Multi-objective optimization design method for pump impeller of magnetic drive pump

Abstract

The invention provides a magnetic drive pump impeller multi-objective optimization design method, and relates to the technical field of impeller multi-objective optimization design methods.The magnetic drive pump impeller multi-objective optimization design method comprises the steps that optimal Latin hypercube sampling is adopted to sample a design parameter space to generate a first sample set, and the total rotational inertia corresponding to each sample point is obtained through a total rotational inertia model; randomly generating a target number of new sample points by adopting an NSGA-III algorithm, and selecting a next generation of parent sample points from the leading edge levels; generating a filial generation sample point until the maximum evolution algebra of the sample point is reached; and setting a magnetic transmission stability dominant screening criterion, and obtaining geometric parameters corresponding to the leading edge sample points meeting the screening condition as optimization data. The total rotational inertia is used as a preposed physical screening criterion, so that the optimization process synchronously considers the specific transmission stability requirement of the magnetic drive pump from the source, and a set of efficient intelligent optimization process is formed in combination with optimal Latin hypercube sampling, rotational inertia-based physical pre-screening and an NSGA-III multi-objective evolutionary algorithm.

Description

Technical Field

[0001] This invention relates to the technical field of multi-objective optimization design methods for impellers, specifically a multi-objective optimization design method for a magnetic pump impeller. Background Technology

[0002] Magnetic drive pumps, due to their leak-free characteristics, are widely used in fields with stringent sealing requirements, such as chemical and pharmaceutical industries. The performance of their core transmission component, the impeller, and the stability of the magnetic drive system directly determine the pump's efficiency and reliability. Traditional magnetic drive pump impeller designs often focus on single hydraulic performance aspects such as efficiency and net positive suction head (NPSH), lacking a systematic consideration of the smoothness of magnetic transmission. Excessive impeller moment of inertia can exacerbate the risk of slippage and overheating of the magnetic coupler, while fluid-induced torque pulsation during impeller operation is directly transmitted to the external magnet, causing vibration and noise throughout the transmission system, affecting bearing life and operational smoothness. While some existing optimization methods attempt to introduce multiple objectives, they are often arbitrary in the initial design space definition and fail to treat moment of inertia and dynamic torque pulsation as clear and independent optimization objectives in conjunction with hydraulic performance optimization. This results in optimization results that cannot simultaneously meet the comprehensive requirements of high efficiency, low cavitation, low pulsation, and smooth magnetic transmission. In the prior art, CN117807893A discloses a method that uses a non-dominated sorting genetic algorithm based on reference points to optimize the hydraulic efficiency and cavitation margin of a high-speed centrifugal pump. It constructs a corresponding objective function and, based on sensitivity analysis, selects three parameters: impeller inlet diameter, impeller outlet width, and blade outlet angle. Using these three parameters as reference points and combining them with the non-dominated sorting genetic algorithm, it performs multi-objective optimization calculations to obtain the optimal geometric parameters corresponding to these three parameters. However, this method does not use the total moment of inertia of the impeller as an initial selection criterion, nor does it consider the torque pulsation coefficient. As one of the three core optimization objectives alongside efficiency and cavitation performance, the unique transmission smoothness requirement of magnetic pumps has not been integrated into the optimization system from the design stage; it has not adopted a strategy combining optimal Latin hypercube sampling, global sensitivity analysis, and adaptive design space update to quickly identify key parameters sensitive to the objective function and their optimization directions in the early stages of iteration, and dynamically adjust parameter boundaries; it has not set a secondary screening criterion dominated by magnetic transmission smoothness, and has not comprehensively considered the engineering matching requirements of rotational inertia and the balance between multiple objectives; therefore, a multi-objective optimization design method for magnetic pump impellers is urgently needed.

[0003] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-objective optimization design method for the impeller of a magnetic pump to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A multi-objective optimization design method for a magnetic pump impeller, comprising the following steps: S1: The impeller is structurally differentiated to determine several structures. The geometric parameters of each structure are determined and the upper and lower limits of the geometric parameters are set. The upper and lower limits of all geometric parameters are statistically analyzed to form the design parameter space. Based on the type of geometric parameters, the total rotational inertia model of the impeller is constructed. A CFD simulation model is constructed with geometric parameters as input and target coefficients as output. The target coefficients are pump hydraulic efficiency, cavitation performance index and torque pulsation coefficient. S2: The design parameter space is sampled using optimal Latin hypercube sampling to generate the first sample set. The total moment of inertia corresponding to each sample point is obtained through the total moment of inertia model. The first sample set is then filtered using the total moment of inertia to obtain the second sample set. S3: Simulate the sample points within the second sample set using a CFD simulation model to obtain the pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient corresponding to each sample point. Update the upper and lower limits of the geometric parameters based on the geometric parameters corresponding to the three sample points when the pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient are optimal. S4: Based on the updated upper and lower limits of the geometric parameters, the NSGA-III algorithm is used to randomly generate a new number of target sample points. For each new sample point, the target coefficient of each new sample point is obtained by simulation through the CFD simulation model. The Pareto dominance method is used to divide the new sample points into different frontier levels based on the target coefficients of the new sample points. The next generation of parent sample points is selected from the frontier levels. S5: Simulate binary crossover and polynomial mutation on the parent sample points to generate offspring sample points until the maximum evolutionary generation of the sample points is reached. Extract the leading sample points of the first leading level in the maximum evolutionary generation to form the Pareto solution set. Set the magnetic transmission stability as the dominant screening criterion to screen the leading sample points in the Pareto solution set and obtain the geometric parameters corresponding to the leading sample points that meet the screening conditions as optimization data.

[0006] Further, the total moment of inertia corresponding to each sample point is calculated, and the specific steps are as follows: The impeller is structurally differentiated into several structures, including the main disk, individual blades, and hub. The geometric parameters of each structure are determined and upper and lower limits are set. The geometric parameters include impeller outlet diameter, impeller inlet diameter, impeller outlet width, blade inlet angle, blade outlet angle, number of blades, blade wrap angle, and hub ratio. Calculate the moment of inertia for each region separately. The moment of inertia of the main disk is obtained by multiplying its own mass by the square of the exit radius, and then multiplying by a coefficient of one-half. The moment of inertia of a single blade is equal to the blade's mass multiplied by the square of one-quarter of the sum of the inlet and outlet diameters. The moment of inertia of the hub is calculated similarly to that of the disk, as half of its mass multiplied by the square of the hub radius. The total moment of inertia of the impeller is equal to the moment of inertia of the main disk, plus the sum of the moments of inertia of all the blades, which is obtained by multiplying the moment of inertia of a single blade by the total number of blades, plus the moment of inertia of the hub.

[0007] Further, the target coefficient is calculated, and the specific steps are as follows: A CFD simulation model is constructed with geometric parameters as input and target coefficients as output. The characteristic flow points of the impeller are determined, namely the characteristic flow point, the small flow point of 0.8 times the characteristic flow point, and the large flow point of 1.2 times the characteristic flow point. The pump hydraulic efficiency of the impeller at each characteristic flow point is calculated using the CFD simulation model. The three pump hydraulic efficiencies are then weighted and summed according to preset weight coefficients. The weight of the pump hydraulic efficiency at the characteristic flow point is 0.6, and the weight of the pump hydraulic efficiency at the two non-characteristic flow points is 0.2 each, forming the first target coefficient for evaluating the impeller characteristics. The cavitation performance index of the impeller at the characteristic flow point is obtained by CFD simulation model, and this index is directly used as the second target coefficient for evaluating the impeller's cavitation resistance. In the CFDF simulation model, the impeller rotation period and sampling interval are set. The instantaneous fluid torque time series data of the impeller during the rotation period are obtained through transient simulation. The maximum and minimum torque values ​​of the impeller during the rotation period are determined based on the time series data, and the average torque value is calculated. The third target coefficient is obtained by dividing the difference between the maximum and minimum torque values ​​by the average torque value.

