Method for measuring section temperature and non-uniform absorption coefficient distribution through multispectral imaging

Abstract

The invention discloses a method for measuring section temperature and non-uniform absorption coefficient distribution through multispectral imaging. The method comprises the following steps: measuring flame boundary radiation intensity under two wavelengths; setting an initial uniform absorption coefficient, and calculating a DRESOR coefficient matrix under each wavelength through a DRESOR method; solving medium temperature distribution by combining a DRESOR coefficient matrix and a modified Tikhonov regularization method, and updating a uniform absorption coefficient based on a residual minimization principle and a Newton iteration method; after medium temperature distribution is obtained, the temperature distribution is fixed, and non-uniform absorption coefficient distribution is obtained through flame boundary radiation intensity inversion; and when a residual error minimization condition is satisfied or a maximum iteration frequency is reached, outputting a final section temperature distribution and non-uniform absorption coefficient distribution result. By means of the scheme, high-precision section temperature and non-uniform absorption coefficient distribution can be obtained based on multispectral imaging information, the result is reliable, and precision is high.

Description

Technical Field

[0001] This invention relates to the field of spectroscopy, specifically to a method for obtaining cross-sectional temperature distribution and non-uniform absorption coefficient distribution based on multispectral image data inversion. Background Technology

[0002] In hypersonic propulsion technology, the scramjet engine is a key component. Its combustion chamber contains intense combustion reactions and hypersonic airflow, and the coupling of these two factors can easily lead to instability phenomena such as flame oscillation and blowout. The cross-sectional temperature distribution within the combustion chamber is not only a crucial parameter characterizing combustion intensity and heat release characteristics, but also an important basis for assessing flame stability and diagnosing combustion inhomogeneity. Simultaneously, in the high-temperature non-uniform flow field caused by airflow variations, fuel distribution, and boundary layer effects, the non-uniform distribution of particulate matter directly affects radiation absorption characteristics, jointly determining the spectral radiation intensity distribution of the flame along with the temperature distribution. Therefore, accurately reconstructing the cross-sectional temperature distribution and the non-uniform absorption coefficient distribution is of great significance for a deeper understanding of the combustion state of the scramjet engine combustion chamber. It is also crucial for analyzing the distribution of combustion products, heat loss mechanisms, and combustion efficiency. However, traditional contact temperature measurement methods are difficult to achieve large-scale, non-disturbance, and precise measurements in high-temperature, high-speed, and spatially non-uniform environments. Multispectral imaging radiometry, with its high spatial and spectral resolution, can simultaneously acquire radiation information at different wavelengths, providing a feasible approach for the joint inversion of cross-sectional temperature and non-uniform absorption coefficient.

[0003] Technical solution

[0004] This invention provides a method for measuring cross-sectional temperature and non-uniform absorption coefficient distribution using multispectral imaging. This method can derive high-precision cross-sectional temperature and non-uniform absorption coefficient distribution based on multispectral imaging information.

[0005] The technical solution used in this invention includes the following steps:

[0006] Step 1: Measure the flame boundary radiation intensity at two wavelengths;

[0007] Step 2: Set the initial uniform absorption coefficient;

[0008] Step 3: Calculate the DRESOR coefficient matrix for each wavelength using the DRESOR method;

[0009] Step 4: Combine the DRESOR coefficient matrix with the modified Tikhonov regularization method to solve for the medium temperature distribution, and update the uniform absorption coefficient based on the principle of residual minimization and Newton's iteration method;

[0010] Step 5: After obtaining the temperature distribution of the medium, fix the temperature distribution and use the flame boundary radiation intensity inversion to obtain the non-uniform absorption coefficient distribution;

[0011] Step 6: Repeat steps 3 to 5 until the residual satisfies the minimization condition or reaches the maximum number of iterations; take the medium temperature distribution obtained when the convergence condition is met as the final cross-sectional temperature distribution, and output it together with the non-uniform absorption coefficient distribution.

