Method for measuring particulate matter concentration based on flame self-emission spectrum radiation

Abstract

The invention provides a method for measuring particulate matter concentration based on flame self-emission spectrum radiation. The method comprises the following steps: firstly, measuring a target flame by adopting a spectrograph to obtain a radiation intensity curve of to-be-measured particles, constructing an error function, iteratively updating the temperature and emissivity of the radiation intensity curve by adopting a steepest descent method, judging whether convergence occurs or not according to the variation before and after the error function and the gradient norm of the error function, and if yes, judging whether the to-be-measured particles are converged. And outputting the final temperature and emissivity. And if not, continuing iteration until convergence. The flame optical thickness is obtained through flame image analysis, and the particle concentration of the flame can be obtained by combining the emissivity and the flame optical thickness with a particle model. Based on flame self-emission characteristic spectrum radiation, the particulate matter concentration is accurately measured in combination with the Planck law and the particulate matter model, and the method has the advantages of being high in real-time performance, high in precision, high in sensitivity and capable of achieving non-contact measurement.

Description

Technical Field

[0001] The present invention relates to the technology for monitoring combustion processes, and particularly to a method for measuring the concentration of particulate matter based on the self-emission spectrum radiation of a flame. Background Art

[0002] A flame is an important manifestation in the combustion process and is widely used in industrial production, transportation, energy conversion and other fields. When fuel burns incompletely under high-temperature conditions, particulate matter is generated. Particulate matter not only affects the combustion efficiency, but also poses hazards to the environment and human health. In a gas generator, particulate matter will also adhere to the pipeline wall and cause blockage, which not only damages components, but also poses risks such as chamber explosion. Therefore, accurately measuring the concentration of particulate matter in a flame is of great significance for optimizing the combustion process, reducing harmful emissions and improving air quality. Traditional methods for measuring particulate matter mainly include the gravity method, light scattering method, electric field method, laser particle size analysis method, etc. These methods can measure the concentration of particulate matter to a certain extent, but they often have disadvantages such as poor real-time performance, strong environmental dependence, low sensitivity to fine particulate matter and complex operation.

[0003] Technical Solution

[0004] In order to achieve accurate and real-time measurement of the concentration of particulate matter in the flame of a gas generator, the present invention provides a method for measuring the concentration of particulate matter based on the self-emission spectrum radiation of a flame, which can obtain a high-precision concentration of particulate matter based on the self-emission spectrum radiation of the flame.

[0005] The technical solution of the present invention is as follows:

[0006] A method for measuring the concentration of particulate matter based on the self-emission spectrum radiation of a flame, comprising the following steps:

[0007] Step 1: Measuring the target flame with a spectrometer to obtain a radiation intensity curve;

[0008] Step 2: Establishing the spectral radiation intensity of the flame particulate matter based on Planck's law;

[0009] Step 3: Defining an error function to represent the error between the actual radiation intensity and the calculated radiation intensity;

[0010] Step 4: Setting an initial temperature T0 and an emissivity ε0, setting an iteration step size α for updating the temperature T and β for updating the emissivity ε(λ), and continuously iterating until the convergence condition is met, and outputting the final temperature T and the emissivity ε(λ);

[0011] Step 5: Obtaining the optical thickness l of the flame from the flame image, and combining the emissivity and the flame optical thickness with the particulate matter model to obtain the concentration of particulate matter in the flame.

[0012] In the above technical solution of the present invention, in step 2, the spectral radiation intensity of the flame particulate matter can be expressed by the following formula 1:

[0013]

[0014] In the above formula, I is the spectral radiation intensity of the flame, with the unit of W / m 3 / sr; ε(λ) is the spectral emissivity of the particulate matter; c1 and c2 are Planck constants; λ is the wavelength, with the unit of nm; T is the temperature, with the unit of K.

[0015] In the above technical solution of the present invention, in step 3, the error function is expressed by the following formula:

[0016]

[0017] In the formula, I measured (λ) is the actually measured radiation intensity.

[0018] In the above technical solution of the present invention, in step 4, the sub-steps of obtaining the final temperature T and emissivity ε(λ) through iteration by the steepest descent method are as follows:

[0019] 1) Set the boundary conditions, where the temperature T is greater than 0, and the emissivity ε(λ) satisfies 0 ≤ ε ≤ 1.

