CN113642140B - Multi-source test slicing design method and system - Google Patents

Multi-source test slicing design method and system Download PDF

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CN113642140B
CN113642140B CN202010393052.5A CN202010393052A CN113642140B CN 113642140 B CN113642140 B CN 113642140B CN 202010393052 A CN202010393052 A CN 202010393052A CN 113642140 B CN113642140 B CN 113642140B
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段晓君
徐琎
晏良
陈璇
肖意可
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National University of Defense Technology
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Abstract

The present invention providesA multi-source test slicing design method includes 1, inputting the number t of kinds of multi-source tests, the number n of test points arranged on each kind of tests k And the number of impact factors p for each test point; 2. setting parameters of the split Latin hypercube according to the input multi-source test parameters; 3. distributing all the test points to t different sets G according to a preset distribution rule k Performing the following steps; 4. for each set G k To G k And the middle elements are independently and randomly arranged for p times to obtain p vectors to obtain a Latin hypercube matrix, and then a design matrix D of the midpoint Latin hypercube is constructed for the matrix to obtain a multi-source test design scheme. The invention ensures that the test points of each type of test in the multi-source test meet certain uniformity and sampling property, and practice proves that the design scheme is constructed according to the design method of the invention, the root mean square error after the test is smaller, and the estimation effect is better than that of the existing typical slice design method.

Description

Multi-source test slicing design method and system
Technical Field
The invention belongs to the field of test design and test evaluation, and particularly relates to a multi-source test design method and system.
Background
In the tests of some special products, often due to economic reasons and the like, only a small number of entity tests, partial semi-physical simulation tests and a large number of simulation tests can be performed, and in the multi-source test design, how to perform reasonable test arrangement, reduce the test evaluation variance and improve the test precision is particularly important.
In the prior art, a piece design is required for multi-source test design, however, many existing piece designs require that the number of times of each piece of test is equal, the use requirements of a small number of entity tests and a large number of simulation tests in product tests cannot be met, especially for tests (such as tests considering meteorological conditions and the like) with qualitative factors and with different levels of the qualitative factors not appearing at equal probability, and an effective test arrangement mode is to arrange more test points on the level of the high-probability factors; in the simulation of Computer tests with adjustable precision, the literature (He X, Rui T, Wu C F J. optimization of Multi-Fidelity Computer Experiments via the EQIE Criterion [ J ]. technometrics.2017, 59 (58-68)) suggests the use of a proportion of low-precision tests, so that the simulation time is reduced as much as possible while ensuring the simulation precision. The algorithm given in the literature (J.Xu, X.He, X.Duan, and Z.Wang, Sliced clothes hypercube designs for computer experiments with indirect batch sizes, IEEE Access 6(2018), pp.60396-60402.) is only applicable to certain specific types of slice designs.
Disclosure of Invention
The invention aims to solve the technical problem of how to reasonably construct test points in each batch of tests for multi-source tests of certain special products, so that the test effect can be obtained, the test evaluation variance is reduced, the test precision is improved, the one-dimensional uniformity and good sampling property can be met, and the multi-source test slice design method and the system are provided.
In order to solve the problem, the technical scheme adopted by the invention is as follows:
a multi-source test slice design method comprises the following steps:
step 1: inputting the number t of the types of the multi-source tests of the product to be tested and the number n of the test points arranged on each type of test k K is more than or equal to 1 and less than or equal to t, and the number p of the influence factors of each test point;
step 2: setting the number of the split Latin hypercube as t, the dimension as p and the size of each piece as n according to the input multi-source test parameters k ，1≤k≤t；
And step 3: distributing all design points to t different sets G according to preset distribution rules k In the set G k A kth slice corresponding to the sliced latin hypercube;
and 4, step 4: for each set G k To G k The medium elements are independently and randomly arranged for p times to obtain p vectors h k,1 ,...,h k,p Let us order
Figure BDA0002486609320000021
Order to
Figure BDA0002486609320000022
And the output matrix D obtains a slicing design scheme of the multi-source test.
Further, the allocation rule in step 3 is:
step 3.1: for i from 1 to
Figure BDA0002486609320000023
Make the intermediate variable set S i,0 ＝S i-1 ∪{i}，
Figure BDA0002486609320000024
Figure BDA0002486609320000025
Calculating intermediate variables
Figure BDA0002486609320000026
Step 3.2: if delta i > 0, then j goes from 1 to delta i Let k be the equation
Figure BDA0002486609320000027
All of n in k The subscript of (1) is the j-th lower subscript, and let u be the set S i,j-1 Satisfies the equation
Figure BDA0002486609320000028
Add element u to the set G k In the middle, let S i,j ＝S i,j-1 \{u}，
Figure BDA0002486609320000029
This process is repeated until i ═ n.
The invention also provides a multisource test slicing design system, which comprises the following modules:
a test parameter acquisition module: the method is used for obtaining the number t of the types of the multi-source tests of the product and the test times n arranged on each type of test k ，1≤kT is less than or equal to t, and the number p of influence factors of the test;
a slicing latin hypercube design module: the method is used for setting the number of the split Latin hypercube to be t, the dimension to be p and the size of each piece to be n according to the input multi-source test parameters k ，1≤k≤t；
An initial allocation module: for distributing all design points to t different sets G according to a preset distribution rule k Performing the following steps;
designing a matrix output module: for each set G k To G, to k The medium elements are independently and randomly arranged for p times to obtain p vectors h k,1 ,...,h k,p Let us order
Figure BDA0002486609320000031
Let midpoint latin hypercube matrix
Figure BDA0002486609320000032
And the output matrix D obtains a multi-source test slicing design scheme.
Further, the allocation rule in the initial allocation module is:
step 2.1: for i from 1 to
Figure BDA0002486609320000033
Make the intermediate variable set S i,0 ＝S i-1 ∪{i}，
Figure BDA0002486609320000034
Figure BDA0002486609320000035
Calculating intermediate variables
Figure BDA0002486609320000036
Step 2.2: if delta i > 0, then j goes from 1 to delta i Let k be the equation
Figure BDA0002486609320000037
All of n in k The subscript of (1) is the j-th lower subscript, and let u be the set S i,j-1 In the equation
Figure BDA0002486609320000038
Add element u to the set G k In the middle, let S i,j ＝S i,j-1 ，{u}，
Figure BDA0002486609320000039
This process is repeated until i ═ n.
The invention also provides a computer readable medium storing a computer program executable by a processor to implement the above slice design method.
The invention also provides computer equipment which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the fragment design method when executing the computer program.
Compared with the prior art, the invention has the following beneficial effects:
all design points are arranged into different sets through a preset distribution rule, then test points in the different sets are randomly arranged to obtain p vectors, the p vectors are combined to form a partitioned Latin hypercube matrix, and finally the design matrix is formed according to a midpoint Latin hypercube method and is output. Experiments prove that the distribution method distributes the test points into different sets, and finally the design matrix formed by the test points in each set is designed for the latin hypercube as well, and is not influenced by the same design times of each piece in the piece latin hypercube design, so that the test points of each type of test in the multi-source test design of the product meet certain uniformity and sampling property. The method can also carry out reasonable test point design arrangement on multi-dimensional and multi-class tests in multi-source tests, and practice proves that the root mean square error is smaller after the test by the design matrix construction method disclosed by the invention, and the estimation effect is better than that of the existing typical fragment design method.
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FIG. 1 is a flow chart of the system of the present invention.
Detailed Description
The design of the piece-dividing Latin Hypercube (Qian P Z G. Sliced Latin Hypercube Designs [ J ]. Journal of the American Statistical association.2012, 107(497):393 399) is widely applied to batch tests, tests with qualitative factors, model cross validation, multi-source tests and the like. In the batch test, each design matrix corresponds to each batch test, and when each batch test is independently analyzed, the design matrix has optimal one-dimensional uniformity and good sampling property; when the overall design matrix is analyzed, the design matrix also has the optimal one-dimensional uniformity and good sampling property. For example, when data is processed simultaneously by a plurality of devices, the uniformity of the split latin hypercube is the same as that of the latin hypercube design, and if a certain device or a plurality of devices fails to obtain data, the data of the rest devices of the split latin hypercube still have certain uniformity, but the uniformity of the latin hypercube design may be poor. For the test containing qualitative factors, each design matrix corresponds to each type of qualitative factor combination, so that the design point of each type of qualitative factor combination and the overall design point have the optimal one-dimensional uniformity and good sampling property. When the fragment design is used for cross validation, part of data of the fragment design can be subjected to model building, and part of data can be subjected to model validation.
The invention is caused by: although the split latin hypercube design has good design performance for batch tests, multi-source tests and the like, the existing split latin hypercube design requires that the test times of each slice are the same. However, due to the test specificity of some products in reality, due to economic reasons, only a small number of entity tests, partial semi-physical simulation tests and a large number of simulation tests can be performed, so that the latin hypercube design method needs to be improved, and the latin hypercube design method can be suitable for the slice design of any parameter for the multi-source test of some special products, so that the test design is proper, the test precision is improved, and the evaluation variance is reduced.
FIG. 1 illustrates an embodiment of a multi-source test slice design method of the present invention, comprising
Step 1: inputting the number t of the types of the multi-source tests of the product and the number n of the test points arranged on each type of test k K is more than or equal to 1 and less than or equal to t, and the number of influencing factors p of each test point;
step 2: setting the number of the split Latin hypercube as t, the dimension as p and the size of each piece as n according to the input multi-source test parameters k ，1≤k≤t；
In this embodiment, assuming a total of 3 types of experiments, where t is 3, the number of tests scheduled in each type of experiment is: n is a radical of an alkyl radical 1 ＝2，n 2 ＝5，n 3 10 total number of test points
Figure BDA0002486609320000051
And (4) designing the slicing when the influence factor p on each test point is 3.
And step 3: distributing all design points to t different sets G according to preset distribution rules k In (1), set G k The kth piece corresponding to the split latin hypercube, k being 1 … t;
the allocation rule is:
step 3.1: for i from 1 to
Figure BDA0002486609320000052
Make the intermediate variable set S i,0 ＝S i-1 ∪{i}，
Figure BDA0002486609320000053
Figure BDA0002486609320000054
Calculating intermediate variables
Figure BDA0002486609320000055
Step 3.2: if delta i > 0, then j goes from 1 to delta i Let k be the equation
Figure BDA0002486609320000056
All of n in k Let u be the set S i,j-1 Satisfies the equation
Figure BDA0002486609320000057
Add element u to the set G k In the middle, let S i,j ＝S i,j-1 ，{u}，
Figure BDA0002486609320000058
This process is repeated until i ═ n. N satisfying the equation k Has a delta i I.e. has delta i A subscript (n) k Where k is a subscript) such that the equation is satisfied, the j-th smallest subscript in this embodiment is the smallest when j is 1, the 2 nd smallest when j is 2, and so on.
In the present embodiment, n is equal to 3 for t 1 ＝2，n 2 ＝5，n 3 For a multi-source design of experiment with 10, 17, and 3, the calculation can be made
(δ 1 ,...,δ n )＝(0,1,2,0,1,0,2,0,2,2,0,1,0,1,1,0,3)。
Due to delta 1 0, thus S 1 1. For i-2, there is S 2,0 ＝S 1 ∪{2}＝{1,2}，δ i Note that k-3 is the only equation that is satisfied
Figure BDA0002486609320000059
Is two subscripts of 1 satisfying the equation
Figure BDA00024866093200000510
The minimum value of the integers.
Thus, S is obtained 2 ＝S 2,1 ＝S 2,0 {1} - {2}, element 1 is added to the set G 3 In (1).
For i-3, there is S 3,0 ＝{2,3}，δ i ＝2。
While k 2 and k 3 satisfy the equation
Figure BDA0002486609320000061
Let k be 2, and have u be 2, set S 3,0 In the equation
Figure BDA0002486609320000062
The smallest element.
Then has S 3,1 (ii) 3, while element 2 is added to the set G 2 In (1).
Then for k 3, S 3,1 The only element u-3 just satisfies the equation
Figure BDA0002486609320000063
Then
Figure BDA0002486609320000064
Adding element 3 to set G 3 In (1).
After the above operations are repeatedly performed on all the test points i 1
Figure BDA0002486609320000065
G 1 ＝{7,14}，G 2 ＝{2,5,9,12,16}，G 3 The classification result of {1,3,4,6,8,10,11,13,15,17 }.
And 4, step 4: for each set G k To G j The medium elements are independently and randomly arranged for p times to obtain p vectors h j,1 ,...,h j,p Let us order
Figure BDA0002486609320000066
Let the normalized matrix
Figure BDA0002486609320000067
And outputting the matrix D to obtain a slicing design scheme required by the multi-source test of the product.
In this embodiment, each test point of the special product has p relevant influencing factors, which mainly include: signal to noise ratio of speed, acceleration and environment, etc
For G 1 ，G 2 And G 3 Randomly arranged, having h 1,1 ＝(7,14)，h 2,1 ＝(12,2,16,9,5)，h 3,1 ＝(15,6,17,11,1,13,10,3,4,8)。
Thus, h (: 1) is
h(:,1)＝(7,14，12,2,16,9,5，15,6,17,11,1,13,10,3,4,8) T
Likewise, other columns of the design matrix may be constructed, and then the design matrix D for the midpoint latin hypercube is constructed as follows:
Figure BDA0002486609320000071
the matrix D has one design point for each behavior, namely the test points of the first two behaviors for the first type of test, the test points of the second type of test from the third row to the seventh row, and the test points of the third type of test from the eighth row to the seventeenth row. For the first design point, namely (13,27,13)/34, the design is normalized to [0,1 ]]The design point of the interval needs to be scaled according to actual needs in use. If the first influencing factor is tested to take a value range of [100,200,200%]The first factor of influence of the design point
Figure BDA0002486609320000072
The corresponding value should be
Figure BDA0002486609320000073
In the same way, the values of other influence factors in the design points can be obtained according to the value ranges of other influence factors and the proportional values of the corresponding influence factors in the design matrix D, so that the value of each influence factor in each design point is obtained.
Different from the random Latin hypercube design, the invention uses the midpoint Latin hypercube design, namely, after obtaining the Latin hypercube matrix h (: l), the midpoint Latin hypercube matrix is taken
Figure BDA0002486609320000074
As a sampling matrix, all one-dimensional test points are located in a zoneM (0, 1/n)],...,((n-1)/n,1]While ensuring that the one-dimensional design point corresponding to the i-th test is (0, 1/n) i ],...,((n i -1)/n i ,1]There is one and only one point in each interval, i 1. The reason the invention considers the use of a midpoint latin hypercube is: for a random latin hypercube design, some generalized split latin hypercubes with different trial times between the slices may not exist.
For example, consider t ═ 3, n 1 ＝1，n 2 ＝n 3 Easy to verify that H is 3, 0.2,0.3,0.5,0.7,0.8,0.9) T Is a one-dimensional Latin hypercube design, but there is no one way to decompose H into G 1 、G 2 、G 3 So that the design requirements of the split Latin hypercube can be met. When H ═ 1/(2n),., (2n-1)/(2n) }, there is always an efficient way of classification that can meet the design requirements of the sliced latin hypercube.
All design points are arranged into different sets through a preset distribution rule, then test points in the different sets are randomly arranged to obtain p vectors, the p vectors are combined to form a partitioned Latin hypercube matrix, and finally a sampling matrix is formed according to a midpoint Latin hypercube method and output. Experiments prove that the distribution method distributes the test points to different sets, and finally the design matrix formed by the test points in each set is also designed as the Latin hypercube and is not influenced by the same design times of each piece in the piece Latin hypercube design, so that the test points of each type of test in the multi-source test can meet certain uniformity and sampling property. In the multi-source test, reasonable test point design arrangement is carried out on multi-dimensional and multi-type tests, and practices prove that the method disclosed by the invention has the advantages of smaller root mean square error and best estimation effect after the test.
The invention also provides a multisource test slicing design system, which comprises the following modules:
a test parameter acquisition module: the method is used for obtaining the number t of the types of the multi-source tests of the product and the test times n arranged on each type of test k K is more than or equal to 1 and less than or equal to t, and influence factors of the testThe number p;
a slicing latin hypercube design module: the method is used for setting the number of the split Latin hypercube to be t, the dimension to be p and the size of each piece to be n according to the input multi-source test parameters k ，1≤k≤t；
An initial allocation module: for distributing all design points to t different sets G according to a preset distribution rule k Performing the following steps;
designing a matrix output module: for each set G k To G k The medium elements are independently and randomly arranged for p times to obtain p vectors h k,1 ,...,h k,p Let us order
Figure BDA0002486609320000081
Order to
Figure BDA0002486609320000082
And the output matrix D obtains a multi-source test slicing design scheme.
The allocation rule in the initial allocation module is:
step 2.1: for i from 1 to
Figure BDA0002486609320000091
Set of intermediate variables S i,0 ＝S i-1 ∪{i}，
Figure BDA0002486609320000092
Figure BDA0002486609320000093
Calculating intermediate variables
Figure BDA0002486609320000094
Step 2.2: if delta i > 0, then j goes from 1 to delta i Let k be the equation
Figure BDA0002486609320000095
All of n in k The j-th smaller subscript ofLet u be the set S i,j-1 Satisfies the equation
Figure BDA0002486609320000096
Add element u to the set G k In the middle, let S i,j ＝S i,j-1 ，{u}，
Figure BDA0002486609320000097
This process is repeated until i ═ n.
The invention also provides a computer readable medium storing a computer program executable by a processor to implement the above slice design method.
The invention also provides computer equipment which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the fragment design method when executing the computer program.
The rationality and robustness of the present invention is verified by experiments below.
Experiment one:
computer simulation tests are adopted to compare the advantages and disadvantages of the method of the invention and other methods:
f 1 (x)＝log(x 1 x 2 x 2 x 4 x 5 )
Figure BDA0002486609320000098
assuming that t computer simulation functions are available, the number of trials scheduled for each computer is n, respectively, due to differences in computational performance and time 1 ,...,n t . There are three types of approaches to deal with this problem: first, selecting a single
Figure BDA0002486609320000099
A design matrix of individual test points, which are randomly assigned to t computers. In the method, a random Latin hypercube design, a midpoint Latin hypercube design and an approximately orthogonal Latin hypercube design can be selected. First, theSelecting t Latin super cube designs with independent structures, wherein each design is n 1 ,...,n t At each test point, the t designs are distributed to t computers. Third, the selection method is flexible slice design (Kong X, AiM, Tsui K L. Flexible sliced designs for computer experiments [ J)]. Annals of the Institute of Statistical Mathematics. 2017, 70(3):631-646. ) And the design of the inventive construction.
Figure BDA0002486609320000101
For the estimation of the mean value mu of the function in its defined domain, the root-mean-square error (root-mean-square error) of the estimation is used to investigate the merits of different design methods, considering two different types of simulation situations: (1) all the computers have correct calculation results, and all the data are used for estimating mu; (2) a computer error causes its data to be unusable and the remaining data is used to estimate μ. For function f 1 Consider the combination t 4, n 1 ＝17，n 2 ＝13，n 3 ＝11，n 4 7; for function f 2 Consider the combination t ═ 3, n 1 ＝9，n 2 ＝7，n 3 6. Table 1 shows the root mean square error obtained after 10,000 replicates. Wherein:
RLH: designing an n-time random Latin hypercube;
MLH: designing a neutral point Latin hypercube for n times;
IMLH: t independent midpoint Latin hypercube designs;
and (3) FSD: flexible slicing design;
SLH the generalized segmented latin hypercube design of the inventive construction.
TABLE 1 comparison of root mean square errors for different methods
Figure BDA0002486609320000102
Simulation results show that the root mean square error of the SLH method constructed by the present invention is minimal in all functional and analog combinations. The design method MLH alone works the same as SLH in the first simulation scenario, but much less in the second scenario. The independently chosen design method IMLH works the same as SLH in the second simulation scenario, but much less in the first scenario. Therefore, the SLH method as a whole and each slice can reduce the estimation variance to the same extent as the ordinary latin hypercube design, allowing for arbitrary number of slices and number of trials.
Experiment two:
according to the measurement mechanism of the radar in the radar target, the factors related to the radar ranging error comprise: dynamic lag error, clutter interference error, distance flicker, etc., and the key factors obtained after screening include:
Figure BDA0002486609320000103
and S/C respectively represents the signal-to-noise ratio of the speed, the acceleration and the environment. The physical and semi-physical tests are now performed, with four states of testing as shown in table 2 below:
table 2: difference of factors under different conditions of semi-physical test and physical test
Figure BDA0002486609320000111
Wherein states 1, 2 correspond to semi-physical tests and states 3,4 correspond to physical tests. Generally, the costs of the tests in the different states are different, and the costs W of the four test states 1 ,W 2 ,W 3 ,W 4 Has a relationship of W 1 ＜W 2 ＜W 3 ＜W 4 . The maximum difference between the semi-physical test and the physical test is the speed
Figure BDA0002486609320000112
And acceleration
Figure BDA0002486609320000113
Consider 16 semi-physical trials with 8 trials of state 1 and state 2 each; 12 physical trials were performed, with 6 trials in state 3 and state 4 each. Therefore, the configuration parameters are required to be $ t _1 $ 2$, $ m _1 $ 8$, $ t _ 2$, $ m _ $SLH method of 2$, $ n _1 $ 16$, $ n _ 2$ 12$, $ n $ 28$, where a fraction of 8 test points is assigned to the physical test and a fraction of 6 test points is assigned to the physical test. In addition, consider 4 other design approaches:
OLHD, a random Latin hypercube design with 28 test points is constructed, 8 test points are randomly arranged for a semi-physical test, and 6 test points are arranged for a physical test.
The OnesLHD is designed by constructing 4 pieces of Latin hypercube with 6 times of tests, and 6 test points are arranged for each type of test.
TwoLHD, two Latin hypercube designs are constructed, one is 2 pieces, each piece is designed for 8 times of tests, and each piece is arranged for a semi-physical test; one was a 2-piece, 6-test design, each of which was assigned to a physical test.
And (3) constructing a flexible slicing design simultaneously comprising 2 test points 8 and 2 test points 6, and arranging 8 test points for a semi-physical test and 6 test points for a physical test.
The radar ranging error models in the semi-physical test and the physical test are respectively assumed as follows:
Figure BDA0002486609320000114
Figure BDA0002486609320000115
wherein f is 1 Denotes a semi-physical test, f 2 Representing a physical test. Estimating μ in the model for different trial design methods 1 ,μ 2 ,μ 3 ,μ 4 And η, wherein μ 1 ,μ 2 ,μ 3 ,μ 4 Respectively the mean values of the models in the four states,
Figure BDA0002486609320000121
wherein
Figure BDA0002486609320000122
λ i Size is given by i The importance and reliability of the content are confirmed. Selecting lambda empirically 1 ＝0.1，λ 1 ＝0.2，λ 1 ＝0.3，λ 1 When the value is 0.4, mu is calculated 4 And the root mean square error of the estimate of η are shown in table 3.
Table 3: root mean square error of different design methods in radar-seeking model
OLHD OneSLHD TwoSLHD FSD SLH
μ 4 0.0660 0.0123 0.0121 0.0122 0.0122
η 0.0276 0.0049 0.0032 0.0061 0.0031
From the results, in estimating μ 4 In time, since each of the OnesLHD, TwoLHD, FSD and SLH is a Latin hypercube design, μ is estimated 4 The effect of the fourth compound is better than that of OLHD. When the eta is estimated, the advantages and disadvantages of the design method of each piece and the whole design need to be considered comprehensively, and the estimation effect of the SLH method is the best. The reason is that compared with the SLH method of the invention, the OLHD method has poorer properties of each piece, the OneSLHD method has better design and overall design properties of each piece, but because the test times of each piece design of the method need to be equal, the selection of test points is limited, the TwoSLHD method has poorer overall design properties, the FSD method has better overall design than the TwoSLLHD method but poorer overall design properties than the SLH method, and the overall design does not reach the optimal one-dimensional uniformity.
In summary, the SLH simulation effect of the present invention is the best when solving the mean value estimation problem in the multi-source test. In the simulation experiment, the performance of each method is stable at different times, and only one group of results is selected for demonstration in the text for space reasons.
The set S in step 3 of the method of the invention is demonstrated below by a mathematical operation i,j-1 Comprising at least one equation satisfying the equation
Figure BDA0002486609320000123
Of (2) is used.
Before the proof, a lemma is given.
Introduction 1: for a given t, n 1 ,n 2 ,...,n t ，
Figure BDA0002486609320000124
a and l are any positive integer satisfying a + l ≦ n. Order set
Figure BDA0002486609320000131
Then there is card (Ω). ltoreq.l, where card (Ω) represents the number of elements of set Ω.
And (3) proving that: definition set
Figure BDA0002486609320000132
Then there is
Figure BDA0002486609320000133
When in use
Figure BDA0002486609320000134
When it is established, because
Figure BDA0002486609320000135
Therefore, it is
Figure BDA0002486609320000136
And card (omega) j ) 0, so
Figure BDA0002486609320000137
When in use
Figure BDA0002486609320000138
When there is
Figure BDA0002486609320000139
Because of the fact that
Figure BDA00024866093200001310
Then
Figure BDA00024866093200001311
As shown in the formulas (1) and (2),
Figure BDA00024866093200001312
the theory is led to obtain the evidence.
Starting from the introduction 1, the following propositional proof is given.
Proposition 1: 1, n, δ for any of i i ＞0，j＝1,...,δ i Set S i,j-1 In which at least one element u satisfies the equation
Figure BDA00024866093200001313
And (3) proving that:
for arbitrary δ i Greater than 0, i 1
Figure BDA0002486609320000141
The element in (A) obtains a new vector pi i In the order of
Figure BDA0002486609320000142
Or when
Figure BDA0002486609320000143
Sometimes has a pi i (k)＜π i (k+1)。
It is easy to know when conditions are
Figure BDA0002486609320000144
For any j ═ 1.. delta i When both are satisfied, lemma 1 holds.
The conditions are demonstrated below:
firstly, the method comprises the steps of,
Figure BDA0002486609320000145
wherein
Figure BDA0002486609320000146
Due to the fact that
Figure BDA0002486609320000147
Is an integer, therefore
Figure BDA0002486609320000148
Then
Figure BDA0002486609320000149
The back syndrome method proves that: if i ∈ {1,..,. n }, k ∈ {1,..,. delta., exists i Are such that
Figure BDA00024866093200001410
Due to card (S) i,0 )≥δ i ≥δ i K +1 > m, then set S i,0 There must be at least (m +1) elements.
Therefore, set S i,0 The m-th large element of (b) must be in the set
Figure BDA00024866093200001411
Whereas its (m +1) th largest element is not in the set.
Let q denote S i,0 The (m +1) th major element of (A), is easily obtained
Figure BDA0002486609320000151
i is the set S i,0 Is the largest element of (a).
Thus, there are
Figure BDA0002486609320000152
Known as card ({ q + 1.,. i-1 }. andn.S) i,0 ) M-1, i.e. set
Figure BDA00024866093200001513
There are i-q-m elements.
For sets
Figure BDA00024866093200001514
Is present in a set of combinations (w, j) such that
Figure BDA0002486609320000153
And v is a set
Figure BDA0002486609320000154
Wherein j' is a minimum element satisfying the equation
Figure BDA0002486609320000155
All of n 1 ,...,n t N after s is arranged from small to large j The location of the location.
Because q ∈ S i,0 ，
Figure BDA00024866093200001515
And q is more than v and less than or equal to w, then q belongs to S w,j′ 。
While v is a set
Figure BDA0002486609320000156
Q < v, thus
Figure BDA0002486609320000157
Namely: q is an element of S w,j′ And is
Figure BDA0002486609320000158
Therefore, there are
Figure BDA0002486609320000159
Thus, for the sets
Figure BDA00024866093200001510
Any one of the elements ofv, there is a set of combinations (w, j) satisfying the equations q + 1. ltoreq. w.ltoreq.i-1 and
Figure BDA00024866093200001511
and it is easy to know that the i-q-m groups of combinations (w, j) are different from each other.
I.e. collections
Figure BDA00024866093200001512
At least comprises i-q-m elements.
Cause inequality
Figure BDA0002486609320000161
Is established, i.e.
Figure BDA0002486609320000162
For vector pi i ，
Figure BDA0002486609320000163
For any j ═ 1.. delta i The-1 is true.
Then it is easy to know
Figure BDA0002486609320000164
For any j ═ k i This is true.
Thus, set
Figure BDA0002486609320000165
At least comprises delta i -k +1 elements.
Therefore, it is not only easy to use
Figure BDA0002486609320000166
This inequality contradicts lemma 1,
so for any j e { 1.,. delta., delta r }，
Figure BDA0002486609320000167
It is not true.
That is to say that the first and second electrodes,
Figure BDA0002486609320000168
this is true. Thus, for any i ═ 1., n, δ i > 0 and j ═ 1 i Set S i,j-1 Contains at least one element satisfying
Figure BDA0002486609320000169
Thus, the effectiveness of the process of the present invention is demonstrated.
The design matrix D constructed by the method is proved to be a flexible parameter slicing Latin hypercube design.
Theorem 1, let D denote any column of the design matrix D, have
(i) The vector d is a random permutation of {1/(2n),3/(2n), (2n-1)/(2n) };
(ii) n is the ith slice for any i ═ 1., t, d i A second latin hypercube design.
And (3) proving that: first proving the set G 1 ,...,G t Is a division of { 1.. multidata., n }, i.e.
(1)
Figure BDA0002486609320000171
(2)
Figure BDA0002486609320000172
Is easy to know, G j E {1,.., n } holds.
Because of the fact that
Figure BDA0002486609320000173
Then all elements in { 1.. multidot.n } are added to G 1 ,...,G t I.e. by
Figure BDA0002486609320000174
Meanwhile, as can be seen from the algorithm flow, when an element in the set { 1.,. n } is added into the set G 1 ,...,G t That element is not added to other sets.
Therefore, it is
Figure BDA0002486609320000175
This holds true for any j, j 'e { 1.,. t }, j ≠ j'.
Thus, set G 1 ,...,G t Is a division of { 1.. multidata.n }.
By vectors d and G 1 ,...,G t It can be seen that the vector d is a random arrangement of {1/(2n),3/(2n) }.
It is easy to know that the number of the main body is less than or equal to the number of the main body,
Figure BDA0002486609320000176
at the same time, the equation is satisfied for each
Figure BDA0002486609320000177
Is in the order of {1,. eta.., n }, G ∈ j In the presence of an element c satisfying
Figure BDA0002486609320000178
Therefore, there are
Figure BDA0002486609320000179
In addition, vector h j,l Is a set G j The random arrangement of elements, l 1.. times.p, and thus, the vector (h) j,l -1/2)/n is in any interval (0, 1/n) j ],...,((n j -1)/n j ,1]With one and only one point.
I.e. n for any i ═ 1.., t, d i The secondary latin hypercube design,the certification is complete.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.

Claims (6)

1. A multi-source test slice design method is characterized by comprising the following steps:
step 1: inputting the number t of the types of the multi-source tests of the products to be tested and the number n of the test points arranged on each type of the tests k K is more than or equal to 1 and less than or equal to t, and the number p of the influence factors of each test point;
step 2: setting the number of the split Latin hypercube as t, the dimension as p and the size of each piece as n according to the input multi-source test parameters k ，1≤k≤t；
And step 3: distributing all design points to t different sets G according to preset distribution rules k Performing the following steps;
and 4, step 4: for each set G k G is k The medium elements are independently randomly arranged for p times to obtain p vectors h k,1 ,...,h k,p Let us order
Figure FDA0002486609310000011
Let midpoint latin hypercube matrix
Figure FDA0002486609310000012
And outputting the matrix D to obtain a multi-source test slicing design scheme of the product to be tested.
2. The multi-source test slice design method of claim 1, wherein: the allocation rule in step 4 is:
step 4.1: for i from 1 to
Figure FDA0002486609310000013
Make the intermediate variable set S i,0 ＝S i-1 ∪{i}，
Figure FDA0002486609310000014
Figure FDA0002486609310000015
Calculating intermediate variables
Figure FDA0002486609310000016
Step 4.2: if delta i > 0, then j goes from 1 to delta i Let k be the equation
Figure FDA0002486609310000017
All of n in k The subscript of (1) is the j-th lower subscript, and let u be the set S i,j-1 Satisfies the equation
Figure FDA0002486609310000018
Add element u to the set G k In the middle, let S i,j ＝S i,j-1 \{u}，
Figure FDA0002486609310000019
This process is repeated until i ═ n.
3. A multi-source test slice design system is characterized by comprising the following modules:
a test parameter acquisition module: the method is used for obtaining the number t of the types of the multi-source tests of the product to be tested and the test times n arranged on each type of test k K is more than or equal to 1 and less than or equal to t, and the number p of the influence factors of each test point;
a slicing latin hypercube design module: the method is used for setting the number of the split Latin hypercube to be t, the dimension to be p and the size of each piece to be n according to the input multi-source test parameters k ，1≤k≤t；
An initial allocation module: for distributing all design points to t different sets G according to a preset distribution rule k Performing the following steps;
designing a matrix output module: for each set G k To G k The medium elements are independently and randomly arranged for p times to obtain p vectors h k,1 ,...,h k,p Let us order
Figure FDA0002486609310000021
Let midpoint latin hypercube matrix
Figure FDA0002486609310000022
And obtaining a multi-source experimental design scheme by the output matrix D.
4. The multi-source test slice design system of claim 3, wherein the allocation rules in the initial allocation module are:
step 4.1: for i from 1 to
Figure FDA0002486609310000023
Make the intermediate variable set S i,0 ＝S i-1 ∪{i}，
Figure FDA0002486609310000024
Calculating intermediate variables
Figure FDA0002486609310000025
Step 4.2: if delta i > 0, then j goes from 1 to delta i Let k be the equation
Figure FDA0002486609310000026
All of n in k The subscript of (1) is the j-th lower subscript, and let u be the set S i,j-1 Satisfies the equation
Figure FDA0002486609310000027
Add element u to the set G k In the middle, let S i,j ＝S i,j-1 ，{u}，
Figure FDA0002486609310000028
This process is repeated until i ═ n.
5. A computer-readable medium storing a computer program, characterized in that the computer program is executable by a processor to implement the method as claimed in claim 1 or 2.
6. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor realizes the steps of the method as claimed in claim 1 or 2 when executing the computer program.
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