A layered superimposed reconstruction modeling method suitable for grinding and shot blasting surface

Abstract

The application discloses a layered superimposed reconstruction modeling method suitable for grinding and shot blasting surfaces, and comprises the following steps: S1, measuring height matrix data of a grinding and shot blasting surface to be superimposed and height matrix data of a grinding surface; S2, using the measured grinding and shot blasting surface data and grinding surface data, and based on a BP neural network, a mapping model of a measured grinding surface main texture and a shot blasting texture depth distribution surface is built; S3, based on the built BP neural network mapping model, using any measured grinding surface to obtain the shot blasting texture depth distribution surface; S4, using the measured grinding and shot blasting surface and the shot blasting texture depth distribution surface, and using a linear interpolation, B-spline surface fitting and time-frequency iteration method, the grinding and shot blasting surface is reconstructed. The method can ensure the stability of height parameters, volume parameters, space parameters, shape parameters, function parameters and composite parameters and the like on the superimposed surface, and greatly reduces experimental cost and time.

Description

Technical Field

[0001] This invention relates to the field of technology, and in particular to a layered superposition reconstruction modeling method applicable to grinding and shot peening surfaces. Background Technology

[0002] Shot peening is a high-performance precision manufacturing process widely used in surface strengthening of critical components such as gears. To study the service performance of such surfaces using digital methods, it is necessary to delve into the characteristics of their surface morphology. Surface morphology typically characterizes the microscopic geometric features of a surface, and its importance in modern manufacturing is increasingly prominent. Rough surface morphology has a significant impact on various service properties of the surface, including friction, wear, lubrication, contact, fatigue resistance, and even corrosion resistance. In practical engineering, we often encounter surface morphologies with multi-layered characteristics, such as worn surfaces and shot-peened surfaces. How to achieve numerical simulation of these layered terrain features is a crucial fundamental research area in the era of intelligent manufacturing. Summary of the Invention

[0003] This invention aims to solve at least one of the technical problems existing in the prior art. To this end, this invention proposes a layered superposition reconstruction modeling method suitable for grinding and shot peening surfaces, which can ensure the stability of parameters such as height, volume, space, morphology, function, and composite parameters on the superimposed surface, and significantly reduce experimental costs and time.

[0004] A layered overlay reconstruction modeling method for grinding and shot peening surfaces according to an embodiment of the present invention includes the following steps:

[0005] S1: Measure the height matrix data of the grinding and shot peening surface to be superimposed and the height matrix data of the grinding surface;

[0006] S2: Using the measured grinding and shot peening surface data and grinding surface data, a mapping model between the measured main texture of the grinding surface and the surface with varying depths of the shot peening texture is built based on a BP neural network.

[0007] S3: Based on the established BP neural network mapping model, use any measured grinding surface to obtain the surface with varying depths of shot peening texture.

[0008] S4: Using measured grinding and shot peening surfaces and the surface with varying depths of shot peening textures, linear interpolation, B-spline surface fitting, and time-frequency iteration methods are employed to reconstruct the grinding and shot peening surface.

[0009] The layered superposition reconstruction modeling method for grinding and shot peening surfaces according to embodiments of the present invention has at least the following beneficial effects:

[0010] This method takes into account the influence of the main texture of the grinding surface on the distribution of shot peening depth, thereby improving the fitting accuracy. This method can reconstruct a large number of high-precision grinding and shot peening surfaces based on a small amount of grinding surface data and shot peening surface data, and can ensure the stability of 26 three-dimensional roughness parameters, including height parameters, volume parameters, spatial parameters, morphological parameters, functional parameters and composite parameters, on the reconstructed grinding and shot peening surface.

[0011] According to some embodiments of the present invention, the measured data includes the mean μ and the root mean square height S. q skewness S sk and peak state S ku The calculation formula is as follows:

[0012] ;

[0013] ;

[0014] ;

[0015] in, z ( x , y ) represents the height matrix scatter points within the defined region, where A is the defined region.

[0016] According to some embodiments of the present invention, in step S1, during measurement, the grinding surface data of the workpiece is measured first, and the grinding and shot peening surface data is measured again after the workpiece has completed the shot peening process; the measured grinding and shot peening surface data and the grinding surface data must originate from the same location on the workpiece.

