Blade structure optimization method based on adaptive differential mutation population search algorithm

Abstract

The present invention proposes a blade structure optimization method based on an adaptive differential variation crowd search algorithm, obtains the simulated instrument coefficient characteristic curve of the initial turbine flowmeter, and calculates the instrument coefficient linearity error δ; uses the three structural parameters of the flowmeter blade radius, blade edge thickness, and blade inclination angle as design variables, and the instrument coefficient linearity error δ as the output target value to perform a simulation orthogonal test; based on the simulation data, the response surface method is used to fit the quadratic regression fitting equation of the target value with respect to the design variable; uses the fitting equation as the fitness function, and uses the crowd search algorithm based on adaptive differential variation to optimize the structural parameters with the minimum fitness value as the optimization target; uses the optimized blade structure for simulation and simulation to obtain the optimized instrument coefficient curve. The present invention realizes the precise optimization of blade structural parameters and improves the metering accuracy of the flowmeter through the improved crowd search algorithm.

Description

Technical Field

[0001] The invention belongs to the field of impeller blade structural parameter optimization, and in particular relates to a turbine flowmeter blade structural optimization method based on an adaptive differential mutation population search algorithm. Background Art

[0002] The cementing mud flowmeter is a tangential turbine flowmeter, which is mainly used in the flow metering of drilling fluid, cement slurry, replacement fluid and other fluids in the cementing project of oil fields. The accurate measurement of fluid volume is of great significance to the quality of cementing operations. However, in actual projects, due to the influence of complex working conditions, the actual flowmeter instrument coefficient characteristic curve deviates from the ideal curve, resulting in an increase in the linearity error δ of the instrument coefficient. The improvement of the flowmeter metering accuracy is mainly achieved through the improvement of the internal structure of the flowmeter, especially the impeller blades. Many scholars use computational fluid dynamics (CFD) fluid simulation to simulate the flow field and metering characteristics under different impeller structures to determine the optimal impeller structure including blade shape and size.

[0003] Although this method has a good optimization effect, the optimal structural parameters can only be determined within a certain variable range, and the accuracy of structural parameter optimization is not achieved. In view of the drawbacks of this optimization method, an optimization method that can determine specific structural parameters is needed to improve the metering accuracy of the turbine flowmeter. Summary of the invention

[0004] Purpose of the invention:

[0005] The present invention proposes a blade structure optimization method based on an adaptive differential mutation crowd search algorithm. Through the improved crowd search algorithm, accurate optimization of blade structure parameters is achieved and the metering accuracy of the flow meter is improved.

[0006] Technical solution:

[0007] A turbine flowmeter blade structure optimization method based on an adaptive differential mutation population search algorithm comprises the following steps:

[0008] Step 1, obtaining the simulated instrument coefficient characteristic curve of the initial turbine flowmeter, and calculating the instrument coefficient linearity error δ;

[0009] Step 2: Take the three structural parameters of the flow meter blade radius, blade edge thickness, and blade inclination angle as design variables, and the instrument coefficient linearity error δ as the output target value to conduct a simulation orthogonal test;

[0010] Step 3: Based on the simulation data, the response surface method is used to fit the quadratic regression fitting equation of the target value with respect to the design variables;

[0011] Step 4: Using the fitting equation in step 3 as the fitness function, the structural parameters are optimized by using a population search algorithm based on adaptive differential mutation and taking the minimum fitness value as the optimization goal;

[0012] Step 5: Use the optimized blade structure to perform simulation and obtain the optimized instrument coefficient curve. The expression of the instrument coefficient linearity error δ in step 1 is as follows:

[0013]

[0014]

[0015] In the formula, K max =Max{K i}, K min =Min{K i}, i = 1, 2, ..., n; n is the number of flow points selected for structural parameter optimization; K i is the instrument coefficient corresponding to the i-th flow point; is the average instrument coefficient; the quadratic regression fitting equation between the design variables and target values ​​fitted in step 3 is:

[0016] δ=48.74314-5.17338×R t +2.77162×a-0.07254×θ-0.41636×R t ×a+4.28292e-4×R t ×θ+0.025524×a×θ+0.14584×R t 2 +4.02328×a 2 +5.70176e-4×θ 2

[0017] In the formula, R t is the blade radius; a is the blade edge thickness; θ is the blade inclination angle.

