CN117932882A - Variable reliability sequential test design method based on maximum entropy attenuation search criterion - Google Patents

Variable reliability sequential test design method based on maximum entropy attenuation search criterion Download PDF

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CN117932882A
CN117932882A CN202311768852.0A CN202311768852A CN117932882A CN 117932882 A CN117932882 A CN 117932882A CN 202311768852 A CN202311768852 A CN 202311768852A CN 117932882 A CN117932882 A CN 117932882A
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晏良
龚卓
段晓君
陈璇
肖意可
王柄霖
刘家伟
孙欣雨
胡家楠
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National University of Defense Technology
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Abstract

The invention relates to the technical field of sequential experiments, in particular to a variable credibility sequential experiment design method based on maximum entropy attenuation search criteria, which comprises the following steps: s1: performing initial test design, and performing corresponding tests on the low-reliability test sample points and the high-reliability test sample points respectively to obtain an initial sample set; s2: constructing a variable credibility proxy model according to the current known sample information; s3: determining a next test point according to the current variable reliability agent model and an acquisition function corresponding to the maximum entropy attenuation search criterion; s4: evaluating performance of the test point in the test of the reliability level of the first t+1 at the x t+1 th, and updating the sample set; s5: judging whether a test stopping condition is met; if yes, stopping the test, and if not, repeating the operations of S2-S5. According to the test design method, the position of a sample point in a next test and the test reliability level can be selected in a self-adaptive mode according to the current data information.

