Solid surface height statistical distribution method

Abstract

The invention provides a solid surface height statistical distribution method, which comprises the following steps of: preparing a sample, shooting an image, and acquiring solid surface images under different magnifications; solid surface images under different magnifying powers are observed, and linear additive performance of the magnifying powers is assumed: constructing a characteristic function: constructing a characteristic function of height probability distribution of the solid surface by utilizing a Levy stable distribution theory; deriving to obtain a feature function form of a height probability density function; fitting the Levy stable distribution parameters; and comparing the fitting effect of the Levy stable distribution and the fitting effect of the Levy normal distribution. Based on the analysis result of the statistical distribution of the surface height, the quality of the surface can be judged, such as detecting surface impurities, measuring surface roughness and judging surface smoothness. The statistical method of the surface height can be used as a powerful means for surface measurement and detection, and important basic data is provided for researching the surface mechanism and performance.

Description

Technical Field

[0001] The invention relates to the field of solid surface morphology distribution, in particular to a solid surface height statistical distribution method. Background Art

[0002] The surface of a solid is rough. In industrial equipment, it is common for solids to come into contact with each other, such as bearings and balls, structures and shock absorbers, etc. When analyzing the numerical model of a large structure, the surface treatment of the solid is often simplified, such as finite element or boundary element, and the surface of the solid is approximated by equations that have analytical expressions, including polynomial equations or chord curve equations.

[0003] With the high requirements for the operating environment of industrial equipment, such as extreme high temperature, extreme vacuum and other environments, the accuracy requirements for numerical models and theoretical analysis are becoming higher and higher, which also puts forward the requirement of high-precision analysis of the distribution of solid surface morphology.

[0004] Generally, under a certain analysis scale, the normal distribution is often used to fit the height distribution of the solid surface. This method is consistent with experience and intuition. However, with the application of high-precision microscopes in the analysis of a large number of solid surfaces, the normal distribution cannot analyze the height distribution of the solid surface well. In fact, the classical statistical distribution methods with probability distribution analytical formulas cannot analyze the solid morphological characteristics well. When the distribution analysis of the morphology of the solid surface of a large structure is insufficient, the misjudgment and evaluation of the surface morphology will lead to wrong material selection and surface treatment decisions, affecting product quality and cost; the existing analysis cannot meet the high requirements of the material surface, such as extreme high temperature, extreme vacuum and other environments, and cannot meet special needs, so its use is limited. To this end, we propose a statistical distribution method for the height of the solid surface to solve the above problems. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for statistical distribution of height of solid surface, so as to solve the problem that the classical statistical distribution methods with probability distribution analytical formulas cannot analyze the solid morphology characteristics well. When the distribution analysis of the morphology of the solid surface is insufficient, it will lead to wrong material selection and surface treatment decisions, and the use of materials will be restricted.

[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a method for statistical distribution of height of a solid surface, comprising the following steps:

[0007] S1. Sample preparation and image capture: Prepare material samples with different formulations, such as rubber samples, use a high-precision microscope to capture the surface of the material samples, and obtain solid surface images at different magnifications;

[0008] S2. Analyze the statistical distribution changes: observe the solid surface images at different magnifications and analyze the statistical distribution changes of the solid surface morphology; as the magnification increases, the observed height distribution becomes more dispersed;

[0009] S3. Assuming linear additivity of magnification: Based on observation, it is assumed that the magnification is linearly additivity; that is, it is assumed that the solid surface height as a random variable has the same probability distribution under different magnifications;

[0010] S4. Construct characteristic function: Use Levy stable distribution theory to construct characteristic function of solid surface height probability distribution; obtain characteristic function form of height probability density function through mathematical derivation;

[0011] S5. Parameter fitting: fitting the parameters of the Levy stable distribution according to the measured height distribution results; the index, tilt parameter, scale parameter and position parameter of the Levy stable distribution can be determined by the least square method or optimization algorithm;

[0012] S6. Compare the fitting effects of Levy stable distribution and normal distribution: Taking the height distribution of the actual solid surface as an example, perform normal distribution fitting and Levy stable distribution fitting; compare the fitting effects of Levy stable distribution and normal distribution to determine which correct distribution method to select.

