Object hyperspectral emissivity fitting smoothing method

Abstract

The invention relates to an object hyperspectral emissivity fitting smoothing method, belongs to the field of material thermophysical property testing and data processing, and solves the problem of false signals in the existing emissivity fitting smoothing process. Comprising the following steps: acquiring spectral emissivity corresponding to each wavelength in a to-be-fitted wavelength range; obtaining a single wavelength radiation entropy of each wavelength based on the spectral emissivity corresponding to each wavelength; a high-order polynomial fitting method is used for the single-wavelength radiation entropy of each wavelength to obtain a smoothed wavelength radiation entropy; and obtaining the fitted and smoothed spectral emissivity of the to-be-fitted wavelength range based on the smoothed wavelength radiation entropy. The method achieves the reasonable fitting and smoothing of the hyperspectral emissivity from the angles of probability and entropy.

Description

Technical Field

[0001] The present invention relates to the field of thermal physical property testing and data processing of materials, and particularly to a method for fitting and smoothing the hyperspectral emissivity of an object. Background Art

[0002] Spectral emissivity measurement plays an important role in scientific research and has very important applications in fields such as remote sensing, materials, stealth, and metallurgy. In the field of materials science, high-temperature emissivity is an important parameter for studying the high-temperature oxidation, corrosion, sintering, and other behaviors of materials. By measuring the high-temperature emissivity, the physical properties and chemical reaction kinetics of materials can be deeply understood, providing theoretical support for the research and development of new materials.

[0003] According to solid-state physics theory, spectral emissivity reflects the microscale photoacoustic coupling characteristics of materials, and it should exhibit certain short-range continuity, smoothness, and certain long-range correlation in hyperspectral data. The spectral emissivity of materials usually has a smooth characteristic, that is, the derivative of the spectral emissivity is continuous when the wavelength changes. This smooth characteristic can be determined by the physical properties and surface state of materials. For example, the spectral emissivity of metal materials is usually relatively smooth because their surfaces are relatively smooth and have a continuous electronic energy band structure. In contrast, the spectral emissivity of semiconductor materials may have some discontinuous transitions, resulting in non-smooth characteristics.

[0004] The spectral emissivity of materials also has short-range and long-range correlations. Short-range correlation refers to the change of spectral emissivity between adjacent wavelengths, while long-range correlation refers to the change trend of spectral emissivity over the entire spectral range. Short-range correlation is usually determined by the local properties and surface state of materials, such as surface defects, chemical adsorption, etc. Long-range correlation is more affected by the overall properties and physical state of materials, such as crystal structure, energy band structure, etc.

[0005] However, during the hyperspectral emissivity measurement process, due to reasons such as detector noise, wavelength calibration, and stray radiation interference, the measured emissivity data is always accompanied by a large amount of fluctuations. Using traditional emissivity smoothing algorithms, the obtained results are prone to violate the basic physical characteristics. Summary of the Invention

[0006] In view of the above analysis, the embodiments of the present invention aim to provide a method for fitting and smoothing the hyperspectral emissivity to solve the problem of false signals appearing in the existing emissivity fitting and smoothing process.

[0007] The object of the present invention is mainly achieved through the following technical solutions:

[0008] The present invention provides a method for fitting and smoothing the hyperspectral emissivity of an object, including the following steps:

[0009] Obtain the spectral emissivity of the object corresponding to each wavelength within the wavelength range to be fitted;

[0010] Obtain the single-wavelength radiation entropy of each wavelength based on the spectral emissivity corresponding to each wavelength;

[0011] Use the high-order polynomial fitting method for the single-wavelength radiation entropy of each wavelength to obtain the smoothed wavelength radiation entropy;

[0012] Obtain the fitted and smoothed spectral emissivity of the wavelength range to be fitted based on the smoothed wavelength radiation entropy.

[0013] Further, the single-wavelength radiation entropy of each wavelength is obtained based on the following formula:

[0014]

[0015] where, is the single-wavelength radiation entropy of wavelength λ i ; is the spectral emissivity corresponding to wavelength λ i ; where i is the sequence number of the i-th wavelength within the wavelength range to be fitted.

