Thin-wall surface deformation measurement method and device based on Kriging model and medium

Abstract

The invention discloses a thin-wall surface deformation measurement method and device based on a Kriging model, and a medium. The method comprises the following steps: S1, generating an initial measurement point; s2, a Kriging model is constructed; s3, dynamically selecting a sampling mode; s4, acquiring a sampling point to be detected; s5, the deformation degree of the thin-wall surface is obtained through actual measurement; and S6, evaluating and iterating. Through prediction and selection of iterative sampling points and in combination with a dynamic adjustment sampling strategy, the number of measurement points is effectively reduced, and the method can overcome the problem of measurement errors caused by coordinate deviation in AACMM handheld measurement. Even if deviation exists between the position of an actual measurement point and the position of a theoretical sampling point, the method still can accurately capture the deformation degree of the thin-wall surface through prediction and iterative optimization of the Kriging model, the reliability of a measurement result is ensured, and the measurement precision, the measurement efficiency, the stability of the method implementation and the applicability and robustness of different workpiece applications are improved.

Description

Technical Field

[0001] The present invention relates to a thin-walled surface deformation measurement method, device and medium based on a Kriging model, belonging to the technical field of shipbuilding measurement. Background Art

[0002] Thin-walled structures are widely used in industrial fields such as shipbuilding. The deformation measurement of thin-walled structural parts is crucial for ensuring product quality. Traditional contact measurement methods, such as coordinate measuring machines (CMM) and articulated arm coordinate measuring machines (AACMM), perform excellently in terms of accuracy, but are often limited in the efficient measurement of thin-walled structures. Especially for the articulated arm coordinate measuring machine (AACMM), although its flexibility and convenience make it widely used in complex environments, due to the influence of human factors during the measurement process, the coordinates of the measurement points are prone to deviation, which in turn affects the final measurement result. This deviation is particularly obvious in the deformation measurement of thin-walled structural parts.

[0003] Existing research mainly focuses on improving the calibration and compensation of AACMM to improve the measurement accuracy of the device itself. However, there is little systematic research on the impact of handheld operation on measurement accuracy, especially on how to deal with the coordinate deviation of measurement points caused by human operation. For the measurement of the deformation degree of thin-walled structures, existing technologies mainly rely on uniform sampling or random sampling strategies. Although these methods are simple, they are prone to unreasonable sampling point distribution in the measurement of complex surface deformations, and even cannot accurately capture key deformation areas, seriously affecting the accuracy and efficiency of the measurement results. Summary of the Invention

[0004] Object of the Invention: Aiming at the deficiencies in the existing technology, the present invention provides a thin-walled surface deformation measurement method, device and medium based on a Kriging model. The present invention effectively reduces the number of measurement points and significantly improves the accuracy and efficiency of thin-walled surface deformation measurement through iterative prediction and selection of sampling points, combined with dynamic adjustment of the sampling strategy, and overcomes the coordinate deviation problem in the handheld operation of AACMM.

[0005] Technical Solution: A thin-walled surface deformation measurement method based on a Kriging model includes the following steps:

[0006] S1. Generate initial measurement points: Use the Hammersley sequence to generate initial sampling points and perform actual measurements on them to obtain the initial measurement points, which serve as the input data for the Kriging model.

[0007] S2. Construct a Kriging model: Based on the initial measurement points in S1, construct a Kriging model to predict the deformation error distribution and mean square error distribution of the thin-walled surface.