[0008] Further, the second sample set is obtained through the following steps: The design parameter space is sampled using optimal Latin hypercube sampling to generate the first sample set, i.e., to generate... sample points Furthermore, based on the total moment of inertia of each sample point, sample points whose total moment of inertia exceeds the preset allowable range are filtered out to obtain a second sample set. For the sample points within the second sample set, simulations are performed using a CFD simulation model to obtain the pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient corresponding to each sample point.

[0009] Furthermore, the second sample set is analyzed, and the specific steps are as follows: A global Sobol sensitivity analysis was performed on the second sample set to calculate the first-order sensitivity index of each geometric parameter to pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient. Specifically: For each target coefficient, the first-order sensitivity index of the target coefficient for individual variation is obtained by calculating the ratio of the variance of the conditional expectation of the target coefficient to the total variance of the target coefficient when a certain geometric parameter is fixed. Here, the conditional expectation of the target coefficient refers to the variance of the sequence of conditional expectation values ​​of the target coefficient at all possible values ​​when a certain geometric parameter is fixed, and the total variance of the target coefficient refers to the overall variance of the target coefficient at all sample points in the second sample set.

[0010] Furthermore, the upper and lower limits of the geometric parameters are updated, and the specific steps are as follows: Three optimal sample points were located, namely the pump with the highest hydraulic efficiency, the lowest cavitation performance index, and the smallest torque pulsation coefficient. The first-order sensitivity index that is higher than the preset maximum index threshold was identified as the high sensitivity index. The distribution characteristics of the high sensitivity index in these sample points were analyzed. That is, if the value of the high sensitivity index in the optimal sample points continuously approaches the boundary of the original design parameter space, it indicates that the optimization direction of the geometric parameter is clearly pointing to the outside of the boundary. The boundary is symmetrically expanded outward according to the preset expansion ratio. For geometric parameters whose first-order sensitivity indices are all below the preset minimum index threshold, they are determined to be insensitive parameters. For insensitive parameters, the value distribution of their values ​​on all sample points in the second sample set is calculated to determine their mean and distribution range. With the mean point as the center, the upper and lower limits of their values ​​are symmetrically shrunk according to the preset shrinkage ratio to form a narrower and more focused new value range. This method is used to update the upper and lower limits of the geometric parameters.

[0011] Furthermore, the sample points are divided into different frontier levels, and the specific steps are as follows: Based on the updated upper and lower limits of the geometric parameters, the NSGA-III algorithm is used to randomly generate a new number of target sample points. For each new sample point, the target coefficient of each new sample point is obtained by simulation through a CFD simulation model. The Pareto dominance method is used to divide the new sample points into different frontier levels based on the target coefficients of the new sample points. The next generation of parent sample points is selected from the frontier levels. The specific method for dividing sample points into different frontier levels is as follows: Set the dominance condition for sample points. If a sample point is no worse than any other sample point in terms of the target coefficient, and is strictly better in at least one target coefficient, it is said to dominate that sample point. Find those points that are not dominated by any other sample points from all sample points and assign them to the first frontier level. Then, temporarily remove these first-level points and find the undominated points again from the remaining points to form the second frontier level. Repeat this process until all sample points have been assigned a frontier level.

[0012] Furthermore, the most suitable next-generation parent sample points are selected from the leading edge level. The specific steps are as follows: Based on the target coefficient distribution in the first frontier level, a set of reference points uniformly distributed on the normalized hyperplane is dynamically generated. Each sample point in the first frontier level is mapped to this hyperplane, and its vertical distance to all reference points is calculated. It is then associated with the nearest reference point. By evaluating the number of sample points associated with each reference point, the sample points corresponding to reference points with fewer associated sample points are preferentially selected as parent sample points. Simulated binary crossover and polynomial mutation are performed on the parent sample points to generate offspring sample points. This calculation is repeated until the maximum number of generations is reached.

[0013] Furthermore, simulated binary crossover and polynomial mutation are performed on the parent sample points to generate offspring sample points. The specific steps are as follows: Randomly pair up the parent sample points. For each pair of parents and all its variables, first perform a crossover operation: independently generate a random number between zero and one for each variable. Based on this random number, calculate the expansion factor of the variable. If the random number is less than or equal to 0.5, the expansion factor is equal to twice the power of 1 / 21 of the random number; if the random number is greater than 0.5, the expansion factor is equal to twice the power of 1 / 21 of the reciprocal of the difference between the two random numbers. Using the calculated expansion factor, generate new values ​​for the variable for two offspring. The value of the first offspring is equal to the value of the first parent multiplied by the expansion factor, plus the value of the second parent multiplied by the expansion factor, and then multiplied by 0.5. The value of the second offspring is obtained by multiplying the value of the first parent by the expansion factor, plus the value of the second parent multiplied by the expansion factor, and then multiplying the sum by 0.5. After crossover, a mutation operation is performed. For each variable in the offspring, a new random number between zero and one is generated to determine the mutation. If this random number is not less than 0.125, the variable remains unchanged. If it is less than 0.125, the mutation calculation begins: First, a new mutation parameter is generated for the variable, which is a random number between zero and one. Then, the proportion of the distance from the current variable value to its lower limit to its total value range is calculated, as well as the proportion of the distance from its upper limit to the current value to the same range. Based on the mutation parameter, the perturbation factor of the variable is calculated. If the mutation parameter is less than 0.5, the perturbation factor is determined by a series of calculations containing the above proportions. If the mutation parameter is greater than or equal to 0.5, the perturbation factor is determined by another set of corresponding calculations. Finally, the new mutated variable value is equal to the original variable value plus the product of the perturbation factor and its total value range. This mutation operation is performed independently for all dimensions of each offspring individual. After completing the crossover and mutation of all parent pairs, all newly generated offspring individuals are aggregated to form offspring sample points.

[0014] The specific steps to obtain optimized data are as follows: Extract all first-front level sample points from the sample points with the maximum evolutionary generation to form the Pareto optimal solution set. Set a magnetic transmission stability-dominant screening criterion to screen the sample points in the Pareto optimal solution set, specifically as follows: An ideal matching space for the total moment of inertia is defined. Sample points whose total moment of inertia deviates from the ideal matching interval in the Pareto optimal solution set are directly removed. The target coefficients of the remaining sample points are normalized. A set of weighted coefficients is preset, and the preset weighted coefficients are weighted and calculated with the target coefficients respectively. A weighted comprehensive performance index is constructed that integrates the highest pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient. At the same time, the variance of the relative deviation between the target coefficient of each sample point and the optimal value on its respective Pareto front is calculated. The geometric parameters corresponding to the sample points with high weighted comprehensive performance index and small variance are selected as optimization data.

