IDW-Kriging-based adaptive sample enhancement method

Abstract

The invention discloses a self-adaptive sample enhancement method based on IDW-Kriging. The method comprises the following steps: configuring initial parameters; preprocessing the sample data in the original sample set to reduce the change degree of the sample data, and obtaining a preprocessed sample set; respectively obtaining an initial IDW interpolation curve and an initial Kriging interpolation curve according to the preprocessed sample data; comparing the initial IDW interpolation curve with the initial Kriging interpolation curve, and automatically searching potential extreme points greater than an interpolation threshold value; simulation is carried out again at the potential extreme points, a new sample data supplementary sample set is obtained, and new sample data is preprocessed; an IDW interpolation curve and a Kriging interpolation curve are obtained again according to the updated sample set; and judging whether the maximum number of iterations is reached, if not, executing the above steps, and if yes, storing the Kriging interpolation curve as an enhanced sample set. According to the method, potential extreme points can be adaptively found, adaptive construction of samples is realized, and numerical simulation density does not need to be adjusted according to empirical judgment.

Description

Technical Field

[0001] The present invention belongs to the technical field of big data model construction, and in particular relates to an adaptive sample enhancement method based on IDW-Kriging. Background Art

[0002] During product design, manufacturing, and operation and maintenance, it is necessary to simulate and predict the mechanical, thermal, electromagnetic and other properties of the product in order to achieve optimal product design and operation control. Traditional methods achieve this goal through two approaches: empirical formulas and numerical simulation. Empirical formulas are only applicable to typical structural calculations, and the calculation errors for complex product performance simulations are large; although numerical simulations have accurate calculation results, they take a long time to calculate, require a lot of computing power, and provide untimely feedback, making it difficult to meet the high-real-time simulation application requirements such as virtual-reality integration and autonomous decision-making in intelligent manufacturing and intelligent operation and maintenance scenarios.

[0003] Surrogate model is a method that has emerged in recent years to predict product performance in real time based on a large amount of sample data. Kriging interpolation is the most widely used surrogate model method. Kriging interpolation can obtain calculation results comparable to numerical simulation in the same calculation time as the empirical formula, so it is widely used in geographic data calculation, structural fatigue life estimation, fluid dynamics optimization, aircraft radar cross-section (RCS) simulation, etc.

[0004] However, in practice, it is found that the Kriging interpolation method has the problem of "large prediction error near extreme points" when processing large gradient data sample sets. When the simulation samples are processed by Kriging, the error between the predicted value and the actual simulation value is very small at the location with small gradient, but at the minimum or maximum value, the error between the Kriging predicted value and the actual simulation value can reach 5dBsm, which is unacceptable in engineering applications. Therefore, in the processing of such data sets, the Kriging interpolation method cannot be directly applied for simulation prediction.

[0005] Although this problem can be alleviated by increasing the number of samples, it is difficult to cover all extreme points with uniform sample density enhancement, and the effect on improving the overall simulation accuracy is very limited. At the same time, sample data cannot increase infinitely, and a large increase in sample data will lead to a sharp increase in the memory and time consumed by Kriging interpolation calculations. Summary of the invention

[0006] In order to solve the above problems existing in the prior art, the present invention provides an adaptive sample enhancement method based on IDW-Kriging. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0007] The present invention provides an adaptive sample enhancement method based on IDW-Kriging, comprising:

[0008] S1: Configure initial parameters, including Kriging parameters θ kriging , IDW interpolation smoothing parameter α, sampling interval, difference threshold and maximum number of iterations of IDW interpolation method and Kriging interpolation method;

[0009] S2: preprocessing the sample data in the original sample set to reduce the degree of variation of the sample data, and obtaining a preprocessed sample set;

[0010] S3: Obtaining an initial IDW interpolation curve and an initial Kriging interpolation curve according to the preprocessed sample set;

[0011] S4: comparing the initial IDW interpolation curve and the initial Kriging interpolation curve to obtain potential extreme value points greater than the difference threshold;

[0012] S5: re-simulating at the potential extreme point to obtain new sample data to supplement the sample set, and pre-processing the new sample data to obtain an updated sample set;

[0013] S6: re-obtaining an IDW interpolation curve and a Kriging interpolation curve according to the updated sample set;

[0014] S7: Determine whether the maximum number of iterations has been reached. If not, execute step S4. If yes, save the Kriging interpolation curve as the enhanced sample set.

[0015] In one embodiment of the present invention, the S2 includes:

[0016] S2.1: A plurality of original sample data are obtained according to actual measurement or simulation methods to form an original sample set, wherein the original sample data in the original sample set includes angular domain sample points or frequency domain sample points, wherein the input data of the angular domain sample points is the incident angle The output data is an RCS value, the input data of the frequency domain sample point is a frequency, and the output data is an RCS value;

[0017] S2.2: Perform data translation on the RCS values ​​of the angular domain sample points or the frequency domain sample points in the original sample data, and define a new RCS value σ′(before)=σ(before)+1, so that the RCS value σ′(before) of each angular domain sample point or frequency domain sample point after data translation is in the interval [1, +∞], where σ(before) is the RCS value of the angular domain sample point or the frequency domain sample point in the original sample data;

[0018] S2.3: Use the log function to transform the data of σ′(before). The conversion formula is:

[0019] σ′(after)=10·lg(σ′(before)),

[0020] Wherein, σ′(after) represents the RCS value of each angular domain sample point or frequency domain sample point after data conversion, that is, the RCS value after preprocessing.

