Material spectral emissivity-temperature separation inversion method

Abstract

The invention relates to a material spectral emissivity-temperature separation inversion method, belongs to the field of material thermophysical property testing and data processing, and solves the problem of low temperature and emissivity measurement accuracy in a high-temperature environment in the prior art. The method comprises the following steps: acquiring spectral radiation brightness corresponding to each wavelength of the material in a wavelength range to be separated; obtaining the blackbody temperature corresponding to each wavelength of the ideal blackbody based on the spectral radiation brightness corresponding to each wavelength; and based on the spectral radiation brightness corresponding to each wavelength and the blackbody temperature corresponding to each wavelength, using an EM optimization strategy to obtain the inverted temperature and the spectral emissivity corresponding to each wavelength of the material. The spectral emissivity of the surface of the material can be accurately measured only by depending on the heat capacity of the material in a high-temperature environment.

Description

Technical Field

[0001] The present invention relates to the field of testing and data processing algorithms, and particularly to a method for separating and inversely calculating the spectral emissivity - temperature of materials. Background Art

[0002] The measurement of high - temperature spectral emissivity plays an important role in scientific research. 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 application of new materials.

[0003] However, there are many difficulties and limitations in the measurement of high - temperature spectral emissivity at the present stage. First, it is difficult to obtain the surface characteristics of materials. In a high - temperature environment, the surface emissivity of materials is affected by many factors, such as material composition, surface state, temperature, etc. These factor changes make it difficult to accurately measure the emissivity characteristics of materials. Second, it is difficult to ensure the stability and reliability of measurement equipment in a high - temperature environment. When measuring emissivity in a high - temperature environment, special measurement equipment and instruments are required, such as infrared thermometers, spectral analyzers, etc. These devices need to maintain stability and reliability in a high - temperature environment to ensure the accuracy and reliability of measurement. Third, data analysis and processing in a high - temperature environment are very difficult. Finally, safety and protection in a high - temperature environment need to be considered emphatically. When measuring emissivity in a high - temperature environment, attention should be paid to safety and protection issues, such as preventing high temperature from harming measurement personnel and preventing high temperature from damaging measurement equipment.

[0004] In the aspect of high - temperature spectral emissivity inversion algorithms, multiple difficulties need to be overcome, including the synchronous measurement of temperature and emissivity, the non - uniformity of emissivity, the stability of light sources and detectors, signal interference and noise, as well as data processing and analysis.

[0005] Aiming at the problems and difficulties in the measurement of spectral emissivity in a high - temperature environment, it is urgent to propose a new type of high - temperature spectral emissivity separation and inversion algorithm to achieve accurate measurement of the surface spectral emissivity of high - temperature materials. Summary of the Invention

[0006] In view of the above analysis, the embodiments of the present invention aim to provide a method for separating and inversely calculating the spectral emissivity - temperature of materials to solve the problem of low accuracy in measuring temperature and emissivity in the existing high - temperature environment.

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

[0008] The present invention provides a method for separating and inversely calculating the spectral emissivity - temperature of materials, including the following steps:

[0009] Obtain the spectral radiance corresponding to each wavelength of the material within the wavelength range to be separated;

[0010] Based on the spectral radiance corresponding to each wavelength, obtain the blackbody temperature corresponding to each wavelength of the ideal blackbody;

[0011] Based on the spectral radiance corresponding to each wavelength and the blackbody temperature corresponding to each wavelength, use the EM optimization strategy to obtain the temperature of the material after inversion and the spectral emissivity corresponding to each wavelength.