[0008] S3. Dynamically select the sampling mode: Set two sampling modes and dynamically select the sampling mode through a probability decreasing function;

[0009] S4. Obtain the sampling points to be measured: Combine the sampling mode selected in S3 with the deformation error distribution and mean square error distribution of the thin-walled surface predicted in S2 to obtain the sampling points to be measured concentrated in the key deformation area of the thin-walled surface;

[0010] S5. Actually measure the deformation degree of the thin-walled surface: Measure the sampling points to be measured in S4 to obtain the actual measurement points, form the actual measurement point set, calculate the distance from each actual measurement point to the theoretical reference surface, and obtain the deformation degree of the thin-walled surface;

[0011] S6. Evaluate and iterate: Evaluate the deformation degree of the thin-walled surface in S5. By analyzing the change trend of the deformation degree, if the deformation degree tends to be stable, terminate the measurement; if the change trend is unstable, update the Kriging model with the current actual measurement point set and re-predict the deformation error distribution and mean square error distribution of the updated thin-walled surface, and return to S3.

[0012] Preferred option, the S2 includes:

[0013] S201. Construct a Kriging model based on the initial measurement points in S1 to obtain the deformation error values of the initial measurement points, and through the deformation error values of the initial measurement points, predict the deformation error distribution and mean square error distribution of the un-sampled area of the thin-walled surface;

[0014] S202. While the Kriging model predicts the deformation error distribution and mean square error distribution of the un-sampled area of the thin-walled surface, calculate the mean square error MSE at the corresponding predicted position to represent the uncertainty of the predicted value at this predicted position.

[0015] Preferred option, the S201 is specifically:

[0016] For n initial measurement points in the error spatial domain, the sampling position The corresponding error observation value is Then for any position within the domain, the Kriging model makes the following prediction:

[0017]

[0018] In the formula, is the predicted value at x, k(x) is a column vector composed of the covariance between the initial measurement points and x, [k(x)] T is its transpose matrix, k(x) = [k(x,x1),k(x,x2),…,k(x,x n )]T , K is the covariance matrix between the initial measurement points, K -1 is the inverse matrix of this matrix, and its specific representation is:

[0019]

[0020] where k(x i , x j ) is the covariance between the initial measurement points x i and x j ,

[0021] The covariance between the initial measurement points is obtained by using a Gaussian covariance model, which is expressed as:

[0022]

[0023] In the formula, θ d is the scale parameter of the d-th dimension, reflecting the similarity in this dimension, x id and x jd represent the coordinate values of the i-th initial measurement point and the j-th initial measurement point in the d-th dimension respectively.

[0024] Preferred option, the specific content of S202 is:

[0025] The larger the mean square error value, the less credible the prediction result. The expression of the mean square error value MSE is:

[0026]

[0027] In the formula, σ 2 is the basic variance of the Kriging model, which is obtained from the following expression:

[0028]

[0029] In the formula, n is the total number of measurement points, O T represents the transpose of the error observation value vector O.

[0030] Preferred option, the specific content of S3 is:

[0031] Sampling mode one and sampling mode two are set, and the probability decreasing function dynamically selects the sampling mode specifically as follows:

[0032] In each iteration, a random number rand is generated, 0 < rand < 1, and it is compared with 1 / i: if rand < 1 / i, then sampling mode one is selected; otherwise, sampling mode two is selected. As the iteration number i increases, 1 / i gradually decreases, the probability of sampling mode one gradually decreases, and the probability of sampling mode two gradually increases.

[0033] Preferred option, S4 is specifically as follows:

[0034] If sampling mode one is selected, then according to the maximum value of the mean square error value MSE in formula (4) of S202, that is, the point with the largest mean square error value MSE is used as the sampling point to be measured;

[0035] If sampling mode two is selected, then according to formula (1) in S201 The maximum value of the predicted value, that is, the point with the largest deformation error distribution value is selected as the sampling point to be measured;

[0036] The area where the sampling points to be measured are obtained by sampling mode one and sampling mode two is the key deformation area of the thin-walled surface.