[0020] 2) Calculate the gradients of the temperature T k and the emissivity ε k (λ) respectively

[0021] The gradient of the error function with respect to T k is:

[0022] where:

[0023] The gradient of the error function with respect to ε k (λ) is:

[0024] where the temperature T k and the emissivity ε k (λ) are the temperature and emissivity at the k-th iteration;

[0025] 3) Update the temperature T k and the emissivity ε k (λ) using the steepest descent method:

[0026]

[0027] α and β are the defined iteration step sizes, T k+1 and ε k+1For the temperature and emissivity of the next iteration.

[0028] 4) To accelerate the iterative convergence rate in the early stage of optimization and improve the accuracy in the later stage, update the iteration step sizes α and β after each iteration:

[0029]

[0030] where k is the number of iterations, η is the control attenuation rate, α0 and β0 are the initial iteration step sizes of temperature and emissivity, α k , β k is the adjusted iteration step size at the k-th iteration;

[0031] 5) Determine whether to converge, introducing two judgment conditions:

[0032] a. Calculate the radiation intensity from the updated temperature and emissivity according to Planck's law, and recalculate the new error function L(T k+1 , ε k+1 ). Use ΔL to represent the difference from the previous error function:

[0033] ΔL = |L(T k+1 , ε k+1 ) - L(T k , ε k )| ≤ δ1

[0034] When the change amount of ΔL is less than the set first threshold δ1, it indicates that the temperature T and emissivity ε obtained by iteration are already close to the optimal solution.

[0035] b. Calculate the gradient norm of the updated error function. When the gradient norm of the error function for the parameters temperature T and emissivity ε is less than the set second threshold δ2, it indicates that the update amplitude of the parameters temperature T and emissivity ε is very small, the convergence process tends to stop, and it is considered to have converged:

[0036]

[0037] is the L2 norm of the gradient vector of the error function L. When both convergence conditions a and b are satisfied, it is considered that the temperature T and emissivity ε at this time are the optimal solutions, and the final temperature T and emissivity ε are output; if both convergence conditions a and b are not satisfied at the same time, repeat the above steps 2) - step 5) until the final temperature and emissivity are output.

[0038] In the above technical solution of the present invention, in step 5, to obtain the optical thickness l of the flame from the flame image, it should be noted that due to the high brightness of the flame, in order to obtain a clear flame contour, a lower exposure time needs to be set when taking the flame image.

[0039]

[0040] In the formula, n f is the number of pixels occupied by the flame diameter, N w is the number of pixels of the image width, and W is the actual width of the image, and the flame optical thickness at the experimental measurement point position is obtained.

[0041] In the above technical solution of the present invention, in step 5, the particulate matter concentration of the flame that can be obtained by combining the emissivity and the flame optical thickness with the particulate matter model is:

[0042]

[0043] where n is the refractive index in the complex refractive index of the particulate matter, and m is the absorption coefficient in the complex refractive index of the particulate matter, which is expressed in the form of a polynomial of the wavelength;

[0044]

[0045] The present invention proposes a method for measuring the particulate matter concentration based on the self-emission spectrum radiation of the flame, which has the advantages of strong real-time performance, high precision, high sensitivity and non-contact, and provides a new method for measuring the particulate matter concentration. The present invention realizes the real-time monitoring and quantitative measurement of the particulate matter concentration during the combustion process by analyzing the characteristics of the self-emission spectrum of the flame. Based on the characteristic spectral radiation of the self-emission of the flame, the present invention combines Planck's law and the particulate matter model to achieve accurate measurement of the particulate matter concentration, and has the advantages of strong real-time performance, high precision, high sensitivity and non-contact measurement. Description of the Drawings

[0046] Figure 1 is the overall flow chart of the method of the present invention;

[0047] Figure 2 is a comparison diagram of the radiation intensity measured by the spectrometer in the embodiment of the present invention and the calculated radiation intensity in the error function changing with the number of iterations;

[0048] Figure 3 is a schematic diagram of the change of the flame emissivity obtained by the steepest descent method iteration with the number of iterations in the embodiment of the present invention;

[0049] Figure 4 is a schematic diagram of the flame optical thickness l obtained from the flame image in the example of the present invention;

[0050] Figure 5 is a graph of the change of the flame particulate matter concentration obtained by combining the emissivity and the flame optical thickness with the particulate matter model in the embodiment of the present invention over time. Detailed Embodiment

[0051] The following describes the specific implementation method of the present invention with reference to the drawings.

