CN115481510B - Radial compressor blade multi-working-condition optimization method and device based on improved NSGA-II algorithm - Google Patents
Radial compressor blade multi-working-condition optimization method and device based on improved NSGA-II algorithm Download PDFInfo
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Abstract
The invention discloses a radial compressor blade multi-working-condition optimization method and device based on an improved NSGA-II algorithm, and relates to the technical field of pneumatic design of radial compressors. Comprising the following steps: acquiring the blade geometric configuration of an original radial compressor; inputting the blade geometric configuration of the original radial compressor into a constructed optimization model based on an improved non-dominant ordering genetic NSGA-II algorithm; and obtaining the optimal blade geometry of the original radial compressor under multiple working conditions based on the blade geometry of the original radial compressor and an optimization model based on an improved NSGA-II algorithm. The invention can improve the solving quality of the multi-working condition optimization problem and the comprehensive aerodynamic performance of the radial compressor.
Description
Technical Field
The invention relates to the technical field of pneumatic design of radial compressors, in particular to a radial compressor blade multi-working-condition optimization method and device based on an improved NSGA-II algorithm.
Background
The radial compressor is an important power device for guaranteeing national defense safety and promoting national economic development, and is widely applied to the strategic demand fields of aerospace, ships, chemical industry, new energy and the like. According to the statistics information related to national energy foundation and standardization committee, the annual power consumption of the industrial compressor system accounts for about 6% -9% of the total national power generation. Along with the target promise and promotion of 'carbon reaching peak and carbon neutralization' proposed by China at the seventy-five united nations, the improvement of the pneumatic performance of the radial compressor has important positive significance on 'energy conservation and emission reduction'.
The blade configuration is usually selected to be carried out under the rated rotation speed when the pneumatic design of the radial compressor is optimized, but in some complex application scenes, the pneumatic comprehensive performance of a plurality of different working conditions is required to be optimized simultaneously, the operation difficulty is increased, and the optimization flow has the characteristic of a typical black box.
The optimizing algorithm is a key link in the pneumatic design optimizing process, and influences the pneumatic comprehensive performance after multi-station optimization. The multi-objective NSGA-II (Non-dominated Sorting Genetic Algorithm, non-dominant ordered genetic algorithm) optimization algorithm is a classical algorithm for solving the 'black box' problem, but is limited to practical application scenarios, and the optimization result is difficult to achieve global optimization in a limited number of iterations. Therefore, the multi-station optimization algorithm is a leading edge hot spot research problem in the field of radial compressor blade design optimization, and is further improved and explored on the basis of NSGA-II.
The defects of NSGA-II are mainly shown in the following steps: it is easy to trap into a locally optimal solution and lose a potentially optimal solution. When the differences among decision variable individuals are large and the fitness evaluation values are similar, the crowding degree operator is adopted to screen the individuals, so that the individuals can be lost, and the diversity of the population is not facilitated.
Disclosure of Invention
The invention provides the multi-objective NSGA-II evolutionary algorithm based on improvement of the multi-objective NSGA-II evolutionary algorithm in order to solve the problem of black box faced by the complex curved surface blade multiplexing Kuang Qidong design optimization of the radial compressor, improve the diversity of population and the optimizing quality of blade geometric configuration.
In order to solve the technical problems, the invention provides the following technical scheme:
in one aspect, the invention provides a radial compressor blade multi-task optimization method based on an improved NSGA-ii algorithm, the method being implemented by electronic equipment, the method comprising:
s1, acquiring the blade geometric configuration of the original radial compressor.
S2, inputting the blade geometric configuration of the original radial compressor into a constructed optimization model based on an improved non-dominant ordering genetic NSGA-II algorithm.
S3, obtaining the optimal blade geometry of the original radial compressor under multiple working conditions based on the blade geometry of the original radial compressor and an optimization model based on an improved NSGA-II algorithm.
Optionally, the obtaining the multi-working condition optimal blade geometry after the original radial compressor blade optimization based on the blade geometry of the original radial compressor and the optimization model based on the improved NSGA-ii algorithm in S3 includes:
S31, performing parameterization expression on the blade geometric configuration of the original radial compressor by adopting a profile mapping parameterization method to obtain a mapping model of the original blade suction surface and the unit spline surface and a mapping model of the original blade pressure surface and the unit spline surface.
S32, obtaining design vertex parameters of the unit spline surface and design space parameters of the unit spline surface by layout, and initializing a sample population P by using a Latin hypercube sampling method t 。
S33, a mapping model based on the original blade suction surface and the unit spline surface, a mapping model based on the original blade pressure surface and the unit spline surface and a sample population P t And obtaining the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade.
S34, obtaining a new blade geometric configuration based on the change amount of the suction surface of the original blade and the change amount of the pressure surface of the original blade.
S35, generating a grid template file based on the blade geometric configuration of the original radial compressor, and carrying out grid division on the new blade geometric configuration according to the grid template file to obtain a blade grid model of the new radial compressor.
S36, performing multi-working-condition steady-state numerical simulation calculation on a new radial compressor blade grid model to obtain a sample population P t Multiple operating pneumatic performance parameters for each individual.
S37, setting an objective function and constraint conditions of a blade geometry optimization flow of a new radial compressor under multiple working conditions, and performing sample population P based on the objective function and constraint conditions t Genetic operator operation is carried out to obtain a offspring population P t * Thereby obtaining the offspring population P t * Multiple operating pneumatic performance parameters for each individual.
S38, based on sample population P t Offspring population P t * A new population is composed and the new population is grouped.
S39, generating a parent population P of the next generation based on the new population after grouping and the Cannability Canberra distance operator model t+1 And step S37 is executed until the preset iteration times are reached, and the optimal blade geometric configuration of the original radial compressor blade after the optimization of the multiple working conditions is output.