[0018] The algorithm flow of the adaptive differential mutation population search algorithm in step 4 is as follows:

[0019] Step 1 Initialization. Randomly assign values ​​to the searcher positions to generate the initial population pop i .

[0020] Step 2 Evaluation: Calculate the fitness value of the search individual.

[0021] Step 3 Variation. According to the current best position gbest r1,t and two random position pops r2,tand pop r3,t Perform an adaptive differential mutation operation on the initial population to generate a mutant population pop i,t+1 .

[0022] Step4 Search. Calculate the search direction of each searcher and the search step size α i .

[0023] Step5 Position update. Update the position according to the search direction and step size.

[0024] Step6 Obtain the best fitness value fitgbest(i) of the searcher individual. If the current searcher fitness value fit(i) < fitgbest(i), then replace fitgbest(i) with fit(i).

[0025] Step7 Obtain the global best fitness value fitzbest(i) of the searcher. If the current searcher fitness value fit(i) < fitzbest(i), then replace fitzbest(i) with fit(i).

[0026] Step8 Iteratively calculate t + 1.

[0027] Step9 When the maximum number of iterations is reached, stop the search and output the optimal structural parameter combination and the minimum linearity error value; otherwise, go to Step2.

[0028] The adaptive differential mutation strategy of the population search algorithm is as follows:

[0029] pop i,t+1 = gbest r1,t + F·(pop r2,t - pop r3,t )

[0030] In the formula, pop i,t+1 is the mutant population; r1, r2, and r3 are three randomly generated integers within the population range and are not equal to each other; gbest r1,t is the current best search position; pop r2,t and pop r3,t are two randomly selected search positions in the population respectively; F is the adaptive differential mutation operator, usually a real constant factor within the range of [0, 2]. Its expression is as follows:

[0031]

[0032] In the formula, F0 is taken as 0.3.

[0033] The calculation methods of the search direction and search step size of the population search algorithm are as follows:

[0034]

[0035]

[0036] In the formula, is the search direction, α i is the search step length; and is a random real number between [0,1]; sign is the sign function; are the searcher's egoistic direction, altruistic direction, and pre-movement direction respectively; δ i is the parameter of Gaussian membership function; u i is the membership degree of the i-th objective function value.

[0037] Beneficial effects:

[0038] The present invention uses a crowd search algorithm based on an adaptive differential mutation strategy to optimize the blade structural parameters of the turbine flowmeter, obtain the optimal blade parameter combination and the minimum instrument coefficient linearity error, and improve the metering accuracy of the turbine flowmeter and the response effect of the blade to the incoming flow impact. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of blade structure optimization of the present invention;

[0040] Figure 2 This is the original impeller structure diagram;

[0041] Figure 3 is the original instrument factor curve;

[0042] Figure 4 It is the pressure cloud diagram on the blade surface before optimization;

[0043] Figure 5 It is to optimize the pressure cloud diagram on the side of the front blade;

[0044] Figure 6 It is the flow chart of adaptive differential mutation population search algorithm;

[0045] Figure 7 It is the iteration curve of the fitness value of the Rastrigin function;

[0046] Figure 8 It is the iteration curve of the fitness value of the Sphere function;

[0047] Fig. 9 It is the iteration curve of the objective function fitness value;

[0048] Fig.10 is the optimized blade structure diagram;

[0049] Fig.11 is the optimized instrument coefficient curve;

[0050] Fig.12 It is the pressure cloud diagram of the blade surface after optimization;

[0051] Fig.13 This is the pressure cloud diagram of the blade side after optimization. DETAILED DESCRIPTION

[0052] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0053] like Figure 1 The turbine flowmeter blade structure optimization method based on the adaptive differential mutation population search algorithm comprises the following steps:

[0054] Step 1, obtaining the simulated instrument coefficient characteristic curve of the initial turbine flowmeter, and calculating the instrument coefficient linearity error δ;

[0055] In this embodiment, firstly, the turbine flowmeter impeller before structural optimization is simulated by fluid simulation software. Figure 2 As shown, the flow meter impeller has six blades in total. The blade surface is a flat profile that transitions at right angles to the blade side. The circular hole in the middle of the impeller is used to install a rolling bearing and connect it to the rotating shaft.