[0012] Further, when using the EM optimization strategy to obtain the temperature of the material after inversion and the spectral emissivity corresponding to each wavelength, in one iteration process:

[0013] Obtain the initial temperature of this iteration and the initial spectral emissivity corresponding to each wavelength;

[0014] In the maximization step of the EM optimization strategy: Based on the initial spectral emissivity of each wavelength, use the free energy minimization method as the maximum likelihood function of the EM optimization strategy to calculate the optimal temperature as the hidden parameter of the EM optimization strategy;

[0015] In the expectation step of the EM optimization strategy: Based on the optimal temperature, obtain the spectral emissivity of each wavelength at this temperature and use the spectral emissivity fitting and smoothing method to obtain the smoothed spectral emissivity of each wavelength as the spectral emissivity expectation value corresponding to each wavelength;

[0016] Use the optimal temperature as the initial temperature for the next iteration, and use the spectral emissivity expectation value corresponding to each wavelength as the initial spectral emissivity for the next iteration, and iterate repeatedly;

[0017] When the spectral emissivity expectation value corresponding to each wavelength and the initial spectral emissivity of each wavelength satisfy the convergence condition, the obtained optimal temperature and the spectral emissivity of each wavelength are used as the temperature after inversion and the spectral emissivity corresponding to each wavelength, and the iteration ends.

[0018] Further, the optimal temperature is calculated using the free energy minimization method based on the initial spectral emissivity of each wavelength, where the formula for the free energy minimization method is:

[0019]

[0020]

[0021]

[0022] where, T opt is the optimal temperature; ΔA is the change in internal energy; C V is the heat capacity of the material; is the initial spectral emissivity at wavelength λ i ; I obs (λ i ) is the spectral radiance corresponding to the wavelength λ i ; I B (λ i , T opt ) is the spectral radiance of a perfect blackbody at wavelength λ i at temperature T opt .

[0023] Furthermore, the spectral emissivity at each wavelength at this temperature is obtained based on the optimal temperature using the following formula

[0024]

[0025] Furthermore, fitting and smoothing the spectral emissivity at each wavelength using the spectral emissivity fitting and smoothing method includes:

[0026] Obtaining the single-wavelength radiation entropy at each wavelength based on the spectral emissivity corresponding to each wavelength;

[0027] Using the high-order polynomial fitting method for the single-wavelength radiation entropy at each wavelength to obtain the smoothed wavelength radiation entropy;

[0028] Obtaining the fitted and smoothed spectral emissivity based on the smoothed wavelength radiation entropy.

[0029] Furthermore, the single-wavelength radiation entropy at each wavelength is obtained based on the following formula:

[0030]

[0031] where 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 number in the wavelength range to be fitted;

[0032] The high-order polynomial fitting method includes: for each wavelength, using the kernel function as a weight to perform local polynomial kernel regression to obtain a high-order polynomial as the regression function, and using the regression function to calculate the single-wavelength radiation entropy at each wavelength as the smoothed wavelength radiation entropy; where local polynomial kernel regression includes: selecting a preset number of wavelengths adjacent to this wavelength, and performing polynomial fitting based on the kernel function within this range;

[0033] Based on the smoothed wavelength radiation entropy, 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 at the smoothed wavelength λ i . is the single-wavelength radiation entropy at the smoothed wavelength λ i .

[0036] Furthermore, the regression function is:

[0037] H(λ i ) = a0 + a1λ i + a2λ i 2 + a3λ i 3 + … + a n λ i n

[0038] Among them, 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;

[0039] The coefficients of the polynomial function are calculated using the following formula:

[0040]

[0041] 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 vector of single-wavelength radiation entropies at each of the wavelengths.

[0042] Furthermore, the Vandermonde matrix X with respect to the wavelength is:

[0043]

[0044] Among them, λ is the smoothed wavelength; i is the i-th wavelength serial number; N is the preset quantity;

[0045] The diagonalized kernel function matrix K is:

[0046] K = diag(k(λ, λ i-N ), … k(λ, λ i ), … k(λ, λ i+N ))

[0047] Among them, k(λ, λ i ) is the kernel function.

[0048] Furthermore, in the first iteration process, the initial temperature is the maximum temperature T max;

[0049] During the first iteration, the initial spectral emissivity at each wavelength is obtained using the following formula based on the maximum temperature:

[0050]

[0051]

[0052] where, is the initial spectral emissivity at wavelength λ i ; T max is the maximum temperature; I obs (λ i ) is the spectral radiance corresponding to the wavelength λ i to be separated; I B (λ i , T max ) is the spectral radiance of a perfect blackbody at wavelength λ i at temperature T max ; C1 is the first radiation constant; C2 is the second radiation constant; e is the natural constant.