[0016] Further, the high-order polynomial fitting method includes: for each wavelength, use the kernel function as a weight to perform local polynomial kernel regression to obtain a high-order polynomial as the regression function, and use the regression function to calculate the single-wavelength radiation entropy of each wavelength as the smoothed wavelength radiation entropy; where, the local polynomial kernel regression includes: select a preset number of wavelengths adjacent to this wavelength, and perform polynomial fitting based on the kernel function within this range.

[0017] Further, the regression function is:

[0018] H(λ i ) = a0 + a1λ i + a2λ i 2 + a3λ i 3 + … + a n λ i n

[0019] where, λ i is the wavelength value of the i-th wavelength; a0, a1...a n are the coefficients of the polynomial function; n is the order of the polynomial function.

[0020] Further, the coefficients of the polynomial function are calculated using the following formula:

[0021]

[0022] Among them, θ is the coefficient vector of the polynomial function; X is the Vandermonde matrix with respect to the wavelength; K is the diagonalized kernel function matrix; Y is the single-wavelength radiation entropy vector of each of the wavelengths.

[0023] Further, the Vandermonde matrix with respect to the wavelength is:

[0024]

[0025] Among them, λ is the smoothed wavelength; i is the i-th wavelength serial number; N is the preset quantity.

[0026] Further, the diagonalized kernel function matrix is:

[0027] K = diag(k(λ, λ i-N ), … k(λ, λ i ), … k(λ, λ i+N ))

[0028] Among them, k(λ, λ i ) is the kernel function; λ is the smoothed wavelength; i is the i-th wavelength; N is the preset quantity.

[0029] Further, the single-wavelength radiation entropy vector of the wavelength is:

[0030]

[0031] Among them, is the single-wavelength radiation entropy of the wavelength λ i ; i is the i-th wavelength; N is the preset quantity.

[0032] Further, the order of the polynomial function is from 2 to 11 orders.

[0033] Further, based on the radiation entropy of the smoothed wavelength, the fitted and smoothed spectral emissivity of the wavelength range to be fitted is obtained using the following formula:

[0034]

[0035] Among them, is the spectral emissivity of the smoothed wavelength λ i ; is the single-wavelength radiation entropy of the smoothed wavelength λ i .

[0036] Compared with the prior art, the present invention can at least achieve one of the following beneficial effects:

[0037] 1. The present invention uses a physical modeling method for the spectral emissivity characteristics of materials based on probability, clarifies the relationship between entropy and the spectral emissivity of materials, and the obtained model has a very clear physical meaning and satisfies various physical constraint conditions of emissivity;

[0038] 2. The present invention uses a high-order polynomial to fit the spectral radiation entropy, which meets the requirements of smoothness and continuity, has a fast operation speed, and a wide application range;

[0039] 3. The local polynomial kernel regression method used in the present invention can balance the short-range correlation and long-range correlation of emissivity by selecting a preset number of wavelengths adjacent to this wavelength and the kernel function, making it more capable of meeting various requirements.

[0040] In the present invention, the above technical solutions can also be combined with each other to achieve more preferred combination schemes. Other features and advantages of the present invention will be described in the subsequent specification, and some advantages can be made obvious from the specification or understood by implementing the present invention. The objectives and other advantages of the present invention can be realized and obtained through the content specifically pointed out in the specification and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The drawings are only for the purpose of showing specific embodiments and are not considered as limiting the present invention. Throughout the drawings, the same reference signs represent the same components.

[0042] Figure 1 It is a schematic flow chart of a hyperspectral emissivity fitting and smoothing method in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0043] The following will specifically describe the preferred embodiments of the present invention with reference to the drawings, where the drawings form a part of this application and are used together with the embodiments of the present invention to explain the principles of the present invention, rather than to limit the scope of the present invention.

[0044] A specific embodiment of the present invention discloses a method for fitting and smoothing the hyperspectral emissivity of an object, as Figure 1 shown, including the following steps:

[0045] Step S1: Obtain the spectral emissivity of the object corresponding to each wavelength within the wavelength range to be fitted;

[0046] Specifically, according to the definition of the blackbody radiation theory, the spectral emissivity of an object is expressed as the ratio of the radiance of the object to the radiance of a blackbody having the same temperature as the object; use instrument equipment to measure the wavelengths absorbed by the object and the radiance values emitted, and by comparing with the radiance values emitted by a blackbody at the same temperature, obtain multiple wavelengths and their corresponding spectral emissivities within the wavelength range to be fitted.