[0037] Preferred option, S5 is specifically as follows:

[0038] Quantify the degree of deformation through the difference between the maximum distance and the minimum distance to ensure the accuracy of the measurement result. The calculation process of the degree of deformation includes the following steps:

[0039] Define the theoretical reference surface: According to the design model of the thin-walled surface, the theoretical reference surface is defined as follows:

[0040] S = f(x, y) (6)

[0041] For the measurement point P i =(x i , y i , z i ) to the directed distance d of the theoretical reference surface S = f(x, y) i is:

[0042]

[0043] In the formula, (x i , y i ) is the measurement point corresponding to the measurement point P i , z i is the height value corresponding to the measurement point P i , f(x i , y i ) is the nominal height of the reference surface, f x (x i , y i ) and f y (x i , y i ) are the partial derivatives of the reference surface in the x and y directions respectively, representing the slope of the surface at this point. The numerator of formula (7) represents the distance from the measurement point to the theoretical surface.

[0044] Calculate the distance D = {d1, d2,..., d n}, the maximum distance d is obtained max and the minimum distance d min ,

[0045] The degree of deformation F of the surface is defined as the distance range from all measurement points to the reference surface, that is, the difference between the maximum distance and the minimum distance, expressed as:

[0046]

[0047] Preferred option, the specific S6 is:

[0048] Calculate the standard deviation of the degree of deformation and set an error threshold. If the standard deviation is greater than or equal to the error threshold, it means that the change trend is unstable. If the standard deviation is less than the error threshold, it means that the change trend is stable, and then terminate the measurement. Specifically:

[0049] When the standard deviation of the height value z of the measurement points is less than the set precision threshold Err, stop the iteration. Suppose there are n measurement points, and the height values of the measurement points are z1, z2,..., z n , then the standard deviation ε of the height values of the measurement points is:

[0050]

[0051] Among them, is the mean value of the height values z of n measurement points:

[0052]

[0053] To avoid the influence of the deviation of the initial measurement points, the program will check the standard deviation of the height values z of the last 30% of the measurement points. If the standard deviation of this part of the measurement points is less than the set precision threshold Err, stop the iteration,

[0054] Suppose the number of the last 30% of the measurement points is T, and the height values of the last T measurement points are z n-T+1 , z n-T+2 ,..., z n , and the standard deviation ε of T measurement points T The calculation formula is:

[0055]

[0056] In the formula, is the mean value of the heights of the last T measurement points:

[0057]

[0058] When ε T < Err, then the standard deviation of the last T measurement points is less than Err, and stop the iteration.

[0059] An electronic device, comprising: at least one processor; and a memory communicatively 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 to enable the at least one processor to execute a thin-walled surface deformation measurement method based on the Kriging model.

[0060] A non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to cause the computer to execute a thin-walled surface deformation measurement method based on the Kriging model.

[0061] Advantageous effects: Through the prediction and selection of iterative sampling points and the combination of dynamic adjustment of the sampling strategy, the present invention effectively reduces the number of measurement points. This method can overcome the measurement error problem caused by coordinate deviation in AACMM handheld measurement. Even if there is a deviation between the actual measurement point position and the theoretical sampling point position, this method can still accurately capture the deformation degree of the thin-walled surface through the prediction and iterative optimization of the Kriging model, ensuring the reliability of the measurement results, improving the measurement accuracy, measurement efficiency, and the stability of method implementation, the applicability to different workpieces, and the robustness of measurement results for different operators. Description of the Drawings

[0062] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained according to the provided drawings without creative efforts.

[0063] Figure 1 It is a flowchart of the method of the present invention;

[0064] Figure 2 It is a schematic diagram of the sampling point selection process of sampling mode 1;

[0065] Figure 3 It is a schematic diagram of the sampling point selection process of sampling mode 2;

[0066] Figure 4 It is a schematic diagram of measuring coordinate deviation using a handheld articulated coordinate measuring arm;

[0067] Figure 5 It is a schematic diagram of calculating the deformation degree of the thin-walled surface by the distance from the measurement point to the theoretical reference surface;

[0068] Figure 6 It is a schematic diagram of the experimental platform measured by a handheld measuring arm;

[0069] Figure 7Deformation measurement result diagrams for different operators. Specific implementation manners

[0070] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts shall fall within the protection scope of the present invention.