[0021] In one embodiment of the present invention, S3 includes:

[0022] S3.1: According to the preprocessed sample set, the RCS values ​​of multiple prediction points are obtained by using the IDW interpolation method, and an IDW interpolation curve is formed according to the multiple prediction points, wherein the preprocessed sample set includes preprocessed angular domain sample points or preprocessed frequency domain sample points, wherein the preprocessed angular domain sample points include incident angle and the corresponding preprocessed RCS value; the preprocessed frequency domain sample point includes the frequency and the corresponding preprocessed RCS value;

[0023] S3.2: Based on the preprocessed sample set, the initial Kriging interpolation curve is obtained using the Kriging interpolation method.

[0024] In one embodiment of the present invention, the S3.1 includes:

[0025] According to the preprocessed sample set, the IDW interpolation method is used to obtain the RCS values ​​of multiple prediction points. The calculation formula is:

[0026]

[0027] Among them, Z represents the predicted point at the preset angle, d Zi represents the distance between the predicted point Z and the known sample point i in the preprocessed sample set, α is the set parameter, and w Zi represents the distance weight value between the predicted point Z and the known sample point i, N represents the number of known sample points in the preprocessed sample set, RCS i is the RCS value of the known sample point i, Represents the predicted value of RCS at the prediction point Z;

[0028] An IDW interpolation curve is formed according to the plurality of prediction points.

[0029] In one embodiment of the present invention, the S4 includes:

[0030] The actual difference of the RCS value of the same prediction point on the initial IDW interpolation curve and the initial Kriging interpolation curve is calculated in turn, and it is determined whether it is greater than a preset difference threshold. If so, the current prediction point is considered to be a potential extreme point, and all potential extreme points on the initial IDW interpolation curve and the initial Kriging interpolation curve are obtained.

[0031] In one embodiment of the present invention, the S5 includes:

[0032] Re-simulating at the potential extreme point using a numerical method, obtaining a corresponding RCS value through input angle or frequency simulation at the potential extreme point, thereby forming new sample data, and supplementing it to the current sample set;

[0033] The new sample data is subjected to data translation and log function processing.

[0034] In one embodiment of the present invention, the S7 includes:

[0035] Determine whether the current number of iterations reaches the maximum number of iterations. If not, execute step S4 to continue searching for potential extreme points on the current IDW interpolation curve and the current Kriging interpolation curve. If yes, obtain the current Kriging interpolation curve.

[0036] The sample data on the current Kriging interpolation curve is converted, and the conversion formula is:

[0037]

[0038] Among them, σ′(after) is the RCS value of the interpolation point on the current Kriging interpolation curve, and σ(after) is the RCS value of the interpolation point of the current Kriging interpolation curve after restoration.

[0039] Another aspect of the present invention provides a storage medium, in which a computer program is stored, and the computer program is used to execute the steps of the adaptive sample enhancement method based on IDW-Kriging as described in any one of the above embodiments.

[0040] Another aspect of the present invention provides an electronic device, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor calls the computer program in the memory, the steps of the adaptive sample enhancement method based on IDW-Kriging as described in any one of the above embodiments are implemented.

[0041] Compared with the prior art, the present invention has the following beneficial effects:

[0042] 1. The present invention proposes an adaptive sample enhancement method based on IDW-Kriging. First, the IDW interpolation method and the Kriging interpolation method are used to obtain the initial IDW interpolation curve and the initial Kriging interpolation curve according to the existing sample data set. The position of the extreme point is predicted by comparing the difference between the two interpolation methods at the same position, and then the sample data is supplemented at the predicted extreme point position. Finally, the overall prediction accuracy of the Kriging interpolation method is significantly improved when a small amount of sample data is supplemented. The method of the present invention can adaptively find the required simulation sample points, and for models of different complexity, adaptive control of the data volume can be achieved without the need to judge the density of the simulation value based on experience like the traditional proxy model. It has a broader application prospect and solves the limitation that the traditional interpolation method needs to adjust the numerical simulation density based on experience.

[0043] 2. The adaptive sample enhancement method of the present invention performs data preprocessing before constructing the proxy model to improve the accuracy of the proxy model, ultimately achieving the goal of reducing the amount of data required for simulation and building a high-quality RCS proxy model. The effectiveness of the adaptive sample enhancement method based on IDW-Kriging of the present invention was verified by the proxy model of the RCS of an aircraft. The results show that the prediction accuracy of the proxy model after adaptive sample enhancement is improved by more than 70% compared with the traditional Kriging model.

[0044] 3. The method of the present invention can better capture small but important local features in curves or three-dimensional surface models. Compared with traditional uniform one-time sampling, the method of the present invention more accurately reconstructs the relationship between the input and output of the target. The number of burrs in the error analysis graph of the proxy model constructed by the present invention is significantly less than that of the uniformly sampled burrs, and the maximum value of the burrs is smaller, that is, the error is smaller.

[0045] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 is a flow chart of an IDW-Kriging-based adaptive sample enhancement method provided by an embodiment of the present invention;

[0047] Figure 2 Schematic diagram of a processing process of an IDW-Kriging adaptive sample enhancement method provided by an embodiment of the present invention;

[0048] Figure 3 is a schematic diagram of an IDW interpolation curve when the parameter α provided by an embodiment of the present invention takes different values;

[0049] Figure 4is the spatial correlation function R and the distance d under different values ​​of the Kriging interpolation parameter θ k The relationship diagram between

[0050] Figure 5 It is a process diagram for demonstrating iteratively adding sample points and correcting the proxy model curve proposed in an embodiment of the present invention;

[0051] Figure 6 It is an angular domain proxy model obtained by the first iteration and the fourth iteration of the adaptive sample enhancement method based on IDW-Kriging of the present invention;

