Fuel centrifugal pump performance optimization method based on parallel adding point agent model

Abstract

The invention discloses a fuel centrifugal pump performance optimization method based on a parallel adding point agent model, and belongs to the field of fuel centrifugal pump optimization design. The method comprises the steps of selecting an initial sample point, establishing an initial database, establishing and reconstructing a Kriging model, solving a newly added sample point by maximizing a PPA function, adding the newly added point into the database, judging whether the model meets a convergence criterion or not at the moment, and the like. Several classic single-target point adding criteria are popularized to the field of parallel computing. Compared with an existing method, the improved point adding criterion can more effectively search in the optimization space, and the optimization efficiency and precision of the model are remarkably improved. In the actual optimization design of the centrifugal pump, the performance of the optimized pump is also obviously improved.

Description

Technical Field

[0001] The invention belongs to the technical field of optimization design of fuel centrifugal pumps, and in particular relates to a fuel centrifugal pump performance optimization method based on a parallel point-adding agent model. 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] At present, most of the optimization research on centrifugal pumps relies on full three-dimensional computational fluid dynamics methods, which solve the gas-liquid distribution problem in the pump by using turbulence models and two-phase models, and complete the optimization design by continuously iterating the relevant parameters of the centrifugal pump. However, modeling, simulation and optimization of centrifugal pumps require a large number of iterative processes, and an effective analytical relationship between geometric parameters and performance parameters has not yet been established. This makes the optimization cycle long and it is easy to fall into a local optimal solution, resulting in large errors in the final performance optimization results, limiting the exploration of the performance potential of the centrifugal pump. Therefore, the optimization method based on the surrogate model is introduced into the optimization design of centrifugal pumps.

[0004] The Kriging model is an efficient interpolation proxy model. It constructs an approximate model by fitting the entire data set with a limited number of sample points, and uses the response values ​​of known points to predict the values ​​of unknown points. 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 forms of point addition criterion functions. The purpose is to select corresponding functions to continuously generate new sampling points and add them to the data set according to the characteristics of the required points, and update the iterative model. However, existing studies often involve complex parameter iteration processes, which is not conducive to its implementation in parallel computing, and there are few cases of applying the improved algorithm to the optimization design of fuel centrifugal pumps. In addition, most existing studies only focus on the optimization of the geometric parameters of the pump, while the research on the profile parameters is relatively limited. Therefore, in view of the above technical problems, how to improve the shortcomings of existing technologies and improve the optimization efficiency and accuracy of the model has become a technical problem in this field. Summary of the invention

[0006] In response to the above technical problems, the present invention provides a fuel centrifugal pump performance optimization method based on a parallel point-adding agent model. The method introduces an improved point-adding 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 to the target problem more accurately and efficiently.

[0007] The present invention solves the above problems by the following technical means:

[0008] A method for optimizing the performance of a fuel centrifugal pump based on a parallel point adding agent model, characterized in that it comprises the following steps:

[0009] 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 ];

[0010] Step 2) Establish or reconstruct the Kriging model, where: the existing database [x 1 ,x 2 ,...,x n ] and its corresponding response value [y 1 ,y 2 ,...,y n ];

[0011] Step 3) Obtain new samples by maximizing the PPA function, where: Obtain the maximum value of the PPA function to obtain q new sample points x new , the qth new point x new Calculated by the following formula:

[0012] In the formula, U(x) is the improved classic point addition criterion function, IF(x) is the constructed influence function, and N is the number of sample points before the iteration starts;

[0013] Specifically, the above-mentioned new point calculation formula takes the PMP criterion as an example, and predicts the maximum value in a single iteration, which is a constant.

[0014] Step 4) Add the new points to the database, where: perform true response value analysis on the new sample points obtained in step 3 to obtain (x new ,y new ), update the current database;

[0015] Step 5) Determine whether the model meets the convergence criteria at this time, where: if the convergence criteria are met, output the current optimal solution and end the iteration; if the convergence criteria are not met, go to step 2 to continue the iteration.

[0016] Preferably, between step 3 and step 4, the method further includes removing duplicate sample points, wherein: detecting whether there are duplicate points in the newly added sample points obtained in step 3 and in the current sample library, and if so, removing the point.