[0053] Furthermore, the blackbody temperature of each wavelength of the perfect blackbody is obtained using the following formula based on the spectral radiance at each wavelength:

[0054]

[0055] where, is the spectral radiance of a perfect blackbody at wavelength λ i at temperature ; C1 is the first radiation constant; C2 is the second radiation constant.

[0056] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0057] 1. The emissivity-temperature separation inversion algorithm used in the present invention can calculate and separate the spectral emissivity and temperature of a material only by relying on the heat capacity function of the material, and this function is known for most materials, with simple calculation and high reliability;

[0058] 2. 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;

[0059] 3. 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;

[0060] 4. The local polynomial kernel regression method used in the present invention can balance the short-range and long-range correlations 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.

[0061] In the present invention, the above technical solutions can also be combined with each other to achieve more preferred combined solutions. Other features and advantages of the present invention will be described in the subsequent description. Moreover, some advantages will be obvious from the description or can be understood by implementing the present invention. The objectives and other advantages of the present invention can be achieved and obtained from the content specifically pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] 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 denote the same components.

[0063] Figure 1 It is a schematic flowchart of a method for separating and inversely calculating the spectral emissivity and temperature of a material in an embodiment of the present invention;

[0064] Figure 2 It is a schematic flowchart of a spectral emissivity fitting and smoothing method in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0065] The following will specifically describe the preferred embodiments of the present invention with reference to the drawings. 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.

[0066] A specific embodiment of the present invention discloses a method for separating and inversely calculating the spectral emissivity and temperature of a material, as Figure 1 shown, including the following steps:

[0067] Step S1: Obtain the spectral radiance corresponding to each wavelength of the material within the wavelength range to be separated;

[0068] Specifically, use an instrument to measure the wavelengths and spectral radiance of the spectrum emitted by the material, i.e., the object to be measured, and remove the data with a signal-to-noise ratio greater than a certain threshold as incorrect data. Optionally, the measuring instrument can be a radiance meter or a spectral radiometer; the material can be a metal material, a semiconductor material, or a polymer organic material.

[0069] The wavelength range to be separated refers to the measurement range set by the instrument; each wavelength refers to a plurality of discrete wavelengths within the wavelength range to be separated.

[0070] Step S2: Obtain the blackbody temperature of each wavelength of the ideal blackbody based on the spectral radiance of each wavelength;

[0071] Specifically, according to Planck's quantum hypothesis, the blackbody temperature of each wavelength is obtained by the following formula based on the spectral radiance of each wavelength when the material is an ideal blackbody:

[0072]

[0073] wherein, is the spectral radiance of an ideal blackbody at wavelength λ i at temperature ; C1 is the first radiation constant with a value of 3.74×10 -16 (W×m 2 ); C2 is the second radiation constant with a value of 1.4398×10 -2 (m×K).

[0074] Step S3: Use the EM optimization strategy based on the spectral radiance corresponding to each wavelength and the blackbody temperature corresponding to each wavelength to obtain the temperature of the material after inversion and the spectral emissivity corresponding to each wavelength.

[0075] Specifically, the EM optimization strategy is an iterative optimization strategy. Each iteration in its calculation method is divided into two steps. One is the expectation step, i.e., the E step, and the other is the maximization step, i.e., the M step, which is to solve the parameter estimation problem in the case of missing data (including latent variables).

[0076] Furthermore, the basic idea of the EM optimization strategy is as follows: First, based on the observed data that has been given, estimate the values of the model parameters (initialization); then, based on the parameter values estimated in the previous step, estimate the values of the missing data, and then re - estimate the parameter values according to the estimated missing data plus the data that has been observed before, and then iterate repeatedly until convergence, and the iteration ends.

