CN107066741B - Pneumatic shape optimization design method based on data mining - Google Patents

Pneumatic shape optimization design method based on data mining Download PDF

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CN107066741B
CN107066741B CN201710252211.8A CN201710252211A CN107066741B CN 107066741 B CN107066741 B CN 107066741B CN 201710252211 A CN201710252211 A CN 201710252211A CN 107066741 B CN107066741 B CN 107066741B
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pod
optimization
data
data mining
design
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CN107066741A (en
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段焰辉
范召林
吴文华
余雷
张培红
刘深深
童福林
赵鹏
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Computational Aerodynamics Institute of China Aerodynamics Research and Development Center
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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Abstract

The invention discloses a pneumatic shape optimization design method based on data mining, which comprises the following steps: firstly, optimally designing a geometric shape by adopting a random search method, and screening data in an optimization process; secondly, carrying out data mining processing on the screened data by using a data mining method based on POD to obtain a group of POD bases with geometric shapes; and thirdly, carrying out geometric shape parameterization on the optimization result of the first step by using the POD base obtained by data mining. Compared with the prior art, the invention has the following positive effects: according to the invention, the process data of the appearance optimization design is subjected to data mining by using a data mining method based on POD, so that design knowledge is obtained; secondary optimization based on design knowledge yields better results at higher efficiency.

