Large part full-feature deformation field high-precision reconstruction method under constraint of limited measuring points

Abstract

The invention belongs to the field of precision manufacturing of aerospace parts, and relates to a high-precision reconstruction method for a full-feature deformation field of a large-scale part under the constraint of a limited measuring point, in particular to a high-precision reconstruction method for the full-feature deformation field of the large-scale part under the constraint of the limited measuring point. The method comprises the following steps: accurately measuring actual three-dimensional coordinates of sampling measurement points of large cabin parts at different mounting stations to obtain actual offset data of limited measurement points of the large cabin parts; then mechanical modeling and analysis are conducted on the cabin structure, and calculation of all characteristic deformation of the large cabin under the horizontal installation station is completed with the help of a finite element method. A result obtained through finite element solution is integrated into an interpolation reconstruction method depending on data driving, and a regression Kriging interpolation model is constructed. High-precision reconstruction of the full-feature deformation field of the large part under the constraint of limited measuring points is achieved, the solving precision of the full-feature deformation field of the large cabin part is effectively guaranteed, and horizontal in-situ integrated high-precision and high-efficiency machining of the large thin-wall spacecraft cabin part is achieved.

Description

Technical Field

[0001] The invention belongs to the field of precision manufacturing of aerospace parts, and relates to a high-precision reconstruction method of a full-feature deformation field of a large part under the constraints of limited measuring points. Background Art

[0002] Large spacecraft equipment is widely used in major aerospace missions such as space station construction, lunar exploration, and planetary exploration in the aerospace field. Large thin-walled spacecraft cabin parts provide the overall configuration of the spacecraft and are key parts to ensure the reliable and stable service of large spacecraft. Their manufacturing accuracy and reliability directly affect the service performance of the spacecraft. For large thin-walled spacecraft cabin parts, horizontal in-situ integrated processing provides a feasible high-precision manufacturing solution. However, due to the large size, small wall thickness, large mass, and low stiffness of such parts, the thin-walled cabin parts will produce irregular elastic deformations that are dozens of times the manufacturing tolerance under the action of gravity and clamping loads during horizontal integrated processing. After the processing is completed, the elastic deformation rebounds and causes the cabin to fail to meet the processing accuracy requirements. Therefore, it is necessary to measure or solve the deformation field of all features of the large thin-walled cabin during horizontal integrated processing with high precision to guide the modification of the cabin processing model, so as to ensure that the final processing accuracy of the large thin-walled cabin parts meets the design index requirements.

[0003] Liu Wei et al.'s patent publication number CN112033298B, "A method for measuring gravity deformation of a spacecraft cabin based on fixed reference points", uses fixed reference points as constraints to achieve high-precision measurement of gravity deformation of a spacecraft cabin, uses fixed reference points as constraints to achieve coordinate system matching of different cabin stations, obtains the coordinates of key points on the cabin after deformation through transfer measurement, and then determines the gravity deformation of any key point of the cabin. However, this method mainly focuses on obtaining the three-dimensional deformation at a given key point on the cabin, and cannot achieve high-precision acquisition of all characteristic deformations of the cabin. Cai Dengan et al.'s patent publication number CN115017754A, "A method for correcting a finite element model considering manufacturing errors", generates a finite element model that introduces different forms of manufacturing errors through programmatic generation, while improving the accuracy of the finite element solution and avoiding the complex operation of artificially introducing defects into the finite element model. However, the final accuracy of the finite element method solution is still affected by model simplification and parameter estimation, and further improving the accuracy usually requires a more complex and time-consuming process. Summary of the invention

[0004] In view of the defects of the prior art, the present invention invents a method for high-precision reconstruction of the full characteristic deformation field of large parts under the constraints of limited measuring points. The method first accurately measures the actual three-dimensional coordinates of the sampling measurement points of large cabin parts at different installation stations, thereby obtaining the actual offset data of its limited measurement points. Then, accurate mechanical modeling and analysis are carried out for the cabin structure, and the calculation of all characteristic deformations of the large cabin under the horizontal installation station is completed with the help of the finite element method; finally, the results obtained by finite element solution are integrated into the data-driven interpolation reconstruction method, and a regression Kriging interpolation model is constructed to achieve high-precision reconstruction of the full characteristic deformation field of large parts under the constraints of limited measuring points. While not increasing the complexity of the measurement operation or the measurement time, the solution accuracy of all characteristic deformation fields of large cabin parts is effectively guaranteed. This method is suitable for high-precision and high-efficiency acquisition of all characteristic deformation fields of large thin-walled spacecraft cabins.

