Response surface method-based optimization method for impeller blade of mining submersible explosion-proof pump
Optimizing the impeller blades of submersible explosion-proof pumps for mining through the response surface method, the problems of high cost and large errors in complex environments of traditional design methods are solved, and the impeller structural parameters are optimized with fewer experiments, which improves the design efficiency and life.
Patent Information
- Application Number
- CN202510618694.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-14
- Publication Date
- 2025-08-15
AI Technical Summary
The existing submersible explosion-proof pump impeller design for mining uses has problems such as friction wear and fatigue failure in complex mine environments. The traditional design methods are expensive and difficult to meet actual needs. There are problems such as errors and inaccurate optimization results in fluid dynamics simulation technology.
The response surface method is used to optimize the impeller blades of submersible explosion-proof pumps for mining. By selecting appropriate optimization parameters, the Box-Behnken experimental design is used to generate an experimental plan, a secondary response model is established and insignificant terms are deleted through analysis of variance. Multi-objective optimization is performed in combination with the non-dominant sorting genetic algorithm II, reducing the number of experiments and improving the accuracy of the model, and finding the optimal solution set of Pareto.
With fewer experiments, the design cost is significantly reduced, the design efficiency is improved, the service life of the impeller is extended, the impeller is adapted to extreme environments, and the impeller performance is improved.
Smart Images
Figure CN120493799A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a method for optimizing impeller blades of a mining submersible explosion-proof pump. Background Art
[0002] With the continuous advancement of mining technology, submersible explosion-proof pumps for mining play a vital role in critical operations such as mine drainage and ventilation. However, in practical applications, the design of existing impellers for these pumps still presents numerous challenges. As the core component of a submersible explosion-proof pump, the impeller accelerates and pressurizes the fluid entering the pump through centrifugal force generated by rotating at a predetermined speed, thereby providing energy to the fluid, enabling it to overcome resistance and be discharged from its original location. The structural design of the impeller directly affects the pump's efficiency, head, and service life during operation.
[0003] Traditional impeller design relies primarily on empirical formulas and real-world experimental methods. While empirical formulas can provide guidance under simple operating conditions and offer low design costs and high efficiency, they often fail to meet actual needs in complex and variable environments like mines. For example, underground, where ambient temperatures are relatively high and fluid pressures are relatively high, and where the fluid often contains large amounts of sand and other debris, the uneven force distribution on traditionally designed impellers can easily lead to frictional wear and fatigue failures, resulting in a short impeller lifespan and relatively difficult maintenance.
[0004] In view of this, in order to further improve the impeller performance to adapt to the impeller's working environment, real experiments are often necessary, but they are costly and difficult, especially when simulating complex working conditions such as mines. The experimental conditions are difficult to fully reproduce, and the experimental cycle is long and the risk is high.
[0005] In recent years, fluid dynamics simulation technology has been widely used in impeller design. Through numerical simulation, it accurately predicts the fluid dynamics characteristics of an impeller under various operating conditions, providing a scientific basis for impeller design. Fluid dynamics simulation not only significantly reduces experimental costs but also shortens design cycles and improves design accuracy.
[0006] However, even with the support of fluid dynamics simulation technology, optimizing impeller design for complex environments such as mines still faces challenges. On the one hand, while existing fluid dynamics simulation theory can meet the accuracy requirements of many industrial fields, it still suffers from certain model errors and observation errors, which cannot be ignored when collecting large amounts of experimental data for subsequent optimization. On the other hand, while existing genetic optimization algorithms (GAs) can effectively meet the optimization needs of single and multi-objective product design, the errors generated by simulation experiments are easily amplified during the iteration process, significantly reducing the practical value of the optimization results. Summary of the Invention
[0007] The purpose of the present invention is to provide an optimization method for the impeller blades of a mining submersible explosion-proof pump based on the response surface methodology, so as to optimize the impeller structural parameters under the condition of a smaller number of experiments, thereby significantly reducing the design cost and improving the design efficiency.