[0017] Preferably, in the process of establishing or reconstructing the Kriging model, modeling is performed based on the DACE toolbox in Matlab software.

[0018] Preferably, in the process of obtaining the newly added samples by maximizing the PPA function, the value range of q is 2 to 10.

[0019] Preferably, in the process of obtaining the newly added samples by maximizing the PPA function, a genetic algorithm is used to obtain the peak value of the PPA function.

[0020] Preferably, the functional expression of the PPA is: Where q is the number of new points required, U(x) is the improved classic point addition criterion function, N is the number of sample points before the iteration starts, and IF(x) is the constructed influence function.

[0021] Preferably, in the process of judging whether the model satisfies the convergence criterion at this time, the current number of iterations k exceeds the specified maximum value k max Or the relative error ε between the current optimal value and the true optimal value is lower than the specified ε max When , the model is judged to meet the convergence condition, where k max The value range is 100 to 150. When the optimal value of the objective function is not 0, ε max The value of is 1%. When the optimal value of the objective function is 0, ε max The value is 0.1%.

[0022] The fuel centrifugal pump performance optimization method based on the parallel point adding agent model of the present invention has the following beneficial effects:

[0023] 1) The Kriging model established based on the improved point-adding criterion in the present invention can provide more accurate prediction values, is the core of centrifugal pump optimization, and has unique technical advantages and application value in the actual optimization design of centrifugal pumps.

[0024] 2) The present invention covers the proposal and application of parallel point addition criteria, which has improved optimization accuracy and efficiency compared with the corresponding serial criteria, and provides a theoretical and practical basis for the expansion of the parallel computing field.

[0025] 3) The present invention proposes a centrifugal pump optimization method based on the Kriging model under the parallel point-adding criterion, which optimizes and improves the design process and results of the pump with an efficient model iteration process and accurate model fitting, and has excellent practical value.

[0026] In summary, the present invention proposes a variety of parallel point addition criteria, and by introducing influence functions, several classic single-objective point addition criteria are extended to the field of parallel computing. The improved point addition criteria can search more effectively in the optimization space, significantly improving the optimization efficiency and accuracy of the model. In the actual centrifugal pump optimization design, the performance of the optimized pump is also significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] 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.

[0028] Figure 1 It is a schematic diagram of the iterative process of the multi-peak EI function;

[0029] Figure 2 It is a flowchart of the iteration of the PPA method;

[0030] Figure 3 It is a schematic diagram of the test results of each serial criterion and the corresponding parallel criterion;

[0031] Figure 4 It is a schematic diagram comparing the performance of each parallel criterion when q=2;

[0032] Figure 5 It is the X-type fuel centrifugal pump impeller model and 3D model diagram;

[0033] Figure 6 It is the weighted cloud diagram and elementary effect diagram of each parameter of centrifugal pump efficiency;

[0034] Figure 7 It is a schematic diagram of the cross section of the meridian flow channel of a centrifugal pump;

[0035] Figure 8 It is the iteration of the optimal efficiency value during the optimization process and the change diagram of the constraint function response value of the newly added point;

[0036] Fig. 9 It is the pressure distribution cloud diagram of the middle section of the centrifugal pump before and after optimization under different working conditions;

[0037] Fig.10 It is the turbulent kinetic energy distribution cloud diagram of the middle section of the centrifugal pump before and after optimization under different working conditions. DETAILED DESCRIPTION

[0038] 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.

[0039] The present invention will be described in detail below with reference to the accompanying drawings.

[0040] Embodiment 1

[0041] This embodiment describes in detail the process of establishing a parallel point adding agent model.

[0042] The Kriging model is also called the Gaussian process model in statistics. If its objective function is regarded as a Gaussian process, the general expression is:

[0043] y=∑b i f i (x)+z(x)

[0044] Where f(x) is a polynomial about x, used for global approximation; b represents the regression coefficient; z(x) is a polynomial with a mean of zero and a variance of σ 2 The Kriging model assumes that there is a certain correlation between random variables at different sampling points in the design space, and the covariance between them can be expressed as:

[0045] Cov[Z(x),Z(x')]=σ 2 R(x,x')