[0015] Compared with the prior art, the beneficial effects of the present invention are: The initial samples are physically feasibility-screened using a total moment of inertia model to eliminate poor designs in advance, ensuring that subsequent optimizations are conducted within the engineering-acceptable moment of inertia range. The parameter space is dynamically updated by analyzing the optimal sample points and global sensitivity analysis results. The torque pulsation of the impeller is directly extracted and quantified through CFD transient simulation and is used as an independent optimization objective of equal importance to efficiency and cavitation. Combined with the screening criterion of "magnetic drive stability dominance", the selected scheme can ensure that while guaranteeing basic hydraulic performance, it minimizes the source of pump vibration and noise, fundamentally improving the operational stability and reliability of the magnetic pump. The NSGA-III algorithm is adopted, which maintains the wide distribution of the population in the three-dimensional target space by introducing a reference point mechanism, ensuring that the final Pareto solution set is uniformly distributed and has a wide coverage of the trade-off scheme. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the overall method flow of the present invention; Figure 2 This is a graph showing the relationship between the moment of inertia of the wheel hub and its diameter. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0018] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0019] Example: Please see Figures 1-2 The present invention provides a technical solution: A multi-objective optimization design method for a magnetic pump impeller, comprising the following steps: S1: The impeller is structurally differentiated to determine several structures. The geometric parameters of each structure are determined and the upper and lower limits of the geometric parameters are set. The upper and lower limits of all geometric parameters are statistically analyzed to form the design parameter space. Based on the type of geometric parameters, the total rotational inertia model of the impeller is constructed. A CFD simulation model is constructed with geometric parameters as input and target coefficients as output. The target coefficients are pump hydraulic efficiency, cavitation performance index and torque pulsation coefficient. In the above process, setting upper and lower limits for geometric parameters is to define a physically feasible and potentially optimized initial range of values ​​for each key design variable, such as impeller outlet diameter and inlet installation angle, based on engineering experience, manufacturing constraints, installation space limitations, and preliminary hydraulic performance predictions. Combining these independent parameter upper and lower limits constitutes a multi-dimensional design parameter space. The fundamental purpose of constructing this space is to define clear search boundaries for all subsequent sampling, simulation, and optimization algorithms, ensuring that the entire optimization process is conducted within a reasonable engineering range, avoiding unrealistic or unmanufacturable design schemes, thereby transforming the complex multi-objective impeller optimization problem into a mathematical optimization problem of finding the optimal parameter combination within a limited space.

[0020] S2: The design parameter space is sampled using optimal Latin hypercube sampling to generate the first sample set. The total moment of inertia corresponding to each sample point is obtained through the total moment of inertia model. The first sample set is then filtered using the total moment of inertia to obtain the second sample set. The specific steps for calculating the total moment of inertia for each sample point are as follows: The impeller is structurally differentiated into several structures, including the main disk, individual blades, and hub. The geometric parameters of each structure are determined and upper and lower limits are set. The geometric parameters include impeller outlet diameter, impeller inlet diameter, impeller outlet width, blade inlet angle, blade outlet angle, number of blades, blade wrap angle, and hub ratio. Calculate the moment of inertia for each region separately. The moment of inertia of the main disk is obtained by multiplying its own mass by the square of the exit radius, and then multiplying by a coefficient of one-half. The moment of inertia of a single blade is equal to the blade's mass multiplied by the square of one-quarter of the sum of the inlet and outlet diameters. The moment of inertia of the hub is calculated similarly to that of the disk, as half of its mass multiplied by the square of the hub radius. The total moment of inertia of the impeller is equal to the moment of inertia of the main disk, plus the sum of the moments of inertia of all the blades, which is obtained by multiplying the moment of inertia of a single blade by the total number of blades, plus the moment of inertia of the hub.

[0021] The formula upon which the above process is based is: in, Indicates the moment of inertia of the main disk; Indicates the mass of the disk; Indicates the impeller outlet diameter; In the above process, the dependent variable on the left side of the formula This represents the moment of inertia of the main disk. Its technical advantage lies in the fact that this physical quantity quantitatively characterizes the magnitude of the disk's inertia against changes in its own angular velocity. It is one of the core fundamental parameters for evaluating the overall moment of inertia of the impeller, thus affecting the starting and speed regulation response characteristics and operational stability of the magnetic pump drive system. The formula shows that the moment of inertia of the disk... It is mainly related to two independent variables: disk mass. and impeller outlet diameter This is because, according to the physical principle of the moment of inertia of a rigid body, the moment of inertia of a homogeneous thin disk rotating about its central axis is determined by its mass distribution, specifically manifested as the product of its mass and the square of its radius; the moment of inertia of a disk... With disk mass It is directly proportional to the mass; the greater the mass, the greater the inertia. Simultaneously, it is related to the impeller outlet diameter. The moment of inertia is proportional to the square of the radius; an increase in diameter will significantly increase the moment of inertia in a square relationship. It is a specific constant determined by the geometry of the homogeneous disk.

[0022] in, Indicates the inertia of a single blade; Indicates the mass of the blade; Indicates the impeller inlet diameter; In the above process, the dependent variable on the left side of the formula This parameter represents the moment of inertia of a single blade. It quantitatively characterizes the inertia of a single blade rotating about the impeller's axis of rotation and is a key component of the total moment of inertia of the impeller. Accurate estimation of this parameter has a direct technical effect on controlling the dynamic characteristics of the impeller from the design stage and ensuring the smooth operation of the magnetic pump. The formula shows that the moment of inertia of a single blade... It mainly depends on the quality of the blade. And a system based on impeller inlet diameter and outlet diameter The calculated characteristic radius is This relationship is based on an engineering model that simplifies the blade to a point mass with its mass concentrated at the blade's average radius, which is approximately equal to the average of the inlet and outlet radii; the moment of inertia of a single blade. With blade mass It is directly proportional to the mass; the greater the mass, the greater the inertia. Simultaneously, it is proportional to the square of the characteristic radius. It is proportional to the square of the impeller inlet diameter, which means that the impeller inlet diameter is proportional to the square of the impeller inlet diameter. and outlet diameter An increase in these parameters will lead to an increase in the blade's inertia. in, Indicates the hub inertia; Indicates the diameter of the wheel hub; Indicates the mass of the wheel hub; In the above process, the dependent variable on the left side of the formula This represents the moment of inertia of the impeller hub. This parameter quantitatively characterizes the magnitude of the hub's inertia when rotating about its central axis. It is a component of the total moment of inertia of the impeller, and its accurate calculation has a clear technical effect on comprehensively evaluating the overall moment of inertia of the impeller and thus optimizing the load matching and dynamic response characteristics of the magnetic pump drive system. The formula shows that the moment of inertia of the hub... It mainly depends on the quality of the wheel hub. and wheel hub diameter This relationship stems from the classic physical model that simplifies the wheel hub into a homogeneous cylinder or disk rotating about its central axis. Its moment of inertia is determined by its mass distribution, specifically expressed as the product of its mass and the square of its radius; the moment of inertia of the wheel hub... With wheel hub quality It is directly proportional to the mass; the greater the mass, the greater the inertia. Simultaneously, it is related to the hub diameter. The moment of inertia is proportional to the square of the radius; an increase in diameter will significantly increase the moment of inertia in a square relationship. It is a constant determined by the specific geometry of a homogeneous solid cylinder or disk.

[0023] In the above embodiments, 20 sets of data on the hub diameter and the corresponding moment of inertia of the hub are given to reflect the change of the moment of inertia of the hub as the hub diameter changes, as shown in Table 1: Table 1: Relationship between the moment of inertia of the wheel hub and the diameter of the wheel hub In Table 1 above, the first thing to be fixed is... You can see the moment of inertia of the wheel hub. With hub diameter The moment of inertia is proportional to the square of the diameter, and an increase in diameter will significantly increase its moment of inertia in a square relationship.

[0024] The total moment of inertia for each sample point is obtained using the total moment of inertia model: in, Indicates the number of blades; This represents the total moment of inertia of the impeller; Represents geometric parameters.