[0008] According to an embodiment of the present invention, a method for optimizing impeller blades of a mining submersible explosion-proof pump based on a response surface methodology is provided, comprising the following steps: Select the optimization parameters: H and efficiency or As the response variable, select the impeller inlet outer diameter D , wheel hub diameter d , impeller outlet width b , blade outlet angle β As optimization parameters, each optimization parameter is divided into three levels: low, medium and high; Experimental design: The Box-Behnken experimental design was used to generate the experimental plan. The optimized parameters were used as input to conduct experiments through fluid dynamics simulation to obtain the head H and efficiency η data under different parameter combinations. Model building and optimization: Based on the obtained lift H and efficiency or A quadratic response model was established for the data, and insignificant terms were removed through variance analysis to optimize the model. The confidence interval width of the optimized model was then added as a penalty function to the objective function. Multi-objective optimization was performed using the non-dominated sorting genetic algorithm II to obtain the Pareto optimal solution set and further the Pareto frontier solution. Verification and application: The performance of the Pareto frontier solution is verified through fluid dynamics simulation, and the optimization parameters corresponding to the Pareto frontier solution under the predetermined working conditions are selected.
[0009] Optionally, the median level parameter in the optimization parameters is obtained according to an empirical function, and the low and high level parameters are determined respectively with given upper and lower deviations; In the experimental design step, use -1 to refer to the low-level parameter, 0 to refer to the median-level parameter, and 1 to refer to the high-level parameter.
[0010] Optionally, the upper and lower deviations are given as 15% to 25% of the median level parameter; Different optimization parameters use the same upper and lower deviations or determine different upper and lower deviation values based on the designer's expectations.
[0011] Optionally, the quadratic response model is:
[0012] In the formulaY is the response variable; X i To optimize the parameters; β 0 is the intercept term; β i is the linear term coefficient; β ii is the coefficient of the quadratic term; β ij is the interaction term coefficient; ϵ is the error term, which represents the random variation not explained by the model.
[0013] Alternatively, the method for removing insignificant terms through ANOVA is: Analyze the optimized parameters and response variables under the quadratic response model, calculate the regression sum of squares, residual sum of squares, mean square sum, F-value, and P value, and delete insignificant items based on the P value; The model was further refitted after removing insignificant terms until all remaining terms were significant.
[0014] Optionally, the specific method of adding the confidence interval width of the model as a penalty function to the objective function is: Given a significance level α = 0.05, calculate each parameter β The confidence interval width is the error term in the quadratic response model ϵ Replaced by the confidence interval width.
[0015] Alternatively, when the non-dominated sorting genetic algorithm II is used for multi-objective optimization, the problem is defined as simultaneously optimizing the inlet outer diameter D , wheel hub diameter d , impeller outlet width b , blade outlet angle β Two objective functions Y h 、 Y η , factors take values within the specified range as constraints.
[0016] Optionally, the operation steps of the non-dominated sorting genetic algorithm II include initializing the population, non-dominated sorting, crowding distance calculation, selection operation, crossover and mutation operation, merging the population, selecting the next generation population, and repeating the operation until the maximum number of iterations is reached, the population diversity is reduced to a certain level, or the objective function value converges.
[0017] Optionally, the crossover operation adopts a multi-point crossover method, and the mutation operation adopts Gaussian mutation.
[0018] Optionally, the method of verifying the performance of the Pareto front solution obtained through fluid dynamics simulation includes checking whether the distribution of the Pareto front is uniform, and comparing the efficiency and head before and after optimization.