[0017] According to some embodiments of the present invention, step S2 includes the following process:

[0018] (1) The measured grinding surface Z1 and the measured grinding and shot peening surface Z2 were standardized so that their mean μ was 0 and their standard deviation was 1.

[0019] (2) Using the height matrix data of the standardized measured grinding surface Z1 and the measured shot peening surface Z2, the approximate texture S of the shot peening depth distribution is constructed, and its calculation formula is: The matrices Z1 and Z2 have the same size.

[0020] (3) Use linear interpolation to remove the grinding texture on surface S and surface Z1, and then perform B-spline surface fitting on surface S and surface Z1 after linear interpolation to obtain the main texture of surface S and surface Z1.

[0021] (4) Based on the BP neural network, a mapping model is constructed with the texture of surface Z1 as input and the texture of surface S as output.

[0022] According to some embodiments of the present invention, the mapping relationship between surface S and surface Z1 is constructed as follows:

[0023] Let a(x,y) be any point on the texture of surface Z1. Then take a point b(x,y) at the same position on the texture of surface S. Next, take the 24 points that are closest to point a. Use these 24 points and point a as the input of the neural network and point b as the output of the neural network to construct a dataset. This process requires traversing all scattered points in the main texture of surface Z1 except for the matrix edges.

[0024] According to some embodiments of the present invention, step S3 includes the following process:

[0025] (1) For any measured grinding surface Z M Linear interpolation and B-spline surface fitting are performed to obtain the surface Z. M The main texture;

[0026] (2) Calculate the predicted shot peening depth distribution texture based on the mapping model in step S2;

[0027] (3) Perform inverse linear interpolation on the predicted shot peening depth distribution texture to obtain surface K.

[0028] According to some embodiments of the present invention, in step S4, the measured shot-peened surface Z is input. P (μ1, S) q1 S sk1 S ku1 ), measured grinding surface Z M (μ2, S) q2 S sk2 S ku2 ) and given grinding and shot peening surface height distribution parameters (μ3, S) q3 S sk3 S ku3 Step S4 includes the following process:

[0029] (1) For shot-peened surfaces Z P and grinding surface Z M Standardize;

[0030] (2) The standardized grinding surface Z M Linear interpolation and B-spline surface fitting are performed to obtain the surface Z. M Main texture Z N ;

[0031] (3) Z N Z P The height matrices are directly added arithmetically to obtain the shot-peened surface Z with the main texture of the ground surface.NP Then, surface Z NP Subtracting the curved surface K yields the shot-peening surface Z, which has a more precise distribution of shot embedding depth and the main texture of the ground surface. NPK ;

[0032] (4) For surface Z M Z NPK The process involves overlaying layers to re-impose fine textures onto the surface; the shot-peened surface is the upper surface, and the grinding surface is the lower surface, thus obtaining the grinding-peened surface Z. MP ;

[0033] (5) Based on the given height distribution parameters (S) of the grinding and shot peening surface sk3 S ku3 ) for Z MP Perform time-frequency iteration, then adjust its μ3 and S q3 The final grinding and shot peening surface Z is obtained. MP .

[0034] According to some embodiments of the present invention, for shot-peened surfaces Z P The calculation formula for standardization is:

[0035] ;

[0036] Wherein, the coefficient k=S q1 / S q2 std2(Z) P ) represents Z P Standard deviation; adjusted S q1 =k;

[0037] For the Z-shaped grinding surface M The standardization process is as follows: set μ2=0, Z M The standard deviation is 1.

[0038] According to some embodiments of the present invention, for Z MP The formula for time-frequency iteration is:

[0039] ;

[0040] in, ifft 2() represents the two-dimensional inverse Fourier transform. fft 2() represents the two-dimensional positive Fourier transform, and the operations between matrices are all dot multiplication and dot division;

[0041] The specific process of the time-frequency iterative method is as follows: First, the Johnson transformation method is used to generate a value with respect to the specified height distribution parameters and Z. MP Given a Gaussian sequence z of the same size, adjust the distribution of each elevation point in z to match that of Z. MPConsistent, and using Fourier transform, Z in the frequency domain MP The amplitude frequency of z is multiplied by the phase frequency of z after adjusting the height distribution, and then an inverse Fourier transform is performed to obtain the new Z. MP1 The newly obtained sequence Z MP1 The height distribution will be closer to z than before, and the autocorrelation function will not change; repeat this process to improve accuracy.