[0005] The technical solution adopted by the present invention is a method for high-precision reconstruction of the full-feature deformation field of large parts under the constraints of limited measuring points, which is characterized in that the method obtains the actual offset at the limited measuring points of large cabin parts by measuring the actual three-dimensional coordinates at the sampling measuring points of large cabin parts at different workstations; then, by accurately modeling and analyzing the cabin structure, the deformation of all features of the large cabin under the horizontal installation station is calculated based on the finite element method; finally, the results obtained by the finite element solution are integrated into the data-driven interpolation reconstruction method, and a regression Kriging interpolation model is constructed to achieve high-precision reconstruction of the full-feature deformation field of large parts under the constraints of limited measuring points. While not increasing the complexity of the measurement operation or the measurement time, the solution accuracy of the full-feature deformation field of large cabin parts is effectively guaranteed. This method is suitable for high-precision and high-efficiency acquisition of the full-feature deformation field of large thin-walled spacecraft cabins. The specific steps of the method are as follows:

[0006] Step 1: Measure the offset of limited measuring points of large cabin parts at different workstations.

[0007] First, 6 target balls are arranged at the conical port on the installation side of the large cabin part as fixed reference points, and n target balls are arranged at the key features on the cylindrical surface of the large cabin part as sampling measurement points Q i (x i ,y i ,z i ). The three-dimensional coordinates of all fixed reference points and sampling measurement points on the large cabin parts are measured in sequence using a laser tracker at different stations. Based on the measurement results of the fixed reference points, a global coordinate system of the cabin fixed to the conical port of the cabin at the horizontal station is established. h -X h Y h Z h}, and transfer the measurement results of the sampling measurement points obtained by the laser tracker at different positions and unify them into the global coordinate system of the cabin.

[0008] Then, the large cabin part 2 is hoisted to the vertical station, and the vertical station is used as an approximate zero gravity station. The three-dimensional coordinates of all fixed reference points and measurement points are measured by a laser tracker at different positions. The cabin global coordinate system {0 v -X v Y v Z v}, and transfer the measurement results of the sampling measurement points obtained by the laser tracker at different positions and unify them into the global coordinate system of the cabin.

[0009] Finally, the cabin global coordinate system is used as the reference coordinate system to unify all measurement data in the horizontal position into the cabin global coordinate system in the vertical position, so as to achieve the unification and matching of all measurement point coordinate systems in different positions. Taking the vertical position as the approximate zero gravity position, the offset D of the cabin sampling measurement point in the horizontal position can be obtained. M (Q i )for:

[0010] D M (Q i )=Q i -Q i ' (1)

[0011] Among them, Q i and Q i ' are the three-dimensional coordinates of the i-th sampling measurement point measured at the vertical and horizontal workstations.

[0012] Step 2: reconstruct the entire characteristic deformation field of the large cabin based on the measured data of limited sampling measurement points by interpolation.

[0013] Get n sampling measurement points Q on the cabin i After the actual measurement values ​​of the deformation at different workstations, the spatial relationship between these known sampling measurement points and any position on the cabin can be determined using the variogram. Based on the ordinary Kriging method, the spatial relationship between any point Q on the cabin j The deformation at can be expressed as:

[0014]

[0015] in, Denotes any point Q on the surface of the large cabin j The deformation vector obtained by solving at i is assigned to the known sampling measurement point Q i The weight factor of .

[0016] At the known sampling measurement point Q i At this point, the deformation vector and the true deformation vector D(Q i ) is zero. In addition, the estimated variance Var[·] between the true value and the predicted value should be minimized at the same time. The corresponding formula is as follows:

[0017]

[0018] Further based on the Kriging equations, the following equation can be obtained:

[0019]

[0020] Where μ is the Lagrange multiplier. The three-dimensional semivariogram function γ(Q i ,Q j ) is used to quantify the spatial correlation, which is composed of the distance from any point Q near the cabin surface j The weight factor λ is determined by the distance between the i-th and k-th adjacent sampling measurement points and the fitted theoretical semivariogram model. By solving the Kriging equations, the weight factor λ can be obtained. i . Then, any point Q on the surface of the large cabin j The deformation at can be calculated by interpolation using formula (2).

[0021] Step 3: Solve the deformation field of all features of large thin-walled cabin parts based on the finite element method.

