CN112268622A - Simultaneous reconstruction algorithm for flame three-dimensional temperature and soot volume fraction distribution - Google Patents
Simultaneous reconstruction algorithm for flame three-dimensional temperature and soot volume fraction distribution Download PDFInfo
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Abstract
The invention discloses a flame three-dimensional temperature and soot volume fraction distribution simultaneous reconstruction algorithm, which comprises the following steps: inputting emergent spectral radiation intensity information of flame radiation rays in different directions, dispersing flame micro-elements, and establishing a flame radiation transmission equation; and setting a target function, performing iterative calculation by using a constructed simultaneous reconstruction algorithm, and reconstructing to obtain flame three-dimensional temperature and smoke black volume fraction distribution. In the algorithm, in the iteration process, the non-negative least square algorithm is nested in the simulated annealing algorithm, so that the search efficiency of the SA algorithm in the process of searching the target function is obviously improved. Meanwhile, the SA algorithm has the advantages of high quality, strong initial value robustness, universality, easiness in implementation and the like, so that the NNLS-SA algorithm has good global search characteristics and is not easy to fall into a local optimal value, and has high precision and good convergence in the process of simultaneously solving the three-dimensional flame temperature and smoke black volume fraction distribution.
Description
Technical Field
The invention relates to a flame three-dimensional temperature and soot volume fraction distribution simultaneous reconstruction algorithm, and belongs to the technical field of flame temperature measurement.
Background
The combustion process is an extremely complex process in which physical and chemical changes couple and interact with each other. The temperature, the volume fraction of soot and the spatial distribution of other related products in the combustion flame are directly related to the safety, effectiveness and cleanness of the energy conversion and utilization process, and the measurement work of the key parameters has important significance for the safe operation, energy conservation and emission reduction of equipment.
In recent years, the development of laser, photoelectron, information and other technologies greatly promotes the deep research and application of non-contact temperature measurement technology. The non-contact temperature measurement technology has the advantage of not interfering the flow field to be measured, and can be roughly divided into two main categories, namely an active non-contact temperature measurement method and a passive non-contact temperature measurement method. The active temperature measurement method is to apply external excitation signals such as light and sound to high-temperature combustion flame, and to measure the temperature by detecting the interaction result of the combustion process and the applied external signals. The passive temperature measurement method does not adopt any external signal, and only detects information generated in the combustion process to measure the flame temperature, mainly refers to a radiation imaging method. Non-invasive soot particle measurement methods in combustion flames can also be divided into two types according to the source of an optical signal in the measurement process, wherein one type is a measurement method based on laser or other externally added light sources, such as an extinction method and a laser-induced incandescent light method; another class is measurement methods based on the emission spectrum of the flame or soot particles themselves, such as bicolor methods and emission CT methods. Laser-based optical measurement methods are widely applied in the field of measurement of flame temperature and smoke volume fraction, however, because the methods all need an additional light source to give an initial signal, the methods bring inconvenience when applied to industrial field measurement, and complicated field conditions bring difficulty to the arrangement of the light source and the detector and the calibration of the light path. These problems can be effectively avoided by measuring the flame's own emission spectral signal to directly calculate the temperature and soot particle volume fraction distribution in the target flame.
The radiation image method is used for measuring the three-dimensional flame temperature and the volume fraction distribution of the smoke black, and the temperature and the volume fraction of the smoke black in a radiation transmission system are solved according to the boundary radiation intensity distribution, which is a typical inverse problem. The existing solving algorithm of the radiation transmission inverse problem mainly comprises the following four types: the first type is a traditional regularization method, which comprises a Tikhonov regularization algorithm, a truncated singular value decomposition algorithm, a least square QR decomposition algorithm and the like; the second category is gradient-based optimization algorithms, including conjugate gradient methods, Levenberg-Marquardt (L-M) algorithms, and the like; the third category is an intelligent optimization algorithm based on random search, which comprises a genetic algorithm, simulated annealing, a particle swarm algorithm, an ant colony algorithm and the like; the fourth category is hybrid optimization algorithms, i.e., combining two or more different types of algorithms into a hybrid algorithm to improve the overall performance of the algorithm.
