Temperature field imaging method based on free energy minimization

Abstract

The invention relates to a temperature field imaging method based on free energy minimization, and belongs to the technical field of temperature field temperature distribution monitoring. Comprising the following steps: acquiring a multispectral image of a to-be-measured temperature field; wherein each pixel point in the multispectral image comprises a plurality of wavelengths and corresponding gray values; the pixel points comprise background pixel points and object pixel points; based on each wavelength and the corresponding gray value of each object pixel point, using pre-calibrated gray value-spectral radiation brightness corresponding data to obtain spectral radiation brightness corresponding to each wavelength of each object pixel point in the multispectral image; based on each wavelength of each object pixel point and the corresponding spectral radiation brightness, obtaining the temperature of each object pixel point by using a spectral emissivity temperature separation inversion method based on free energy minimization; and obtaining a temperature distribution diagram of the temperature field based on the temperature of each object pixel point. The accurate and efficient inversion of the temperature distribution state of the temperature field is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of temperature distribution monitoring in a temperature field, and particularly to a temperature field imaging method based on free energy minimization. Background Art

[0002] High-temperature measurement is of great significance in many scientific research and industrial applications. Understanding the behavior and properties of substances under extreme conditions relies on the support of high-temperature measurement techniques.

[0003] In the aerospace field, high-temperature measurement techniques have extensive applications. In terms of high-temperature structure monitoring, when aerospace vehicles re-enter the atmosphere, the heat generated by high-speed friction will cause the temperature on the surfaces of wings and fuselages to rise sharply. At this time, using high-temperature measurement techniques, the temperature on the surfaces of these structures can be monitored in real time to prevent problems such as burning or deformation caused by excessive temperature, thus ensuring the safety of the aircraft. In terms of high-temperature monitoring of propulsion systems, the engines and rocket propulsion systems of aerospace vehicles will generate extremely high temperatures during operation. Real-time monitoring of the temperature of these parts can ensure the normal operation of the propulsion system to prevent accidents such as combustion and explosion. In terms of high-temperature gas flow monitoring, when aerospace vehicles fly at high speeds, the gas flow on the surfaces of wings and fuselages will be very intense, and these flowing high-temperature gases will affect the performance and stability of the aircraft. Through high-temperature measurement techniques, the situation of these high-temperature gas flows can be monitored in real time, thereby optimizing the design and performance of the aircraft.

[0004] Existing multi-spectral temperature inversion algorithms, such as those using visible light, infrared bands, or thermal infrared bands for inversion, although they can achieve the inversion of emissivity and temperature, still have some deficiencies in practical applications, mainly including: some prior knowledge may be difficult to obtain or there may be uncertainties, such as the spectral characteristics of known target objects, environmental conditions, etc., thus affecting the accuracy and reliability of the inversion results; the target object may be in a non-thermal equilibrium state, resulting in inaccuracies and uncertainties in the inversion results; and usually a large amount of data needs to be processed and complex calculations need to be carried out, such as multivariate spectral analysis, neural networks, etc., which limits its feasibility and popularity in practical applications.

[0005] Therefore, in view of the above problems, there is an urgent need to propose a temperature imaging inversion method to make up for the deficiencies of traditional multi-spectral temperature measurement methods. Summary of the Invention

[0006] In view of the above analysis, the embodiments of the present invention aim to provide a temperature field imaging method based on free energy minimization to solve the problems of low accuracy and complex calculation of existing multi-spectral temperature measurement.

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

[0008] The present invention provides a temperature field imaging method based on free energy minimization, including the following steps:

[0009] Obtain a multi-spectral image of the temperature field to be measured; wherein, each pixel in the multi-spectral image includes multiple wavelengths and corresponding gray values; the pixel points include background pixel points and object pixel points;

[0010] Based on the wavelengths and corresponding gray values of each object pixel point, use the pre-calibrated gray value-spectral radiance correspondence data to obtain the spectral radiance corresponding to each wavelength of each object pixel point in the multi-spectral image;

[0011] Based on the wavelengths and their corresponding spectral radiance of each object pixel point, use the spectral emissivity-temperature separation inversion method based on free energy minimization to obtain the temperature of each object pixel point;

[0012] Based on the temperatures of each object pixel point, obtain the temperature distribution map of the temperature field.

