Method, apparatus, and medium for measuring thin-walled surface deformation based on the Kriging model.
The Kriging model-based method addresses AACMM measurement inaccuracies by dynamically adjusting the sampling strategy, enhancing accuracy and efficiency in thin-walled structure deformation measurements.
Patent Information
- Authority / Receiving Office
- JP · JP
- Patent Type
- Patents
- Current Assignee / Owner
- JIANGSU UNIV OF SCI & TECH
- Filing Date
- 2025-09-22
- Publication Date
- 2026-05-20
AI Technical Summary
Conventional methods for measuring thin-walled structure deformation, particularly using articulated arm coordinate measuring machines (AACMM), suffer from coordinate deviations due to human factors, leading to inaccurate and inefficient measurements, especially in complex environments.
A method utilizing a Kriging model to dynamically adjust the sampling strategy through iterative prediction and selection of sampling points, reducing measurement points and improving accuracy and efficiency by concentrating on important deformation regions.
The method effectively reduces measurement errors and improves accuracy and efficiency by optimizing the Kriging model's prediction and iteration, ensuring reliable and robust deformation measurements across different operators and workpieces.
Smart Images
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Abstract
Description
Technical Field
[0001] The present invention relates to a thin-walled surface deformation measurement method, apparatus, and medium based on a Kriging model, and belongs to the technical field of shipbuilding measurement.
Background Art
[0002] Thin-walled structures are widely applied in industrial fields such as shipbuilding, and the deformation measurement of thin-walled structural members is important for ensuring product quality. Conventional contact measurement methods such as coordinate measuring machines (CMM) and articulated arm coordinate measuring machines (AACMM) are excellent in accuracy but limited in terms of efficient measurement of thin-walled structures. In particular, the articulated arm coordinate measuring machine (AACMM) is widely applied to complex environments due to its flexibility and convenience. However, since it is affected by human factors during the measurement process, coordinate deviations are likely to occur at the measurement points, which further affects the final measurement results. Such deviations are more prominent especially in the deformation measurement of thin-walled structural members.
[0003] Conventional research mainly focuses on improving the measurement accuracy of the device itself by improving the calibration and compensation of AACMM. However, there is little systematic research on the influence of hand-held operation on measurement accuracy, especially on how to deal with the coordinate deviation of measurement points caused by artificial operation. For the measurement of the deformation degree of thin-walled structures, the prior art mainly relies on uniform sampling or random sampling strategies. These methods are simple, but in the measurement of complex surface deformations, the distribution of sampling points is likely to be unreasonable, and thus important deformation regions cannot be accurately identified, which seriously affects the accuracy and efficiency of the measurement results.
Summary of the Invention
Problems to be Solved by the Invention
[0004] In response to the shortcomings of the prior art, the present invention provides a thin-walled surface deformation measurement method, apparatus, and medium based on the Kriging model. By combining the dynamic adjustment of the sampling strategy through iterative prediction and selection of sampling points, the present invention effectively reduces the number of measurement points, significantly improves the accuracy and efficiency of thin-walled surface deformation measurement, and solves the problem of coordinate deviation in AACMM handheld operation. [Means for solving the problem]
[0005] The thin-walled surface deformation measurement method based on the Kriging model is: Step S1 involves generating initial measurement points using a Hammersley sequence, actually measuring them to obtain initial measurement points, and using these as input data for a Kriging model. Step S2 involves constructing a Kriging model based on the initial measurement points in S1, thereby predicting the deformation error distribution and mean squared error distribution of the thin-walled surface. Step S3 involves setting two sampling modes and dynamically selecting the sampling mode using a probability decrease function, Step S4 involves acquiring sampling points to be measured, which combines the sampling mode selected in S3 with the deformation error distribution and mean squared error distribution of the thin-walled surface predicted in S2, thereby acquiring sampling points to be measured that are concentrated in important deformation regions of the thin-walled surface. Step S5 involves measuring the sampling points to be measured in S4, obtaining actual measurement points, configuring them as an actual set of measurement points, calculating the distance from each actual measurement point to the theoretical reference plane, and obtaining the degree of deformation of the thin-walled surface, and actually measuring and obtaining the degree of deformation of the thin-walled surface. Step S6 includes evaluating and iterating, where the degree of deformation of the thin-walled surface in S5 is evaluated, and the trend of change in the degree of deformation is analyzed. If the degree of deformation is moving towards stability, the measurement is terminated; if the trend of change is unstable, the Kriging model is updated using the current actual set of measurement points, the deformation error distribution and the mean squared error distribution of the thin-walled surface after the update are re-predicted, and the process returns to S3.