[0077] In this embodiment, the EM optimization strategy includes the following steps in one iteration process:

[0078] Step S301: Obtain the initial temperature of this iteration and the initial spectral emissivity corresponding to each wavelength;

[0079] Specifically, in the first iteration process, the initial temperature is the maximum temperature T max among the blackbody temperatures of each wavelength.

[0080] In the first iteration process, the initial spectral emissivity of each wavelength is obtained by the following formula based on the maximum temperature:

[0081]

[0082]

[0083] in, is the wavelength λ i The initial spectral emissivity of max is the maximum temperature; I obs (λ i ) is the wavelength to be separated λ i The corresponding spectral radiance; I B (λ i , T max ) is the wavelength λ i At temperature T max The spectral radiation brightness of an ideal black body at time; e is a natural constant.

[0084] Step S302, executing the maximization step of the EM optimization strategy: using the free energy minimization method as the maximum likelihood function of the EM optimization strategy based on the initial spectral emissivity of each wavelength to calculate the optimal temperature as the hidden parameter of the EM optimization strategy;

[0085] Specifically, when the emissivity of a certain wavelength point is calculated based on measured data, it is often implied that the data is under a certain temperature condition, and it is also implied that the emissivity of other wavelength points can be calculated based on the temperature, that is, the emissivity information obtained is related to the temperature.

[0086] In this embodiment, the emissivity-temperature separation algorithm based on free energy minimization refers to calculating entropy using spectral emissivity and calculating internal energy using material heat capacity, and achieving optimal temperature acquisition by minimizing free energy.

[0087] In statistics, KL divergence is generally used to measure the "distance" between two probability distribution functions, which can describe P to a certain extent. i and Q i The relative distance between two distributions:

[0088]

[0089] Similarly, in thermodynamics, the KL divergence corresponds to the sum of the entropy changes of the system and the environment in these two different states:

[0090]

[0091] Where λS is the change in entropy; ΔU env is the change in internal energy of the environment; ΔS sys is the entropy of the system; ΔS env is the entropy of the environment; T0 is the temperature.

[0092] Specifically, according to the definition of Holmhertz free energy:

[0093] A=U-TS

[0094] Assume that the volume and energy of the system can be neglected relative to the environment, and the temperature change of the environment before and after the energy exchange with the system can be neglected. Then, the total change in free energy of the system and the environment before and after the state change can be defined as:

[0095] ΔA = ΔU - TΔS = ΔU - TD KL (ε2||ε1)

[0096] Among them, ΔU is the change in internal energy of the system, which can be calculated through the heat capacity. The formula is:

[0097] ΔU = C v (T - T0)

[0098] Among them, C v is the heat capacity of the material, which is generally a function of temperature: C v (T) = f(T); Many scientists have accurately measured the heat capacity values of various substances at various temperatures by experimental methods and obtained empirical expressions representing the relationship between heat capacity and temperature.

[0099] Furthermore, the optimal temperature T is calculated using the free energy minimization method as the maximum likelihood function of the maximization step of the EM optimization strategy opt ;

[0100] Specifically, the formula of the free energy minimization method is:

[0101]

[0102]

[0103]

[0104] Among them, T opt is the optimal temperature, which is a hidden parameter of the EM optimization strategy; ΔA is the change in internal energy; C V is the heat capacity of the material; is the initial spectral emissivity at wavelength λ i ; I obs (λ i ) is the spectral radiance corresponding to the wavelength λ i to be separated; I B (λ i , T opt ) is the spectral radiance of the ideal blackbody at wavelength λ i at temperature T opt .

[0105] Step S303, perform the expected step of the EM optimization strategy: Based on the optimal temperature, obtain the spectral emissivity of each wavelength at this temperature and use the spectral emissivity fitting smoothing method to obtain the smoothed spectral emissivity of each wavelength as the spectral emissivity expectation value corresponding to each wavelength;

[0106] Specifically, use the following formula to calculate the spectral emissivity of each wavelength at the optimal temperature

[0107]

[0108] Furthermore, use the spectral emissivity fitting smoothing method to perform fitting smoothing on the spectral emissivity of each wavelength;

[0109] Specifically, during the measurement process, due to reasons such as detector noise, wavelength calibration, and stray radiation interference, the measured data is always accompanied by a large amount of fluctuations. Therefore, the calculated material spectral emissivity is also accompanied by a large amount of fluctuations. Effective fitting smoothing of the material's spectral emissivity is also very crucial in this embodiment.