[0013] Further, the obtaining of the multi-spectral image of the temperature field to be measured includes:

[0014] Use an optical receiving system to receive the light emitted by the temperature field to be measured;

[0015] The light passing through the optical receiving system is divided into spectra of several wavelengths by a prism spectrometer;

[0016] The spectra of each wavelength respectively enter the corresponding detectors to obtain the gray values corresponding to each spectrum;

[0017] Generate a multi-spectral image based on the wavelengths and corresponding gray values of each spectrum.

[0018] Further, based on a pre-set gray threshold, judge the gray values corresponding to each wavelength of each pixel point in the multi-spectral image. When the gray values corresponding to each wavelength of the pixel point are all lower than the threshold, the pixel point is used as a background pixel point, and the remaining pixel points in the multi-spectral image are used as object pixel points.

[0019] Further, traverse the object pixel points in the multi-spectral image, and use the spectral emissivity-temperature separation inversion method based on free energy minimization for each object pixel point to obtain the temperature of each object pixel point, including:

[0020] Based on the spectral radiance corresponding to each wavelength of the object pixel point, obtain the blackbody radiation temperature of each wavelength;

[0021] Based on the maximum temperature T in the blackbody radiation temperatures of each wavelength max, obtain the equivalent spectral emissivity of each of the wavelengths;

[0022] Based on the maximum temperature T max and the equivalent spectral emissivity of each of the wavelengths, use the EM optimization strategy to obtain the temperature of the object pixel point after inversion.

[0023] Further, based on the spectral radiance corresponding to each of the wavelengths, use Planck's formula to obtain the blackbody radiation temperature of each of the wavelengths, and obtain the maximum temperature T max .

[0024] Further, based on the maximum temperature T max among the blackbody radiation temperatures of each of the wavelengths, use the following formula to obtain the equivalent spectral emissivity of each of the wavelengths

[0025]

[0026] where is the equivalent 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 to be separated i ; I B (λ i , T max ) is the spectral radiance of an ideal blackbody at wavelength λ i at temperature T max .

[0027] Further, the step of using the EM optimization strategy to obtain the temperature of the object pixel point after inversion based on the maximum temperature T max and the equivalent spectral emissivity of each of the wavelengths includes:

[0028] Take the maximum temperature T max and the equivalent spectral emissivity of each of the wavelengths as the initial temperature of the first iteration of the EM optimization strategy and the initial spectral emissivity of each of the wavelengths;

[0029] In the maximization step of the EM optimization strategy: Based on the initial spectral emissivity of each of the wavelengths, 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;

[0030] In the expectation step of the EM optimization strategy: Based on the optimal temperature, obtain the spectral emissivity of each of the wavelengths at this temperature as the spectral emissivity expectation value corresponding to each wavelength;

[0031] Use the optimal temperature and the expected values of spectral emissivities corresponding to each of the wavelengths as the initial temperature for the next iteration and the initial spectral emissivities for each of the wavelengths;

[0032] When the expected values of spectral emissivities corresponding to each of the wavelengths and the initial spectral emissivities for each of the wavelengths satisfy the convergence condition, the obtained optimal temperature is used as the temperature of the object pixel point after inversion, and the iteration ends.

[0033] Further, the optimal temperature T obtained by using the free energy minimization method opt , and its formula is as follows:

[0034]

[0035]

[0036] wherein, 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 ; is the spectral emissivity of the material at wavelength λ i at temperature T opt .

[0037] Further, based on the optimal temperature, the spectral emissivities at each of the wavelengths at this temperature are obtained using the following formula

[0038]

[0039] Further, the convergence condition of the EM optimization strategy is to calculate value, and when it is less than a preset value, the iteration ends.

[0040] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0041] 1. The multi-spectral image imaging method used in the present invention can, based on the image segmentation result, use the emissivity temperature inversion calculation method to calculate the temperatures of each point on the image respectively, and can monitor the temperature distribution of the entire temperature field in real time.