[0052] Figure 7 It is a schematic diagram of error analysis of the angular domain proxy model obtained by the first iteration and the fourth iteration of the adaptive sample enhancement method based on IDW-Kriging of the present invention;

[0053] Figure 8 It is a fitted scatter plot of the first iteration and the fourth iteration of the adaptive sample enhancement method based on IDW-Kriging of the present invention;

[0054] Fig. 9 It is a comparison of the frequency domain proxy models obtained by the first iteration and the fourth iteration of the adaptive sample enhancement method based on IDW-Kriging of the present invention;

[0055] Fig.10 It is an angular domain error analysis diagram of the proxy model constructed by the traditional Kriging method and the proxy model constructed by the method of the present invention;

[0056] Fig.11 It is a scatter plot of the angular domain fitting of the proxy model constructed by the traditional Kriging method and the method of the present invention;

[0057] Fig.12 It is a frequency domain error analysis comparison diagram of the proxy model constructed by the traditional Kriging method and the method of the present invention. DETAILED DESCRIPTION

[0058] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, an adaptive sample enhancement method based on IDW-Kriging proposed by the present invention is described in detail below in combination with the accompanying drawings and specific implementation methods.

[0059] The above and other technical contents, features and effects of the present invention are clearly presented in the following detailed description of the specific implementation modes in conjunction with the accompanying drawings. Through the description of the specific implementation modes, the technical means and effects adopted by the present invention to achieve the predetermined purpose can be more deeply and specifically understood. However, the attached drawings are only for reference and explanation purposes and are not used to limit the technical solutions of the present invention.

[0060] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants are intended to cover non-exclusive inclusion, so that an article or device including a series of elements includes not only those elements, but also other elements that are not explicitly listed. In the absence of more restrictions, the elements defined by the statement "including one..." do not exclude the existence of other identical elements in the article or device including the elements.

[0061] Embodiment 1

[0062] In this embodiment, an adaptive sample enhancement method based on IDW (Inverse Distance Weight) and Kriging (Kriging interpolation) is proposed to improve the accuracy of the Kriging interpolation surface model, in order to solve the problem of large prediction errors near extreme points when performing Kriging interpolation on a large gradient data sample set.

[0063] See also Figure 1 and Figure 2 , Figure 1 is a flow chart of an IDW-Kriging-based adaptive sample enhancement method provided by an embodiment of the present invention; Figure 2 This is a schematic diagram of a processing process based on an IDW-Kriging adaptive sample enhancement method provided by an embodiment of the present invention. The basic idea of ​​the adaptive sample enhancement method is: by performing IDW interpolation and Kriging interpolation on the original sample set respectively, by comparing the difference between the two interpolation methods at the same position, the extreme position of the proxy model surface is automatically perceived; then the sample data is supplemented at the extreme position and added to the existing data sample set; the above operation is continuously iterated to achieve adaptive enhancement of the data sample and significantly reduce the prediction error.

[0064] The specific steps of the adaptive sample enhancement method include:

[0065] S1: Configure initial parameters, including Kriging parameters θ kriging, IDW interpolation smoothing parameter α, sampling interval, difference threshold between IDW interpolation method and Kriging interpolation method, and maximum number of iterations.

[0066] In this embodiment, the Kriging parameter θ kriging is set to 5, the IDW interpolation smoothing parameter α is set to 2, the sampling interval is set to 1 degree, the difference threshold between the IDW interpolation method and the Kriging interpolation method is set to 1, that is, when the difference between the IDW interpolation method and the Kriging interpolation method at the same position is greater than 1, the interpolation point is added, and the maximum number of iterations is set to 4. In this embodiment, RCS (Radar Cross Section) is used as an example for simulation, including frequency domain simulation and angular domain simulation, which correspond to the construction of a relatively gentle proxy model and a drastic proxy model.

[0067] S2: Preprocess the sample data in the original sample set to reduce the degree of variation of the sample data and obtain a preprocessed sample set. This embodiment uses a numerical method to simulate the original sample points (i.e., sample data) used to train the proxy model to form the original sample set, and reduces the impact of large gradient data on the proxy model by Log function processing and translation data.

[0068] This step specifically includes:

[0069] S2.1: Obtain multiple original sample data according to actual measurement or simulation methods to form an original sample set.

[0070] Usually, the sample data in the original sample set should be in the form of xy, that is, the sample data corresponding to the input and the output, or in the form of (x, y)-z, that is, the sample data corresponding to one output with multiple inputs. In this embodiment, the Feko simulation software is used to simulate the angular domain sample points or the frequency domain sample points by numerical method to form the original sample set, that is, the original sample data in the original sample set includes the angular domain sample points or the frequency domain sample points, wherein the angular domain sample points are the incident angles. (pitch angle, azimuth) and RCS value in a one-to-one correspondence format, and the frequency domain sample point is in a one-to-one correspondence format between frequency and RCS value. That is to say, if the sample set is used to train the angular domain proxy model, the input of the angular domain proxy model is The output is the RCS value corresponding to the angle; if the sample set is used to train the frequency domain proxy model, the input of the frequency domain proxy model is the frequency, and the output is the RCS value at the frequency.

[0071] S2.2: Perform data shift on the original sample data before interpolation.

[0072] This step requires data preprocessing of the original sample data in the original sample set to reduce the degree of variation of the sample data. Since the object values ​​that the proxy model needs to build may vary greatly, the log function is used for processing. The calculation formula for this conversion is:

[0073] σ(after)=10·lgσ(before)

[0074] Among them, σ(before) represents the original sample data in the original sample set, and σ(after) represents the value required to build the proxy model after transformation.

