion function values ​​can be obtained. Combining these point-adding criterion function values ​​forms the point-adding matrix (PAM):

[0048]

[0049] In the formula, This represents the value of the criterion function obtained for 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 m-th objective value y is... m (x) is the function value at the k-th point relative to the m-th optimization objective in the current Pareto front solution. The improvement amount is defined as:

[0050]

[0051] The improvement matrix (IM) expression is as follows:

[0052]

[0053] Combining the IM with the Euler distance improvement criterion yields a multi-objective Euler distance criterion based on improvement expectations, as shown in the following equation:

[0054]

[0055] Following this idea, the magnitude of the PAM value can also clearly indicate the improvement of the sample points to the optimal value. The IM value in the above formula can be replaced with the PAM value to form the PAM criterion based on Eulerian distance. Thus, several point addition criteria for single-objective optimization problems can be extended to the field of multi-objective optimization.

[0056] For the MP criterion, its calculation expression does not contain a current optimal value term. However, when generalized to the MPM criterion, for an optimization objective, the improvement (MP value) at any unknown point with respect to the current optimal value is the same. Therefore, it needs to be improved so that it can provide corresponding improvement values ​​for different optimal points of the same optimization objective. The improved expression is as follows:

[0057]

[0058] In the formula, Indicates the first in MPM k The m-th element of the row, This represents the response value corresponding to the k-th point in the m-th optimization objective in the current Pareto front solution. This is the predicted value given by the Kriging model for the m-th optimization objective for sample point x. For ease of description, the modified addition criterion function is uniformly named U(x). In the MPM criterion,

[0059]

[0060] The MPM criterion based on the Euler distance criterion can be expressed as follows:

[0061]

[0062] Similarly, the LCB function can be rewritten as follows:

[0063]

[0064] in, The prediction variance given by the Kriging model for the m-th optimization objective for sample point x, in the LCBM criterion:

[0065]

[0066] The corresponding LCBM criterion is stated as follows:

[0067]

[0068] The expressions for the EI and PI criteria already include the current optimal value, so they do not need to be rewritten. In the corresponding EIM and PIM criterion expressions, U(x) is the original EI and PI function expression. When using the PPA criterion for iteration, the point in the design space with the largest corresponding PPA value is selected as the new point. The PPA criterion is used to calculate the new point x. new The expression is:

[0069]

[0070] After extending the classic point-adding criterion to the multi-objective domain, this invention further applies the improved point-adding criterion to parallel computing. The matrix obtained by multiplying the element values ​​in the PAM criterion by the influence function is called PPAM (Paralleledpoint adding matrix), and its expression is as follows:

[0071]

[0072] in, It is calculated by the following formula:

[0073]

[0074] Where, x (1) For the first new point, IF m Let m be the influence function constructed based on the m-th surrogate model. From this, the PMPM, PEIM, PPIM, and PLCBM criteria can be obtained. Taking the PMPM criterion as an example, the expression for the q-th sample point required by the PMPM criterion within one period is:

[0075]

[0076] in, Let n be the k-th element in the m-th row of the current Pareto solution set, where n is the dimension of the optimization problem. θ m Let q = 1, and let θ = 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 yields the expressions for obtaining the q-th sample point using other criteria. When iterating using the PPAM criterion, each newly added point is the point with the largest PPAM value in the corresponding formula. The q-th newly added point is calculated by the following formula:

[0077]

[0078] Example 2

[0079] The flowchart for solving multi-objective optimization problems based on improved PAM and PPAM criteria is shown below. Figure 2 As shown, the specific iteration includes the following steps:

[0080] (1) Selection of initial sample points and establishment of the initial database. Using the Latin hypercube sampling method, n initial sample points [x1, x2, ..., xn] are extracted according to the dimension d of the optimization problem. n The initial sample library is obtained by analyzing the actual response values ​​of the samples. Latin hypercube sampling is implemented using the built-in `lhsdesign` function in Matlab. 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, the corresponding mathematical function is directly called to obtain the corresponding [y1, y2, ..., y...]. n If the target problem is an engineering problem, the actual response value can be obtained through finite element software such as Ansys.

[0081] (2) Establishment of the Kriging model. The initial database [x1, x2, ..., x] obtained in step (1) is used... n ] and their corresponding response values ​​[y1, y2, ..., y n Based on the DACE toolbox in Matlab software, Kriging models were built for each of the m optimization objectives, resulting in a total of m models.