[0013] In the preferred embodiment, in S2, when the magnification is 1, the solid surface visible to the naked eye has a mean of 0 and a variance of 0, that is, a mathematically ideal plane; the magnification is a generalized variance, and as the magnification increases, the observed height distribution becomes more dispersed;

[0014] The mean is a constant by adjusting the zero position.

[0015] In the preferred embodiment, in S3, the steps of solid surface height as a random variable having the same probability distribution are:

[0016] A1: Assume that the magnification is linearly additivity, that is, assume that the following two random variables have the same probability distribution:

[0017] h(x;ζ1)+h(x;ζ2),h(x;ζ1+ζ2)(1);

[0018] Where x = (x1, x2) is the two-dimensional coordinate of the solid surface, ζ represents the magnification relative to the original observation scale, and h is the height of the solid surface morphology at the corresponding position and the corresponding magnification scale;

[0019] Formula (1) is written in the form of probability density function:

[0020]

[0021] Among them, P h is the probability density function of the corresponding topography height h at a certain magnification ζ;

[0022] A2: The scaling transformation that formula (2) needs to satisfy is:

[0023]

[0024] Among them, λ is the scaling factor, H is the Hurst index of the self-affine analysis;

[0025] A3: Formula (3) shows that the two random variables in formula (4) have the same probability distribution:

[0026]

[0027] In the preferred embodiment, formula (4) indicates that the solid surface height is a random variable that satisfies the Levy stable distribution when the magnification of the random variable is assumed to have linear additivity.

[0028] In the preferred embodiment, in step S4, the steps of constructing the characteristic function of the solid surface height probability distribution using the Levy stable distribution theory are as follows:

[0029] B1: The height probability distribution function is the inverse Fourier transform of its characteristic function:

[0030]

[0031] in is the characteristic function of the probability density function, is the Fourier transform kernel, is the frequency domain height;

[0032] B2: Perform Fourier transform on formula (3) to obtain formula (6):

[0033]

[0034] B3: Take the natural logarithm of formula (6) and obtain formula (8):

[0035]

[0036] Formula (8) gives formula (9),

[0037]

[0038] In the preferred embodiment, in step S4, the steps of obtaining the characteristic function form of the height probability density function through mathematical derivation are:

[0039] C1: The characteristic function and complex logarithm function of the height probability distribution should be even functions, which corresponds to the form of formula (10):

[0040]

[0041] C2: By using formulas (9) and (10), we get formula (12):

[0042] Right now The real part of is positive, and formula (12) can be written as formula (13):

[0043] Where c1∈R + ,c2∈R;

[0044] C3: Formula (13) is equivalently expressed in the form of the common formula (13) of the Levy stable distribution,

[0045] C4: In formula (14), the formula for φ is (15);

[0046]

[0047] Where 1 / H is the exponent of the Levy distribution, β∈[-1,1] is the skew parameter, and γ∈R + is the scale parameter;

[0048] Where 1 / H is the exponent of the Levy distribution, β∈[-1,1] is the skew parameter, and γ∈R + is the scale parameter;

[0049] C5: According to the linear additivity of the magnification rate, the random variable pairs have the same distribution and convolution relationship of the probability density function, and the characteristic function of the probability density function of the height is obtained as formula (23);

[0050]

[0051] In the preferred embodiment, the steps of making the following pairs of random variables have the same distribution according to the linear additivity of the magnification to obtain the characteristic function of the probability density function of the height are:

[0052] D1: The linear additivity of the magnification makes the random variable pairs in formula (16) and formula (17) have the same distribution h(x;ζ1)+h(x;ζ2),h(x;ζ1+ζ2)+b(16);

[0053]

[0054] Where b is an arbitrary constant;

[0055] D2: According to the convolution relationship of the probability density function (18) and the formula (19) that the characteristic function corresponding to the height probability density function needs to satisfy, the corresponding logarithmic relationship formula (20) is obtained:

[0056]

[0057]

[0058]

[0059] D3: According to formula (20), we get formula (21):

[0060]

[0061] Among them, δ0∈R is the location parameter.

