CN113656890A - Aircraft optimization method based on mixed radial basis function neural network - Google Patents

Aircraft optimization method based on mixed radial basis function neural network Download PDF

Info

Publication number
CN113656890A
CN113656890A CN202110912288.XA CN202110912288A CN113656890A CN 113656890 A CN113656890 A CN 113656890A CN 202110912288 A CN202110912288 A CN 202110912288A CN 113656890 A CN113656890 A CN 113656890A
Authority
CN
China
Prior art keywords
radial basis
aircraft
basis function
optimization
neural network
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202110912288.XA
Other languages
Chinese (zh)
Inventor
龙腾
叶年辉
史人赫
刘震宇
太鑫辉
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Institute of Technology BIT
Original Assignee
Beijing Institute of Technology BIT
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Institute of Technology BIT filed Critical Beijing Institute of Technology BIT
Priority to CN202110912288.XA priority Critical patent/CN113656890A/en
Publication of CN113656890A publication Critical patent/CN113656890A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/15—Vehicle, aircraft or watercraft design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/045—Combinations of networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/08—Learning methods

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Evolutionary Computation (AREA)
  • General Physics & Mathematics (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • Software Systems (AREA)
  • Artificial Intelligence (AREA)
  • Molecular Biology (AREA)
  • Computer Hardware Design (AREA)
  • Biophysics (AREA)
  • Computing Systems (AREA)
  • Biomedical Technology (AREA)
  • Data Mining & Analysis (AREA)
  • Mathematical Physics (AREA)
  • Computational Linguistics (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • General Health & Medical Sciences (AREA)
  • Health & Medical Sciences (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Medical Informatics (AREA)
  • Automation & Control Theory (AREA)
  • Aviation & Aerospace Engineering (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Feedback Control In General (AREA)

Abstract

The invention discloses an aircraft optimization method based on a hybrid radial basis function neural network, and belongs to the field of aircraft design optimization. The method adopts a Latin hyper-square test design method to construct initial sample points and randomly group the initial sample points into a training sample point set and an evaluation sample point set. The method comprises the steps of training neural networks of different radial basis function types by using training sample points, solving weight coefficients of the neural networks of different radial basis function types and weighting by using evaluation sample points and generalized inverse matrixes, so that the advantages of the radial basis function of different types are fully utilized to improve approximation accuracy, the construction risk of the single-core radial basis function neural network caused by the lack of prior information can be effectively reduced, finally, the constructed hybrid radial basis function neural network is optimized by combining with an intelligent optimization algorithm, and the rapid optimization of the performance of an aircraft system is realized. The method has important significance in the aspects of relieving the calculation time consumption of aircraft optimization, improving the optimization efficiency and the like.