[0046] In the formula, R(x,x') represents the correlation matrix, whose value is only related to the distance of the variables in space, and the R value decreases as the distance increases. The expression of the Kriging model can be determined by solving the parameters of the interpolation model established by the sample set using the covariance concept, maximum likelihood method and genetic algorithm, and the eigenvalues ​​of the unknown points are linked to the eigenvalues ​​of the known points to complete the prediction of the unknown points. The final prediction value and prediction error expressions are as follows:

[0047]

[0048] In order to improve the accuracy of the Kriging model in solving optimization problems, in addition to the initial sampling, new sample points can be continuously collected according to different adding point criteria to update the model so that it is constantly close to the true function to achieve the optimization purpose. Several common adding point criteria are as follows:

[0049] 1) MP criteria

[0050] The MP criterion completes model iteration by continuously analyzing the true response value at the minimum predicted value of the model. Its sub-optimization problem can be expressed as:

[0051]

[0052] 2) PI criteria

[0053] The PI criterion combines the predicted value and the prediction error, and expresses it as the probability that each point in the sample space is better than the current optimal value. The function value is between 0 and 1, and its mathematical expression is:

[0054]

[0055] The sub-optimization problem is formulated as:

[0056] max P[I(x)]

[0057] 3) EI criteria

[0058] The EI function defines the improvement of the current optimization target as I(x)=max(y min -y(x),0), we can know the improvement of the unknown point to the current optimal value, and the mathematical expectation is obtained as follows:

[0059]

[0060] The sub-optimization problem of the EI criterion is expressed as follows:

[0061] max E[I(x)]

[0062] 4) LCB criteria

[0063] The LCB criterion is obtained by simply combining the model's prediction value and prediction error:

[0064]

[0065] The parameter A is a constant that controls the balance between local exploration and global exploration. When A→0, At this time, the LCB function degenerates into the MP function; and when A→∞, The influence of becomes negligible, and minimizing LCB(x) is equivalent to maximizing The LCB function degenerates into the MSE function, and the sub-optimization problem of the LCB criterion can be expressed as:

[0066] min LCB(x)

[0067] In the following example, the parameter A is taken as 1.

[0068] In order to achieve parallel addition, the concept of influence function is introduced as the basis for parallel addition. Through the influence function, multiple peaks of the addition criterion function can be searched simultaneously in one iteration cycle to achieve parallel addition. Its mathematical expression is:

[0069]

[0070] Where x is the coordinate of any point in space, 0 is the coordinate of the specified point, obtained at the maximum value of the point addition criterion, R(x) is the correlation function, used to calculate the relative distance between two points in space, and m is the dimension of the optimization problem. Its function value is between 0 and 1, and is positively correlated with the distance from any point in space to the specified point. When it is judged that the distance to the specified point is too close, the function value is 0, and when the distance to the specified point is far, the function value is 1.

[0071] From this, we can get the influence function expression after given q points:

[0072]

[0073] In the formula, parameter N is the total number of sample points before the iteration starts, and m is the dimension of the optimization problem. Applying an influence function to a multi-peak point adding function and selecting a designated point as the current maximum point can reduce the value near the point to 0, thereby exposing the remaining peak points or points with greater optimization potential, and achieving the purpose of searching for multiple peak points.

[0074] Apply the serial point addition principle to the field of parallel computing. Figure 1 The iterative schematic diagram of searching for multi-peaks of multi-peak EI function under the influence of influence function is given.

[0075] The parallel criterion can be obtained by combining the serial addition criterion with the influence function. For the convenience of description, all sub-optimization problems of the addition criterion are unified into a maximization problem.

[0076] The sub-optimization problem of the MP criterion is rewritten as:

[0077]

[0078] The parallelization of the MP criterion is called the PMP (Paralleled minimized prediction) criterion. When the PMP criterion is used for iteration, if q points need to be collected at one time, the qth point is obtained by the following formula:

[0079]

[0080] In actual use, it is found that if the function value to be fitted is both positive and negative, and the maximum value of the function is only slightly greater than zero, it will make it difficult for the influence function to play a role, or even its role can be ignored. Therefore, the PMP criterion expression is modified as follows:

[0081]

[0082] The improved point addition criterion function is named U(x), then in the PMP criterion:

[0083]

[0084] The expression of the improved PMP criterion for collecting the qth point in one iteration cycle is:

[0085]

[0086] It should be noted that since the original MP criterion only contains the predicted value term of the model but does not integrate the prediction error, the MP function value at the existing sample points fails to show obvious characteristics (such as the function value is too large or too small). Therefore, when using the PMP criterion iteration, a step of detecting and eliminating duplicate sample points needs to be added.

