A fuel centrifugal pump performance optimization method based on parallel point insertion proxy model

Abstract

The application discloses a kind of based on parallel point adding agent model's fuel centrifugal pump performance optimization method, belong to fuel centrifugal pump optimization design field, this method packet initial sample point selection and initial database establishment, the establishment and reconstruction of Kriging model, by the way of maximizing PPA function to obtain new sample point, add new point to database, judge whether the model meets convergence criterion at this time and the like steps, the method proposes a variety of parallel point adding criteria, by introducing influence function, several kinds of classic single-target point adding criteria are generalized to parallel computing field.Compared with existing methods, the improved point adding criteria can more effectively search in the optimization space, significantly improving the model optimization efficiency and accuracy.In actual centrifugal pump optimization design, the performance of the optimized pump is also significantly improved.

Description

Technical Field

[0001] This invention belongs to the field of fuel centrifugal pump optimization design technology, and particularly relates to a fuel centrifugal pump performance optimization method based on a parallel point-addition proxy model. 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] Currently, most centrifugal pump optimization research relies on fully three-dimensional computational fluid dynamics (CFD) methods. These methods use turbulence and two-phase models to address the gas-liquid distribution within the pump and achieve optimal design through iterative optimization of relevant pump parameters. However, modeling, simulating, and optimizing centrifugal pumps requires numerous iterations, and an effective analytical relationship between geometric and performance parameters has not yet been established. This results in long optimization cycles and a high risk of getting trapped in local optima, leading to significant errors in the final performance optimization results and limiting the potential of centrifugal pump performance. Therefore, surrogate model-based optimization methods have been introduced into the optimization design of centrifugal pumps.

[0004] The Kriging model is an efficient interpolation surrogate model that constructs an approximate model by fitting a finite number of sample points to the entire dataset. It uses the response values ​​of known points to predict the values ​​of unknown points and is widely used in optimization design. After extracting initial sample points, an effective method to improve the accuracy of optimization results is to construct a point 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 function has various forms. Its purpose is to continuously generate new sampling points and add them to the dataset based on the characteristics of the required points, thereby updating the iterative model. However, existing studies often involve complex parameter iteration processes, which is not conducive to its implementation in parallel computing. Furthermore, there are few cases of applying improved algorithms to the optimization design of fuel centrifugal pumps. In addition, most existing studies only focus on the optimization of pump geometric parameters, while research on profile parameters is relatively limited. Therefore, addressing the above technical problems and improving the shortcomings of existing technologies to enhance the optimization efficiency and accuracy of the model has become a key technical challenge in this field. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method for optimizing the performance of a fuel centrifugal pump based on a parallel point-addition proxy model. 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.

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

[0008] A method for optimizing the performance of a fuel centrifugal pump based on a parallel point-addition proxy model, characterized by the following steps:

[0009] 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 ];

[0010] Step 2) Build or reconstruct the Kriging model, where: it is derived from the existing database [x1, x2, ..., x...]. n ] and their corresponding response values ​​[y1, y2, ..., y n ];

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

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

[0013] Specifically, the above formula for calculating the newly added points is based on the PMP criterion. The predicted maximum value is a constant in a single iteration.

[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 criterion at this time. If the convergence criterion is met, output the current optimal solution and end the iteration; if the convergence condition is not met, go to step 2 to continue the iteration.

[0016] Preferably, between step 3 and step 4, duplicate sample points are removed, wherein: it is detected whether there are any duplicate points in the current sample library among the newly added sample points obtained in step 3; if so, the point is removed.

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

[0018] Preferably, in the process of obtaining new samples by maximizing the PPA function, the value of q ranges from 2 to 10.

[0019] Preferably, 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.

[0020] Preferably, the functional expression of the PPA is: In the formula, q is the number of new points to be added, U(x) is the improved classical point addition criterion function, N is the number of existing sample points before the iteration begins, and IF(x) is the constructed influence function.

