Mixed-flow pump parameter optimization method based on adaptive clustering improved NSGA-II

Abstract

The invention discloses a mixed-flow pump parameter optimization method based on adaptive clustering improved NSGA-II, and the method comprises the steps: selecting to-be-optimized design parameters of a mixed-flow pump based on the structural characteristics of the mixed-flow pump; the design parameters are combined to form a mixed-flow pump design scheme, and each design scheme of the pump serves as an individual; parameter and data structure setting and population initialization are carried out; rapidly exploring a feasible region through improved NSGA-II multi-generation iteration, and performing global coarse screening; local fine search is carried out on elite individuals obtained through global coarse screening so as to improve the quality of a solution set; and obtaining a mixed-flow pump parameter optimization result based on a local fine search result. According to the method, the structural optimization efficiency of the mixed-flow pump can be improved, and the obtained optimization scheme can meet the actual requirements of multi-parameter design of the mixed-flow pump under complex working conditions.

Description

Technical Field

[0001] The present invention relates to the technical field of mixed flow pump parameter optimization, and in particular to a mixed flow pump structure optimization method based on an improved NSGA-II algorithm. Background Art

[0002] In the specific design process of the mixed flow pump structure, it is necessary to comprehensively consider the influence of multiple mixed flow pump design parameters on the performance of the mixed flow pump. The mixed flow pump design parameters include but are not limited to the impeller inlet diameter D1 (mm), the impeller outlet diameter D2 (mm), the impeller inlet width b1 (mm), the impeller outlet width b2 (mm), the number of blades Z, the blade leading edge placement angle β1 (r) (°), the blade trailing edge placement angle β2 (r) (°), the blade wrap angle φ (r) (°), the blade thickness distribution t (r) (mm), the guide vane installation angle α (°), the guide vane number Z d , guide vane inlet and outlet radius R in ,R out (mm), etc. Furthermore, mixed-flow pumps typically need to achieve both high efficiency and high head under multiple operating conditions (e.g., 0.8, 1.0, and 1.2 times the design flow rate). Their performance indicators are often comprehensively evaluated using a weighted average. Therefore, the multiple parameters involved in mixed-flow pump structural design can be viewed as a multi-parameter optimization problem.

[0003] In existing technology, mixed-flow pump structural design typically involves simulating different structures to determine pump performance parameters, but this approach is inefficient. While optimization algorithms have been employed to solve multi-parameter optimization problems, such as using NSGA-II for multi-parameter optimization of hydraulic components like pump impellers, existing algorithms still suffer from slow convergence, low accuracy, and a tendency to fall into local optimal solutions. Furthermore, there is no clear solution for multi-parameter optimization of mixed-flow pumps. Summary of the Invention

[0004] In order to address the deficiencies in the prior art, this application proposes a mixed flow pump structure optimization method based on an improved NSGA-II algorithm. In view of the need to comprehensively consider multiple design parameters and multiple operating conditions in the structural design of a mixed flow pump, the present invention uses an improved NSGA-II algorithm to solve the multi-parameter optimization problem of a mixed flow pump, which can improve the efficiency of the mixed flow pump structure optimization. The obtained optimization scheme can meet the actual needs of multi-parameter parameter design of a mixed flow pump under complex working conditions.

[0005] The technical solutions adopted in the present invention are as follows:

[0006] A mixed flow pump parameter optimization method based on adaptive clustering improved NSGA-II includes the following steps:

[0007] Step 1: Based on the structural characteristics of the mixed flow pump, select the design parameters of the mixed flow pump to be optimized;

[0008] Step 2: Combining design parameters to form a mixed flow pump design scheme, taking each pump design scheme as an individual; setting parameters and data structure, and initializing the population;

[0009] Step 3: Rapidly explore the feasible region through multiple iterations of the improved NSGA-II and perform global coarse screening;

[0010] Step 4: Perform local fine search on the elite individuals obtained from the global coarse screening to improve the quality of the solution set;

[0011] Step 5: Obtain the mixed flow pump parameter optimization results based on the results of the local fine search.

