A method for simultaneously reconstructing particulate temperature and radiation characteristics parameters of complex combustion systems

Abstract

This invention provides a method for simultaneously reconstructing the temperature and radiation characteristic parameters of particulate matter in complex combustion systems. The method includes: measuring the spectral radiation intensity of the combustion flame of the particulate matter under test using a spectrometer; calculating the theoretical spectral radiation intensity of the flame based on a wavelength-temperature bivariate emissivity model; setting initial parameters and constructing a residual function with respect to unknown parameters; transforming the residual function into a quadratic model using Taylor expansion; solving for and updating the iteration step size using the Cholesky decomposition method and the Cauchy point method; updating the unknown parameters using the iteration step size, calculating the sum of squared residuals, and performing convergence testing; and updating the unknown parameters and the actual temperature of the particulate matter required for the radiation characteristic parameter model when the convergence condition is met. This invention provides high-precision particulate matter temperature and radiation characteristic parameters based on flame spectral radiation intensity, offering advantages of high accuracy and rapid convergence in complex combustion environments with gas-liquid-solid multiphase coupling.

Description

Technical Field

[0001] This invention relates to the field of particulate temperature and radiation characteristic parameters measurement technology in complex combustion systems, and in particular to a method for simultaneously reconstructing the particulate temperature and radiation characteristic parameters of solid rocket motor plumes. Background Technology

[0002] Solid rocket motors have been widely used in both military and civilian fields due to their advantages such as fast response, short preparation time, high thrust, and low cost. The plume of a solid rocket motor is characterized by high temperature, high speed, and strong radiation; plume temperature is a crucial parameter characterizing the engine's operating state and performance. Accurate measurement of the solid rocket motor plume temperature is of significant reference value for understanding the internal combustion process and overall engine performance. Solid rocket motor plumes differ from conventional liquid rocket motor plumes, exhibiting not only high temperature, high speed, and high pressure flow characteristics, but also the presence of phase-change solid particles (Al₂O₃) in the combustion gases. This gas-liquid-solid multiphase coupling leads to low accuracy and poor global convergence in traditional radiation thermometry methods based on the "wavelength-emissivity" radiation characteristic parameter model. Therefore, developing a method for simultaneously reconstructing particulate temperature and radiation characteristic parameters of complex combustion systems based on the "wavelength-temperature-emissivity" radiation characteristic parameter model is of great importance. Summary of the Invention

[0003] The purpose of this invention is to provide a method for reconstructing the temperature and radiation characteristics of particulate matter in complex combustion systems, especially those involving solid rocket motor plumes, based on the flame spectral radiation intensity.

[0004] The objective of this invention can be achieved through the following technical measures: a method for simultaneously reconstructing the particulate temperature and radiation characteristic parameters of a complex combustion system, the method comprising:

[0005] Step 1: Use a spectrometer to measure the spectral radiation intensity of the combustion flame of the particulate matter to be tested;

[0006] Step 2: Calculate the theoretical spectral radiation intensity of the flame based on the wavelength-temperature bivariate emissivity model;

[0007] Step 3: Set initial parameters and construct a residual function for the unknown parameters based on the flame detection spectral radiance intensity and the theoretical spectral radiance intensity;

[0008] Step 4: Apply Taylor expansion to transform the residual function into a quadratic model;

[0009] Step 5: Combine the Cholesky decomposition method and the Cauchy point method to solve for the update iteration step size;

[0010] Step 6: Update the unknown parameters using the iteration step size, calculate the sum of squared residuals, and perform convergence testing;

[0011] Step 7: When the convergence condition is met, update the unknown parameters required for the radiation characteristic parameter model and the actual temperature of the particulate matter.