[0021] Preferably, during the process of determining whether the model meets the convergence criterion, the current iteration number 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 k , the model is judged to satisfy the convergence condition, where k max The value of ε ranges from 100 to 150. When the optimal value of the objective function is not 0, ε max The value of ε 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 additive proxy model of the present invention has the following beneficial effects:

[0023] 1) The Kriging model established by this invention based on the improved addition criterion can provide more accurate prediction values. It 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) This invention covers the proposal and application of the parallel addition criterion. Compared with the corresponding serial criterion, its optimization accuracy and efficiency are improved, providing theoretical and practical basis for the expansion of the field of parallel computing.

[0025] 3) This invention proposes a centrifugal pump optimization method based on the Kriging model under the parallel addition criterion. It optimizes and improves the pump design process and results with efficient model iteration process and accurate model fitting, and has superior practical value.

[0026] In summary, this invention proposes several parallel point-addition criteria. By introducing influence functions, it extends several classic single-objective point-addition criteria to the field of parallel computing. The improved point-addition criteria can search more effectively within the optimization space, significantly improving the model's optimization efficiency and accuracy. In practical centrifugal pump optimization design, the performance of the optimized pump is also significantly improved. 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 the iterative process of the multi-peak EI function;

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

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

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

[0032] Figure 5 This is a model and 3D model of the impeller of an X-type fuel centrifugal pump;

[0033] Figure 6 It is a weighted cloud diagram and an elementary effect diagram of the various parameters of centrifugal pump efficiency;

[0034] Figure 7 This is a schematic diagram of the cross-section of the meridional channel of a centrifugal pump;

[0035] Figure 8 This is a graph showing the iteration of the optimal efficiency value during the optimization process and the changes in the constraint function response value of newly added points;

[0036] Figure 9 These are cloud maps showing the pressure distribution at the mid-section of the centrifugal pump before and after optimization under different operating conditions;

[0037] Figure 10 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

[0038] 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.

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

[0040] Example 1

[0041] This embodiment details the process of establishing a parallel point-addition proxy model.

[0042] The Kriging model, also known as the Gaussian process model in statistics, treats its objective function as a Gaussian process, and its general expression is:

[0043] y=∑b i f i (x)+z(x)

[0044] In the formula, f(x) is a polynomial in x, used for global approximation; b represents the regression coefficient; z(x) is a polynomial with zero mean and σ variance. 2 The stochastic process is used to approximate local biases. The Kriging model posits that random variables are correlated at different sampling points in the design space, and their covariance 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 depends only on the distance between 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 from the sample set using methods such as the concept of covariance, the maximum likelihood method, and genetic algorithms. This links the feature values ​​of unknown points with the feature values ​​of known points, completing the prediction of unknown points. The final expressions for the predicted value and prediction error are as follows:

[0047]

[0048] To improve the accuracy of the Kriging model in solving optimization problems, in addition to initial sampling, new sample points can be continuously collected according to different point-addition criteria to update the model, making it increasingly closer to the true function, thereby achieving the optimization goal. Several common point-addition criteria are as follows:

[0049] 1) MP Criterion

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

[0051]

[0052] 2) PI Criterion

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

[0054]

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

[0056] max P[I(x)]

[0057] 3) EI Criteria

[0058] The EI function defines the improvement of the current optimization objective as I(x) = max(y). min By calculating -y(x),0), we can determine the magnitude of the improvement of the current optimal value by the unknown point. Taking its expected value yields the following formula:

[0059]

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

[0061] max E[I(x)]

[0062] 4) LCB Criterion

[0063] The LCB criterion is obtained by simply combining the model's predicted values ​​and prediction errors:

[0064]

[0065] Here, parameter A is a constant that controls the balance between local discovery and global exploration. When A→0, At this point, the LCB function degenerates into the MP function; and when A→∞... The effect 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 examples below, parameter A = 1.

[0068] To achieve parallel point addition, the concept of an influence function is introduced as the foundation for parallel point addition. Through the effect of the influence function, multiple peaks of the point addition criterion function can be searched simultaneously within one iteration cycle, thus achieving parallel point addition. Its mathematical expression is:

[0069]

[0070] Where x is the coordinate of any point in space, x0 is the coordinate of the specified point (obtained at the maximum value of the 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 the distance to the specified point is too close, the function value is 0; when the distance to the specified point is far, the function value is 1.