[0052] The method flow described in the present invention is to measure the radiation information emitted by the target flame using a spectrometer, select the band with relatively smooth measured flame radiation intensity, and continuously perform iteration through the steepest descent method until the convergence condition is met, and then output the final temperature and emissivity. Combining the emissivity with the flame optical thickness in the flame image and the particulate matter model, the particulate matter concentration can be obtained. The overall process is shown in Figure 1 the following figure.

[0053] 1. Measure the spectral information emitted by the gas generator flame using a spectrometer to obtain the radiation intensity of the flame;

[0054] 2. Based on Planck's law, establish that the spectral radiation intensity of the flame particulate matter can be expressed by the following formula:

[0055]

[0056] In the above formula, I is the spectral radiation intensity of the flame, with the unit of W / m 3 / sr; ε(λ) is the spectral emissivity of the particulate matter. c1 and c2 are Planck constants; λ is the wavelength, with the unit of nm; T is the temperature, with the unit of K.

[0057] 3. Define an error function to represent the error between the actual radiation intensity and the calculated radiation intensity. The error function is expressed by the following formula:

[0058]

[0059] In the formula, I measured (λ) is the actually measured radiation intensity.

[0060] 4. Set the initial temperature T0 = 1000K, the initial emissivity ε0 = 1, the initial values of the iteration step sizes α and β are both 0.01, the η attenuation rate is 0.005, and the selected wavelength range is 600 - 800nm.

[0061] 1) Set the boundary condition that the temperature T is greater than 0, and the emissivity ε(λ) is 0 ≤ ε ≤ 1.

[0062] 2) Calculate the gradients of the temperature T k and the emissivity ε k (λ) respectively:

[0063] The gradient of the error function with respect to T k is:

[0064] Among them:

[0065] The gradient of the error function with respect to ε k (λ) is:

[0066] Among them, the temperature T k and the emissivity ε k (λ) are the temperature and emissivity at the k-th iteration;

[0067] 3) Update T k and the emissivity ε k (λ) using the steepest descent method:

[0068]

[0069] α and β are the defined iteration step sizes, T k+1 and ε k+1 are the temperature and emissivity for the next iteration.

[0070] 4) To accelerate the iterative convergence speed in the early stage of optimization and improve the accuracy in the later stage, update the iteration step sizes α and β after each iteration:

[0071]

[0072] In the formula, k is the number of iterations, η is the control attenuation rate, α0, β0 are the initial iteration step sizes of the temperature and emissivity, α k , β k are the adjusted iteration step sizes at the k-th iteration;

[0073] 5) Determine whether to converge, introducing two judgment conditions:

[0074] a. Calculate the radiation intensity from the updated temperature and emissivity using Planck's law, and recalculate the new error function L(T k+1 , ε k+1 ), and use ΔL to represent the difference from the previous error function:

[0075] ΔL = |L(T k+1 , ε k+1 ) - L(T k , ε k )| ≤ δ1

[0076] When the change amount of ΔL is less than the set first threshold δ1, it indicates that the iteratively obtained temperature T and emissivity ε are close to the optimal solution.

[0077] b. Calculate the gradient norm of the updated error function. When the gradient norm of the error function with respect to the parameters temperature T and emissivity ε is less than the set second threshold δ2, it indicates that the update amplitude of the parameters temperature T and emissivity ε is very small, the convergence process tends to stop, and it is considered to have converged:

[0078]

[0079] When both convergence conditions a and b are satisfied, the temperature T and emissivity ε at this time are considered to be the optimal solutions, and the final temperature T and emissivity ε are output; if both convergence conditions a and b are not satisfied, the above steps 2)-5) are repeated until convergence is achieved.

[0080] 5. The optical thickness of the flame is obtained from the flame image as 1.2 m, and the particulate matter concentration of the flame can be obtained by combining the emissivity and the particulate matter model of the flame.

[0081] When measuring the particulate matter concentration of the gas generator flame using a spectrometer, the measuring point is located 1.5 m away from the nozzle of the gas generator, and the measurement of the particulate matter concentration of the gas generator is used as a calculation example.

[0082] Select the 600-800 nm band of the measured radiation intensity of the gas generator flame for solving the particulate matter concentration, and the analysis of the calculation results is shown in Figure 2 、 Figure 3 、 Figure 4 、 Figure 5 。 Figure 2 It is a comparison diagram of the radiation intensity of the gas generator flame measured by the spectrometer in the 600-800 nm band and the calculated radiation intensity in the error function varying with the number of iterations. Figure 3 It is the result of the variation of the flame emissivity of the gas generator flame obtained by the steepest descent method iteration with the number of iterations. Figure 4 It is the flame optical thickness l obtained from the gas generator flame image. Figure 5 It is a variation diagram of the measured particulate matter concentration of the gas generator flame with time.