Description

Aircraft optimization method based on mixed radial basis function neural network
Technical Field
The invention relates to an aircraft optimization method based on a hybrid radial basis function neural network, and belongs to the field of aircraft design optimization.
Background
With the development of computer software and hardware technology, high-precision simulation analysis models are widely applied in the field of aircraft overall design, such as Finite Element Analysis (FEA), Computational Fluid Dynamics (CFD) and the like. While high-precision analytical models improve the accuracy of analysis and design confidence, they also significantly increase the computational cost of the simulation, e.g., aircraft CFD models typically require several hours to complete a pneumatic simulation analysis. Because the traditional optimization methods (such as genetic algorithm, particle swarm algorithm and the like) usually need to directly call thousands of analysis models to search a design space, the design optimization of the aircraft faces technical bottlenecks of high time consumption, low efficiency and long period. In order to reduce the calculation cost of the aircraft system design optimization problem, a common method is to construct a proxy model by a mathematical means to approximate the original optimization problem and replace the original simulation analysis model for optimization. Compared with other proxy models, the radial basis function neural network has remarkable advantages in the aspects of robustness, approximation performance, construction efficiency and the like, and is widely applied to complex system design. Considering that the aircraft analysis model is a "black box" function with unknown mathematical structure, it is difficult to determine the optimal radial basis function type in advance. In order to overcome the difficulties, a hybrid radial basis function neural network modeling method is researched, through combined weighting of radial basis function neural networks of different radial basis types, the advantages of different types of radial basis functions are fully utilized to improve approximation accuracy, the risk of agent model construction caused by lack of prior information is reduced, and rapid optimization of an aircraft is finally realized.
In order to better explain the technical scheme of the invention, the following briefly introduces the involved models:
the radial basis function neural network is an efficient single hidden layer feedforward neural network, and has the advantages of simple topological structure, capability of approximating any nonlinear function and the like. The radial basis function neural network adopts a radial basis function as an activation function of hidden layer neurons, and takes a linear combination of hidden layer outputs as an output layer. The regression prediction model corresponding to the output layer of the radial basis function neural network is shown as the formula (1).
Figure BDA0003204235850000011
Wherein n ispIs the number of hidden neurons, betaiThe link weight, x, for the ith hidden layer neuron and the output layer neuroniIs the center of the corresponding hidden layer neuron, c is the shape coefficient,
Figure BDA0003204235850000021
is a radial basis function. Common radial basis function types are shown in table 1.
TABLE 1 common radial basis function types
Figure BDA0003204235850000022
When the number of hidden layer neurons is the number of training sample points and the center of each hidden layer neuron is a training sample point, the radial basis function neural network becomes an interpolation type proxy model, and the basic form of the interpolation type proxy model is shown in a formula (2).
Figure BDA0003204235850000023
Wherein n issIs the number of sample points. The link weight vector β can be obtained by solving the interpolation condition shown in equation (3).
Figure BDA0003204235850000024
Disclosure of Invention
The invention discloses an aircraft optimization method based on a mixed radial basis function neural network, which aims to solve the technical problems that: the method comprises the steps of weighting a plurality of mixed radial basis function neural networks by generalized inverse solution of weight coefficients, constructing the mixed radial basis function neural networks, fully utilizing the advantages of different types of radial basis functions to improve approximation precision, reducing agent model construction risks caused by lack of prior information, and improving approximation performance, optimization efficiency and robustness of different aircraft problems.
The purpose of the invention is realized by the following technical scheme.
The invention discloses an aircraft optimization method based on a hybrid radial basis function neural network, which adopts a Latin hyper-square test design method to construct initial sample points and randomly group the initial sample points into a training sample point set and an evaluation sample point set. The method comprises the steps of training neural networks of different radial basis function types by using training sample points, solving weight coefficients of the neural networks of different radial basis function types and weighting by using evaluation sample points and generalized inverse matrixes, so that the advantages of the radial basis function of different types are fully utilized to improve approximation accuracy, the construction risk of the single-core radial basis function neural network caused by the lack of prior information can be effectively reduced, finally, the constructed hybrid radial basis function neural network is optimized by combining with an intelligent optimization algorithm, and the rapid optimization of the performance of an aircraft system is realized. The method has important significance in the aspects of relieving the calculation time consumption of aircraft optimization, improving the optimization efficiency and the like.