[0022] On the basis of limited measurement points, the deformation information of all cabin features that conform to the cabin geometry and physical characteristics is introduced; the cabin of a large thin-walled spacecraft is a typical thin-walled structure composed of aluminum alloy plates. Through accurate mechanical modeling and analysis of the cabin structure, the deformation of all features of the large cabin under the horizontal installation station is calculated based on the finite element method. The physical properties of aluminum alloy materials, such as the influence of elastic modulus, Poisson's ratio and other parameters on deformation are fully considered. At the same time, structural factors such as the cabin geometry, size and connection method between components are carefully analyzed. The cabin is divided into many tiny units for discretization. The force and deformation of each unit are simulated under the horizontal installation state due to its own gravity and possible external clamping force, assembly force and other loads, and then the accurate deformation data of all features of the entire large cabin in various dimensions are integrated.

[0023] Then, the three-dimensional coordinates and deformation vectors of all finite element mesh nodes of the large cabin are extracted, and the finite element mesh nodes Q j The deformation vector D at can be described as follows:

[0024] D FEM(Q j )=D(x j ,y j ,z j ) (5)

[0025] Among them, x j ,y j and z j Represent all finite element mesh nodes Q of the spacecraft cabin j The spatial coordinates of .

[0026] Step 4: Reconstruct the deformation field of the large cabin by combining the finite point measurement data with the finite element method solution results.

[0027] After obtaining the finite element solution results of the large cabin, a regression kriging interpolation model was constructed to integrate the solution results of the physical model into the data-driven interpolation reconstruction method. By incorporating the global trend variable into the ordinary kriging interpolation model, the results of the finite element solution can be integrated into the data-driven interpolation reconstruction method.

[0028] The regression kriging interpolation model is expressed as follows:

[0029]

[0030] in, is the cabin deformation field obtained from the regression Kriging model, represents the global trend component of the cabin deformation field, Corresponding to the finite element mesh node Q j The residual error of the solution relative to the global trend component.

[0031] In the standard regression kriging model, the global trend component is usually determined by linear regression. By replacing the global trend component of the cabin deformation field with the finite element solution result, the finite measurement point Q i The residual deviation ε of the deformation vector at FEM (Q i ):

[0032] ε FEM (Q i )=D M (Q i )-D FEM (Q i ) (7)

[0033] Further, the finite element mesh node Q j The residual deviation at is interpolated using the Kriging method to obtain the deformation field of all the characteristics of the cabin.

[0034]

[0035] Among them, γ i is assigned to the known sampling measurement point Q i The weight coefficient of the residual deviation of the deformation finite element solution result.

[0036] Finally, the weight coefficient γ is determined by satisfying the conditions of unbiasedness and minimization of estimated variance. i , determine the regression kriging model based on the finite element solution trend results and the actual measurement results of a limited number of points, so as to incorporate a limited number of actual measurement points into the deformation field trend results obtained from the finite element solution. This method improves the accuracy of the deformation field solution without increasing the complexity or calculation time of the finite element analysis.

[0037] The significant effect and benefit of the present invention is that when this method solves the complete characteristic deformation field of large-scale thin-walled complex cabin parts, the efficiency of point-by-point measurement of all characteristic deformations of the large cabin is too low, and the interpolation solution results based on limited measurement data and the finite element solution results are insufficiently accurate. By integrating the solution results of the physical model into the data-driven interpolation reconstruction method, the solution accuracy of all characteristic deformation fields of large cabin parts is effectively guaranteed without increasing the complexity of the measurement operation or the measurement time. This method is suitable for high-precision and high-efficiency acquisition of all characteristic deformation fields of large thin-walled spacecraft cabins. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 —Overall flow chart of the method.

[0039] Figure 2 —Schematic diagram of horizontal measurement of large cabin parts, where 1 is a large cabin, 2 is a laser tracker, 3 is a support device, 4 is a rotating fixture, {O h -X h Y h Z h}—Global coordinate system of the cabin under horizontal installation.

[0040] Figure 3 —Schematic diagram of vertical measurement of large cabin parts, where {O v -X v Y v Z v}—Global coordinate system of the cabin under vertical installation.

[0041] Figure 4 —Comparison of the absolute deviations of the deformation of the cabin in the X direction at the verification point obtained by different methods, the horizontal axis is the number of the verification measurement point, the vertical axis is the absolute deviation (mm).

[0042] Figure 5—Comparison chart of the absolute deviation of the deformation of the cabin in the Y direction at the verification point obtained by different methods, the horizontal axis is the number of the verification measurement point, the vertical axis is the absolute deviation (mm).