[0071] Therefore, the expression for the influence function given q points can be obtained:

[0072]

[0073] In the formula, parameter N represents the total number of sample points before the iteration begins, and m represents the dimension of the optimization problem. By applying an influence function to a multi-peaked point-addition function and selecting a point as the current maximum value, the values ​​near that point are reduced to 0, thereby exposing other peak points or points with greater optimization potential, achieving the goal of searching for multiple peak points.

[0074] Applying the serial addition principle to the field of parallel computing. Figure 1 An iterative diagram illustrating the search for multiple peaks using a multi-peak EI function under the influence of an influence function is presented.

[0075] By combining the serial addition criterion with the influence function, the parallel criterion can be obtained. For the sake of convenience, the sub-optimization problems of all addition criteria are unified into maximization problems.

[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 using the PMP criterion for iteration, if q points need to be collected at once, the qth point is obtained by the following formula:

[0079]

[0080] In practical application, it was found that if the function value to be fitted has both positive and negative values, and the maximum value of the function is only slightly greater than zero, the influence function will be difficult to play, or even its effect will be negligible. Therefore, the PMP criterion expression is modified as follows:

[0081]

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

[0083]

[0084] The improved PMP criterion for collecting the q-th point in one iteration cycle is expressed as follows:

[0085]

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

[0087] Similarly, the function value of the LCB function, like that of the MP function, may have both positive and negative values ​​within its definition space. The following modifications are made to it:

[0088]

[0089] In the PLCB criteria:

[0090]

[0091] The expression for the PLCB criterion in collecting the q-th point in one iteration cycle is:

[0092]

[0093] Since the original LCB function expression integrates the prediction error term, repeated sample points will not be collected when using the PLCB criterion for iteration.

[0094] Both the EI and PI criterion expressions integrate the model's prediction error term, and since they are essentially maximization problems, U(x) in the parallelization generalization of these two criteria represents the classic EI and PI function expressions. Similarly, the parallelization criterion expressions corresponding to these criteria can be obtained. The four proposed parallel point-adding criteria are uniformly named the PPA (Parallel Point Adding) criterion. The PPA criterion is then used to iteratively calculate the new point x. new The calculation formula is:

[0095]

[0096] Example 2

[0097] This embodiment elaborates on the iterative process of the parallel point addition criterion, such as... Figure 2 As shown.

[0098] Step (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 ], and perform real response value analysis on them to obtain the initial sample library [y1, y2, ..., y n The Latin hypercube sampling is implemented using the built-in `lhsdesign` function in Matlab. The initial sample size `n` is typically set to 10 times the dimension of the optimization problem. If the target problem is a standard mathematical problem, 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.

[0099] Step (2): Building / Reconstructing the Kriging Model. This involves using the existing database [x1, x2, ..., x...]. n ] and their corresponding response values ​​[y1, y2, ..., y n Based on the DACE toolbox in Matlab software, the Kriging model is built / reconstructed.

[0100] Step (3): Obtain new sample points by maximizing the PPA function. Find the maximum value of the PPA function to obtain q new sample points. Taking the PMP criterion as an example, during the iteration process, the qth new sample point... The parameter q is determined by the designer; in this embodiment, q is set to 2, 4, and 8. Since PPA functions are all analytic functions with clear and explicit inputs and outputs, the peak value of the function is generally obtained by using intelligent optimization algorithms to solve the optimization problem of the surrogate model with added criteria. In this embodiment, a genetic algorithm is used to solve the problem.

[0101] Step (4): Remove duplicate sample points. Check if there are any duplicate points in the current sample library among the newly added sample points obtained in step (3). If so, remove the point. Among the four PPA criteria, only the PMP criterion includes only the predicted value of the model and does not integrate the prediction error. It may collect duplicate sample points. Therefore, this step is only for the PMP criterion. The other criteria are skipped to step (5).

[0102] Step (5): Add the new points to the database. Analyze the true response values ​​of the new sample points obtained in step (3) to obtain (x... new ,y new Update the current database.

[0103] Step (6): Determine whether the model meets the convergence criterion. The convergence of the current model is determined. This is generally based on the current iteration number k and the relative error ε between the current optimal value and the true optimal value; both must not 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, the iteration continues to step (2).

