Surface morphology reconstruction method and system integrating machine learning and spatial frequency analysis

Abstract

The present invention provides a surface morphology reconstruction method and system integrating machine learning and spatial frequency analysis, including: step 1: using the analytical formula of the spatial frequency method to generate a large number of two-dimensional arrays representing rough surfaces; step 2: by analyzing the height distribution and frequency energy proportion of the generated surface, combined with the machine learning method, extracting the characteristic variables of the analytical formula; step 3: combining the test or simulation method to establish the relationship between the characteristic parameters and the surface performance, which is used for performance prediction and surface reconstruction in specific scenarios. The present invention can realize the surface morphology feature extraction based on the spatial frequency analysis method, reconstruct the rough surface suitable for current carrying performance prediction, and thus improve the practical significance of the surface reconstruction method in performance prediction.

Description

Technical Field

[0001] The present invention relates to the technical field of surface morphology reconstruction, and in particular to a surface morphology reconstruction method and system integrating machine learning and spatial frequency analysis. Background Art

[0002] The contact surface morphology directly affects the physical and chemical properties of the material, which in turn affects the macroscopic performance of the machine or system. At the macroscopic scale, surface morphology reconstruction is of great significance for understanding tribological properties, wettability, and catalytic activity; at the microscopic scale, surface morphology reconstruction also plays a key role in the functionality and stability of nanodevices. In addition, understanding and controlling the surface reconstruction process helps to optimize the manufacturing and processing of materials and improve their performance in high-performance applications.

[0003] Surface morphology reconstruction is usually divided into reconstruction based on statistical methods and reconstruction based on analytical formulas. Among them, reconstruction based on statistical methods uses statistical quantities (such as surface roughness, peak and trough distribution, etc.) to describe and generate surface morphology, while reconstruction based on analytical formulas relies on specific mathematical models and formulas to simulate changes in surface morphology. However, the reconstruction method based on statistical methods lacks a physical explanation for the formation mechanism of surface morphology and cannot effectively identify the micro-features of the surface morphology, especially the curvature characteristics of micro-asperities. This results in the reconstructed surface being of low accuracy when predicting properties that are sensitive to the curvature of micro-asperities, such as current-carrying performance.

[0004] At present, the spatial frequency analysis method has proposed a new idea for the spatial reconstruction of rough surfaces. By adjusting the proportion of high-frequency and low-frequency components and the amplitude factor of the overall fluctuation in the spatial frequency method, the rough surface reconstruction under different spatial frequency characteristic parameters can be achieved. However, due to the addition of random variables, it is difficult to extract characteristic parameters from the actual rough surface, which restricts the application of the spatial frequency analysis method.

[0005] Patent document CN106021661A discloses a surface analysis, simulation and reconstruction system, which solves the problems of surface analysis, simulation and reconstruction; the surface analysis module is composed of five submodules, namely surface input, multi-scale surface analysis, roughness surface analysis, data display and data output, which can independently realize the analysis function of the user-specified surface; the surface simulation module is composed of six submodules, namely surface parameter and function input, roughness surface simulation, roughness surface error analysis, multi-scale surface simulation, multi-scale surface error analysis and data output, which can independently realize the simulation function of the user-specified surface; the surface analysis and surface simulation modules are used together to realize the reconstruction function of the user-specified surface. However, this patent cannot completely solve the existing technical problems, nor can it meet the requirements of the present invention. Summary of the invention

[0006] In view of the defects in the prior art, the object of the present invention is to provide a surface morphology reconstruction method and system integrating machine learning and spatial frequency analysis.

[0007] The surface morphology reconstruction method integrating machine learning and spatial frequency analysis provided by the present invention comprises:

[0008] Step 1: Use the analytical formula of the spatial frequency method to generate a large number of two-dimensional arrays representing the rough surface;

[0009] Step 2: By analyzing the height distribution and frequency energy ratio of the generated surface and combining machine learning methods, the characteristic variables of the analytical formula are extracted;

[0010] Step 3: Combine experimental or simulation methods to establish the relationship between characteristic parameters and surface performance for performance prediction and surface reconstruction in specific scenarios.