[0062] In the preferred embodiment, in S5, the step of fitting the Levy stable distribution parameters according to the measured height distribution result is:

[0063] E1: The specific form of the solution of the probability distribution equation of the unpressured altitude, and the determination of the unknown function through its boundary conditions

[0064] E2: Determine the fitting parameters α, β, γ, δ;

[0065] E3: Assuming the linear additivity of the magnification, the probability distribution form is obtained, and the Levy stable distribution parameters are fitted to the measured height distribution results;

[0066] E4: Simultaneously perform normal distribution fitting on .

[0067] The present invention provides a method for statistical distribution of height of a solid surface. According to the method for statistical distribution of height of a solid surface of the present application, the distribution of the morphology of the solid surface can be refined. The statistical distribution method with higher precision can meet the requirements of the use environment of standard industrial equipment and can adapt to environments such as extreme high temperature and extreme vacuum. Through the distribution statistics of surface height, a model of surface morphology can be established to describe the characteristics of the surface morphology, such as roughness, waviness, etc., as well as characteristics such as surface defects and geometric shapes. Through the statistical analysis of the distribution of surface height, the surface morphology can be designed and optimized to achieve functions such as smooth surface, easy cleaning, high smoothness, low friction, and surface wear resistance, so as to meet the needs of different applications, especially the requirements of extreme environments.

[0068] Based on the analysis results of the statistical distribution of surface height, the quality of the surface can be judged, such as detecting surface impurities, measuring surface roughness, and judging surface finish. The statistical method of surface height can be used as a powerful means of surface measurement and detection, and provides important basic data for studying surface mechanisms and properties. Therefore, the height statistical distribution method of the solid surface of this application is an important means of surface morphology analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0070] Figure 1 It is a schematic diagram of the overall process of the present invention;

[0071] Figure 2 This is a real shot of the rubber surface when the solid material of the present invention is rubber;

[0072] Figure 3 : is the frequency histogram of the rubber surface height distribution of the present invention and its distribution fitting, wherein the horizontal axis unit is meter;

[0073] Figure 4 : is the frequency histogram of the rubber surface height distribution of the present invention and its distribution fitting, wherein the horizontal axis unit is meter; DETAILED DESCRIPTION

[0074] Embodiment 1:

[0075] like Figures 1 to 4 A method for statistically distributing height of a solid surface comprises the following steps:

[0076] S1. Sample preparation and image capture: Prepare material samples with different formulations, such as rubber samples, use a high-precision microscope to capture the surface of the material samples, and obtain solid surface images at different magnifications;

[0077] S2. Analyze the statistical distribution changes: observe the solid surface images at different magnifications and analyze the statistical distribution changes of the solid surface morphology; as the magnification increases, the observed height distribution becomes more dispersed;

[0078] S3. Assuming linear additivity of magnification: Based on observation, it is assumed that the magnification is linearly additivity; that is, it is assumed that the solid surface height as a random variable has the same probability distribution under different magnifications;

[0079] S4. Construct characteristic function: Use Levy stable distribution theory to construct characteristic function of solid surface height probability distribution; obtain characteristic function form of height probability density function through mathematical derivation;

[0080] S5. Parameter fitting: fitting the parameters of the Levy stable distribution according to the measured height distribution results; the index, tilt parameter, scale parameter and position parameter of the Levy stable distribution can be determined by the least square method or optimization algorithm;

[0081] S6. Compare the fitting effects of Levy stable distribution and normal distribution: Taking the height distribution of the actual solid surface as an example, perform normal distribution fitting and Levy stable distribution fitting; compare the fitting effects of Levy stable distribution and normal distribution to determine which correct distribution method to select.