[0012] The objective of this invention can also be achieved through the following technical measures:

[0013] In step 1, based on the wavelength-temperature bivariate emissivity model, the theoretical spectral radiance of the flame is expressed as the following formula 1:

[0014]

[0015] In the formula, I represents the theoretical spectral radiance of the flame, with units of W / m². 3 / sr; a0 and a1 are unknown coefficients in the radiation characteristic parameter model; T is the particulate temperature in K; λ is the wavelength band used in the calculation in m; c1 and c2 are Planck's constants.

[0016] In step 3, set the initial parameters a0, a1, T, and the initial trust region radius Δ0, and construct the residual function as shown in the following formula 2:

[0017]

[0018] In the formula, The residual is given by parameter a = [a0, a1, T], which is the parameter to be determined.

[0019] In step 4, the residual function f(a) is expanded using Taylor series near different bands, and the quadratic approximation model of the residual function is expressed as the following formula 3:

[0020]

[0021] In the formula, p is the iteration step size. Let p be the transpose of the gradient, H be the Hessian matrix of the residual function, and p be the transpose of the gradient. T This is the transpose of the iteration step size.

[0022] Step 4, constructing the quadratic approximation model of the residual function includes:

[0023] 4a. Calculate the transpose of the gradient according to the following formula 7.

[0024]

[0025] In the formula, and These are the partial derivatives of the residual sum of squares f(a) with respect to the unknown coefficients of the radiation characteristic parameter model and the particulate temperature, respectively.

[0026] 4b. Calculate the second-order partial derivatives of each unknown parameter based on the residual function f(a), and construct the Hessian matrix H according to the following formula 8:

[0027]

[0028] In step 5, based on the Cholesky decomposition method and the Cauchy point method, the trust region radius Δ is determined. k The inner solution iteration step size makes the quadratic approximation model m(p) k To obtain the minimum value, the iterative step size solution is expressed as the following formula 4:

[0029]

[0030] In the formula, a0 and a1 are the unknown coefficients of the radiation characteristic parameter model; T is the particulate temperature in K; k is the number of calculations; and p is the iteration step size.

[0031] Step 5, solving for the flame temperature based on the Cholesky decomposition method and the Cauchy point method includes:

[0032] 5a. The iteration step size p can be set by adjusting the gradient of the quadratic approximation model m(p). The value is 0, which is obtained using formulas 9 and 10:

[0033]

[0034] 5b. When matrix H is positive and definite, H is decomposed using the Cholesky decomposition method according to the following formula 11:

[0035] H = LL T (11)

[0036] In the formula, L is a lower triangular matrix;

[0037] 5c. Obtain the iteration step size p according to formulas 7-11;

[0038] 5d. When matrix H is not positive definite or cannot be decomposed, the Cauchy point method is used to solve for the iteration step size p within the initial trust region radius Δ0. The iteration step size direction of the Cauchy point is set to the negative gradient direction, and the calculation of the iteration step size o is expressed as the following formula 12:

[0039]

[0040] In the formula, α is the iteration step size factor, and the iteration step size p is a vector composed of the changes in the unknown parameters.

[0041] In step 6, use the iteration step size p k The updated solution parameters are expressed as follows: Formula 5:

[0042]

[0043] The iteration step size is solved by combining the Cholesky decomposition method and the Cauchy point method. After updating the unknown parameters using the iteration step size, the sum of squared residuals is calculated again and convergence is checked. If convergence is achieved, the results are the unknown parameters of the radiation characteristic parameter model and the true temperature of the particulate matter. If the convergence condition is not met, the trust region radius is adjusted based on the ratio of the actual decrease in the residual function to the predicted decrease in the residual function, and the unknown parameters of the radiation characteristic parameter model and the particulate matter temperature are updated.

[0044] In step 6, if the convergence condition is not met, the reduction amount Δf is determined based on the actual residual function. actual and the decrease in the predicted residual function Δf pred The effectiveness of the current iteration step size is determined by calculating the ratio ρ according to the following formula 6:

[0045]

[0046] If ρ > 0.75, the trust region radius needs to be increased; if ρ < 0.25, the trust region radius needs to be decreased; otherwise, the values ​​remain unchanged.