[0011] Preferably, the step 1 comprises:

[0012] According to the basic formula of the spatial frequency method, the cutoff frequency N, spectral index b, and gain factor A of the spatial frequency are determined, and its two-dimensional function is;

[0013]

[0014] Among them, g(m,n) is a normal distribution function with a mean of 0 and a standard deviation of 1; u(x,y) is a uniform distribution function on [0, 2π]; x,y represent the x and y coordinates of any point on the rough surface; m,n represent the x and y spatial frequency values ​​superimposed at any point on the rough surface, which are m and n respectively; β represents the attenuation factor of the amplitude with frequency in the spectrum diagram;

[0015] Arbitrarily set the three characteristic parameters N, b, and A to generate surface topography, including two-dimensional grayscale images and three-dimensional topography images;

[0016] In the set range of surface morphology, a characteristic parameter combination of [N0, b0, A0] is randomly generated, and a two-dimensional array of the rough surface is generated accordingly.

[0017] Preferably, the step 2 comprises:

[0018] For the generated two-dimensional array, extract its height distribution map;

[0019] Extract the full width corresponding to the 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, and 5% height lines in the height distribution graph to form the first one-dimensional array of (1,19);

[0020] Using the two-dimensional Fourier transform method, the two-dimensional spectrum corresponding to the two-dimensional array of the rough surface is drawn. For a two-dimensional function f(x, y), its two-dimensional Fourier transform F(u, v) is:

[0021]

[0022] Among them, (x, y) is the coordinate in the spatial domain; (u, v) is the coordinate in the frequency domain; e -i2π(ux+vy) is the transformation kernel, which represents the complex form of rotation;

[0023] Taking the origin (0, 0) in the two-dimensional spectrum as the center, extract the radii corresponding to energy proportions of 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, and 5% to form a second one-dimensional array of (1,19);

[0024] The energy proportion and the corresponding radius are combined into (x, y), a continuous curve is fitted using a spline curve, and the radius change rate at the corresponding position is extracted to form a third one-dimensional array of (1, 19);

[0025] Combine the three one-dimensional arrays into a one-dimensional array arrays, and get each one-dimensional array arrays and its corresponding [N, b, A] array;

[0026] The model is trained using a regression method. The model input is a one-dimensional array of shape (1, 57), corresponding to the height and spectral characteristics of the surface morphology; the model output is a one-dimensional array of shape (1, 3), corresponding to the spatial frequency characteristic parameters of the surface.

[0027] Preferably, the square logarithmic error is used as the loss function of the model; the number of decision trees in the model is 500, and the maximum depth of each tree is 10; the learning rate of the model is 0.05.

[0028] Preferably, the static contact resistance is measured in combination with the electrical contact interface structure, material, and contact form characteristics that need to be predicted, and the surface morphology of the contact point is obtained using a white light interferometer and a three-dimensional profilometer, which is saved in the form of a 200*200 two-dimensional array, and the formed data pair is (static contact resistance, spatial frequency characteristic parameters of the rough surface);

[0029] The trained model is used to extract the characteristic parameters (N, b, A) of the real rough surface, and the machine learning regression method is used again to train the association model between these three characteristic parameters and the static contact resistance. The input of the association model is the spatial frequency characteristic parameters of the rough surface, and the output is the static contact resistance of the interface.

[0030] The surface morphology reconstruction system integrating machine learning and spatial frequency analysis provided by the present invention comprises:

[0031] Module M1: Generate a large number of two-dimensional arrays representing rough surfaces using the analytical formula of the spatial frequency method;

[0032] Module M2: By analyzing the height distribution and frequency energy ratio of the generated surface and combining machine learning methods, the characteristic variables of the analytical formula are extracted;

[0033] Module M3: Combine experimental or simulation methods to establish the relationship between characteristic parameters and surface performance for performance prediction and surface reconstruction in specific scenarios.