[0012] Furthermore, the design parameters to be optimized for the mixed flow pump include but are not limited to the impeller inlet diameter D1, the impeller outlet diameter D2, the impeller inlet width b1, the impeller outlet width b2, the number of blades Z, the blade leading edge placement angle β1(r), the blade trailing edge placement angle β2(r), the blade wrap angle φ(r), the blade thickness distribution t(r), the guide vane installation angle α, the number of guide vanes Z d , guide vane inlet and outlet radius R in ,R out .

[0013] Furthermore, when the population is initialized, the objective function F(x) is established based on the weighted average efficiency η and the weighted average head H, which is expressed as:

[0014] minF(x)=[f1(x),f2(x)]

[0015]

[0016] Where f1(x) is the objective function of efficiency, η j (x) is the efficiency under the jth working condition when the design parameter is x; f2(x) is the objective function of the head, H j (x) is the lift under the jth operating condition when the design parameter is x; M is the number of operating conditions considered; w 1,j and w 2,j are the weight coefficients of efficiency and head under the jth working condition respectively.

[0017] Furthermore, the steps of global coarse screening are as follows:

[0018] Step 3.1: For the current population, sort the individuals in the population by non-dominated order according to the objective function value; perform cluster analysis on the sorted population, group the elite frontier according to the clustering results, and obtain the current Pareto frontier;

[0019] Step 3.2: Evaluate the convergence of the current Pareto frontier. When convergence slows down, dynamically adjust the mutation rate or trigger additional local search operators.

[0020] Step 3.3: Select the parent from the current elite set for crossover and perform the crossover operation to generate the offspring population Q. t , and then perform mutation operation to obtain elite individuals.

[0021] Furthermore, K-means clustering algorithm was used for cluster analysis.

[0022] Furthermore, the method for convergence evaluation is as follows:

[0023] Define the evaluation function G(PF t ), recorded as:

[0024]

[0025] Based on G(PF t ) The convergence of the change in the number of consecutive generations is judged to be slow, which can be recorded as:

[0026] ΔG t =|G(PF t )-G(PF t-k )|

[0027] When ΔG t <∈ converge When , it is judged that the convergence is slow, ∈ converge is the preset convergence threshold value, w1 and w2 are the weights of the two items respectively.

[0028] Furthermore, the mutation operation is recorded as:

[0029]

[0030] Where: p m (t) is the mutation rate, p m,base is the basic mutation rate; α is an adjustment coefficient; ∈ max is the maximum target variation, used for normalization.

[0031] Furthermore, local fine search: when the iteration of global coarse screening reaches the predetermined number of generations or convergence conditions, each elite individual is optimized with its design parameters as the initial point, using a gradient or greedy strategy based perturbation optimization; under the premise of ensuring the step size δ and the number of iterations, the individual parameters are gradually adjusted in the direction of improving the target value in order to obtain a better objective function value.

[0032] A computer storage medium stores a computing program thereon. When the computer program is executed by a processor, the mixed flow pump parameter optimization method based on the adaptive clustering improved NSGA-II is realized.

[0033] Furthermore, the storage medium is in various forms such as hard disk, solid state disk, USB flash drive, and SD card.

[0034] Beneficial effects of the present invention:

[0035] (1) Based on the traditional NSGA-II optimization algorithm, the method of the present invention innovatively integrates the adaptive hybrid mutation operator mechanism and the dynamic adjustment method of evolutionary parameters. It can intelligently switch the mutation type and adjust genetic parameters such as crossover rate and mutation rate according to population diversity and convergence state, significantly improving the algorithm's ability to escape local optimality and global search, and effectively improving the accuracy and convergence efficiency of the multi-parameter optimization design results of mixed flow pumps under complex working conditions.

[0036] (2) The present invention proposes a diversity enhancement strategy based on adaptive clustering. Through dynamic clustering and congestion adjustment in each generation of evolution, uniform coverage and diversity maintenance of the solution set are achieved, making the final Pareto optimal solution set more representative and better meeting the actual needs of multi-parameter design of mixed flow pumps under complex working conditions.

