CN113987745A - Sampling method for optimizing spatial layout of load sample points - Google Patents
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Abstract
The invention discloses a sampling method for optimizing spatial distribution of load sample points, which relates to the technical field of random sampling and solves the technical problem that the spatial distribution of the load sample points is not uniform enough; on the basis of a high-dimensional algorithm, the idea of step-by-step optimization is adopted, so that the extraction of load sample points is not required to be carried out again under the condition of increasing load variables, the effectiveness of original load data is kept, and the calculation time is saved; the method is provided for efficiently solving the problem of sampling of the load uncertainty sample, and has practical engineering significance.
Description
Technical Field
The application relates to the technical field of random sampling, in particular to a sampling method for optimizing spatial layout of load sample points.
Background
Various uncertainty factors are ubiquitous in engineering practice, such as external loading of the structure, etc., and these dynamic or uncertainty factors often lead to failure of the structural design. When considering the structural response under the dynamic environmental load, a mathematical model needs to be established to effectively describe the uncertain information by obtaining load samples with uniform spatial distribution. At present, the problems of large repeatability, slow iteration and the like exist based on Monte Carlo sampling; latin hypercube sampling cannot effectively capture data characteristics of all spatial positions, so that the subsequent calculation accuracy is reduced. Therefore, a sampling method with uniform spatial layout of load samples is needed to obtain reasonable representative sample points for the subsequent study of complex problems such as uncertainty in dynamic environment.
Disclosure of Invention
The application provides a sampling method for optimizing spatial layout of load sample points, which aims to achieve uniform spatial distribution of the load sample points under the condition of randomness of load data and provide reasonable data points for researching uncertainty problems.
The technical purpose of the application is realized by the following technical scheme:
a sampling method for optimizing a spatial layout of load sample points, comprising:
s1: carrying out layered random sampling on the value of the cumulative distribution function of the load variable to obtain a cumulative distribution probability value;
s2: taking an inverse function of the cumulative distribution function and substituting the cumulative distribution probability value to obtain a corresponding first load sample point combination;
s3: calculating the minimum distance between each load sample point and the other load sample points in the first load sample point combination, and calculating the variance of the minimum distances of all the load sample points;
s4: and adjusting part of sample data combinations in the first load sample point combination to reduce the variance, and obtaining the load sample point combination with the optimal spatial layout until the variance of the minimum distances of all load sample points can not be reduced.
The beneficial effect of this application lies in: the sampling method for optimizing the spatial layout of the load sample points considers the variance of all the minimum distances, can jump out the defect of local optimum, realizes the uniform distribution of the load sample space, and provides reasonable sample points for the subsequent fitting calculation; on the basis of a high-dimensional algorithm, the idea of step-by-step optimization is adopted, so that the extraction of load sample points is not required to be carried out again under the condition of increasing load variables, the effectiveness of original load data is kept, and the calculation time is saved; the method is provided for efficiently solving the problem of sampling of the load uncertainty sample, and has practical engineering significance.
Drawings
FIG. 1 is a flow chart of a method described herein;
FIG. 2 is a schematic diagram of the distribution of force heat samples in step (1) of the present application;
FIG. 3 is a schematic diagram of the distribution of force-to-noise samples after optimizing the spatial layout in step (2) according to an embodiment of the present disclosure;
FIG. 4 is a diagram of variance of all minimum distances in step (2) of an embodiment of the present application.
Detailed Description
The technical solution of the present application will be described in detail below with reference to the accompanying drawings.
Fig. 1 is a flowchart of a sampling method for optimizing a spatial layout of load sample points according to the present application, and as shown in fig. 1, the sampling method includes:
step S1: and carrying out layered random sampling on the value of the cumulative distribution function of the load variable to obtain a cumulative distribution probability value.
Specifically, the step S1 includes:
generating a cumulative distribution function of the load variables according to the probability distribution obeyed by the load variables, wherein the value taking interval is [0,1]]The cumulative distribution function of (a) is equally divided to obtain m sub-intervals, each sub-interval is randomly sampled to obtain a cumulative distribution probability value Pi(x) Comprises the following steps:
wherein, Pi(x) Representing the ith cumulative distribution probabilityThe value, rand (1, 1), represents the range [0,1]]The random number in (d) and m represent the number of equally divided sub-sections.
Step S2: and taking an inverse function of the cumulative distribution function and substituting the cumulative distribution probability value to obtain a corresponding first load sample point combination.
Specifically, the step S2 includes:
xi＝F-1(Pi(x))
wherein x isiSample value representing the ith load sample point, i ∈ [1, n ]]N represents the total number of load sample points, then all xiForming the first load sample point combination; f-1Representing the inverse of the cumulative distribution function.