[0047] In step 7, the adjusted trust region radius Δ is used. k+1 Substitute the updated parameters into step 3, and repeat steps 4-6 until the convergence condition is met; at this point, the calculated... and T k+1 These are the parameters required for the radiation characteristic parameter model and the actual temperature of the particulate matter, respectively.

[0048] This invention relates to a method for simultaneously reconstructing the temperature and radiation characteristics of particulate matter in complex combustion systems, specifically based on the spectral radiation intensity of flames. This method is particularly relevant to the temperature and radiation characteristics of particulate matter in solid rocket motor plumes. The method begins by acquiring the spectral radiation intensity of the combustion flame of the particulate matter under test using a spectrometer. Initialization is then performed on the wavelength range used for calculation, the unknown parameters of the "wavelength-temperature-emissivity" radiation characteristic parameter model, the particulate temperature, and the trust region radius. Subsequently, the residual squares are calculated band by band, and a residual function is constructed. Taylor expansion is applied to transform the residual function into a quadratic model. The iteration step size is updated using the Cho1esky decomposition method and the Cauchy point method. After updating the unknown parameters using the iteration step size, the sum of squared residuals is calculated again, and convergence is evaluated. If convergence is achieved, the result represents the unknown parameters of the radiation characteristic parameter model and the actual particulate temperature. If convergence is not met, the trust region radius is adjusted based on the ratio of the actual decrease in the residual function to the predicted decrease in the residual function, and the unknown parameters of the radiation characteristic parameter model and the particulate temperature are updated accordingly. The "wavelength-temperature-emissivity" radiation characteristic parameter model and particulate temperature calculation method provided by this invention have the advantages of high accuracy and fast convergence in complex combustion environments with gas-liquid-solid multiphase coupling. It can provide high-precision particulate temperature and radiation characteristic parameters based on flame spectral radiation intensity. Attached Figure Description

[0049] Figure 1 A flowchart of a specific embodiment of the method for simultaneously reconstructing the temperature and radiation characteristics parameters of particulate matter in a complex combustion system according to the present invention;

[0050] Figure 2 This is a graph showing the spectrometer response value and the detected spectral radiance intensity in a specific embodiment of the present invention;

[0051] Figure 3 This is a schematic diagram showing the result of the fitted radiation intensity changing with the number of iterations before the sum of squared residuals converges in a specific embodiment of the present invention.

[0052] Figure 4 This is a schematic diagram showing the results of particle temperature and residual sum of squares changing with the number of iterations based on the spectral radiation intensity of a solid rocket motor plume in a specific embodiment of the present invention.

[0053] Figure 5 This is a schematic diagram showing the result of the emissivity changing with the number of iterations based on the "wavelength-temperature-emissivity" radiation characteristic parameter model in a specific embodiment of the present invention. Detailed Implementation

[0054] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0055] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments of the present invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, and / or combinations thereof.

[0056] like Figure 1 As shown, Figure 1 This is a flowchart of a method for simultaneously reconstructing the temperature and radiation characteristics of particulate matter in a complex combustion system according to the present invention. The method includes the following steps:

[0057] 1) The intensity of the spectral radiation of the flame under test is obtained by measuring it with a spectrometer;

[0058] 2) Based on the wavelength-temperature bivariate emissivity model, the theoretical spectral radiance of a flame is expressed as follows: Formula 1:

[0059]

[0060] In the formula, I represents the spectral radiance of the flame, with units of W / m². 3 / sr; a0 and a1 are unknown coefficients in the radiation characteristic parameter model; T is the particulate temperature in K; λ is the wavelength band used in the calculation in m; c1 and c2 are Planck's constants.

[0061] 3) Set initial parameters a0, a1, T, and initial trust region radius Δ0, and construct the residual function as shown in Formula 2 below:

[0062]

[0063] In the formula, The residual is given by parameter a = [a0, a1, T], which is the parameter to be determined.