[0034] Preferably, the module M1 comprises:

[0035] According to the basic formula of the spatial frequency method, the cutoff frequency N, spectral index b, and gain factor A of the spatial frequency are determined, and its two-dimensional function is;

[0036]

[0037] Among them, g(m,n) is a normal distribution function with a mean of 0 and a standard deviation of 1; u(x,y) is a uniform distribution function on [0, 2π]; x,y represent the x and y coordinates of any point on the rough surface; m,n represent the x and y spatial frequency values ​​superimposed at any point on the rough surface, which are m and n respectively; β represents the attenuation factor of the amplitude with frequency in the spectrum diagram;

[0038] Arbitrarily set the three characteristic parameters N, b, and A to generate surface topography, including two-dimensional grayscale images and three-dimensional topography images;

[0039] In the set range of surface morphology, a characteristic parameter combination of [N0, b0, A0] is randomly generated, and a two-dimensional array of the rough surface is generated accordingly.

[0040] Preferably, the module M2 comprises:

[0041] For the generated two-dimensional array, extract its height distribution map;

[0042] Extract the full width corresponding to the 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, and 5% height lines in the height distribution graph to form the first one-dimensional array of (1,19);

[0043] Using the two-dimensional Fourier transform method, the two-dimensional spectrum corresponding to the two-dimensional array of the rough surface is drawn. For a two-dimensional function f(x, y), its two-dimensional Fourier transform F(u, v) is:

[0044]

[0045] Among them, (x, y) is the coordinate in the spatial domain; (u, v) is the coordinate in the frequency domain; e -i2π(ux+vy) is the transformation kernel, which represents the complex form of rotation;

[0046] Taking the origin (0, 0) in the two-dimensional spectrum as the center, extract the radii corresponding to energy proportions of 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, and 5% to form a second one-dimensional array of (1,19);

[0047] The energy proportion and the corresponding radius are combined into (x, y), a continuous curve is fitted using a spline curve, and the radius change rate at the corresponding position is extracted to form a third one-dimensional array of (1, 19);

[0048] Combine the three one-dimensional arrays into a one-dimensional array arrays, and get each one-dimensional array arrays and its corresponding [N, b, A] array;

[0049] The model is trained using a regression method. The model input is a one-dimensional array of shape (1, 57), corresponding to the height and spectral characteristics of the surface morphology; the model output is a one-dimensional array of shape (1, 3), corresponding to the spatial frequency characteristic parameters of the surface.

[0050] Preferably, the square logarithmic error is used as the loss function of the model; the number of decision trees in the model is 500, and the maximum depth of each tree is 10; the learning rate of the model is 0.05.

[0051] Preferably, the static contact resistance is measured in combination with the electrical contact interface structure, material, and contact form characteristics that need to be predicted, and the surface morphology of the contact point is obtained using a white light interferometer and a three-dimensional profilometer, which is saved in the form of a 200*200 two-dimensional array, and the formed data pair is (static contact resistance, spatial frequency characteristic parameters of the rough surface);

[0052] The trained model is used to extract the characteristic parameters (N, b, A) of the real rough surface, and the machine learning regression method is used again to train the association model between these three characteristic parameters and the static contact resistance. The input of the association model is the spatial frequency characteristic parameters of the rough surface, and the output is the static contact resistance of the interface.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] (1) The present invention mainly solves the problem that the current surface reconstruction method based on statistical methods (such as roughness, kurtosis, and skewness) cannot accurately predict the service performance (mainly including current carrying performance, wetting performance, optical properties, and friction and wear performance) of electrical connectors, conductive slip rings, solar panels, transmission friction pairs, etc.; the present invention can extract the spatial frequency characteristic parameters of any actual rough surface, reconstruct a similar surface and use it for current carrying performance prediction, which greatly improves the reconstruction accuracy of the rough surface and enriches the physical connotation of the characteristic parameters; at the same time, the proposed surface reconstruction method is used to support the generation and analysis of wear morphology of the friction and wear test system, solving the problem of in-situ testing of wear morphology;