[0082] (3) Calculate the current Pareto solution set. Analyze and compare the current database [y1, y2, ..., y...]. n To determine the dominance relationship between the elements, the current Pareto solution set is calculated, typically using a non-dominated sorting algorithm.

[0083] (4) Acquisition of new points. New points x are obtained by solving the sub-optimization problem based on the aforementioned PAM / PPAM criteria. new Taking the MPM criterion and PMPM criterion as examples, when calling the MPM criterion, the new point is obtained by finding the maximum value of equation (22), that is... When applying the PMPM criterion, the formula for calculating the qth new point is: The maximum value in the formula is obtained by calculation, that is The necessary parameter descriptions have been given above. In one iteration cycle, the number of new points q is specified by the designer; in subsequent examples, the value of q is taken as 2 and 4 respectively.

[0084] (5) Update the database and Pareto front solutions. Analyze the true response values ​​of 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 front solutions, and update the current Pareto solution set.

[0085] (6) Termination Condition. Determine whether to stop iteration at this point. If computational resources are insufficient, the stopping criterion is set to the number of iterations of the model or the number of times the true value of the newly added point is evaluated. If computational resources are sufficient, the overall accuracy of the model is used as the stopping condition. If the termination condition is met, stop iteration and output the current Pareto solution set; otherwise, go to step (4) and continue iterating the model.

[0086] Example 3

[0087] This embodiment details the test process of the multi-objective optimization method. To verify the multi-objective optimization capabilities of several serial and parallel criteria, a comparison of the criteria is performed on the classic DTLZ2 example, which has six optimization parameters and three optimization objectives. The initial number of sample points is determined based on the dimension of the test example and is set to 60. The convergence condition is k ≤ k max Where, parameter k is the current iteration number, k max The maximum allowed number of iterations is set to 120. The hypervolume metric is used to measure the multi-objective optimization capability of different algorithms, with the reference point for calculating the hypervolume value set to [2.5, 2.5, 2.5]. Twenty repeated trials using different criteria were conducted on the test case to reduce experimental error. The iteration results of hypervolume for each criterion on the DTLZ2 test function are shown in [details omitted]. Figure 3 The results show that in the early iterations, the optimization speed increases significantly with the increase of the q value, and the optimization efficiency of the parallel criterion is higher than that of the serial criterion.

[0088] At the same time, it should be noted Figure 3 In some cases, the q-value increases, but the final hypervolume index does not increase. This is because after a few search iterations, an approximate front solution set is obtained. When the number of sample points in the sample library reaches a certain level, the fitted Pareto front is very close to the true Pareto front of the example, and the hypervolume value will not change significantly in subsequent iterations. Therefore, considering computational cost, when using parallel criteria for optimization, the parallel criterion with q=2 is preferred. In summary, the four parallel point-addition criteria proposed in this invention outperform the original serial criteria in most cases in terms of optimization ability and efficiency, with the improvement being particularly significant when q=2. In practical engineering optimization problems, since the number of true value evaluations is usually limited, it is necessary to compare the optimization capabilities of serial and parallel criteria with the same number of true value evaluations. The maximum number of true value evaluations is set to 120, with other settings remaining unchanged. The hypervolume iteration process of the DTLZ2 example is shown below. Figure 4 The results show that the utilization rate of sample points in the parallel criterion is not as good as that in the serial criterion, and the utilization rate of sample points decreases as the q value increases.

[0089] Therefore, in subsequent multi-objective optimization of centrifugal pumps, selecting the serial criterion with higher sample point utilization is more in line with the actual application environment. The performance of four serial criteria on the testing problem is compared. Figure 5 Hypervolume box plots for each criterion on the test problem are presented in 20 repeated trials. The results show that on the DTLZ2 example, the MPM criterion is superior in terms of median and mean, while the EIM criterion is superior in terms of standard deviation.

[0090] A further comparison of these two criteria, Figure 6 The results show a comparison between the fitted Pareto front and the true Pareto front when the final hypervolume index is minimized in 20 iterations.

[0091] The results show that the approximate Pareto front acquired by the EIM criterion has many discrete points in the plane, but the overall difference with the MPM criterion is small, with no obvious superiority or inferiority. Therefore, in terms of the robustness of the criteria, Table 1 shows the comparison of the parameter indices of the two methods on the DTLZ2 example.