[0082] In the preferred embodiment, in S2, by changing the magnification, the statistical distribution of the solid surface morphology is changing, not constant. When the magnification is 1, the solid surface visible to the naked eye can be considered to have a mean of 0 and a variance of 0, that is, a mathematically ideal plane; the magnification is similar to a generalized variance. As the magnification increases, the observed height distribution becomes more dispersed;

[0083] The mean can also be considered a constant by adjusting the zero point position. From this structure, by changing the magnification, it can be known that the statistical distribution of the solid surface morphology is changing, not constant. A special example is that when the magnification is 1, that is, the solid surface visible to the naked eye, it can be considered to have a mean of 0 and a variance of 0, that is, a mathematically ideal plane. Alternatively, it can be considered that the magnification is similar to a generalized variance. As the magnification increases, the observed height distribution becomes more dispersed. In the normal distribution, the magnification multiplied by the constant coefficient is the distribution variance, and it is additive.

[0084] In the preferred embodiment, in S3, the steps of solid surface height as a random variable having the same probability distribution are:

[0085] A1: Assume that the magnification is linearly additivity, that is, assume that the following two random variables have the same probability distribution:

[0086] h(x;ζ1)+h(x;ζ2),h(x;ζ1+ζ2)(1);

[0087] Where x = (x1, x2) is the two-dimensional coordinate of the solid surface, ζ represents the magnification relative to the original observation scale, and h is the height of the solid surface morphology at the corresponding position and the corresponding magnification scale;

[0088] Formula (1) is written in the form of probability density function:

[0089]

[0090] Among them, P h is the probability density function of the corresponding topography height h at a certain magnification ζ;

[0091] A2: The scaling transformation that formula (2) needs to satisfy is:

[0092]

[0093] Among them, λ is the scaling factor, H is the Hurst index of the self-affine analysis;

[0094] A3: Formula (3) shows that the two random variables in formula (4) have the same probability distribution:

[0095]

[0096] In the preferred embodiment, formula (4) indicates that the solid surface height is a random variable that satisfies the Levy stable distribution when the magnification of the random variable is assumed to have linear additivity.

[0097] In the preferred embodiment, in step S4, the steps of constructing the characteristic function of the solid surface height probability distribution using the Levy stable distribution theory are as follows:

[0098] B1: The height probability distribution function is the inverse Fourier transform of its characteristic function:

[0099]

[0100] in is the characteristic function of the probability density function, is the Fourier transform kernel, is the frequency domain height;

[0101] B2: Perform Fourier transform on formula (3) to obtain formula (6):

[0102]

[0103] B3: Take the natural logarithm of formula (6) and obtain formula (8):

[0104]

[0105] Formula (8) gives formula (9),

[0106]

[0107] In the preferred embodiment, in step S4, the steps of obtaining the characteristic function form of the height probability density function through mathematical derivation are:

[0108] C1: The characteristic function and complex logarithm function of the height probability distribution should be even functions, which corresponds to the form of formula (10):

[0109]

[0110] C2: By using formulas (9) and (10), we get formula (12):

[0111] Right now The real part of is positive, and formula (12) can be written as formula (13):

[0112] Where c1∈R + ,c2∈R;

[0113] C3: Formula (13) is equivalently expressed in the form of the common formula (13) of the Levy stable distribution,

[0114] C4: In formula (14), the formula for φ is (15);

[0115]

[0116] Where 1 / H is the exponent of the Levy distribution, β∈[-1,1] is the skew parameter, and γ∈R + is the scale parameter;

[0117] C5: According to the linear additivity of the magnification rate, the random variable pairs have the same distribution and convolution relationship of the probability density function, and the characteristic function of the probability density function of the height is obtained as formula (23);

[0118]