[0055] (2) The present invention provides a surface morphology reconstruction method based on the fusion of machine learning and spatial frequency analysis, which is mainly used to extract features and reconstruct morphology of rough surfaces, and improve the prediction ability of the reconstructed surface for current carrying, wetting, optics, friction and wear properties. The purpose of the present invention is to establish a mathematical connection between surface morphology and performance, and then realize the mapping of surface feature analysis to macroscopic current carrying performance, so as to solve the problem of low accuracy caused by the current use of statistical characteristics of the surface to predict its current carrying, wetting, optical and other properties;

[0056] (3) The present invention can realize the surface morphology feature extraction based on the spatial frequency analysis method, reconstruct a rough surface suitable for current-carrying performance prediction, and thus improve the practical significance of the surface reconstruction method in performance prediction; it can perform fast and accurate feature extraction on any actual surface, thereby improving the integration of the tool. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0058] Figure 1 The workflow diagram for surface topography reconstruction based on the fusion of machine learning and spatial frequency analysis;

[0059] Figure 2a and Figure 2b They are grayscale and three-dimensional images of the two-dimensional spectrum of the surface reconstructed based on the spatial frequency method;

[0060] Figure 3 is the height distribution map of random rough surface;

[0061] Figure 4a and Figure 4b They are the grayscale image and three-dimensional image of the two-dimensional spectrum of the rough surface. DETAILED DESCRIPTION

[0062] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0063] Example 1

[0064] The present invention provides a surface morphology reconstruction method that integrates machine learning and spatial frequency analysis. First, the analytical formula of the spatial frequency method is used to generate a large number of two-dimensional arrays that symbolize rough surfaces. The characteristic variables of the analytical formula are extracted by analyzing the height distribution and frequency energy ratio of the generated surface in combination with the machine learning method. Finally, the relationship between the characteristic parameters and the surface performance is established in combination with the experimental or simulation method, which is used for performance prediction and surface reconstruction in specific scenarios.

[0065] like Figure 1 , specifically including the following steps:

[0066] S1, according to the basic formula of spatial frequency method, determine the three characteristic parameters of spatial frequency: cutoff frequency N, spectrum index (frequency energy attenuation index) b, and gain factor A;

[0067]

[0068] Among them, g(m,n) is a normal distribution function with a mean of 0 and a standard deviation of 1; u(x,y) is a uniform distribution function on [0, 2π];

[0069] x, y represent the x and y coordinates of any point on the rough surface; m, n represent the x and y spatial frequency values ​​superimposed at any point on the rough surface, which are m and n respectively; β represents the attenuation factor of the amplitude with frequency in the spectrum diagram;

[0070] S2, arbitrarily set the three characteristic parameters N, b, and A, and use the formula in S1 to generate the surface morphology (including two-dimensional grayscale image and three-dimensional morphology image, taking N=5, b=1, A=0.001 as an example, see Figure 2);

[0071] S3, within the set interval, randomly generates a characteristic parameter combination of [N0, b0, A0] and generates a two-dimensional array of the rough surface accordingly.

[0072] The python code for randomly generating feature parameter combinations is as follows:

[0073] N_range=(1,25) # the range of N

[0074] A_range=(0.001,0.010) #the range of A

[0075] b_range=(0.5,2.0) #b range

[0076] N0=np.random.randint(N_range[0],N_range[1]+1)

[0077] A0=np.random.uniform(A_range[0],A_range[1])

[0078] b0=np.random.uniform(b_range[0],b_range[1])

[0079] S4, for the generated two-dimensional array, first extract its height distribution map (taking N=5, b=1, A=0.001 as an example);

[0080] S5, according to Figure 3 , extract the full width corresponding to the 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, and 5% height lines in the height distribution graph to form a one-dimensional array (arrays_1) of (1,19);