[0071] In the description of the present invention, it should be understood that the orientation or positional relationships indicated by the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc. are based on the orientation or positional relationships shown in the accompanying drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention.

[0072] In the present invention, unless otherwise clearly specified and defined, the first feature being "above" or "below" the second feature may include the first and second features being in direct contact, or may include the first and second features not being in direct contact but being in contact through other features therebetween. Moreover, the first feature being "above", "over" and "on" the second feature includes the first feature being directly above and obliquely above the second feature, or merely indicating that the horizontal height of the first feature is higher than that of the second feature. The first feature being "below", "under" and "beneath" the second feature includes the first feature being directly below and obliquely below the second feature, or merely indicating that the horizontal height of the first feature is less than that of the second feature.

[0073] As Figure 1 shown, a thin-walled surface deformation measurement method based on the Kriging model includes the following steps:

[0074] S1. Generate initial measurement points: Use the Hammersley sequence to generate initial sampling points, and perform actual measurements on them to obtain the initial measurement points, which serve as the input data for the Kriging model. The Hammersley sequence is a low-discrepancy sequence that can cover the entire surface with fewer sampling points, ensuring the representativeness and uniformity of the sampling points. The initial sampling points generated by the Hammersley sequence serve as the input data for the Kriging model, providing a basis for subsequent deformation error prediction;

[0075] S2. Construct a Kriging model: Based on the initial measurement points in S1, construct a Kriging model to predict the deformation error distribution and mean square error distribution on the thin-walled surface. The Kriging method is an interpolation method based on spatial statistics, which can describe the spatial correlation between known points through the covariance function, so as to predict the error of unknown points. In the present invention, a Gaussian covariance function is used to describe the spatial correlation between measurement points, and the deformation error and its uncertainty distribution of unknown points are predicted through the deformation error data of known sampling points, providing a theoretical basis for subsequent sampling point selection.

[0076] S201. Based on the initial measurement points in S1, construct a Kriging model to obtain the deformation error values of the initial measurement points, and through the deformation error values of the initial measurement points, predict the deformation error distribution and mean square error distribution of the unsampled area on the thin-walled surface:

[0077] For the n initial measurement points in the error spatial domain, the sampling positions The corresponding error observation values are Then, for any position within the defined domain, the Kriging model makes predictions as shown below:

[0078]

[0079] In the formula, is the predicted value at x, k(x) is a column vector composed of the covariance between the initial measurement points and x, [k(x)] T is its transpose matrix, k(x) = [k(x, x1), k(x, x2), …, k(x, x n )] T , K is the covariance matrix between the initial measurement points, K -1 is the inverse matrix of this matrix, and its specific representation is:

[0080]

[0081] Among them, k(x i , x j ) is the covariance between the initial measurement point x i and x j ,

[0082] The covariance between the initial measurement points is obtained by using a Gaussian covariance model, and is expressed as:

[0083]

[0084] In the formula, θ d is the scale parameter of the d-th dimension, reflecting the similarity in this dimension, x id and x jdThey respectively represent the coordinate values of the $i$-th initial measurement point and the $j$-th initial measurement point in the $d$-th dimension.

[0085] S202. While the Kriging model predicts the deformation error distribution and mean square error distribution in the unsampled area of the thin-walled surface, it calculates the mean square error MSE at the corresponding predicted position to represent the uncertainty of the predicted value at this predicted position:

[0086] The larger the mean square error value, the less credible the prediction result. The expression of the mean square error value MSE is:

[0087]

[0088] In the formula, $\sigma$ 2 is the basic variance of the Kriging model, which is obtained from the following expression:

[0089]

[0090] In the formula, $n$ is the total number of measurement points, $O$ T represents the transpose of the error observation value vector $O$.