[0075] Due to the characteristics of the log function, when the original sample data σ(before) is in the interval [0, 1], σ(after) will change dramatically. Therefore, this embodiment preprocesses the RCS values ​​of the angular domain sample points or the frequency domain sample points in the original sample data before interpolation, and defines new sample data σ′(before)=σ(before)+1, so that after the data is shifted, the RCS value σ′(before) of each angular domain sample point or frequency domain sample point is in the interval [1, +∞], where σ(before) is the RCS value of the angular domain sample point or the frequency domain sample point in the original sample data.

[0076] S2.3: Use the log function to transform the new sample data σ′(before). The transformation formula is:

[0077] σ′(after)=10·lg(σ′(before))

[0078] Among them, σ′(after) represents the output data of each angular domain sample point or frequency domain sample point after data conversion, that is, the preprocessed RCS value, which together with the corresponding input data constitute the preprocessed sample data.

[0079] S3: Obtain an initial IDW interpolation curve and an initial Kriging interpolation curve according to the preprocessed sample set.

[0080] Step S3 of this embodiment specifically includes:

[0081] S3.1: According to the preprocessed sample set, the RCS values ​​of multiple prediction points are obtained by using the IDW interpolation method, and an IDW interpolation curve is formed according to the multiple prediction points.

[0082] The preprocessed sample set includes preprocessed angular domain sample points or preprocessed frequency domain sample points, wherein the preprocessed angular domain sample points include the incident angle and the corresponding preprocessed RCS value (after step S2.2 and step S2.3); the preprocessed frequency domain sample points include the frequency and the corresponding preprocessed RCS value (after step S2.2 and step S2.3).

[0083] The IDW (Inverse Distance Weight) interpolation method solves the value of the prediction point based on the distance between the prediction point and the sample point. When calculating the attribute value of a point in space, the IDW interpolation method assigns a larger weight to its surrounding values, and the weight value decreases as the distance increases.

[0084] Assume that the position coordinates of sample points A and B are (x a ,y a ) and (x b ,y b ), then the distance between sample points A and B is defined as:

[0085]

[0086] Among them, d ab is the distance between two sample points A and B. For any predicted point Z at different angles, the calculation formula for its RCS value is as follows:

[0087]

[0088] Among them, d Zi represents the distance between the predicted point Z and the known sample point i in the preprocessed sample set. In this embodiment, the known sample point is a preprocessed angular domain sample point or a preprocessed frequency domain sample point. α is a set parameter. w Zi Represents the distance weight value between the predicted point Z and the known sample point i. The larger the distance between the predicted point Z and the known sample point i, the greater the distance weight value w. Zi The smaller it is, N represents the number of known sample points i in the preprocessed sample set. RCS i is the RCS value of the known sample point i. Represents the predicted value of the RCS of the prediction point Z. When α approaches 0, Approaches the average value of the RCS of all known sample points. When α approaches infinity, Approach the value of the known sample point closest to the predicted point. By adjusting the value of α, interpolation point curves with different degrees of smoothness can be obtained. Among them, the known sample point i is the sample point in the original sample set that has been preprocessed in step S2.

[0089] Then, an IDW interpolation curve can be formed according to the multiple prediction points.

[0090] See also Figure 3, Figure 3 1 is a schematic diagram of the IDW interpolation curve when the parameter α provided by the embodiment of the present invention takes different values. It can be seen that the smaller the parameter α is, the flatter the fitted IDW interpolation curve (corresponding to the red curve in the figure) is, and the larger the parameter α is, the steeper the fitted IDW interpolation curve is. Specifically, Figure 3 (a) is the interpolation result when the parameter α = 0.5. Since the parameter α is very small, the correlation between the predicted point (corresponding to the interpolation point in the figure) and the known sample point (corresponding to the real data in the figure) is little affected by the distance, and the interpolation curve tends to fluctuate around the mean of the known sample points. When the α value is 0, the interpolation curve degenerates to the mean of the sample points. Figure 3 (d) is the interpolation result when the parameter α=4. Since the value of the parameter α is large, the correlation between the predicted point and the known sample point will weaken rapidly with the increase of distance. The predicted point is more affected by the adjacent points. The interpolation curve is closer to the real data formed by the known points, and the interpolation curve will approximately pass through the interpolation point.

[0091] S3.2: Based on the preprocessed sample set, an initial Kriging interpolation curve is obtained using the Kriging interpolation method.

[0092] The Kriging interpolation method uses the data of known points in space to predict the data values ​​of unknown points through weighted summation, but its weight is not simply calculated based on the inverse of the distance, but a set of optimal coefficients is calculated. This method is an existing interpolation method based on optimal, unbiased linear prediction, relying on the spatial autocorrelation of data for prediction. The expression of the Kriging model is:

[0093] G(x)=g T (x)β+z(x)

[0094] Where, g(x) = [g1(x), g2(x), …, g p (x)] T is the polynomial matrix of x, β=[β1,β2,…,β p ] T is the regression coefficient, and p is the number of polynomials. T (x)β is a parameterized polynomial model, which can be constant, linear or second-order polynomial. z(x) is a random process with mean 0.

[0095] Since g(x) has little effect on the fitting result of the Kriging interpolation method, a simple constant polynomial is used in this embodiment, and the conditions are p=1, g(x)=1, that is, g T (x)β=β.