[0043] Figure 6 —Comparison of the absolute deviations of the cabin deformation in the Z direction at the verification point obtained by different methods, the horizontal axis is the verification measurement point number, the vertical axis is the absolute deviation (mm).

[0044] Figure 7 —Comparison of the maximum absolute deviation of cabin deformation at the verification point obtained by different methods.

[0045] Figure 8 —Comparison of the average absolute deviation of cabin deformation at all verification points obtained by different methods. DETAILED DESCRIPTION

[0046] In order to make the objectives, technical solutions and advantages of the embodiments of the present invention more clear, the specific implementation methods of the present invention will be described in detail below in combination with the technical solutions and the accompanying drawings.

[0047] Due to the large size, small wall thickness, large mass and low stiffness of the spacecraft cabin, the thin-walled cabin parts will produce irregular elastic deformation dozens of times the manufacturing tolerance during horizontal integrated processing under the action of gravity and clamping load. After the processing is completed, the elastic deformation rebounds and the cabin cannot meet the processing accuracy requirements. In order to achieve high-precision reconstruction of the full characteristic deformation field of large thin-walled cabins, a high-precision reconstruction method for the full characteristic deformation field of large parts under the constraints of limited measurement points was invented. The overall process is shown in the attached figure. Figure 1 shown.

[0048] Taking a large thin-walled cabin sample with an outer diameter of 3600mm, a length of 6200mm and a material of 7075 aluminum alloy as an example, the implementation process of the present invention is described in detail. Figure 2 As shown, the method first arranges 6 fixed reference points, 50 sampling measurement points and 150 verification measurement points on the large thin-walled cabin sample, installs the large thin-walled cabin sample horizontally, uses a laser tracker to measure the fixed reference points, sampling measurement points and verification measurement points at 4 different positions, establishes the cabin global coordinate system under the horizontal station based on the measurement results of the fixed reference points, and obtains the three-dimensional coordinates of all sampling measurement points and verification measurement points in the cabin global coordinate system under the horizontal station.

[0049] Then, the large thin-walled cabin sample is installed vertically, as shown in the attached Figure 3As shown, the laser tracker is reused to re-measure the fixed reference points, sampling measurement points and verification measurement points at three different stations. Similarly, the global coordinate system of the cabin under the vertical station is established based on the measurement results of the fixed reference points, and the three-dimensional coordinates of all sampling measurement points and verification measurement points in the global coordinate system of the cabin under the vertical station are obtained.

[0050] The global coordinate systems of the large thin-walled cabin samples at the vertical and horizontal workstations are matched to the same reference, the matching between the cabin measurement points at different workstations is achieved, the geometric displacement vectors of the sampling measurement points and the verification measurement points at different workstations are solved, and the gravity deformation of the large thin-walled cabin samples is determined.

[0051] After obtaining 50 sampling measurement points Q on the cabin i Actual measured value of deformation at different working positions D M (Q i ), the spatial relationship between these known sampling measurement points and any position on the cabin can be determined using the variogram, and the deformation vector at any point on the cabin can be solved based on the ordinary Kriging method.

[0052] The structural shape of the large thin-walled cabin sample, support device and rotating fixture was established in ANSYS. The elastic modulus of the cabin material was defined as E = 71.7 GPa, Poisson's ratio ν = 0.33, and density ρ = 2.81 g / cm according to the prior material parameters. 2 , define the mesh unit type as tetrahedral unit, the unit mesh size as 5mm, and establish a finite element solution model for the elastic deformation of the cabin under various loads such as its own gravity and external clamping force. Post-processing obtains the topological relationship between the finite element mesh, unit, and node of the large thin-walled cabin, as well as the coordinate values ​​and deformation displacement vectors of the finite element mesh nodes of the large thin-walled cabin before and after elastic deformation under gravity and clamping, that is, all finite element mesh nodes Q of the large thin-walled cabin. j The deformation vector D at FEM (Q j ).