[0019] In the embodiment of the present invention, by selecting appropriate optimization parameters, the lift H and efficiency or As the key response variable, the impeller inlet outer diameter is selected D , wheel hub diameter d , impeller outlet width b , blade outlet angle β As optimization parameters, each optimization parameter was divided into three levels, clarifying the core elements of optimization. A Box-Behnken experimental design was employed, which allows for the construction of a reasonable experimental plan with a relatively small number of experiments, significantly reducing the number of experiments and the experimental cost compared to a full experimental design. Data was obtained through fluid dynamics simulation, avoiding the high cost and difficulties of real-world experiments. A quadratic response model was established and optimized by removing insignificant terms using analysis of variance (ANOVA), effectively improving model accuracy. The model confidence interval width was added as a penalty function to the objective function, and multi-objective optimization was performed using the non-dominated sorting genetic algorithm II (NSGA-II). This approach improves optimization efficiency while considering multiple objectives, finding the Pareto optimal solution set, and avoiding excessive amplification of simulation experimental errors during the iterative process, further enhancing the reliability of the optimization results. Finally, the performance of the Pareto frontier solution was verified through fluid dynamics simulation, ensuring that the optimized impeller meets actual operating conditions, improving efficiency, extending service life, and adapting to extreme environments. This achieved the goal of optimizing impeller structural parameters with a relatively small number of experiments, reducing design costs, and improving design efficiency. BRIEF DESCRIPTION OF THE DRAWINGS
[0020] Figure 1 The present invention is a flow chart of an optimization method for impeller blades of a mining submersible explosion-proof pump based on the response surface methodology in one embodiment.
[0021] Figure 2 This figure compares the liquid flow path obtained by optimizing the impeller blades of a submersible explosion-proof mining pump using the response surface methodology in one embodiment, and the flow path obtained by using the initial empirical function. The optimized flow path represents the liquid flow path obtained by the embodiment of the present invention, while the unoptimized flow path represents the liquid flow path obtained only by using the initial empirical function.
[0022] Figure 3 This is a three-dimensional model diagram of an impeller obtained by optimizing the impeller blades of a mining submersible explosion-proof pump based on the response surface methodology in one embodiment.
[0023] Figure 4This is a comparison chart of flow channel anti-vibration performance parameters obtained before and after optimization of impeller blades of a mining submersible explosion-proof pump based on the response surface methodology in one embodiment. DETAILED DESCRIPTION
[0024] The following will describe the technical solution of the present invention clearly with reference to the accompanying drawings. In this experimental scheme, the pump speed is 3000r / min and the flow rate is 10m 3 / h mining explosion-proof pump parameters were optimized, and the impeller with the rated head of 15m was taken as the empirical function for comparison.
[0025] like Figure 1 The flow chart of this method is shown below. H ,efficiency or As the response variable, the basic size of the impeller is selected as the inlet outer diameter D , wheel hub diameter d , impeller outlet width b , blade outlet angle β , as the optimized parameters, and these parameters are divided into three levels: low, medium and high according to the experience of impeller design. The median level parameters are obtained according to the experience function, which are D=109.4mm, d=29.12mm, b=14.55mm, β= The low and high levels are designated as 10.7° with an upper and lower deviation of 20%, respectively. Low, medium, and high are represented by -1, 0, and 1, respectively.
[0026] Regarding the amount of upper and lower deviations, different deviation amounts can be set according to the different requirements of different parameters, but the deviation amount should not be too small, not less than 15% of the median level parameter, nor too large, not more than 25% of the median level parameter.
[0027] Since parameters determine performance, the above parameters are called optimization parameters as the objects to be optimized, and the change of parameters will lead to the change of product performance. H and efficiency or etc. will inevitably change with the change of the optimization parameters, so they are called response variables corresponding to the optimization parameters.
[0028] The experimental scheme was generated by Box-Behnken experimental design, as shown in Table 1: Through fluid dynamics simulation, appropriate fluid dynamics models and parameters are selected according to the actual environment. The basic parameters of the impeller are set according to the experiment, and experiments are carried out to complete the matrix in the previous step.
[0029] 4. Based on the experimental results, establish a quadratic response model of the response variable:
[0030] In the formula Y is the response variable; X i To optimize the parameters; β 0 is the intercept term; β i is the linear term coefficient; β ii is the coefficient of the quadratic term; β ij are the interaction coefficients, and the specific values of these coefficients are fitted through the given matrix operation software. ϵ is the error term, which represents the random variation not explained by the model. The next section will determine the value of the error term before performing multi-objective optimization.
[0031] The improved model is obtained by removing non-significant items through ANOVA / P value. The specific implementation process is as follows: 5.1. Calculate the sum of squares of regression (SSR):
[0032] in It is i The predicted value of the observation, is the mean of the response variable.
[0033] Further calculation of the sum of squares (SSE):
[0034] In the formula Y _i It is i observations.