[0047] On the other hand, from a microscopic perspective, particles are in a thermally excited state due to thermal effects. The excited particles can undergo radiative de-excitation through processes such as phonon-photon coupling, or non-radiative de-excitation through relaxation processes. Therefore, the emissivity can be regarded as the probability of radiative de-excitation of a single particle in the thermally excited state, and this probability is 1 in an ideal black body.

[0048] Furthermore, for an object composed of a large number of particles, the radiation intensity can be regarded as a statistic. Under the assumption of identical particles, the radiative de-excitation behavior of a large number of particles can be described by the binomial distribution, that is, the probability that exactly m particles out of N thermally excited particles undergo radiative de-excitation is:

[0049]

[0050] According to the characteristics of the binomial distribution, the expected number of radiatively de-excited particles is:

[0051]

[0052] The radiation intensity generated by the radiative de-excitation of this part of the particles, compared with the radiation luminance of the ideal black body, is the spectral emissivity of the object corresponding to the corresponding wavelength.

[0053] Step S2: Obtain the single-wavelength radiation entropy at each wavelength based on the spectral emissivity corresponding to each wavelength;

[0054] Furthermore, according to the probability characteristics of the emissivity and the Lebesgue measure, the entropy of the system at this wavelength can be measured by the following formula:

[0055]

[0056] where g(m) is the degeneracy of the state when exactly m particles undergo radiative de-excitation, and its numerical value is indicating that there are g(m) microscopic states with the same energy.

[0057] Furthermore, from the above formula, it can be deduced that:

[0058] H λ =-N[ε λ lnε λ +(1-ε λ )ln(1-ε λ )]

[0059] Therefore, the single-wavelength radiation entropy of a single particle at each wavelength is:

[0060]

[0061] where is the wavelength λi The single-wavelength radiation entropy; is the spectral emissivity corresponding to the wavelength λ; To avoid the situation where the spectral emissivity is greater than or equal to 1 or less than or equal to 0 (in these cases i the calculation result is a complex number), take the modulus of the calculation result to obtain

[0062] It can be seen from this that the entropy of the system is equal to the entropy of a single particle multiplied by the total number of particles N, and its magnitude is related to the emissivity of the material in different wavelength bands.

[0063] Step S3, use the high-order polynomial fitting method for the single-wavelength radiation entropy of each wavelength to obtain the smoothed wavelength radiation entropy;

[0064] Specifically, the high-order polynomial fitting method includes: for each wavelength, use the kernel function as the weight for local polynomial kernel regression to obtain a high-order polynomial as the regression function, and use the regression function to calculate the single-wavelength radiation entropy of each wavelength as the smoothed wavelength radiation entropy; among them, local polynomial kernel regression includes: select a preset number of wavelengths adjacent to this wavelength, and perform polynomial fitting based on the kernel function within this range.

[0065] It should be noted that the preset number is the number of data points participating in the calculation on both sides of the smoothing point, which controls how many adjacent data points are used for the calculation; the larger the preset number range, the smoother the result. Preferably, the preset number N is selected to be 10 - 50.

[0066] Furthermore, according to solid-state physics theory, the spectral emissivity reflects the microscale photoacoustic coupling characteristics of the material, and it should exhibit certain short-range continuity, smoothness, and certain long-range correlation in hyperspectral data. The smoothness of the material spectral emissivity means that its derivative is continuous when the wavelength changes. The short-range correlation and long-range correlation are the external manifestations of the material energy band structure. When the material is a mixture, the long-range correlation and short-range correlation weaken, but still maintain relatively high spectral continuity and smoothness.

[0067] Furthermore, the continuity and smoothness of the material spectral emissivity are due to the fact that the radiation entropy H λ at different wavelengths at the microscopic level has smooth and continuous characteristics.

[0068] Specifically, high-order polynomial fitting is a commonly used method in data analysis and machine learning. It can fit a set of data into a high-order polynomial model. This method can improve the fitting accuracy of the data to a certain extent.

[0069] ​The basic idea of high-order polynomial fitting is to find an optimal polynomial function to fit a given data set, thereby minimizing the error between the fitting function and the original data set. To achieve this goal, we need to select a suitable polynomial function and solve the coefficients of the polynomial function by the least squares method.