Optionally, the parameterizing the blade geometry of the original radial compressor by using a profile mapping parameterizing method in S31, to obtain a mapping model of the original blade suction surface and the unit spline surface and a mapping model of the original blade pressure surface and the unit spline surface includes:
s311, based on the blade geometric configuration of the original radial compressor, unitizing the geometric molded line of the blade suction surface of the original radial compressor and the geometric molded line of the blade pressure surface of the original radial compressor.
S312, constructing a unit mapping spline surface.
S313, obtaining a mapping model of the suction surface of the original blade and the unit spline surface and a mapping model of the pressure surface of the original blade and the unit spline surface according to the geometric molded line of the suction surface of the original blade after unitization, the geometric molded line of the pressure surface of the original blade after unitization and the unit mapping spline surface.
Optionally, the mapping model based on the original blade suction surface and the unit spline surface, the mapping model based on the original blade pressure surface and the unit spline surface, and the sample population P in S33 t Obtaining the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade comprises the following steps:
mapping model based on original blade suction surface and unit spline surface, mapping model based on original blade pressure surface and unit spline surface and sample population P t The method comprises the steps of solving characteristic parameters of a nonlinear equation set of a mapping model of an original blade suction surface and a unit spline surface and characteristic parameters of a nonlinear equation set of a mapping model of an original blade pressure surface and a unit spline surface, and further solving the variation of the original blade suction surface and the variation of the original blade pressure surface by perturbing design vertex parameters of the unit spline surface.
Optionally, deriving the new blade geometry based on the amount of change in the suction side of the original blade and the amount of change in the pressure side of the original blade in S34 includes:
and superposing the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade on the curved surface of the original blade to obtain a new blade geometric configuration.
Optionally, the genetic operator operation in S37 includes a selection operation, a crossover operation, and a mutation operation.
Wherein the selecting operation adopts a tournament selecting method.
Optionally, the sample-based population P in S38 t Offspring population P t * Forming a new population and grouping the new population includes:
s381, based on sample population P t Offspring population P t * A new population is formed.
S382, based on the dominant and non-dominant relations among individuals in the new population, the new population is subjected to rapid non-dominant sorting, and the layered population is obtained.
S383, grouping the layered population based on the elimination strategy.
Optionally, the Canberra distance operator model in S39 is shown in the following formula (1):
wherein ,xi and yi Two different populations of individuals, n being the number of design variables.
In another aspect, the present invention provides a radial compressor blade multi-condition optimization apparatus based on an improved NSGA-ii algorithm, where the apparatus is applied to implement a radial compressor blade multi-condition optimization method based on an improved NSGA-ii algorithm, and the apparatus includes:
And the acquisition module is used for acquiring the blade geometric configuration of the original radial compressor.
And the input module is used for inputting the blade geometric configuration of the original radial compressor into the established optimization model based on the improved non-dominant ranking genetic NSGA-II algorithm.
And the output module is used for obtaining the optimal blade geometry of the original radial compressor in multiple working conditions after the blade of the original radial compressor is optimized based on the blade geometry of the original radial compressor and an optimization model based on an improved NSGA-II algorithm.
Optionally, the output module is further configured to:
s31, performing parameterization expression on the blade geometric configuration of the original radial compressor by adopting a profile mapping parameterization method to obtain a mapping model of the original blade suction surface and the unit spline surface and a mapping model of the original blade pressure surface and the unit spline surface.
S32, obtaining design vertex parameters of the unit spline surface and design space parameters of the unit spline surface by layout, and initializing a sample population P by using a Latin hypercube sampling method t 。
S33, a mapping model based on the suction surface of the original blade and a unit spline surface, and the pressure surface of the original blade and a unit spline surfaceMapping model of spline surface and sample population P t And obtaining the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade.
S34, obtaining a new blade geometric configuration based on the change amount of the suction surface of the original blade and the change amount of the pressure surface of the original blade.
S35, generating a grid template file based on the blade geometric configuration of the original radial compressor, and carrying out grid division on the new blade geometric configuration according to the grid template file to obtain a blade grid model of the new radial compressor.
S36, performing multi-working-condition steady-state numerical simulation calculation on a new radial compressor blade grid model to obtain a sample population P t Multiple operating pneumatic performance parameters for each individual.
S37, setting an objective function and constraint conditions of a blade geometry optimization flow of a new radial compressor under multiple working conditions, and performing sample population P based on the objective function and constraint conditions t Genetic operator operation is carried out to obtain a offspring population P t * Thereby obtaining the offspring population P t * Multiple operating pneumatic performance parameters for each individual.
S38, based on sample population P t Offspring population P t * A new population is composed and the new population is grouped.
S39, generating a parent population P of the next generation based on the new population after grouping and the Cannability Canberra distance operator model t+1 And step S37 is executed until the preset iteration times are reached, and the optimal blade geometric configuration of the original radial compressor blade after the optimization of the multiple working conditions is output.
Optionally, the output module is further configured to:
s311, based on the blade geometric configuration of the original radial compressor, unitizing the geometric molded line of the blade suction surface of the original radial compressor and the geometric molded line of the blade pressure surface of the original radial compressor.
S312, constructing a unit mapping spline surface.
S313, obtaining a mapping model of the suction surface of the original blade and the unit spline surface and a mapping model of the pressure surface of the original blade and the unit spline surface according to the geometric molded line of the suction surface of the original blade after unitization, the geometric molded line of the pressure surface of the original blade after unitization and the unit mapping spline surface.
Optionally, the output module is further configured to:
mapping model based on original blade suction surface and unit spline surface, mapping model based on original blade pressure surface and unit spline surface and sample population P t The method comprises the steps of solving characteristic parameters of a nonlinear equation set of a mapping model of an original blade suction surface and a unit spline surface and characteristic parameters of a nonlinear equation set of a mapping model of an original blade pressure surface and a unit spline surface, and further solving the variation of the original blade suction surface and the variation of the original blade pressure surface by perturbing design vertex parameters of the unit spline surface.