Description

Pneumatic shape optimization design method based on data mining
Technical Field
The invention relates to a pneumatic shape optimization design method based on data mining.
Background
The process of pneumatic optimization design is also a process of data manufacturing, particularly, the application of the random search optimization method can generate massive process data, but only the final optimization result (certain data or a small part of data) is stored and applied, the massive process data implies design knowledge related to optimization, the design knowledge in the data is acquired and utilized by using a data mining technology, and the method is favorable for recognizing deeper design rules and constructing and improving the optimization design result.
The application of the data mining technology in the aerodynamic shape optimization design focuses on the analysis of multi-objective optimization design results. Japanese JAXA performs data mining on the results of the multi-objective optimization problem by a square difference analysis method, a rough set method, a self-organized mapping method, and an intrinsic Orthogonal Decomposition method (POD), respectively, and aims to help a designer select a final result in a non-inferior solution set. The Wang Wei in China utilizes K-Means cluster analysis, a rough set attribute importance algorithm and a decision tree method to process and analyze optimization process data, and obtains a direct implicit rule of blade optimization design variables and a target function. Guoshendong and the like adopt data mining technologies such as significant variable identification, total variation analysis, self-organization mapping and the like to mine knowledge of a design space, and the obtained design knowledge and an optimized design result are mutually verified.
The application of the current data mining in the aerodynamic shape optimization design mainly has the following defects:
the method is mainly used for result display of multi-dimensional and multi-target problems, and design knowledge cannot be provided;
the data mining for optimizing the design process data and the design space can only provide qualitative design knowledge, cannot quantify, and cannot directly provide guidance for subsequent optimization design.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides an aerodynamic shape optimization design method based on data mining.
The technical scheme adopted by the invention for solving the technical problems is as follows: a pneumatic shape optimization design method based on data mining comprises the following steps:
firstly, optimally designing a geometric shape by adopting a random search method, and screening data in an optimization process;
secondly, carrying out data mining processing on the screened data by using a data mining method based on POD to obtain a group of POD bases with geometric shapes;
and thirdly, carrying out geometric shape parameterization on the optimization result of the first step by using the POD base obtained by data mining.
Compared with the prior art, the invention has the following positive effects: according to the invention, the process data of the appearance optimization design is subjected to data mining by using a data mining method based on POD, so that design knowledge is obtained; secondary optimization based on design knowledge yields better results at higher efficiency.
Detailed Description
A pneumatic shape optimization design method based on data mining comprises the following steps:
firstly, optimizing and designing the geometric shape by adopting an optimization method of random search, storing process data of the optimized design, formulating a screening criterion according to design knowledge to be obtained, and screening the optimized process data.
The process of the random search method for optimally designing the geometric shape is as follows:
1) inputting: the variation range of design variables, the number n of samples (different methods are named differently, genetic algorithm is called individual, particle swarm method is called particle, etc.)sMaximum number of iteration steps n of the optimization methoditeA convergence criterion;
2) initialization: randomly determining n over a range of design variablessA sample is obtained;
3) and (3) convergence judgment: meet convergence criteria or reach maximum convergence step number, jump to 5), otherwise go to 4)
4) Updating a sample: updating the sample according to an evolution method of a specific optimization method;
5) and (3) outputting: and (4) optimal individuals.
Assuming the above optimization is at nopt(nopt≤nite) At the end of step, n is generateds×noptSamples, which are the optimization process data. Not all of these data contain favorable design knowledge and therefore must be screened.
Accurate screeningThe objective function is determined to yield improved data. The data obtained by screening comprises geometric and flow field information, and the data mining method only aims at the geometric data, so that only the geometric data is reserved. The data is expressed as a set of vectors: g1,g2,…,gmThe data in each vector is a sequence of three-dimensional coordinates of grid points of the geometric surface, e.g. giCan be expressed as:
Figure BDA0001272411300000031
wherein, X, Y and Z are the sequence of three coordinate values of the grid point according to the grid point number. If the number of the geometry surface grid points is n, the dimension of each vector is 3 n.
And secondly, carrying out data mining processing on the screened data by using a data mining method based on POD (POD) to obtain design knowledge. The design knowledge gained from this method is a set of geometric POD bases.
Firstly, solving the POD base requires data mining processing on data in the first step, and the processing method comprises the following steps:
si＝gi-g0
wherein s isiRepresenting snapshots, g0Either as an average of the grid point coordinate vectors or as an optimized initial profile. Minus g0In order to analyze the amount of disturbance for all geometries.
Secondly, the POD base can be obtained according to the Snapshot POD method:
Figure BDA0001272411300000045
the solving method is as follows: using the snapshot obtained in the first step: g1,g2,…,gmConstructing a matrix R by the following method:
Figure BDA0001272411300000041
after obtaining the matrix R, solving the eigenvalue and the eigenvector of the matrix, wherein the solving method comprises the following steps:
Ra＝λa
after the characteristic value and the characteristic vector are obtained, the solving method of the POD base is as follows:
Figure BDA0001272411300000042
wherein
Figure BDA0001272411300000043
The k-th POD base is indicated,
Figure BDA0001272411300000044
and the ith element of the feature vector corresponding to the kth feature value is represented.
And thirdly, carrying out geometric shape parameterization on the optimization result of the first step by using a POD base obtained by data mining, and carrying out second optimization. Using POD bases for parameterization has two advantages: firstly, the dimension reduction effect is achieved on the optimization design problem, and only about ten POD bases are needed to accurately express the geometric shape; secondly, the design space is reduced, and the design knowledge contained in the POD base limits the variation range of the geometric shape. The dimension reduction can improve the efficiency of optimization design, and a smaller design space is more beneficial to optimizing the optimization problem.
The parameterization method represents the geometry as follows:
Figure BDA0001272411300000051
wherein nBasis represents the number of POD bases used, i.e. the number of design variables in quadratic optimization, aiThe coefficient representing the ith POD base is a design variable in quadratic optimization. Determining nBasis by Error analysis method, firstly using different numbers of bases to represent target geometric shape, and then obtaining average Error Error of POD base representation shapeaveAnd maximum ErrormaxThe two errors are calculated as follows:
Figure BDA0001272411300000052
Figure BDA0001272411300000053
wherein
Figure BDA0001272411300000054
The jth element of the geometry vector represented by the POD base,
Figure BDA0001272411300000055
the jth element representing the exact geometry vector. The variation curves of the average error and the maximum error along with the number of the bases are obtained, the value of the error can be determined according to the expression precision (determined by practical engineering application) of the geometric model, and the number of the bases, namely nBasis, can be determined on the curves according to the value of the error.
The following NASA Rotor 37 blade design is an example to illustrate the technical effect brought by the method of the invention:
for the NASA Rotor 37 blade, under the design state, the optimal design is carried out at the peak efficiency point, the optimal design target is to improve the adiabatic efficiency, and meanwhile, the relative change of the flow rate and the total pressure ratio is limited within 0.5%. The configuration of the first optimization is as follows:
Figure BDA0001272411300000056
the optimization method comprises the following steps: the particle swarm method adopts 100 particles in total, and optimizes the method for 30 steps.
Figure BDA0001272411300000057
The parameterization method comprises the following steps: selecting three sections of the blade, suction surface and pressure of each section
Each surface is provided with 10 Hicks-Henne-shaped functions, and the total number of the functions is 60 design variables.
After the first optimization step is finished, 3000 process data are generated in total, wherein the improvement of the objective function accounts for 85%, and 2550 data are obtained by screening. After processing these data and finding the POD base, the result of the first optimization is shown as POD. It can be seen from the error analysis that only 8 POD bases are required to accurately express the geometric shape. A second optimization can now be carried out. The configuration of the second optimization is as follows:
Figure BDA0001272411300000061
the optimization method comprises the following steps: the particle swarm method adopts 40 particles in total, and optimizes 10 steps.
Figure BDA0001272411300000062
The parameterization method comprises the following steps: POD-based parameterization method, 8 design variables.
The results of the two optimizations are as follows:
efficiency of thermal insulation Total pressure ratio Flow (kg/m)
Initial profile 0.8588 1.9971 20.81
First optimization results 0.8685 1.9877 20.90
Second optimization results 0.8709 1.9874 20.91