[0096] z(x) can approximate the area of ​​the fitting surface. z(x) obeys the normal distribution, and its mean, variance, and covariance can be expressed as:

[0097] E[z(x)]=0

[0098] Var[z(x)]=σ 2

[0099] Cov[z(x i ), z(x j )]=σ 2 R(x i , x j , θ), i, j=1,2,…,m

[0100] Where σ is the standard deviation of the random error, R(x i , x j ,θ) represents any two sample points x i and x j The spatial correlation function of the Kriging model determines the fitting accuracy of the Kriging model. m represents the total number of sample points. Similar to the IDW interpolation method, the sample point x i and x j The closer the distance is, the greater the correlation is. θ represents the target to be optimized. i =x j When the RCS is equal, R(x i , x j ,θ)=1; when x i -x j →∞, R(x i , x j ,θ)→0. Spatial correlation function R(x i , x j ,θ) is expressed as:

[0101]

[0102] in, The subscript k indicates the kth component, d k =x ik -x jk , d k Represents a known sample point x i The kth component of j The distance between the kth components of , where n represents the number of components.

[0103] The RCS value of the interpolation point (prediction point) predicted by the Kriging interpolation method can be expressed by a linear combination of the RCS values ​​of the known sample points in the known sample set:

[0104]

[0105] Where Y = [Y1, Y2, ..., Y m ] T represents the RCS value of a known sample point, c is the coefficient matrix, and the formula G(x)=g T (x)β+z(x) we can get:

[0106] Y=Fβ+Z

[0107] Where F = [g T (x1), g T (x2),…,g T (x m )] T , {x1, x2, …, x m} are known sample points, Z = [z(x1), z(x2), …, z(x m )] T .

[0108] The prediction error of the Kriging model is:

[0109]

[0110] In order to make the mean of the Kriging model prediction error 0, it is necessary to satisfy Right now:

[0111] c T F T (x) = 0

[0112] The mean square error of the prediction error of the Kriging model is:

[0113]

[0114] Among them, r=[R(x, x1, θ), R(x, x2, θ),…, R(x, x m ,θ)], use the correlation function to calculate the correlation between the predicted sample points and the known sample points, R is the correlation matrix:

[0115]

[0116] In order to minimize the root mean square error of the prediction results of the Kriging model, it is necessary to meet the constraint condition and predict the error mean c. T F T When (x) = 0, find the optimal coefficient matrix c. It can be solved by the Lagrange multiplier method:

[0117] L(c,λ)=σ 2 (1+c TRc-2c T r)-λ T [c T F T (x)]

[0118] Where λ is the Lagrange multiplier. Taking the partial derivative of c and abbreviating it into matrix form, we can get:

[0119]

[0120] Solving the above formula we can get:

[0121]

[0122]

[0123] According to the above formula, the predicted response value can be obtained

[0124]

[0125] By generalized least squares we get:

[0126]

[0127]

[0128] For constant type g(x), the above expression can be simplified to:

[0129]

[0130]

[0131] Among them, 1 represents an n-dimensional unit vector.

[0132] The expression predicted by the Kriging model is:

[0133]

[0134] To calculate and σ 2 , we can use maximum likelihood estimation to calculate the value of θ in the matrix R:

[0135]

[0136] In the Kriging model, the mean Variance σ 2Convert to a function containing θ variables, and construct a Kriging model by solving the optimization problem in the above formula. The present invention uses the DACE toolbox provided by Matlab to solve θ, which requires the upper and lower boundary values ​​and initial values ​​of θ to be given, and calculates the θ value by maximum likelihood estimation.

[0137] Then, β and z(x) are obtained through θ, so as to obtain G(x), which is the initial Kriging interpolation curve obtained by the Kriging interpolation method.

[0138] See also Figure 4 , Figure 4 is the spatial correlation function R and the distance d under different values ​​of the Kriging interpolation parameter θ k It can be seen from the relationship diagram that the smaller the Kriging interpolation parameter θ is, the stronger the correlation is, and the larger the parameter θ is, the greater the spatial correlation function R is and the distance d is. k The weaker the correlation.

[0139] S4: Compare the initial IDW interpolation curve and the initial Kriging interpolation curve to obtain potential extreme points greater than the difference threshold.

[0140] Specifically, the actual difference of the RCS value of the same prediction point on the initial IDW interpolation curve and the initial Kriging interpolation curve is calculated in turn to determine whether it is greater than the preset difference threshold. If so, the current prediction point is considered to be a potential extreme point. If not, the next prediction point is sequentially determined to obtain all potential extreme points on the initial IDW interpolation curve and the initial Kriging interpolation curve, where the same prediction point refers to the incident angle on the initial IDW interpolation curve and the initial Kriging interpolation curve. Points with equal angles (sample points in the angular domain) or frequencies (sample points in the frequency domain).

[0141] For example, for the angular domain sample points, the initial IDW interpolation curve and the initial Kriging interpolation curve both include a preset number of prediction points, and the horizontal coordinates of the prediction points on the two curves (corresponding to the incident angle ) correspond to the same, the ordinate (corresponding to the RCS value) may be different, and the actual difference of the ordinate of the prediction point at the same abscissa on the initial IDW interpolation curve and the initial Kriging interpolation curve is calculated in turn, and it is determined whether the actual difference is greater than the preset difference threshold. If so, the current prediction point is considered to be a potential extreme point. According to the above method, all potential extreme points on the curve. See Figure 5 , Figure 5 is a process diagram of demonstrating iteratively adding sample points and correcting the proxy model curve proposed in an embodiment of the present invention. Figure 5(a) It can be seen that in the first iteration process, a large number of potential extreme points are obtained by comparing the maximum difference values ​​of the two interpolation methods.

[0142] S5: Re-simulate at the potential extreme point to obtain new sample data to supplement the sample set, and pre-process the new sample data to obtain an updated sample set.