[0104] Example 3

[0105] This embodiment details a test case for a single-objective optimization method, comparing the optimization efficiency of several parallel criteria with the original serial criteria, and the optimization accuracy of the parallel criteria, on the commonly used Hartmann 3 example. This example has three dimensions, and its expression is as follows:

[0106]

[0107] α=(1.0,1.2,3.0,3.2) T

[0108]

[0109] Where, 0≤x i For ≤1, i=1,2,3, the global optimum of the Hartmann 3 function is -3.86278.

[0110] The initial number of sample points is set to 15. A dual convergence criterion is used as the convergence condition: when the maximum number of iterations has not been reached, iteration stops if the relative error between the found optimal value and the true optimal value is less than a preset constant. If the current iteration number k loops to the given maximum iteration number k... max Stop iteration when k ≤ k max Maximum number of iterations k max Set it to 120.

[0111] The relative error expression is:

[0112]

[0113] The Kriging model was constructed using the DACE toolbox built into Matlab software. For the DACE toolbox, the regression function was set to regpoly0, the correlation function to corrgauss, and the hyperparameter θ of the Kriging model took values ​​in the range

[10] . -3 10 3 The initial value of is set to 1. For the maximization sub-optimization problem of each optimization criterion, a genetic algorithm is used to solve it, with the number of generations set to 500 and the maximum number of iterations to 100. The Latin hypercube sampling method is used to extract 30 different sample points according to the example parameters, and 30 repeated trials are conducted.

[0114] The optimization comparison results of each serial criterion and its corresponding parallel criterion are as follows: Figure 3 As shown in the figure, the results indicate that the four parallel point-addition criteria outperform the original serial criteria in terms of both optimization accuracy and efficiency in most cases. Only the PMP criterion shows a slower convergence speed in the later stages, but it exhibits a faster convergence speed and higher optimization accuracy in the early stages of iteration.

[0115] It was also noted that during the iteration process, the optimization efficiency of the corresponding criterion improved with the increase of the q value. However, the efficiency improvement became less significant with increasing q value, and the convergence ability of the model decreased in the later stages of iteration as the q value increased. Therefore, fewer parallel update points should be selected to balance optimization efficiency and computational resources. Considering all factors, when using parallel criteria for optimization, a parallel criterion with q=2 is preferred.

[0116] Compare the various parallel criteria for q=2. Figure 4 Box plots of the optimal values ​​versus the number of iterations after 30 iterations on the test function for several parallel criteria are presented. The results show that the PEI-2 criterion performs best in both convergence accuracy and number of iterations.

[0117] Therefore, considering the iteration accuracy and speed of each parallel addition criterion, the PEI-2 criterion is considered to be the best performing criterion among the several criteria, and this criterion will be selected for the efficiency optimization design of the fuel centrifugal pump.

[0118] Example 4

[0119] This embodiment details the application of this method in the optimization of fuel centrifugal pumps. The method is used to optimize the design of an X-type aviation fuel centrifugal pump, aiming to improve pump efficiency. The efficiency calculation expression for the centrifugal pump is:

[0120]

[0121] In the formula, ρ is the density of the working medium, g is the gravitational acceleration, Q is the design flow rate, P is the shaft power, and H is the head, which characterizes the net increase in energy gained per unit mass of fluid through the pump. Its calculation formula is:

[0122]

[0123] In the formula, P in P out These are the pump inlet and outlet pressures, respectively.

[0124] The performance parameters and some key 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 provided.

[0125] Table 1. Parameters of Type X Aviation Fuel Centrifugal Pump

[0126]

[0127] Before performing optimization design, sensitivity analysis is needed to select parameters that have a significant impact on pump efficiency. As can be seen from the efficiency calculation expression for centrifugal pumps, the efficiency value is related to the head, and related pump parameters also affect the head. Therefore, sensitivity analysis needs to be performed on both head and efficiency. The identified candidate variables are: impeller outlet diameter D2, impeller outlet width b2, blade inlet angle β1, blade outlet angle β2, number of blades z, and impeller inlet diameter D1.