[0053] The result D obtained by finite element solution FEM (Q j ) is integrated into the data-driven interpolation reconstruction method, a regression kriging interpolation model is established, and the weight coefficient γ is determined by satisfying the conditions of unbiasedness and minimization of estimated variance. i , to incorporate a limited number of actual measurement points into the deformation field trend results obtained from the finite element solution, and obtain all the finite element mesh nodes Q of the large thin-walled cabin solved by the proposed method j The deformation vector at

[0054] In order to verify the effectiveness of the proposed method in solving the cabin deformation field, the deformation measurement results of 150 verification measurement points in the horizontal position are used as the standard value, and the absolute values ​​of the solution deviations of the deformation components in different directions at the verification points by different methods are compared. Figure 4 , Attachment Figure 5 and attached Figure 6 The deformation of the cabin in the three directions of X, Y and Z, obtained by the finite element method, finite point interpolation and this method, and the absolute deviation comparison diagram at the verification point are shown in the figure. The results in the figure show that compared with the solution results of the finite element method, the absolute value of the deviation obtained by the proposed method is significantly reduced at 150 verification points, while compared with the solution results of the interpolation method, the absolute value of the deviation obtained by the proposed method is significantly reduced at most verification points, and the fluctuation range of the absolute value of the deviation is significantly reduced. At the same time, in three different directions, the average value of the absolute deviation at the verification point of the solution results obtained by the proposed method is smaller than that of the solution results of the other two methods.

[0055] To further illustrate the effectiveness of the proposed method, the maximum and average absolute values ​​of the deviations of the cabin deformation components in different directions obtained by different methods at all 150 verification measurement points are compared. The calculation results of the maximum and average absolute values ​​of the deviations are shown in the attached figure. Figure 7 and attached Figure 8 As shown. Figure 7 and attached Figure 8 In the results, the maximum absolute deviation of the proposed method in the X, Y and Z directions was reduced by 60.99%, 66.74% and 66.00% respectively, and the average absolute deviation was reduced by 68.98%, 81.33% and 52.87% respectively compared with the finite element method. Similarly, in the X, Y and Z directions, the maximum absolute deviation of the proposed method was reduced by 16.39%, 29.24% and 39.62% respectively, and the average absolute deviation was reduced by 40.67%, 68.26% and 24.51% respectively compared with the interpolation solution method. The results show that the maximum and average absolute values ​​of the deviations obtained by the proposed method are significantly reduced compared with the results of the finite element method and the interpolation solution method.

[0056] It is explained that the method for high-precision reconstruction of the full characteristic deformation field of large parts under the constraints of limited measuring points of the present invention can effectively ensure the solution accuracy of the full characteristic deformation field of large cabin parts without increasing the complexity of measurement operations or increasing measurement time, and achieve high-precision reconstruction of the full characteristic deformation field of large thin-walled cabins, which in turn plays an important guiding role in achieving horizontal in-situ integrated high-precision machining of large thin-walled spacecraft cabin parts.