[0012] In the above technical solution of the present invention, in step 3, based on the current uniform absorption coefficient, the DRESOR coefficient matrix corresponding to the two wavelengths is calculated using the DRESOR method, and the measured flame boundary radiation intensity is expressed as a coupling function of the medium temperature distribution and the absorption coefficient distribution.

[0013]

[0014] Among them, I λ (j) represents the flame boundary radiation intensity, in W / m². 3 / sr;T i λ represents the medium temperature in Kelvin (K); λ represents the wavelength in meters (m); C1 and C2 are 3.7418 × 10⁻⁶ respectively. -16 W·m 2 1.4388×10 -2 m·K is Planck's constant, ΔV represents the volume of a spatial unit, j represents the number of pixels, and R d κ represents the DRESOR number and the absorption coefficient.

[0015] In step 3, equation (1) is rewritten in matrix form as follows:

[0016] I λ =B I I bλ (T) (2)

[0017] In the formula, I λ I is the matrix form of the flame boundary radiation intensity. bλ B represents the blackbody radiation intensity distribution. I This is the DRESOR coefficient matrix.

[0018] In the above technical solution of the present invention, in step 4, the measured flame boundary radiation intensity at two wavelengths is substituted into the left side of equation (2) as input. In each iteration, the current uniform absorption coefficient is fixed, and the medium temperature distribution is solved by combining the DRESOR coefficient matrix and the modified Tikhonov regularization method. The uniform absorption coefficient is updated based on the principle of residual minimization and Newton's iteration method.

[0019] In step 4, the iterative update sub-steps for temperature and uniform absorption coefficient are as follows:

[0020] a. The medium temperature distribution is obtained by combining the DRESOR coefficient matrix with the modified Tikhonov regularization method:

[0021]

[0022] In the formula, T represents the temperature distribution of the medium; D is the regularization matrix; and α is the regularization parameter.

[0023] b. Substitute the obtained medium temperature distribution into equation (1) to calculate the spectral radiation intensity, and compare it with the flame boundary radiation intensity at wavelength λ1. The residual can be calculated by the following formula:

[0024]

[0025] In the formula, p is the total number of pixels. Let λ be the flame boundary radiation intensity at wavelength λ1. Let λ represent the spectral radiation intensity at wavelength λ1 obtained from the nth iteration.

[0026] c. Update the uniform absorption coefficient using the following formula:

[0027]

[0028] In the formula, Let λ be the flame boundary radiation intensity at wavelength λ2, n be the iteration number, and κ be the intensity of the flame boundary radiation. n and κ n+1 These are the absorption coefficients for the nth and (n+1)th iterations, respectively. Let δκ be the spectral radiance at wavelength λ2 in the nth iteration. n This is a very small increment, typically taken as -0.1κ. n , This is the spectral radiance calculated after giving κ a very small increment.

[0029] d. Determine if the iteration termination condition is met. If it is met, stop the iteration; otherwise, repeat steps a to c to continue the iteration and minimize the residual.

[0030] In the above technical solution of the present invention, in step 5, the non-uniform absorption coefficient distribution can be obtained from the measured flame boundary radiation intensity:

[0031] After obtaining the temperature distribution of the medium, I bλ As a known item, it is merged into B. I Thus, the flame boundary radiation intensity can be expressed as a function that depends only on the non-uniform absorption coefficient; accordingly, equation (2) can be rewritten as:

[0032] I λ =B′ I κ a(6)

[0033] In equation (6), κ a The absorption coefficient distribution is non-uniform, and the coefficient matrix B′ I With non-uniform absorption coefficient κ a related:

[0034] B′ I =B I I bλ (T) / κ a (7)

[0035] Then the non-uniform absorption coefficient distribution κ a It can be obtained through the following formula:

[0036]

[0037] This invention proposes a method for measuring cross-sectional temperature and non-uniform absorption coefficient distribution using multispectral imaging. This method offers advantages such as wide applicability, high computational efficiency, and non-invasive measurement, providing a novel approach for measuring cross-sectional temperature and non-uniform absorption coefficient distribution. Based on the inversion principle of multi-wavelength radiation intensity, this invention combines the DRESOR method and a modified Tikhonov regularization algorithm to achieve high-precision reconstruction of flame cross-sectional temperature and non-uniform absorption coefficient distribution, offering advantages such as wide applicability, high computational efficiency, and non-invasive measurement. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating the overall process of the method described in this invention.