[0056] Select 1, 1.2, 1.4, 1.6, 1.8, 2m within the flow range 3 / min six flow points, simulate the impeller rotation process under fluid impact state, and obtain the instrument coefficient curve within the flow change range, such as Figure 3 As shown, the linearity error δ of the instrument coefficient is calculated to be 3.1060%.

[0057] pass Figure 3 It is found that the instrument coefficient shows an overall increasing trend within the flow range, resulting in a linearity error, while the ideal instrument coefficient does not change with flow and remains a constant value.

[0058] Obtained through post-processing software Figure 4 Blade surface pressure cloud map, Figure 5 Blade side pressure cloud map. Observation of the cloud map shows that the maximum pressure on the blade surface of the original structure is distributed at the center, but the distribution and overall pressure are too uneven, and a large area of ​​negative pressure appears on the side of the blade, which will reduce the reliability of the blade structure itself and the uniformity of the flow field near the impeller.

[0059] In order to reduce the linearity error of the instrument coefficient and improve the pressure distribution on the blade surface, the blade structure of the flow meter needs to be optimized.

[0060] Step 2: Take the three structural parameters of the flow meter blade radius, blade edge thickness, and blade inclination angle as design variables, and the instrument coefficient linearity error δ as the output target value to conduct a simulation orthogonal test;

[0061] Selected variable range: Blade radius R t The range is 17 to 20 mm, the blade edge thickness a range is 0.39 to 0.78 mm, and the blade inclination angle range is 0 to 30°.

[0062] According to the method in step 1, the impellers with different structural parameter combinations are simulated and calculated respectively, and the maximum and minimum instrument coefficients Kmax, Kmin, and linearity error δ of each test group are obtained. The three-factor four-level simulation orthogonal test is designed as shown in Table 1:

[0063] Table 1 Simulation orthogonal test data table

[0064]

[0065] Step 3: Based on the simulation data, the response surface method is used to fit the quadratic regression fitting equation of the target value with respect to the design variables;

[0066] The experimental data of the response surface method are fitted. In order to achieve better fitting accuracy, the fitting method uses a quadratic regression equation with cross terms. The fitting equation is as follows:

[0067] δ=48.74314-5.17338×R t +2.77162×a-0.07254×θ-0.41636×R t ×a+4.28292e-4×R t ×θ+0.025524×a×θ+0.14584×R t 2 +4.02328×a 2 +5.70176e-4×θ 2

[0068] The fitted equation needs to be subjected to variance analysis to determine the applicability of the equation. 2 =87.6547, P value is 0.0029<0.005, and the function model is considered to be highly significant; the P value of the lack-of-fit term is 0.1405>0.05, indicating that the lack-of-fit of the model is not significant. Therefore, the quadratic regression fitting equation can well express the relationship between the response value and the variable value, and is used in parameter optimization calculation.

[0069] Step 4: Using the fitting equation in step 3 as the fitness function, the structural parameters are optimized by using a population search algorithm based on adaptive differential mutation and taking the minimum fitness value as the optimization goal;

[0070] The fitting equation in Step 3 is the fitness function in the optimization algorithm, which is substituted into the algorithm for parameter optimization. The algorithm flow of the adaptive differential mutation population search algorithm is as Figure 6 shown.

[0071] Step1 Initialization. Randomly assign values to the positions of the searchers to generate the initial population pop i .

[0072] Step2 Evaluation. Calculate the fitness values of the search individuals.

[0073] Step3 Mutation. According to the current best position gbest r1,t and two random positions pop r2,t , pop r3,t , through the differential mutation strategy model introducing the adaptive mutation operator F, perform adaptive differential mutation operation on the initial population to generate the mutant population pop i,t+1 ;

[0074] Step4 Search. According to the search direction calculation model, obtain the search direction of each searcher According to the search step calculation model, obtain the search step α of each searcher i .

[0075] Step5 Position update. According to the search direction and the step α i , perform position update according to the searcher position update calculation model.