[0025] The above process, through the establishment of a precise physical model, directly links the abstract "moment of inertia," a key performance indicator of magnetic transmission, with the specific geometric parameters and structural mass of the impeller, achieving rapid and quantitative prediction of the moment of inertia. This model abandons the lagging mode of traditional empirical estimation or ex-post verification, decomposing the impeller into three typical components: the main disk, blades, and the hub. Based on the classical moment of inertia formula, it uses core dimensions such as the outlet radius, the average inlet and outlet diameters, and the hub radius, along with their corresponding masses, to calculate the inertia contribution of each component. Finally, the total inertia is obtained through weighted summation. This allows designers to predict the impeller inertia level during the parameter design stage, laying the foundation for controlling the load of the magnetic transmission system from the source. Embedding this model into the front-end screening stage of the optimization process produces a crucial preprocessing effect. After generating a large number of parameter samples, the total moment of inertia corresponding to each sample can be quickly calculated based on the model without the need for time-consuming CFD simulation. This allows for the elimination of unreasonable designs whose moment of inertia exceeds the allowable range in engineering. This step acts like a "physical feasibility" filter, preemptively eliminating a large number of high-risk design schemes that may lead to slippage, overheating, or even failure of the magnetic coupler. This greatly reduces the search space for subsequent high-cost CFD simulations and optimization algorithms, significantly improving the efficiency and engineering practicality of the entire optimization process and ensuring that the optimization exploration always stays on track that meets the basic requirements of magnetic transmission stability.

[0026] The specific steps for calculating the target coefficient are as follows: A CFD simulation model is constructed with geometric parameters as input and target coefficients as output. The characteristic flow points of the impeller are determined, namely the characteristic flow point, the small flow point of 0.8 times the characteristic flow point, and the large flow point of 1.2 times the characteristic flow point. The pump hydraulic efficiency of the impeller at each characteristic flow point is calculated using the CFD simulation model. The three pump hydraulic efficiencies are then weighted and summed according to preset weight coefficients. The weight of the pump hydraulic efficiency at the characteristic flow point is 0.6, and the weight of the pump hydraulic efficiency at the two non-characteristic flow points is 0.2 each, forming the first target coefficient for evaluating the impeller characteristics. The cavitation performance index of the impeller at the characteristic flow point is obtained by CFD simulation model, and this index is directly used as the second target coefficient for evaluating the impeller's cavitation resistance. In the CFDF simulation model, the impeller rotation period and sampling interval are set. The instantaneous fluid torque time series data of the impeller during the rotation period are obtained through transient simulation. The maximum and minimum torque values ​​of the impeller during the rotation period are determined based on the time series data, and the average torque value is calculated. The third target coefficient is obtained by dividing the difference between the maximum and minimum torque values ​​by the average torque value.

[0027] The formula upon which the above process is based is: in, This represents the first target coefficient of the impeller; This indicates that geometric parameters are calculated using CFD. The pump hydraulic efficiency is reduced; This indicates that geometric parameters are calculated using CFD. The pump hydraulic efficiency is reduced; This indicates that geometric parameters are calculated using a CFD simulation model. The pump hydraulic efficiency is reduced; In the above process, the weighting coefficients of 0.6, 0.2, and 0.2 are primarily based on the operating conditions and design priorities of the magnetic pump in actual operation. The characteristic flow point is assigned the highest weight of 0.6 because this operating condition is the pump's most critical and longest-running rated operating point, ensuring its high efficiency is the primary design objective. Simultaneously, assigning weights of 0.2 each to the low and high flow points reflects consideration of the pump's robustness under partial or slightly overload conditions. This aims to guide the designed impeller not only to be highly efficient at the design point but also to maintain relatively good efficiency within a certain flow range nearby, thereby achieving a wider high-efficiency operating range and improving the pump's practical operational adaptability and economy.

[0028] Geometric parameters at characteristic flow points The cavitation performance index obtained through CFD simulation model is used as the second target coefficient: in, This represents the second target coefficient of the impeller; Indicates geometric parameters at characteristic flow points The following are the cavitation performance indicators obtained through CFD simulation models; In the CFDF simulation model, the impeller rotation period and sampling interval are set. The instantaneous fluid torque time series data of the impeller during the rotation period are obtained through transient simulation. The extreme value and average value of the impeller torque during the rotation period are determined based on the time series data. The torque pulsation coefficient is calculated and used as the third target coefficient. in, This indicates the maximum torque during the impeller's rotation cycle; This represents the minimum torque during the impeller's rotation cycle; This represents the average torque during the impeller's rotational cycle. This represents the third target coefficient of the impeller.

[0029] In the above process, a comprehensive evaluation system consisting of three independent and complementary target coefficients was constructed to achieve a multi-dimensional and refined quantitative assessment of the magnetic pump impeller performance. The first target coefficient, by weighted fusion of the hydraulic efficiency at the design point and its nearby flow points, not only focuses on the optimal performance under rated operating conditions but also emphasizes the impeller's ability to maintain high efficiency during flow fluctuations in actual operation, thereby guiding the design towards impellers with a wide and efficient operating range and good adaptability. The second target coefficient directly adopts the required net positive suction head (NPSH) at the design flow rate, focusing on the impeller's anti-cavitation, a key reliability indicator, to ensure that the optimized impeller has excellent suction performance at the core operating point. The third objective coefficient innovatively introduces a torque pulsation coefficient. This coefficient extracts dynamic fluctuation data of fluid torque within the impeller rotation cycle through CFD transient simulation and calculates its relative pulsation amplitude. For the first time, it transforms the key dynamic factor affecting the stability of the magnetic drive system—periodic torque disturbance—into a quantifiable and optimizable objective. This allows the optimization algorithm to proactively explore designs that are more uniform in the flow field structure and effectively reduce periodic flow separation and vortices, thereby reducing the vibration load transmitted to the magnetic coupler from the source. These three objective coefficients work together to incorporate hydraulic efficiency, cavitation performance, and transmission smoothness—which are traditionally considered separately—into a unified optimization framework. They represent the pump's energy characteristics, reliability, and operational quality, respectively, enabling subsequent multi-objective optimization algorithms to systematically explore the optimal balance between these key performance indicators. Ultimately, this guides the design of a high-quality impeller with superior overall performance, particularly suitable for the special application scenario of magnetic drive. The CFD simulation model here refers to a fully parameterized and automated virtual fluid experimental system based on computational fluid dynamics principles. Taking the impeller's geometric parameters as input, the model automatically constructs its three-dimensional fluid domain and meshes it. By solving the fundamental physical equations of fluid motion, it accurately simulates the internal flow state of the impeller under different operating conditions. Therefore, it is essentially a digital "virtual pump test bench" capable of quantitatively predicting various performance characteristics of a given impeller design in actual operation. This CFD model can be used to calculate target coefficients because it can simulate real physical processes. By setting different inlet flow conditions, the model can calculate the pump hydraulic efficiency of the impeller at the characteristic flow point, the low flow point (0.8 times the characteristic flow rate), and the high flow point (1.2 times the characteristic flow rate). Weighted summation of these three efficiency values ​​is used to guide the design of an impeller that is not only highly efficient at the rated point but also maintains good performance under flow fluctuations. Simultaneously, at the characteristic flow point, the CFD model can simulate the cavitation process through its built-in cavitation model, thereby directly predicting the key indicator for measuring cavitation resistance—the cavitation performance index.

[0030] The specific steps to obtain the second sample set are as follows: The design parameter space is sampled using optimal Latin hypercube sampling to generate the first sample set, i.e., to generate... sample points Furthermore, based on the total moment of inertia of each sample point, sample points whose total moment of inertia exceeds the preset allowable range are filtered out to obtain a second sample set. For the sample points within the second sample set, simulations are performed using a CFD simulation model to obtain the pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient corresponding to each sample point.