[0039] Figure 2 The simulated flame boundary radiation intensity distribution is shown for wavelengths of 720 nm and 665 nm.

[0040] Figure 3 To reconstruct the camera layout;

[0041] Figure 4 To reconstruct the calculated cross-sectional temperature distribution map;

[0042] Figure 5a To reconstruct the non-uniform absorption coefficient distribution obtained from the calculation; Figure 5b This is a graph showing the relative error. Detailed Implementation

[0043] The method described in this invention involves measuring the flame boundary radiation intensity at two wavelengths using a multispectral device, calculating the DRESOR coefficient matrix using the DRESOR method, solving for the medium temperature distribution using a modified Tikhonov regularization algorithm, updating the uniform absorption coefficient based on the residual minimization principle and Newton's iteration method, obtaining the medium temperature distribution, fixing this temperature distribution, and using the flame boundary radiation intensity to invert and obtain the non-uniform absorption coefficient distribution. This process is iterated until the convergence condition is met, outputting the final cross-sectional temperature distribution and non-uniform absorption coefficient distribution results. The specific process is as follows: Figure 1 As shown.

[0044] Step 1. Measure the simulated flame boundary radiation intensity at wavelengths λ1 = 720 nm and λ2 = 665 nm within the combustion chamber of the scramjet engine using a multispectral imaging device. The results are as follows: Figure 2 As shown;

[0045] Step 2. Set the initial uniform absorption coefficient to 0.6m. -1 ;

[0046] Step 3. Based on the current uniform absorption coefficient, calculate the DRESOR coefficient matrix corresponding to the two wavelengths λ1 and λ2 using the DRESOR method. The flame boundary radiation intensity can be expressed in the following form:

[0047]

[0048] In the formula, The cumulative radiation intensity along the optical path of the multispectral camera, expressed in W / m². 3 / sr; V is the spatial volume unit; ω is the scattering rate; λ is the wavelength in meters; κ is the uniform absorption coefficient in meters. 1 ; The DRESOR number represents the distance from point r” along this direction. The emitted radiant energy is r w The ratio of received; I bλ (r′) represents the blackbody radiation intensity, measured in W / m. 3 / sr.

[0049] like Figure 3 As shown, four cameras are distributed around the center of the grid, dividing the computational plane into M = 10 × 10 = 100 medium grid cells. The field of view of each of the four cameras is set to 100°, and the camera target surface is divided into p = 4 × 100 = 400 pixel cells. The wall temperature is set to 900K, and the wall emissivity is set to 1.0. Equation (9) can be rewritten as follows:

[0050]

[0051] In the formula, Iλ (j) represents the flame boundary radiation intensity, in W / m². 3 / sr;T i λ represents the medium temperature in Kelvin (K); λ represents the wavelength in meters (m); C1 and C2 are 3.7418 × 10⁻⁶ respectively. -16 W·m 2 1.4388×10 -2 m·K is Planck's constant, ΔV represents the volume of a spatial unit, i represents the number of medium units, j represents the number of pixels, and R d The number of drains (R) represents the number of drains (κ), and the uniform absorption coefficient (R) represents the uniform absorption coefficient (κ). d (i→j) represents the share of the total radiant energy emitted by the i-th spatial unit that is received by the j-th imaging unit per unit area and unit angle. Therefore, the radiant intensity received by the camera can be expressed as a function that depends only on the internal temperature of the system and the DRESOR number, where the DRESOR number is determined by the system's geometry and its radiative parameter distribution, and can be obtained numerically using the Monte Carlo method.

