A Sequential Experimental Design Method Based on Maximum Entropy Search Criterion

Abstract

The present invention relates to the technical field of sequential experiments, and in particular to a sequential experiment design method based on the maximum entropy search criterion, which specifically includes the following steps: S1: perform initial experiment design to obtain an initial sample set; S2: construct a proxy model based on currently known sample information; S3: determine the next test point based on the current proxy model according to the acquisition function corresponding to the maximum entropy search criterion; S4: evaluate the performance at the test point and update the sample set; S5: determine whether the test stop condition is met, if so, stop the test; if not, repeat the operations of S2-S5. The sequential experiment design method uses the currently obtained test information to guide the sampling of the next test in a "testing and evaluating" manner; at the same time, the method can explore the overall system and take into account the sampling of larger uncertain areas in the test space.

Description

Technical Field

[0001] The invention relates to the technical field of sequential experiments, and more specifically, to a sequential experiment design method based on the maximum entropy search criterion. Background Art

[0002] The optimization and evaluation of complex systems are usually carried out through experiments, such as collision tests, aircraft wing optimization design, and seeker anti-interference tests and evaluations. Regardless of the form of the test, it is carried out under the constraints of certain test resources and cannot be carried out indefinitely. In order to better achieve the purpose of the test, the test needs to be designed. Only by conducting tests through standardized test plans to obtain relevant information on system performance can we effectively obtain data and then use evaluation methods to obtain performance judgments under a certain risk level.

[0003] In traditional design methods, the distribution of all sample points needs to be determined at the beginning of the experiment, and the positions of test points cannot be dynamically adjusted according to the test results, such as uniform design and Latin hypercube design. The sample size required by such methods will soar as the number of test factors increases, and they cannot meet the needs of complex system experiments.

[0004] In view of the above problems, in order to improve the utilization efficiency of sample data and reduce the demand for test samples, a sequential experiment design method has emerged in the prior art. This method is a "testing and evaluating" design method. This method makes full use of the currently acquired test data to provide guidance for the next test, so as to achieve the test purpose quickly and save test resources. The sequential experiment design method is widely used in scientific research, industry, agriculture, medicine and other fields. The Bayesian optimization method is an efficient optimization method. This type of method has the characteristic of guiding the next test based on the current test data, so it can be applied to sequential experiment design. However, the sampling points selected by this method in the iterative process are usually concentrated near the optimal point. If the Bayesian optimization method is directly used for experimental design, the final experimental design cannot meet the needs of fully obtaining the global information of the system.

[0005] Therefore, the applicant has modified the maximum entropy search criterion in view of the shortcomings of the above-mentioned sequential experiment design method based on Bayesian optimization, and thus invented a sequential experiment design method based on the maximum entropy search criterion. Summary of the invention

[0006] The purpose of the present invention is to provide a sequential experiment design method based on the maximum entropy search criterion, which can set the experimental sample point positions more specifically, thereby improving the optimization efficiency, finding the boundary performance of the target response more quickly, and obtaining the overall information of the target response in the experimental space.

[0007] The present invention is implemented in this way: a sequential experiment design method based on the maximum entropy search criterion specifically comprises the following steps:

[0008] S1: Conduct initial experimental design and obtain the initial sample set;

[0009] S2: Build a proxy model based on the currently known sample information;

[0010] S3: Based on the current proxy model, the next test point is determined according to the acquisition function corresponding to the maximum entropy search criterion;

[0011] The acquisition function is:

[0012]

[0013] in,

[0014]

[0015] represents information entropy, ψ(·) represents the density function of the standard normal distribution; y adj is the corrected prediction mean of the surrogate model at the candidate sample point x;

[0016] S4: Evaluate the performance at the test point and update the sample set;

[0017] S5: Determine whether the test stop condition is met. If so, stop the test; if not, repeat the operations of S2-S5.

[0018] Furthermore, the proxy model is a Kriging model;

[0019] Furthermore, the corrected prediction mean of the Kriging model at the candidate sample point x is:

[0020]

[0021] in, k is the correction factor, Used to adjust the impact of prediction uncertainty on sampling tendency, is a penalty term used to reduce the tendency to sample areas with smaller prediction uncertainty.

[0022] The present invention also provides an application of a sequential test design method based on a maximum entropy search criterion in the evaluation of the anti-interference performance of a radar seeker.