[0031] S3: Simulate the sample points within the second sample set using a CFD simulation model to obtain the pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient corresponding to each sample point. Update the upper and lower limits of the geometric parameters based on the geometric parameters corresponding to the three sample points when the pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient are optimal. The analysis of the second sample set follows these steps: A global Sobol sensitivity analysis was performed on the second sample set to calculate the first-order sensitivity index of each geometric parameter to pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient. Specifically: For each target coefficient, the first-order sensitivity index of the target coefficient for individual variation is obtained by calculating the ratio of the variance of the conditional expectation of the target coefficient to the total variance of the target coefficient when a certain geometric parameter is fixed. Here, the conditional expectation of the target coefficient refers to the variance of the sequence of conditional expectation values ​​of the target coefficient at all possible values ​​when a certain geometric parameter is fixed, and the total variance of the target coefficient refers to the overall variance of the target coefficient at all sample points in the second sample set.

[0032] In the above process, it provides a quantitative and global approach to accurately identify the independent impact of each geometric parameter on the three key performance indicators. By calculating the first-order sensitivity index, it can clearly distinguish which parameters are "sensitive" and whose individual changes have a significant impact on the objective function, and which are "insensitive" parameters with a weak impact. This allows for the classification, management, and precise control of design variables in subsequent design space updates and optimization searches. This provides crucial data-driven decision-making support for subsequent adaptive adjustment of parameter boundaries, focusing computational resources on key variables, and understanding the causal relationship between design variables and performance, effectively avoiding blind optimization. The upper and lower limits of the geometric parameters are updated through the following steps: Three optimal sample points were located, namely the pump with the highest hydraulic efficiency, the lowest cavitation performance index, and the smallest torque pulsation coefficient. The first-order sensitivity index that is higher than the preset maximum index threshold was identified as the high sensitivity index. The distribution characteristics of the high sensitivity index in these sample points were analyzed. That is, if the value of the high sensitivity index in the optimal sample points continuously approaches the boundary of the original design parameter space, it indicates that the optimization direction of the geometric parameter is clearly pointing to the outside of the boundary. The boundary is symmetrically expanded outward according to the preset expansion ratio. For geometric parameters whose first-order sensitivity indices are all below the preset minimum index threshold, they are determined to be insensitive parameters. For insensitive parameters, the value distribution of their values ​​on all sample points in the second sample set is calculated to determine their mean and distribution range. With the mean point as the center, the upper and lower limits of their values ​​are symmetrically shrunk according to the preset shrinkage ratio to form a narrower and more focused new value range. This method is used to update the upper and lower limits of the geometric parameters.

[0033] In the above process, an adaptive dynamic update mechanism for the design space was implemented. Its core effect is to guide the optimization search to focus on more promising regions, significantly improving the efficiency and quality of optimization. By analyzing the boundary approximation characteristics of high-sensitivity parameters in the optimal sample points, the algorithm can intelligently identify which parameters have not yet been fully released within the original boundary, and accordingly symmetrically expand its boundary, actively opening up new exploration directions for the algorithm that may have better performance. This avoids missing the global optimal solution due to a conservative initial range setting, reflecting the optimization idea of ​​"active exploration". Simultaneously, this mechanism performs a reverse "focusing" operation on insensitive parameters. By analyzing their distribution in the existing samples, it narrows their value range around the mean point, essentially eliminating invalid variation intervals where these parameters have little impact on the objective function. This not only reduces invalid searches in these dimensions, lowering the effective dimensionality and complexity of the problem, but also allows limited sampling and computational resources to be concentrated on optimizing the truly dominant sensitive parameters. This strategy combining "exploration" and "focusing" dynamically shapes a more compact and goal-oriented design subspace, enabling subsequent evolutionary algorithms to perform more efficient and accurate searches within this space, thus approximating the true global Pareto front faster and more accurately. The determination of the preset maximum and minimum index thresholds is usually based on statistical judgment or empirical rules of the distribution of global Sobol sensitivity analysis results. A typical method is to calculate the first-order sensitivity index of all geometric parameters to all target coefficients and sort them by value; the lower bound of the sensitivity index corresponding to the top 30% of parameters can be set as the "preset maximum index threshold" to screen out "high-sensitivity" parameters that have a significant dominant impact on performance; at the same time, the upper bound of the sensitivity index corresponding to the bottom 30% of parameters can be set as the "preset minimum index threshold" to identify non-sensitive parameters that have little impact on performance. The preset expansion and contraction ratios are usually set based on rules of thumb, the need for exploration and convergence balance in the optimization problem, and the size of the parameter value range itself. The expansion ratio is generally set to a small percentage value, such as 5% to 20%, with the aim of cautiously exploring outwards within a controllable range to avoid falling into unreasonable regions or significantly increasing the invalid search space due to overexpansion. The contraction ratio, on the other hand, can be set to a relatively large percentage value, such as 30% to 50%, with the aim of quickly focusing on the high-frequency distribution area of ​​non-sensitive parameters, significantly compressing their range of variation, thereby reducing the dimensionality and complexity of subsequent optimization.

[0034] S4: Based on the updated upper and lower limits of the geometric parameters, the NSGA-III algorithm is used to randomly generate a new number of target sample points. For each new sample point, the target coefficient of each new sample point is obtained by simulation through the CFD simulation model. The Pareto dominance method is used to divide the new sample points into different frontier levels based on the target coefficients of the new sample points. The next generation of parent sample points is selected from the frontier levels. The sample points are divided into different frontier levels. The specific steps are as follows: Based on the updated upper and lower limits of the geometric parameters, the NSGA-III algorithm is used to randomly generate a new number of target sample points. For each new sample point, the target coefficient of each new sample point is obtained by simulation through a CFD simulation model. The Pareto dominance method is used to divide the new sample points into different frontier levels based on the target coefficients of the new sample points. The next generation of parent sample points is selected from the frontier levels. The specific method for dividing sample points into different frontier levels is as follows: Set the dominance condition for sample points. If a sample point is no worse than any other sample point in terms of the target coefficient, and is strictly better in at least one target coefficient, it is said to dominate that sample point. Find those points that are not dominated by any other sample points from all sample points and assign them to the first frontier level. Then, temporarily remove these first-level points and find the undominated points again from the remaining points to form the second frontier level. Repeat this process until all sample points have been assigned a frontier level.

[0035] In the above process, all sample points are divided into multiple frontier levels from best to worst based on the superiority of their objective vectors, i.e., Pareto dominance. The first frontier level is the Pareto optimal solution set in the current population. This hierarchical mechanism ensures that the selection pressure is always directed towards simultaneously improving all objectives: the algorithm will prioritize retaining and breeding individuals at higher frontier levels. This not only guides the entire population to converge toward the true Pareto front, but also lays the foundation for maintaining the diversity of the solution set by retaining all individuals within the same frontier level. This is a key step in achieving the core objective of multi-objective optimization algorithms—finding a set of widely distributed approximate optimal solutions that balance multiple objectives well.

[0036] The specific steps for selecting the most suitable next-generation parent sample points from the leading edge level are as follows: Based on the target coefficient distribution in the first frontier level, a set of reference points uniformly distributed on the normalized hyperplane is dynamically generated. Each sample point in the first frontier level is mapped to this hyperplane, and its vertical distance to all reference points is calculated. It is then associated with the nearest reference point. By evaluating the number of sample points associated with each reference point, the sample points corresponding to reference points with fewer associated sample points are preferentially selected as parent sample points. Simulated binary crossover and polynomial mutation are performed on the parent sample points to generate offspring sample points. This calculation is repeated until the maximum number of generations is reached.