[0037] (3) The present invention adopts a two-stage hybrid optimization process that combines global evolution with local search, which not only ensures the full exploration of a large range of parameter space, but also enables fine optimization of elite individuals, effectively combining the advantages of global coarse screening and local development, and further improving the comprehensive performance of the mixed flow pump structure design.

[0038] (4) The present invention proposes an engineering implementation solution that integrates software and hardware. The optimization algorithm can be developed using a general programming language and is applicable to various hardware platforms such as servers, desktops, and industrial computers. It has good engineering portability and scalability and can be easily integrated with industrial design tools such as CFD simulation platforms, promoting the promotion and application of multi-parameter optimization algorithms in actual engineering and facilitating the automation and intelligent upgrade of product development. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 The research framework of the entire patent content is presented.

[0040] Figure 2 This is a structural diagram of the improved NSGA-II algorithm of the present invention. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0042] Combined with attachment Figure 1 、2 , the present invention proposes a mixed flow pump parameter optimization method based on adaptive clustering improved NSGA-II, which includes the following steps:

[0043] Step 1: Based on the structural characteristics of the mixed flow pump, select the design parameters of the mixed flow pump to be optimized, including but not limited to the impeller inlet diameter D1 (mm), impeller outlet diameter D2 (mm), impeller inlet width b1 (mm), impeller outlet width b2 (mm), number of blades Z, blade leading edge placement angle β1 (r) (°), blade trailing edge placement angle β2 (r) (°), blade wrap angle φ (r) (°), blade thickness distribution t (r) (mm), guide vane installation angle α (°), guide vane number Z d , guide vane inlet and outlet radius R in ,R out (mm), etc.

[0044] Step 2: Based on the above-mentioned mixed flow pump design parameters to be optimized, a mixed flow pump design scheme is formed by combining the design parameters. Each design scheme of the pump is regarded as an individual; the parameters and data structure are set, and the population is initialized. The details are as follows:

[0045] Parameter and data structure setting: set population size N, maximum iteration number T max , cluster number K, local search step size δ, convergence threshold ∈ and other key parameters. The current population P, candidate population Q and elite set E are stored in an array or list structure, and appropriate data structures are set to record individual target values ​​and cluster labels for subsequent calculations and operations.

[0046] Population initialization: Based on the variable parameter space, the initial population P0 is randomly generated, and the weighted average efficiency η[%] and weighted average lift H[m] of each individual are calculated as the objective function F(x).

[0047] minF(x)=[f1(x),f2(x)]

[0048]

[0049] Where f1(x) is the objective function of efficiency, η j (x) is the efficiency under the jth working condition when the design parameter is x; f2(x) is the objective function of the head, H j (x) is the lift under the jth operating condition when the design parameter is x; M is the number of operating conditions considered; w 1,j and w 2,j are the weight coefficients of efficiency and head under the jth working condition respectively.

[0050] Step 3: Use the improved NSGA-II multi-generation iteration to quickly explore the feasible region and perform global coarse screening. The global coarse screening is performed according to the iteration t=1,2,...,T max The specific steps are as follows:

[0051] Step 3.1, non-dominated sorting and elite selection:

[0052] For the current population P t-1 ∪Q t-1 , perform non-dominated sorting on the individuals in the population according to their objective function values;

[0053] For the sorted population, the K-means clustering algorithm is used to perform cluster analysis, and the elite frontiers are grouped according to the clustering results to obtain the current Pareto frontier.

[0054] Step 3.2: Convergence evaluation and operator adjustment:

[0055] Before executing genetic operators (crossover, mutation), the convergence of the current Pareto frontier is evaluated, such as comparing the changes in the optimal target values ​​of the last few generations or calculating the population diversity index. When convergence slows down, the mutation rate is dynamically adjusted or additional local search operators are appropriately triggered. Specifically, when the improvement of the Pareto frontier target within several consecutive generations (such as 5 generations) is less than the set threshold, the mutation rate is automatically increased. The adjustment steps are:

[0056] 1. Calculate the change in the mean of the objective function in recent generations;

[0057] 2. If the change is lower than the threshold, the mutation rate is increased from the base value p m0 Upgrade to The smaller the improvement, the higher the mutation rate; where α is the adjustment coefficient, ΔF is the target improvement, and ∈ is the convergence threshold.