[0042] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0043] The present invention will be further described below with reference to the accompanying drawings and embodiments, wherein:

[0044] Figure 1 Flowchart for modeling layered overlays of grinding and shot peening surfaces;

[0045] Figure 2 Flowchart for constructing a surface mapping model of the depth distribution of the main texture and shot peening texture on the measured grinding surface;

[0046] Figure 3 This is a flowchart for obtaining the surface texture depth distribution based on a neural network;

[0047] Figure 4 Comparison of linear interpolation and B-spline surface fitting before and after;

[0048] Figure 5 The surface with varying depths of shot peening texture output from a neural network mapping model;

[0049] Figure 6 The microstructure of the reconstructed grinding and shot peening surface;

[0050] Figure 7 Symmetric autocorrelation function plot for reconstructing the microstructure of the surface after shot peening. Detailed Implementation

[0051] Embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0052] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, etc., are based on the orientation or positional relationship shown in the drawings and are only for the convenience of describing this invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0053] In the description of this invention, "multiple" refers to two or more. The use of "first" and "second" is for distinguishing technical features only and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or the order in which the indicated technical features are presented.

[0054] In the description of this invention, unless otherwise explicitly defined, terms such as "setting," "installing," and "connecting" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0055] Reference Figures 1 to 7 A layered superposition reconstruction modeling method for grinding and shot peening surfaces according to an embodiment of the present invention includes the following steps:

[0056] S1: Measure the height matrix data of the grinding and shot peening surface to be superimposed and the height matrix data of the grinding surface; specifically, the data to be measured includes the mean μ and the root mean square height S. q skewness S sk and peak state S ku The above data were obtained by measuring equipment such as a white light interferometer.

[0057] Furthermore, the height S q skewness S sk and peak state S ku The calculation formula is:

[0058] ;

[0059] ;

[0060] ;

[0061] By comparing and analyzing the calculated values ​​with the measured values, the difference is obtained. Then, the time-frequency iteration method is used to control the data difference between the calculated values ​​and the measured values ​​within a small range.

[0062] S2: Using the measured grinding and shot peening surface data and the grinding surface data, a mapping model between the measured main texture of the grinding surface and the surface with varying depths of the shot peening texture is built based on a BP neural network; specifically, the entire process of step S2 is as follows: Figure 2As shown, the process includes the following:

[0063] (1) The measured grinding surface Z1 and the measured grinding and shot peening surface Z2 were standardized so that the mean μ of both was 0 and the standard deviation was 1.

[0064] (2) Using the height matrix data of the standardized measured grinding surface Z1 and the measured shot peening surface Z2, the approximate texture S of the shot peening depth distribution is constructed, and its calculation formula is:

[0065] ;

[0066] In the formula, the matrix sizes of Z1 and Z2 need to be consistent, and their specific positions on the workpiece also need to be consistent. That is, the difference between the two surfaces is only one shot peening process. During measurement, the grinding surface data of the workpiece is measured first, and the grinding and shot peening surface data is measured again after the workpiece has completed the shot peening process. The measured grinding and shot peening surface data and the grinding surface data come from the same position on the workpiece.

[0067] (3) The grinding texture on surfaces S and Z1 is removed by linear interpolation. Then, B-spline surface fitting is performed on the linearly interpolated surfaces S and Z1 to obtain the main textures of surfaces S and Z1. Specifically, the interpolation interval can be set to an appropriate value according to the actual situation during the linear interpolation process. For example, in this application, the interpolation interval is set to 5, that is, the length and width of the original height matrix are reduced by 5 times, but the height matrix interval is increased by 5 times. Then, B-spline surface fitting is performed on the interpolated surfaces S and Z1 to further filter out the fine textures on the surfaces and finally retain the main textures of the two surfaces.