[0042] 2. The emissivity temperature inversion calculation method 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.

[0043] 3. The present invention uses a hyperspectral emissivity fitting and smoothing method, 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, makes the smoothed emissivity have a very clear physical meaning, and satisfies various physical constraints of the emissivity. Moreover, a high-order polynomial is used to fit the spectral radiation entropy, which meets the requirements of smoothing and continuity, and has a fast operation speed.

[0044] 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 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 achieved and obtained from the content specifically pointed out in the specification and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] 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.

[0046] Figure 1 It is a schematic flow chart of a temperature field imaging method based on free energy minimization in an embodiment of the present invention;

[0047] Figure 2 It is a schematic flow chart of a spectral emissivity temperature separation and inversion method in an embodiment of the present invention;

[0048] Figure 3 It is a schematic diagram of the iterative process of the EM optimization strategy in an embodiment of the present invention;

[0049] Figure 4 It is a schematic flow chart of a spectral emissivity fitting and smoothing method in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0050] The following will specifically describe the preferred embodiments of the present invention in conjunction with 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.

[0051] A specific embodiment of the present invention discloses a temperature field imaging method based on free energy minimization, as Figure 1 shown, including the following steps:

[0052] Step S1, obtain a multi-spectral image of the temperature field to be measured; wherein, each pixel point in the multi-spectral image includes multiple wavelengths and corresponding gray values; the pixel points include background pixel points and object pixel points;

[0053] Specifically, a multi-spectral image refers to an image containing several channels (2 - 100 channels). Each channel is a grayscale image representing the scene brightness obtained according to the sensitivity of the sensor used to generate the band.

[0054] Furthermore, the method for obtaining a multi-spectral image is as follows: Use an optical receiving system to receive the light emitted by the temperature field to be measured; the light passing through the optical receiving system is split into spectra of several wavelengths by a prism beam splitter; the spectra of each wavelength enter the corresponding detectors respectively to obtain the grayscale values corresponding to each spectrum; based on the wavelengths of each spectrum and the corresponding grayscale values, a multi-spectral image is generated.

[0055] Specifically, the detector is an instrument that outputs grayscale values according to image elements; the number of detectors is the same as the number of wavelengths split by the prism beam splitter.

[0056] Furthermore, based on a preset grayscale threshold, the grayscale values corresponding to each wavelength of each pixel point in the multi-spectral image are judged. When the grayscale values corresponding to each wavelength of a pixel point are all lower than the threshold, this pixel point is used as a background pixel point, and the remaining pixel points in the multi-spectral image are used as object pixel points.

[0057] Step S2: Based on the wavelengths and the corresponding grayscale values of each object pixel point, use the pre-calibrated grayscale value - spectral radiance corresponding data to obtain the spectral radiance corresponding to each wavelength of each object pixel point in the multi-spectral image;

[0058] Specifically, the pre-calibrated data is grayscale value - spectral radiance value corresponding data.

[0059] Step S3: Based on the wavelengths and the corresponding spectral radiance of each object pixel point, use the spectral emissivity temperature separation inversion method based on free energy minimization to obtain the temperature of each object pixel point;

[0060] Specifically, traverse the object pixel points in the multi-spectral image. As Figure 2 shown, for each object pixel point, use the spectral emissivity temperature separation inversion method based on free energy minimization to obtain the temperature of each object pixel point, including:

[0061] Step S301: Based on the spectral radiance corresponding to each wavelength of the object pixel point, obtain the blackbody radiation temperature of each wavelength;

[0062] Specifically, according to Planck's quantum hypothesis, based on the spectral radiance corresponding to each wavelength of the object pixel point, use the following formula to obtain the blackbody temperature of each wavelength when the material is an ideal blackbody:

[0063]

[0064] Among them, is the spectral radiance of an ideal black body 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).

[0065] Step S302: Based on the maximum temperature T max among the blackbody radiation temperatures of each wavelength, obtain the equivalent spectral emissivity of each wavelength;

[0066] Specifically, the formula for obtaining the equivalent spectral emissivity of each wavelength based on the surface emissivity of an object is:

[0067]

[0068]

[0069] Among them, 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 an ideal black body at wavelength λ i at temperature T max ; 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); e is the natural constant.