The regularization algorithm is a type of algorithm which is widely applied in the radiation transmission inverse problem solution, but the method can only process simple inverse problems about the solution of a linear equation system. For the problem of simultaneous reconstruction of flame temperature and smoke volume fraction, the problem is a typical nonlinear problem, and therefore, the simultaneous reconstruction of flame temperature and smoke volume fraction distribution cannot be realized by adopting a regularization method only. Gradient-based optimization algorithms are a class of nonlinear optimization algorithms. The algorithm has the advantages of high convergence rate and good result stability, but the algorithm generally has the defects of dependence on an initial value, difficulty in processing a local optimal value and the like. Compared with the traditional method, the intelligent optimization algorithm is developed later, but has the advantages of not depending on an initial value, not needing to differentiate the optimized function and the like.
Therefore, by taking advantage of different algorithms, the different algorithms are organically combined to form a hybrid optimization algorithm, respective advantages are exerted, and a new idea is provided for simultaneously solving the volume fraction distribution of the temperature and the smoke black. Although the intelligent optimization algorithm provides more possibilities for the organic combination of different algorithms, due to the defects of premature convergence of a genetic algorithm, stagnation of an ant colony algorithm searching process, low precision of a particle swarm algorithm, easiness in dispersion and the like, the application of the existing hybrid optimization algorithm in the research of the radiation transmission inverse problem is less, and particularly, the problem of simultaneous reconstruction of flame three-dimensional temperature and smoke black volume fraction distribution is rarely researched, so that the proposal of a new hybrid optimization algorithm and the improvement of the existing hybrid algorithm are still to be further researched.
Disclosure of Invention
The invention aims to solve the technical problem of providing an algorithm for simultaneously reconstructing three-dimensional flame temperature and smoke black volume fraction distribution aiming at the defects of the existing solving algorithm.
In order to solve the technical problems, the invention adopts the technical scheme that:
an algorithm for simultaneously reconstructing three-dimensional flame temperature and smoke black volume fraction distribution is characterized by comprising the following steps:
firstly, inputting emergent spectral radiation intensity information of flame radiation rays in different directions, dispersing flame micro-elements, and establishing a flame radiation transmission equation;
the first step comprises the following steps:
(11) the emergent spectral radiation intensity information of the input flame radiation rays in different directions comprises Iλ(R)(x, y, z, θ, ψ) and Iλ(G)(x,y,z,θ,ψ)；
Wherein, Iλ(R)(x, y, z, theta, psi) as a starting point coordinate (x, y, z), a zenith angle of a direction coordinate theta, and a circumferential angle psi; i isλ(G)(x, y, z, theta, psi) as initial point coordinates (x, y, z), zenith angle of direction coordinates theta, and circumferential angle psi;
(12) dispersing the flame micro-elements, and performing three-dimensional grid division on the flame micro-elements;
(13) recording the length and the number of each light ray passing through different flame micro-elements according to the radiation intensity information input in the step (11), and establishing the following equation:
in the formula, nKRepresenting the total number of flame micro-elements penetrated by the light with the serial number K; k is lightThe serial number of (2); i isλK(s) is the lambda spectral radiation intensity of the radiation ray with sequence number K in the s direction;
is serial number nKThe absorption coefficient of the infinitesimal body of (2); i.e. ip,jpRepresents the flame micro-element body through which the light passes along the transmission direction;
the black body radiation intensity of the lambda spectrum of the flame radiation light with the serial number K passing through the vn-th flame micro element body;