[0068] (4) Based on a backpropagation neural network, a mapping model is constructed using the texture of surface Z1 as input and the texture of surface S as output. Specifically, the mapping relationship between surface S and surface Z1 is constructed as follows:

[0069] Let's take any point a(x,y) on the texture of surface Z1. Then, at the same position on the texture of surface S, we also need to take a point b(x,y). Next, we take the 24 points closest to point a. These 24 points, along with point a, are used as the input to a neural network, and point b is used as the output of the neural network, constructing a dataset. This process requires traversing all scattered points in the main texture of surface Z1 except for the matrix edges. That is, for any point taken at any position on the main texture of surface S, there exists a corresponding 5*5 height matrix at the same position on surface Z1.

[0070] Figure 4 The image shows a comparison of surface S before and after linear interpolation and B-spline surface fitting in step S2.

[0071] S3: Based on the constructed BP neural network mapping model, obtain the surface texture depth distribution using any measured grinding surface; specifically, the entire process of step S3 is as follows: Figure 3 As shown. Based on the above mapping model, the process of obtaining the surface depth distribution of shot peening texture through any measured grinding surface is as follows:

[0072] (1) For any measured grinding surface Z M Perform the same linear interpolation and B-spline surface fitting as described above to obtain surface Z. M The main texture; the interpolation interval here is also set to 5, which means that the length and width of the original height matrix are reduced by a factor of 5, but the height matrix interval is increased by a factor of 5.

[0073] (2) Based on the principle of constructing neural network mapping relationship in the above process, the surface Z is... M The main texture is split into multiple 5*5 height matrices. All 5*5 matrices are used as input to the neural network to obtain the predicted scatter values. By piecing together all the predicted scatter values, the predicted shot peening depth distribution texture can be restored.

[0074] (3) Next, linear interpolation and B-spline surface fitting are performed on the restored distribution texture in sequence. The interpolation interval is set to 0.2, that is, the length and width of the original height matrix are increased by 5 times, but the height matrix interval is reduced by 5 times, thus obtaining the surface K.

[0075] The measured grinding surface Z M according to Figure 3 The process is fed into a pre-built neural network model, and the resulting predicted shot peening depth distribution on the surface is as follows: Figure 5 As shown.

[0076] S4: Using measured grinding and shot-peened surfaces and the surface with varying shot-peened texture depths, the grinding and shot-peened surface is reconstructed using linear interpolation, B-spline surface fitting, and time-frequency iteration. Specifically, the measured shot-peened surface Z is first input. P (μ1, S) q1 S sk1 S ku1 ), measured grinding surface Z M (μ2, S) q2 S sk2 S ku2 ) and given grinding and shot peening surface height distribution parameters (μ3, S) q3 S sk3 S ku3 ); Measured Z of shot-peened surface P Data and measured grinding surface Z M The data comes from the same material, but belongs to different workpieces; the shot-peened surface Z... PThe data is from shot peening of the polished surface followed by shot peening, while the Z-shaped surface of the ground surface... M The data was collected after the workpiece surface had been ground.

[0077] Step S4: Refer to the entire process. Figure 1 As shown, the process includes the following:

[0078] (1) For shot-peened surfaces Z P and grinding surface Z M Standardize; for shot-peened surfaces Z P The calculation formula for standardization is:

[0079] ;

[0080] Wherein, the coefficient k=S q1 / S q2 std2(Z) P ) represents Z P Standard deviation; adjusted S q1 =k;

[0081] For the Z-shaped grinding surface M The standardization process is as follows: set μ2=0, Z M The standard deviation is 1;

[0082] (2) The standardized grinding surface Z M Linear interpolation and B-spline surface fitting are performed to obtain the surface Z. M Main texture Z N The interpolation interval here is also set to 5.