Step S3: and calculating the minimum distance between each load sample point in the first load sample point combination and the rest load sample points, and calculating the variance of the minimum distances of all the load sample points.
Specifically, the step S3 includes:
s31: calculating a minimum distance of each load sample point in the first set of load sample points from the remaining load sample points, comprising:
di＝min(dij)
wherein dij represents the distance between a load sample point i and a load sample point j, i belongs to [1, n ], j belongs to [1, n ], and i is not equal to j; l denotes the sample dimension, where l is 2; di represents the minimum distance between the ith load sample point and the remaining n-1 load sample points.
S32: the variance of the minimum distances for all load sample points is calculated as:
where Var (d) represents the variance of all minimum distances,
the average of the minimum distances is indicated.
Step S4: and adjusting part of sample data combinations in the first load sample point combination to reduce the variance, and obtaining the load sample point combination with the optimal spatial layout until the variance of the minimum distances of all load sample points can not be reduced.
Specifically, the step S4 includes:
s41: counting all minimum distances, D ═ D1, D2,. di.. dn ]; where di represents the minimum distance between the ith load sample point and the remaining load sample points, and D represents a vector of all minimum distances.
S42: finding out the maximum value and the minimum value in all the minimum distances, wherein minD ═ min (D) and maxD ═ max (D) exist; where minD represents the minimum value in vector D and maxD represents the maximum value in vector D.
S43: and acquiring load sample points corresponding to the minD and the maxD respectively, exchanging high-dimensional data of the load sample points corresponding to the minD and the maxD respectively, generating new load sample points, and obtaining a second load sample point combination.
S44: comparing the variances of all the minimum distances of the first load sample point combination and the second load sample point combination, and if the variance corresponding to the second load sample point combination is smaller, returning to step S41 to be executed again; if the variance corresponding to the first load sample point combination is small, go to step S45.
S45: if 2 or more elements remain in the current vector D, removing the maximum value maxD and the minimum value minD in the current vector D, selecting a new maximum value maxD and a new minimum value minD from the vector D, and going to step S43; if the number of remaining elements in the current vector D is less than 2, go to step S46.
In step S45, removing the maximum value maxD and the minimum value minD in the current D means ignoring the maximum value maxD and the minimum value minD in the current D, selecting a new maximum value maxD and a new minimum value minD in the vector D, going to step S43, obtaining load sample points corresponding to the new minD and the new maxD, exchanging high-dimensional data of the load sample points corresponding to the new minD and the new maxD, generating new load sample points, and forming a new load sample point combination.
S46: and outputting a sample result when the current load sample point combination reaches the condition of optimal spatial layout.
As a specific implementation, a high-dimensional layout design is performed on the basis of a low-dimensional layout, and a high-dimensional uniform spatial distribution without changing the original data combination is realized by adjusting only the data combination of the sample points with high dimensionality, which includes:
(dijl+1)2＝(xj(l+1)-xi(l+1))2+(dijl)2
namely, it is
di＝min (dijl+1)
Wherein, dijl+1And the distance between the load sample point i and the load sample point j in the dimension of l +1 is represented, wherein l is more than or equal to 2.
In order to calculate the structural response result of a multi-field dynamic environment of a certain thermal protection structure, load sample points with uniform sample spatial layout need to be selected. The dynamic environment is designed as follows: the force load is 180-220N, the temperature of the surface of the structure is 720-880 ℃, the ambient noise is 150-180 db, and in consideration of the worst case, the variables are considered to be uniformly distributed. The sampling method is used for obtaining a sampling result under 2-dimensional (force, heat) combination, as shown in FIG. 2; the sampling results under a 3-dimensional (force, heat, noise) combination obtained by the sampling method for optimizing the spatial layout of the load sample points are projected on a force-heat plane, as shown in fig. 3.
The sampling method comprises the following steps:
(1) firstly, the values of the cumulative distribution function of the load variables are hierarchically sampled, and corresponding sample points are obtained through an inverse function.
The method specifically comprises the following substeps:
11) and generating an accumulative distribution function of the load variable, and equally dividing the value range [0,1] by 100. Randomly sampling in each subinterval to obtain a random probability value:
wherein P isi(x) Represents the probability value of the ith cumulative distribution, and rand (1, 1) is [0,1]]Random numbers within a range.
12) Negating the cumulative distribution function and substituting it into a probability value Pi(x) Obtaining corresponding load sample point data:
xi＝F-1(Pi(x))
wherein x isiRepresenting the ith sample value, F-1The inverse of the cumulative distribution function is shown, and the result of step (1) is shown in FIG. 2.