[0052] Performing a matrix transformation on equation (10) yields:

[0053] I λ =B I I bλ (T) (11)

[0054] B(j,i)=4κR d (i→j)ΔV i ,i=1,…,mj=1,…,p (12)

[0055]

[0056] Among them I λ The matrix form of the flame boundary radiation intensity, and the blackbody radiation intensity I. bλ Related to the cross-sectional temperature that needs to be reconstructed; the DRESOR coefficient matrix B consists of B(j,i). I It is related to complex radiative transfer processes.

[0057] Step 4. Set the maximum number of iterations to 50 and perform iterative updates of temperature and uniform absorption coefficient;

[0058] a. The medium temperature distribution is obtained by combining the DRESOR coefficient matrix with the modified Tikhonov regularization method:

[0059]

[0060] In the formula, T represents the temperature distribution of the medium; D is the regularization matrix; and α is the regularization parameter.

[0061] b. Substitute the obtained medium temperature distribution into equation (1) to calculate the spectral radiation intensity, and compare it with the flame boundary radiation intensity at wavelength λ1. The residual can be calculated by the following formula:

[0062]

[0063] In the formula, p is the total number of pixels. Let λ be the flame boundary radiation intensity at wavelength λ1. Let λ represent the spectral radiation intensity at wavelength λ1 obtained from the nth iteration.

[0064] c. Update the uniform absorption coefficient κ using the following formula:

[0065]

[0066] In the formula, Let λ be the flame boundary radiation intensity at wavelength λ2, n be the iteration number, and κ be the intensity of the flame boundary radiation. n and κ n+1 These are the uniform absorption coefficients for the nth and (n+1)th iterations, respectively. Let δκ be the spectral radiance at wavelength λ2 in the nth iteration. n This is a very small increment, typically taken as -0.1κ. n , This is the spectral radiance calculated after giving κ a very small increment.

[0067] d. Repeat steps a to c to continue iterating until the residual is minimized or the maximum number of iterations is reached.

[0068] Step 5. Obtain the non-uniform absorption coefficient distribution by inverting the flame boundary radiation intensity;

[0069] After obtaining the temperature distribution of the medium, I bλ As a known item, it is merged into B. I Thus, the flame boundary radiation intensity can be expressed as a function that depends only on the non-uniform absorption coefficient. Accordingly, equation (11) can be rewritten as:

[0070] I λ =B′ I κ a (17)

[0071] In equation (17), κ a The absorption coefficient distribution is non-uniform, and the coefficient matrix B′ I With non-uniform absorption coefficient κ a related:

[0072] B′ I =B I I bλ (T) / κa (18)

[0073] Then the non-uniform absorption coefficient distribution κ a It can be obtained through the following formula:

[0074]

[0075] Step 6. Repeat steps 3 to 5 until the residual satisfies the minimization condition or the maximum number of iterations is reached. The medium temperature distribution obtained when the convergence condition is met is taken as the final cross-sectional temperature distribution and output together with the non-uniform absorption coefficient distribution.

[0076] Figure 4 The cross-sectional temperature distribution obtained from the reconstruction calculation is presented. Figure 5a The distribution of non-uniform absorption coefficients obtained from reconstruction calculations is presented. Figure 5b The relative error curves for calculating the non-uniform absorption coefficient distribution are presented, based on the simulated non-uniform absorption coefficient distribution.

[0077] Depend on Figure 5b It can be seen that the reconstructed non-uniform absorption coefficient distribution is close to the benchmark, with a maximum error of less than 6.9%, proving the accuracy of the method.

[0078] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered to fall within the protection scope of the present invention.

Claims

1. A method of multispectral imaging to measure the distribution of temperature and non-uniform absorption coefficient in a section, characterized in that, The method comprises: Step 1: measuring flame boundary radiation intensity at two wavelengths; Step 2: setting an initial uniform absorption coefficient; Step 3: calculating a DRESOR coefficient matrix at each wavelength by the DRESOR method; Step 4: combining the DRESOR coefficient matrix and the modified Tikhonov regularization method to solve the medium temperature distribution, and updating the uniform absorption coefficient based on the residual minimization principle and the Newton iteration method; Step 5: after obtaining the medium temperature distribution, the non-uniform absorption coefficient distribution is obtained by inverse calculation based on the flame boundary radiation intensity; Step 6: Steps 3 to 5 are repeatedly executed until the residual error meets the minimization condition or the maximum iteration number is reached; the medium temperature distribution obtained when the convergence condition is met is taken as the final cross-sectional temperature distribution, and is output together with the non-uniform absorption coefficient distribution.