[0081] S6, the basic idea of ​​2D Fourier transform is to decompose a complex 2D signal into multiple simple waveforms (sine waves and cosine waves) of different frequencies and directions. The superposition of these waveforms can completely reconstruct the original signal. In image processing, this means that the image can be decomposed into its constituent frequencies. Using the 2D Fourier transform method, the 2D spectrum corresponding to the 2D array of the rough surface is drawn, and its grayscale image and 3D image are shown in Figure 4; for a 2D function f(x, y), its 2D Fourier transform F(u, v) is defined as:

[0082]

[0083] Among them, (x, y) is the coordinate in the spatial domain; (u, v) is the coordinate in the frequency domain; e -i2π(ux+vy) is the transformation kernel, which represents the complex form of rotation.

[0084] S7, according to the drawing result of Figure 4, with the origin (0,0) in the two-dimensional spectrum as the center, extract the radii corresponding to energy proportions of 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, and 5% to form a one-dimensional array (arrays_2) of (1,19);

[0085] S8, the energy proportion and the corresponding radius form (x, y), use the spline curve to fit a continuous curve and extract the radius change rate of the corresponding position (95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, 5%) to form a one-dimensional array (arrays_3) of (1, 19); its python code implementation method is:

[0086]

[0087] S9, combine the three one-dimensional arrays arrays_1, arrays_2, and arrays_3 into a one-dimensional array arrays, so as to obtain each one-dimensional array arrays and its corresponding [N, b, A] array;

[0088] S10, using Xgboost regression method (other machine learning methods with regression function can also be used) to train the model (model 1), the input of model 1 is a one-dimensional array of shape (1, 57), corresponding to the height and spectral characteristics of the surface morphology; the output of model 1 is a one-dimensional array of shape (1, 3), corresponding to the spatial frequency characteristic parameters of the surface, and the reference hyperparameter settings are as follows (adaptive adjustment can be made according to specific problems).

[0089]

[0090] The above settings show that:

[0091] (1) The loss function of the model is the square log error, which is very sensitive to small target values ​​and is suitable for situations where both the predicted value and the actual value are positive and relatively small.

[0092] (2) The number of decision trees in the model is 500. This parameter controls the complexity of the model and the length of the training process. Increasing this value can improve the performance of the model, but it also increases the computational cost and the risk of overfitting;

[0093] (3) The learning rate of the model is 0.05. It determines the contribution of each tree to the final prediction. A smaller learning rate means a smaller update at each step, which usually makes the model training more robust, but at the same time requires more trees to be trained to achieve better performance;

[0094] (4) The maximum depth of each tree is 10. The depth of the tree is an important parameter of model complexity. Deeper trees can learn more complex patterns, but are also prone to overfitting.

[0095] S11, combining the electrical contact interface structure, material, contact form and other characteristics to be predicted, measuring its static contact resistance, and using a white light interferometer, a three-dimensional profilometer, etc. to obtain the surface morphology of the contact point, and saving it in the form of a 200*200 two-dimensional array, the formed data pair is (static contact resistance, spatial frequency characteristic parameters of the rough surface);

[0096] S12, using the model trained in S10 to extract the characteristic parameters (N, b, A) of the real rough surface, and again using the machine learning regression method to train the association model of these three characteristic parameters and the static contact resistance (Model 2), the training process of Model 2 is consistent with that of Model 1. However, it should be noted that the input of Model 2 is the spatial frequency characteristic parameters of the rough surface, and the output is the static contact resistance of the interface;

[0097] S13, combining Model 1 with Model 2 can realize feature extraction, morphology reconstruction and static contact resistance prediction for any rough surface.

[0098] Example 2

[0099] The present invention also provides a surface morphology reconstruction system that integrates machine learning and spatial frequency analysis. The surface morphology reconstruction system that integrates machine learning and spatial frequency analysis can be realized by executing the process steps of the surface morphology reconstruction method that integrates machine learning and spatial frequency analysis. That is, those skilled in the art can understand the surface morphology reconstruction method that integrates machine learning and spatial frequency analysis as a preferred implementation of the surface morphology reconstruction system that integrates machine learning and spatial frequency analysis.