[0110] Furthermore, as Figure 2 shown, the spectral emissivity fitting smoothing method includes:

[0111] Step S3031, obtain the single-wavelength radiation entropy of each wavelength based on the spectral emissivity corresponding to each wavelength;

[0112] Specifically, 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:

[0113]

[0114] where g(m) is the state degeneracy when exactly m particles radiate and de-excite, and its numerical value is indicating that there are g(m) microscopic states with the same energy.

[0115] Furthermore, from the above formula, it can be deduced that:

[0116] H λ =-N[ε λ lnε λ +(1 - ε λ )ln(1 - ε λ )]

[0117] Therefore, the single-wavelength radiation entropy of a single particle at each wavelength is:

[0118]

[0119] where, is the single-wavelength radiation entropy at wavelength λ i ; is the spectral emissivity corresponding to 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), the modulus of the calculation result is taken to obtain

[0120] 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.

[0121] Step S3032: Use the high-order polynomial fitting method for the single-wavelength radiation entropy of each wavelength to obtain the smoothed wavelength radiation entropy;

[0122] Specifically, the high-order polynomial fitting method includes: for each wavelength, using the kernel function as a weight to perform local polynomial kernel regression to obtain a high-order polynomial as the regression function, and using 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: selecting a preset number of wavelengths adjacent to this wavelength, and performing polynomial fitting based on the kernel function within this range.

[0123] 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 in the calculation; the larger the preset number range, the smoother the result. Preferably, the preset number N is selected to be 10 - 50.

[0124] 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.

[0125] Furthermore, the continuity and smoothness of the material spectral emissivity are due to the fact that the radiation entropy H λ at different wavelengths has smooth and continuous characteristics at the microscopic level.

[0126] Specifically, high-order polynomial fitting is a method commonly used 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.

[0127] ​The basic idea of high-order polynomial fitting is to find an optimal polynomial function to fit a given data set, so as to minimize 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.

[0128] Specifically, we can select an nth-order 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:

[0129] H(λ i ) = a0 + a1λ i + a2λ i 2 + a3λ i 3 + … + a n λ i n

[0130] where λ i is the wavelength value of the ith 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, so as to obtain an optimal polynomial function to fit the data.

[0131] 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 on 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.

[0132] Specifically, the order of the polynomial is from 2 to 11, preferably an odd order.

[0133] In this embodiment, the order is preferably 5.

[0134] As can be seen from the above, as long as the polynomial coefficients of the radiation entropy at different wavelengths are obtained, the emissivity of the material 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.

[0135] Therefore, in this embodiment, the kernel regression method is adopted to fit the entropy, so as to meet the requirements of smoothness and continuity while reducing the hard constraint of its long-range correlation.

[0136] 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 point for regression. Its essence is to use the kernel function as a weight function to establish a non-linear regression model.

[0137] 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):

[0138] J(θ) = (Xθ - Y) T K(Xθ - Y)

[0139] 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.

[0140] Therefore, according to the following coefficient calculation formula of the polynomial function can be obtained:

[0141]

[0142] Furthermore, the Vandermonde matrix X with respect to the wavelength is:

[0143]

[0144] where λ is the smoothed wavelength; i is the sequence number of the i-th wavelength currently selected; and N is the preset quantity.

[0145] 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.

[0146] Furthermore, the diagonalized kernel function matrix K is:

[0147] K = diag(k(λ, λ i-N ), … k(λ, λ i ), … k(λ, λ i+N ))

[0148] where k(λ, λ i ) is the kernel function; λ is the smoothed wavelength; i is the sequence number of the i-th wavelength currently selected; and N is the preset quantity.