[0035] Further calculation of the sum of squares:
[0036] in, k is the number of terms in the model, which is 30, with 15 terms in each response variable. n is the number of observations, which is 25 since the experiment contains four factors.
[0037] The F-value is calculated using the following formula:
[0038] The P value was further calculated using the following formula:
[0039] in F _calc It is calculated F -value, df1 and df 2 are the degrees of freedom of the numerator and denominator respectively.
[0040] according to P -value, remove the items with insignificant terms ( P >0.05).
[0041] After removing insignificant terms, refit the model and repeat the above steps until all remaining terms are significant.
[0042] As needed, the width of the confidence interval of the improved model can be calculated and added to the improved model as the objective function as a penalty function. The specific implementation method is as follows: Given a significance level α = 0.05, for each parameter in the quadratic response model in step 4 β , its 100×(1- α )% confidence interval is:
[0043] in is the estimated value of the parameter, a / 2,np yes t- Critical value of the distribution with degrees of freedom n−p ( n is the number of observations, p is the number of parameters in the model, i.e. n=25, p=4), SE ( ) is the standard error of the parameter estimate.
[0044] Calculate the confidence interval width. For any β, the confidence interval width is:
[0045] The error term in the aforementioned quadratic response model ϵ Directly replace it with the confidence interval width, that is:
[0046] in l It is the penalty coefficient, which controls the intensity of the penalty term. Its value can be selected according to the actual situation. Here it is selected as 0.1.
[0047] Let's look at the process of performing multi-objective optimization using NSGA-11 and obtaining the Pareto optimal solution set: Problem definition: There are two objective functions Y h 、 Y η , which depend on four factors: the inlet outer diameter D, wheel hub diameter d , impeller outlet width b , blade outlet angle β The goal is to optimize these two objective functions simultaneously. There is a conflict between these two objectives, and a Pareto optimal solution set needs to be found.
[0048] Provide constraints: the optimization parameters take values within a specified range, and the range takes the high and low levels of each optimization parameter as the upper and lower bounds respectively.
[0049] Initialize the population accordingly: First, randomly generate the initial population, that is, randomly generate N Each factor of each individual takes a random value within the allowed range. Then the initial population is evaluated, that is, the two objective function values of each individual are calculated.
[0050] Then, a non-dominated sort is performed: if individual A is no worse than individual B on all objectives and is better than B on at least one objective, then A is said to dominate B. The population is divided into different non-dominated layers. The first layer is the set of non-dominated individuals, the second layer is the set of non-dominated individuals in the population remaining after removing the first layer, and so on.
[0051] Crowding distance calculation: First, the crowding distance is initialized to 0 for all individuals. Then, the crowding distance is calculated. For each objective function, the individuals are sorted according to the objective function value, and the crowding distance of each individual is calculated. The crowding distance is the sum of the distances between adjacent individuals on the objective function.
[0052] Further selection operation is performed: starting from the first layer, individuals are selected in sequence until the population size reaches N. If the number of individuals in a layer exceeds the number of remaining individuals to be selected, selection is performed based on the crowding distance.
[0053] Further crossover and mutation operations are performed. First, a crossover operation is performed to randomly select two parent individuals and generate two offspring individuals through crossover. The number of parameters is not large, so the multi-point crossover method is selected. Then, a mutation operation is performed to mutate the generated offspring individuals, changing the values of certain factors of the individuals with a certain probability. Since there are known empirical values, it can be considered as an approximate rotation, so Gaussian mutation can be used.
[0054] Next, we merge the populations: merge the parent population and the child population to form a temporary population of size 2N. Non-dominated sorting and crowding distance calculation: perform non-dominated sorting and crowding distance calculation on the temporary population.
[0055] Further selection of the next generation population: N individuals are selected based on non-dominated sorting and crowding distance to form the next generation population. The process is then iterated using matrix calculation software.
[0056] The above steps are then terminated and outputted, and the above steps are repeated until the maximum number of iterations is reached, the population diversity is reduced to a certain level, or the objective function value converges. The final Pareto optimal solution set outputted contains the solution that achieves the best balance between the two objective functions.