[0064] The initial parameters a0, a1, T, and the initial trust region radius Δ0 can be set to 0.01, 0.001, 1000, and 1, respectively.

[0065] 4) Apply Taylor expansion to the residual function f(a) near different bands. The quadratic approximation model of the residual function is expressed as the following formula 3:

[0066]

[0067] In the formula, p is the iteration step size. p is the transpose of the gradient. T H is the transpose of the iteration step size, and H is the Hessian matrix of the residual function.

[0068] Constructing a quadratic approximation model of the residual function involves the following sub-steps:

[0069] 4a. Calculate the transpose of the gradient according to the following formula 7.

[0070]

[0071] In the formula, and Let f(a) be the partial derivatives of the residual sum of squares with respect to the unknown coefficients of the radiation characteristic parameter model and the particulate temperature, respectively.

[0072] 4b. Calculate the second-order partial derivatives of each unknown parameter based on the residual function f(a), and construct the Hessian matrix H according to the following formula 8:

[0073]

[0074] 5) Based on the Cho1esky decomposition method and the Cauchy point method, in the trust region radius Δ k The inner solution iteration step size makes the quadratic approximation model m(o) k To obtain the minimum value, the iterative step size solution is expressed as the following formula 4:

[0075]

[0076] In the formula, k represents the number of calculations.

[0077] Solving for flame temperature based on the Cholesky decomposition method and Cauchy point method involves the following sub-steps:

[0078] 5a. The iteration step size p can be set by adjusting the gradient of the quadratic approximation model m(p). The value is 0, which is obtained using formulas 9 and 10:

[0079]

[0080] 5b. When matrix H is positive and definite, H is decomposed using the Cholesky decomposition method according to the following formula 11:

[0081] H = LL T (11)

[0082] In the formula, L is a lower triangular matrix.

[0083] 5c. Obtain the iteration step size according to formulas 7-11.

[0084] 5d. When the matrix H is not positive definite or cannot be decomposed, the Cauchy point method is used to solve for the iteration step size p within the initial trust region radius Δ0. The iteration step size direction of the Cauchy point is set to the negative gradient direction. The calculation of the iteration step size p is expressed as the following formula 12:

[0085]

[0086] In the formula, θ is the iteration step size factor, and the iteration step size p is a vector composed of the changes in the unknown parameters.

[0087] 6) Use iteration step size p k The updated solution parameters are expressed as follows: Formula 5:

[0088]

[0089] Calculate the residuals based on the updated solution parameters, and determine whether the convergence condition is met. If it is met, then T is... k This represents the final particulate temperature.

[0090] 7) If the convergence condition is not met, reduce the amount of Δf according to the actual residual function. actual and the decrease in the predicted residual function Δf pred The effectiveness of the current iteration step size is determined by calculating the ratio ρ according to the following formula 6:

[0091]

[0092] If ρ > 0.75, the trust region radius needs to be increased; if ρ < 0.25, the trust region radius needs to be decreased; otherwise, the values ​​remain unchanged.

[0093] Determining the validity of the selected iteration step size and modifying the trust region radius involves the following sub-steps:

[0094] 7a. Decrease in actual residual function Δf actual and the decrease in the predicted residual function Δf pred They are represented as follows:

[0095] Δf actual =f(a)-f(a+p) (13)

[0096] Δf pred =m(0)-m(p) (14)

[0097] 7b. The reduction amount Δf based on the actual residual function actual and the decrease in the predicted residual function Δf pred The effectiveness of the current iteration step size is determined by calculating the ratio ρ according to the following formula 6:

[0098]

[0099] If ρ > 0.75, the trust region radius Δ can be increased. k+1 =2Δ k If ρ < 0.25, the trust region radius Δ needs to be reduced. k+1 =0.5Δ k If 0.25 < ρ < 0.75, the trust region radius Δ needs to be maintained. k+1 =Δ k constant.