[0037] In the above process, by introducing a reference point association mechanism, the problem of how to effectively select and maintain population diversity from the same non-dominated front level in a high-dimensional target space is cleverly solved. This method transforms the abstract requirement of "distribution" into a concrete and operable selection criterion: by associating sample points with uniformly distributed reference points, and prioritizing individuals that "represent" scarce directions (i.e., have fewer associated sample points) as parents, this ensures that the evolutionary process does not over-concentrate on a local region of the Pareto front, but rather explores all possible parts of the front evenly. This guides the final Pareto solution set to not only have good convergence (i.e., close to the true front) but also broad distribution (i.e., covering different trade-off regions of the front), resulting in a comprehensive and diverse set of candidate optimization design schemes.

[0038] S5: Simulate binary crossover and polynomial mutation on the parent sample points to generate offspring sample points until the maximum evolutionary generation of the sample points is reached. Extract the leading sample points of the first leading level in the maximum evolutionary generation to form the Pareto solution set. Set the magnetic transmission stability as the dominant screening criterion to screen the leading sample points in the Pareto solution set and obtain the geometric parameters corresponding to the leading sample points that meet the screening conditions as optimization data.

[0039] Simulated binary crossover and polynomial mutation are performed on the parent sample points to generate offspring sample points. The specific steps are as follows: Randomly pair up the parent sample points. For each pair of parents and all its variables, first perform a crossover operation: independently generate a random number between zero and one for each variable. Based on this random number, calculate the expansion factor of the variable. If the random number is less than or equal to 0.5, the expansion factor is equal to twice the power of 1 / 21 of the random number; if the random number is greater than 0.5, the expansion factor is equal to twice the power of 1 / 21 of the reciprocal of the difference between the two random numbers. Using the calculated expansion factor, generate new values ​​for the variable for two offspring. The value of the first offspring is equal to the value of the first parent multiplied by the expansion factor, plus the value of the second parent multiplied by the expansion factor, and then multiplied by 0.5. The value of the second offspring is obtained by multiplying the value of the first parent by the expansion factor, plus the value of the second parent multiplied by the expansion factor, and then multiplying the sum by 0.5. After crossover, a mutation operation is performed. For each variable in the offspring, a new random number between zero and one is generated to determine the mutation. If this random number is not less than 0.125, the variable remains unchanged. If it is less than 0.125, the mutation calculation begins: First, a new mutation parameter is generated for the variable, which is a random number between zero and one. Then, the proportion of the distance from the current variable value to its lower limit to its total value range is calculated, as well as the proportion of the distance from its upper limit to the current value to the same range. Based on the mutation parameter, the perturbation factor of the variable is calculated. If the mutation parameter is less than 0.5, the perturbation factor is determined by a series of calculations containing the above proportions. If the mutation parameter is greater than or equal to 0.5, the perturbation factor is determined by another set of corresponding calculations. Finally, the new mutated variable value is equal to the original variable value plus the product of the perturbation factor and its total value range. This mutation operation is performed independently for all dimensions of each offspring individual. After completing the crossover and mutation of all parent pairs, all newly generated offspring individuals are aggregated to form offspring sample points.

[0040] The formula upon which the above process is based is: in, Indicates the first Expansion factors of each variable; Indicates the first Random numbers for dimensional variables; Indicates the variable dimension index, and And in sequence, they represent the impeller outlet diameter, impeller inlet diameter, impeller outlet width, blade inlet angle, blade outlet angle, number of blades, blade wrap angle, and hub ratio; In the above process, the index is set as This is a core parameter in the simulated binary crossover operator that controls the distribution shape of offspring individuals. A higher exponent value makes the generated offspring more likely to be close to the parent individuals, thereby enhancing the convergence accuracy of the algorithm; while setting the threshold of 0.5 is to make the expansion factor... The calculation is symmetric about this point, ensuring that when a random number is generated... When generated uniformly between 0 and 1, the expansion factor Crossover can take values ​​less than 1 and greater than 1 with equal probability, which allows the crossover operation to produce offspring that are located between the parent and child generations. It can also produce offspring located outside the parent generation. This achieves a balance between fine-grained local search and global exploration.

[0041] Based on the expansion factor, two crossover offspring values ​​are generated: in, and Representing the parent generation and In the The value of the dimension variable; and This represents each parent sample point in a parent pair; Indicates the parent generation The generated first Cross-off offspring values ​​of dimensional variables; Indicates the parent generation The generated first Cross-off offspring values ​​of dimensional variables; In the above process, multiplying by a coefficient of 0.5 is a generalization to ensure that the offspring value generated by the crossover operation is mathematically a generalized form of the arithmetic mean of the two weighted parent values, thereby maintaining the numerical stability and rationality of the generated offspring individuals. Specifically, regardless of the expansion factor... How to determine the value, formula Therefore, after multiplying by 0.5, the child value is essentially derived from the parent value. and by and The sum is a linear combination of the weights, which ensures that the sum of the two weights is always 1, so that the generated new value always lies within the interval generated by the parent value or its reasonable extension range.

[0042] For the father generation For each offspring individual, generate a random number for mutation assessment in each variable dimension. Check if the random number is less than 0.125. If it is, do not perform mutation and directly output the crossover offspring value. If less than Then, the corresponding dimension's mutation parameters are generated, and the perturbation factor is calculated based on the mutation parameters: in, and They represent the first Lower and upper bounds of a dimensional variable; Indicates the first The normalized distance from the dimension variable to the lower bound; Indicates the first The normalized distance from the dimensional variable to the upper bound; Indicates the first Variation parameters of dimensional variables; Indicates the first The current value of the dimension variable before mutation; Indicates the first The disturbance factor of the dimensional variable; In the above process, the calculation of the mutation perturbation factor is designed in this way to achieve a boundary-aware, controllable polynomial mutation strategy. Its core purpose is to determine the relative position of the current value within the feasible region, i.e., through... and The distance to the upper and lower boundaries is quantized to adaptively adjust the probability distribution of mutations. When the current value is close to the lower limit, the formula... The term, i.e., the distribution index, is 21. Corresponding to the crossover, it increases the probability of upward mutation; conversely, as it approaches the upper limit, the probability of downward mutation increases, thus guiding mutation to occur within the feasible region and greatly reducing the probability of generating invalid solutions outside the boundary. Simultaneously, through random numbers... The judgment of the threshold of 0.5, and the high-order power operation, result in the disturbance. It has a high probability of producing small disturbances and a low probability of producing large disturbances.

[0043] The variation parameters are calculated as follows: in, Indicates the parent generation The generated first Variation parameters of the values ​​of a dimensional variable; In the above process, by using the disturbance factor Its value range is approximately [-1, 1] multiplied by the total range of variation of the parameter. , to obtain a value that is the same as the original value The absolute perturbation amplitude has the same dimensions; this perturbation amplitude is then added to the original value to directly calculate the new parameter value after variation. This calculation method ensures that the mutation operation can be based on the current value. It generates an effective offset and can also pass through The sign and magnitude of the offset precisely control its direction and magnitude, and ultimately map the new value back to the original value. Within the defined space of actual design parameters, it is ensured that the generated solutions are always within the range allowed by the engineering.

[0044] For the father generation The generated offspring individuals also undergo a mutation check. Random numbers for mutation checks are generated for each variable dimension. The value of each random number is checked against a value less than 0.125. If the value is greater than 0.125, mutation is not performed, and the crossover offspring value is directly output. If the value is less than 0.125... Then, the corresponding dimension's mutation parameters are generated; all Each parent generation produces Individual offspring are collected to form offspring sample points.