[0006] Preferably, S2 is Step S201 involves constructing the Kriging model based on the initial measurement points in S1 to obtain the deformation error values of the initial measurement points, and predicting the deformation error distribution and mean squared error distribution of the unsampled region of the thin-walled surface based on the deformation error values of the initial measurement points. The Kriging model includes step S202, which predicts the deformation error distribution and the mean squared error distribution of the unsampled region of the thin-walled surface, and calculates the mean squared error MSE at the corresponding predicted position to represent the degree of uncertainty of the predicted value at that predicted position.
[0007] Preferably, S201 is For n initial measurement points in the error space domain, the sampling position
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[0008] [[ID=3S9]]Preferably, the S202 is The larger the mean square error value, the less reliable the prediction result. The expression formula of the mean square error value MSE is as follows
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[0009] Preferably, the S3 is specifically as follows Set sampling mode 1 and sampling mode 2, and specifically, the probability reduction function dynamically selects the sampling mode as follows: For each iteration, generate a random number rand such that 0 < rand < 1, compare it with 1 / i. If rand < 1 / i, select sampling mode 1; conversely, select sampling mode 2. As the number of iterations i increases, 1 / i gradually decreases, the probability of selecting sampling mode 1 gradually decreases, and the probability of selecting sampling mode 2 gradually increases. [[ID=The following applies:
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[0012] Preferably, S6 is specifically, The measurement is terminated by calculating the standard deviation of the degree of deformation, setting an error threshold, indicating that the trend of change is unstable if the standard deviation is greater than or equal to the error threshold, and indicating that the trend of change is stable if the standard deviation is less than the error threshold. Specifically, this is done as follows: If the standard deviation of the height value z of the measurement point is less than a predetermined precision threshold Err, the iteration is stopped, n measurement points are set, and the height values of the measurement points are z1, z2, ..., z nThen, the standard deviation ε of the height values at the measurement points is as follows:
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[0013] The electronic device includes at least one processor and a memory communicatively connected to the at least one processor. Among them, instructions executable by the at least one processor are stored in the memory, and the instructions are executed by the at least one processor so that the at least one processor can execute a thin-walled surface deformation measurement method based on the Kriging model.
[0014] In a non-temporary computer-readable storage medium storing computer instructions, the computer instructions are used to cause the computer to execute a thin-walled surface deformation measurement method based on the Kriging model. [Effects of the Invention]
[0015] This invention, by combining the iterative prediction and selection of sampling points with the dynamic adjustment of the sampling strategy, effectively reduces the number of measurement points, and this method can solve the problem of measurement errors due to coordinate deviations in AACMM handheld measurements. Even if there is a deviation between the actual measurement point position and the theoretical sampling point position, this method can still accurately acquire the degree of deformation of thin-walled surfaces by optimizing the prediction and iteration of the Kriging model, ensuring the reliability of the measurement results, and improving measurement accuracy, measurement efficiency, stability of method implementation, applicability to different workpieces, and robustness of measurement results for different operators.
[0016] To more clearly illustrate embodiments of the present invention or technical concepts in the prior art, the following briefly describes the drawings necessary for describing the embodiments or prior art. Clearly, the drawings in the following description are merely embodiments of the present invention, and those skilled in the art can obtain other drawings based on the provided drawings without any creative work. [Brief explanation of the drawing]
[0017] [Figure 1] This is a flowchart of the method of the present invention. [Figure 2] This is a schematic diagram of the sampling point selection process in sampling mode 1. [Figure 3] This is a schematic diagram of the sampling point selection process in sampling mode 2. [Figure 4] This is a schematic diagram showing how to measure coordinate deviation using a handheld joint coordinate measurement arm. [Figure 5] This is a schematic diagram illustrating the calculation of the degree of deformation of a thin-walled surface based on the distance from the measurement point to the theoretical reference plane. [Figure 6] This is a schematic diagram of the experimental platform measured by a handheld measuring arm. [Figure 7] These are deformation measurement results diagrams from different operators. [Modes for carrying out the invention]
[0018] The technical concepts in the embodiments of the present invention will be clearly and completely described below with reference to the drawings of the embodiments, and it will be clear that the embodiments described are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art without creative work based on the embodiments of the present invention are all within the scope of protection of the present invention.