Optionally, the output module is further configured to:
and superposing the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade on the curved surface of the original blade to obtain a new blade geometric configuration.
Optionally, the genetic operator operations include a selection operation, a crossover operation, and a mutation operation.
Wherein the selecting operation adopts a tournament selecting method.
Optionally, the output module is further configured to:
s381, based on sample population P t Offspring population P t * A new population is formed.
S382, based on the dominant and non-dominant relations among individuals in the new population, the new population is subjected to rapid non-dominant sorting, and the layered population is obtained.
S383, grouping the layered population based on the elimination strategy.
Optionally, the Canberra distance operator model is represented by the following formula (1):
wherein ,xi and yi Two different populations of individuals, n being the number of design variables.
In one aspect, an electronic device is provided, the electronic device including a processor and a memory, the memory having stored therein at least one instruction loaded and executed by the processor to implement the above-described radial compressor blade multi-task optimization method based on an improved NSGA-ii algorithm.
In one aspect, a computer readable storage medium having stored therein at least one instruction loaded and executed by a processor to implement the above-described radial compressor blade multi-task optimization method based on the modified NSGA-ii algorithm is provided.
The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
in the scheme, the multi-working-condition optimization method for the radial compressor blade based on the improved NSGA-II algorithm can effectively improve the diversity of the population in the multi-objective optimization process, improve the solving quality of the 'black box' problem, obtain excellent global optimization solution in limited iteration times, and improve the optimizing quality and efficiency of the multi-working-condition geometric configuration of the radial compressor blade. Meanwhile, the adopted profile parameterization method can realize flexible configuration of the complex curved surface blade of the radial compressor; the increased radial constraint on the geometric control parameters is beneficial to the generation of smooth blades; ensuring the intersection of the impeller and the casing is beneficial to improving the grid generation rate in the optimization process.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic flow diagram of a radial compressor blade multi-task optimization method based on an improved NSGA-II algorithm provided by an embodiment of the invention;
FIG. 2 is a flowchart of a radial compressor blade multi-task optimization method for improving NSGA-II algorithm provided by an embodiment of the invention;
FIG. 3 is a block diagram of a radial compressor blade multi-task optimization apparatus based on an improved NSGA-II algorithm provided by an embodiment of the present invention;
fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
In order to make the technical problems, technical solutions and advantages to be solved more apparent, the following detailed description will be given with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, an embodiment of the present invention provides a method that may be implemented by an electronic device. As shown in the method flowchart of fig. 1, the process flow of the method may include the steps of:
in one aspect, the invention provides a radial compressor blade multi-task optimization method based on an improved NSGA-ii algorithm, the method being implemented by electronic equipment, the method comprising:
s1, acquiring the blade geometric configuration of the original radial compressor.
S2, inputting the blade geometric configuration of the original radial compressor into a constructed optimization model based on an improved non-dominant ordering genetic NSGA-II algorithm.
S3, obtaining the optimal blade geometry of the original radial compressor under multiple working conditions based on the blade geometry of the original radial compressor and an optimization model based on an improved NSGA-II algorithm.
Optionally, the obtaining the multi-working condition optimal blade geometry after the original radial compressor blade optimization based on the blade geometry of the original radial compressor and the optimization model based on the improved NSGA-ii algorithm in S3 includes:
s31, performing parameterization expression on the blade geometric configuration of the original radial compressor by adopting a profile mapping parameterization method to obtain a mapping model of the original blade suction surface and the unit spline surface and a mapping model of the original blade pressure surface and the unit spline surface.
Optionally, the parameterizing the blade geometry of the original radial compressor by using a profile mapping parameterizing method in S31, to obtain a mapping model of the original blade suction surface and the unit spline surface and a mapping model of the original blade pressure surface and the unit spline surface includes:
s311, based on the blade geometric configuration of the original radial compressor, unitizing the geometric molded line of the blade suction surface of the original radial compressor and the geometric molded line of the blade pressure surface of the original radial compressor.
In a possible implementation manner, as shown in fig. 2, a multi-working-condition optimization method of a radial compressor blade based on an improved NSGA-ii algorithm is adopted, a profile mapping parameterization method is adopted to parameterize and express the blade geometry of an original radial compressor, and a mapping model of an original blade suction surface and a unit spline surface and a mapping model of a pressure surface and a unit spline surface are created.
Specifically, unitizing geometric molded lines of an original blade suction surface and a pressure surface to generate unitized mapping spline surfaces, wherein the process of establishing a mapping model comprises the following steps:
the unitizing method of the original blade profile suction surface and the pressure surface molded lines is the same, wherein the abscissa mathematical definition is shown in the following formula (1):
in the formula ,xi,j Is the abscissa after unitizing the molded line, i is the arc length segment number on the molded line, j is the molded line mark, h a Is the arc length of the a section, h j Is the j-th line.
The unitization method of the original blade suction surface and the pressure surface molded lines is the same, and the ordinate mathematical definition is shown in the following formula (2):
in the formula ,yi,j The ordinate of the molded line after unitization is the arc length number on the molded line, j is the molded line mark, h o Is the arc length of the o segment, and h i And (5) an i-th molded line.
S312, constructing a unit mapping spline surface.
In one possible embodiment, the mathematical expression of the method for generating the mapped spline surface is shown in the following formula (3):
in the formula ,
is the point coordinates on the unitized mapping spline surface, T a,c Is spline surface control vertex coordinates, a is the label of the abscissa on the spline surface, e is the control vertex number of the abscissa on the spline surface, c is the label of the ordinate on the spline surface, f is the control vertex number of the ordinate on the spline surface, ">
and />
Is a Bernstein basis function, where t 0 and t1 Is a mapping parameter.