(2) And calculating the minimum distance between each load sample point and the rest load sample points, counting all the minimum distances and obtaining a variance value. The variance is reduced by adjusting the data combination of the load sample points, all the minimum distance values are ensured to be close to each other, and the target of uniform spatial distribution of the load samples is achieved.
The method specifically comprises the following substeps:
21) calculate the minimum distance of each load sample point from the remaining sample points:
di＝min(dij2)
wherein dij2Represents the distance between the load sample point i and the load sample point j under consideration of the force and thermal variables (i e [1, 100]]；j∈[1，100]And i ≠ j), di represents the minimum distance between the ith load sample point and the remaining load sample points.
22) Counting all the minimum distances in the step (21), reducing the variance by adjusting the sample data combination corresponding to the maximum value and the minimum value in the minimum distances, and realizing the uniform layout of the sample space:
(ii) counting all minimum distances:
D＝[d1，d2，...，d100]
wherein di represents the minimum distance between the ith point and the rest load sample points (i belongs to [1, 100]), and D is a vector formed by all the minimum distances;
finding out the maximum value and the minimum value in the minimum distance:
minD＝min(D)；maxD＝max(D)
wherein minD represents the minimum value in the vector D, and maxD represents the maximum value in the vector D;
finding out load sample points corresponding to minD and maxD, and generating new load sample points by exchanging high-dimensional data of the load sample points;
and comparing the variance of all the minimum distances of the original sample with the variance of all the minimum distances of the new sample. If the variance corresponding to the new sample is small, turning to the first step, and if the variance corresponding to the original sample is small, turning to the fifth step;
where Var (d) represents the variance of all minimum distances,
represents the average of the minimum distances, n represents the total number of sample points;
if 2 or more elements remain in the current vector D, removing the maximum value maxD and the minimum value minD in the current vector D, then selecting a new maximum value maxD and a new minimum value minD from the vector D, and turning to the third step; if the number of the remaining elements in the current vector D is less than 2, the procedure goes to step (c).
And sixthly, considering that the current load sample point is the condition with optimal spatial distribution, and outputting a sample result. The distribution of the force-heat sample points is shown in fig. 3 (a), and the variance change is shown in fig. 4 (a).
23) High-dimensional uniform spatial distribution is carried out on the basis of low dimensionality, the principle is the same as 22), and high-dimensional uniform spatial distribution under the condition of original data combination is not changed by only adjusting the data combination of high dimensionality of the load sample point:
di＝min(dij3)
wherein dij3Represents the distance between load sample point i and load sample point j under consideration of the force thermal noise variable (i e [1, 100)]；j∈[1，100]And i ≠ j); the distribution of the force thermal noise sample points is shown in fig. 3(b), and the variance change is shown in fig. 4 (b).
The foregoing is an exemplary embodiment of the present application, and the scope of the present application is defined by the claims and their equivalents.
Claims (6)
1. A sampling method for optimizing a spatial layout of load sample points, comprising:
s1: carrying out layered random sampling on the value of the cumulative distribution function of the load variable to obtain a cumulative distribution probability value;
s2: taking an inverse function of the cumulative distribution function and substituting the cumulative distribution probability value to obtain a corresponding first load sample point combination;
s3: calculating the minimum distance between each load sample point and the other load sample points in the first load sample point combination, and calculating the variance of the minimum distances of all the load sample points;
s4: and adjusting part of sample data combinations in the first load sample point combination to reduce the variance, and obtaining the load sample point combination with the optimal spatial layout until the variance of the minimum distances of all load sample points can not be reduced.
2. The method of claim 1, wherein the step S1 includes:
generating a cumulative distribution function of the load variables according to the probability distribution obeyed by the load variables, wherein the value taking interval is [0,1]]The cumulative distribution function of (a) is equally divided to obtain m sub-intervals, each sub-interval is randomly sampled to obtain a cumulative distribution probability value Pi(x) Comprises the following steps:
wherein, Pi(x) Representing the probability value of the ith cumulative distribution, rand (1, 1) representing the range [0, 1%]The random number in (d) and m represent the number of equally divided sub-sections.
3. The method of claim 2, wherein the step S2 includes:
xi＝F-1(Pi(x))
wherein x isiSample value representing the ith load sample point, i ∈ [1, n ]]N represents the total number of load sample points, then allxiForming the first load sample point combination; f-1Representing the inverse of the cumulative distribution function.