[0083] The above is the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art of this technology, without departing from the principle described in the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as falling within the protection scope of the present invention.

Claims

1. A method for measuring particle concentration based on flame self-emission spectrum radiation, characterized in that: The steps include: Step 1: Use a spectrometer to measure the target flame and obtain a radiation intensity curve; Step 2: Based on Planck's law, establish the spectral radiation intensity of flame particles; Step 3: Define an error function to represent the error between the actual radiation intensity and the calculated radiation intensity; Step 4: Set the initial temperature T0 and emissivity ε0, set the iteration step α to update the temperature T and β to update the emissivity ε(λ), iterate continuously through the steepest descent method until the convergence condition is met, and output the final temperature T and emissivity ε(λ); Step 5: The flame optical thickness l is obtained from the flame image, and the particle concentration can be obtained by combining the emissivity and flame optical thickness with the particle model.

2. The method for measuring particle concentration based on flame spontaneous emission spectrum radiation according to claim 1, characterized in that: In step 2, the spectral radiation intensity of flame particles can be expressed as the following formula 1: In the above formula, I is the flame spectral radiation intensity, the unit is W / m 3 / sr; ε(λ) is the spectral emissivity of the particle; c1 and c2 are Planck constants; λ is the wavelength in nm; T is the temperature in K.

3. The method for measuring particle concentration based on flame spontaneous emission spectrum radiation according to claim 1, characterized in that: In step 3, the error function is expressed as the following formula: In the formula, I measured (λ) is the actual measured radiation intensity.

4. The method for measuring particle concentration based on flame spontaneous emission spectrum radiation according to claim 1, characterized in that: In step 4, the sub-steps of iterating through the steepest descent method to obtain the final temperature T and emissivity ε(λ) are as follows: 1) Set the boundary conditions, temperature T is greater than 0, and emissivity ε(λ) is 0≤ε≤1; 2) For temperature T k and emissivity ε k (λ) Calculate the gradient: Error function for T k The gradient of is: in: The error function is k (The gradient of the hook is: Among them, the temperature T k and emissivity ε k (λ) is the temperature and emissivity at the kth iteration; 3) Update the temperature T using the steepest descent method k and emissivity ε k (λ): α and β are defined as the iteration step size, T k+1 and ε k+1 for the temperature and emissivity of the next iteration; 4) In order to accelerate the iterative convergence speed in the early stage of optimization and improve the accuracy in the later stage, the iteration step sizes α and β are updated after each iteration: Where k is the number of iterations, η is the control decay rate, α0, β0 are the initial iteration steps of temperature and emissivity, and α k , β k is the adjusted iteration step size at the kth iteration; 5) To determine whether convergence occurs, two judgment conditions are introduced: a. Calculate the radiation intensity using Planck's law based on the updated temperature and emissivity, and recalculate the new error function L(T k+1 , ε k+1 ), and use ΔL to represent the difference between the error function and the previous one: ΔL=|L(T k+1 ,he k+1 )-L(T k ,he k )|≤δ1 When the change of ΔL is less than the set first threshold δ1, it means that the temperature T and emissivity ε obtained by iteration are close to the optimal solution; b. Calculate the gradient norm of the updated error function. When the gradient norm of the error function for the parameter temperature T and the emissivity ε is less than the set second threshold δ2, it means that the update amplitude of the parameter temperature T and the emissivity ε is very small, and the convergence process tends to stop, and it is considered to have converged: is the L2 norm of the gradient vector of the error function L. When the convergence conditions a and b are met at the same time, the temperature T and emissivity ε are considered to be the optimal solution, and the final temperature T and emissivity ε are output.

5. The method for measuring particle concentration based on flame spontaneous emission spectrum radiation according to claim 1, characterized in that: In step 5, the flame optical thickness l can be obtained from the flame image: Where n f is the number of pixels occupied by the flame diameter, N w is the number of pixels of the image width, and W is the actual width of the image.

6. The method for measuring particle concentration based on flame spontaneous emission spectrum radiation according to claim 1, characterized in that: In step 5, the calculation formula for the particle concentration is: In the formula, f v is the particle concentration, n is the refractive index in the complex refractive index of the particle, and m is the absorption coefficient in the complex refractive index of the particle, expressed as a polynomial of wavelength;

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