[0100] 8) Use the adjusted trust region radius Δ k+1 Substitute the updated parameters into step 3), and repeat steps 4) through 7) until the convergence condition is met. The calculated result is... and T k+1 These are the parameters required for the final "wavelength-temperature-emissivity" radiation characteristic parameter model and the actual temperature of the particulate matter, respectively.

[0101] This invention utilizes a spectrometer to measure the spectral radiance intensity curve of a solid rocket motor plume, defines the wavelength range of the spectral radiance curve, and uses the spectral radiance intensity within this range as input data. Based on the "wavelength-temperature-emissivity" radiation characteristic parameter model, Cholesky decomposition method, and Cauchy point method, radiation characteristic parameters and particulate temperature are reconstructed. The sum of squares of the residuals between the detected spectral radiance intensity and the fitted spectral radiance intensity is used as the convergence criterion. The unknown parameters after iterative correction are input to repeat the next iteration. The above steps are repeated until the iteration converges, which yields the parameters and particulate temperature required for the final "wavelength-temperature-emissivity" radiation characteristic parameter model.

[0102] In a specific embodiment of the present invention, the method for simultaneously reconstructing the particulate temperature and radiation characteristics parameters of a complex combustion system includes:

[0103] 101. Measure the spectral radiation intensity of a flame using a spectrometer and output a continuous band spectral radiation intensity curve. Set the continuous band λ range to 640nm-760nm, with parameters a0=0.01, a1=0.001, T=1200K, and the initial trust region radius Δ0=1.

[0104] 102. Based on the wavelength-temperature bivariate emissivity model, the theoretical spectral radiance of a flame is expressed as follows: Equation 1:

[0105]

[0106] In the formula, I represents the theoretical spectral radiance of the flame, with units of W / m². 3 / sr; a0 and a1 are undetermined coefficients of the emissivity model; T is the particulate temperature in K; λ is the wavelength band used in the calculation in m; c1 and c2 are Planck's constants.

[0107] 103. Set initial parameters a0, a1, T, and initial trust region radius Δ0, and construct the residual function as shown in the following formula 2:

[0108]

[0109] In the formula, The flame spectral radiation intensity measured by the spectrometer. The flame spectral radiation intensity is obtained based on the emissivity model, and the parameter a = [a0, a1, T] is the parameter to be obtained.

[0110] 104. Applying Taylor expansion to the residual function f(a) near different bands, the quadratic approximation model of the residual function is expressed as the following formula 3:

[0111]

[0112] In the formula, p is the iteration step size. p is the transpose of the gradient. T H is the transpose of the iteration step size, and H is the Hessian matrix of the residual function.

[0113] Calculate the transpose of the gradient using the following formula 15.

[0114]

[0115] In the formula, and Let f(a) be the partial derivatives of the residual sum of squares with respect to the unknown coefficients of the radiation characteristic parameter model and the particulate temperature, respectively.

[0116] The second-order partial derivatives of each unknown parameter are calculated based on the residual function f(a), and the Hessian matrix H is constructed according to the following formula 8:

[0117]

[0118] 105. Solve for the iteration step increment p within the trust region radius Δ0 to minimize the quadratic approximation model m(p). The iteration step size solution is expressed as the following formula 16:

[0119]

[0120] 106. Updating the solution parameters using the iteration step size p is expressed as the following formula 17:

[0121]

[0122] T 1 =T+p T (17)

[0123] Calculate the residuals based on the updated solution parameters, determine whether the convergence condition is met, and output the result if it is met.

[0124] 107. If the convergence condition is not met, reduce the amount Δf according to the actual residual function. actual and the decrease in the predicted residual function Δf pred The effectiveness of the current iteration step size is determined by calculating the ratio ρ according to the following formula 6:

[0125]

[0126] If ρ > 0.75, the trust region radius Δ2 = 2Δ1 can be increased; if ρ < 0.25, the trust region radius Δ2 = 0.5Δ1 needs to be decreased; if 0.25 < ρ < 0.75, the trust region radius Δ2 = Δ1 needs to be kept unchanged.