[0143] Specifically, a numerical method is used to re-simulate at the potential extreme point to obtain new sample data, that is, the corresponding RCS value (the value of the ordinate) is simulated by the input angle or frequency (the value of the horizontal axis) at the potential extreme point, and the new sample data is added to the current sample set as the new sample data. Subsequently, the new sample data is subjected to data translation and log function processing. The specific process is the same as step S2 and will not be repeated here. In this embodiment, Figure 5 The blue circle sample points in the figure represent the RCS values ​​corresponding to the incident angles of the potential extreme points obtained by simulation. These newly added sample points will be added to the existing sample data set for the next simulation.

[0144] It should be noted that before the next step of interpolation curve fitting, the new sample data needs to be preprocessed, that is, data translation and log function processing similar to step S2, and used together with the original sample set in the sample set that has been preprocessed for subsequent interpolation curve fitting.

[0145] S6: Re-obtain the IDW interpolation curve and the Kriging interpolation curve according to the updated sample set.

[0146] Specifically, the current IDW interpolation curve and Kriging interpolation curve are recalculated based on the sample data in the updated sample set that has been processed by data translation and log function. Figure 5 It is the four-iteration process of the adaptive sample enhancement method based on IDW-Kriging of the present invention. The gray curve is the result obtained by Kriging interpolation, and the red curve is the result obtained by IDW interpolation.

[0147] S7: Determine whether the current number of iterations reaches the maximum number of iterations. If not, execute step S4. If yes, save the Kriging interpolation curve as the enhanced sample set.

[0148] Specifically, it is determined whether the current number of iterations reaches the preset maximum number of iterations. If not, step S4 is executed, that is, the potential extreme points on the current IDW interpolation curve and the current Kriging interpolation curve are continued to be found. If so, the current Kriging interpolation curve is obtained.

[0149] Since the RCS values ​​of the sample data in the sample set are subjected to data translation and log function processing before the above interpolation, the RCS values ​​of the sample data are restored in this step. Specifically, the sample data on the current Kriging interpolation curve is converted. The conversion formula is:

[0150]

[0151] Among them, σ′(after) is the RCS value of the interpolation point on the current Kriging interpolation curve, and σ(after) is the RCS value of the interpolation point of the current Kriging interpolation curve after restoration. The converted sample data is in the same format as the original sample data, that is, the incident angle The converted sample data are in the format of value or frequency-RCS value, and all the converted sample data together constitute the final proxy model.

[0152] The effect of the adaptive sample enhancement method based on IDW-Kriging of the present invention is further illustrated by simulation experiments below.

[0153] This embodiment provides an example of constructing an aircraft angle domain proxy model, which contains a large number of peak points with drastic changes. Figure 6 and Figure 7 , Figure 6 It is an angular domain proxy model obtained by the first iteration and the fourth iteration of the adaptive sample enhancement method based on IDW-Kriging of the present invention. It can be seen that the number of burrs in the angular domain proxy model after four iterations is significantly less than the number of burrs before the iteration, and the effect of the proxy model is significantly improved. Figure 7 This is a schematic diagram of the error analysis of the angular domain proxy model obtained by the first and fourth iterations of the adaptive sample enhancement method based on IDW-Kriging of the present invention. The method proposed by the present invention accurately reconstructs the change of the target's RCS with the incident angle by adaptively iterating to find potential peak points. Figure 8 , Figure 8 It is the fitting scatter plot of the first iteration and the fourth iteration of the adaptive sample enhancement method based on IDW-Kriging of the present invention. It can be seen that the effect of the fitting scatter plot is significantly improved after iteration. In the first iteration, due to the small number of sample points, a large number of predicted values ​​obtained by the proxy model deviate greatly from the true values. By adaptively sampling to find the location of the potential RCS narrow peak, after four iterations, the effect of the fitting scatter plot is significantly improved, and most of the RCS values ​​are close to or equal to the true values. The method of the present invention effectively reduces the amount of data that the proxy model deviates from the true simulation data value, and is suitable for the construction of proxy models for objects with drastic numerical changes.

[0154] The present invention also provides an example of constructing a frequency domain proxy model, in which the curve changes more gently. Fig. 9 , Fig. 9 The comparison of the frequency domain proxy model obtained by the first iteration and the fourth iteration of the adaptive sample enhancement method based on IDW-Kriging of the present invention shows that the method proposed by the present invention can correctly find the narrow peak and supplement the sampling points, making the frequency domain proxy model more accurate, and can still significantly improve the construction of relatively gentle proxy models. The method of the present invention is suitable for the construction of proxy models with gentle numerical changes.

[0155] The present invention also provides a comparison of the errors of the traditional Kriging method and the present invention method in constructing a drastic change proxy model. Fig.10 , Fig.10 It is an angular domain error analysis diagram of the proxy model constructed by the traditional Kriging method and the proxy model constructed by the method of the present invention, wherein: Fig.10 (a) is the error analysis diagram of the Kriging proxy model obtained by uniform sampling of the same amount of data. Fig.10 (b) is an error analysis diagram obtained by using the proxy model obtained by the method of the present invention. The uniform sampling method (Kriging method) can basically reconstruct the trend of the target RCS changing with the angle, but it performs poorly in some locations where the extreme value changes are large. The method proposed in the present invention better captures these small but important local features and more accurately reconstructs the change of the target RCS with the incident angle. The number of burrs in the proxy model obtained by the method of the present invention is significantly less than the number of burrs obtained by uniform sampling, and the maximum value of the burrs is smaller, that is, the error is smaller. It can be seen that when the amount of data is the same, the error of the proxy model obtained using the method of the present invention is significantly reduced.