4. The method of claim 3, wherein the step S3 includes:
s31: calculating a minimum distance of each load sample point in the first set of load sample points from the remaining load sample points, comprising:
di＝min(dij)
wherein dij represents the distance between a load sample point i and a load sample point j, i belongs to [1, n ], j belongs to [1, n ], and i is not equal to j; l denotes the sample dimension, where l is 2; di represents the minimum distance between the ith load sample point and the remaining n-1 load sample points;
s32: the variance of the minimum distances for all load sample points is calculated as:
where Var (d) represents the variance of all minimum distances,
the average of the minimum distances is indicated.
5. The method of claim 4, wherein the step S4 includes:
s41: counting the minimum distance of all current load sample points, and then D ═ D1, D2.., di.,. dn ]; where di represents the minimum distance between the ith load sample point and the remaining load sample points, and D represents a vector made up of all minimum distances:
s42: finding out the maximum value and the minimum value in all the minimum distances, wherein minD ═ min (D) and maxD ═ max (D) exist; wherein minD represents the minimum value in the vector D, and maxD represents the maximum value in the vector D;
s43: acquiring load sample points corresponding to minD and maxD respectively, exchanging high-dimensional data of the load sample points corresponding to minD and maxD respectively, generating new load sample points, and obtaining a second load sample point combination;
s44: comparing the variances of all the minimum distances of the first load sample point combination and the second load sample point combination, and if the variance corresponding to the second load sample point combination is smaller, returning to step S41 to be executed again; if the variance corresponding to the first load sample point combination is smaller, go to step S45;
s45: if 2 or more elements remain in the current vector D, removing the maximum value maxD and the minimum value minD in the current vector D, selecting a new maximum value maxD and a new minimum value minD from the vector D, and going to step S43; if the number of remaining elements in the current vector D is less than 2, go to step S46;
s46: and outputting a sample result when the current load sample point combination reaches the condition of optimal spatial layout.
6. The method of claim 4, wherein when the load sample points are high dimensional data, then:
(dijl+1)2＝(xj(l+1)-xi(l+1))2+(dijl)2
namely, it is
di＝min(dijl+1)
Wherein, dijl+1And the distance between the load sample point i and the load sample point j in the dimension of l +1 is represented, wherein l is more than or equal to 2.
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Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20190228122A1 (en) * | 2017-07-19 | 2019-07-25 | Xiamen University Of Technology | Method of fast identifying the distribution rule of wind speed |
| CN111177966A (en) * | 2019-12-30 | 2020-05-19 | 北京航空航天大学 | Guided missile structure uncertain load interval reconstruction method based on Bayesian theory |
| CN112328971A (en) * | 2020-11-10 | 2021-02-05 | 中国船舶重工集团海装风电股份有限公司 | Double-peak three-parameter Weibull distribution fitting method based on random number |
| CN113221263A (en) * | 2021-04-20 | 2021-08-06 | 浙江工业大学 | Mechanical product structure failure optimization method considering distribution parameter uncertainty |
| US20210264078A1 (en) * | 2019-10-17 | 2021-08-26 | Zhejiang University | Robust optimization design method for mechanical arm based on hybrid interval and bounded probabilistic uncertainties |
-
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- 2021-09-22 CN CN202111106130.XA patent/CN113987745A/en active Pending
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20190228122A1 (en) * | 2017-07-19 | 2019-07-25 | Xiamen University Of Technology | Method of fast identifying the distribution rule of wind speed |
| US20210264078A1 (en) * | 2019-10-17 | 2021-08-26 | Zhejiang University | Robust optimization design method for mechanical arm based on hybrid interval and bounded probabilistic uncertainties |
| CN111177966A (en) * | 2019-12-30 | 2020-05-19 | 北京航空航天大学 | Guided missile structure uncertain load interval reconstruction method based on Bayesian theory |
| CN112328971A (en) * | 2020-11-10 | 2021-02-05 | 中国船舶重工集团海装风电股份有限公司 | Double-peak three-parameter Weibull distribution fitting method based on random number |
| CN113221263A (en) * | 2021-04-20 | 2021-08-06 | 浙江工业大学 | Mechanical product structure failure optimization method considering distribution parameter uncertainty |
Non-Patent Citations (2)
| Title |
|---|
| 宋述芳;吕震宙;: "高维小失效概率可靠性分析的序列重要抽样法", 西北工业大学学报, no. 06, 30 December 2006 (2006-12-30) * |
| 尹宜勇;付宁善;廖频;宋正河;: "基于DTW距离的拖拉机传动轴载荷样本长度计算方法", 农业工程学报, no. 12, 23 June 2020 (2020-06-23) * |
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