[0127] 108. Using the adjusted trust region radius Δ2, substitute the updated parameters into Formula 2, and repeat steps 103-107 until the convergence condition is met. The calculated result is... and T k+1 These are the parameters required for the final "wavelength-temperature-emissivity" radiation characteristic parameter model and the particulate temperature, respectively.

[0128] The temperature of the solid rocket motor plume under the condition of Mach number 2.4 was measured using a spectrometer. The measuring point was located 120 mm away from the engine nozzle on the central axis of the engine. The measured spectral radiation intensity data of the solid rocket motor plume was used as a calculation example.

[0129] Figure 2 This presents the spectrometer response values ​​and spectral radiance curves of the solid rocket motor plume obtained from spectrometer measurements. The unknown parameters were solved using the 690nm-760nm spectral radiance band, and the analysis results are shown below. Figure 3 , Figure 4 and Figure 5 . Figure 3 The result is the fitted radiation intensity as a function of the number of iterations before the sum of squared residuals converges. Figure 4 The results show the changes in particulate temperature and residual sum of squares as a function of iteration number, reconstructed from the spectral radiation intensity of a solid rocket motor plume flame. Figure 5 This is the result of the spectral emissivity changing with the number of iterations based on the "wavelength-temperature-emissivity" radiation characteristic parameter model.

[0130] For the embodiments of the present invention described above, common knowledge such as specific structures and characteristics in the solutions are not described in detail; the embodiments are described in a step-by-step manner, and the technical features involved in each embodiment can be combined with each other as long as they do not conflict with each other. The same or similar parts between the embodiments can be referred to each other.

[0131] 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 for simultaneously reconstructing the temperature and radiation characteristics parameters of particulate matter in a complex combustion system, characterized in that, The methods for simultaneously reconstructing the particulate temperature and radiation characteristics parameters of complex combustion systems include: Step 1: Use a spectrometer to measure the spectral radiation intensity of the combustion flame of the particulate matter to be tested; Step 2: Calculate the theoretical spectral radiation intensity of the flame based on the wavelength-temperature bivariate emissivity model; Step 3: Set initial parameters. Construct a residual function with respect to the unknown parameters based on the flame detection spectral radiance and the theoretical spectral radiance, expressed as the formula: In the formula, For residuals, parameters For the parameters to be found, , Initial parameters for the radiation characteristic parameter model, The initial temperature of the particulate matter; Step 4: Apply Taylor expansion to transform the residual function into a quadratic model; Step 5: Combine the Cholesky decomposition method and the Cauchy point method to solve for the update iteration step size; Step 6: Update the unknown parameters using the iteration step size, calculate the sum of squared residuals, and perform convergence testing; Step 7: If convergence is achieved, the results at this point are the unknown parameters of the radiation characteristic parameter model and the true temperature of the particulate matter. If the convergence condition is not met, the trust region radius is adjusted based on the ratio of the decrease in the actual residual function to the decrease in the predicted residual function, and the adjusted trust region radius is used. Substitute the updated parameters into step 3, and repeat steps 4-6 until the convergence condition is met; at this point, the calculated... , and These are the parameters required for the radiation characteristic parameter model and the actual temperature of the particulate matter, respectively. , These are the initial parameters for the radiation characteristic parameter model. denoted as , where is the initial temperature of the particulate matter, and k is the number of calculations.

2. The method for simultaneously reconstructing the particulate temperature and radiation characteristics parameters of a complex combustion system according to claim 1, characterized in that, In step 1, based on the wavelength-temperature bivariate emissivity model, the theoretical spectral radiance of the flame is expressed as follows: Equation 1: (1) In the formula, The theoretical spectral radiance of a flame is expressed in units of . ; , These are the initial coefficients for the radiation characteristic parameter model; The initial temperature of the particulate matter, in units of ; The bands used in the calculation are in units of ; , is Planck's constant.