[0058] 3. The dynamically adjusted mutation rate is used for the current and subsequent genetic mutation operations until the population convergence is restored, and then the mutation rate is restored to the baseline value.

[0059] In addition, if convergence stagnates and diversity decreases significantly, additional local perturbations are performed on some elite individuals to locally develop the neighborhood space of the elite solution to improve search accuracy and escape from local optimality.

[0060] More specifically, when selecting from the elite layer and passing on to the next generation of elites, it is ensured that at least a certain proportion (e.g., 20%) of representative individuals are selected from each cluster to maintain uniform coverage of the target space.

[0061] More specifically, the method for convergence evaluation is as follows:

[0062] Set PFt For the Pareto frontier of the tth generation, define an evaluation function G(PF t ), for example, the weighted average objective value of all non-dominated solutions:

[0063]

[0064] Among them, w1 and w2 are the weights of the two items respectively.

[0065] The judgment condition of slow convergence can be based on G(PF t ) in successive generations:

[0066] ΔG t =|G(PF t )-G(PF t-k )|

[0067] When ΔG t <∈ converge When , it is judged that the convergence is slow, ∈ converge It is the preset convergence threshold value.

[0068] Step 3.3, genetic operation: According to the above evaluation function G(PF t ), select the parent from the current elite set for crossover. Perform the crossover operation to generate the offspring population Q t , and then perform the following mutation operations:

[0069]

[0070] Where: p m (t) is the mutation rate, p m,base is the basic mutation rate; α is an adjustment coefficient; ∈ max is the maximum target variation, used for normalization.

[0071] The above convergence evaluation can control the cross-mutation intensity, such as increasing mutation perturbation when convergence is insufficient.

[0072] Step 4: Perform a local fine search on the elite individuals obtained from the global coarse screening to improve the quality of the solution set. Specifically: When the iterations of the global coarse screening reach a predetermined number of generations or convergence conditions, perform a local search on some or all individuals in the current elite solution set.

[0073] Specifically, each elite individual is initialized with its design parameters and optimized using a gradient-based or greedy strategy. While maintaining the step size δ and the number of iterations, the individual parameters are gradually adjusted in the direction of increasing the target value to achieve a better objective function value.

[0074] In the local search process, problem domain knowledge, such as CFD sensitivity information, can be used to improve search efficiency.

[0075] Step 5: Obtain the mixed flow pump parameter optimization results based on the results of the local fine search.

[0076] A computer storage medium stores a computing program thereon. When the computer program is executed by a processor, the mixed flow pump parameter optimization method based on the adaptive clustering improved NSGA-II is realized.

[0077] The aforementioned computer program was developed using the Python mainstream programming language framework, offering excellent platform compatibility and can be deployed and run on a variety of electronic devices, including servers, personal computers, and industrial control terminals. Servers can be single physical servers or virtualized clusters, while terminal devices can include desktop computers, laptops, tablets, and industrial control computers.

[0078] The computer device that implements the method of the present invention generally includes basic modules such as a processor, a memory, and a network interface. The processor can be a general-purpose CPU, or other programmable logic chips such as a digital signal processor (DSP), an application-specific integrated circuit (ASIC), and a field-programmable gate array (FPGA) can be used to provide sufficient computing power support for optimization calculations. The memory includes internal memory and non-volatile storage media, the latter of which can be used to store the operating system, Python runtime environment, and the program files described in the present invention. Through the network interface, efficient data interaction with a remote server, simulation platform, or database can be achieved.

[0079] The Python program presented in this paper has a clear structure and is easy to maintain and expand. Users can input the mixed-flow pump structural parameters and optimization objectives, invoke the optimization algorithm's main process, and automatically optimize the parameters and visualize the design results. The program can run independently or be integrated into an industrial design simulation platform to achieve automated engineering optimization.