S313, obtaining a mapping model of the suction surface of the original blade and the unit spline surface and a mapping model of the pressure surface of the original blade and the unit spline surface according to the geometric molded line of the suction surface of the original blade after unitization, the geometric molded line of the pressure surface of the original blade after unitization and the unit mapping spline surface.
In a possible implementation manner, a mapping model of the suction surface and the pressure surface is built, and the mathematical expressions of the two mapping models are the same, wherein the mathematical expressions are shown in the following formula (4):
in the formula ,zi,j Is the amount of change in the original blade surface.
S32, obtaining design vertex parameters of the unit spline surface and design space parameters of the unit spline surface by layout, and initializing a sample population P by using a Latin hypercube sampling method t 。
In one possible implementation, the design vertex variables and design space are specified first, and then the Latin hypercube sampling method is used to initialize the samples.
Specifically, 80 sample points are initialized, each dimension variable is divided into 80 cells, each sample point is randomly distributed among the cells, and when the selected 80 sample points are projected to any one dimension, there is only one sample point in each cell in the dimension.
S33, a mapping model based on the original blade suction surface and the unit spline surface, a mapping model based on the original blade pressure surface and the unit spline surface and a sample population P t And obtaining the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade.
Optionally, the mapping model based on the original blade suction surface and the unit spline surface, the mapping model based on the original blade pressure surface and the unit spline surface, and the sample population P in S33 t Obtaining the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade comprises the following steps:
mapping model based on original blade suction surface and unit spline surface, mapping model based on original blade pressure surface and unit spline surface and sample population P t The method comprises the steps of solving characteristic parameters of a nonlinear equation set of a mapping model of an original blade suction surface and a unit spline surface and characteristic parameters of a nonlinear equation set of a mapping model of an original blade pressure surface and a unit spline surface, and further solving the variation of the original blade suction surface and the variation of the original blade pressure surface by perturbing design vertex parameters of the unit spline surface.
In a feasible implementation mode, based on the obtained mapping model and sample population, a strong-robustness optimization algorithm is adopted to solve characteristic parameters of a nonlinear equation set of the mapping model, and the change amount of the surface of the original blade is further solved by perturbing a spline surface.
The optimization algorithm can be a Monte Carlo algorithm or a heuristic algorithm and the like.
Compared with the general algorithm, the Monte Carlo algorithm has the characteristics of strong robustness, insensitivity to initial values and the like, and can better solve the problem of multi-dimension or complex factors.
The perturbed spline surface may be a design vertex parameter that perturbs the unit spline surface.
Specifically, the process of solving the local parameters of the nonlinear equation set of the mapping model by adopting the Monte Carlo algorithm with strong robustness comprises the following steps:
and (3) establishing an error model of the mapping function and the real blade data points, wherein the mathematical expression is shown in the following formula (5):
wherein s, t is a mapping parameter, Q is the error between the mapping value and the true value, X real Is true coordinates, T a,c Is the spline surface control vertex coordinates, a is the label of the abscissa on the spline surface, e the control vertex points of the abscissa on the spline surface, c is the label of the ordinate on the spline surface, f the control vertex points of the ordinate on the spline surface, 
and />
Is a bernstein basis function, where s and t are mapping parameters.
First, the mapping parameter (s, t) =(s) 0 ,t 0 ) Calculate the initial difference Q 0 A positive number u is set. Next, in the interval [ -u, u]Generating a random number vector n, calculating Q 1 ＝Q 0 (s 0 +n s ,t 0 +n t ). When Q is 1 ＜Q 0 (s,t)＝(s 0 +n s ,t 0 +n t )，Q 0 ＝Q 1 . If the randomly generated sets of random vectors still do not satisfy Q 1 ＜Q 0 Let u=u/2, so cycle calculation until Q 0 ＜ε，(s,t)＝(s best ,t best ) The mapping parameters are obtained.
S34, obtaining a new blade geometric configuration based on the change amount of the suction surface of the original blade and the change amount of the pressure surface of the original blade.
Optionally, deriving the new blade geometry based on the amount of change in the suction side of the original blade and the amount of change in the pressure side of the original blade in S34 includes:
and superposing the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade on the curved surface of the original blade to obtain a new blade geometric configuration.
In one possible embodiment, the mathematical expression for the new blade geometry is shown in the following formula (6):
A opt ＝A ori +ΔA (6)
in the formula ,Aopt Is the new blade coordinate value, A ori Is the original blade coordinate value, Δa is the original variation.
S35, generating a grid template file based on the blade geometric configuration of the original radial compressor, and carrying out grid division on the new blade geometric configuration according to the grid template file to obtain a blade grid model of the new radial compressor.
In a possible implementation manner, based on the grid template file generated by the original radial compressor impeller, the new blade geometry obtained in the step S34 is subjected to grid division, and a new radial compressor blade grid model is generated; the grid master topology adopts H & I, the tip clearance topology adopts HO, and an Autogrid5 module of FINE/TURBO is adopted to generate a grid template of the trb file.
S36, performing multi-working-condition steady-state numerical simulation calculation on a new radial compressor blade grid model to obtain a sample population P t Multiple-working-condition air-borne of each individualEnergy parameters.
In a possible implementation mode, the aerodynamic performance numerical calculation of the rated working condition and the common working condition is performed on the new radial compressor blade grid model obtained in the step five based on Numeca software.
S37, setting an objective function and constraint conditions of a blade geometry optimization flow of a new radial compressor under multiple working conditions, and performing sample population P based on the objective function and constraint conditions t Genetic operator operation is carried out to obtain a offspring population P t * Thereby obtaining the offspring population P t * Multiple operating pneumatic performance parameters for each individual.
Optionally, the genetic operator operation in S37 includes a selection operation, a crossover operation, and a mutation operation.