[0156] Fig.11 The angular domain fitting scatter plots of the proxy model constructed using the traditional Kriging method and the method of the present invention are all fitting scatter plots of 44820 samples fitting 65341 data. Among them, Fig.11 (a) is the fitting scatter plot of the traditional uniform sampling method. Fig.11 (b) is the fitting scatter plot obtained by the IDW-Kriging adaptive method proposed in the present invention. The location of the narrow peak in the RCS data can be found by the adaptive sampling method of the present invention. It can be clearly seen in the fitting scatter plot that the method of the present invention effectively reduces the amount of data that deviates from the true simulation data value. The proxy model constructed by the present invention with the same amount of data is far superior to the Kriging proxy model with uniform sampling.

[0157] The present invention provides a comparison of the errors between the traditional Kriging method to construct a proxy model and the method of the present invention to construct a smoothly changing proxy model. Fig.12, Fig.12 This is a frequency domain error analysis comparison diagram of the proxy model constructed by the traditional Kriging method and the method of the present invention. It can be seen that under the same data volume, the method of the present invention finds two narrow peaks well, making the model more accurate. The ordinary uniform sampling method cannot capture these details.

[0158] Furthermore, Table 1 gives the root mean square error analysis of the proxy models obtained by different methods in the angular domain, wherein the sample points refer to the sample points before the curve fitting, and the ratio of the data volume before and after the fitting refers to the ratio of the number of sample points before the curve fitting to the number of prediction points after the fitting. Under the initial uniformly sampled sample set, the RMSE (Root Mean Square Error) of the obtained proxy model is 1.1404; after four iterations of the IDW-Kriging-1 method (similar to the method of the present invention but not including the data preprocessing process of step S2), the RMSE of the proxy model obtained is 0.2352, and the root mean square error of the obtained proxy model has decreased by 79.66%, which indicates that the method of increasing sample points through adaptive iteration effectively improves the accuracy of the results. Further, after adding the data preprocessing process (IDW-Kriging-2, i.e., the method of the present invention), the RMSE is 0.1685, and the root mean square error has decreased by 28.36% again.

[0159] Table 1. Angular domain error analysis

[0160]

[0161] Table 2 shows the root mean square error analysis of the proxy models obtained by different methods in the frequency domain. Under the initial uniformly sampled sample set, the RMSE (Root Mean Square Error) of the obtained proxy model is 0.4560. After four iterations of the IDW-Kriging-1 method (similar to the method of the present invention but does not include the data preprocessing process of step S2), the RMSE of the proxy model obtained is 0.1275, and the root mean square error of the obtained proxy model has decreased by 72.04%. Furthermore, after adding the data preprocessing process (IDW-Kriging-2, i.e., the method of the present invention), the RMSE is 0.951, and the root mean square error has decreased by another 25.41%, indicating that data preprocessing can also improve the accuracy of the proxy model.

[0162] Table 2. Frequency domain error analysis

[0163]

[0164] Table 3 is the root mean square error analysis of the proxy model obtained by the traditional Kriging method and the IDW-Kriging-based method in the angular domain under the same number of samples. Compared with the traditional Kriging uniform sampling, the root mean square of the proxy model obtained by the IDW-Kriging-based method (IDW-Kriging-1, similar to the method of the present invention but not including the data preprocessing process of step S2) decreased by 70.09%, which shows that the IDW-Kriging-based method of this article effectively improves the accuracy of the results. Compared with the traditional Kriging interpolation method, highly representative samples can be found to avoid redundant simulations and reduce the amount of calculation required for simulation. By comparing Kriging-1, IDW-Kriging-1 and IDW-Kriging-2, it can be seen that in order to achieve a close RMSE, the IDW-Kriging-based method of the present invention uses a smaller amount of data. Further, after adding the data preprocessing process (IDW-Kriging-2, i.e., the method of the present invention), the RMSE decreases again.

[0165] Table 1. Angular domain error analysis

[0166]

[0167] Table 4 shows the root mean square error analysis of the surrogate model obtained by the traditional Kriging method and the IDW-Kriging method in the frequency domain under the same number of samples. The root mean square of the surrogate model obtained by the IDW-Kriging method (IDW-Kriging-1, similar to the method of the present invention but not including the data preprocessing process of step S2) decreased by 65.34% compared with the traditional uniform sampling (IDW-Kriging-1). Furthermore, after adding the data preprocessing process (IDW-Kriging-2, i.e., the method of the present invention), the RMSE decreased again.

[0168] Table 4. Frequency domain error analysis

[0169]

[0170] The present invention is based on the IDW-Kriging adaptive sample enhancement method. By comparing the interpolation results of the two interpolation models of IDW and Kriging, according to the preset difference threshold, the extreme value position of the Kriging interpolation surface can be automatically sensed, and the position of the sample point to be supplemented can be determined, thereby solving the problem of uniform sampling ignoring the peak point; by simulating the sample point at the position, expanding the sample set data points, re-interpolating and calculating to obtain new IDW and Kriging interpolation results; by iteratively adaptively searching for potential extreme value points and performing sample expansion, the prediction accuracy of the Kriging model can be significantly improved. After reaching the maximum number of iterations, the Kriging interpolation model is saved and used as a proxy model, which can greatly reduce the number and time required for simulation, and the accuracy is better than that of the traditional Kriging model.

[0171] Another embodiment of the present invention provides a storage medium, wherein a computer program is stored in the storage medium, and the computer program is used to execute the steps of the adaptive sample enhancement method based on IDW-Kriging described in the above embodiment. Another aspect of the present invention provides an electronic device, including a memory and a processor, wherein a computer program is stored in the memory, and when the processor calls the computer program in the memory, the steps of the adaptive sample enhancement method based on IDW-Kriging described in the above embodiment are implemented. Specifically, the above-mentioned integrated module implemented in the form of a software function module can be stored in a computer-readable storage medium. The above-mentioned software function module is stored in a storage medium, including several instructions for enabling an electronic device (which can be a personal computer, a server, or a network device, etc.) or a processor (processor) to execute some steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a disk or an optical disk.