[0076] Step6 Obtain the best fitness value fitgbest(i) of the searcher individual. If the current searcher fitness value fit(i) < fitgbest(i), then replace fitgbest(i) with fit(i).

[0077] Step7 Obtain the global best fitness value fitzbest(i) of the searcher. If the current searcher fitness value fit(i) < fitzbest(i), then replace fitzbest(i) with fit(i).

[0078] Step8 Iterative calculation t + 1.

[0079] Step9 When the maximum number of iterations is reached, stop the search and output the optimal structural parameter combination R t , a and θ, as well as the minimum linearity error value δ; otherwise, go to Step2.

[0080] The main formulas involved in the adaptive differential mutation population search algorithm are as follows:

[0081] Differential mutation strategy model:

[0082] pop i,t+1 =gbest r1,t +F·(pop r2,t -pop r3,t )

[0083] Adaptive differential mutation operator F calculation model:

[0084]

[0085] Search Direction Computational model:

[0086]

[0087] In the formula, They are the searcher's selfish direction, altruistic direction, and pre-action direction respectively.

[0088] Search step calculation model:

[0089]

[0090] Seeker location update calculation model:

[0091]

[0092] In the formula, x i (t) is the current searcher position, x i (t+1) is the updated position.

[0093] The main parameter settings of the adaptive differential mutation population search algorithm are as follows:

[0094] (1) The upper limit of the population search space is [20 0.78 30], and the lower limit is [17 0.39 0];

[0095] (2) F0 in the original mutation operator is set to 0.3;

[0096] (3) The population size is 100 and the maximum number of iterations is 100, at which point a stable minimum fitness value can be obtained;

[0097] (4) Membership degree u i The upper limit is 0.95 and the lower limit is 0.11.

[0098] The minimum fitness value is the global minimum value of the linearity error of the target instrument coefficient.

[0099] In order to verify the iterative calculation performance of the improved crowd search algorithm, two classic test functions, Rastrigin and Sphere, are used for iterative calculation tests. The function expressions are as follows: Rastrigin function:

[0100]

[0101] Sphere function:

[0102]

[0103] The iterative calculation results are as follows Figure 7 , Figure 8 By observing the fitness value iteration curve, it can be found that compared with the crowd search algorithm and the particle swarm algorithm, the improved algorithm has a faster iterative calculation speed and the calculation performance is significantly improved.

[0104] The adaptive differential mutation population search algorithm is used to iteratively calculate the established objective function. The iteration curve is as follows: Fig. 9 As shown, the optimal blade structural parameters are calculated as shown in Table 2:

[0105] Table 2 Blade parameter optimization results

[0106]

[0107] The optimized blade structure is as follows Fig.10 As shown in the figure, compared with the original blade structure, the blade has a larger inclination angle and the blade edge thickness is smaller, so that the blade surface has an arc profile, and the blade radius changes relatively little. After the blade structure is optimized, the linearity error of the instrument coefficient δ is reduced from 3.1060% to 0.4452%, and the optimization effect is obvious.

[0108] Step 5: Use the optimized blade structure to perform simulation and obtain the optimized instrument factor curve.

[0109] The optimized impeller structure was used for simulation verification. Under the same calculation conditions, the optimized instrument coefficient curve obtained by simulation calculation is as follows Fig.11 As shown in the figure, it can be found that the linearity error of the flow meter coefficient after structural parameter optimization is significantly reduced compared with that before optimization. The instrument coefficient is between 1.0 and 2.0 m 3 / min range, the changes tend to be stable, achieving higher measurement accuracy.

[0110] Fig.12From the pressure cloud map of the optimized blade surface, it can be found that the maximum pressure on the optimized blade surface under stable working conditions appears in the right half of the blade, with a maximum pressure of 0.0463MPa. The pressure transitions to the middle of the blade at 0.034MPa, and decreases to 0.01MPa towards the edge of the blade. The pressure gradually decreases from the left. Compared with the results before optimization, the pressure distribution on the optimized blade surface is more uniform as a whole.