[0091] S3. Dynamically select the sampling mode: Set two sampling modes and dynamically select the sampling mode through a probability decreasing function:

[0092] Set sampling mode one and sampling mode two. The specific process of dynamically selecting the sampling mode by the probability decreasing function is as follows:

[0093] In each iteration, generate a random number $rand$, where $0 \lt rand \lt 1$, and compare it with $1 / i$. If $rand \lt 1 / i$, then select sampling mode one; otherwise, select sampling mode two. As the number of iterations $i$ increases, $1 / i$ gradually decreases, the probability of sampling mode one gradually decreases, and the probability of sampling mode two gradually increases.

[0094] S4. Obtain the sampling points to be measured: Combine the sampling mode selected in S3 with the deformation error distribution and mean square error distribution of the thin-walled surface predicted in S2 to obtain the sampling points to be measured concentrated in the key deformation area of the thin-walled surface:

[0095] As Figure 2 shown, if sampling mode one is selected, then according to the maximum value of the mean square error value MSE in formula (4) in S202, that is, the point with the largest mean square error value MSE is used as the sampling point to be measured. Sampling mode one can avoid local convergence, enabling the Kriging model to fully explore each area of the thin-walled surface in the initial stage and improving the global prediction ability. At this stage, by selecting the position with the maximum value of the mean square error value MSE, it can be ensured that the measurement points are distributed as much as possible to cover all areas where large errors may exist, thereby improving the measurement accuracy.

[0096] As Figure 3 shown, if sampling mode two is selected, then according to the formula (1) in S201 the maximum value of the predicted value, that is, the point with the largest deformation error distribution value is selected as the sampling point to be measured; Sampling mode two focuses on the local deformation extreme value region. Compared with the traditional equally spaced sampling point distribution, sampling mode two preferentially selects the regions with larger deformation and higher error for sampling, thus avoiding the deficiency that equally spaced sampling points may not be able to accurately capture the deformation concentrated region. Through sampling mode two, the measurement points are concentrated in the local region with larger deformation, further optimizing the sampling distribution. Compared with the uniform sampling method, sampling mode two can effectively improve the measurement accuracy of the high deformation region, enabling the measurement resources to be more concentratedly applied to the key deformation region, thereby improving the overall measurement accuracy and efficiency.

[0097] The regions where the sampling points to be measured are obtained by sampling mode one and sampling mode two are the key deformation regions on the thin-walled surface.

[0098] As Figure 4 shown, S5. Obtain the deformation degree of the thin-walled surface through actual measurement: Use AACMM to measure the sampling points to be measured in S4, obtain the actual measurement points, and form an actual measurement point set. Calculate the distance from each actual measurement point to the theoretical reference surface to obtain the deformation degree of the thin-walled surface:

[0099] Quantify the deformation degree by the difference between the maximum distance and the minimum distance to ensure the accuracy of the measurement result. The calculation process of the deformation degree includes the following steps:

[0100] Define the theoretical reference surface: According to the design model of the thin-walled surface, the theoretical reference surface is defined as follows:

[0101] S = f(x, y) (6)

[0102] For the measurement point P i =(x i , y i , z i ), the directed distance d i to the theoretical reference surface S = f(x, y) is:

[0103]

[0104] In the formula, (x i , y i ) is the measurement point corresponding to the measurement point P i , z i is the height value corresponding to the measurement point P i , f(x i , y i ) is the nominal height of the reference surface, fx (x i , y i ) and f y (x i , y i ) are the partial derivatives of the reference surface in the x and y directions respectively, representing the slope of the surface at that point. The numerator of formula (7) represents the distance from the measurement point to the theoretical surface.

[0105] Calculate the distance D = {d1, d2, …, d n} from each measurement point to the theoretical reference surface, and obtain the maximum value d max and the minimum value d min of the distance.