[0087] Similarly, the function value of the LCB function is the same as the MP function. It may have positive and negative values ​​in the definition space. The following modifications are made to it:

[0088]

[0089] In the PLCB guidelines:

[0090]

[0091] The expression of the PLCB criterion collecting the qth point in one iteration cycle is:

[0092]

[0093] Since the expression of the original LCB function integrates the prediction error term, no repeated sample points will be collected when the PLCB criterion is used for iteration.

[0094] Both the EI and PI criterion expressions incorporate the prediction error term of the model, and since it is a maximization problem itself, in the parallel generalization of these two criteria, U(x) is the classical EI and PI function expressions. Similarly, the corresponding parallel criterion expressions can be obtained. The four proposed parallel point-adding criteria are uniformly named the PPA (Parallel point adding) criterion. Call the PPA criterion to iteratively obtain the newly added point x new The calculation formula is as follows:

[0095]

[0096] Example 2

[0097] This example elaborates in detail the iterative process of the parallel point-adding criterion, as Figure 2 shown.

[0098] Step (1): Selection of initial sample points and establishment of an initial database. Through the Latin hypercube sampling method, according to the dimension d of the optimization problem, n initial sample points [x 1 , x 2 ,..., x n are extracted, and their true response values are analyzed to obtain the initial sample library [y 1 , y 2 ,..., y n . Among them, the Latin hypercube sampling is implemented through 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 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 values are obtained through finite element software such as Ansys.

[0099] Step (2): Establishment / reconstruction of the Kriging model. From the existing database [x 1 , x 2 ,..., x n and its corresponding response values [y 1 , y 2 ,..., y n , based on the DACE toolbox in the Matlab software, establish / reconstruct the Kriging model.

[0100] Step (3): Obtain the newly added sample points by maximizing the PPA function. Maximize the PPA function to obtain q newly added sample points. Taking the PMP criterion as an example, in the iterative process, the qth newly added point The parameter q is determined by the designer. In this embodiment, q is 2, 4, and 8. Since PPA functions are analytical functions with clear input and output, an intelligent optimization algorithm is generally used to solve the point-adding criterion sub-optimization problem in the proxy model to obtain the peak value of the function. In this embodiment, a genetic algorithm is used to solve it.

[0101] Step (4): Remove duplicate sample points. Check whether there are any duplicate points in the new sample points obtained in step (3). If so, remove the point. Among the four PPA criteria, only the PMP criterion contains only the predicted value item of the model without integrating the prediction error, which may collect duplicate sample points. Therefore, this step is only for the PMP criterion, and the other criteria jump to step (5).

[0102] Step (5): Add the new points to the database. Perform true response value analysis on the new sample points obtained in step (3) to obtain (x new ,y new ) to update the current database.

[0103] Step (6): Determine whether the model meets the convergence criteria. Determine whether the current model converges or not. Generally, it is determined by the current number of iterations k and the relative error ε between the current optimal value and the true optimal value. Both cannot exceed the specified maximum value k. max , ε max The specific value is determined by the designer. If the convergence criterion is met, the current optimal solution is output and the iteration ends. If the convergence condition is not met, go to step (2) to continue the iteration.

[0104] Embodiment 3

[0105] This example describes in detail the single-objective optimization method test case, and compares the optimization efficiency of several parallel criteria and the original serial criteria and the optimization accuracy of several parallel criteria on the commonly used Hartmann3 example. This example has three dimensions, and its expression is:

[0106]

[0107] α=(1.0,1.2,3.0,3.2) T

[0108]

[0109] Where 0≤x i ≤1,i=1,2,3, the global optimal value of Hartmann3 function is -3.86278.

[0110] The number of initial sample points is set to 15. The dual convergence criterion is used as the convergence condition, that is, when the maximum number of iterations is not reached, the relative error between the searched optimal value and the true optimal value is less than a preset constant as the condition for stopping iteration. If the current number of iterations k cycles to the given maximum number of iterations k max The iteration stops when k≤k max . Maximum number of iterations k max Set to 120.