[0045] The above process defines a set of finely controlled genetic operations, namely crossover and mutation mechanisms. The crossover operation uses an expansion factor dynamically calculated based on random numbers to linearly combine the parameters of the parent individuals. When this factor is near zero, the offspring values ​​are closer to the parent mean, tending to search locally near the parents; when the factor deviates from zero, the offspring values ​​will exceed the parent range, tending to explore a wider new region. This design allows the algorithm to adaptively adjust the search strategy according to random probability, which is the main driving force for the population to evolve towards the Pareto front. The mutation operation serves as a crucial supplement for maintaining population diversity and breaking through local optima. It is triggered with a low probability (judgment threshold of 0.125), corresponding to approximately one mutation opportunity per dimension on average. Once triggered, the mutation process fully considers the relative position of the current value within the feasible region, reflected by the normalized distance to the upper and lower bounds. It utilizes a complex but symmetric perturbation factor calculation formula to ensure that the mutation generates sufficient novelty while keeping the new value within reasonable boundaries with a high probability, avoiding the generation of invalid solutions. This "boundary-aware" intelligent mutation enhances the algorithm's ability to explore the boundaries of the feasible region. This series of operations collectively ensures the efficiency and robustness of the evolutionary process. Crossover is responsible for the directional fusion of superior genes, guiding population convergence; mutation, on the other hand, injects new genes with controlled randomness, preventing premature convergence. The combination of these two methods enables the NSGA-III algorithm to effectively traverse and search for excellent compromise designs that simultaneously optimize the three potentially conflicting objectives of hydraulic efficiency, cavitation performance, and torque pulsation coefficient within the complex eight-dimensional geometric parameter space, thereby generating a widely distributed set of Pareto optimal solutions with high quality.

[0046] The specific steps to obtain optimized data are as follows: Extract all first-front level sample points from the sample points with the maximum evolutionary generation to form the Pareto optimal solution set. Set a magnetic transmission stability-dominant screening criterion to screen the sample points in the Pareto optimal solution set, specifically as follows: An ideal matching space for the total moment of inertia is defined. Sample points whose total moment of inertia deviates from the ideal matching interval in the Pareto optimal solution set are directly removed. The target coefficients of the remaining sample points are normalized. A set of weighted coefficients is preset, and the preset weighted coefficients are weighted and calculated with the target coefficients respectively. A weighted comprehensive performance index is constructed that integrates the highest pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient. At the same time, the variance of the relative deviation between the target coefficient of each sample point and the optimal value on its respective Pareto front is calculated. The geometric parameters corresponding to the sample points with high weighted comprehensive performance index and small variance are selected as optimization data.

[0047] In the above process, firstly, the rigid constraint of the ideal matching space of total moment of inertia ensures that the selected scheme meets the basic physical conditions for the smooth operation of the magnetic drive system, completing the transformation from a multi-objective optimization solution to an engineering feasible solution. Subsequently, by constructing a weighted comprehensive performance index, a quantitative comprehensive score is performed on the three conflicting objectives of efficiency, cavitation, and torque pulsation according to preset weights, realizing the single-value ranking of multiple objectives. At the same time, the variance of the relative deviation of the objective coefficients is introduced as a measure of "balance" to screen out design schemes that not only have high comprehensive scores but also have balanced performance development in each component without obvious shortcomings. Finally, this method can stably and objectively select the final optimized geometric parameters that best meet the comprehensive design objectives of "high efficiency, reliability, and stability" of the magnetic pump from numerous non-dominated solutions, greatly improving the engineering practical value of the optimization results. Preset weighting coefficients are typically determined based on engineering experience and design requirements. Specifically, systematic decision-making methods such as expert scoring can be employed. For example, if magnetic drive smoothness is defined as the highest priority objective, a higher weight, such as 0.5, can be assigned to the torque pulsation coefficient. Hydraulic efficiency and net positive suction head (NPSH) are allocated their remaining weights according to the importance of actual operating conditions, such as 0.25 each. Furthermore, weights can be dynamically adjusted through sensitivity analysis of multiple simulation results, or multiple weighting schemes can be preset and compared based on the market positioning of the actual product series, such as a preference for high efficiency, high reliability, or low vibration. The final determined weighting combination should accurately reflect the designer's relative importance ranking of the three optimization objectives.

[0048] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0049] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0050] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0051] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A multi-objective optimization design method for a magnetic pump impeller, characterized by the following steps: include: S1: The impeller is structurally differentiated to determine several structures. The geometric parameters of each structure are determined and the upper and lower limits of the geometric parameters are set. The upper and lower limits of all geometric parameters are statistically analyzed to form the design parameter space. Based on the type of geometric parameters, the total rotational inertia model of the impeller is constructed. A CFD simulation model is constructed with geometric parameters as input and target coefficients as output. The target coefficients are pump hydraulic efficiency, cavitation performance index and torque pulsation coefficient. S2: The design parameter space is sampled using optimal Latin hypercube sampling to generate the first sample set. The total moment of inertia corresponding to each sample point is obtained through the total moment of inertia model. The first sample set is then filtered using the total moment of inertia to obtain the second sample set. S3: Simulate the sample points within the second sample set using a CFD simulation model to obtain the pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient for each sample point. Update the upper and lower limits of the geometric parameters based on the geometric parameters corresponding to the three sample points when the pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient are optimal. S4: Based on the updated upper and lower limits of the geometric parameters, the NSGA-III algorithm is used to randomly generate a new number of target sample points. For each new sample point, the target coefficient of each new sample point is obtained by simulation through the CFD simulation model. The Pareto dominance method is used to divide the new sample points into different frontier levels based on the target coefficients of the new sample points. The next generation of parent sample points is selected from the frontier levels. S5: Simulate binary crossover and polynomial mutation on the parent sample points to generate offspring sample points until the maximum evolutionary generation of the sample points is reached. Extract the leading sample points of the first leading level in the maximum evolutionary generation to form the Pareto solution set. Set the magnetic transmission stability as the dominant screening criterion to screen the leading sample points in the Pareto solution set and obtain the geometric parameters corresponding to the leading sample points that meet the screening conditions as optimization data.

2. The multi-objective optimization design method for a magnetic pump impeller according to claim 1, characterized in that, The specific steps for calculating the total moment of inertia for each sample point are as follows: The impeller is structurally differentiated into several structures, including the main disk, individual blades, and hub. The geometric parameters of each structure are determined and upper and lower limits are set. The geometric parameters include impeller outlet diameter, impeller inlet diameter, impeller outlet width, blade inlet angle, blade outlet angle, number of blades, blade wrap angle, and hub ratio. Calculate the moment of inertia for each region separately. The moment of inertia of the main disk is obtained by multiplying its own mass by the square of the exit radius, and then multiplying by a coefficient of one-half. The moment of inertia of a single blade is equal to the blade's mass multiplied by the square of one-quarter of the sum of the inlet and outlet diameters. The moment of inertia of the hub is calculated similarly to that of the disk, as half of its mass multiplied by the square of the hub radius. The total moment of inertia of the impeller is equal to the moment of inertia of the main disk, plus the sum of the moments of inertia of all the blades, which is obtained by multiplying the moment of inertia of a single blade by the total number of blades, plus the moment of inertia of the hub.

3. The multi-objective optimization design method for a magnetic pump impeller according to claim 2, characterized in that, The specific steps for calculating the target coefficient are as follows: A CFD simulation model is constructed with geometric parameters as input and target coefficients as output. The characteristic flow points of the impeller are determined, namely the characteristic flow point, the small flow point of 0.8 times the characteristic flow point, and the large flow point of 1.2 times the characteristic flow point. The pump hydraulic efficiency of the impeller at each characteristic flow point is calculated using the CFD simulation model. The three pump hydraulic efficiencies are then weighted and summed according to preset weight coefficients. The weight of the pump hydraulic efficiency at the characteristic flow point is 0.6, and the weight of the pump hydraulic efficiency at the two non-characteristic flow points is 0.2 each, forming the first target coefficient for evaluating the impeller characteristics. The cavitation performance index of the impeller at the characteristic flow point is obtained by CFD simulation model, and this index is directly used as the second target coefficient for evaluating the impeller's cavitation resistance. In the CFDF simulation model, the impeller rotation period and sampling interval are set. The instantaneous fluid torque time series data of the impeller during the rotation period are obtained through transient simulation. The maximum and minimum torque values ​​of the impeller during the rotation period are determined based on the time series data, and the average torque value is calculated. The third target coefficient is obtained by dividing the difference between the maximum and minimum torque values ​​by the average torque value.