The invention discloses an aircraft optimization method based on a hybrid radial basis function neural network, which comprises the following steps:
step A: determining initial conditions and algorithm parameters of an aircraft system optimization problem, wherein the initial conditions comprise an optimized aircraft analysis model, design variables of the optimization problem, an objective function, constraint conditions and a design space; the algorithm parameters comprise the number n of training sample pointstAnd evaluating the number of sample points nw。
And B: generating initial sample points by an optimal Latin hyper-square design method, calculating the real response value of a model at the sample points, and grouping the sample points into training sample points and evaluation sample points.
Generating n scale in design space by adopting optimal Latin hyper-square design method (Maximim-OLHD)t+nwAnd calculating the true response value of the aircraft analysis model at the sample point. On the basis, randomly dividing the sample points into two groups with different numbers, wherein one group has the size of ntFor training the set of sample points for training radial basis function neural networks of different radial basis types, another set of sizes nwTo evaluate a set of sample points for computing a hybrid neural network combining weight coefficient vector.
And C: and training the radial basis function neural networks of different types of kernel functions based on the interpolation conditions of the response values of the real models at the training sample points to obtain the radial basis function neural networks of the corresponding kernel function types.
And (4) for the jth radial basis function neural network with different types of kernel functions, training by using the training sample point set generated in the step (B) according to the selected radial basis kernel function, wherein a calculation formula is shown as a formula (4).
Figure BDA0003204235850000031
Wherein, cjIs the shape coefficient, beta, of the j radial basis function neural networkjWeight vectors are linked for the jth radial basis function neural network,
Figure BDA0003204235850000041
for the jth radial basis function, the response value y of the aircraft analysis model is obtained by the equation (5) and the training sample pointtThus obtaining the product.
Figure BDA0003204235850000042
Step D: based on the interpolation condition of the response value of the real model at the evaluation sample point, the combined weight coefficients corresponding to the radial basis function neural networks of different types of kernel functions are obtained by adopting the generalized inverse matrix to obtain the hybrid radial basis function neural network, so that the complex optimization process of the weight coefficients in the traditional hybrid agent model method can be avoided, and the approximate modeling efficiency of the aircraft is improved. By combining the advantages of different radial basis function neural networks, the risk of constructing the proxy model caused by lack of prior information is reduced, and the robustness and the approximation performance of different aircraft optimization problems are improved.
Combining the weight coefficient vector omega according to the evaluation sample point and the interpolation conditionjSatisfy formula (6)
Figure BDA0003204235850000043
In the formula, ωjFor the combining weight coefficients of the jth neural network,
Figure BDA0003204235850000044
and m is the number of types of radial basis functions and is the output of the predictive aircraft analysis model of the jth neural network. Converting equation (6) into a matrix form, i.e.
Bω＝yw (7)
In the formula, ywIn order to evaluate the aircraft analysis model response value of the sample point, B is a coefficient matrix, and a specific expression is shown in a formula (8).
Figure BDA0003204235850000045
Considering that the number of the evaluation sample point sets is larger than the number of the types of the radial basis functions, the formula (7) is an over-determined equation set, and a generalized quasi-matrix is adopted to obtain a weight coefficient vector, namely
ω＝(BHB)-1BHyw (9)
And (3) performing weighted combination on the radial basis function neural networks of different radial basis types according to the formula (6), namely solving the weight coefficient through the generalized inverse matrix to obtain the hybrid radial basis function neural network, so that the complex optimization process of the weight coefficient in the traditional hybrid agent model method can be avoided, and the approximate modeling efficiency of the aircraft is improved.
Step E: approximation model for aircraft systems using heuristic optimization algorithms
Figure BDA0003204235850000051
And optimizing to obtain an approximate optimal solution of the aircraft system, calling a high-precision analysis model to calculate to obtain a response value of the black box system at the optimal solution, and outputting the obtained optimal solution and the response value as a final optimization result of the aircraft system, namely outputting a final optimization scheme of the aircraft based on the mixed radial basis function neural network.
Step F: the aircraft optimization method based on the hybrid radial basis function neural network, which is described in the steps A to E, is applied to the field of aircraft optimization including a high-time-consumption simulation analysis model, and corresponding engineering problems are solved.
The aircraft optimization field in the step F comprises structural optimization including high time-consuming finite element analysis, pneumatic optimization including high-precision fluid mechanics analysis and multidisciplinary design optimization of a complex aircraft system, and can effectively improve optimization efficiency and shorten a design period.
The complex aircraft system comprises a solid rocket engine, an orbit satellite platform, a missile and a civil aircraft.