[0023] Furthermore, the radar seeker anti-interference performance evaluation includes evaluating the influence of the towing distance and the ship speed on the angular tracking accuracy.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] The present invention adopts the modified information gain as the acquisition function. The resulting sequential design method has the characteristics of avoiding densely sampled areas and tending to sample areas with strong prediction uncertainty while maintaining a strong sampling tendency for sample points near the optimal point of the system. It can not only achieve "mining" near the optimal point of the system, but also "explore" areas with sparse test points, avoiding the final design method from aggregating in the test space, thereby ensuring global optimization of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a flow chart of a sequential experiment design method based on maximum entropy search criterion provided by an embodiment of the present invention;

[0027] Figure 2 is a schematic diagram of a distance dragging anti-interference test provided by an embodiment of the present invention;

[0028] FIG3( a ) is a diagram showing the distribution of sample points in the sequential experiment design method provided by an embodiment of the present invention;

[0029] FIG3( b ) is a diagram showing the distribution of sample points in the Latin hypercube experimental design method provided in an embodiment of the present invention;

[0030] FIG3( c ) is a diagram showing the distribution of sample points in a uniform design according to an embodiment of the present invention;

[0031] Figure 4 It is a comparison chart of response errors of the model prediction maximum points of the sequential experimental design, Latin hypercube design, and uniform design provided in the embodiment of the present invention. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0033] The implementation of the present invention is described in detail below in conjunction with specific embodiments.

[0034] The same or similar numbers in the drawings of this embodiment correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right" and the like indicate directions or positional relationships based on the directions or positional relationships shown in the drawings, it is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific direction, be constructed and operated in a specific direction. Therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes and cannot be understood as limitations on this patent. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0035] Reference Figure 1-4 The figure shows a preferred embodiment of the present invention.

[0036] A sequential experiment design method based on maximum entropy search criterion specifically comprises the following steps:

[0037] S1: Conduct initial experimental design and obtain the initial sample set D0;

[0038] S2: Based on the currently known sample information D t Constructing the proxy model f t (x);

[0039] S3: In the current proxy model f t (x), the next test point x is determined according to the acquisition function corresponding to the maximum entropy search criterion. t+1 = arg max a t (x);

[0040] In this embodiment, the proxy model f t (x) is the Kriging model, which predicts the mean value of the system response at each candidate sample point x The predicted standard deviation

[0041] The acquisition function of this embodiment is constructed based on the maximum entropy search criterion, and its calculation method is as follows:

[0042] (1) By Kriging model f t (x) Get the posterior Gaussian distribution, sample the function K times from it, and maximize the function to obtain the maximum value y * = arg max f t K samples of (x);

[0043] (2) The predicted mean value of the Kriging model at the candidate sample point x The predicted standard deviation Get the modified predicted mean:

[0044]

[0045] in, k is the correction factor, Used to adjust the impact of prediction uncertainty on sampling tendency, is a penalty term used to reduce the tendency to sample areas with smaller prediction uncertainty;

[0046] (3) The information gain between the corrected prediction result and the maximum value of the function is regarded as the acquisition function, which is calculated as follows:

[0047]

[0048] in,

[0049]

[0050] represents information entropy, and ψ(·) represents the density function of the standard normal distribution.

[0051] S4: Evaluate test point x t+1 The performance at which the sample set D is updated t+1 ;

[0052] S5: Determine whether the test stop condition is met. If so, stop the test; if not, repeat the operations of S2-S5.

[0053] Specific examples:

[0054] Taking the digital simulation of the anti-interference performance evaluation of a certain type of anti-ship radar seeker as an example, the technical solution of this embodiment is further explained. This example focuses on the angle tracking accuracy under different level combinations of test factors. (Unit: °) boundary performance.

[0055] like Figure 2 As shown, the angular tracking accuracy Affected by many factors such as towing distance, ship speed, ship direction, interference power, interference bandwidth, and specific missile targets, this embodiment selects the towing distance (unit: km) and ship speed (unit: knot) as experimental variables, fixes other factors at a certain level, and studies the experimental variable diagonal tracking accuracy. impact.

[0056] This example compares uniform design, Latin hypercube design, and sequential design method based on maximum entropy search criteria. In the experiment, Kriging model was used to build the model, and then the accuracy of the maximum point position predicted by the model under the current sample data was compared. In this case, Inference Regret (IR) was used to evaluate the prediction error of the maximum value of the seeker angle tracking accuracy of the model constructed under different test schemes. IR is calculated as follows:

[0057] IR=y max -y(x * );

[0058] Among them, x * =arg maxf(x) is the maximum point predicted by the model, y max =max y(x) is the maximum value of the real response of the model. In fact, IR is the difference between the response at the maximum value point predicted by the model and the actual maximum value of the response. IR can quantitatively reflect the accuracy of the model's prediction of the maximum value point.

[0059] For the sequential design method of the maximum entropy search criterion, first, 10 sample points are designed as the initial sample D0 through Latin hypercube. Then, new sample points are added one by one based on the Kriging model and the maximum entropy search criterion until the total number of samples reaches 20. When the total number of samples reaches 20, the experiment is stopped. For Latin hypercube design and uniform design, since the design scheme of one-time design is highly correlated with the sample size, experimental design schemes are provided under each sample capacity condition between [10,20].