[0100] The surface morphology reconstruction system integrating machine learning and spatial frequency analysis provided by the present invention includes: module M1: using the analytical formula of the spatial frequency method to generate a large number of two-dimensional arrays representing rough surfaces; module M2: by analyzing the height distribution and frequency energy ratio of the generated surface, combined with the machine learning method, the characteristic variables of the analytical formula are extracted; module M3: combining experiments or simulation methods to establish the relationship between characteristic parameters and surface performance, which is used for performance prediction and surface reconstruction in specific scenarios.

[0101] The module M1 comprises:

[0102] According to the basic formula of the spatial frequency method, the cutoff frequency N, spectral index b, and gain factor A of the spatial frequency are determined, and its two-dimensional function is;

[0103]

[0104] Among them, g(m,n) is a normal distribution function with a mean of 0 and a standard deviation of 1; u(x,y) is a uniform distribution function on [0, 2π]; x,y represent the x and y coordinates of any point on the rough surface; m,n represent the x and y spatial frequency values ​​superimposed at any point on the rough surface, which are m and n respectively; β represents the attenuation factor of the amplitude with frequency in the spectrum diagram;

[0105] Arbitrarily set the three characteristic parameters N, b, and A to generate surface topography, including two-dimensional grayscale images and three-dimensional topography images;

[0106] In the set range of surface morphology, a characteristic parameter combination of [N0, b0, A0] is randomly generated, and a two-dimensional array of the rough surface is generated accordingly.

[0107] The module M2 comprises:

[0108] For the generated two-dimensional array, extract its height distribution map;

[0109] Extract the full width corresponding to the 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, and 5% height lines in the height distribution graph to form the first one-dimensional array of (1,19);

[0110] Using the two-dimensional Fourier transform method, the two-dimensional spectrum corresponding to the two-dimensional array of the rough surface is drawn. For a two-dimensional function f(x, y), its two-dimensional Fourier transform F(u, v) is:

[0111]

[0112] Among them, (x, y) is the coordinate in the spatial domain; (u, v) is the coordinate in the frequency domain; e -i2π(ux+vy) is the transformation kernel, which represents the complex form of rotation;

[0113] Taking the origin (0, 0) in the two-dimensional spectrum as the center, extract the radii corresponding to energy proportions of 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, and 5% to form a second one-dimensional array of (1,19);

[0114] The energy proportion and the corresponding radius are combined into (x, y), a continuous curve is fitted using a spline curve, and the radius change rate at the corresponding position is extracted to form a third one-dimensional array of (1, 19);

[0115] Combine the three one-dimensional arrays into a one-dimensional array arrays, and get each one-dimensional array arrays and its corresponding [N, b, A] array;

[0116] The model is trained using a regression method. The model input is a one-dimensional array of shape (1, 57), corresponding to the height and spectral characteristics of the surface morphology; the model output is a one-dimensional array of shape (1, 3), corresponding to the spatial frequency characteristic parameters of the surface.

[0117] The squared logarithmic error is used as the loss function of the model; the number of decision trees in the model is 500, and the maximum depth of each tree is 10; the learning rate of the model is 0.05.

[0118] Combined with the electrical contact interface structure, material, and contact form characteristics that need to be predicted, the static contact resistance is measured, and the surface morphology of the contact point is obtained using a white light interferometer and a three-dimensional profilometer, which are saved in the form of a 200*200 two-dimensional array. The resulting data pair is (static contact resistance, spatial frequency characteristic parameters of the rough surface);

[0119] The trained model is used to extract the characteristic parameters (N, b, A) of the real rough surface, and the machine learning regression method is used again to train the association model between these three characteristic parameters and the static contact resistance. The input of the association model is the spatial frequency characteristic parameters of the rough surface, and the output is the static contact resistance of the interface.