[0128] Using the Latin hypercube sampling method, 100 combinations of the above parameters were selected, 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 defined as follows:

[0129]

[0130] 15°≤β1≤45°

[0131] 15°≤β2≤25°

[0132] 3≤Z≤7

[0133]

[0134] Figure 6 This is a primary effect diagram for the parameters of head and efficiency of a centrifugal pump. A larger absolute value of the sample mean indicates a more significant influence of the parameter on the response value (higher sensitivity), while a larger sample standard deviation indicates a more significant interaction between the parameter and other variables. The sensitivity of each parameter to head, ranked from highest to lowest, is: D2, z, β2, b2, D1, β1. The sensitivity of each parameter to efficiency, ranked from highest to lowest, is: D2, b2, D1, z, β2, β1.

[0135] In the optimization design of pumps, the number of blades is generally not involved. Therefore, taking into account the sensitivity analysis results of efficiency, D2, b2 and β2 of the impeller geometry parameters are selected as optimization parameters.

[0136] Besides geometric parameters, the profile parameters of a centrifugal pump also affect its performance. Figure 7 A schematic diagram of the meridional flow channel cross-section of a centrifugal pump is provided.

[0137] This invention mainly studies the parameters of the wheel hub profile, and the calculation formulas for the parameters k1 and k2 that determine the characteristics of the wheel hub profile are as follows:

[0138]

[0139] In addition to k1 and k2, an additional optimization parameter Δz is added, defined as the axial distance between the impeller center profile and the impeller inlet. (This has already been defined...) Figure 7 The selected parameters are shown in Table 2, along with their initial values ​​and ranges.

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

[0141]

[0142]

[0143] Single-objective optimization of centrifugal pump efficiency is performed based on the PEI criterion. Since the true maximum efficiency of the centrifugal pump is unknown, the maximum number of evaluations based on the true efficiency is used as the stopping criterion, with a maximum allowed number of evaluations k. max =120.

[0144] Figure 8 The iterative process of achieving the optimal efficiency in the current centrifugal pump optimization problem and the actual function response values ​​for newly added points are presented. The efficiency optimization problem is a maximization problem; during optimization, all efficiency response values ​​are multiplied by -1 to transform it into a minimization problem. The optimal efficiency value satisfying the conditions among the original 60 sample points is 70.25%. After 60 iterations, with a total of 120 sample points added, the final optimal efficiency obtained is 74.15%, an improvement of 12.16% compared to the prototype pump's 66.11%.

[0145] Table 3 shows the changes in relevant parameters of the pump before and after optimization. After optimization, the impeller inlet width and outlet diameter both increased, while the blade outlet installation angle decreased slightly. Simultaneously, the axial profile parameter decreased, while parameter k1 increased slightly. Furthermore, parameter k2 reached its lower limit.

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

[0147]

[0148] 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. Figure 9 The pressure distribution cloud diagrams of the centrifugal pump's mid-section before and after optimization are presented under the above operating conditions. The diagrams show that the pump pressure gradually decreases with increasing flow rate. Under different operating conditions, the low-pressure regions at the leading edge of the main blade, the volute tongue, and the leading edge of the splitter blades are all reduced in the optimized pump. The pressure of the optimized pump increases significantly, the pressure gradient in the volute section decreases, and the overall pressure stratification is more pronounced, with a more uniform pressure distribution and a lower minimum pressure. Due to the increased blade length, the impeller's ability to perform work on the fluid is enhanced, resulting in improved centrifugal pump efficiency after optimization.

[0149] To compare the flow of liquid within the centrifugal pump before and after optimization under different operating conditions, Figure 10 The turbulent kinetic energy distribution contour plot of the centrifugal pump's mid-section is presented. With increasing flow rate, the turbulent kinetic energy generally decreases. Under low flow rate conditions (0.8Q), the turbulent kinetic energy distribution is further reduced. d Under the optimized conditions, the turbulent kinetic energy in the pump is slightly higher than that in the prototype pump. However, under rated operating conditions and high flow rate conditions, the turbulent kinetic energy in the tongue section is significantly reduced after optimization, and the turbulent distribution on the back of the blade is significantly reduced towards the blade inlet. The turbulent loss in the pump is reduced, indicating that the fluid flow in the optimized pump is more stable and the efficiency is higher.