Wherein the selecting operation adopts a tournament selecting method.
In a possible embodiment, the offspring population P t * Obtaining a offspring population P by adopting the steps S33-S36 t * Multiple operating pneumatic performance parameters for each individual.
Further, the following operations are adopted for selection, crossover and mutation respectively:
selecting, namely taking out a certain number of individuals from the population each time (sampling is put back), selecting the best individuals to enter the offspring population, and repeating the operation until the offspring population reaches the original population scale; the amount of removal is calculated using the value of the relative tournament size, and decreasing the relative tournament size will increase the randomness of the selection process, and increasing the tournament size will result in more duplication of the best individuals in the sub-population, a regimen based on survival of the fittest individuals.
Crossover operations, where the chromosomes of two individuals cross at two points, genes between the two points are interchanged on the two chromosomes, resulting in two new individuals.
And the mutation operation is carried out, and one gene value in the chromosome is selected for mutation, so that the diversity of the population is increased, and the premature fall is avoided.
S38, base In the sample population P t Offspring population P t * A new population is composed and the new population is grouped.
Optionally, the sample-based population P in S38 t Offspring population P t * Forming a new population and grouping the new population includes:
s381, based on sample population P t Offspring population P t * A new population is formed.
S382, based on the dominant and non-dominant relations among individuals in the new population, the new population is subjected to rapid non-dominant sorting, and the layered population is obtained.
S383, grouping the layered population based on the elimination strategy.
In a possible embodiment, the population P in step S37 is combined t and Pt * Forming a new population, rapidly sorting the new population in a non-dominant manner through the dominant and non-dominant relationship among individuals, dividing the new population into multiple layers, and dividing the whole layered population into three groups M based on a elimination strategy 1 ,M 2 ,M 3 。
Wherein the fast non-dominant ranking step is as follows, for all i, j=1, 2 … … n, and j+.i, n is population size, comparing individuals x i And individual x j The dominant and non-dominant relationship method between the two is as follows: if there is no individual x j Is better than x i X is then i Marking as a non-dominant individual; let i=i+1, repeat the operation until all non-dominant individuals are found. The non-dominant individual set obtained by the above steps is the first non-dominant layer of the population, and so on, until the entire population is stratified.
The mathematical expression of the dominance is shown in the following formula (7):
in the formula ,x1 and x2 Two possible solutions to the double objective optimization problem (minimum problem), feasible solution x, respectively 1 The corresponding objective functions are f (x 1) and g(x1 ) Feasible solution x 2 The corresponding objective functions are f (x 2) and g(x2 ) If f (x 1 )＜f(x 2 ) And g (x) 1 )＜g(x 2 ) Then call x 1 Dominant x 2 。
Wherein, the step of the elimination strategy is as follows, M 1 The number of individuals in the population is not more than 1/2 of the population size, M 2 The number of individuals in the population is not smaller than the population size, and the remaining individuals are divided into M 3 . Second, delete M 3 The remaining M 1 and M2 And forming a population Q. Finally, generating the next generation population through a Canberra distance operator model.
S39, generating a parent population P of the next generation based on the new population after grouping and a Canberra distance operator model t+1 And step S37 is executed until the preset iteration times are reached, and the optimal blade geometric configuration of the original radial compressor blade after the optimization of the multiple working conditions is output.
In a possible implementation mode, based on a Canberra distance operator model sensitive to similar individuals, excellent individuals are screened out to generate a next generation parent population P t+1 。
The Canberra distance operator model has excellent classification capabilities. The difference is represented by the numerator in the Canberra distance formula, and the denominator normalizes the difference, so that the processing steps of the decision process on data with different scales are simplified; and when the comparison value is close, the molecules are also close to 0, and the molecular difference is amplified, so that the Canberra distance measure is very sensitive to the change of similar individuals, and the similarity between decision variables can be well distinguished.
Based on the advantages of invariance of the scale of the Canberra distance, very sensitivity to the change of the value close to 0 (> 0) and the similar value, and the like, the Canberra distance is applied to the generation of the parent population of the next generation, so that the calculation process can be simplified, the logic is clear and easy to understand, and the operation is simple.
Optionally, the Canberra distance operator model screening procedure is as follows: first, M 1 and M2 Is divided into a group Q. Second, find the emptyTwo individuals with the smallest inter-density, at least one of them belonging to M 2 The method comprises the steps of carrying out a first treatment on the surface of the Again, if an individual belongs to M 1 Another one belongs to M 2 Deleting the part belonging to M directly from Q 2 If both individuals belong to M 2 Deleting the individual with the minimum space density with other individuals in Q; finally return to the second step until M 1 and M2 The total number reaches the population scale.
Wherein, the Canberra distance operator d (x, y) mathematical model of two individuals is shown as the following formula (8):
wherein ,xi and yi Two different populations of individuals, n being the number of design variables.
Further, the iteration times t of the evolution process are specified according to the total time of optimization time consumption max The method comprises the steps of carrying out a first treatment on the surface of the Judging whether the cycle ending condition is met, if yes, ending the optimization flow; if not, returning to the step S37 to continue optimizing until the end condition is met, and further obtaining the multi-working-condition optimal aerodynamic geometry of the radial compressor blade.
The method comprises the steps of establishing a multi-working-condition optimization model of a radial compressor blade; generating an initial population by Latin hypercube sampling, dividing Pareto (Pareto) grades through rapid non-dominant sorting, screening excellent individuals based on a population elimination strategy and a Canberra distance operator model, generating a next generation parent population, and generating a child population by operating genetic operators (performing crossover, genetics and mutation) of the parent population; combining the parent population and the offspring population to obtain a new next generation total population; performing the same operation on the new population and circularly performing the operation; and based on experience, the optimal solution is selected from the Pareto front as the optimal geometric configuration of the radial compressor blade, so that the solving quality of the multi-task optimization problem is improved, and the comprehensive aerodynamic performance of the radial compressor is improved.