[0070] Step S303: Based on the maximum temperature T max and the equivalent spectral emissivity of each wavelength, use the EM optimization strategy to obtain the temperature of the object pixel point after inversion.

[0071] 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).

[0072] Furthermore, the basic idea of the EM optimization strategy is as follows: First, based on the given observed data, 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. Next, based on the estimated missing data and the previously observed data, re-estimate the parameter values, and then iterate repeatedly until convergence, at which point the iteration ends.

[0073] Furthermore, as Figure 3 shown, the iterative process of the EM optimization strategy includes the following steps:

[0074] Step S3031: Use the maximum temperature T max and the equivalent spectral emissivity at each wavelength as the initial temperature and the initial spectral emissivity at each wavelength for the first iteration of the EM optimization strategy;

[0075] Step S3032: In the maximization step of the EM optimization strategy: Based on the initial spectral emissivity at 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;

[0076] Specifically, when calculating the emissivity at a certain wavelength point based on the measured data, it often implies that the data is under a certain temperature condition, and it also implies that the emissivities at other wavelength points can be calculated based on this temperature, that is, the obtained emissivity information is related to the temperature.

[0077] In this embodiment, the emissivity-temperature separation algorithm based on free energy minimization refers to calculating the entropy using the spectral emissivity and calculating the internal energy using the material heat capacity, and obtaining the optimal temperature through free energy minimization.

[0078] In statistics, the KL divergence is generally used to measure the "distance" between two probability distribution functions, and can describe the relative distance between two distributions P i and Q i to a certain extent:

[0079]

[0080] 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:

[0081]

[0082] where ΔS is the change in entropy; ΔU env is the change in the 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.

[0083] Specifically, according to the definition of Helmholtz free energy:

[0084] A = U - TS

[0085] Assume that the volume and energy of the system can be ignored relative to the environment, and the temperature change of the environment before and after energy exchange with the system can be ignored. Then, the total free energy change of the system and the environment before and after the state change can be defined as:

[0086] ΔA = ΔU - TΔS = ΔU - TD KL (ε2||ε1)

[0087] Among them, ΔU is the change in the internal energy of the system, which can be calculated through the heat capacity. The formula is:

[0088] ΔU = C v (T - T0)

[0089] 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 different temperatures by experimental methods and obtained the empirical expressions representing the relationship between heat capacity and temperature.

[0090] 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 ;

[0091] Specifically, the formula of the free energy minimization method is:

[0092]

[0093]

[0094]

[0095] Among them, T opt is the optimal temperature and is the 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 to be separated i ; I B (λ i , T opt ) is the spectral radiance of the ideal blackbody at wavelength λ i at temperature T opt .

[0096] Step S3033, in the expected step of the EM optimization strategy: based on the optimal temperature, obtain the spectral emissivity of each wavelength at this temperature as the expected value of the spectral emissivity corresponding to each wavelength;

[0097] Specifically, use the following formula to calculate the spectral emissivity of each wavelength at the optimal temperature

[0098]

[0099] Furthermore, 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. It is also very crucial to effectively fit and smooth the spectral emissivity of the material in this embodiment.

[0100] Specifically, as Figure 4 shown, use the spectral emissivity fitting and smoothing method to fit and smooth the spectral emissivity of each wavelength, including the following steps:

[0101] Step S30331: Obtain the single-wavelength radiation entropy of each wavelength based on the spectral emissivity corresponding to each wavelength;

[0102] 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:

[0103]

[0104] 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.

[0105] Furthermore, from the above formula, it can be deduced that:

[0106] H λ =-N[ε λ lnε λ +(1 - ε λ )ln(1 - ε λ )]

[0107] Therefore, the single-wavelength radiation entropy of a single particle at each wavelength is:

[0108]

[0109] where, is the single-wavelength radiation entropy of wavelength λ i ; is the spectral emissivity corresponding to the wavelength λ; in order 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

[0110] 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.

[0111] Step S30332, use the high-order polynomial fitting method for the single-wavelength radiation entropy of each of the said wavelengths to obtain the smoothed wavelength radiation entropy;

[0112] Specifically, 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 of the said wavelengths 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.