[0172] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. An adaptive sample enhancement method based on IDW-Kriging, characterized in that: include: S1: Configure initial parameters, including Kriging parameters θ kriging , IDW interpolation smoothing parameter α, sampling interval, difference threshold and maximum number of iterations of IDW interpolation method and Kriging interpolation method; S2: preprocessing the sample data in the original sample set to reduce the degree of variation of the sample data, and obtaining a preprocessed sample set; S3: Obtaining an initial IDW interpolation curve and an initial Kriging interpolation curve according to the preprocessed sample set; S4: comparing the initial IDW interpolation curve and the initial Kriging interpolation curve to obtain potential extreme value points greater than the difference threshold; S5: re-simulating at the potential extreme point to obtain new sample data to supplement the sample set, and pre-processing the new sample data to obtain an updated sample set; S6: re-obtaining an IDW interpolation curve and a Kriging interpolation curve according to the updated sample set; S7: Determine whether the maximum number of iterations has been reached. If not, execute step S4. If yes, save the Kriging interpolation curve as the enhanced sample set.

2. The IDW-Kriging-based adaptive sample enhancement method according to claim 1, characterized in that: The S2 includes: S2.1: A plurality of original sample data are obtained according to actual measurement or simulation methods to form an original sample set, wherein the original sample data in the original sample set includes angular domain sample points or frequency domain sample points, wherein the input data of the angular domain sample points is the incident angle The output data is an RCS value, the input data of the frequency domain sample point is a frequency, and the output data is an RCS value; S2.2: Perform data translation on the RCS values ​​of the angular domain sample points or the frequency domain sample points in the original sample data, and define a new RCS value σ′(before)=σ(before)+1, so that the RCS value σ′(before) of each angular domain sample point or frequency domain sample point after data translation is in the interval [1,+∞], where σ(before) is the RCS value of the angular domain sample point or the frequency domain sample point in the original sample data; S2.3: Use the log function to transform the data of σ′(before). The conversion formula is: σ′(after)=10·lg(σ′(before)), Wherein, σ′(after) represents the RCS value of each angular domain sample point or frequency domain sample point after data conversion, that is, the RCS value after preprocessing.

3. The IDW-Kriging-based adaptive sample enhancement method according to claim 1, characterized in that: The S3 includes: S3.1: According to the preprocessed sample set, the RCS values ​​of multiple prediction points are obtained by using the IDW interpolation method, and an IDW interpolation curve is formed according to the multiple prediction points, wherein the preprocessed sample set includes preprocessed angular domain sample points or preprocessed frequency domain sample points, wherein the preprocessed angular domain sample points include incident angle and the corresponding preprocessed RCS value; the preprocessed frequency domain sample point includes the frequency and the corresponding preprocessed RCS value; S3.2: Based on the preprocessed sample set, the initial Kriging interpolation curve is obtained using the Kriging interpolation method.

4. The IDW-Kriging-based adaptive sample enhancement method according to claim 3, characterized in that: The S3.1 includes: According to the preprocessed sample set, the IDW interpolation method is used to obtain the RCS values ​​of multiple prediction points. The calculation formula is: Among them, Z represents the predicted point at the preset angle, d Zi represents the distance between the predicted point Z and the known sample point i in the preprocessed sample set, α is the set parameter, and w Zi represents the distance weight value between the predicted point Z and the known sample point i, N represents the number of known sample points in the preprocessed sample set, RCS i is the RCS value of the known sample point i, Represents the predicted value of RCS at the prediction point Z; An IDW interpolation curve is formed according to the plurality of prediction points.

5. The IDW-Kriging-based adaptive sample enhancement method according to claim 1, characterized in that: The S4 includes: The actual difference of the RCS value of the same prediction point on the initial IDW interpolation curve and the initial Kriging interpolation curve is calculated in turn, and it is determined whether it is greater than a preset difference threshold. If so, the current prediction point is considered to be a potential extreme point, and all potential extreme points on the initial IDW interpolation curve and the initial Kriging interpolation curve are obtained.

6. The IDW-Kriging-based adaptive sample enhancement method according to claim 2, characterized in that: The S5 includes: Re-simulating at the potential extreme point using a numerical method, obtaining a corresponding RCS value through input angle or frequency simulation at the potential extreme point, thereby forming new sample data, and supplementing it to the current sample set; The new sample data is subjected to data translation and log function processing.

7. The IDW-Kriging-based adaptive sample enhancement method according to claim 1, characterized in that: The S7 includes: Determine whether the current number of iterations reaches the maximum number of iterations. If not, execute step S4 to continue searching for potential extreme points on the current IDW interpolation curve and the current Kriging interpolation curve. If yes, obtain the current Kriging interpolation curve. The sample data on the current Kriging interpolation curve is converted, and the conversion formula is: Among them, σ′(after) is the RCS value of the interpolation point on the current Kriging interpolation curve, and σ(after) is the RCS value of the interpolation point of the current Kriging interpolation curve after restoration.

8. A storage medium storing a computer program, wherein the computer program is used to execute the steps of the adaptive sample enhancement method based on IDW-Kriging according to any one of claims 1 to 7.

9. An electronic device, comprising a memory and a processor, wherein the memory stores a computer program, and when the processor calls the computer program in the memory, the steps of the adaptive sample enhancement method based on IDW-Kriging as claimed in any one of claims 1 to 7 are implemented.

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