[0106] The deformation degree F of the surface is defined as the range of the distances from all measurement points to the reference surface, that is, the difference between the maximum distance and the minimum distance, expressed as:

[0107]

[0108] As Figure 5 shown, S6, Evaluation and Iteration: Evaluate the deformation degree of the thin-walled surface in S5. By analyzing the change trend of the deformation degree, if the deformation degree tends to be stable, terminate the measurement; if the change trend is unstable, update the Kriging model with the current actual measurement point set, and re-predict the deformation error distribution and mean square error distribution of the updated thin-walled surface, and return to S3:

[0109] Calculate the standard deviation of the deformation degree and set an error threshold. If the standard deviation is greater than or equal to the error threshold, it means the change trend is unstable; if the standard deviation is less than the error threshold, it means the change trend is stable, and then terminate the measurement. Specifically:

[0110] When the standard deviation of the height value z of the measurement points is less than the set precision threshold Err, stop the iteration. Suppose there are n measurement points, and the height values of the measurement points are z1, z2,..., z n , then the standard deviation ε of the height values of the measurement points is:

[0111]

[0112] Among them, is the mean value of the height values z of the n measurement points:

[0113]

[0114] To avoid the influence of the deviation of the initial measurement points, the program will check the standard deviation of the height values Z of the last 30% of the measurement points. If the standard deviation of this part of the measurement points is less than the set precision threshold Err, stop the iteration.

[0115] Let the number of the last 30% of the measurement points be T, and the height values of the last T measurement points be z n-T+1 , z n-T+2 ,..., z n-T+1 , and the standard deviation ε of the T measurement points T The calculation formula is as follows:

[0116]

[0117] In the formula, is the average height of the last T measurement points:

[0118]

[0119] When ε T < Err, the standard deviation of the last T measurement points is less than Err, and the iteration stops. In this embodiment, the value of T is set to 10 and Err is 0.02. When the above preset conditions are met, it proves that the measurement result is stable.

[0120] S7. Verification, as Figure 6 and Figure 7 shown,

[0121] S701. Experimental design: In order to verify the effectiveness and robustness of the method of the present invention, as well as the result stability of the method under the operation of different operators, and the applicability on thin-walled experimental parts of different sizes, multiple operators perform deformation measurement experiments on two thin-walled workpieces of different sizes: workpiece 1: 100×100×1 mm, workpiece 2: 300×300×1 mm, and collect data of 400 points and 900 points respectively through dense sampling, and calculate the deformation degree as the standard value.

[0122] S702. Analysis of the measurement results of the operators: Multiple operators use the handheld articulated coordinate measuring arm AACMM to perform multi-point measurement on these two workpieces. Each operator independently measures workpiece 1 and workpiece 2. In the measurement of workpiece 1, the method of this article can achieve the same accuracy as the 7×7 equidistant sampling method and the 40-point Hammersley method within 30 measurement points, that is, within the accuracy standard. This shows that the method of this article can reach the accuracy standard with fewer points, reflecting its excellent sampling efficiency and accuracy advantages; in the measurement of workpiece 2, the experimental results show a similar trend. When using less than 40 measurement points, the method of this article can be equivalent to the 8×8 equidistant sampling method and the 50-point Hammersley method, and the accuracy can converge within the accuracy standard (0.01 mm). In particular, the method of this article can converge with fewer points, and the result rules of different operators are consistent, further verifying the robustness of the method in the measurement results of different operators.

[0123] S703. Applicability verification for workpieces of different sizes: In the measurements of workpiece 1 and workpiece 2, the method proposed in this paper demonstrated high measurement accuracy and stability. Especially in the measurement of workpiece 1, the method in this paper only required 28 points to meet the accuracy standard, while equidistant sampling and Hammersley sequence sampling required 49 points and 40 points respectively; in the measurement of workpiece 2, the method in this paper only needed 39 points to reach the accuracy standard, while equidistant sampling and Hammersley sequence sampling required 64 points and 50 points respectively, verifying the applicability and robustness of this method for workpieces of different sizes. The method in this paper reduced the number of measurement points by 42.9% and 39.1% in the measurements of workpiece 1 and workpiece 2 respectively, while maintaining higher measurement accuracy.