3. The method for simultaneously reconstructing the particulate temperature and radiation characteristics parameters of a complex combustion system according to claim 1, characterized in that, In step 4, the residual function Using Taylor expansion near different bands, the quadratic approximation model of the residual function is expressed as follows: Equation 3: (3) In the formula, The iteration step size, For the transpose of the gradient, This is the transpose of the iteration step size. Let be the Hessian matrix of the residual function.

4. The method for simultaneously reconstructing the particulate temperature and radiation characteristics parameters of a complex combustion system according to claim 3, characterized in that, Step 4, constructing the quadratic approximation model of the residual function includes: 4a. Calculate the transpose of the gradient according to the following formula 7. : (7) In the formula, , and Sum of squared residuals For the unknown coefficients of the radiation characteristic parameter model and the partial derivatives of particulate temperature; 4b. Based on residual function Calculate the second-order partial derivatives of each unknown parameter, and construct the Hessian matrix according to the following formula 8. : (8)。 5. The method for simultaneously reconstructing the particulate temperature and radiation characteristics parameters of a complex combustion system according to claim 4, characterized in that, In step 5, based on the Cholesky decomposition method and the Cauchy point method, the trust region radius is determined. The inner solution iteration step size makes the quadratic approximation model To obtain the minimum value, the iterative step size is calculated as shown in Formula 4 below: (4) In the formula, , These are the unknown coefficients in the radiation characteristic parameter model; The particulate temperature is expressed in units of . ; To calculate the number of times, This is the iteration step size.

6. The method for simultaneously reconstructing the particulate temperature and radiation characteristics parameters of a complex combustion system according to claim 5, characterized in that, Step 5, solving for the flame temperature based on the Cholesky decomposition method and the Cauchy point method includes: 5a. Iteration step size By setting a quadratic approximation model gradient The value is 0, which is obtained using formulas 9 and 10: (9) (10) 5b. When the matrix When the time is positive, the Cholesky decomposition method is used to... Decompose according to the following formula 11: (11) In the formula, It is a lower triangular matrix; 5c. Obtain the iteration step size according to formulas 7-11. ; 5d. When the matrix When the value is not positive definite or cannot be decomposed, the Cauchy point method is used to solve for the radius of the initial trust region. Iteration step size within Set the iteration step direction of the Cauchy point to the negative gradient direction, and set the iteration step size... The calculation is expressed as the following formula 12: (12) In the formula, This is the iteration step size factor, where the iteration step size is... It is a vector consisting of the changes in unknown parameters.

7. The method for simultaneously reconstructing the particulate temperature and radiation characteristics parameters of a complex combustion system according to claim 6, characterized in that, In step 6, use the iteration step size The updated solution parameters are expressed as follows: Formula 5: (5) The iteration step size is solved by combining the Cholesky decomposition method and the Cauchy point method. After updating the unknown parameters using the iteration step size, the sum of squared residuals is calculated again and convergence is checked. If convergence is achieved, the results are the unknown parameters of the radiation characteristic parameter model and the true temperature of the particulate matter. If the convergence condition is not met, the trust region radius is adjusted based on the ratio of the actual decrease in the residual function to the predicted decrease in the residual function, and the unknown parameters of the radiation characteristic parameter model and the particulate matter temperature are updated.

8. The method for simultaneously reconstructing the particulate temperature and radiation characteristics parameters of a complex combustion system according to claim 7, characterized in that, In step 6, if the convergence condition is not met, the amount of reduction is determined based on the actual residual function. and the reduction in the predicted residual function Calculate the ratio according to the following formula 6. Determine the validity of the current iteration step size: (6) if If the value is greater than 0.75, the trust region radius needs to be increased. If the value is less than 0.25, the trust region radius needs to be reduced; otherwise, the values ​​remain unchanged.

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