[0092] Table 1 Comparison of results of the two optimization methods on the test problem.

[0093]

[0094] The results show that, when other indicators are relatively similar, the standard deviation of the EIM criterion performs better. Therefore, considering both the frontier performance and characteristic indicators of the two criteria, the EIM criterion is considered the optimal choice.

[0095] Example 4

[0096] The X-type aviation fuel centrifugal pump was optimized using the above method, and its model diagram is shown below. Figure 7 As shown. The goal is to optimize and improve both the pump's head and efficiency. The expression for calculating the actual head of a centrifugal pump is:

[0097]

[0098] In the formula, H T For the pump's theoretical infinite head, h hT Ψ2 is the hydraulic loss of the pump, D2 is the impeller outlet diameter of the centrifugal pump, Ψ2 is the impeller outlet displacement coefficient, b2 is the impeller outlet width, and β2 is the blade outlet placement angle.

[0099] The expression for calculating the hydraulic efficiency of a centrifugal pump is as follows:

[0100]

[0101] The performance parameters and some main structural parameters of the X-type aviation fuel centrifugal pump are shown in Table 2.

[0102] Table 2X Type Aviation Fuel Centrifugal Pump Parameter Table

[0103]

[0104] Based on the analysis of the sensitivity of various parameters to head and efficiency, D2, b2, and β2 of the structural parameters, k1 and k2 of the profile parameters, and Δz of the parameter were selected as the optimization parameters. Δz is defined as the axial distance between the impeller center profile and the impeller inlet. Points k1 and k2 are the points for determining the position of the hub profile of the meridional flow channel of the centrifugal pump, such as... Figure 8 As shown. Its calculation formula is as follows:

[0105]

[0106] The initial values ​​and ranges of each optimization parameter are shown in Table 3.

[0107] Table 3 Initial values ​​and range of variation for each optimization parameter

[0108]

[0109] Multi-objective optimization of centrifugal pump head and efficiency was performed based on the EIM criterion. The complex correlation coefficient was used as the stopping condition for the model iteration. The formula for calculating the complex correlation coefficient is shown below:

[0110]

[0111] In the formula, y i Let be the true value of the i-th sample point. These are the model prediction values ​​for the corresponding sample points. R is the average of the response values ​​of all sample points. 2 The closer the value is to 1, the higher the approximation accuracy of the model. v This represents the number of sample points in the test set. Since the head value is relatively large, a certain degree of error in the model prediction is allowed; the stopping iteration of the head model is determined by Ro. 2 The value is set to 0.85, and the R-squared value of the efficiency model is... 2 The value was set to 0.9. After 273 iterations, the model's accuracy reached the convergence requirement, at which point the R-value of the head and efficiency model was [value missing]. 2 The values ​​are 0.8753 and 0.9262 respectively. The accuracy test results for the two models are as follows: Figure 9 .

[0112] Using the converged model as the fitness function, the MOPSO algorithm is called to search for Pareto front solutions throughout the optimization space. The initial population size is set to 200, the current Pareto front pool size is 100, and the algorithm is iterated 500 times. The resulting Pareto fronts are as follows: Figure 10 .

[0113] All 100 points in the Pareto front are non-dominated solutions. Theoretically, these 100 points are the optimal solutions to the optimization problem in this section. Compared with the head, we value the improvement of centrifugal pump efficiency more. Therefore, we construct the following formula to select the final optimization result from the 100 points in the Pareto front.

[0114]

[0115] In the formula, η ori With H ori η represents the efficiency and head of the prototype pump. P With H P To obtain the efficiency and head at the midpoint of the Pareto front, calculate the value of I at the midpoint of the Pareto front. P The point with the largest value represents the point with the most significant efficiency improvement. The relevant parameters for the extracted optimal point are given in Table 4. After optimization, the pump head increased by 11.11% and the efficiency increased by 10.82%.

[0116] Table 4 Comparison of centrifugal pump performance before and after optimization

[0117]

[0118] To compare the performance of the centrifugal pump before and after optimization under different operating conditions in detail, at 0.8Q... d Q d and 1.2Q d The performance of the centrifugal pump before and after optimization was compared and analyzed under operating conditions.