[0019] In the description of this invention, the directions or positional relationships indicated by terms such as "up," "down," "front," "back," "left," "right," "vertical," "horizontal," "top," "bottom," "inside," and "outside" are based on the directions or positional relationships shown in the drawings and are merely for the convenience and simplification of the description of this invention. They do not indicate or imply that a specified device or element necessarily has a specific direction or must be configured and operated in a specific direction, and should not be understood as limiting the invention.
[0020] In the present invention, unless otherwise specifically defined and limited, the presence of a first feature "above" or "below" a second feature may include direct contact between the first and second features, or it may include contact between the first and second features by another feature between them, without direct contact. Furthermore, the presence of a first feature "above," "above," and "on the top surface" of a second feature may include the first feature being directly above and diagonally above the second feature, or simply indicating that the horizontal height of the first feature is higher than that of the second feature. The presence of a first feature "below," "below," and "on the bottom surface" of a second feature may include the first feature being directly below and diagonally below the second feature, or simply indicating that the horizontal height of the first feature is lower than that of the second feature.
[0021] As shown in Figure 1, the thin-walled surface deformation measurement method based on the Kriging model includes the following steps S1 to S7.
[0022] S1: Generate initial measurement points: Initial sampling points are generated using the Hammersley sequence, and these points are actually measured to obtain the initial measurement points, which are then used as input data for the Kriging model. The Hammersley sequence is a low-difference sequence that covers the entire surface with a small number of sampling points, ensuring representativeness and uniformity of the sampling points. The initial sampling points generated by the Hammersley sequence are used as input data for the Kriging model, providing a basis for subsequent deformation error prediction.
[0023] S2: Constructing a Kriging model: By constructing a Kriging model based on the initial measurement points in S1, the deformation error distribution and mean squared error distribution of the thin-walled surface are predicted. The Kriging method is an interpolation method based on spatial statistics, and by describing the spatial correlation between known points using a covariance function, it is possible to predict errors for unknown points. In this invention, the spatial correlation between measurement points is described using a Gaussian covariance function, and the deformation error of unknown points and its uncertainty distribution are predicted using deformation error data from known sampling points, providing a theoretical basis for the selection of subsequent sampling points.
[0024] By constructing a Kriging model based on the initial measurement points in S201 and S1, the deformation error values of the initial measurement points are obtained, and the deformation error distribution and mean squared error distribution of the unsampled area of the thin-walled surface are predicted based on the deformation error values of the initial measurement points. For n initial measurement points in the error space domain, the sampling position
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[0025] The S202, Kriging model predicts the deformation error distribution and mean squared error distribution of the unsampled area of the thin-walled surface, and calculates the mean squared error (MSE) at the corresponding predicted location, thereby representing the degree of uncertainty of the predicted value at that location. A larger mean squared error (MSE) indicates less reliable prediction results, and the expression for the mean squared error (MSE) is as follows:
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[0026] S3. Dynamically select the sampling mode: Set two types of sampling modes and dynamically select the sampling mode according to the probability reduction function: Setting sampling mode 1 and sampling mode 2, and the probability reduction function dynamically selecting the sampling mode is specifically as follows: For each iteration, generate a random number rand, where 0 < rand < 1, compare it with 1 / i. If rand < 1 / i, select sampling mode 1; conversely, select sampling mode 2. As the number of iterations i increases, 1 / i gradually decreases, the probability of selecting sampling mode 1 gradually decreases, and the probability of selecting sampling mode 2 gradually increases.
[0027] S4. Obtain the measurement target sampling points: Combine the sampling mode selected in S3 and the deformation error distribution and mean square error distribution of the thin-walled surface predicted in S2 to obtain the measurement target sampling points concentrated in the important deformation regions of the thin-walled surface: As shown in FIG. 2, when sampling mode 1 is selected, based on the maximum value of the mean square error value MSE in Equation (4) in S202, that is, the point where the mean square error value MSE is the largest is used as the measurement target sampling point. Sampling mode 1 can avoid local convergence. As a result, the Kriging model can fully explore each region of the thin-walled surface at the initial stage, improving the global prediction ability. At this stage, by selecting the position of the maximum value of the mean square error value MSE, it is ensured that all regions where there may be large errors in the distribution of the measurement points are covered as much as possible, thereby improving the measurement accuracy.
[0028] As shown in FIG. 3, when sampling mode 2 is selected, the
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[0029] The regions where the measurement target sampling points obtained by sampling mode 1 and sampling mode 2 are located are important deformation regions on the thin-walled surface.