Has the advantages that:
1. the aircraft optimization method based on the hybrid radial basis function neural network disclosed by the invention combines the advantages of different radial basis function neural networks, reduces the risk of constructing the proxy model caused by lack of prior information, improves the robustness of the hybrid radial basis function neural network for approximating different optimization problems, enables the optimization method to be suitable for the optimization problems with different numerical characteristics, and has important significance for improving the optimization quality of a complex aircraft system.
2. According to the aircraft optimization method based on the hybrid radial basis function neural network, the sample points are grouped and combined with the generalized inverse matrix to solve the combined weight coefficient of the hybrid radial basis function neural network, so that the complex optimization calculation solution of the weight coefficient in the traditional hybrid agent model method can be avoided, and the approximate modeling efficiency of a black box system is improved.
Drawings
FIG. 1 is a schematic diagram of a hybrid neural network topology;
FIG. 2 is a flow chart of a hybrid radial basis function neural network-based aircraft optimization method;
FIG. 3 is an initial protocol cartridge configuration;
FIG. 4 shows the optimized configuration of the powder column;
FIG. 5 is a graph comparing pressure time curves before and after optimization;
FIG. 6 is a graph comparing time curves of the thrust before and after optimization.
Detailed Description
For a better understanding of the objects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings.
As shown in fig. 2, the aircraft optimization method based on the hybrid radial basis function neural network disclosed in this embodiment is suitable for aircraft optimization problems with different numerical characteristics, and is helpful for improving optimization efficiency and reducing design cost. The specific implementation of this example is as follows:
step A: determining initial conditions and algorithm parameters of an aircraft system optimization problem, wherein the initial conditions comprise an optimized aircraft analysis model, design variables of the optimization problem, an objective function, constraint conditions and a design space.
The algorithm parameters comprise the number n of training sample pointstAnd evaluating the number of sample points nw. The algorithm parameter setting is shown in equation (10).
Figure BDA0003204235850000061
In the formula, nvRepresenting the dimensions of the aircraft system optimization problem.
And B: generating initial sample points by an optimal Latin hyper-square design method, calculating the real response value of a model at the sample points, and grouping the sample points into training sample points and evaluation sample points.
Generating n scale in design space by adopting optimal Latin hyper-square design method (Maximim-OLHD)t+nwAnd calculating the true response value of the aircraft analysis model at the sample point. On the basis, randomly dividing the sample points into two groups with different numbers, wherein one group has the size of ntFor training the set of sample points for training radial basis function neural networks of different radial basis types, another set of sizes nwTo evaluate a set of sample points for computing a hybrid neural network combining weight coefficient vector.
And C: and training the radial basis function neural networks of different types of kernel functions based on the interpolation conditions of the response values of the real models at the training sample points to obtain the radial basis function neural networks of the corresponding kernel function types.
In this example, three radial basis functions as shown in table 2 were chosen as the neural network sum function. And (4) for the j radial basis function neural network with different types of kernel functions, training by using the training sample point set generated in the step (B) according to the selected radial basis kernel function, wherein the calculation formula is shown as a formula (11).
Figure BDA0003204235850000071
Wherein, cjThe shape coefficients of the jth neural network are all set to 1 in the embodiment; beta is ajWeight vectors are linked for the jth radial basis function neural network,
Figure BDA0003204235850000072
for the jth radial basis function, the aircraft analysis model response value y can be obtained by the equation (12) and the training sample pointtThus obtaining the product.
Figure BDA0003204235850000073
TABLE 2 radial basis function types selected for the examples
Figure BDA0003204235850000074
Step D: based on the interpolation condition of the response value of the real model at the evaluation sample point, the combined weight coefficients corresponding to the radial basis function neural networks of different types of kernel functions are obtained by adopting the generalized inverse matrix to obtain the hybrid radial basis function neural network, so that the complex optimization process of the weight coefficients in the traditional hybrid agent model method can be avoided, and the approximate modeling efficiency of the aircraft is improved. By combining the advantages of different radial basis function neural networks, the risk of constructing the proxy model caused by lack of prior information is reduced, and the robustness and the approximation performance of different aircraft optimization problems are improved.
Combining the weight coefficient vector omega according to the evaluation sample point and the interpolation conditionjSatisfy formula (13)
Figure BDA0003204235850000075
In the formula, ωjFor the combining weight coefficients of the jth neural network,
Figure BDA0003204235850000076
and (3) outputting the predicted aircraft analysis model of the jth neural network, wherein m is the number of radial basis function types. Converting equation (13) into a matrix form, i.e.