[0083] (3) Z N Z P The height matrices are directly added arithmetically to obtain the shot-peened surface Z with the main texture of the ground surface. NP Then, surface Z NP Subtracting the curved surface K yields the shot-peening surface Z, which has a more precise distribution of shot embedding depth and the main texture of the ground surface. NPK ;

[0084] (4) For surface Z M Z NPK The process involves overlaying layers to re-impose fine textures onto the surface; the shot-peened surface is the upper surface, and the grinding surface is the lower surface, thus obtaining the grinding-peened surface Z. MP ;

[0085] It is important to understand that here, the Z-surface... M Z NPKThe superposition was performed using the method mentioned by Pawel Pawlus in the paper "Simulation of stratified surface topographies".

[0086] (5) Based on the given height distribution parameters (S) of the grinding and shot peening surface sk3 S ku3 ) for Z MP Perform time-frequency iteration, then adjust its μ3 and S q3 The final grinding and shot peening surface Z is obtained. MP The reconstructed grinding and shot peening surface is as follows: Figure 6 As shown, the corresponding symmetric autocorrelation function is as follows: Figure 7 As shown. For surface Z MP Performing time-frequency iterations can improve fitting accuracy.

[0087] In some embodiments of the present invention, Z MP The formula for time-frequency iteration is:

[0088]

[0089] in, ifft 2() represents the two-dimensional inverse Fourier transform. fft 2() represents the two-dimensional positive Fourier transform, and the operations between matrices are all dot multiplication and dot division;

[0090] The specific process of the time-frequency iteration method is as follows:

[0091] First, we need to use the Johnson transformation method to generate a Z-axis with specified height distribution parameters. MP Given a Gaussian sequence z of the same size, adjust the distribution of each elevation point in z to match that of Z. MP Consistent, and using Fourier transform to transform Z in the frequency domain MP The amplitude frequency of z is multiplied by the phase frequency of z after adjusting the height distribution, and then an inverse Fourier transform is performed to obtain the new Z. MP1 The newly obtained sequence Z MP1 The height distribution will be closer to z than before, and the autocorrelation function will not change; repeating the above process several times will yield higher accuracy. (Refer to...) Figure 4 As shown in the table, the reconstruction accuracy is high, with the error generally kept within 10%. Only parameter S... dr The error is 18.8%.

[0092] This method considers the influence of the main texture of the grinding surface on the depth distribution of shot peening, thereby improving the fitting accuracy. This method can reconstruct a large number of high-precision grinding and shot-peened surfaces based on a small amount of grinding surface data and shot-peened surface data, and can guarantee the reconstruction of 26 three-dimensional roughness parameters (refer to...) on the grinding and shot-peened surface, including height parameters, volume parameters, spatial parameters, morphological parameters, functional parameters, and composite parameters. Figure 4 The stability of the table.

[0093] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A layered superposition reconstruction modeling method suitable for grinding and shot peening surfaces, characterized in that, Includes the following steps: S1: Measure the height matrix data of the grinding and shot peening surface to be superimposed and the height matrix data of the grinding surface; S2: Using the measured grinding and shot peening surface data and grinding surface data, a mapping model between the measured main texture of the grinding surface and the surface with varying depths of the shot peening texture is built based on a BP neural network. S3: Based on the constructed BP neural network mapping model, input any measured grinding surface to obtain the surface with varying depths of shot peening texture; S4: Using the measured grinding and shot peening surfaces and the predicted surface with varying shot peening texture depths, the grinding and shot peening surfaces are reconstructed using linear interpolation, B-spline surface fitting, and time-frequency iteration. The measured data includes the mean μ, and step S2 includes the following process: (1) The measured grinding surface Z1 and the measured grinding and shot peening surface Z2 were standardized so that their mean μ was 0 and their standard deviation was 1. (2) Using the height matrix data of the standardized measured grinding surface Z1 and the measured shot peening surface Z2, the approximate texture S of the shot peening depth distribution is constructed, and its calculation formula is: The matrices Z1 and Z2 have the same size. (3) Use linear interpolation to remove the grinding texture on surface S and surface Z1, and then perform B-spline surface fitting on surface S and surface Z1 after linear interpolation to obtain the main texture of surface S and surface Z1. (4) Based on the BP neural network, a mapping model is constructed with the texture of surface Z1 as input and the texture of surface S as output. The mapping relationship between surface S and surface Z1 is constructed as follows: Take any point a(x,y) on the texture of surface Z1, and also take a point b(x,y) at the same position on the texture of surface S. Then take the 24 points that are closest to point a. Use these 24 points and point a as the input of the neural network, and point b as the output of the neural network to construct a dataset. This process requires traversing all scattered points in the main texture of surface Z1 except for the matrix edges.