[0030] As shown in Figure 4, the degree of deformation of the thin-walled surface in S5 is actually measured and obtained: the sampling points to be measured in S4 are measured using AACMM, the actual measurement points are obtained, these are constructed as an actual set of measurement points, the distance from each actual measurement point to the theoretical reference plane is calculated, and the degree of deformation of the thin-walled surface is obtained: The degree of deformation is quantified by the difference between the maximum and minimum distances, ensuring the accuracy of the measurement results. The calculation process for the degree of deformation is as follows: Based on the design model of the thin-walled surface, the representation of the theoretical reference plane is defined as follows: S=f(x,y)(6) Measurement point P i =(x i ,y i ,z i ) to the directed distance d from the theoretical reference surface S=f(x,y) i The following applies:
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[0031] As shown in Figure 5, S6 evaluates and iterates: the degree of deformation of the thin-walled surface in S5 is evaluated, and the trend of change in the degree of deformation is analyzed. If the degree of deformation is moving towards stabilization, the measurement is terminated. If the trend of change is unstable, the Kriging model is updated using the current actual set of measurement points, the deformation error distribution and mean squared error distribution of the thin-walled surface are re-predicted after the update, and the process returns to S3. The process involves calculating the standard deviation of the deformation, setting an error threshold, indicating that the trend is unstable if the standard deviation is greater than or equal to the error threshold, and terminating the measurement if the standard deviation is less than the error threshold, indicating that the trend is stable. Specifically, this is done as follows: If the standard deviation of the height value z of the measurement points is less than a predetermined precision threshold Err, the iteration is stopped, n measurement points are set, and the height values of the measurement points are z1, z2, ..., zn Then, the standard deviation ε of the height values at the measurement points is as follows:
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[0032] S7. Verify, as shown in FIGS. 6 and 7.
[0033] S701, Experimental Design: In order to verify the effectiveness and robustness of the method of the present invention, the stability of the results under the operation of different operators, and its applicability to thin-walled test members of different sizes, multiple operators will conduct deformation measurement experiments on two thin-walled workpieces of different sizes: workpiece 1 of 100 × 100 × 1 mm and workpiece 2 of 300 × 300 × 1 mm. Data will be collected at 400 points and 900 points respectively by dense sampling, and the degree of deformation will be calculated as a standard value.
[0034] S702, Analysis of Operator Measurement Results: Multiple operators perform multi-point measurements on these two types of workpieces using the handheld joint coordinate measuring arm AACMM. Each operator independently measures workpiece 1 and workpiece 2. During the measurement of workpiece 1, the method of the present invention can achieve the same accuracy as the 7x7 equally spaced sampling method and the Hammersley method with 40 points using no more than 30 measurement points, i.e., it reaches within the accuracy standard. This demonstrates the superior sampling efficiency and accuracy of the method of the present invention, as it can reach the accuracy standard with a small number of points. During the measurement of workpiece 2, the experimental results show a similar trend. When using fewer than 40 measurement points, this method can be equivalent to the 8x8 equally spaced sampling method and the Hammersley method with 50 points, and in both cases, the accuracy can converge within the accuracy standard (0.01 mm). In particular, this method can converge with a small number of points, and the results discipline of different operators is consistent, further verifying the robustness of the method's measurement results for different operators.
[0035] S703, Verification of applicability to workpieces of different sizes: During the measurement of workpiece 1 and workpiece 2, the method exhibits high measurement accuracy and stability in both cases. In particular, during the measurement of workpiece 1, the method can reach the accuracy standard with 28 points, while equally spaced sampling and Hammersley sequence sampling require 49 points and 40 points, respectively. During the measurement of workpiece 2, the method can reach the accuracy standard with only 39 points, while equally spaced sampling and Hammersley sequence sampling require 64 points and 50 points, respectively, thus verifying the applicability and robustness of the method to workpieces of different sizes. The method maintains higher measurement accuracy while reducing the number of measurement points by 42.9% and 39.1% respectively during the measurement of workpiece 1 and workpiece 2.
[0036] As the experimental results show, the method of the present invention can effectively reduce errors between operators, improve measurement consistency, and significantly improve measurement accuracy. Compared to conventional methods, the method of the present invention exhibits higher accuracy and a faster convergence rate during deformation measurement, and its adaptability and stability in actual production environments are verified.