[0070] Specifically, we can select an nth-degree polynomial function with respect to the independent variable λ i to fit the data. In this embodiment, this polynomial function as the regression function can be expressed as:

[0071] H(λ i ) = a0 + a1λ i + a2λ i 2 + a3λ i 3 + … + a n λ i n

[0072] where λ i is the wavelength value of the i-th wavelength; a0, a1 … a n are the coefficients of the polynomial function, and n is the order of the polynomial function. By the least squares method, we can solve the optimal values of these coefficients, thereby obtaining an optimal polynomial function to fit the data.

[0073] It should be noted that high-order polynomial fitting may cause the problem of overfitting in some cases. Overfitting means that when fitting the data, in order to achieve a better fitting effect, the original data set is overfitted, resulting in a poor prediction effect for new data. Therefore, when performing high-order polynomial fitting, it is necessary to select the order of the polynomial according to the specific situation and make appropriate adjustments and optimizations.

[0074] Specifically, the order of the polynomial is from 2 to 11, preferably an odd order.

[0075] In this embodiment, the order is preferably 5.

[0076] As can be seen from the above, as long as the polynomial coefficients of the radiation entropy at different wavelengths are obtained, the material emissivity can be fitted and smoothed. However, if a fixed polynomial is used, this fitting method has strong long-range correlation, which does not conform to the actual material characteristics.

[0077] Therefore, in this embodiment, the kernel regression method is used to fit the entropy, so that while meeting the requirements of smoothness and continuity, the hard constraint of its long-range correlation is reduced.

[0078] Specifically, traditional linear regression can only fit a straight line. Kernel regression is a regression method based on non-linear mapping, which is a method that only uses multiple data points near the data points for regression. Its essence is to use the kernel function as a weight function to establish a non-linear regression model.

[0079] Furthermore, according to the least squares method, local polynomial kernel regression is to solve the coefficients θ of the polynomial function to minimize the following objective function J(θ):

[0080] J(θ) = (Xθ - Y) T K(Xθ - Y)

[0081] where θ is the coefficient vector of the polynomial function; X is the Vandermonde matrix with respect to the wavelength; K is the diagonalized kernel function matrix; and Y is the single-wavelength radiation entropy vector of each of the wavelengths.

[0082] Therefore, according to the following coefficient calculation formula of the polynomial function can be obtained:

[0083]

[0084] Furthermore, the Vandermonde matrix X with respect to the wavelength is:

[0085]

[0086] where λ is the smoothed wavelength; i is the serial number of the i-th wavelength currently selected; and N is the preset quantity.

[0087] It should be noted that in the matrix, if i - N is less than 1, it is calculated starting from 1; if i + N is greater than the total number of wavelengths within the wavelength range to be fitted, it is only calculated up to the last wavelength.

[0088] Furthermore, the diagonalized kernel function matrix K is:

[0089] K = diag(k(λ, λ i-N ), … k(λ, λ i ), … k(λ, λ i+N ))

[0090] where k(λ, λ i ) is the kernel function; λ is the smoothed wavelength; i is the serial number of the i-th wavelength currently selected; and N is the preset quantity.

[0091] Specifically, the kernel function defines the similarity measurement method of the input data in the feature space. Common kernel functions include Gaussian kernel function, polynomial kernel function, sigmoid kernel function, etc.

[0092] Preferably, the Gaussian kernel function regression model is selected in the present invention:

[0093]

[0094] Among them, σ is the standard deviation.

[0095] Specifically, the Gaussian kernel function can be regarded as a weight negatively correlated with the distance from the center; when smoothing, adjusting the standard deviation is to adjust the influence degree of the surrounding wavelengths on the current wavelength. Increasing σ increases the influence degree of the distant wavelengths on the central wavelength, and the filtering result is smoother.

[0096] Furthermore, the single-wavelength radiation entropy vector of the wavelength is:

[0097]

[0098] Among them, is the single-wavelength radiation entropy of wavelength λ i ; i is the serial number of the i-th wavelength currently selected; N is the preset quantity.

[0099] So far, after substituting the wavelength λ i into the regression function H(λ), the calculated H(λ i ) is the entropy after smoothing of this wavelength

[0100] Step S4, obtain the fitted and smoothed spectral emissivity of the wavelength range to be fitted based on the smoothed wavelength radiation entropy.