[0057] Finally, the Pareto frontier verification is performed through fluid dynamics simulation to check whether the distribution of the Pareto frontier is uniform, and the fluid dynamics simulation under the same conditions is performed to test whether its performance is improved.
[0058] The final liquid flow channel and the flow channel with the initial empirical function value are compared. Figure 2 As shown, the final factor optimization solution is: D=110.11mm, d=30.01mm, b=8.15mm, β= 25.8°.
Claims
1. An optimization method for impeller blades of a mining submersible explosion-proof pump based on response surface methodology, characterized in that: The following steps are involved: Select the optimization parameters: H and efficiency η As the response variable, select the impeller inlet outer diameter D , wheel hub diameter d , impeller outlet width b , blade outlet angle β As optimization parameters, each optimization parameter is divided into three levels: low, medium and high; Experimental design: The Box-Behnken experimental design was used to generate the experimental plan. The optimized parameters were used as input to conduct experiments through fluid dynamics simulation to obtain the head H and efficiency η data under different parameter combinations. Model building and optimization: Based on the obtained lift H and efficiency η A quadratic response model was established for the data, and insignificant terms were removed through variance analysis to optimize the model. The confidence interval width of the optimized model was then added as a penalty function to the objective function. Multi-objective optimization was performed using the non-dominated sorting genetic algorithm II to obtain the Pareto optimal solution set and further the Pareto frontier solution. Verification and application: The performance of the Pareto frontier solution is verified through fluid dynamics simulation, and the optimization parameters corresponding to the Pareto frontier solution under the predetermined working conditions are selected.
2. The optimization method according to claim 1, characterized in that The median level parameter in the optimization parameters is obtained according to the empirical function, and the low and high level parameters are determined respectively with given upper and lower deviations; In the experimental design step, use -1 to refer to the low-level parameter, 0 to refer to the median-level parameter, and 1 to refer to the high-level parameter.
3. The optimization method according to claim 2, characterized in that The given upper and lower deviations are 15% to 25% of the median level parameter; Different optimization parameters use the same upper and lower deviations or determine different upper and lower deviation values based on the designer's expectations.
4. The optimization method according to claim 1, characterized in that The quadratic response model is: , where Y is the response variable; X i To optimize the parameters; β 0 is the intercept term; β i is the linear term coefficient; β ii is the coefficient of the quadratic term; β ij is the interaction term coefficient; ϵ is the error term, which represents the random variation not explained by the model.
5. The optimization method according to claim 1, characterized in that The method for removing insignificant items through variance analysis is: Analyze the optimized parameters and response variables under the quadratic response model, calculate the regression sum of squares, residual sum of squares, mean square sum, F-value, and P value, and delete insignificant items based on the P value; The model was further refitted after removing insignificant terms until all remaining terms were significant.
6. The optimization method according to claim 1, characterized in that: The specific method of adding the confidence interval width of the model as a penalty function to the objective function is: Given a significance level α = 0.05, calculate each parameter β The confidence interval width is the error term in the quadratic response model ϵ Replaced by the confidence interval width.
7. The optimization method according to claim 1, characterized in that: When the non-dominated sorting genetic algorithm II is used for multi-objective optimization, the problem is defined as optimizing simultaneously the inlet outer diameter. D , wheel hub diameter d , impeller outlet width b , blade outlet angle β Two objective functions Y h 、 Y η , factors take values within the specified range as constraints.
8. The optimization method according to claim 7, characterized in that: The operation steps of the non-dominated sorting genetic algorithm II include initializing the population, non-dominated sorting, crowding distance calculation, selection operation, crossover and mutation operation, merging the population, selecting the next generation population, and repeating the operation until the maximum number of iterations is reached, the population diversity is reduced to a certain level, or the objective function value converges.
9. The optimization method according to claim 8, characterized in that: The crossover operation adopts a multi-point crossover method, and the mutation operation adopts Gaussian mutation.
10. The optimization method according to claim 1, characterized in that: The method of verifying the performance of the Pareto front solution obtained through fluid dynamics simulation includes checking whether the distribution of the Pareto front is uniform and comparing the efficiency and head before and after optimization.