[0113] 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.

[0114] 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.

[0115] 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.

[0116] Specifically, high-order polynomial fitting is a commonly used method in data analysis and machine learning, which 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.

[0117] ​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 using the least squares method.

[0118] Specifically, we can choose 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:

[0119] H(λ i ) = a0 + a1λ i + a2λ i 2 + a3λ i 3 + … + a n λ i n

[0120] 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 using the least squares method, we can solve the optimal values of these coefficients, thereby obtaining an optimal polynomial function to fit the data.

[0121] It should be noted that high-order polynomial fitting may cause overfitting problems 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.

[0122] Specifically, the order of the polynomial is from 2 to 11, preferably an odd order.

[0123] In this embodiment, the order is preferably 5.

[0124] 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 a strong long-range correlation, which does not conform to the actual material characteristics.

[0125] Therefore, in this embodiment, kernel regression 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.

[0126] 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 uses only 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.

[0127] 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):

[0128] J(θ) = (Xθ - Y) T K(Xθ - Y)

[0129] 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.

[0130] Therefore, according to the coefficient calculation formula of the polynomial function can be obtained:

[0131]

[0132] Furthermore, the Vandermonde matrix X with respect to the wavelength is:

[0133]

[0134] where λ is the smoothed wavelength; i is the sequence number of the i-th wavelength currently selected; and N is the preset quantity.

[0135] 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.

[0136] Furthermore, the diagonalized kernel function matrix K is:

[0137] K = diag(k(λ,λ i-N ),…k(λ,λ i ),…k(λ,λ i+N ))

[0138] 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.

[0139] 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.

[0140] Preferably, the Gaussian kernel function regression model is selected in the present invention:

[0141]

[0142] Among them, σ is the standard deviation.

[0143] 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.

[0144] Furthermore, the single-wavelength radiation entropy vector of the wavelength is:

[0145]

[0146] Among them, is the single-wavelength radiation entropy of wavelength λ i ; i is the i-th wavelength serial number selected currently; N is the preset quantity.

[0147] 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 of this wavelength

[0148] Step S30333: Obtain the fitted and smoothed spectral emissivity based on the smoothed wavelength radiation entropy.

[0149] 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:

[0150]

[0151] Among them, is the spectral emissivity of the smoothed wavelength λ i , which is the spectral emissivity expectation value of the wavelength λ i in this iteration; is the single-wavelength radiation entropy of the smoothed wavelength λ i .

[0152] Step S3034: Use the optimal temperature and the spectral emissivity expectation values corresponding to each wavelength as the initial temperature and the initial spectral emissivities of each wavelength for the next iteration;

[0153] Step S3035: When the spectral emissivity expectation values corresponding to each wavelength and the initial spectral emissivities of each wavelength satisfy the convergence condition, use the obtained optimal temperature as the temperature of the object pixel point after inversion, and end the iteration.

[0154] 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.

[0155] 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 1E-8.

[0156] Furthermore, in this embodiment, the Anderson acceleration algorithm is preferably used to accelerate the EM optimization strategy iteration process, which can greatly improve the algorithm convergence speed.

[0157] Step S4: Obtain the temperature distribution map of the temperature field based on the temperatures of the respective object pixel points.

[0158] In summary, a temperature field imaging method based on free energy minimization according to an embodiment of the present invention has the following beneficial effects:

[0159] 1. The multi-spectral image imaging method used in the present invention can calculate the temperatures of each point on the image respectively using the emissivity temperature inversion calculation method based on the image segmentation result, and can monitor the temperature distribution of the entire temperature field in real time.

[0160] 2. The emissivity temperature inversion calculation method 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.

[0161] 3. The present invention uses a hyperspectral emissivity fitting and smoothing method, a physical modeling method for the spectral emissivity characteristics of materials based on probability, which clarifies the relationship between entropy and the spectral emissivity of materials, making the smoothed emissivity have a very clear physical meaning, satisfying various physical constraint conditions of emissivity, and using a high-order polynomial to fit the spectral radiation entropy, meeting the requirements of smoothing and continuity, and having a fast operation speed.