Bω＝yw(14) In the formula, ywIn order to evaluate the aircraft analysis model response value of the sample point, B is a coefficient matrix, and a specific expression is shown in formula (15).
Figure BDA0003204235850000081
Considering that the number of the evaluation sample point sets is larger than the number of the types of the radial basis functions, the formula (14) is an over-determined equation set, and a generalized quasi-matrix is adopted to obtain a weight coefficient vector, namely
ω＝(BHB)-1BHyw (16)
The radial basis function neural networks of different radial basis types are subjected to weighted combination according to the formula (16), namely, the mixed radial basis function neural network is obtained by solving the weight coefficient through the generalized inverse matrix, so that the complex optimization process of the weight coefficient in the traditional mixed proxy model method can be avoided, and the approximate modeling efficiency of the aircraft is improved. Step E: approximation model for aircraft systems using heuristic optimization algorithms
Figure BDA0003204235850000082
And optimizing to obtain an approximate optimal solution of the aircraft system, calling a high-precision analysis model to calculate to obtain a response value of the black box system at the optimal solution, and outputting the obtained optimal solution and the response value as a final optimization result of the aircraft system. In this embodiment, a differential evolution algorithm is selected as a heuristic optimization algorithm for solving an aircraft system approximation model.
Step F: the aircraft optimization method based on the hybrid radial basis function neural network, which is described in the steps A to E, is applied to the field of aircraft optimization including a high-time-consumption simulation analysis model, and corresponding engineering problems are solved.
To better illustrate the objects and engineering utility of the present invention, the invention is further illustrated by an example of a solid rocket motor, with reference to the accompanying drawings and tables.
In this case, the mathematical model of the optimization problem is shown in equation (17) as the engine mass ratio PSRMMaximum objective function, taking into account the engine operating time tworkAverage working thrust of engine
Figure BDA0003204235850000083
Deviation of maximum thrust and average thrust of engine
Figure BDA0003204235850000084
Average jetOutlet pressure intensity
Figure BDA0003204235850000085
Diameter of nozzle outlet
Figure BDA0003204235850000086
And fraction of packed column
Figure BDA0003204235850000087
The constraint of (2). The design variable value range of the optimization problem is as follows: dcomb∈[0.6m,0.7]，Ith∈[1.2e7N·s,1.6e7N·s]，Rfront∈[0.04m,0.08m]，Rcore∈[0.10m,0.16m]，Rrear∈[0.18m,0.24m]，Hfin∈[0.35m,0.55m]，Lfin∈[0.20m,0.60m]，αfin∈[30°,60°]，Rthroat∈[0.10m,0.14m]，ε∈[12,20]，αnoz∈[45°,55°]，βnoz∈[12°,17°]。
Figure BDA0003204235850000091
The aircraft optimization method based on the hybrid radial basis function neural network is set as follows: the number of training samples is 240, the number of evaluation samples is 60, the initial population of the differential evolution algorithm is 100, the scaling factor is 0.8, the mutation probability is 0.9, and the maximum evolution algebra is 500. To further illustrate the optimization efficiency of the aircraft optimization method based on the hybrid radial basis function neural network, the maximum number of calls of the genetic algorithm is set to 500 in comparison with the standard genetic algorithm. The optimized optimal solution design variable pairs are shown in table 1, the constraint comparison conditions are shown in table 2, and the objective function pairs are shown in table 3.
TABLE 1 comparison of design variables of solid rocket engine schemes before and after optimization
Figure BDA0003204235850000101
TABLE 2 comparison of constraint conditions of solid rocket engine schemes before and after optimization
Figure BDA0003204235850000102
TABLE 3 comparison of objective function of solid rocket engine scenarios before and after optimization
Figure BDA0003204235850000103
The optimization result shows that compared with a genetic algorithm, the calculation cost of the method can be reduced by more than 40%, meanwhile, a scheme which meets the actual engineering requirement and has a high impact quality ratio can be obtained, the expected invention purpose is realized, and the reasonability, the effectiveness and the engineering practicability of the method are verified.
The above detailed description is intended to illustrate the objects, aspects and advantages of the present invention, and it should be understood that the above detailed description is only exemplary of the present invention, and is not intended to limit the scope of the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. An aircraft optimization method based on a hybrid radial basis function neural network is characterized in that: comprises the following steps of (a) carrying out,
step A: determining initial conditions and algorithm parameters of an aircraft system optimization problem, wherein the initial conditions comprise an optimized aircraft analysis model, design variables of the optimization problem, an objective function, constraint conditions and a design space; the algorithm parameters comprise the number n of training sample pointstAnd evaluating the number of sample points nw；
And B: generating initial sample points by an optimal Latin hyper-square design method, calculating the real response value of a model at the sample points, and grouping the sample points into training sample points and evaluation sample points;
and C: training radial basis function neural networks of different types of kernel functions based on interpolation conditions of real model response values at training sample points to obtain radial basis function neural networks of corresponding kernel function types;