[0080] The storage medium of the present invention stores Python program instructions for implementing the above-mentioned optimization method. The storage medium can be in various forms such as a hard disk, a solid-state drive, a USB flash drive, an SD card, etc. The above-mentioned various implementation methods are only preferred examples. Those skilled in the art can carry out diversified deployment and adaptation according to actual application scenarios. Any variation or replacement based on the core idea of ​​the present invention should fall within the scope of protection of the present invention.

[0081] To overcome the slow convergence and insufficient precision of existing algorithms for multi-parameter optimization of mixed-flow pumps, this paper proposes an improved solution that integrates local search with an adaptive convergence assessment mechanism. During population evolution, the objective function improvement of Pareto frontier individuals generated in each generation is dynamically evaluated. When the solution set convergence rate decreases or becomes trapped in a local optimum, the execution frequency and step size of the local greedy search operator are automatically increased, focusing on optimizing the neighborhood space of elite solutions. By organically combining global evolution with local directed search, the present invention significantly improves the accuracy of the optimal solution and the ability to obtain the global optimal solution, accelerating the convergence of multi-parameter optimization and providing a higher-quality design reference for practical projects. Furthermore, the present invention integrates an adaptive hybrid mutation operator mechanism that dynamically switches between different mutation operators based on the current population convergence state and diversity, enhancing the algorithm's ability to escape local optima and the global exploration depth of the objective space. Furthermore, a dynamic adjustment method for evolutionary parameters is proposed. By analyzing the convergence rate and objective function improvement during the optimization process in real time, parameters such as the crossover rate and mutation rate are automatically adjusted to achieve adaptive control of algorithm parameters, further enhancing optimization efficiency and the algorithm's adaptability to complex design problems.

[0082] In order to solve the problems of uneven distribution and insufficient representativeness of solution sets in the multi-parameter optimization of mixed-flow pumps, the present invention proposes a diversity enhancement module based on adaptive clustering. This module uses the K-means clustering algorithm to dynamically group the current Pareto frontier solutions during each generation of evolution, and introduces clustering information during elite selection and crowding calculation to ensure that representative individuals are evenly selected from each cluster. At the same time, a crowding penalty is imposed on areas with dense solution distribution, and excellent solutions in sparse areas are preferentially retained, thereby achieving uniform coverage of the target space. This measure greatly improves the diversity and engineering applicability of the solution set, making the final optimization results more representative and practical.

[0083] At the same time, the present invention adopts a hybrid optimization strategy, combining the evolutionary algorithm with the local search to form a two-stage search process. In the first stage, global coarse screening optimization is carried out, and the feasible domain is quickly explored through the improved NSGA-II multi-generation iteration; in the second stage, local fine search is carried out for the elite individuals obtained in the first stage to further improve the quality of the solution set. This two-stage strategy takes into account the advantages of global exploration and local development, improves the convergence efficiency and the performance of the final solution. Through the above improvements, the algorithm of the present invention can effectively avoid falling into the local optimum, obtain a Pareto optimal solution set with higher accuracy and more uniform distribution, and meet the needs of multi-parameter design of large mixed flow pump structures. In addition, the present invention provides an engineering implementation solution that integrates software and hardware. The optimization method can be deployed and run on a variety of computer devices such as servers, desktops, and industrial computers. The system includes hardware modules such as processors, memories, and network interfaces, and supports efficient data interaction with external simulation platforms and databases, which facilitates industrial application integration and engineering promotion.

[0084] The above embodiments are intended only to illustrate the design concepts and features of the present invention. Their purpose is to enable those skilled in the art to understand the contents of the present invention and implement them accordingly. The scope of protection of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design concepts disclosed in the present invention are within the scope of protection of the present invention.

Claims

1. A mixed flow pump parameter optimization method based on adaptive clustering improved NSGA-II, characterized in that: The steps include: Step 1: Based on the structural characteristics of the mixed flow pump, select the design parameters of the mixed flow pump to be optimized; Step 2: Combining design parameters to form a mixed flow pump design scheme, taking each pump design scheme as an individual; setting parameters and data structure, and initializing the population; Step 3: Rapidly explore the feasible region through multiple iterations of the improved NSGA-II and perform global coarse screening; Step 4: Perform local fine search on the elite individuals obtained from the global coarse screening to improve the quality of the solution set; Step 5: Obtain the mixed flow pump parameter optimization results based on the results of the local fine search.