[0162] The above is only a specific and preferred 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 by the protection scope of the present invention.

Claims

1. A temperature field imaging method based on free energy minimization, characterized in that The method includes the following steps: Obtain a multi-spectral image of the temperature field to be measured; wherein, each pixel in the multi-spectral image includes multiple wavelengths and corresponding gray values; the pixels include background pixels and object pixels; Based on the wavelengths and corresponding gray values of each object pixel, use the pre-calibrated gray value - spectral radiance correspondence data to obtain the spectral radiance corresponding to each wavelength of each object pixel in the multi-spectral image; Based on the wavelengths and corresponding spectral radiances of each object pixel, use the spectral emissivity temperature separation inversion method based on free energy minimization to obtain the temperature of each object pixel; Based on the temperatures of each object pixel, obtain the temperature distribution map of the temperature field.

2. The method according to claim 1, wherein The obtaining of the multi-spectral image of the temperature field to be measured includes: Use an optical receiving system to receive the light emitted by the temperature field to be measured; The light passing through the optical receiving system is split into spectra of several wavelengths by a prism spectrometer; The spectra of each wavelength respectively enter the corresponding detectors to obtain the gray values corresponding to each spectrum; Based on the wavelengths and corresponding gray values of each spectrum, generate a multi-spectral image.

3. The method according to claim 2, wherein Based on a pre-set gray threshold, judge the gray values corresponding to each wavelength of each pixel in the multi-spectral image. When the gray values corresponding to each wavelength of a pixel are all lower than the threshold, this pixel is used as a background pixel, and the remaining pixels in the multi-spectral image are used as object pixels.

4. The method according to claim 3, wherein Traverse the object pixels in the multi-spectral image. For each object pixel, use the spectral emissivity temperature separation inversion method based on free energy minimization to obtain the temperature of each object pixel, including: Based on the spectral radiance corresponding to each wavelength of the object pixel, obtain the blackbody radiation temperature of each wavelength; The maximum temperature T among the blackbody radiation temperatures at each of the wavelengths max , to obtain the equivalent spectral emissivity at each of the wavelengths; Based on the maximum temperature T max and the equivalent spectral emissivity at each of the wavelengths, the temperature of the object pixel after inversion is obtained using the EM optimization strategy.

5. The method according to claim 4, characterized in that, Based on the spectral radiance corresponding to each of the wavelengths, the blackbody radiation temperature of each of the wavelengths is obtained using Planck's formula, and the maximum temperature value T among them is obtained. max .

6. The method according to claim 5, wherein The maximum temperature T among the blackbody radiation temperatures at each of the wavelengths max , and the equivalent spectral emissivity at each of the wavelengths is obtained using the following formula Among them, is the equivalent 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 .

7. The method according to any one of claims 4-6, characterized in that, Based on the maximum temperature T max and the equivalent spectral emissivity at each wavelength using the EM optimization strategy to obtain the temperature of the object pixel points after inversion, including: Take the maximum temperature T max and the equivalent spectral emissivity of each of the wavelengths as the initial temperature for the first iteration of the EM optimization strategy and the initial spectral emissivity of each of the wavelengths; 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 as the spectral emissivity expectation value corresponding to each wavelength; Use the optimal temperature and the spectral emissivity expectation values corresponding to each wavelength as the initial temperature and the initial spectral emissivity of each wavelength for the next iteration; When the spectral emissivity expectation values corresponding to each wavelength and the initial spectral emissivity of each wavelength satisfy the convergence condition, the obtained optimal temperature is used as the temperature of the object pixel after inversion, and the iteration ends.

8. The method according to claim 7, wherein The optimal temperature T calculated using the free energy minimization method opt , and its formula is as follows: 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 ; is the spectral emissivity of the material at wavelength λ i at temperature T opt .

9. The method according to claim 8, wherein Based on the optimal temperature, the spectral emissivity at each of the wavelengths at this temperature is obtained using the following formula 10. The method according to claim 7, characterized in that The convergence condition of the EM optimization strategy is to calculate and end the iteration when its value is less than a pre-set value.

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