[0119] Figure 11 Pressure distribution contour maps of the centrifugal pump's mid-section before and after optimization are presented. The results show... Figure 11 Under all three operating conditions, the pressure inside the optimized pump was higher than that of the original pump. In addition, the low-pressure area at the leading edge of the main blade, the volute tongue, and the leading edge of the splitter blade was reduced in the optimized pump, and the overall pressure stratification was more obvious and the pressure distribution was more uniform.

[0120] Figure 12 The turbulent kinetic energy distribution contour maps of the centrifugal pump's mid-section before and after optimization are presented under different operating conditions. Figure 12 In the process, the multi-objective optimized pump exhibits higher turbulent kinetic energy under low flow conditions. Under rated conditions, the turbulent kinetic energy of the optimized pump in the volute section is significantly reduced. However, under high flow conditions, although the turbulent kinetic energy of the optimized pump in the volute section is slightly higher than that of the prototype pump, the liquid flow in the impeller section is significantly smoother.

[0121] Therefore, under all operating conditions, the pressure distribution and turbulent kinetic energy distribution of the multi-objective optimized pump are both better than those of the prototype pump, verifying the feasibility of this method in practical centrifugal pump optimization problems.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate 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 addition criterion, characterized in that, Includes the following steps: Step 1) Select initial sample points and establish an initial database, wherein: the Latin hypercube sampling method is used, based on the dimension of the optimization problem. Extract initial sample points And by analyzing their actual response values, an initial sample library is obtained. ; Step 2) Establish the Kriging model, where: the initial database obtained in Step 1 and their corresponding response values ,right Kriging models were established for each optimization objective, resulting in a total of [number] Kriging models constructed. One model; Step 3) Calculate the current Pareto solution set, where: analyze and compare the current database. Calculate the current Pareto solution set based on the dominance relationship between them; Step 4) Collect new points, where: new points are obtained by solving a sub-optimization problem based on the Point Addition Matrix (PAM) / Parallel Point Addition Matrix (PPAM) criterion. When using the PAM criterion for iteration, Calculated using the following formula ， When using the PPAM criterion for iteration, the first... q The new points are calculated using the following formula. ， In the formula, The improved point-addition criterion function is calculated using the following formula: ， In the formula, This indicates the th solution in the current Pareto front. The first optimization objective is... Each point corresponds to a response value. For the first The Kriging model with one optimization objective is applied to the sample points. The given predicted value, To optimize the dimensions of the problem, This represents the number of points in the current Pareto solution set. For the first The Kriging model corresponding to the optimization objective value; Step 5) Update the database and Pareto front solution, perform true response value analysis on the newly added sample points, and update and reconstruct the solution. Each Kriging model compares the dominance relationship between the newly added point and the current Pareto front solution, and updates the current Pareto solution set accordingly. Step 6) Determine the termination condition, where: when computing resources are insufficient, the stopping criterion is set to the number of iterations of the model or the number of times the true value of the newly added point is evaluated; when computing resources are sufficient, the overall accuracy of the model is used as the stopping condition; if the current termination condition is met, the iteration stops and the current Pareto solution set is output; otherwise, go to step 4 and continue iterating the model.

2. The multi-objective optimization method for a fuel centrifugal pump based on an improved addition criterion as described in claim 1, characterized in that, In the process of selecting initial sample points and establishing the initial database, Latin hypercube sampling is implemented using the lhsdesign function built into the Matlab software. 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 result. If the target problem is an engineering problem, the actual response value is obtained through finite element software.

3. The multi-objective optimization method for a fuel centrifugal pump based on an improved addition criterion as described in claim 1, characterized in that, The Kriging model was established using the DACE toolbox in Matlab software.

4. The multi-objective optimization method for a fuel centrifugal pump based on an improved addition criterion as described in claim 1, characterized in that, The calculation of the current Pareto solution set is performed using a non-dominated sorting algorithm.

5. A multi-objective optimization method for a fuel centrifugal pump based on an improved addition criterion, as described in claim 1, is characterized in that... During the process of collecting new data points, the value of the number of new data points q is between 2 and 5.

6. The multi-objective optimization method for a fuel centrifugal pump based on an improved addition criterion as described in claim 1, characterized in that, During the process of collecting newly added points, when the number of newly added points... At that time, the PPAM criterion becomes the original PAM criterion.

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