4. The multi-objective optimization design method for a magnetic pump impeller according to claim 1, characterized in that, The specific steps to obtain the second sample set are as follows: The design parameter space is sampled using optimal Latin hypercube sampling to generate the first sample set, i.e., to generate... sample points Furthermore, based on the total moment of inertia of each sample point, sample points whose total moment of inertia exceeds the preset allowable range are filtered out to obtain a second sample set. For the sample points within the second sample set, simulations are performed using a CFD simulation model to obtain the pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient corresponding to each sample point.

5. The multi-objective optimization design method for a magnetic pump impeller according to claim 4, characterized in that, The specific steps for analyzing the second sample set are as follows: A global Sobol sensitivity analysis was performed on the second sample set to calculate the first-order sensitivity index of each geometric parameter to pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient. Specifically: For each target coefficient, the first-order sensitivity index of the target coefficient for individual variation is obtained by calculating the ratio of the variance of the conditional expectation of the target coefficient to the total variance of the target coefficient when a certain geometric parameter is fixed. Here, the conditional expectation of the target coefficient refers to the variance of the sequence of conditional expectation values ​​of the target coefficient at all possible values ​​when a certain geometric parameter is fixed, and the total variance of the target coefficient refers to the overall variance of the target coefficient at all sample points in the second sample set.

6. The multi-objective optimization design method for a magnetic pump impeller according to claim 5, characterized in that, The specific steps for updating the upper and lower limits of geometric parameters are as follows: Three optimal sample points were located, namely the pump with the highest hydraulic efficiency, the lowest cavitation performance index, and the smallest torque pulsation coefficient. The first-order sensitivity index that is higher than the preset maximum index threshold was identified as the high sensitivity index. The distribution characteristics of the high sensitivity index in these sample points were analyzed. That is, if the value of the high sensitivity index in the optimal sample points continuously approaches the boundary of the original design parameter space, it indicates that the optimization direction of the geometric parameter is clearly pointing to the outside of the boundary. The boundary is symmetrically expanded outward according to the preset expansion ratio. For geometric parameters whose first-order sensitivity indices are all below the preset minimum index threshold, they are determined to be insensitive parameters. For insensitive parameters, the value distribution of their values ​​on all sample points in the second sample set is calculated to determine their mean and distribution range. With the mean point as the center, the upper and lower limits of their values ​​are symmetrically shrunk according to the preset shrinkage ratio to form a narrower and more focused new value range. This method is used to update the upper and lower limits of the geometric parameters.

7. The multi-objective optimization design method for a magnetic pump impeller according to claim 6, characterized in that, The sample points are divided into different frontier levels. The specific steps are as follows: Based on the updated upper and lower limits of the geometric parameters, the NSGA-III algorithm is used to randomly generate new sample points of the target number. For each new sample point, the target coefficient of each new sample point is obtained by simulation through the CFD simulation model. The Pareto dominance method is used to divide the new sample points into different frontier levels, and the next generation parent sample points are selected from the frontier levels. The specific method for dividing sample points into different frontier levels is as follows: Set the dominance condition for sample points. If a sample point is no worse than any other sample point in terms of the target coefficient, and is strictly better in at least one target coefficient, it is said to dominate that sample point. Find those points that are not dominated by any other sample points from all sample points and assign them to the first frontier level. Then, temporarily remove these first-level points and find the undominated points again from the remaining points to form the second frontier level. Repeat this process until all sample points have been assigned a frontier level.

8. The multi-objective optimization design method for a magnetic pump impeller according to claim 7, characterized in that, The specific steps for selecting the most suitable next-generation parent sample points from the leading edge level are as follows: Based on the target coefficient distribution in the first frontier level, a set of reference points uniformly distributed on the normalized hyperplane is dynamically generated. Each sample point in the first frontier level is mapped to this hyperplane, and its vertical distance to all reference points is calculated. It is then associated with the nearest reference point. By evaluating the number of sample points associated with each reference point, the sample points corresponding to reference points with fewer associated sample points are preferentially selected as parent sample points. Simulated binary crossover and polynomial mutation are performed on the parent sample points to generate offspring sample points. This calculation is repeated until the maximum number of generations is reached.

9. The multi-objective optimization design method for a magnetic pump impeller according to claim 8, characterized in that, Simulated binary crossover and polynomial mutation are performed on the parent sample points to generate offspring sample points. The specific steps are as follows: Randomly pair up the parent sample points. For each pair of parents and all its variables, first perform a crossover operation: independently generate a random number between zero and one for each variable, and calculate the expansion factor of the variable based on this random number. If the random number is less than or equal to 0.5, the expansion factor is equal to twice the power of 1 / 21 of the random number. If the random number is greater than 0.5, then the expansion factor is equal to twice one minus the reciprocal of the random number difference raised to the power of 1 / 21. Using the calculated expansion factor, generate new values ​​for the variable for two offspring. The value of the first offspring is equal to the value of the first parent multiplied by the expansion factor, plus the value of the second parent multiplied by the expansion factor, and then multiplied by 0.

5. The value of the second offspring is obtained by multiplying the value of the first parent by the expansion factor, plus the value of the second parent multiplied by the expansion factor, and then multiplying the sum by 0.

5. After crossover, a mutation operation is performed. For each variable in the offspring, a new random number between zero and one is generated to determine the mutation. If this random number is not less than 0.125, the variable remains unchanged. If it is less than 0.125, the mutation calculation begins: First, a new mutation parameter is generated for the variable, which is a random number between zero and one. Then, the proportion of the distance from the current variable value to its lower limit to its total value range is calculated, as well as the proportion of the distance from its upper limit to the current value to the same range. Based on the mutation parameter, the perturbation factor of the variable is calculated. If the mutation parameter is less than 0.5, the perturbation factor is determined by a series of calculations containing the above proportions. If the mutation parameter is greater than or equal to 0.5, the perturbation factor is determined by another set of corresponding calculations. Finally, the new mutated variable value is equal to the original variable value plus the product of the perturbation factor and its total value range. This mutation operation is performed independently for all dimensions of each offspring individual. After completing the crossover and mutation of all parent pairs, all newly generated offspring individuals are aggregated to form offspring sample points.

10. A multi-objective optimization design method for a magnetic pump impeller according to claim 9, characterized in that, The specific steps to obtain optimized data are as follows: Extract all first-front level sample points from the sample points with the maximum evolutionary generation to form the Pareto optimal solution set. Set a magnetic transmission stability-dominant screening criterion to screen the sample points in the Pareto optimal solution set, specifically as follows: An ideal matching space for the total moment of inertia is defined. Sample points whose total moment of inertia deviates from the ideal matching interval in the Pareto optimal solution set are directly removed. The target coefficients of the remaining sample points are normalized. A set of weighted coefficients is preset, and the preset weighted coefficients are weighted and calculated with the target coefficients respectively. A weighted comprehensive performance index is constructed that integrates the highest pump hydraulic efficiency, cavitation performance index, and torque pulsation coefficient. At the same time, the variance of the relative deviation between the target coefficient of each sample point and the optimal value on its respective Pareto front is calculated. The geometric parameters corresponding to the sample points with high weighted comprehensive performance index and small variance are selected as optimization data.

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