Claims (2)

1. A pneumatic shape optimization design method based on data mining is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps of firstly, optimally designing the geometric shape by adopting a random search method, and screening data in the optimization process, wherein:
the method for optimally designing the geometric shape by adopting the random search method comprises the following steps:
1.1 inputting: variation range of design variables, number of samples nsMaximum iteration step number n of optimization methoditeAnd a convergence criterion;
1.2 initialization: randomly determining n over a range of design variablessA sample is obtained;
1.3 judging convergence: if the convergence criterion is met or the maximum convergence step number is reached, entering a step 1.4; otherwise, updating the sample according to the evolution method of the specific optimization method, and then returning to the step 1.1;
1.4 outputting: (ii) the most preferred individual;
the method for screening the data in the optimization process comprises the following steps:
with a set of vectors: g1,g2,…,gmRepresenting the geometric data retained after screening, wherein the data in each vector is the sequential arrangement of the three-dimensional coordinates of the geometric shape surface grid points, and is represented as:
Figure FDA0002303571720000011
wherein, X, Y and Z are sequences formed by three coordinate values of grid points according to grid point numbers in sequence, the dimension of each vector is 3n, and n is the number of grid points on the surface of the geometric shape;
step two, carrying out data mining processing on the screened data by using a data mining method based on POD to obtain a group of POD bases with geometric shapes:
2.1 calculating s as followsi：
si＝gi-g0
Wherein s isiRepresenting snapshots, g0The mean value of the grid point coordinate vectors or the optimized initial shape;
2.2 Using the snapshot obtained in step 2.1: g1,g2,…,gmConstructing a matrix R by the following method:
Figure FDA0002303571720000021
2.3 solving eigenvalues and eigenvectors of the matrix R:
Ra＝λa
2.4 solving for the POD base using the following equation:
Figure FDA0002303571720000022
wherein
Figure FDA0002303571720000023
The k-th POD base is indicated,
Figure FDA0002303571720000024
representing the ith element of the feature vector corresponding to the kth feature value;
thirdly, carrying out geometric shape parameterization on the optimization result of the first step by using a POD base obtained by data mining:
3.1 the geometry is expressed as:
Figure FDA0002303571720000025
wherein nBasis represents the number of POD groups used, aiCoefficients representing the ith POD base;
3.2 calculate nBasis using error analysis method.
2. The aerodynamic shape optimization design method based on data mining of claim 1, characterized in that: the method for calculating nBasis by adopting an error analysis method comprises the following steps:
(1) representing the target geometry using different numbers of POD bases;
(2) obtaining an average Error of a POD-based expressed profileaveAnd maximum Errormax：
Figure FDA0002303571720000026
Figure FDA0002303571720000027
In the formula (I), the compound is shown in the specification,
Figure FDA0002303571720000028
the jth element of the geometry vector represented by the POD base,
Figure FDA0002303571720000029
the jth element representing the exact geometry vector;
(3) obtaining a variation curve of the average error and the maximum error along with the number of the bases, determining the value of the error according to the expression precision of the geometric model, and determining the number of the bases on the curve by using the value of the error to obtain nBasis.
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