[0037] In this specification, each embodiment is described progressively, with each embodiment focusing on its differences from the others, and similar and identical parts between embodiments should be referred to alternately. The apparatus disclosed in the embodiments corresponds to the method disclosed in the embodiments, and therefore its description is relatively simple; relevant sections should be referred to in the description of the method.
[0038] Based on the above description of the disclosed examples, those skilled in the art can implement or use the present invention. Various modifications to these examples will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other examples without departing from the spirit or scope of the invention. Accordingly, the present invention is not limited to these examples shown herein, but fits to the broadest extent that is consistent with the principles and novel features disclosed herein.
Claims
1. A method for measuring thin-walled surface deformation based on the Kriging model, Step S1 involves generating initial measurement points using a Hammersley sequence, actually measuring them to obtain initial measurement points, and using these as input data for a Kriging model. Step S2 involves constructing a Kriging model based on the initial measurement points in S1, thereby predicting the deformation error distribution and mean squared error distribution of the thin-walled surface. Step S3 involves setting two sampling modes and dynamically selecting the sampling mode using a probability decrease function, Step S4 for acquiring sampling points to be measured, which involves combining the sampling mode selected in S3 with the deformation error distribution and mean squared error distribution of the thin-walled surface predicted in S2 to acquire sampling points to be measured that are concentrated in important deformation regions of the thin-walled surface. Step S5 involves measuring the sampling points to be measured in S4, obtaining actual measurement points, configuring them as an actual set of measurement points, calculating the distance from each actual measurement point to the theoretical reference plane, and obtaining the degree of deformation of the thin-walled surface, and actually measuring and obtaining the degree of deformation of the thin-walled surface. Step S6 includes evaluating and repeating the process, where the degree of deformation of the thin-walled surface in S5 is evaluated, and the trend of change in the degree of deformation is analyzed. If the degree of deformation is moving towards stability, the measurement is terminated; if the trend of change is unstable, the Kriging model is updated using the current actual set of measurement points, the deformation error distribution and the mean squared error distribution of the thin-walled surface after the update are re-predicted, and the process returns to S3. The above S3 is specifically as follows: Setting sampling mode 1 and sampling mode 2, and the probability decrease function dynamically selecting the sampling mode, is specifically as follows: A thin-walled surface deformation measurement method based on the Kriging model, wherein a random number rand is generated in each iteration, and if 0 < rand < 1, it is compared with 1 / i, and if rand < 1 / i, sampling mode 1 is selected, and conversely, sampling mode 2 is selected, and as the number of iterations i increases, 1 / i gradually decreases, the probability of selecting sampling mode 1 gradually decreases, and the probability of selecting sampling mode 2 gradually increases.
2. The aforementioned S2 is, Step S201 involves constructing the Kriging model based on the initial measurement points in S1 to obtain the deformation error values of the initial measurement points, and predicting the deformation error distribution and mean squared error distribution of the unsampled region of the thin-walled surface based on the deformation error values of the initial measurement points. A method for measuring thin-walled surface deformation based on the Kriging model according to claim 1, comprising step S202, which predicts the deformation error distribution and the mean squared error distribution of the unsampled region of the thin-walled surface, and calculates the mean squared error MSE at the corresponding predicted position to represent the degree of uncertainty of the predicted value at the predicted position.
3. Specifically, S201 is as follows: For n initial measurement points in the error space domain, the sampling position [Number 29] The corresponding error observation is: [Number 30] Here, m represents the error value corresponding to each sampling position, and in this case, for any position within the defined domain, the Kriging model achieves the prediction shown below. [Number 31] [k(x)] is the predicted observed value at x, O is the known error observed value vector, and k(x) is a column vector composed of the covariance between the initial measurement point and x. Ｔ This is its transpose matrix, k(x) = [k(x, x １ ), k(x, x ２ ),...,k(x, x ｎ )] Ｔ And K is the covariance matrix between the initial measurement points, and K －１ The inverse of the matrix is, specifically, expressed as follows: [Number 32] Among them, k(x ｉ , x ｊ ) is the covariance between the initial measurement points x ｉ and x ｊ , and The covariance between the initial measurement points is obtained using a Gaussian covariance model and is expressed as follows: [Number 33] In the formula, θ ｄ This is the scale parameter for the dth dimension, which reflects the similarity in that dimension, and x ｉｄ and x ｊｄ The thin-walled surface deformation measurement method based on the Kriging model according to claim 2, wherein represents the coordinate values in the d-th dimension of the i-th initial measurement point and the j-th initial measurement point, respectively.