The improved algorithm can obviously improve the solving quality of the multi-objective optimization problem while considering the population convergence, the index data of the HVR (Hyper Volume Ratio, super volume ratio) after the algorithm improvement is shown in the following table 1, and the convergence index of the GD (Generational Distance, displacement) after the algorithm improvement is shown in the following table 2.
TABLE 1
TABLE 2
By the multi-working-condition optimization method for the radial compressor blade, the optimal geometric configuration of the complex curved surface blade of the radial compressor is obtained, the comprehensive aerodynamic performance of the multi-working conditions of the radial compressor blade is improved, and the performance parameter improvement conditions are as shown in the following table 3, namely the aerodynamic performance comparison before and after the application example optimization (rated working conditions) and the aerodynamic performance comparison before and after the application example optimization (common working conditions) of the table 4. Meanwhile, the adopted profile parameterization method can realize flexible configuration of the complex curved surface blade of the radial compressor; the increased radial constraint on the geometric control parameters is beneficial to the generation of smooth blades; ensuring the intersection of the impeller and the casing is beneficial to improving the grid generation rate in the optimization process. The technology has strong universality and has certain positive significance for promoting the development of the pneumatic design technology of the radial compressor blade.
TABLE 3 Table 3
| Parameters (parameters) | Initial value | Optimum value | Increment value |
| Adiabatic efficiency | 84.5％ | 85.3％ | +0.8％ |
| Total pressure ratio | 2.50 | 2.504 | +0.16％ |
| Flow (kg/s) | 0.1107 | 0.1202 | +8.58％ |
| Margin of margin | 12.1％ | 12.6％ | +0.5％ |
TABLE 4 Table 4
| Parameters (parameters) | Initial value | Optimum value | Increment value |
| Adiabatic efficiency | 86.14％ | 86.79％ | +0.65％ |
| Total pressure ratio | 1.6 | 1.602 | +0.13％ |
| Flow (kg/s) | 0.7735 | 0.8391 | +8.48％ |
| Margin of margin | 14.1％ | 14.3％ | +0.2％ |
Research results show that the pneumatic performance curve after optimization obviously moves upwards, and the pneumatic performance is obviously improved: the heat insulation efficiency of the rated working condition is improved by 0.8%, and the total pressure ratio is improved by 0.16%; the heat insulation efficiency of the common working condition is improved by 0.65%, the total pressure ratio is improved by 0.13%, and the margin is also ensured.
Compared with the traditional design optimization method, the radial compressor blade multi-working-condition optimization method based on the improved NSGA-II algorithm can effectively improve the problem of black boxes, improves the comprehensive aerodynamic performance of multiple working conditions, achieves the purpose of shape optimization, verifies the feasibility and universality of the method, and has good popularization and application values.
According to the embodiment of the invention, the multi-working-condition optimization method of the radial compressor blade can effectively improve the solving quality of the 'black box' problem, obtain excellent global optimization solution in limited iteration times, and improve the optimizing efficiency of the multi-working-condition geometric configuration of the radial compressor blade. Meanwhile, the adopted profile parameterization method can realize flexible configuration of the complex curved surface blade of the radial compressor; the increased radial constraint on the geometric control parameters is beneficial to the generation of smooth blades; ensuring the intersection of the impeller and the casing is beneficial to improving the grid generation rate in the optimization process.
As shown in fig. 3, an embodiment of the present invention provides a radial compressor blade multi-condition optimization apparatus 300 based on an improved NSGA-ii algorithm, where the apparatus 300 is applied to implement a radial compressor blade multi-condition optimization method based on an improved NSGA-ii algorithm, and the apparatus 300 includes:
an acquisition module 310 is configured to acquire a blade geometry of the original radial compressor.
An input module 320 for inputting the vane geometry of the original radial compressor into a constructed optimization model based on an improved non-dominant ordered genetic NSGA-ii algorithm.
And the output module 330 is configured to obtain an optimal multi-working-condition blade geometry after the blade of the original radial compressor is optimized based on the blade geometry of the original radial compressor and an optimization model based on an improved NSGA-ii algorithm.
Optionally, the output module 330 is further configured to:
s31, performing parameterization expression on the blade geometric configuration of the original radial compressor by adopting a profile mapping parameterization method to obtain a mapping model of the original blade suction surface and the unit spline surface and a mapping model of the original blade pressure surface and the unit spline surface.
S32, obtaining design vertex parameters of the unit spline surface and design space parameters of the unit spline surface by layout, and initializing a sample population P by using a Latin hypercube sampling method t 。
S33, a mapping model based on the original blade suction surface and the unit spline surface, a mapping model based on the original blade pressure surface and the unit spline surface and a sample population P t And obtaining the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade.
S34, obtaining a new blade geometric configuration based on the change amount of the suction surface of the original blade and the change amount of the pressure surface of the original blade.
S35, generating a grid template file based on the blade geometric configuration of the original radial compressor, and carrying out grid division on the new blade geometric configuration according to the grid template file to obtain a blade grid model of the new radial compressor.
S36, performing multi-working-condition steady-state numerical simulation calculation on a new radial compressor blade grid model to obtain a sample population P t Multiple operating pneumatic performance parameters for each individual.
S37, setting an objective function and constraint conditions of a blade geometry optimization flow of a new radial compressor under multiple working conditions, and performing sample population P based on the objective function and constraint conditions t Genetic operator operation is carried out to obtain a offspring population P t * Thereby obtaining the offspring population P t * Multiple operating pneumatic performance parameters for each individual.
S38, based on sample population P t Offspring population P t * A new population is composed and the new population is grouped.