[0120] Those skilled in the art know that, in addition to implementing the system, device and its various modules provided by the present invention in a purely computer-readable program code, it is entirely possible to implement the same program in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers and embedded microcontrollers by logically programming the method steps. Therefore, the system, device and its various modules provided by the present invention can be considered as a hardware component, and the modules included therein for implementing various programs can also be considered as structures within the hardware component; the modules for implementing various functions can also be considered as both software programs for implementing the method and structures within the hardware component.

[0121] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A surface morphology reconstruction method integrating machine learning and spatial frequency analysis, characterized in that: include: Step 1: Use the analytical formula of the spatial frequency method to generate a large number of two-dimensional arrays representing the rough surface; Step 2: By analyzing the height distribution and frequency energy ratio of the generated surface and combining machine learning methods, the characteristic variables of the analytical formula are extracted; Step 3: Establish the relationship between characteristic parameters and surface properties by combining experimental or simulation methods for performance prediction and surface reconstruction; The step 1 comprises: According to the basic formula of the spatial frequency method, the cutoff frequency N, spectral index b, and gain factor A of the spatial frequency are determined, and its two-dimensional function is: Among them, g(m,n) is a normal distribution function with a mean of 0 and a standard deviation of 1; u(m,n) is a uniform distribution function on [0, 2π]; x, y represent the x and y coordinates of any point on the rough surface; m, n represent the x and y spatial frequency values ​​superimposed at any point on the rough surface, which are m and n respectively; β represents the attenuation factor of the amplitude with frequency in the spectrum diagram; Arbitrarily set the three characteristic parameters N, b, and A to generate surface topography, including two-dimensional grayscale images and three-dimensional topography images; In the set range of surface morphology, a characteristic parameter combination of [N0, b0, A0] is randomly generated, and a two-dimensional array of the rough surface is generated accordingly; The step 2 comprises: For the generated two-dimensional array, extract its height distribution map; Extract the full width corresponding to the 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, and 5% height lines in the height distribution graph to form the first one-dimensional array of (1,19); Using the two-dimensional Fourier transform method, the two-dimensional spectrum corresponding to the two-dimensional array of the rough surface is drawn. For a two-dimensional function f(x, y), its two-dimensional Fourier transform F(u, v) is: Among them, (x, y) is the coordinate in the spatial domain; (u, v) is the coordinate in the frequency domain; e -i2π(ux+vy) is the transformation kernel, which represents the complex form of rotation; Taking the origin (0, 0) in the two-dimensional spectrum as the center, extract the radii corresponding to energy proportions of 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, and 5% to form a second one-dimensional array of (1,19); The energy proportion and the corresponding radius are combined into (x, y), a continuous curve is fitted using a spline curve, and the radius change rate at the corresponding position is extracted to form a third one-dimensional array of (1, 19); Combine the three one-dimensional arrays into a one-dimensional array arrays, and get each one-dimensional array arrays and its corresponding [N, b, A] array; The model is trained using a regression method. The model input is a one-dimensional array of shape (1, 57), corresponding to the height and spectral characteristics of the surface morphology; the model output is a one-dimensional array of shape (1, 3), corresponding to the spatial frequency characteristic parameters of the surface.

2. The surface morphology reconstruction method integrating machine learning and spatial frequency analysis according to claim 1, characterized in that: The squared logarithmic error is used as the loss function of the model; the number of decision trees in the model is 500, and the maximum depth of each tree is 10; the learning rate of the model is 0.

05.

3. The surface morphology reconstruction method integrating machine learning and spatial frequency analysis according to claim 1, characterized in that: Combined with the electrical contact interface structure, material, and contact form characteristics that need to be predicted, the static contact resistance is measured, and the surface morphology of the contact point is obtained using a white light interferometer and a three-dimensional profilometer, which are saved in the form of a 200*200 two-dimensional array. The resulting data pair is (static contact resistance, spatial frequency characteristic parameters of the rough surface); The trained model is used to extract the characteristic parameters (N, b, A) of the real rough surface, and the machine learning regression method is used again to train the association model between these three characteristic parameters and the static contact resistance. The input of the association model is the spatial frequency characteristic parameters of the rough surface, and the output is the static contact resistance of the interface.