[0111] The relative error expression is:

[0112]

[0113] The Kriging model was constructed using the DACE toolbox built into the Matlab software. For the DACE toolbox, the regression function was set to regpoly0, the correlation function was set to corrgauss, and the hyperparameter θ of the Kriging model was set to the range of [10 -3 ,10 3 ], and its initial value is set to 1. For the maximization sub-optimization problem of each optimization criterion, the genetic algorithm is used to solve it, and the number of children of the genetic algorithm is set to 500 and the maximum number of iterations is set to 100. The Latin hypercube sampling method is used to extract 30 groups of different sample points according to the example parameter settings, and 30 repeated tests are performed.

[0114] The optimization comparison results of each serial criterion and the corresponding parallel criterion are as follows: Figure 3 The results show that the four parallel point addition criteria are better than the original serial criteria in terms of optimization accuracy and efficiency in most cases. Only the convergence speed of the PMP criterion slows down in the later stage, but it shows a faster convergence speed and higher optimization accuracy in the early stage of iteration.

[0115] At the same time, it is noted that in the iterative process, as the q value increases, the efficiency of the corresponding criterion optimization increases. However, the efficiency improvement becomes less obvious as the q value increases, and the larger the q value, the lower the convergence ability of the model in the later iteration. Therefore, fewer parallel update points should be selected to balance the optimization efficiency and computing resources. After comprehensive consideration, when selecting the parallel criterion for optimization, the parallel criterion of q=2 is more inclined to be selected.

[0116] The parallel criteria for q=2 are compared. Figure 4 The box plots of the optimal values ​​and iteration numbers of several parallel criteria after 30 iterations on the test function are given. The results show that the PEI-2 criterion performs best in terms of both convergence accuracy and iteration number.

[0117] Therefore, considering the iteration accuracy and speed of each parallel addition criterion comprehensively, it is believed that the PEI-2 criterion is the best criterion among several criteria, and this criterion will be used for the efficiency optimization design of the fuel centrifugal pump in the future.

[0118] Embodiment 4

[0119] This embodiment describes in detail the optimization application of this method in a fuel centrifugal pump. The above method is used to optimize the design of an X-type aviation fuel centrifugal pump, requiring the pump efficiency performance to be optimized and improved. The efficiency calculation expression of the centrifugal pump is:

[0120]

[0121] In the formula, ρ is the density of the working medium, g is the acceleration of gravity, Q is the design flow rate, P is the shaft power, and H is the head, which represents the net increase in energy obtained by the unit mass of fluid through the pump. The calculation formula is:

[0122]

[0123] Where P in , P out are the inlet and outlet pressures of the pump respectively.

[0124] The performance parameters and some main geometric parameters of the X-type aviation fuel centrifugal pump are shown in Table 1. Figure 5 A schematic diagram of its 3D model is given.

[0125] Table 1X aviation fuel centrifugal pump parameters

[0126]

[0127] Before optimizing the design, it is necessary to select the parameters that have a greater impact on the pump efficiency through sensitivity analysis. From the efficiency calculation expression of the centrifugal pump, it can be seen that the efficiency value is related to the head, and the relevant parameters of the pump will also affect the head, so it is necessary to perform sensitivity analysis on the head and efficiency at the same time. The candidate variables determined are: impeller outlet diameter D 2 , Impeller outlet width b 2 , Blade inlet placement angle β 1 , Blade outlet placement angle β 2 , number of blades z and impeller inlet diameter D 1 .

[0128] The Latin hypercube sampling method was used to extract 100 sets of the above parameter combinations, and the head and efficiency response values ​​of these combinations were calculated through simulation to perform sensitivity analysis of pump efficiency. The upper and lower limits of each parameter are specified as follows:

[0129]

[0130] 15°≤β 1 ≤45°

[0131] 15°≤β 2 ≤25°

[0132] 3≤Z≤7

[0133]

[0134] Figure 6 This is the elementary effect diagram of each parameter of centrifugal pump head and efficiency. The larger the absolute value of the sample mean, the more obvious the effect of the parameter on the response value (higher sensitivity), and the larger the sample standard deviation, the more obvious the cross-effect between the parameter and other variables. The sensitivity of each parameter to the head is ranked from large to small: D 2 , z, β 2 , b 2 , D 1 , β 1 The sensitivity of each parameter to efficiency is ranked from large to small: D 2 , b 2 , D 1 , z, β 2 , β 1 .