S39, generating a parent population P of the next generation based on the new population after grouping and the Cannability Canberra distance operator model t+1 And step S37 is executed until the preset iteration times are reached, and the optimal blade geometric configuration of the original radial compressor blade after the optimization of the multiple working conditions is output.
Optionally, the output module 330 is further configured to:
s311, based on the blade geometric configuration of the original radial compressor, unitizing the geometric molded line of the blade suction surface of the original radial compressor and the geometric molded line of the blade pressure surface of the original radial compressor.
S312, constructing a unit mapping spline surface.
S313, obtaining a mapping model of the suction surface of the original blade and the unit spline surface and a mapping model of the pressure surface of the original blade and the unit spline surface according to the geometric molded line of the suction surface of the original blade after unitization, the geometric molded line of the pressure surface of the original blade after unitization and the unit mapping spline surface.
Optionally, the output module 330 is further configured to:
mapping model based on original blade suction surface and unit spline surface, mapping model based on original blade pressure surface and unit spline surface and sample population P t The method comprises the steps of solving characteristic parameters of a nonlinear equation set of a mapping model of an original blade suction surface and a unit spline surface and characteristic parameters of a nonlinear equation set of a mapping model of an original blade pressure surface and a unit spline surface, and further solving the variation of the original blade suction surface and the variation of the original blade pressure surface by perturbing design vertex parameters of the unit spline surface.
Optionally, the output module 330 is further configured to:
and superposing the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade on the curved surface of the original blade to obtain a new blade geometric configuration.
Optionally, the genetic operator operations include a selection operation, a crossover operation, and a mutation operation.
Wherein the selecting operation adopts a tournament selecting method.
Optionally, the output module 330 is further configured to:
s381, based on sample population P t Offspring population P t * A new population is formed.
S382, based on the dominant and non-dominant relations among individuals in the new population, the new population is subjected to rapid non-dominant sorting, and the layered population is obtained.
S383, grouping the layered population based on the elimination strategy.
Optionally, the Canberra distance operator model is represented by the following formula (1):
wherein ,xi and yi Two different populations of individuals, n being the number of design variables.
According to the embodiment of the invention, the multi-working-condition optimization method of the radial compressor blade can effectively improve the solving quality of the 'black box' problem, obtain excellent global optimization solution in limited iteration times, and improve the optimizing efficiency of the multi-working-condition geometric configuration of the radial compressor blade. Meanwhile, the adopted profile parameterization method can realize flexible configuration of the complex curved surface blade of the radial compressor; the increased radial constraint on the geometric control parameters is beneficial to the generation of smooth blades; ensuring the intersection of the impeller and the casing is beneficial to improving the grid generation rate in the optimization process.
Fig. 4 is a schematic structural diagram of an electronic device 400 according to an embodiment of the present invention, where the electronic device 400 may have a relatively large difference due to different configurations or performances, and may include one or more processors (central processing units, CPU) 401 and one or more memories 402, where at least one instruction is stored in the memories 402, and the at least one instruction is loaded and executed by the processor 401 to implement the following method for optimizing multiple working conditions of a radial compressor blade based on an improved NSGA-ii algorithm:
S1, acquiring the blade geometric configuration of the original radial compressor.
S2, inputting the blade geometric configuration of the original radial compressor into a constructed optimization model based on an improved non-dominant ordering genetic NSGA-II algorithm.
S3, obtaining the optimal blade geometry of the original radial compressor under multiple working conditions based on the blade geometry of the original radial compressor and an optimization model based on an improved NSGA-II algorithm.
In an exemplary embodiment, a computer readable storage medium, such as a memory comprising instructions executable by a processor in a terminal to perform the above-described radial compressor blade multi-task optimization method based on the modified NSGA-ii algorithm is also provided. For example, the computer readable storage medium may be ROM, random Access Memory (RAM), CD-ROM, magnetic tape, floppy disk, optical data storage device, etc.
It will be understood by those skilled in the art that all or part of the steps for implementing the above embodiments may be implemented by hardware, or may be implemented by a program for instructing relevant hardware, where the program may be stored in a computer readable storage medium, and the storage medium may be a read-only memory, a magnetic disk or an optical disk, etc.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.
Claims (8)
1. A radial compressor blade multi-task optimization method based on an improved NSGA-ii algorithm, the method comprising:
s1, acquiring the geometric configuration of a blade of an original radial compressor;
s2, inputting the blade geometric configuration of the original radial compressor into a constructed optimization model based on an improved non-dominant ordering genetic NSGA-II algorithm;
s3, obtaining the optimal blade geometry of the original radial compressor under multiple working conditions after blade optimization based on the blade geometry of the original radial compressor and an optimization model based on an improved NSGA-II algorithm;
the step S3 of obtaining the optimized multi-working condition optimal blade geometry of the original radial compressor blade based on the blade geometry of the original radial compressor and an optimized model based on an improved NSGA-II algorithm comprises the following steps:
s31, performing parameterization expression on the blade geometric configuration of the original radial compressor by adopting a profile mapping parameterization method to obtain a mapping model of an original blade suction surface and a unit spline surface and a mapping model of an original blade pressure surface and a unit spline surface;
S32, obtaining design vertex parameters of the unit spline surface and design space parameters of the unit spline surface by layout, and initializing a sample population by using a Latin hypercube sampling methodP t ；
S33, based on the mapping model of the original blade suction surface and the unit spline surface, the mapping model of the original blade pressure surface and the unit spline surface and the sample populationP t Obtaining the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade;
s34, obtaining a new blade geometric configuration based on the variable quantity of the suction surface of the original blade and the variable quantity of the pressure surface of the original blade;
s35, generating a grid template file based on the blade geometric configuration of the original radial compressor, and carrying out grid division on the new blade geometric configuration according to the grid template file to obtain a blade grid model of the new radial compressor;
s36, performing multi-working-condition steady-state numerical simulation calculation on the new radial compressor blade grid model to obtain a sample populationP t Multiple working condition pneumatic performance parameters of each individual;
s37, setting an objective function and constraint conditions of a blade geometry optimization flow of a new radial compressor under multiple working conditions, and carrying out population optimization on the sample based on the objective function and constraint conditions P t Genetic operator operation is carried out to obtain offspring population
Thereby obtaining the offspring population->
Multiple working condition pneumatic performance parameters of each individual;
s38, based on the sample populationP t Population of offspring
Forming a new population, and grouping the new population;
s39, generating a parent population of the next generation based on the new population after grouping and the Canberra distance operator model
And step S37 is executed until the preset iteration times are reached, and the optimal blade geometric configuration of the original radial compressor blade after the optimization of the multiple working conditions is output.