4. A surface morphology reconstruction system integrating machine learning and spatial frequency analysis, characterized in that: include: Module M1: Generate a large number of two-dimensional arrays representing rough surfaces using the analytical formula of the spatial frequency method; Module M2: By analyzing the height distribution and frequency energy ratio of the generated surface and combining machine learning methods, the characteristic variables of the analytical formula are extracted; Module M3: Combine experimental or simulation methods to establish the relationship between characteristic parameters and surface properties for performance prediction and surface reconstruction; The module M1 comprises: According to the basic formula of the spatial frequency method, the cutoff frequency N, spectral index b, and gain factor A of the spatial frequency are determined, and its two-dimensional function is: Among them, g(m,n) is a normal distribution function with a mean of 0 and a standard deviation of 1; u(m,n) is a uniform distribution function on [0, 2π]; x, y represent the x and y coordinates of any point on the rough surface; m, n represent the x and y spatial frequency values ​​superimposed at any point on the rough surface, which are m and n respectively; β represents the attenuation factor of the amplitude with frequency in the spectrum diagram; Arbitrarily set the three characteristic parameters N, b, and A to generate surface topography, including two-dimensional grayscale images and three-dimensional topography images; In the set range of surface morphology, a characteristic parameter combination of [N0, b0, A0] is randomly generated, and a two-dimensional array of the rough surface is generated accordingly; The module M2 comprises: For the generated two-dimensional array, extract its height distribution map; Extract the full width corresponding to the 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, and 5% height lines in the height distribution graph to form the first one-dimensional array of (1,19); Using the two-dimensional Fourier transform method, the two-dimensional spectrum corresponding to the two-dimensional array of the rough surface is drawn. For a two-dimensional function f(x, y), its two-dimensional Fourier transform F(u, v) is: Among them, (x, y) is the coordinate in the spatial domain; (u, v) is the coordinate in the frequency domain; e -i2π(ux+vy) is the transformation kernel, which represents the complex form of rotation; Taking the origin (0, 0) in the two-dimensional spectrum as the center, extract the radii corresponding to energy proportions of 95%, 90%, 85%, 80%, 75%, 70%, 65%, 60%, 55%, 50%, 45%, 40%, 35%, 30%, 25%, 20%, 15%, 10%, and 5% to form a second one-dimensional array of (1,19); The energy proportion and the corresponding radius are combined into (x, y), a continuous curve is fitted using a spline curve, and the radius change rate at the corresponding position is extracted to form a third one-dimensional array of (1, 19); Combine the three one-dimensional arrays into a one-dimensional array arrays, and get each one-dimensional array arrays and its corresponding [N, b, A] array; The model is trained using a regression method. The model input is a one-dimensional array of shape (1, 57), corresponding to the height and spectral characteristics of the surface morphology; the model output is a one-dimensional array of shape (1, 3), corresponding to the spatial frequency characteristic parameters of the surface.

5. The surface morphology reconstruction system integrating machine learning and spatial frequency analysis according to claim 4, characterized in that: The squared logarithmic error is used as the loss function of the model; the number of decision trees in the model is 500, and the maximum depth of each tree is 10; the learning rate of the model is 0.

05.

6. The surface morphology reconstruction system integrating machine learning and spatial frequency analysis according to claim 4, characterized in that: Combined with the electrical contact interface structure, material, and contact form characteristics that need to be predicted, the static contact resistance is measured, and the surface morphology of the contact point is obtained using a white light interferometer and a three-dimensional profilometer, which are saved in the form of a 200*200 two-dimensional array. The resulting data pair is (static contact resistance, spatial frequency characteristic parameters of the rough surface); The trained model is used to extract the characteristic parameters (N, b, A) of the real rough surface, and the machine learning regression method is used again to train the association model between these three characteristic parameters and the static contact resistance. The input of the association model is the spatial frequency characteristic parameters of the rough surface, and the output is the static contact resistance of the interface.

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