Description

Variable reliability sequential test design method based on maximum entropy attenuation search criterion
Technical Field
The invention relates to the technical field of sequential experiments, in particular to a variable reliability sequential experiment design method based on maximum entropy attenuation search criteria.
Background
For complex systems, the assembly test needs to consume a large amount of manpower and material resources, and is difficult to develop in a large amount. In order to reduce the cost of acquiring the system performance information, simulation tests constructed according to corresponding mechanisms under similar conditions are generated. For example, the technology is equivalent to "virtual" development of a test in a computer, and the test result has a certain deviation from a real assembly test, but can show certain characteristics of a real system as a whole, so that the technology has certain reference value. Depending on the level of accuracy, a test with a higher level of accuracy such as a mounting test may be referred to as a High-reliability (HF) test, and a test with a relatively lower level of accuracy may be referred to as a Low-reliability (LF) test. The data precision of the high-reliability test is high, but the acquisition cost of the data is high, and if the system performance is optimized and evaluated by the high-reliability test, the test cost is difficult to bear; the data acquisition cost of the low-reliability test is lower, but the accuracy level is difficult to meet the requirement, and if the low-reliability test is only relied on for optimization and evaluation, the finally obtained optimization and evaluation result is difficult to reflect the real characteristics of the system. Under the background, performance optimization and evaluation methods for multi-credibility tests are developed, the methods utilize the respective advantages of the high/low credibility tests, more low-credibility test points are used for reducing the overall test cost, and a small number of high-credibility test points are used for guaranteeing the accuracy of the evaluation result, so that the contradiction relation between the test cost and the evaluation accuracy can be effectively balanced, and huge potential is shown in the optimization and evaluation of a complex system.
Similar to the design method for the single confidence test, the test design method for the multi-confidence test can be roughly divided into two types: a one-time test design method and a sequential test design method; the disposable test design method uses all available resources for obtaining all sample points at one time, and the corresponding test design scheme is usually determined before the test starts and does not change along with the test result; the sequential test design method is to select sample points of the next test in a targeted manner according to the current test data information in the test evaluation process, and to realize efficient optimization and evaluation of the system in iteration.
For multiple credibility tests, sequential test design not only needs to determine the position of a sample point of each test, but also needs to determine the corresponding test credibility level; the traditional sequential design method can only provide guidance for the selection of the sample point positions, and is difficult to meet the actual requirements of the multi-credibility test. Thus, the applicant has devised a variable confidence sequential trial design method based on maximum entropy decay search criteria.
Disclosure of Invention
The invention aims to provide a variable reliability sequential test design method based on maximum entropy attenuation search criteria, which can adaptively select the position of a sample point and the test reliability level of a next test according to current data information.
The invention is realized in such a way that the variable reliability sequential test design method based on maximum entropy attenuation search criteria specifically comprises the following steps:
S1: performing initial test design, and performing corresponding tests on the low-reliability test sample points and the high-reliability test sample points respectively to obtain an initial sample set;
S2: constructing a variable credibility proxy model according to the current known sample information;
s3: determining a next test point according to the current variable reliability agent model and an acquisition function corresponding to the maximum entropy attenuation search criterion;
The acquisition function is as follows:
wherein, Representing the ratio of the cost of the first confidence level sample relative to the cost of the highest confidence sample,/>The information gain of the high-reliability sample x under the current CoKriging model is obtained; /(I)The residual information gain of the high-reliability sample x is calculated under a hypothetical CoKriging model after the first reliability level sample x is added to the data set;
S4: evaluating performance of the test point in the test of the reliability level of the first t+1 at the x t+1 th, and updating the sample set;
s5: judging whether a test stopping condition is met; if yes, stopping the test, and if not, repeating the operations of S2-S5.
Further, the information gain of the high-reliability sample x under the current CoKriging modelThe calculation mode of (a) is as follows:
residual information gain of the high confidence sample x The calculation mode of (a) is as follows:
wherein,
Phi (·) and phi (·) represent the probability density function and the cumulative distribution function, respectively, of the standard normal distribution; k is the number of function samples, y * is the maximum value of the function, y *＝argmaxf(t) (x).
Further, the variable reliability proxy model is CoKriging model.
The invention also provides application of the variable reliability sequential test design method based on the maximum entropy attenuation search criterion in complex equipment system evaluation and optimization.
Compared with the prior art, the invention has the beneficial effects that: the sequential test design method adopts the acquisition function corresponding to the maximum entropy attenuation search criterion, can combine different credible data information, and improves the optimization and evaluation efficiency of the system; meanwhile, the sequential design method can flexibly use the low-reliability samples in the optimization and evaluation process of the system, and reduce the requirements for the high-reliability samples, so that the test cost is reduced.
Drawings
FIG. 1 is a flow chart of a variable confidence sequential trial design method based on maximum entropy decay search criteria provided by an embodiment of the present invention;
FIG. 2 (a) is a schematic diagram of a low-confidence Kriging model created from 50 digital simulation test data provided by an embodiment of the present invention;
FIG. 2 (b) is a schematic diagram of a high-reliability Kriging model constructed by 6 semi-physical simulation test data according to an embodiment of the present invention;
FIG. 2 (c) is a schematic diagram of a CoKriging model constructed from 50 digital simulation test data and 6 semi-physical simulation test data, provided by an embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The implementation of the present invention will be described in detail below with reference to specific embodiments.
The same or similar reference numerals in the drawings of the present embodiment correspond to the same or similar components; in the description of the present invention, it should be understood that, if there is an azimuth or positional relationship indicated by terms such as "upper", "lower", "left", "right", etc., based on the azimuth or positional relationship shown in the drawings, it is only for convenience of describing the present invention and simplifying the description, but it is not indicated or implied that the apparatus or element referred to must have a specific azimuth, be constructed and operated in a specific azimuth, and thus terms describing the positional relationship in the drawings are merely illustrative and should not be construed as limitations of the present patent, and specific meanings of the terms described above may be understood by those skilled in the art according to specific circumstances.