2. The mixed flow pump parameter optimization method based on adaptive clustering improved NSGA-II according to claim 1 is characterized in that: The design parameters of the mixed flow pump to be optimized include but are not limited to the impeller inlet diameter D1, impeller outlet diameter D2, impeller inlet width b1, impeller outlet width b2, number of blades Z, blade leading edge placement angle β1(r), blade trailing edge placement angle β2(r), blade wrap angle φ(r), blade thickness distribution t(r), guide vane installation angle α, guide vane number Z d , guide vane inlet and outlet radius R in ,R out .

3. The mixed flow pump parameter optimization method based on adaptive clustering improved NSGA-II according to claim 1 is characterized in that: When the population is initialized, the objective function F(x) is established based on the weighted average efficiency η and the weighted average head H, which can be expressed as: minF(x)=[f1(x),f2(x)] Where f1(x) is the objective function of efficiency, η j (x) is the efficiency under the jth working condition when the design parameter is x; f2(x) is the objective function of the head, H j (x) is the lift under the jth operating condition when the design parameter is x; M is the number of operating conditions considered; w 1,j and w 2,j are the weight coefficients of efficiency and head under the jth working condition respectively.

4. The mixed flow pump parameter optimization method based on adaptive clustering improved NSGA-II according to claim 1 is characterized in that: The steps for global coarse screening are as follows: Step 3.1: For the current population, sort the individuals in the population by non-dominated order according to the objective function value; perform cluster analysis on the sorted population, group the elite frontier according to the clustering results, and obtain the current Pareto frontier; Step 3.2: Evaluate the convergence of the current Pareto frontier. When convergence slows down, dynamically adjust the mutation rate or trigger additional local search operators. Step 3.3: Select the parent from the current elite set for crossover and perform the crossover operation to generate the offspring population Q. t , and then perform mutation operation to obtain elite individuals.

5. The mixed flow pump parameter optimization method based on adaptive clustering improved NSGA-II according to claim 4 is characterized in that: K-means clustering algorithm was used for cluster analysis.

6. The mixed flow pump parameter optimization method based on adaptive clustering improved NSGA-II according to claim 4 is characterized in that: The convergence evaluation method is as follows: Define the evaluation function G(PF t ), recorded as: Based on G(PF t ) The convergence of the change in the number of consecutive generations is judged to be slow, which can be recorded as: ΔG t =|G(PF t )-G(PF t-k )| When ΔG t <∈ converge When , it is judged that the convergence is slow, ∈ converge is the preset convergence threshold value, w1 and w2 are the weights of the two items respectively.

7. The mixed flow pump parameter optimization method based on adaptive clustering improved NSGA-II according to claim 6, characterized in that: The mutation operation is recorded as: Where: p m (t) is the mutation rate, p m,base is the basic mutation rate; α is an adjustment coefficient; ∈ max is the maximum target variation, used for normalization.

8. The mixed flow pump parameter optimization method based on adaptive clustering improved NSGA-II according to claim 1 is characterized in that: Local fine search: When the iteration of global coarse screening reaches the predetermined number of generations or convergence conditions, a perturbation optimization based on gradient or greedy strategy is adopted for each elite individual with its design parameters as the initial point; Under the premise of ensuring the step size δ and the number of iterations, the individual parameters are gradually adjusted in the direction of improving the target value in order to obtain a better objective function value.

9. A computer storage medium, characterized in that A computing program is stored thereon, and when the computer program is executed by the processor, the method for optimizing parameters of a mixed flow pump based on an adaptive clustering improved NSGA-II as described in claim 1 is implemented.

10. A computer storage medium according to claim 9, characterized in that: The storage medium is in various forms such as hard disk, solid state disk, USB flash drive, and SD card.

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