[0101] Specifically, based on the smoothed wavelength radiation entropy, the following formula is used to obtain the fitted and smoothed spectral emissivity of the wavelength range to be fitted:

[0102]

[0103] Among them, is the spectral emissivity of the smoothed wavelength λ i ; is the single-wavelength radiation entropy of the smoothed wavelength λ i .

[0104] To sum up, a high-spectral-emissivity fitting and smoothing method according to an embodiment of the present invention has the following beneficial effects:

[0105] 1. The present invention uses a physical modeling method for the spectral emissivity characteristics of materials based on probability, clarifies the relationship between entropy and the spectral emissivity of materials, and the obtained model has a very clear physical meaning and satisfies various physical constraint conditions of emissivity;

[0106] 2. The present invention uses a high-order polynomial to fit the spectral radiation entropy, which meets the requirements of smoothness and continuity, and at the same time has a fast operation speed and a wide application range;

[0107] 3. The locally polynomial kernel regression method used in the present invention can balance the short-range correlation and long-range correlation of the emissivity by selecting a preset number of wavelengths adjacent to this wavelength and the kernel function, making it more capable of meeting various requirements.

[0108] As described above, only the preferred specific embodiments of the present invention are provided, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for fitting and smoothing the hyperspectral emissivity of an object, characterized in that, It includes the following steps: Obtain the spectral emissivity of the object corresponding to each wavelength within the wavelength range to be fitted; Obtain the single-wavelength radiation entropy of each wavelength based on the spectral emissivity corresponding to each wavelength; Use the high-order polynomial fitting method for the single-wavelength radiation entropy of each wavelength to obtain the smoothed wavelength radiation entropy; Obtain the fitted and smoothed spectral emissivity of the wavelength range to be fitted based on the smoothed wavelength radiation entropy; 2. The method according to claim 1, wherein Obtain the single-wavelength radiation entropy of each wavelength based on the following formula: Among them, is the single-wavelength radiation entropy at wavelength λ i ; is the spectral emissivity corresponding to wavelength λ i ; where i is the i-th wavelength serial number within the wavelength range to be fitted.

3. The method according to claim 1, wherein The high-order polynomial fitting method includes: for each wavelength, use the kernel function as the weight to perform local polynomial kernel regression to obtain a high-order polynomial as the regression function, and use the regression function to calculate the single-wavelength radiation entropy of each wavelength as the smoothed wavelength radiation entropy; wherein, the local polynomial kernel regression includes: select a preset number of wavelengths adjacent to this wavelength, and perform polynomial fitting based on the kernel function within this range.

4. The method according to claim 3, wherein The regression function is: H(λ i ) = a0 + a1λ i + a2λ i 2 + a3λ i 3 + … + a n λ i n where λ i is the wavelength value of the i-th wavelength; a0, a1…a n are the coefficients of the polynomial function; n is the order of the polynomial function.

5. The method according to claim 4, characterized in that The coefficients of the polynomial function are calculated using the following formula: wherein, θ is the coefficient vector of the polynomial function; X is the Vandermonde matrix with respect to the wavelength; K is the diagonalized kernel function matrix; Y is the single-wavelength radiation entropy vector of each wavelength.

6. The method according to claim 5, characterized in that, The Vandermonde matrix with respect to the wavelength is: wherein, λ is the smoothed wavelength; i is the i-th wavelength serial number; N is the preset number.

7. The method according to claim 5, wherein The diagonalized kernel function matrix is: K = diag(k(λ,λ i-N ),…k(λ,λ i ),…k(λ,λ i+N )) Among them, k(λ,λ i ) is the kernel function; λ is the smoothed wavelength; i is the i-th wavelength; N is the preset number.

8. The method according to claim 5, wherein The single-wavelength radiation entropy vector of the wavelength is: wherein, is the single-wavelength radiation entropy at wavelength λ i , i is the i-th wavelength, and N is the preset quantity.

9. The method according to claim 4, wherein The order of the polynomial function is from 2 to 11 orders.

10. The method according to claim 1, characterized in that, Based on the smoothed wavelength radiation entropy, obtain the fitted and smoothed spectral emissivity of the wavelength range to be fitted using the following formula: Among them, is the spectral emissivity at the smoothed wavelength λ i ; is the single-wavelength radiation entropy at the smoothed wavelength λ i .

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