[0060] Figure 3 compares the design schemes of different experimental design methods under the condition that the total number of samples is 15. It can be clearly seen that in the scheme corresponding to the sequential design, most of the newly added samples are concentrated near the real maximum point, and some points fall in the area where the sample points are sparse in the experimental space. In the schemes corresponding to the Latin hypercube design and the uniform design, the sample points are relatively evenly dispersed, and less information is obtained near the maximum point.

[0061] The prediction effects of the models corresponding to the three design methods are compared as follows: Figure 4As shown in the figure, with the addition of new samples, the response error IR of the Kriging model corresponding to the sequential design for the prediction of the maximum point decreases rapidly. When the total sample size is 15, the IR decreases to close to 0; when the total sample size is 10, the IR decreases to 0. This shows that the sequential design method can be targeted to supplement the test at the location with higher angular tracking amount, and finally determine its extreme point. In contrast, when using Latin hypercube design or uniform design, increasing the total sample size has limited effect on reducing IR. Sometimes, the IR value will increase after increasing the sample size. This is because the scheme of the one-time test design is closely related to the total sample size, and the schemes corresponding to different sample numbers are not closely related. In addition, this type of design method does not pay attention to the response value of the sample.

[0062] Based on the above comparison results, it can be seen that under the condition of the same number of samples, the sequential design method can set the locations of the experimental sample points more specifically, thereby improving the optimization efficiency and finding the boundary performance of the target response more quickly.

[0063] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A sequential test design method for evaluating the anti-interference performance of a radar seeker, characterized in that: The specific steps include: S1: Conduct initial experimental design and obtain the initial sample set; Specifically, the towing distance and the ship speed are selected as the test variables, other factors are fixed at a certain level, and the test variables are used as sample points to be brought into the simulation program to obtain the corresponding response output value, that is, the diagonal tracking accuracy. The coordinates of each sample point in the sample set represent the specific values ​​of the two parameters, the ship speed and the towing distance. The other factors include but are not limited to the ship direction, interference power, interference bandwidth and projectile target; S2: Build a proxy model based on the currently known sample information; Specifically, the sample point coordinates of the ship speed and the towing distance are regarded as independent variables, and the corresponding angular tracking accuracy is regarded as the dependent variable, and a function reflecting the relationship between the angular tracking accuracy and the ship speed and the towing distance is established, namely, the proxy model; S3: Based on the current proxy model, the next test point is determined according to the acquisition function corresponding to the maximum entropy search criterion; The acquisition function is calculated as follows: S31, by the agent model f t (x) Get the posterior Gaussian distribution, sample the function K times from it, and maximize the function to obtain the maximum value y * = arg max f t K samples of (x); S32, the predicted mean value of the surrogate model at the candidate sample point x The predicted standard deviation Get the corrected predicted mean y adj ; S33, compare the corrected prediction result with the function maximum value y * The information gain between is regarded as the acquisition function, which is calculated as follows: in, In the formula, y adj is the corrected prediction mean of the surrogate model at the candidate sample point x; Represents y adj The information entropy of ; ψ(·) represents the probability density function of the standard normal distribution; k is the correction parameter, Used to adjust the impact of prediction uncertainty on sampling tendency, is a penalty term used to reduce the tendency to sample areas with smaller prediction uncertainty; S4: Use the prediction error of the maximum value of the seeker angle tracking accuracy of the model constructed by IR evaluation to evaluate the performance at the test point and update the sample set; The IR is calculated as follows: IR=y max -y(x * ); Among them, x * =arg maxf(x) is the maximum point predicted by the model, y max =max y(x) is the maximum value of the true response of the model; S5: Determine whether the test stop condition is met. If so, stop the test; if not, repeat the operations of S2-S5.

2. A sequential test design method for evaluating the anti-interference performance of a radar seeker according to claim 1, characterized in that: The proxy model is a Kriging model.

3. A sequential test design method for evaluating the anti-interference performance of a radar seeker according to claim 2, characterized in that: The corrected prediction mean of the Kriging model at the candidate sample point x is: in, k is the correction factor, Used to adjust the impact of prediction uncertainty on sampling tendency, is a penalty term used to reduce the tendency to sample areas with smaller prediction uncertainty.

4. Application of a sequential experimental design method for radar seeker anti-interference performance evaluation according to any one of claims 1 to 3 in radar seeker anti-interference performance evaluation.

5. The use according to claim 4, characterized in that: The radar seeker anti-interference performance evaluation includes evaluating the influence of towing distance and ship speed on angular tracking accuracy.

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