[0124] The experimental results show that the method of the present invention can effectively reduce the error differences among operators, improve the measurement consistency, and significantly improve the measurement accuracy. Compared with the traditional method, the method of the present invention shows higher accuracy and faster convergence speed in deformation measurement, verifying its adaptability and stability in the actual production environment.

[0125] Each embodiment in this specification is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and reference can be made to the description in the method part for relevant parts.

[0126] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A thin-walled surface deformation measurement method based on the Kriging model, characterized in that: It includes the following steps: S1. Generate initial measurement points: Use the Hammersley sequence to generate initial sampling points, and conduct actual measurements on them to obtain the initial measurement points, which serve as the input data for the Kriging model; S2. Construct the Kriging model: Based on the initial measurement points in S1, construct the Kriging model to predict the deformation error distribution and mean square error distribution of the thin-walled surface; S3. Dynamically select the sampling mode: Set two sampling modes and dynamically select the sampling mode through a probability decreasing function; S4. Obtain the sampling points to be measured: Combine the sampling mode selected in S3 with the deformation error distribution and mean square error distribution of the thin-walled surface predicted in S2 to obtain the sampling points to be measured concentrated in the key deformation areas of the thin-walled surface; S5. Actually measure the deformation degree of the thin-walled surface: Measure the sampling points to be measured in S4 to obtain the actual measurement points, and form an actual measurement point set. Calculate the distance from each actual measurement point to the theoretical reference surface to obtain the deformation degree of the thin-walled surface; S6. Evaluate and iterate: Evaluate the deformation degree of the thin-walled surface in S5. By analyzing the change trend of the deformation degree, if the deformation degree tends to be stable, terminate the measurement; If the change trend is unstable, update the Kriging model with the current actual measurement point set, and re-predict the deformation error distribution and mean square error distribution of the updated thin-walled surface, and return to S3.

2. The thin-walled surface deformation measurement method based on the Kriging model according to claim 1, characterized in that: The S2 includes: S201. Based on the initial measurement points in S1, construct the Kriging model to obtain the deformation error values of the initial measurement points, and through the deformation error values of the initial measurement points, predict the deformation error distribution and mean square error distribution of the un-sampled areas of the thin-walled surface; S202. While the Kriging model predicts the deformation error distribution and mean square error distribution of the un-sampled areas of the thin-walled surface, calculate the mean square error MSE at the corresponding predicted positions to represent the uncertainty of the predicted values at these predicted positions.

3. The thin-walled surface deformation measurement method based on the Kriging model according to claim 2, wherein: The S201 is specifically: For n initial measurement points in the error space domain, the sampling positions The corresponding error observations are where m represents the error value corresponding to each sampling position. Then, for any position within the domain, the Kriging model makes a prediction as shown below: In the formula, is the predicted observed value at x, O is the vector of known error observed values, k(x) is the column vector formed by the covariance between the initial measurement points and x, and [k(x)] T is its transpose matrix, k(x) = [k(x, x1), k(x, x2), …, k(x, x n )] T , K is the covariance matrix between the initial measurement points, and K -1 is the inverse matrix of this matrix, and its specific representation is: Among them, k(x i , x j ) is the covariance between the initial measurement point x i and x j , Adopt the Gaussian covariance model to obtain the covariance between the initial measurement points, expressed as: where θ d is the scale parameter of the d-th dimension, reflecting the similarity in this dimension, x id and x jd represent the coordinate values of the i-th initial measurement point and the j-th initial measurement point in the d-th dimension, respectively.

4. The thin-walled surface deformation measurement method based on the Kriging model according to claim 3, characterized in that: The S202 is specifically: The larger the mean square error value, the less credible the prediction result. The expression of the mean square error value MSE is: where σ 2 is the basic variance of the Kriging model and is obtained from the following expression: where n is the total number of measurement points, and O T represents the transpose of the error observation value vector O.