2. The method of multispectral imaging of temperature and non-uniform absorption coefficient distribution in a section according to claim 1, characterized in that, In step 3, according to the current uniform absorption coefficient, the DRESOR coefficient matrix at two wavelengths is calculated by the DRESOR method, and the measured flame boundary radiation intensity is expressed as a coupling function of the medium temperature distribution and the uniform absorption coefficient distribution; where I λ (j) is the flame boundary radiance in W / m 3 / sr; T i is the medium temperature in K; λ is the wavelength in m; C1 and C2 are 3.7418 x 10 -16 W·m 2 , 1.4388 x 10 -2 m·K, respectively; h is the Planck constant, AV represents the volume of the spatial element, i indicates the number of medium elements, j represents the number of pixels, R d represents the DRESOR number, and κ represents the uniform absorption coefficient.

3. The method of multispectral imaging of temperature and non-uniform absorption coefficient distribution in a section according to claim 2, characterized in that, In step 3, formula (1) is rewritten in matrix form as: I λ = B I I bλ (T) (2) where I λ is the matrix form of the flame boundary radiance intensity, I bλ is the blackbody radiance distribution; B I is the DRESOR coefficient matrix.

4. The method of multispectral imaging to measure temperature and non-uniform absorption coefficient distribution of a section according to claim 3, wherein, In step 4, the measured flame boundary radiation intensity at two wavelengths is respectively substituted into formula (2) as input, and the current uniform absorption coefficient is fixed in each iteration, and the medium temperature distribution is solved by combining the DRESOR coefficient matrix and the modified Tikhonov regularization method, and the uniform absorption coefficient is updated based on the residual minimization principle and the Newton iteration method.

5. The method of multispectral imaging to measure temperature and non-uniform absorption coefficient distribution of a section according to claim 4, wherein, In step 4, the iteration update sub-step of solving the medium temperature distribution and the uniform absorption coefficient is as follows: a. The medium temperature distribution is obtained by combining the DRESOR coefficient matrix and the modified Tikhonov regularization method: In the formula, T is the medium temperature distribution; D is the regularization matrix, and a is the regularization parameter; b. The calculated medium temperature distribution is substituted into formula (1) to calculate the spectral radiation intensity, and compared with the flame boundary radiation intensity at wavelength λ1, and the residual error can be calculated by formula (3): where p is the total number of pixels, is the flame boundary radiation intensity at wavelength λ1, represents the spectral radiation intensity at wavelength λ1 obtained by the n-th iteration calculation; c. The uniform absorption coefficient κ is updated by formula (4): wherein is the flame boundary radiance at wavelength λ2, n is the iteration number, κ n and κ n+1 are the uniform absorption coefficients for the n and n+1 iterations, respectively, is the spectral radiance at wavelength λ2for the n iteration, δκ n is a very small increment, is the spectral radiance calculated after giving κ a very small increment; d. Steps a to c are repeated for iteration until the residual error is minimized or the maximum iteration number is reached.

6. The method of multispectral imaging of temperature and non-uniform absorption coefficient distribution in a section according to claim 3, characterized in that, In step 5, the non-uniform absorption coefficient distribution is obtained from the measured flame boundary radiation intensity: After obtaining the medium temperature distribution, the I bλ As a known item incorporated into B I Thus, the flame boundary radiance intensity is expressed as a function only related to the non-uniform absorption coefficient; accordingly, equation (2) can be rewritten as: I λ = B' I κ a (6) In formula (6), κ a is a non-uniform absorption coefficient distribution, the coefficient matrix B′ I is related to the non-uniform absorption coefficient κ a : B′ I = B I I bλ (T) / K a (7) where the non-uniform absorption coefficient distribution K a may be obtained by

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