Claims

1. A high-precision reconstruction method for the full-feature deformation field of a large part under the constraints of limited measuring points, characterized in that: The method measures the actual three-dimensional coordinates of the sampling measurement points of the large cabin parts at different workstations to obtain the actual offset at the limited measurement points of the large cabin parts; then, the deformation of all the characteristics of the large cabin at the horizontal installation workstation is calculated based on the finite element method by accurately modeling and analyzing the cabin structure; The results of finite element solution are integrated into the data-driven interpolation reconstruction method to build a regression Kriging interpolation model to achieve high-precision reconstruction of the full characteristic deformation field of large parts under the constraints of limited measurement points. This effectively ensures the accuracy of the solution of the full characteristic deformation field of large cabin parts without increasing the complexity of measurement operations or the measurement time. The specific steps of the method are as follows: Step 1, measuring the offset of the limited measuring points of the large cabin parts at different workstations; First, the large thin-walled cabin sample is installed horizontally, and 6 target balls are arranged at the conical port on the installation side of the large cabin part as fixed reference points, and n target balls are arranged at the key features on the cylindrical surface of the large cabin part as sampling measurement points Q. i (x i ,y i ,z i ); A laser tracker is used to measure the three-dimensional coordinates of all fixed reference points and sampling measurement points on the large cabin parts in turn at different positions, and a cabin global coordinate system fixed to the cabin conical port at a horizontal position is established based on the measurement results of the fixed reference points. h -X h Y h Z h }, and transfer and unify the measurement results of the sampling measurement points obtained by the laser tracker at different stations to the global coordinate system of the cabin; Then, the large cabin part 2 is hoisted to the vertical station, and the vertical station is used as an approximate zero gravity station. The three-dimensional coordinates of all fixed reference points and measurement points are measured by a laser tracker at different positions. The cabin global coordinate system {0 v -X v Y v Z v }, and transfer and unify the measurement results of the sampling measurement points obtained by the laser tracker at different stations to the global coordinate system of the cabin; Finally, the cabin global coordinate system is used as the reference coordinate system, and all the measurement data in the horizontal position are unified into the cabin global coordinate system in the vertical position, so as to achieve the unification and matching of the coordinate systems of all the measurement points in different positions; the vertical position is used as the approximate zero gravity position, and the offset D of the cabin sampling measurement point in the horizontal position is obtained. M (Q i )for: D M (Q i )=Q i -Q i ' (1) Among them, Q i and Q i ' are the three-dimensional coordinates of the i-th sampling measurement point measured at the vertical and horizontal workstations; Step 2, reconstructing the entire characteristic deformation field of the large cabin based on the measured data of limited sampling measurement points by interpolation; Get n sampling measurement points Q on the cabin i After the actual measurement values ​​of the deformation at different workstations, the spatial relationship between these known sampling measurement points and any position on the cabin can be determined using the variogram. Based on the ordinary Kriging method, the spatial relationship between any point Q on the cabin j The deformation at is expressed as: in, Denotes any point Q on the surface of the large cabin j The deformation vector obtained by solving at i is assigned to the known sampling measurement point Q i The weight factor of At the known sampling measurement point Q i At this point, the deformation vector and the true deformation vector D(Q i ) is zero; in addition, the estimated variance Var[·] between the true value and the predicted value should be minimized at the same time; the corresponding formula is as follows: Based on the Kriging equations, the following equations are obtained: Where μ is the Lagrange multiplier; the three-dimensional semivariogram function γ(Q i ,Q j ) is used to quantify the spatial correlation, which is composed of the distance from any point Q near the cabin surface j The distance between the i-th and k-th adjacent sampling measurement points and the fitted theoretical semivariogram model are determined; by solving the Kriging equations, the weight factor λ is obtained. i ; Therefore, any point Q on the surface of the large cabin j The deformation at is calculated by interpolation using formula (2); Step 3, solving the deformation field of all characteristics of large thin-walled cabin parts based on the finite element method; On the basis of limited measurement points, all characteristic deformation information of the cabin that conforms to the geometric and physical characteristics of the cabin is introduced; the large thin-walled spacecraft cabin is a typical thin-walled structure composed of aluminum alloy plates. The deformation of all characteristics of the large cabin under the horizontal installation station is calculated based on the finite element method; the physical properties of aluminum alloy materials, such as the influence of parameters such as elastic modulus and Poisson's ratio on deformation, are fully considered, and the geometric shape, size and structural factors of the connection method between the components of the cabin are carefully analyzed. The cabin is divided into many tiny units for discretization processing, and the force and deformation of each unit under the horizontal installation state are simulated due to its own gravity and possible external clamping force, assembly force and other loads. Then, the accurate deformation data of all characteristics of the entire large cabin in each dimension are integrated; then, the three-dimensional coordinates and deformation vectors of all finite element mesh nodes of the large cabin are extracted, and all finite element mesh nodes Q j The deformation vector D at is described as follows: D FEM (Q j )=D(x j ,y j ,z j ) (5) Among them, x j ,y j and z j Represent all finite element mesh nodes Q of the spacecraft cabin j The spatial coordinates of Step 4, combining the finite point measurement data with the finite element method solution results to reconstruct the large cabin deformation field; The results of the physical model were integrated into the data-driven interpolation and reconstruction method, and a regression kriging interpolation model was constructed. The results of the finite element solution were integrated into the data-driven interpolation and reconstruction method by incorporating the global trend variable into the ordinary kriging interpolation model. The regression kriging interpolation model is expressed as follows: in, is the cabin deformation field obtained from the regression Kriging model, represents the global trend component of the cabin deformation field, Corresponding to the finite element mesh node Q j The residual error of the solution relative to the global trend component; In the standard regression kriging model, the global trend component is usually determined by linear regression; by replacing the global trend component of the cabin deformation field with the finite element solution result, the finite measurement point Q i The residual deviation ε of the deformation vector at FEM (Q i ): ε FEM (Q i )=D M (Q i )-D FEM (Q i ) (7) For the finite element mesh node Q j The residual deviation at is interpolated by the Kriging method to obtain the deformation field of all the characteristics of the cabin; Among them, γ i is assigned to the known sampling measurement point Q i Weight coefficient of residual deviation of deformation finite element solution result; Finally, the weight coefficient γ is determined by satisfying the conditions of unbiasedness and minimization of estimated variance. i , determine the regression kriging model based on the finite element solution trend results and the actual measurement results of a limited number of points, and incorporate a limited number of actual measurement points into the deformation field trend results obtained from the finite element solution; this method improves the accuracy of the deformation field solution without increasing the complexity or calculation time of the finite element analysis.

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