A sequential experimental design method for response mutations

Abstract

The present invention discloses a sequential test design method for response mutation, which is intended to solve the problem that when there is a mutation in the response in the confrontation test under a complex electromagnetic environment, the test results obtained based on uniform design and traditional sequential design are difficult to effectively reflect the changing characteristics of equipment performance, especially the performance mutation process; the uniformity of the design scheme is described by using the rollable L2-deviation, the degree of mutation of the test response is characterized by the gradient modulus of the test point, the objective function is defined by organically combining the two, and the test design scheme is obtained by continuously iterating to improve the objective function value. The test design scheme generated by the sequential test design method for response mutation provided by the present invention is more densely distributed at the response mutation.

Description

Technical Field

[0001] This invention relates to the field of statistical experimental design technology, specifically to a sequential experimental design method for response mutations. Background Technology

[0002] Experimental design, also known as experimental design, refers to the mathematical principles and implementation methods for developing appropriate experimental plans according to predetermined objectives to facilitate effective statistical analysis of experimental results. The design of an experiment involves arranging the experiment, considering factors such as the type of problem to be solved, the degree of generality expected of the conclusions, the desired power level for testing, the homogeneity of experimental units, and the cost and time required for each experiment. Appropriate factors and levels are selected to provide the specific procedures for experimental implementation and the framework for data analysis. Factors: The variables to be examined in the experiment are called factors (or influences). Factors are experimental parameters that affect the test results. Levels: The possible states of a factor are called its levels. Response: The result of the experiment is called the response (or output). Experimental design: The overall arrangement of the experiment after clarifying the factors and levels. [1] .

[0003] Traditional experimental design methods, such as orthogonal design and uniform design, are all one-time overall designs. That is, before the experiment, a plan is constructed according to the controllable factor M, levels Q, and number of trials n, based on the corresponding optimal criteria. After the experiment is executed according to the plan, data is statistically analyzed. If additional experiments are needed after data analysis and processing, this is called sequential design. Traditional sequential design still only considers the controllable factor and the uniformity of its levels.

[0004] However, in combat tests under complex electromagnetic environments, it is necessary to discover the various responses of equipment under different test conditions. However, because the responses of electronic information equipment in complex electromagnetic environments are often abrupt, when the input factors and levels are designed uniformly, only response results at typical level values ​​can be obtained. This makes it difficult for the acquired test data to effectively reflect the changing characteristics of equipment performance, especially the abrupt performance processes, thus affecting the accuracy of data modeling and analysis. If subsequent sequential supplementary test designs still adopt the traditional uniform design scheme, it will not help to solve the abrupt response situation, thus greatly impacting the comprehensiveness of understanding the test response and a more comprehensive assessment of the equipment's capabilities. Therefore, subsequent sequential design methods, while considering the uniformity of input factors and levels, must also consider covering as much of the surrounding area as possible in response abrupt changes, thereby enabling a more comprehensive assessment of the equipment's capabilities. Summary of the Invention

[0005] The purpose of this invention is to provide a sequential test design method for response mutations, in order to solve the problem mentioned in the background art that when there are mutations in the test response during confrontation tests in complex electromagnetic environments, the test results obtained based on uniform design and traditional sequential design are difficult to effectively reflect the changing characteristics of equipment performance, especially the performance mutation process.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a sequential experimental design method for response mutations, characterized in that: the specific operation steps of the sequential experimental design method for response mutations are as follows:

[0007] S1: Given the initial design size n0 and the design size n1 in response to a sudden change;

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

[0009] S3: Execute the experiment of D0 and obtain the response set Y = {y k :k=1,2,…,n0};

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

[0011] S5: Determine if there is a sudden change in the response. If not, end; otherwise, proceed to S6.

[0012] S6: For X = {x} k :k=1,2,…,n0} and Y={y k Modeling the group k = 1, 2, ..., n0, we obtain...

[0013] S7: Generate a uniform design scheme D1 of size n1, let And the experimental response set corresponding to D is obtained using the data model in S6.

[0014] S8: Calculate the objective function

[0015] S9: Randomly permuting any two columns in D1 yields... The experimental response set corresponding to D′ is obtained using the data model in S6.

[0016] S10: Calculate the objective function

[0017] S11: Judge the two obtained obj and obj′. If obj < obj′, then let D = D′, obj = obj′. Further judge whether all permutations have been completed. If yes, end; otherwise, return to S9 to re-loop.