2. The method of claim 1, wherein the parameterizing the blade geometry of the original radial compressor by using the profile mapping parameterization method in S31 to obtain a mapping model of an original blade suction surface and a unit spline surface and a mapping model of an original blade pressure surface and a unit spline surface includes:
s311, unitizing a geometric line of a blade suction surface of the original radial compressor and a geometric line of a blade pressure surface of the original radial compressor based on the blade geometric configuration of the original radial compressor;
s312, constructing a unit mapping spline surface;
S313, obtaining a mapping model of the suction surface of the original blade and the unit spline surface and a mapping model of the pressure surface of the original blade and the unit spline surface according to the geometric molded line of the suction surface of the original blade after unitization, the geometric molded line of the pressure surface of the original blade after unitization and the unit mapping spline surface.
3. The method according to claim 1, wherein the mapping model based on the original blade suction surface and the unit spline surface, the mapping model of the original blade pressure surface and the unit spline surface, and the sample population in S33P t Obtaining the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade comprises the following steps:
mapping model based on original blade suction surface and unit spline surface, original blade pressure surface and unit splineMapping model of strip curved surface and sample populationP t The method comprises the steps of solving characteristic parameters of a nonlinear equation set of a mapping model of an original blade suction surface and a unit spline surface and characteristic parameters of a nonlinear equation set of a mapping model of an original blade pressure surface and a unit spline surface, and further solving the variation of the original blade suction surface and the variation of the original blade pressure surface by perturbing design vertex parameters of the unit spline surface.
4. The method of claim 1, wherein the deriving a new blade geometry in S34 based on the amount of change in the original blade suction side and the amount of change in the original blade pressure side comprises:
and superposing the variable quantity of the suction surface of the original blade and the variable quantity of the pressure surface of the original blade on the curved surface of the original blade to obtain a new blade geometric configuration.
5. The method of claim 1, wherein the genetic operator manipulation in S37 comprises a selection manipulation, a crossover manipulation, and a mutation manipulation;
wherein the selecting operation employs a tournament selection method.
6. The method of claim 1, wherein the step S38 is based on the sample populationP t Population of offspring
Forming a new population and grouping the new population comprises:
s381, based on the sample populationP t Population of offspring
Forming a new population;
s382, based on the dominant and non-dominant relationship among individuals in the new population, carrying out rapid non-dominant sorting on the new population to obtain a layered population;
s383, grouping the layered population based on the elimination strategy.
7. The method of claim 1, wherein the Canberra distance operator model in S39 is represented by the following formula (1):
wherein ,
and />
Two different populations of individuals, n being the number of design variables.
8. A radial compressor blade multi-condition optimization device based on an improved NSGA-ii algorithm, the device comprising:
the acquisition module is used for acquiring the blade geometric configuration of the original radial compressor;
the input module is used for inputting the blade geometric configuration of the original radial compressor into a constructed optimization model based on an improved non-dominant ordering genetic NSGA-II algorithm;
the output module is used for obtaining the optimal blade geometry of the original radial compressor under multiple working conditions after the blade optimization based on the blade geometry of the original radial compressor and an optimization model based on an improved NSGA-II algorithm;
the output module is further used for:
s31, performing parameterization expression on the blade geometric configuration of the original radial compressor by adopting a profile mapping parameterization method to obtain a mapping model of an original blade suction surface and a unit spline surface and a mapping model of an original blade pressure surface and a unit spline surface;
s32, layout is obtainedDesign vertex parameters of unit spline surface and design space parameters of unit spline surface, and initializing sample population by Latin hypercube sampling method P t ；
S33, based on the mapping model of the original blade suction surface and the unit spline surface, the mapping model of the original blade pressure surface and the unit spline surface and the sample populationP t Obtaining the variation of the suction surface of the original blade and the variation of the pressure surface of the original blade;
s34, obtaining a new blade geometric configuration based on the variable quantity of the suction surface of the original blade and the variable quantity of the pressure surface of the original blade;
s35, generating a grid template file based on the blade geometric configuration of the original radial compressor, and carrying out grid division on the new blade geometric configuration according to the grid template file to obtain a blade grid model of the new radial compressor;
s36, performing multi-working-condition steady-state numerical simulation calculation on the new radial compressor blade grid model to obtain a sample populationP t Multiple working condition pneumatic performance parameters of each individual;
s37, setting an objective function and constraint conditions of a blade geometry optimization flow of a new radial compressor under multiple working conditions, and carrying out population optimization on the sample based on the objective function and constraint conditionsP t Genetic operator operation is carried out to obtain offspring population
Thereby obtaining the offspring population->
Multiple working condition pneumatic performance parameters of each individual;
S38, based on the sample populationP t Population of offspring
Forming a new population, and grouping the new population;
s39, generating a parent population of the next generation based on the new population after grouping and the Canberra distance operator model
And step S37 is executed until the preset iteration times are reached, and the optimal blade geometric configuration of the original radial compressor blade after the optimization of the multiple working conditions is output. />
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