step D: based on the interpolation condition of the response value of the real model at the evaluation sample point, the combined weight coefficients corresponding to the radial basis function neural networks of different types of kernel functions are obtained by adopting the generalized inverse matrix to obtain a mixed radial basis function neural network, so that the complex optimization process of the weight coefficients in the traditional mixed agent model method can be avoided, and the approximate modeling efficiency of the aircraft is improved; by combining the advantages of different radial basis function neural networks, the risk of constructing the proxy model caused by lack of prior information is reduced, and the robustness and the approximation performance of different aircraft optimization problems are improved;
step E: approximation model for aircraft systems using heuristic optimization algorithms
Figure FDA0003204235840000011
And optimizing to obtain an approximate optimal solution of the aircraft system, calling a high-precision analysis model to calculate to obtain a response value of the black box system at the optimal solution, and outputting the obtained optimal solution and the response value as a final optimization result of the aircraft system, namely outputting a final optimization scheme of the aircraft based on the mixed radial basis function neural network.
2. The hybrid radial basis function neural network-based aircraft optimization method of claim 1, wherein:
further comprising step F: applying the aircraft optimization method based on the hybrid radial basis function neural network from the step A to the step E to the aircraft optimization field containing a high-time-consumption simulation analysis model to solve the corresponding engineering problem;
the aircraft optimization field in the step F comprises structural optimization including high time-consuming finite element analysis, pneumatic optimization including high-precision fluid mechanics analysis and multidisciplinary design optimization of a complex aircraft system, and can effectively improve optimization efficiency and shorten a design period.
3. The hybrid radial basis function neural network-based aircraft optimization method of claim 2, wherein: the complex aircraft system comprises a solid rocket engine, an orbit satellite platform, a missile and a civil aircraft.
4. An aircraft optimization method based on a hybrid radial basis function neural network, according to claim 1, 2 or 3, characterized in that: the step B is realized by the method that,
generating n scale in design space by adopting optimal Latin hyper-square design method (Maximim-OLHD)t+nwAnd calculating a true response value of the aircraft analysis model at the sample point; on the basis, randomly dividing the sample points into two groups with different numbers, wherein one group has the size of ntFor training the set of sample points for training radial basis function neural networks of different radial basis types, another set of sizes nwTo evaluate a set of sample points for computing a hybrid neural network combining weight coefficient vector.
5. The hybrid radial basis function neural network-based aircraft optimization method of claim 4, wherein: the step C is realized by the method that,
for the j radial basis function neural network with different types of kernel functions, training by using the training sample point set generated in the step B according to the selected radial basis kernel function, wherein a calculation formula is shown as a formula (4);
Figure FDA0003204235840000021
wherein, cjIs the shape coefficient, beta, of the j radial basis function neural networkjWeight vectors are linked for the jth radial basis function neural network,
Figure FDA0003204235840000022
for the jth radial basis function, the response value y of the aircraft analysis model is obtained by the equation (5) and the training sample pointtObtaining;
Figure FDA0003204235840000023
6. the hybrid radial basis function neural network-based aircraft optimization method of claim 5, wherein: the step D is realized by the method that,
combining the weight coefficient vector omega according to the evaluation sample point and the interpolation conditionjSatisfy formula (6)
Figure FDA0003204235840000024
In the formula, ωjFor the combining weight coefficients of the jth neural network,
Figure FDA0003204235840000025
outputting a predictive aircraft analysis model of a jth neural network, wherein m is the number of types of radial basis functions; converting equation (3) into a matrix form, i.e.
Bω＝yw (4)
In the formula, ywB is a coefficient matrix, and a specific expression is shown as a formula (8) in order to evaluate the aircraft analysis model response value of a sample point;
Figure FDA0003204235840000031
considering that the number of the evaluation sample point sets is larger than the number of the types of the radial basis functions, the formula (4) is an over-determined equation set, and a generalized quasi-matrix is adopted to obtain a weight coefficient vector, namely
ω＝(BHB)-1BHyw (6)
The radial basis function neural networks of different radial basis types are subjected to weighted combination according to the formula (3), namely, the mixed radial basis function neural network is obtained by solving the weight coefficient through the generalized inverse matrix, so that the complex optimization process of the weight coefficient in the traditional mixed agent model method can be avoided, and the approximate modeling efficiency of the aircraft is improved.
CN202110912288.XA 2021-08-10 2021-08-10 Aircraft optimization method based on mixed radial basis function neural network Pending CN113656890A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110912288.XA CN113656890A (en) 2021-08-10 2021-08-10 Aircraft optimization method based on mixed radial basis function neural network

