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An efficient Maximin Latin hypersquare sampling method

A Latin super-square, efficient technology, used in special data processing applications, instruments, electrical digital data processing, etc.

Pending Publication Date: 2019-01-11
BEIJING INSTITUTE OF TECHNOLOGYGY
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

Aiming at this defect, the technical problem to be solved by a kind of efficient Maximin Latin hypercube sampling method (A novel algorithm of maximinLatin hypercube design using successive integer programming, SIP) disclosed by the present invention is: with successive local enumeration (Successive Local Enumeration, SLE ) based on the Latin hypercube experiment design method, using the integer programming method to optimize the objective function and realize the sampling of design sample points, which has the following advantages: First, the integer programming method is used to optimize, avoiding the amount of calculation caused by a large number of enumerations, reducing The calculation is time-consuming and the efficiency of the algorithm is improved, so that the method is more suitable for engineering applications; the second is that through the integer programming method, although the optimal solution cannot be guaranteed, a better solution can be found, and at the same time, it is greatly alleviated. The boundary effects produced by the SLE method make the overall performance of the sample points better and can ensure the spatial uniformity of the sampling points.

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  • An efficient Maximin Latin hypersquare sampling method
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  • An efficient Maximin Latin hypersquare sampling method

Examples

Experimental program
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Effect test

Embodiment 1

[0054] The following uses a two-dimensional (m=2) problem, taking sample points n=4 as an implementation example to illustrate the specific implementation process of the SIP method. In the process, the 2-norm is used to calculate the distance between two sample points. image 3 It is a specific implementation diagram in the sampling problem (m=2, n=4) of sample points in two dimensions and 4 points in the present invention. Using an efficient Maximin Latin hypersquare sampling method disclosed in this embodiment to generate 4 sample points in this space, the specific steps are as follows:

[0055] Step A: If image 3 As shown, the space is divided into a 4×4 chessboard, each cell is a column, and each cell has four cells.

[0056] Step B: Randomly generate a design sample point P in the first cell 1 (1,2) as the first point in the sample set. The sample set is P={P 1}.

[0057] Step C: For the second point, considering the projection uniformity, the coordinates (1,2) have...

Embodiment 2

[0071] Embodiment 2: Test example

[0072] In order to better illustrate the advantages of the SIP method in the application of optimization methods for surrogate model design, the radial basis function (RBF) is selected and tested on five numerical examples. The mathematical model of the calculation example is shown in Table 1. Using the SIP and MATLAB function lhsdesign(LHD) respectively, except for the fifth problem where 100 design sample points were sampled, the rest of the problems were sampled with 50 design sample points, and K-point method was used for cross-validation, where K was 10. Calculate R for each group 2 , RAAE and RMAE three evaluation indicators and take the average, R 2 The closer to 1, the closer RAAE and RMAE are to 0, indicating the higher global approximation accuracy. The global approximation accuracy is related to the spatial uniformity of the design sample points. The better the spatial uniformity of the sample points, the higher the global accu...

Embodiment 3

[0083] Embodiment 3: engineering calculation example

[0084] Taking the aerodynamic design optimization of an airfoil as an example, the application of the SIP method in the design optimization of high-dimensional complex aircraft is introduced. The NACA0012 airfoil is selected as the initial airfoil, and the airfoil is parametrically modeled by the shape function perturbation method. Five weight coefficients are selected as design variables for the upper and lower airfoils, namely x ui ,x li (i=1,2,3,4,5), a total of 10 design variables. The mathematical model of airfoil aerodynamic optimization problem is as follows:

[0085]

[0086] In the formula, -C L / D is a negative lift-to-drag ratio, t max Indicates the maximum thickness of the airfoil, t baseline Indicates the maximum thickness of the reference airfoil, cl is the lift coefficient, cl baseline is the lift coefficient of the reference airfoil, x is the design variable, x lb and x up are the lower bound and ...

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Abstract

The invention discloses an efficient Maximin Latin hypersquare sampling method, which belongs to the technical field of engineering design optimization. The method includes dividing the design space into a hypercube, taking the minimum distance as a local objective function, and using integer programming method to maximize the objective function, thereby generating sample points successively, wherein the integer programming method is a branch-and-bound method, that is, the problem is branched, bound and pruned, so as to obtain the optimal solution of the integer programming problem; applying the integer programming method to a surrogate model . The method can significantly improve the global optimization ability and optimization efficiency of the surrogate model optimization design method,ensure the spatial uniformity of sampling points, is suitable for engineering design optimization field including the high-precision analysis model, can effectively improve the engineering design optimization efficiency and shorten the design cycle. The multidisciplinary design optimization fields of the complex engineering system include the fields of aircraft, automobile and ship.

Description

technical field [0001] The invention relates to a high-efficiency Maximin Latin hypersquare sampling method, which belongs to the technical field of engineering design optimization. Background technique [0002] With the continuous development of computer technology, high-precision simulation models are widely used in engineering design to improve analysis accuracy and design feasibility. However, traditional design optimization methods often directly invoke high-precision analysis models for design optimization, so there are technical bottlenecks such as high time consumption, long cycle, and low efficiency in practical applications. Second, modern engineering design optimization problems often involve multiple disciplines, and the disciplines are coupled with each other. Taking aircraft design optimization as an example, the design process often involves multiple disciplines such as aerodynamics, structure, and stealth, and the analysis of a single high-precision model is...

Claims

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Application Information

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IPC IPC(8): G06F17/50
CPCG06F30/20
Inventor 龙腾周星宇唐亦帆
Owner BEIJING INSTITUTE OF TECHNOLOGYGY
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