[0018] Preferably, the initial design of S1 is D = {x} k The set Y = {k = 1, 2, ..., n} represents a uniform design scheme. However, in tests conducted in complex electromagnetic environments, due to the nonlinearity of the equipment's response to environmental factors, the corresponding response set Y = {y k The distribution of :k=1,2,…,n0} may exhibit abrupt changes in certain regions.

[0019] Preferably, the mapping model between the response and the input in S6 can be specifically represented as follows: The fitted model can then be further expressed as:

[0020]

[0021] Where g i (x) is a linear or quadratic function, r(q,x,x) k ) for x and x k Related functions, G = [g l (x i )] 1≤i≤n,1≤l≤p ,

[0022] Preferably, the objective function for the sequential design in S8 for responding to abrupt changes is defined as:

[0023]

[0024] Where D is X = {x} k :k=1,2,…n}(x k =(x k1 ,x k2 ,…,x ks ) T () is an experimental design generated by sequential experimental design; By fitting the test point set x through a model i The predicted response obtained; To design the D-type rollable L2-tolerance, (WD2(D)) 2 A smaller value indicates better design uniformity; For test point x i The gradient magnitude at x is used to measure the experimental point x. i The degree of change in response at dis(x) iThe larger the value of λ, the stronger the abrupt change in response, and more test sites need to be arranged near that point; λ is used to prevent (WD2(D)). 2 and The penalty constants are on different orders of magnitude. This objective function takes into account both the uniformity of the experimental design and the abrupt changes in the response set. This allows the design point set to maintain the statistical inference capability of the original model, while arranging more experimental points at the points of response abrupt change. By using algorithms such as simulated annealing for multiple iterations, a local optimum design will eventually be obtained.

[0025] Compared with existing technologies, the beneficial effects of this invention are as follows: In cases where there are abrupt changes in the experimental response, addressing the difficulty of effectively embodying the performance mutation process in uniform designs and traditional sequential designs, this invention provides a sequential experimental design method for response mutations. This method comprehensively considers the uniformity of the experimental design scheme and the mutability of the response set. It utilizes a rollable L2-bias to describe the uniformity of the design scheme and uses the gradient magnitude of the experimental points to characterize the degree of mutation in the experimental response. Based on this, a sequential experimental design optimization objective function is constructed, and the experimental design scheme is obtained by iteratively improving the objective function value. Compared with traditional sequential design methods, the experimental design schemes generated by the sequential experimental design method for response mutations provided by this invention are more densely distributed at the point of response mutation, and can better reflect the mutation process of the response. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of a sequential experimental design method for response mutations according to the present invention;

[0027] Figure 2 This is a response distribution diagram of the initial design scheme in an application example of the sequential experimental design method for response mutations according to the present invention;

[0028] Figure 3 This is an application example of a sequential experimental design method for responding to sudden changes in response, showing the response distribution of a conventional sequential scheme.

[0029] Figure 4 This is a response distribution diagram of the method of the present invention in an application example of a sequential experimental design method for response mutations. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] Please see Figure 1-4 This invention provides a technical solution: a sequential experimental design method for response mutations, characterized in that: the specific operation steps of the sequential experimental design method for response mutations are as follows:

[0032] S1: Given the initial design size n0 and the design size n1 in response to a sudden change;

[0033] S2: Generate a uniform design scheme of size n0. D0: X = {x k :k=1,2,…,n0};

[0034] S3: Execute the experiment of D0 and obtain the response set Y = {y k :k=1,2,…,n0};

[0035] S4: Draw a distribution diagram of the response set within its value range;

[0036] S5: Determine if there is a sudden change in the response. If not, end; otherwise, proceed to S6.

[0037] S6: For X = {x} k :k=1,2,…,n0} and Y={y k Modeling the group k = 1, 2, ..., n0, we obtain...

[0038] S7: Generate a uniform design scheme D1 of size n1, let And the experimental response set corresponding to D is obtained using the data model in S6.

[0039] S8: Calculate the objective function

[0040] S9: Randomly permuting any two columns in D1 yields... The experimental response set corresponding to D′ is obtained using the data model in S6.

[0041] S10: Calculate the objective function

[0042] S11: Judge the two obtained obj and obj′. If obj < obj′, then let D = D′, obj = obj′. Further judge whether all permutations have been completed. If yes, end; otherwise, return to S9 to re-loop.