[0119] In the preferred embodiment, the steps of making the following pairs of random variables have the same distribution according to the linear additivity of the magnification to obtain the characteristic function of the probability density function of the height are:

[0120] D1: The linear additivity of the magnification makes the random variable pairs in formula (16) and formula (17) have the same distribution h(x;ζ1)+h(x;ζ2),h(x;ζ1+ζ2)+b(16);

[0121]

[0122] D2: According to the convolution relationship of the probability density function (18) and the formula (19) that the characteristic function corresponding to the height probability density function needs to satisfy, the corresponding logarithmic relationship formula (20) is obtained:

[0123]

[0124]

[0125]

[0126] D3: According to formula (20), we get formula (21):

[0127]

[0128] Among them, δ0∈R is the location parameter.

[0129] In the preferred embodiment, in S5, the step of fitting the Levy stable distribution parameters according to the measured height distribution result is:

[0130] E1: Determine the undetermined function when solving the probability distribution equation for surface height under no pressure

[0131] E2: Determine the fitting parameters α, β, γ, δ;

[0132] E3: Assuming the linear additivity of the magnification, the probability distribution form is obtained, and the Levy stable distribution parameters are fitted to the measured height distribution results;

[0133] E4: Simultaneously perform normal distribution fitting on .

[0134] Embodiment 2:

[0135] Further explanation in conjunction with Example 1: A method for statistical distribution of height of a solid surface, wherein the solid is a rubber material. Material samples of different formulations are prepared (taking rubber as an example); the surface of the material sample is photographed using a high-precision microscope;

[0136] Prepare samples and capture images: Prepare material samples with different formulas, such as rubber samples, use a high-precision microscope to capture the surface of the material samples, and obtain solid surface images at different magnifications; observe the solid surface images at different magnifications, and use the Levy stable distribution theory to construct the characteristic function of the solid surface height probability distribution; obtain the characteristic function form of the height probability density function through mathematical derivation;

[0137] Parameter fitting: Comparison of the fitting effects of the Levy stable distribution and the normal distribution Assume that the magnification is linearly additivity, that is, assume that the following two random variables have the same probability distribution:

[0138] h(x;ζ1)+h(x;ζ2),h(x;ζ1+ζ2)(1);

[0139] Written in the form of probability density function, that is

[0140]

[0141] Note that the probability density function needs to satisfy the scaling transformation, then we have

[0142]

[0143] The above formula shows that the following two random variables have the same probability distribution:

[0144]

[0145] The above formula shows that the height of the solid surface is a random variable that satisfies the Levy stable distribution when the magnification of the random variable is assumed to be linearly additivity. Note that the height probability distribution function is the Fourier inverse transform of its characteristic function.

[0146]

[0147] Perform Fourier transform on formula (3) and we get

[0148]

[0149] Take the natural logarithm of the above formula and take

[0150]

[0151] get

[0152]

[0153] From the above formula, it is easy to get

[0154]

[0155] The characteristic function of the height probability distribution and its complex logarithm function should be an even function, then Should have the following form

[0156]

[0157] Note:

[0158]

[0159] Then there is

[0160]

[0161] Right now The real part of is positive (generally, not considering the case of zero), and it can be written as follows:

[0162]

[0163] Where c1∈R +,c2∈R; Here, in order to make the meaning of the characteristic function of height and its logarithm clearer, the above formula can also be equivalently expressed as the common form of Levy stable distribution:

[0164]

[0165] in,

[0166]

[0167] Where 1 / H is the exponent of the Levy distribution, β∈[-1,1] is the skew parameter, and γ∈R + is the scale parameter. tan(πα / 2) and Guaranteed can take on all real numbers. In fact, the more general linear additivity of the magnification makes the following pairs of random variables have the same distribution:

[0168] h(x;ζ1)+h(x;ζ2),h(x;ζ1+ζ2)+b (16);

[0169]

[0170] At this time, the convolution relationship of the probability density function is:

[0171]

[0172] The characteristic function corresponding to the height probability density function needs to satisfy:

[0173]

[0174] The corresponding logarithmic relationship is:

[0175]

[0176] At this time, the following form is given:

[0177]

[0178] Among them, δ0∈ R It is called the position parameter. The formula given above is not continuous. Here is a continuous form:

[0179]

[0180] Finally, the characteristic function that gives the probability density function of the height is:

[0181]

[0182] And record it as, highly subject to stable distribution:

[0183] h:S(α,β,γ,δ),α;1 / H (24);

[0184] The above process is consistent with the form given by the probability distribution equation of the given unpressurized altitude. The specific form of the solution of the probability distribution equation of the unpressurized altitude is determined by its boundary conditions to determine the unknown function Assuming the linear additivity of the magnification, the probability distribution form needs to be fitted to the Levy stable distribution parameters α, β, γ, and δ for the measured height distribution results.

[0185] The height distribution frequency histogram of the actual rubber surface is given below, and normal distribution fitting and Levy stable distribution fitting are performed. The normal distribution fitting parameters are:

[0186] μ=-8.30313×10 -20 ,σ=4.94326×10 -6 (25);

[0187] The fitting parameters of the Levy stable distribution are:

[0188] α=1.73326, β=-0.146955, γ=2.4919×10 -6 ,δ=1.37961×10 -7 (26);

[0189] Among them, the stable distribution α=1.73326, which is somewhat different from 2; it can also be seen from the attached that the fitting effect of the Levy stable distribution is better, and the fitting effect of the normal distribution is worse (compare the difference between the normal distribution and the height distribution). It is more appropriate to select the Levy stable distribution for fitting the height distribution of the actual rubber surface. The Levy stable distribution theory is the Levy stable distribution theory. α is between 0 and 2 or equal to 2, which is called Levy stable distribution in advanced statistics. α equal to 2 is called normal distribution, which is a special case of Levy stable distribution. When α is equal to 2, the fitting effect of normal distribution is better. If α is between 0 and 2, the fitting effect of Levy stable distribution is better. The above-mentioned embodiments are only preferred technical solutions of the present invention and should not be regarded as limitations of the present invention. The embodiments and features in the embodiments of the present application can be arbitrarily combined with each other without conflict. The protection scope of the present invention shall be the technical solutions recorded in the claims, including the equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A method for statistical distribution of height of a solid surface, characterized in that: The following steps are involved: S1. Sample preparation and image capture: Prepare material samples with different formulations, use a high-precision microscope to capture the surface of the material samples, and obtain solid surface images at different magnifications; S2. Analyze the statistical distribution changes: observe the solid surface images at different magnifications and analyze the statistical distribution changes of the solid surface morphology; as the magnification increases, the observed height distribution becomes more dispersed; S3. Assuming linear additivity of magnification: Based on observation, it is assumed that the magnification is linearly additivity; that is, it is assumed that the solid surface height as a random variable has the same probability distribution under different magnifications; S4. Construct characteristic function: Use Levy stable distribution theory to construct characteristic function of solid surface height probability distribution; obtain characteristic function form of height probability density function through mathematical derivation; S5. Parameter fitting: fitting the parameters of the Levy stable distribution according to the measured height distribution results; the index, tilt parameter, scale parameter and position parameter of the Levy stable distribution can be determined by the least square method or optimization algorithm; S6. Compare the fitting effects of Levy stable distribution and normal distribution: perform normal distribution fitting and Levy stable distribution fitting; compare the fitting effects of Levy stable distribution and normal distribution to determine which correct distribution method to select.

2. A method for statistically distributing the height of a solid surface according to claim 1, characterized in that: in S2, when the magnification is 1, the solid surface visible to the naked eye has a mean of 0 and a variance of 0, i.e., a mathematically ideal plane; the magnification is a generalized variance, and as the magnification increases, the observed height distribution becomes more dispersed; The mean is a constant by adjusting the zero position.