[0135] In the optimization design of the pump, the change of the number of blades is generally not involved. Therefore, considering the sensitivity analysis results of the efficiency, the impeller geometric parameters D 2 , b 2 and β 2 as optimization parameters.

[0136] In addition to geometric parameters, the centrifugal pump's profile parameters also affect the pump's performance. Figure 7 A schematic diagram of the cross section of the meridian flow channel of a centrifugal pump is given.

[0137] The present invention mainly studies the hub profile parameters and determines the parameters k of the hub profile characteristics. 1 and k 2 The calculation formula is as follows

[0138]

[0139] Divide k 1 With k 2 In addition, an additional optimization parameter Δz is added, which is defined as the axial distance between the impeller middle profile and the impeller inlet, which has been Figure 7 The initial values ​​and variation ranges of each optimization parameter are shown in Table 2.

[0140] Table 2 Initial values ​​and variation ranges of each optimization parameter

[0141]

[0142]

[0143] The single-objective optimization of the centrifugal pump efficiency is completed based on the PEI criterion. Since the maximum true efficiency of the centrifugal pump is unknown, the maximum true value evaluation number is used as the stopping criterion, and the maximum allowed evaluation number k max =120.

[0144] Figure 8 The iteration of the optimal efficiency value in the current centrifugal pump optimization problem and the true response value of the function of the newly added point are given. The efficiency optimization problem is a maximization problem. During the optimization, all efficiency response values ​​are multiplied by -1 to convert it into a minimization problem. The optimal efficiency value that meets the conditions in the original 60 sample points is 70.25%. After 60 iterations, a total of 120 sample points are added and the final optimal efficiency is 74.15%, which is 12.16% higher than the 66.11% of the prototype pump.

[0145] Table 3 shows the changes in the relevant parameters of the pump before and after optimization. After optimization, the impeller inlet width and outlet diameter increased, while the blade outlet placement angle decreased slightly. At the same time, the axial profile parameters decreased, while the parameter k 1 Slightly increased, in addition, the parameter k 2 The lower limit of the value was reached.

[0146] Table 3 Comparison of pump parameters before and after optimization

[0147]

[0148] 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. Fig. 9 The pressure distribution cloud diagram of the middle section of the centrifugal pump before and after optimization under the above working conditions is given. It can be seen from the figure that as the flow rate increases, the pressure in the pump gradually decreases. Under different working conditions, the low-pressure areas at the leading edge of the main blades, the volute baffles and the leading edge of the splitter blades of the optimized pump are reduced. The pressure of the optimized pump is significantly increased, the pressure gradient of the volute part is reduced, the overall pressure stratification is more obvious in the optimized pump, the pressure distribution is more uniform, and the minimum pressure decreases. Due to the increase in blade length, the ability of the entire impeller to do work on the fluid is enhanced, and the efficiency of the centrifugal pump is improved after optimization.

[0149] In order to compare the flow of liquid in the centrifugal pump before and after optimization under different working conditions, Fig.10 The turbulent kinetic energy distribution cloud diagram of the middle section of the centrifugal pump is given. With the increase of flow rate, the turbulent kinetic energy generally shows a downward trend. d), the turbulent kinetic energy in the optimized pump is slightly higher than that in the prototype pump, while under rated conditions and large flow conditions, the turbulent kinetic energy of the optimized diaphragm part is significantly reduced, the turbulence distribution on the back of the blade is significantly reduced toward the blade inlet, and the turbulent loss in the pump is reduced, indicating that the fluid flow in the optimized pump is more stable and more efficient.

[0150] Therefore, under all working conditions, the pressure of the optimized pump is better than that of the prototype pump. Under low flow conditions, the turbulent kinetic energy performance is not as good as that of the prototype pump, but under rated conditions and high flow conditions, it is better than the prototype pump. This verifies the feasibility and superiority of the proposed method in practical applications.