the light ray has a serial number nKThe geometric length of the flame micro-elements of (a); λ is the wavelength of the flame radiation;
the radiation transmission equation of all directions of light rays is combined to obtain the following equation:
Iλ＝AIbλ (2)
wherein, IλVector [ I ] formed by spectral emergent radiation intensity of flame in all directionsλ1,Iλ2,…,Iλm,…,IλK](ii) a A is a coefficient matrix formed by calculating coefficients A,
Ibλvector formed by black body radiation intensity of flame micro-element
V is the total number of flame control bodies (number of each infinitesimal body is 1,2, V, …, V), the total number of flame control bodies passing through is n for the flame radiation ray with the serial number K, and the number of each infinitesimal body passing through along the ray direction is V1, V2, vip，…，vn。
The detailed calculation formula of A is shown as formula (3),
setting a target function, performing iterative calculation by using a constructed simultaneous reconstruction algorithm (formula 4-14), and reconstructing to obtain flame three-dimensional temperature and smoke black volume fraction distribution;
(21) setting an objective function F, and initializing an absorption coefficient vector k ═ k0Inner loop maximum iteration number loopmaxThe threshold epsilon for whether the iteration process is terminated, the number of initialization inner loops Loop is 1, the number of outer loops Loop is 1, and the initial annealing temperature T of the annealing plans,0；
F＝||I′λ(G)-Iλ(G)|| (4)
Wherein, Iλ(G)、I′λ(G)Respectively the measured and calculated spectral radiation intensity of G wavelength and the initial value vector kappa of the absorption coefficient0Is a vector which is randomly and continuously distributed;
(22) initializing a coefficient matrix a ═ a according to equation (3)0Calculating an initial objective function Fg，
Fg＝||A0Ibλ(G)-Iλ(G)|| (5)
Randomly selecting the p-th component kappa in the absorption coefficient vector kappapDisturbing by using the formulas (6) and (7) to obtain a new absorption coefficient vector kappanewAnd updating the coefficient matrix A according to the formula (3) to obtain Anew:
κnew,p＝κp+delta (6)
Wherein delta follows a standard normal distribution of equation 7:
delta～N(0,1) (7)
by the updated coefficient matrix AnewAnd the radiation intensity I of the blackbody spectrum under the current iteration numberbλ(G)Calculating an estimate I 'of the radiation intensity vector at the flame G wavelength for the current iteration number'λ(G)(κnew)：
I′λ(G)(κnew)＝AnewIbλ(G) (8)
Calculating a current state objective function Fl：
Fl＝||I′λ(G)(κnew)-Iλ(G)|| (9)
Wherein I in the iterative processbλ(G)Obtained by the following method:
firstly, the spectral radiation intensity vector I of the measured R wavelength is utilizedλ(R)The vector kappa of the absorption coefficient updated in the iterative processnewCoefficient matrix AnewSolving the formula (2) by using a non-negative least square algorithm to obtain the blackbody spectral radiation intensity I of each infinitesimal body of the flame under the R wavelengthbλ(R)Solving the temperature value T of each infinitesimal body of the flame by the formula (10)f；
Tf＝c2/λ(R)ln{c1/[λ(R)5πIbλ(R)]+1} (10)
In the formula, c1Is a first radiation constant, c2Is a second radiation constant; t isfIs the temperature of each flame infinitesimal body; λ (R) is the R wavelength of the light;
then, the temperature of each flame infinitesimal body obtained by the formula (10) is used for calculating the blackbody spectral radiation intensity I of each flame infinitesimal body under the G wavelength according to the formula (11)bλ(G)；
Wherein λ (G) is the G wavelength of light;
the solving steps of the non-negative least square algorithm are as follows:
the method comprises the following steps: setting the sequence gamma as an empty set, and setting the sequence Z as [1,2,3 …, M]And I isbλ＝0。
Step two: calculating M-dimensional vector, eta ═ AT(Iλ-AIbλ)。
Step three: if the sequence Z is an empty set or for all sequences i e Z, ω is satisfiediLess than or equal to 0, turn to
And step eleven, otherwise, carrying out the next step.
Step four: find the exponent q, so that ηq＝max{ωi:i∈Z}。
Step five: the exponent q is shifted from the sequence Z into the sequence Γ.