3. The method for statistically distributing the height of a solid surface according to claim 1, wherein: in S3, the step of the solid surface height having the same probability distribution as a random variable is: A1: Assume that the magnification is linearly additivity, that is, assume that the following two random variables have the same probability distribution: h(x;ζ1)+h(x;ζ2),h(x;ζ1+ζ2)(1); in, x = (x1, x2) is the two-dimensional coordinate of the solid surface, ζ represents the magnification relative to the original observation scale, and h is the height of the solid surface morphology at the corresponding position and the corresponding magnification scale; Formula (1) is written in the form of probability density function: Among them, P h is the probability density function of the corresponding topography height h at a certain magnification ζ; A2: The scaling transformation that formula (2) needs to satisfy is: Among them, λ is the scaling factor, H is the Hurst index of the self-affine analysis; A3: Formula (3) shows that the two random variables in formula (4) have the same probability distribution: Among them, λ is the scaling factor, h is the solid surface topography height, and H is the Hurst index of the self-affine analysis.

4. A method for statistically distributing height of a solid surface according to claim 3, characterized in that: Formula (4) shows that the solid surface height is a random variable that satisfies the Levy stable distribution when the magnification of the random variable is assumed to be linearly additivity.

5. The method for statistically distributing height of a solid surface according to claim 3, characterized in that: In step S4, the steps of constructing the characteristic function of the solid surface height probability distribution using the Levy stable distribution theory are as follows: B1: The height probability distribution function is the inverse Fourier transform of its characteristic function: in is the characteristic function of the probability density function, is the Fourier transform kernel, is the frequency domain height; B2: Perform Fourier transform on formula (3) to obtain formula (6): B3: Take the natural logarithm of formula (6) and take We get formula (8): Formula (8) gives formula (9), 6. The method for statistically distributing height of a solid surface according to claim 1, characterized in that: In step S4, the steps of obtaining the characteristic function form of the height probability density function through mathematical derivation are: C1: The characteristic function and complex logarithm function of the height probability distribution should be even functions. Formula (10): C2: By using formulas (9) and (10), we get formula (12): Right now The real part of is positive, and formula (12) can be written as formula (13): Where c1∈R + ,c2∈R; C3: Formula (13) is equivalently expressed in the form of the common formula (13) of the Levy stable distribution, C4: In formula (14), the formula for φ is (15); Where 1 / H is the exponent of the Levy distribution, β∈[-1,1] is the skew parameter, and γ∈R + is the scale parameter; C5: According to the linear additivity of the magnification rate, the random variable pairs have the same distribution and convolution relationship of the probability density function, and the characteristic function of the probability density function of the height is obtained as formula (23); 7. A method for statistically distributing height of a solid surface according to claim 6, characterized in that: According to the linear additivity of magnification, the steps to make the following pairs of random variables have the same distribution and obtain the characteristic function of the probability density function of the height are: D1: The linear additivity of the magnification makes the random variable pairs in formula (16) and formula (17) have the same distribution h(x;ζ1)+h(x;ζ2),h(x;ζ1+ζ2)+b(16); (λ1+λ2) H h+b(17); Where b is an arbitrary constant; D2: According to the convolution relationship of the probability density function (18) and the formula (19) that the characteristic function corresponding to the height probability density function needs to satisfy, the corresponding logarithmic relationship formula (20) is obtained: D3: According to formula (20), we get formula (21): Among them, δ0∈R is the location parameter.

8. The method for statistically distributing height of a solid surface according to claim 1, wherein: S5 In the above, according to the measured height distribution results, the steps of fitting the parameters of the Levy stable distribution are as follows; E1: Determine the undetermined function when solving the probability distribution equation for surface height under no pressure E2: Determine the fitting parameters α, β, γ, δ; E3: Assuming the linear additivity of the magnification, the probability distribution form is obtained, and the Levy stable distribution parameters α, β, γ, and δ are fitted to the measured height distribution results; E4: Simultaneously perform normal distribution fitting on .

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