[0149] Specifically, the kernel function defines the similarity measurement method of the input data in the feature space. Commonly used kernel functions include Gaussian kernel function, polynomial kernel function, sigmoid kernel function, etc.

[0150] Preferably, the Gaussian kernel function regression model is selected in the present invention:

[0151]

[0152] Among them, σ is the standard deviation.

[0153] 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.

[0154] Further, the single-wavelength radiation entropy vector of the wavelength is:

[0155]

[0156] 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.

[0157] Up to this point, after substituting the wavelength λ i into the regression function H(λ), the calculated H(λ i ) is the entropy after smoothing for this wavelength

[0158] Step S3033: Obtain the fitted and smoothed spectral emissivity based on the smoothed wavelength radiation entropy.

[0159] Specifically, based on the smoothed wavelength radiation entropy, the fitted and smoothed spectral emissivity of the wavelength range to be fitted is obtained using the following formula:

[0160]

[0161] Among them, is the spectral emissivity of the smoothed wavelength λ i , which is the expected value of the spectral emissivity of the wavelength λ i for this iteration; is the single-wavelength radiation entropy of the smoothed wavelength λ i .

[0162] Step S304: Use the optimal temperature as the initial temperature for the next iteration, and use the expected values of the spectral emissivities corresponding to each wavelength as the initial spectral emissivities for the next iteration, and iterate repeatedly;

[0163] Step S305: When the expected values of the spectral emissivities corresponding to each wavelength and the initial spectral emissivities of each wavelength satisfy the convergence condition, the obtained optimal temperature and the spectral emissivities of each wavelength are used as the temperature after inversion and the spectral emissivities corresponding to each wavelength, and the iteration ends.

[0164] Specifically, the method for judging the convergence condition is to calculate the value of, and when it is less than a specific value, it is judged that the convergence condition is satisfied.

[0165] It should be noted that the specific value can be adjusted according to the actual situation and accuracy requirements; in this embodiment, the specific value is taken as 1E-8.

[0166] Furthermore, in this embodiment, the Anderson acceleration algorithm is preferably used to accelerate the iteration process of the EM optimization strategy, which can greatly improve the algorithm convergence speed.

[0167] In summary, a method for separating and inversely calculating the spectral emissivity - temperature of a material according to an embodiment of the present invention has the following beneficial effects:

[0168] 1. The emissivity - temperature separation inversion algorithm used in the present invention can separately calculate the spectral emissivity and temperature of the material only by relying on the heat capacity function of the material, and this function is known for most materials, with simple calculation and high reliability;

[0169] 2. 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 very clear physical meanings and satisfies various physical constraint conditions of the emissivity;

[0170] 3. The present invention uses a high - order polynomial to fit the spectral radiation entropy, which satisfies the requirements of smoothness and continuity, and at the same time has a fast operation speed and a wide application range;

[0171] 4. The local polynomial kernel regression method used in the present invention can balance the short - range and long - range correlations 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.

[0172] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of 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 separating and inversely retrieving the spectral emissivity - temperature of a material, characterized in that, It includes the following steps: Obtain the spectral radiance corresponding to each wavelength of the material within the wavelength range to be separated; Based on the spectral radiance corresponding to each wavelength, obtain the blackbody temperature corresponding to each wavelength of an ideal blackbody; Based on the spectral radiance corresponding to each wavelength and the blackbody temperature corresponding to each wavelength, use the EM optimization strategy to obtain the temperature of the material after inversion and the spectral emissivity corresponding to each wavelength.