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110912288.XA CN113656890A (en) 2021-08-10 2021-08-10 Aircraft optimization method based on mixed radial basis function neural network

Publications (1)

Publication Number Publication Date
CN113656890A true CN113656890A (en) 2021-11-16

Family

ID=78491000

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110912288.XA Pending CN113656890A (en) 2021-08-10 2021-08-10 Aircraft optimization method based on mixed radial basis function neural network

Country Status (1)

Country Link
CN (1) CN113656890A (en)

Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102682173A (en) * 2012-05-13 2012-09-19 北京理工大学 Optimization design method based on self-adaptive radial basis function surrogate model for aircraft
CN104766137A (en) * 2015-03-27 2015-07-08 中国人民解放军信息工程大学 Network security posture prediction method based on evidence theory
CN105550744A (en) * 2015-12-06 2016-05-04 北京工业大学 Nerve network clustering method based on iteration
CN109117954A (en) * 2018-08-13 2019-01-01 北京理工大学 Black smoker design optimization method based on hybrid radial base neural net
CN110243603A (en) * 2019-05-30 2019-09-17 沈阳化工大学 Based on Welch conversion-radial direction base nerve net Fault Diagnosis of Roller Bearings
CN111478314A (en) * 2020-03-20 2020-07-31 广西电网有限责任公司电力科学研究院 Transient stability assessment method for power system
EP3822880A1 (en) * 2018-10-22 2021-05-19 Ennew Digital Technology Co., Ltd. Load prediction method and apparatus based on neural network

Patent Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102682173A (en) * 2012-05-13 2012-09-19 北京理工大学 Optimization design method based on self-adaptive radial basis function surrogate model for aircraft
CN104766137A (en) * 2015-03-27 2015-07-08 中国人民解放军信息工程大学 Network security posture prediction method based on evidence theory
CN105550744A (en) * 2015-12-06 2016-05-04 北京工业大学 Nerve network clustering method based on iteration
CN109117954A (en) * 2018-08-13 2019-01-01 北京理工大学 Black smoker design optimization method based on hybrid radial base neural net
EP3822880A1 (en) * 2018-10-22 2021-05-19 Ennew Digital Technology Co., Ltd. Load prediction method and apparatus based on neural network
CN110243603A (en) * 2019-05-30 2019-09-17 沈阳化工大学 Based on Welch conversion-radial direction base nerve net Fault Diagnosis of Roller Bearings
CN111478314A (en) * 2020-03-20 2020-07-31 广西电网有限责任公司电力科学研究院 Transient stability assessment method for power system

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
龙腾;刘建;WANG G GARY;刘莉;史人赫;郭晓松;: "基于计算试验设计与代理模型的飞行器近似优化策略探讨", 机械工程学报, no. 14, pages 79 - 99 *

Similar Documents

Publication Publication Date Title
CN110222828B (en) Unsteady flow field prediction method based on hybrid deep neural network
CN110263925A (en) A kind of hardware-accelerated realization framework of the convolutional neural networks forward prediction based on FPGA
CN110210072B (en) Method for solving high-dimensional optimization problem based on approximate model and differential evolution algorithm
CN113642105A (en) Multi-scale model construction method and device of ship power system and electronic equipment
CN113449474A (en) Pipe forming quality prediction method based on improved Husky algorithm optimization BP neural network
CN111027250B (en) Modeling method for special-shaped curved surface reinforcement shell based on grid deformation technology
CN112580855A (en) Cable group steady-state temperature rise prediction method based on self-adaptive variation PSO-BP neural network
CN116049977B (en) Parameter multi-objective optimization method for aero-engine combustion chamber
CN112414668A (en) Wind tunnel test data static bomb correction method, device, equipment and medium
He et al. Aerodynamic optimisation of a high-speed train head shape using an advanced hybrid surrogate-based nonlinear model representation method
CN113868956A (en) Two-stage self-adaptive combined proxy model modeling method
CN115659843A (en) Method for constructing display dynamics model by using artificial intelligence technology
CN115017808A (en) Pipeline erosion prediction method based on improved butterfly algorithm optimization HKELM
CN114564787A (en) Bayesian optimization method, device and storage medium for target-related airfoil design
CN115879335A (en) Fluid multi-physical-field parameter prediction method based on graph-generated neural network
Tang et al. A hydrodynamic prediction model of throttle orifice plate using space filling and adaptive sampling method
CN113656890A (en) Aircraft optimization method based on mixed radial basis function neural network
CN116401755B (en) CNN-LSTM-Attention network structure-based solid rocket engine total thrust prediction method
CN117421703A (en) Depth sign regression accelerator and depth sign regression method
CN114329315B (en) Static aeroelastic rapid solving method based on dynamic modal decomposition technology
CN114880971A (en) Implicit method adopted by computational fluid dynamics software
CN113240094A (en) SVM-based LSTM hyper-parameter optimization method, system, medium and device
Yang et al. Non-matching meshes data transfer using Kriging model and greedy algorithm
Zhu et al. Multi-objective optimization design of airfoil and wing
Zhao Neural network with data augmentation in multi-objective prediction of multi-stage pump

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination