A sequential trial design method based on the balance of response distribution

Abstract

The present invention discloses a sequential test design method based on response distribution balance. The main purpose is to discover various response situations of equipment under various test conditions through tests in countermeasure tests in complex electromagnetic environments. Therefore, in many cases, in addition to considering the uniformity of the test plan, the balance of the response distribution also needs to be pursued. For test design, not only the optimal uniformity of the input end of the test, that is, factors and levels, needs to be considered, but also the output end of the test, that is, the balance and maximum coverage of the test response distribution. In the present invention, an optimization objective function is constructed during the early stage for the uniform test design scheme and during the subsequent sequential test to ensure that the factors, levels, and responses all achieve uniformity, and the corresponding algorithm flow is given.

Description

Technical Field

[0001] The present invention relates to the technical field of statistical experiment design, in particular to a sequential experiment design method based on response distribution balance. Background Art

[0002] Experimental design, also known as experimental design, is a mathematical principle and implementation method for formulating appropriate experimental plans according to predetermined objectives to facilitate effective statistical analysis of experimental results. The design of an experiment is an arrangement of the experiment. It is necessary to consider the type of problem to be solved by the experiment, the degree of universality to be given to the conclusions, the desired power of the test, the homogeneity of the experimental units, the cost and time of each experiment, etc., to select appropriate factors and corresponding levels, thereby providing the specific procedures for implementing the experiment and the framework for data analysis. Among them, factors: The variables that need to be examined in the experiment are called factors (or factors). Factors are experimental parameters that affect the test results. Levels: The optional states of factors are called factor levels. Response: The result of the experiment is called the response (or output). Experimental design: The overall arrangement plan of the experiment after clarifying the factors and levels.

[0003] Traditional experimental design methods, such as orthogonal and uniform designs, are all one-shot designs. That is, before the experiment, an experimental plan is constructed using optimal criteria based on the controllable factors M, levels Q, and the number of runs n. After the experiment is executed according to the experimental plan, data statistics and analysis are performed. If additional experiments are required after data analysis and processing, this is a sequential design. Traditional sequential designs still only consider the controllable factors and the uniformity of their levels.

[0004] However, in complex electromagnetic environment countermeasure testing, it is necessary to discover the various responses of equipment under various test conditions. Therefore, in many cases, we must not only consider the uniformity of the test plan, but also the uniformity of the response—for example, this response serves as the input for subsequent test plans. This new requirement for complex electromagnetic environment countermeasure testing is reflected in the experimental design. Later sequential test designs must not only consider the input end of the test, that is, the optimal uniformity of factors and levels, but also the output end of the test, that is, the uniformity and maximum coverage of the test response. Summary of the invention

[0005] The purpose of the present invention is to provide a sequential test design method based on response distribution balance to solve the problem raised in the above background technology that both the uniformity of the test scheme and the balance of the test response distribution need to be taken into account in the confrontation test under a complex electromagnetic environment.

[0006] To achieve the above object, the present invention provides the following technical solution: A sequential test design method based on response distribution balance, characterized in that the specific operation steps of the sequential test design method based on response distribution balance are as follows:

[0007] S1: Given the initial design size n0 and the n1 of the response mutation design;

[0008] S2: Generate a uniform design scheme D0 of size n0: X = {x k : k = 1, 2,..., n0};

[0009] S3: Execute the test of D0 to obtain the response set Y = {y k : k = 1, 2,..., n0};

[0010] S4: Draw the distribution map of the response set within its value range;

[0011] S5: Judge whether the response distribution is balanced;

[0012] S6: Draw a conclusion.

[0013] Preferably, the initial design D0 in S1 is a uniform design scheme. However, in the test of a complex electromagnetic environment, due to the non-linearity of the response of the equipment to environmental factors, the distribution of the corresponding response set Y = {y k : k = 1, 2,..., n0} is likely to be uneven.

[0014] Preferably, in S5, the test response distribution balance is judged for the data obtained from the test. If the requirements are not met, further processing is carried out. The specific steps are as follows:

[0015] S5-1: Model X = {x k : k = 1, 2,..., n0} and Y = {y k : k = 1, 2,..., n0} to obtain the data model

[0016] S5-2: Generate a uniform design scheme D1 of size n1. Let And use the data model in S5-1 to obtain the test response set corresponding to D

[0017] S5-3: Calculate the objective function

[0018] S5-4: Randomly permute any two columns in D1 to obtain And use the data model in S5-1 to obtain the test response set corresponding to D′

[0019] S5-5: Calculate the objective function

[0020] Preferably, it is determined whether obj' > obj in S5-3 and S5-5. If so, let D = D', obj = obj', and further determine whether all permutations have been completed. If so, end; if not, return to step S5-4 for recycling.

[0021] Preferably, the mapping model between the response and the input in S5-1 can be specifically expressed as Then the fitting model can be further expressed as:

[0022]

[0023] where g i (x) is a linear or quadratic function, and r(θ, x, x k ) is the correlation function between x and x k ; G = [g l (x i )] 1≤i≤n,1≤l≤p ,

[0024] Preferably, the objective function of the sequential design based on the response distribution balance in S5-3 is defined as:

[0025]

[0026] where D: X = {x k : k = 1, 2, … n} is the test plan generated by the sequential experimental design, where x k = (x k1 , x k2 , …, x ks ) T is any test point in the test plan; is the predicted response set obtained by fitting the test point set x k in D through the model; is the rollable L2-deviation of the design D, and the smaller (WD2(D)) 2 is, the better the design uniformity; is the Shannon information entropy of the response set, where m represents the number of different values in the response set, and p i represents the probability that the i-th value in the response set appears, the larger it is, the better the distribution uniformity; λ is used to prevent (WD2(D)) 2 and Penalty constants of different orders of magnitude. This objective function comprehensively considers the consistency of the experimental design scheme and the response set, which enables the design point set to maintain the statistical inference ability of the original model while making the response distribution more uniform. By using algorithms such as simulated annealing for multiple iterations, a locally optimal design will ultimately be obtained.

[0027] Compared with the prior art, the beneficial effects of the present invention are as follows: Aiming at the problem that it is difficult to balance the uniformity of the experimental design scheme and the balance of the response distribution in the confrontation test under complex electromagnetic environments by using uniform design and traditional sequential design, the present invention provides a sequential experimental design method based on the balance of response distribution. This method comprehensively considers the uniformity of the experimental design scheme and the balance of the response distribution, uses the rollable L2 - deviation to describe the uniformity of the design scheme, and uses the information entropy of the experimental response to characterize the balance of the experimental response distribution. On this basis, an optimization objective function for sequential experimental design is constructed, and the experimental design scheme is obtained by continuously iterating to increase the value of the objective function. Compared with the traditional sequential design method, the experimental design scheme generated by the sequential experimental design method based on the balance of response distribution provided by the present invention can balance the uniformity of the experimental design scheme and the balance of the response distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Flowchart of the sequential experimental design method with response balance based on the balance of response distribution of the present invention;

[0029] Figure 2 Response distribution diagram of the initial design scheme in the application example of the sequential experimental design method based on the balance of response distribution of the present invention;

[0030] Figure 3 Response distribution of the conventional sequential scheme of the sequential experimental design method based on the balance of response distribution of the present invention;

[0031] Figure 4 Response distribution diagram of the sequential experimental design method based on the balance of response distribution of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0032] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0033] Please refer to Figures 1-4, the present invention provides a technical solution: a sequential experimental design method based on response distribution balance, characterized in that the specific operation steps of the sequential experimental design method based on response distribution balance are as follows:

[0034] S1: Given the initial design size n0 and the n1 of the response mutation design;

[0035] S2: Generate a uniform design scheme D0 of size n0: X = {x k : k = 1, 2,..., n0};

[0036] S3: Execute the experiment of D0 to obtain the response set Y = {y k : k = 1, 2,..., n0};

[0037] S4: Draw the distribution diagram of the response set within its value range;

[0038] S5: Judge whether the response distribution is balanced;

[0039] S6: Draw a conclusion.

[0040] Furthermore, in S5, the experimental response distribution balance is judged for the data obtained from the experiment. If it does not meet the requirements, further processing is carried out. The specific steps are as follows:

[0041] S5-1: Model X = {x k : k = 1, 2,..., n0} and Y = {y k : k = 1, 2,..., n0} to obtain

[0042] S5-2: Generate a uniform design scheme D1 of size n1. Let And obtain the experimental response set corresponding to D using the data model in S5-1

[0043] S5-3: Calculate the objective function

[0044] S5-4: Randomly permute any two columns in D1. Let And obtain the experimental response set corresponding to D′ using the data model in S5-1

[0045] S5-5: Calculate the objective function

[0046] Furthermore, judge whether obj′ > obj in S5-3 and S5-5. If so, let D = D′, obj = obj′, and further judge whether all permutations have been completed. If so, end. If not, return to step S5-4 for another cycle.

[0047] Further, the initial design D0 in S1 is a uniform design scheme. However, in the experiment of a complex electromagnetic environment, due to the non-linearity of the equipment's response to environmental factors, the distribution of the corresponding response set Y = {y k : k = 1, 2, …, n0} is likely to be non-uniform.

[0048] The specific implementation steps of this method are shown in the appendix Figure 1 . Next, we will use an application example and combine it with the attached drawings to elaborate on the specific implementation manners of the present invention in detail.

[0049] We take the experiment of a certain electronic information equipment as an application example of the present invention. This experiment has two controllable input factors x1, x2 and a non-linear response y. The value ranges of both factors are [-3, +3]. Therefore, we respectively take the levels [-3, -2, -1, 0, 1, 2, 3] of the two factors, with 7 levels each.

[0050] Step 1: Use the uniform design method to generate an initial design scheme D0 = {x k : k = 1, 2, … 14}, as shown in the following table.

[0051]

[0052] Step 2: Execute the above experimental scheme to obtain the corresponding response set {y k : k = 1, 2, … 14}, as shown in the following table. The distribution diagram is shown in the appendix Figure 2 . It can be seen from the figure that the value range of the response is very unevenly distributed within the range of [-5, 5], and most of them are concentrated in the interval range of [-1, 1].

[0053]

[0054] Step 3: Build a model for the response set Y = {y k : k = 1, 2, … n0} and the input set X = {x k : k = 1, 2, …, n0} to obtain a prediction model

[0055] Step 4: Given the sample size n1 = 14 of the sequential scheme, generate a uniform design scheme D1 with a size of n1. Let Use the data model in Step 3 to predict the response corresponding to D and calculate the objective function of D

[0056] Step 5: Randomly permute any two columns in the initial scheme D1 to obtain a new D1, and calculate the objective function of When obj′ > obj, record D = D′ and obj = obj′;

[0057] Step 6: Determine whether all permutations have been completed. If so, output the current optimal design matrix; if not, return to Step 4 for another loop.

[0058] The sequential design scheme (D1) for response balance and the corresponding response table finally obtained in this example are as follows:

[0059]

[0060] And in combination with the attached drawings of the specification Figure 4 It can be clearly seen that the technical solution is significantly balanced in the distribution of responses.

[0061] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A sequential trial design method based on the balance of response distribution, characterized in that: The specific operation steps of the sequential test design method based on response distribution balance are as follows: S1: Given the initial design size n0 and n1 for response mutation design; S2: Generate a uniform design plan D0 with a size of n0: X = {x k : k = 1, 2, …, n0}; S3: Conduct the test of D0 to obtain the response set Y = {y k : k = 1, 2, …, n0}; S4: Draw the distribution diagram of the response set within its value range; S5: Determine whether the response distribution is balanced; In S5, the balance of the test response distribution of the data obtained from the test is judged. If it does not meet the requirements, further processing is carried out. The specific steps are as follows: S5-1: Model X = {x k : k = 1, 2, …, n0} and Y = {y k : k = 1, 2, …, n0} to obtain a data model S5-2: Generate a uniform design plan D1 with a size of n1, and let and obtain the experimental response set Y corresponding to D using the data model in S5-1; S5-3: Calculate the objective function S5-4: Randomly permute any two columns in D1 to obtain and use the data model in S5-1 to obtain the corresponding experimental response set Y' of D'; S5-5: Calculate the objective function Judge whether obj′ > obj in S5-3 and S5-5. If so, let D = D′ and obj = obj′, and further judge whether all permutations have been completed. If so, end. If not, return to step S5-4 for recycling; S6: Draw a conclusion.

2. The sequential test design method based on response distribution balance according to claim 1, characterized in that: The data model in S5-1 can be specifically represented as: where g i (x) is a linear or quadratic function, and r(θ, x, x k ) is a correlation function of x and x k related, 3. The sequential test design method based on response distribution balance according to claim 1, characterized in that: The objective function in S5-3 where D: X = {x k : k = 1, 2, … n} is the experimental plan generated by sequential experimental design, where x k =(x k1 , x k2 , …, x ks ) T is any test point in the experimental plan; is the predicted response set obtained by fitting the model to the test point set in D; For the design D of the rollable L2 - deviation, (WD2(D)) 2 The smaller it is, the better the design uniformity; is the Shannon information entropy of the response set, where m represents the number of different values in the response set, and p i represents the probability of the i - th value appearing in the response set, The larger it is, the better it represents the uniformity of the distribution; λ is a penalty constant used to prevent the difference in the order of magnitude between (WD2(D)) 2 and . The objective function comprehensively considers the consistency between the experimental design scheme and the response set, which enables the design point set to maintain the statistical inference ability of the original model, while the response distribution becomes more uniform. By using the simulated annealing algorithm for multiple iterations, a local optimal design will finally be obtained.

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