[0043] In summary, in conjunction with the appendix to the instruction manual... Figure 1 The following examples further illustrate this:

[0044] We use an experiment with a certain electronic information equipment as an application example of this invention. The experiment has two controllable input factors x1 and x2, and a response y with a sudden change. The values ​​of both factors are in the range of [-3, +3]. Therefore, we take the levels of the two factors as [-3, -2, -1, 0, 1, 2, 3], with 7 levels for each.

[0045] Step 1: Generate an initial design scheme D0 with n0 = 14 using the traditional uniform design method: Let it be denoted as X = {x k :k=1,2,…,n0}. In this example, the initial design scheme D0 is:

[0046]

[0047] Step 2: Execute the above experimental plan to obtain the corresponding response set {y}. k For the data set k = 1, 2, ..., 14, analyze the locations of abrupt changes in the data using graphs or the first difference of the data. See the attached response distribution diagram for this example. Figure 2 As can be seen from the graph, the response values ​​are distributed within the range of [-5, 5], with the vast majority concentrated in the interval [-1, 1]. However, there is a sudden change between [-5, -1], lacking a corresponding response point. In this example, the scheme and response table are as follows:

[0048]

[0049] Step 3, for the response set Y = {y k :k=1,2,…n0} and input set X={x k Modeling is performed on the {k = 1, 2, ..., n0} to obtain the prediction model.

[0050] Step 4: Given the sample size n1 = 7 for the sequential scheme, generate a uniform design scheme D1 of size n1. Let... Predict the response corresponding to D using the data model in step 3. And calculate the objective function.

[0051] Step 5: Randomly permutate any two columns in D1 to obtain a new design matrix. Calculate the objective function of D′ When obj′>obj, let D=D′, obj=obj′;

[0052] Step 6: Further determine whether all substitutions have been completed. If yes, end the process; otherwise, return to step 4 and repeat the loop.

[0053] The final sequential design scheme (D1) for responding to sudden changes and the corresponding response table obtained in this example are as follows:

[0054]

[0055] Figure 4 The figure shows the response distribution of the method of the present invention. It can be clearly seen from the figure that the method of the present invention has a denser distribution at the change in response compared with the traditional method.

[0056] 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 make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A sequential experimental design method for response mutation, characterized in that: The specific operation steps of the sequential experimental design method for response mutation are as follows: S1: given initial design size n0 and response mutation design n1; S2: Generate a uniform design D0 of size n0: X = {x k :k=1,2,…,n0}; S3: Execute the experiment of D0 and obtain the response set Y = {y k :k=1,2,…,n0}; S4: Draw a distribution diagram of the response set within its range; S5: Determine whether there is a mutation in the analysis response, if not, end, if yes, go to S6; S6: for X = {x k :k=1,2,…,n0} and Y={y k :k=1,2,…,n0} model, we get S7: Generate a uniform design D1 of size n1, let And use the data model in S6 to get the experimental response set corresponding to D S8: Calculate the objective function S9: Randomly permute any two columns in D1 to obtain And use the data model in S6 to get the experimental response set corresponding to D′ S10: Calculate the objective function S11: Judge the obj and obj′ obtained twice. If obj<obj′, set D=D′, obj=obj′, and further judge whether all replacements are completed. If so, end. If not, return to S9 for recycling.

2. The sequential experimental design method for response mutation according to claim 1, characterized in that: The data model in S6 It can be specifically expressed as: where g i (x) is a linear or quadratic function, r(q,x,x k ) for x and x k Related functions, G=[g l (x i )] 1≤i≤n,1≤l≤p , 3. The sequential experimental design method for response mutation according to claim 1, characterized in that: The objective function in S8 Where D is X={x k :k=1,2,…n}(x k =(x k1 ,x k2 ,…,x ks ) T ) is a trial protocol resulting from a sequential trial design; is the set of test points x fitted by the model i The predicted response obtained; To design the D rollable L2-deviation, (WD2(D)) 2 The smaller it is, the better the design uniformity; is the test point x i The gradient modulus at the test point x i The degree of response mutation at the position, dis(x i ) is larger, the stronger the response mutation is, and more test points need to be arranged near this point; λ is used to prevent (WD2(D)) 2 and The objective function takes into account the penalty constants of different orders of magnitude. This allows the design point set to maintain the statistical inference ability of the original model, while arranging more test points at the response mutation point. By using algorithms such as simulated annealing for multiple iterations, the local optimal design will eventually be obtained.

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