2. The layered superposition reconstruction modeling method for grinding and shot peening surfaces according to claim 1, characterized in that: The measured data also includes the root mean square height S q skewness S sk and peak state S ku The calculation formula is as follows: ； ； ； in, z ( x , y ) represents the height matrix scatter points within the defined region, where A is the defined region.

3. The layered superposition reconstruction modeling method for grinding and shot peening surfaces according to claim 2, characterized in that: In step S1, during measurement, the grinding surface data of the workpiece is measured first, and the grinding and shot peening surface data is measured again after the workpiece has completed the shot peening process; the measured grinding and shot peening surface data and the grinding surface data must come from the same location on the workpiece.

4. The layered superposition reconstruction modeling method for grinding and shot peening surfaces according to claim 2, characterized in that: Step S3 includes the following process: (1) For any measured grinding surface Z M Linear interpolation and B-spline surface fitting are performed to obtain the surface Z. M The main texture; (2) Calculate the predicted shot peening depth distribution texture based on the mapping model in step S2; (3) Perform inverse linear interpolation on the predicted shot peening depth distribution texture to obtain surface K.

5. The layered superposition reconstruction modeling method for grinding and shot peening surfaces according to claim 4, characterized in that: In step S4, input the measured Z of the shot-peened surface. P (μ1, S) q1 S sk1 S ku1 ), measured grinding surface Z M (μ2, S) q2 S sk2 S ku2 ) and given grinding and shot peening surface height distribution parameters (μ3, S) q3 S sk3 S ku3 ); Step S4 includes the following process: (1) For shot-peened surfaces Z P and grinding surface Z M Standardize; (2) The standardized grinding surface Z M Linear interpolation and B-spline surface fitting are performed to obtain the surface Z. M Main texture Z N ; (3) Z N Z P The height matrices are directly added arithmetically to obtain the shot-peened surface Z with the main texture of the ground surface. NP Then, surface Z NP Subtracting the curved surface K yields the shot-peening surface Z, which includes the shot embedding depth distribution and the main texture of the ground surface. NPK ; (4) For surface Z M Z NPK The process involves overlaying layers to re-impose fine textures onto the surface; the shot-peened surface is the upper surface, and the grinding surface is the lower surface, thus obtaining the grinding-peened surface Z. MP ; (5) Based on the given height distribution parameters (S) of the grinding and shot peening surface sk3 S ku3 ) for Z MP Perform time-frequency iteration, then adjust its μ3 and S q3 The final grinding and shot peening surface Z is obtained. MP .

6. The layered superposition reconstruction modeling method for grinding and shot peening surfaces according to claim 4, characterized in that: Z-shaped surface of shot peening P The calculation formula for standardization is: ； Wherein, the coefficient k=S q1 / S q2 std2(Z) P ) represents Z P Standard deviation; For the Z-shaped grinding surface M The standardization process is as follows: set μ2=0, Z M The standard deviation is 1.

7. The layered superposition reconstruction modeling method for grinding and shot peening surfaces according to claim 4, characterized in that: For Z MP The formula for time-frequency iteration is: ； in, ifft 2() represents the two-dimensional inverse Fourier transform. fft 2() represents the two-dimensional Fourier forward transform; The specific process of the time-frequency iterative method is as follows: First, the Johnson transformation method is used to generate a value with respect to the specified height distribution parameters and Z. MP Given a Gaussian sequence z of the same size, adjust the distribution of each elevation point in z to match that of Z. MP Consistent, and using Fourier transform, Z in the frequency domain MP The amplitude frequency of z is multiplied by the phase frequency of z after adjusting the height distribution, and then an inverse Fourier transform is performed to obtain the new Z. MP1 The newly obtained sequence Z MP1 The height distribution will be closer to z than before, and the autocorrelation function will not change; repeat this process to improve accuracy.

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