Referring to fig. 1-2, a preferred embodiment of the present invention is provided.
The variable reliability sequential test design method based on maximum entropy attenuation search criteria specifically comprises the following steps:
S1: performing initial test design, and performing corresponding tests on the low-reliability test sample point and the high-reliability test sample point respectively to obtain an initial sample set D (0);
S2: constructing CoKriging model f (t) (x) according to the current known sample information D (t);
S3: determining a next test point x t+1,lt+1＝argmax αDMES,t (x, l) according to the current variable reliability agent model and an acquisition function corresponding to a maximum entropy decay search (DECREASED MAX-value Entropy Search, DMES) criterion;
in this embodiment, coKriging model f (t) (x) is a variable confidence proxy model constructed from existing multi-confidence data that can provide a predictive mean for different confidence level models And prediction standard deviationThe higher l is the confidence level of the sample, the higher the data confidence.
The maximum entropy decay search criterion is the core of the method. The criterion is an entropy-based variable confidence sequential criterion extended by a maximum entropy search (Max-value Entropy Search, MES) criterion, aiming at finding samples that maximize the attenuation of the sample information gain. Taking data of two credibility levels as an example, the acquisition function corresponding to the DMES criterion can be calculated by the following procedure:
(1) Obtaining a posterior Gaussian distribution from CoKriging model f (t) (x), sampling the function K times from the posterior Gaussian distribution, and maximizing the function to obtain K samples of a function maximum y *＝argmaxf(t) (x);
(2) Respectively calculating information gain of high-reliability sample x under current CoKriging model And under a hypothetical CoKriging model with a hypothetical first confidence level sample x added to the dataset, the remaining information gain/>, of the high confidence sample xThe calculation mode is as follows:
wherein,
Wherein, phi (·) and phi (·) represent the probability density function and the cumulative distribution function of the standard normal distribution, respectively;
(3) And calculating the difference value of the information gain before and after the addition of the imaginary sample, wherein the difference value between the two information gain and the imaginary sample represents the degree of entropy attenuation before and after the first credibility level x is determined, namely the information contained in the sample. On the basis of which the cost ratio CR l is introduced, the acquisition function corresponding to the DMES criterion can be obtained as follows:
wherein, The smaller the ratio, which represents the ratio of the cost of the first confidence level sample to the cost of the highest confidence sample, the lower the cost of the hierarchical sample. This term represents the sampling propensity between different confidence samples due to acquisition costs, balancing the high potential value of the high confidence samples themselves with the high costs.
S4: evaluating the performance of the test point x t+1 in the first t+1 credibility level test, and updating a sample set D t+1;
S5: judging whether the test stopping condition is met: if yes, stopping the test; otherwise, repeating the operations of S2-S5.
Specific examples:
Taking the evaluation of the anti-interference performance boundary of a certain anti-ship missile radar seeker as an example, the application of the variable reliability sequential design in the evaluation and optimization of a complex equipment system is shown. In the performance boundary evaluation process of a certain type of radar seeker, in order to save test resources, an evaluator develops a numerical simulation test, a semi-physical simulation test and a mounting test in stages. The data of the numerical simulation test are relatively cheapest and easy to obtain, however, the reliability level is low, and the test data at the stage can be used for establishing a low-reliability agent model to represent the overall system trend. The semi-physical simulation test has a relatively high data reliability level, but has high acquisition cost, so that the quantity of the semi-physical simulation test is limited. In order to fully utilize the data information, the data information can be regarded as high-reliability data, and the high-reliability data is combined with a low-reliability model obtained in a numerical simulation test to obtain a variable-reliability proxy model.
The low confidence Kriging model built from 50 digital simulation test data, the high confidence Kriging model built from only 6 semi-physical simulation test data, and the CoKriging model built from a combination of these two sets of data are shown in fig. 2, respectively. It can be seen that fig. 2 (a) shows complex variations throughout the test space, indicating that the model has substantially knowledge of the overall information of the low confidence system. However, comparing fig. 2 (b), it can be seen that the relative size between the two distinct peaks predicted in fig. 2 (a) is different from fig. 2 (b), and that there are three peaks in fig. 2 (a), and that the depiction of one of the peaks by fig. 2 (b) is significantly biased.
Sequential sampling is performed to compare the optimization effects according to the following three modes:
(1) Based on a high-reliability proxy model, sequentially sampling by using an EI criterion;
(2) Based on CoKriging model, sequentially sampling by utilizing VFEI criterion;
(3) Sequential sampling is performed using DMES criteria based on CoKriging model.
For ease of comparison, the average lift rate (Average Improvement Rate, AIR) is defined as follows:
Wherein Y h is high-reliability sample data, namely the measuring precision of the angle of the guide head obtained by a semi-physical simulation test, Representing newly performed semi-physical simulation test data. When the AIR is more than or equal to 30%, stopping optimizing, namely stopping the condition that the AIR is more than or equal to 30%.
The sampling results corresponding to the different methods are shown in table 1, and it can be seen that the method adopting the variable reliability sequential design can obtain more than 30% of optimization promotion only through 2 times of semi-physical simulation tests, and compared with the method, the optimization process based on single reliability can obtain similar effects only through 4 times of semi-physical simulation tests. By using variable reliability optimization, the total number of high-precision samples required for achieving the optimization effect is reduced from 10 samples to 8 samples, and the total test cost can be reduced by 20% under the condition that the numerical simulation test cost is not calculated.
The optimization effect of the DMES criterion and VFEI criterion are then compared. It can be seen that the VFEI criteria directed optimization process was chosen to be performed only twice with low confidence tests, and both in the middle of the optimization process; in contrast, the optimization process corresponding to the DMES criterion uses a large amount of low-reliability data in the early stage, only supplements a high-reliability test in the middle, and finally directly obtains the high-reliability optimization result. From the AIR value, the DMES criterion and VFEI criterion were only subjected to two high-confidence tests, but the DMES criterion corresponded to a better improvement effect than VFEI criterion, and the optimization effect exceeded about 2.4%. The test results show that the DMES criterion can fully utilize the low-reliability data information and grasp global trend more, so that optimization can be carried out more pertinently.
Table 1 sampling results corresponding to different methods
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.