4. Specifically, S202 means: A larger mean squared error (MSE) indicates less reliable prediction results, and the expression for the mean squared error (MSE) is as follows: [Number 34] In the formula, σ ２ This is the fundamental variance of the Kriging model, and is obtained from the following equation: [Number 35] In the formula, n is the total number of measurement points, O Ｔ The thin-walled surface deformation measurement method based on the Kriging model according to claim 3, wherein is the transpose of the error observation vector O.
5. S4 is specifically as follows: When selecting the sampling mode 1, the measurement target sampling point is determined based on the maximum value of the mean squared error value MSE in equation (4) in S202, that is, the point where the mean squared error value MSE is maximized. When selecting the sampling mode 2, the equation (1) in S201 [Number 36] Based on the maximum value of the predicted value, that is, the point where the deformation error distribution value is maximized is selected as the sampling point to be measured. The thin-walled surface deformation measurement method based on the Kriging model according to claim 4, wherein the region where the measurement target sampling points obtained by the sampling mode 1 and the sampling mode 2 are located is an important deformation region of the thin-walled surface.
6. Specifically, S5 refers to: The degree of deformation is quantified by the difference between the maximum and minimum distances, thereby ensuring the accuracy of the measurement results. The calculation process for the degree of deformation is as follows: Based on the design model of the thin-walled surface, the representation of the theoretical reference plane is defined as follows: S=f(x,y)(6) Measurement point P ｉ = (x ｉ , y ｉ , z ｉ ) to the directed distance d from the theoretical reference surface S = f(x, y) ｉ The following applies: [Number 37] In the formula, (x ｉ , y ｉ ) is the measurement point P ｉ This is the measurement point corresponding to z ｉ The measurement point P ｉ This is the height value corresponding to f(x ｉ , y ｉ ) is the nominal height of the reference surface, and f ｘ (x ｉ , y ｉ ) and f ｙ (x ｉ , y ｉ The terms ) are the partial derivatives of the reference surface in the x and y directions, respectively, and represent the slope of the reference surface at that point, and the numerator of equation (7) represents the distance from the measurement point to the theoretical surface, the step of defining the theoretical reference surface, The distance D = {d} from each measurement point to the theoretical reference surface. １ d ２ , . . . , d ｎ Calculate the value of the distance d. ｍａｘ and minimum value d ｍｉｎ The steps include obtaining, The degree of deformation F of the curved surface is defined as the distance range from all the measurement points to the reference curved surface, i.e., the difference between the maximum distance and the minimum distance, and is expressed as follows: [Number 38] A method for measuring thin-walled surface deformation based on the Kriging model as described in claim 1.
7. Specifically, S6 refers to, The measurement is terminated by calculating the standard deviation of the degree of deformation, setting an error threshold, indicating that the trend of change is unstable if the standard deviation is greater than or equal to the error threshold, and indicating that the trend of change is stable if the standard deviation is less than the error threshold. Specifically, this is done as follows: If the standard deviation of the height value z of the measurement point is less than a predetermined precision threshold Err, the iteration is stopped, n measurement points are set, and the height value of the measurement point is z １ , z ２ , . . . , z ｎ Therefore, the standard deviation ε of the height value of the measurement point is as follows: [Number 39] This is the average value of the height z of n measurement points: [Number 40] To avoid the influence of the initial measurement point deviation, the processor checks the standard deviation of the height value z of the last 30% of the measurement points, and if the standard deviation of the measurement points in this portion is less than the predetermined precision threshold Err, the iteration is stopped. Let T be the number of measurement points in the last 30%, and z be the height value of the last T measurement points. ｎ－Ｔ＋１ , z ｎ－Ｔ＋２ , ..., z ｎ Therefore, the standard deviation ε of the T measurement points Ｔ The formula for calculating this is as follows: [Number 41] This is the average of the heights of the last T measurement points: [Number 42] ε Ｔ <If Err, the standard deviation of the last T measurement points is less than Err, and the iteration is stopped, a thin-walled surface deformation measurement method based on the Kriging model according to claim 1.
8. An electronic device comprising at least one processor and a memory communicably connected to the at least one processor, wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can perform the method according to claims 1 to 7.
9. A non-temporary computer-readable storage medium in which a program is stored, The program is a non-temporary computer-readable storage medium used to cause a computer to perform the method according to claims 1 to 7.