[0150] Therefore, under all operating conditions, the optimized pump outperforms the prototype pump in terms of pressure. While its turbulent kinetic energy performance is inferior to the prototype pump at low flow rates, it surpasses it under rated and high flow rate conditions. This verifies the feasibility and superiority of the proposed method in practical applications.

[0151] This invention proposes several parallel optimization criteria, extending several classic single-objective optimization criteria to the field of parallel computing by introducing influence functions. The improved optimization criteria can search the optimization space more effectively, significantly improving the model's optimization efficiency and accuracy. In practical centrifugal pump optimization design, the performance of the optimized pump is also significantly improved.

[0152] To verify the feasibility and superiority of this invention, mathematical examples were used for verification. By comparing the current optimal value during the iteration process, the performance of different point-addition criteria in optimization problems was evaluated, and the point-addition criterion with the highest optimization efficiency and accuracy was selected. This process not only verified the advantages of the improved point-addition criterion in optimization efficiency and optimization ability, but also provided certain theoretical support for the optimization application of the point-addition criterion in practical engineering.

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

[0154] In summary, this invention proposes an innovative solution for optimizing the efficiency of fuel centrifugal pumps by improving the classic point-addition criterion, and successfully extends the classic point-addition criterion to parallel processing. This improvement effectively solves the common problems in centrifugal pump optimization design, such as long optimization cycles and susceptibility to local optima, thus improving optimization efficiency and accuracy. This solution provides strong technical support for centrifugal pump optimization design, and through numerical examples and application in practical designs, it fully demonstrates the advantages of this invention in terms of performance and application prospects.

[0155] 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 parallel point-based surrogate model based performance optimization method for fuel centrifugal pumps, characterized in that, Comprising the following steps: Step 1) selecting initial sample points and establishing an initial database, wherein: according to the dimension of the optimization problem, a certain number of initial sample points are selected by using a Latin hypercube sampling method extracting a certain number of initial sample points , and analyzing the true response values to obtain an initial sample database ; Step 2) Establish or reconstruct Kriging model, wherein: from the existing database and its corresponding response value ; Step 3) finding the new sample by maximizing the PPA function, where the maximum of the PPA function is found to obtain the new sample point , the new sample point is calculated by the following equation, ， wherein is the constructed influence function, is the number of sample points available before iteration starts, is the improved classical point addition criterion function; Parallelization of MP criterion is extended in PMP criterion: ； Parallelization of MP criterion is extended in PLCB criterion: ； Step 4) adding the new points into the database, wherein: the real response value analysis is performed on the new sample points obtained in step 3 to obtain , and the current database is updated; Step 5) judging whether the model meets the convergence criterion at this time, wherein: if the convergence criterion is met, output the current optimal solution and end the iteration; if the convergence criterion is not met, go to step 2 to continue iteration; Candidate variables that need to be determined for the fuel centrifugal pump include: impeller outlet diameter , impeller outlet width , blade inlet angle , blade outlet angle , number of blades , and impeller inlet diameter .

2. The method of claim 1, wherein the method is characterized by, Between step 3 and step 4, it also includes eliminating duplicate sample points, wherein: detecting whether there is a duplicate point in the newly added sample points obtained in step 3 with the current sample library, and if there is, the point is eliminated.

3. The method of claim 1, wherein the method further comprises: In the process of establishing or reconstructing the Kriging model, the DACE toolbox in Matlab software is used for modeling.

4. The method of claim 1, wherein, The value of the PPA function is maximized in the process of adding new samples, is in the range of 2 to 10.

5. The method of claim 1, wherein, In the process of adding new samples by maximizing the PPA function, genetic algorithm is used to obtain the peak value of the PPA function.

6. The method of claim 1, wherein the method further comprises: In the process of judging whether the model meets the convergence criterion at this time, the current iteration number exceeds the specified maximum value or the relative error between the current optimal value and the true optimal value is lower than the specified , then it is judged that the model meets the convergence condition, wherein, the value of is in the range of 100 to 150, when the optimal value of the objective function is not 0, the value of is 1%, when the optimal value of the objective function is 0, and the value of is 0.1%.

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