Claims (4)

1. The variable reliability sequential test design method based on maximum entropy attenuation search criteria is characterized by comprising the following steps of:
S1: performing initial test design, and performing corresponding tests on the low-reliability test sample points and the high-reliability test sample points respectively to obtain an initial sample set;
S2: constructing a variable credibility proxy model according to the current known sample information;
s3: determining a next test point according to the current variable reliability agent model and an acquisition function corresponding to the maximum entropy attenuation search criterion;
The acquisition function is as follows:
wherein, Representing the ratio of the cost of the first confidence level sample relative to the cost of the highest confidence sample,/>The information gain of the high-reliability sample x under the current CoKriging model is obtained; /(I)The residual information gain of the high-reliability sample x is calculated under a hypothetical CoKriging model after the first reliability level sample x is added to the data set;
S4: evaluating performance of the test point in the test of the reliability level of the first t+1 at the x t+1 th, and updating the sample set;
s5: judging whether a test stopping condition is met; if yes, stopping the test, and if not, repeating the operations of S2-S5.
2. The maximum entropy decay search criterion based variable confidence sequential trial design method of claim 1, wherein the information gain of the high confidence sample x under the current CoKriging modelThe calculation mode of (a) is as follows:
residual information gain of the high confidence sample x The calculation mode of (a) is as follows:
wherein,
Phi (·) and phi (·) represent the probability density function and the cumulative distribution function, respectively, of the standard normal distribution; k is the number of function samples, y * is the maximum value of the function, y *＝arg maxf(t) (x).
3. The maximum entropy decay search criterion based variable confidence sequential trial design method of claim 1, wherein the variable confidence proxy model is a CoKriging model.
4. Use of the variable reliability sequential trial design method based on maximum entropy decay search criteria of any of claims 1-3 in complex equipment system assessment and optimization.
CN202311768852.0A 2023-12-21 2023-12-21 Variable reliability sequential test design method based on maximum entropy attenuation search criterion Pending CN117932882A (en)

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