2. The method according to claim 1, characterized in that When using the EM optimization strategy to obtain the temperature of the material after inversion and the spectral emissivity corresponding to each wavelength, in one iteration process: Obtain the initial temperature of this iteration and the initial spectral emissivity corresponding to each wavelength; In the maximization step of the EM optimization strategy: Based on the initial spectral emissivity of each wavelength, use the free energy minimization method as the maximum likelihood function of the EM optimization strategy to calculate the optimal temperature as the hidden parameter of the EM optimization strategy; In the expectation step of the EM optimization strategy: Based on the optimal temperature, obtain the spectral emissivity of each wavelength at this temperature and use the spectral emissivity fitting and smoothing method to obtain the smoothed spectral emissivity of each wavelength as the spectral emissivity expectation value corresponding to each wavelength; Use the optimal temperature as the initial temperature of the next iteration, and use the spectral emissivity expectation value corresponding to each wavelength as the initial spectral emissivity of the next iteration, and iterate repeatedly; When the spectral emissivity expectation value corresponding to each wavelength and the initial spectral emissivity of each wavelength satisfy the convergence condition, the obtained optimal temperature and the spectral emissivity corresponding to each wavelength are used as the temperature after inversion and the spectral emissivity corresponding to each wavelength, and the iteration ends.

3. The method according to claim 2, wherein When calculating the optimal temperature based on the initial spectral emissivity of each wavelength using the free energy minimization method, where the formula of the free energy minimization method is: Among them, T opt is the optimal temperature; ΔA is the change in internal energy; C V is the heat capacity of the material; is the initial spectral emissivity at wavelength λ i ; I obs (λ i ) is the spectral radiance corresponding to the wavelength λ i to be separated; I B (λ i , T opt ) is the spectral radiance of a perfect blackbody at wavelength λ i at temperature T opt .

4. The method according to claim 3, wherein Based on the optimal temperature, the spectral emissivity of each of the wavelengths at this temperature is obtained using the following formula 5. The method according to claim 4, wherein When using the spectral emissivity fitting and smoothing method to fit and smooth the spectral emissivity of each wavelength, it includes: Based on the spectral emissivity corresponding to each wavelength, obtain the single-wavelength radiation entropy of 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; Based on the smoothed wavelength radiation entropy, obtain the fitted and smoothed spectral emissivity.

6. The method according to claim 5, characterized in that, Based on the following formula, obtain the single-wavelength radiation entropy of each wavelength: 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. 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; 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; Based on the smoothed wavelength radiation entropy, use the following formula to obtain the fitted and smoothed spectral emissivity of the wavelength range to be fitted: Among them, is the spectral emissivity at the smoothed wavelength λ i ; is the single-wavelength radiation entropy at the smoothed wavelength λ i .

7. The method according to claim 6, characterized in that, The regression function is: H(λ i ) = a0 + a1λ i + a2λ i 2 + a3λ i 3 +…+ a n λ i n Among them, 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; The coefficients of the polynomial function are calculated using the following formula: Where θ is the coefficient vector of the polynomial function; X is the Vandermonde matrix about the wavelength; K is the diagonalized kernel function matrix; Y is the vector of the single-wavelength radiation entropy of each wavelength.

8. The method according to claim 7, wherein The Vandermonde matrix X about the wavelength is: Wherein, λ is the wavelength after smoothing; i is the serial number of the i-th wavelength; N is the preset quantity; The diagonalized kernel function matrix K 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.

9. The method according to claim 2, characterized in that During the first iteration, the initial temperature is the maximum temperature T among the blackbody temperatures of each of the wavelengths max ; In the first iteration process, the initial spectral emissivity at each wavelength is obtained by using the following formula based on the maximum temperature: wherein, is the initial spectral emissivity at wavelength λ i ; T max is the maximum value of the temperature; I obs (λ i ) is the spectral radiance corresponding to the wavelength λ i to be separated; I B (λ i , T max ) is the spectral radiance of a perfect blackbody at wavelength λ i at temperature T max ; C1 is the first radiation constant; C2 is the second radiation constant; e is the natural constant.

10. The method according to claim 1, wherein Based on the spectral radiance at each wavelength, the blackbody temperature at each wavelength of the ideal blackbody is obtained by using the following formula: wherein, is the spectral radiance of a perfect blackbody at a wavelength λ i at a temperature ; C1 is the first radiation constant; C2 is the second radiation constant.

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