[0111] Fig.13 This is the pressure cloud map of the optimized blade side. The reduction in blade edge thickness and the increase in blade inclination angle result in a better response of the blade when the incoming flow impacts the blade. The side negative pressure of the blade is significantly reduced, and the overall negative pressure on the side is around -0.038MPa. Compared with the blade structure before optimization, there is no obvious pressure mutation on the blade side as a whole, and the pressure transition is more uniform.

[0112] Through the above analysis results, the blade structure optimization effect of the present invention is significant.

Claims

1. A blade structure optimization method based on an adaptive differential mutation population search algorithm, characterized in that: The method includes the following steps: Step 1, obtain the simulation instrument coefficient characteristic curve of the initial turbine flowmeter, and calculate the instrument coefficient linearity error δ; Step 2, take the three structural parameters of the flowmeter blade radius, blade edge thickness, and blade tilt angle as design variables, and the instrument coefficient linearity error δ as the output target value, and conduct a simulation orthogonal experiment; Step 3, based on the simulation data, apply the response surface method to fit the quadratic regression fitting equation of the target value with respect to the design variables; Step 4, take the fitting equation in Step 3 as the fitness function, and through the population search algorithm based on adaptive differential mutation, with the minimum fitness value as the optimization goal, conduct structural parameter optimization; Step 5, use the optimized blade structure for simulation to obtain the optimized instrument coefficient curve; The algorithm flow of the adaptive differential mutation population search algorithm is as follows: Step 1: Initialize and randomly assign values ​​to the searcher positions to generate the initial population pop i ; Step 2 Evaluation, calculate the fitness value of the search individual; Step 3: Variation, based on the current best position gbest r1,t and two random position pops r2,t and pop r3,t , perform adaptive differential mutation operation on the initial population to generate a mutant population pop i,t+1 ; Step 4 Search, calculate the search direction of each searcher And the search step length α i ; Step 5 Position update, update the position according to the search direction and step size; Step 6 Obtain the best fitness value fitgbest(i) of the searcher individual. If the current searcher fitness value fit(i) < fitgbest(i), then replace fitgbest(i) with fit(i); Step 7 Obtain the global best fitness value fitzbest(i) of the searcher. If the current searcher fitness value fit(i) < fitzbest(i), then replace fitzbest(i) with fit(i); Step 8 Iteratively calculate t + 1; Step 9 When the maximum number of iterations is reached, stop the search and output the optimal structural parameter combination and the minimum linearity error value; otherwise, go to Step 2; The adaptive differential mutation operation of the population search algorithm is as follows: pop i,t+1 =gbest r1,t +F·(pop r2,t -pop r3,t ) In the formula, pop i,t+1 is the mutant population; r1, r2, r3 are three randomly generated integers within the population range and are not equal to each other; gbest r1,t is the current best search position; pop r2,t and pop r3,t are two random search positions in the population; F is an adaptive differential mutation operator, usually a real constant factor in the range [0,2]; its expression is as follows: In the formula, F0 takes 0.

3.

2. The blade structure optimization method based on the adaptive differential mutation population search algorithm according to claim 1 is characterized in that: The expression of the instrument coefficient linearity error δ in Step 1 is as follows: In the formula, K max =Max{K i }, K min =Min{K i }, i = 1, 2, ..., n; n is the number of flow points selected for structural parameter optimization; K i is the instrument coefficient corresponding to the i-th flow point; is the average instrument factor.

3. The blade structure optimization method based on the adaptive differential mutation population search algorithm according to claim 1 is characterized in that: The quadratic regression fitting equation fitted in Step 3 is: δ=48.74314-5.17338×R t +2.77162×a-0.07254×θ-0.41636×R t ×a+4.28292e-4×R t ×θ+0.025524×a×θ+0.14584×R t 2 +4.02328×a 2 +5.70176e-4×θ 2 In the formula, R t is the blade radius; a is the blade edge thickness; θ is the blade inclination angle.

4. The blade structure optimization method based on the adaptive differential mutation population search algorithm according to claim 1 is characterized by: The calculation methods of the search direction and search step size of the population search algorithm are as follows: In the formula, is the search direction, α i is the search step length; and is a random real number between [0,1]; sign is the sign function; are the searcher's egoistic direction, altruistic direction, and pre-movement direction respectively; δ i is the parameter of Gaussian membership function; u i is the membership degree of the i-th objective function value.

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