5. The thin-walled surface deformation measurement method based on the Kriging model according to claim 4, wherein: The S3 is specifically: Set sampling mode one and sampling mode two. The probability decreasing function dynamically selects the sampling mode specifically as: In each iteration, generate a random number rand, 0 < rand < 1, and compare it with 1 / i: If rand < 1 / i, select sampling mode one; otherwise, select sampling mode two. As the iteration number i increases, 1 / i gradually decreases, the probability of sampling mode one gradually decreases, and the probability of sampling mode two gradually increases.

6. The thin-walled surface deformation measurement method based on the Kriging model according to claim 5, characterized in that: The S4 is specifically: If sampling mode one is selected, then according to the maximum value of the mean square error MSE in formula (4) in S202, that is, take the point with the largest mean square error value MSE as the sampling point to be measured; If sampling mode 2 is selected, then according to formula (1) in S201 the maximum value of the predicted value, that is, the point with the largest deformation error distribution value is selected as the sampling point to be measured; The areas where the sampling points to be measured are obtained by sampling mode one and sampling mode two are the key deformation areas of the thin-walled surface.

7. The thin-walled surface deformation measurement method based on the Kriging model according to claim 1, wherein: The S5 is specifically: Quantify the degree of deformation by the difference between the maximum distance and the minimum distance to ensure the accuracy of the measurement results. The calculation process of the degree of deformation includes the following steps: Define the theoretical reference surface: According to the design model of the thin-walled surface, the theoretical reference surface is defined as follows: S = f(x, y) (6) For the measurement point P i =(x i , y i , z i ), the directed distance d from the theoretical reference surface S = f(x, y) is i as follows: where (x i , y i ) is the measurement point corresponding to measurement point P i , z i is the height value corresponding to measurement point P i , f(x i , y i ) is the nominal height of the reference surface, f x (x i , y i ) and f y (x i , y i ) are the partial derivatives of the reference surface in the x and y directions respectively, representing the slope of the surface at that point. The numerator of formula (7) represents the distance from the measurement point to the theoretical surface. Calculate the distance D = {d1, d2, …, d n} from each measurement point to the theoretical reference surface, and obtain the maximum value d max and the minimum value d min , The degree of deformation F of the curved surface is defined as the distance range from all measurement points to the reference curved surface, that is, the difference between the maximum distance and the minimum distance, expressed as:

8. The thin-walled surface deformation measurement method based on the Kriging model according to claim 1, characterized in that: The specific S6 is: Calculate the standard deviation of the degree of deformation and set an error threshold. If the standard deviation is greater than or equal to the error threshold, it indicates that the change trend is unstable. If the standard deviation is less than the error threshold, it indicates that the change trend is stable, and then the measurement is terminated. Specifically: When the standard deviation of the height value z of the measurement points is less than the set precision threshold Err, stop the iteration. Suppose there are n measurement points, and the height values of the measurement points are z1, z2,..., z n , then the standard deviation ε of the height values of the measurement points is: Among them, is the mean value of the height values z of n measurement points: To avoid the influence of the deviation of the initial measurement points, the program checks the standard deviation of the height values z of the last 30% of the measurement points. If the standard deviation of this part of the measurement points is less than the set accuracy threshold Err, the iteration is stopped. Let the number of the last 30% of the measurement points be T, and the height values of the last T measurement points be z n-T+1 , z n-T+2 ,..., z n , and the standard deviation ε of the T measurement points T The calculation formula is as follows: wherein, is the average height of the last T measurement points: When ε T <Err, and the standard deviation of the last T measurement points is less than Err, then stop the iteration.

9. An electronic device, comprising: At least one processor; And a memory communicatively 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 execute the method according to claims 1-8.

10. A non-transitory computer-readable storage medium storing computer instructions, wherein, The computer instructions are used to cause the computer to execute the method according to claims 1-8.

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