[0151] The present invention proposes a variety of parallel point addition criteria, and by introducing influence functions, several classic single-objective point addition criteria are extended to the field of parallel computing. The improved point addition criteria can search more effectively in the optimization space, significantly improving the optimization efficiency and accuracy of the model. In the actual centrifugal pump optimization design, the performance of the optimized pump is also significantly improved.

[0152] In order to verify the feasibility and superiority of the present invention, mathematical examples are used for testing. By comparing the current optimal values ​​in the iterative process, the performance of different point-adding criteria in the optimization problem is evaluated, and the point-adding criteria with the highest optimization efficiency and accuracy are screened out. This process not only verifies the advantages of the improved point-adding criteria in optimization efficiency and optimization ability, but also provides certain theoretical support for the optimization application of the point-adding criteria in actual engineering.

[0153] Finally, in terms of centrifugal pump applications, the present invention has achieved significant practical results. By applying the improved parallel addition criterion to the optimal design of centrifugal pumps, the results show that the efficiency of the pump has been improved to a certain extent. This result not only verifies the effectiveness of the improved addition criterion in actual engineering, but also provides a certain theoretical basis and practical application examples for the field of optimal design of centrifugal pumps.

[0154] In summary, the present invention proposes an innovative solution to solve the optimization design of fuel centrifugal pump efficiency by improving the classic point-adding criterion, and successfully promotes the parallelization of the classic point-adding criterion. This improvement effectively solves the common problems of long optimization cycle and easy to fall into local optimal solution in the optimization design of centrifugal pumps, and improves the optimization efficiency and accuracy. 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.

[0155] 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 fuel centrifugal pump performance optimization method based on a parallel point adding agent model, 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 or reconstruct the Kriging model, where: the existing database [x1, x2, ..., x n ] and its corresponding response value [y1,y2,...,y n ]; Step 3) Obtain new samples by maximizing the PPA function, where: Obtain the maximum value of the PPA function to obtain q new sample points x new , the qth new point x new Calculated by the following formula: In the formula, IF(x) is the constructed influence function, N is the number of sample points before the iteration starts, and U(x) is the improved classic point addition criterion function; Step 4) Add the new points to the database, where: perform true response value analysis on the new sample points obtained in step 3 to obtain (x new ,y new ), update the current database; Step 5) Determine whether the model meets the convergence criteria at this time, where: if the convergence criteria are met, output the current optimal solution and end the iteration; if the convergence criteria are not met, go to step 2 to continue the iteration.

2. The method for optimizing the performance of a fuel centrifugal pump based on a parallel point adding agent model according to claim 1, characterized in that: Between step 3 and step 4, the method further includes removing duplicate sample points, wherein: detecting whether there are duplicate points in the newly added sample points obtained in step 3 and in the current sample library, and if so, removing the point.

3. The method for optimizing the performance of a fuel centrifugal pump based on a parallel point adding agent model according to claim 1, characterized in that: In the process of establishing or reconstructing the Kriging model, modeling is performed based on the DACE toolbox in Matlab software.

4. The method for optimizing the performance of a fuel centrifugal pump based on a parallel point adding agent model according to claim 1, characterized in that: In the process of obtaining new samples by maximizing the PPA function, the value range of q is 2 to 10.

5. The method for optimizing the performance of a fuel centrifugal pump based on a parallel point adding agent model according to claim 1, characterized in that: In the process of obtaining new samples by maximizing the PPA function, a genetic algorithm is used to obtain the peak value of the PPA function.

6. The method for optimizing the performance of a fuel centrifugal pump based on a parallel point adding agent model according to claim 1, characterized in that: The functional expression of the PPA is: Where q is the number of new points required, U(x) is the improved classic point addition criterion function, N is the number of sample points before the iteration starts, and IF(x) is the constructed influence function.

7. The method for optimizing the performance of a fuel centrifugal pump based on a parallel point adding agent model according to claim 1, characterized in that: In the process of judging whether the model meets the convergence criteria, the current number of iterations k exceeds the specified maximum value k max Or the relative error ε between the current optimal value and the true optimal value is lower than the specified ε max When , the model is judged to meet the convergence condition, where k max The value range is 100 to 150. When the optimal value of the objective function is not 0, ε max The value of is 1%. When the optimal value of the objective function is 0, ε max The value is 0.1%.

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