Step six: a. theΓDenoted as an S M matrix. If i ∈ Γ, the ith column of matrix A is the new matrix AΓColumn i. If i ∈ Z, then the new matrix AΓIs a zero vector and calculates a least squares problem
Defines only the solution Z satisfying the correspondence of the element i in the sequence ΓiZ corresponding to element i in the sequence ZiIs a zero solution.
Step seven: if all Z corresponding to the element i in the sequence gamma are satisfiediAre both greater than 0, then IbλZ and go to step two, otherwise proceed to the next step.
Step eight: the exponent u is found in the sequence Γ elements so that it satisfies the following relationship.
Step nine: is provided with
Let Ibλ＝Ibλ+β(Z-Ibλ)。
Step ten: index of all satisfactions
Moves from sequence Γ into sequence Z, and goes to step six.
Step eleven: and finishing the calculation.
(23) Calculating Δ F ═ Fl－FgUpdating the objective function value FgAnd an absorption coefficient vector κ;
if Δ F<0, the annealing process is in the stateAs an important state, the absorption coefficient vector k ═ knewAn objective function Fg＝Fl；
If Δ F>If the state is 0 and the state is important, the determination is made based on the probability w that the solid is in the state, and the calculation of the probability function is shown in equation (12). Generating a [0,1 ] by a random data generator]Random number xi of interval, if w>Xi, the new state is the important state, and the updated absorption coefficient vector k is equal to knewAn objective function Fg＝Fl(ii) a Otherwise, the absorption coefficient vector and the target function are not updated;
w＝exp[-ΔF/(kbTs)] (12)
wherein k isbIs the Boltzmann constant, TsAn annealing temperature for an annealing plan;
(24) judging whether the inner circulation is stopped:
judging whether the loop of the iteration times of the internal loop is less than the loop of the maximum iteration times of the internal loopmaxAnd if so, looping to step (22); otherwise, stopping the internal circulation and carrying out the next step;
(25) judging whether the external circulation is stopped:
judging whether the iteration reaches the convergence condition according to the formula (13), if not, updating the outer Loop frequency Loop to Loop +1, and updating the annealing temperature T of the annealing plan according to the annealing mode of the formula (14)sLooping to step (22); otherwise, the circulation is stopped, and the next step is carried out;
Ts＝Ts,0·αLoop (14)
in the formula, α is a temperature decay rate, and is usually selected to be 0.7. ltoreq. α.ltoreq.1.0.
(27) Calculating the temperature and the volume fraction of the smoke black, and outputting the result:
calculating the temperature T of each micro element of the flame when the iteration is stopped according to the formula (13)endAnd absorption coefficient kappaendOutputting the temperature and the absorption coefficient, and according to the following formula,calculating the volume fraction of the smoke black;
a＝1.811+0.1263lnλ+0.0217ln2λ+0.0417ln3λ (17)
b＝0.5821+0.1213lnλ+0.2309ln2λ+0.0011ln3λ
in the formula (f)vIs the soot volume fraction of the flame infinitesimal body; kappaendIs the absorption coefficient of the flame infinitesimal body; and E (m) is the complex refractive index m of the soot varying with the wavelength, which is a function of a-bi, wherein a and b are the real part and the imaginary part of the complex refractive index m of the soot, respectively.
Has the advantages that:
1. the problem of simultaneous reconstruction of flame three-dimensional temperature and soot volume fraction distribution is a typical nonlinear solving problem, and the temperature and soot volume fraction need to be decoupled in the solving process, and meanwhile, the accuracy of the solving result needs to be ensured. The invention utilizes a Simulated Annealing (SA) algorithm to carry out global search on the objective function value, and simultaneously embeds a Non-Negative Least square (NNLS) algorithm in the SA algorithm to solve the flame temperature field in the searching process so as to obtain the reconstruction result of high-precision temperature and smoke volume fraction.
In the global search process of the SA algorithm, the absorption coefficient values of one or more micro-elements are updated every time, so that the global search time is longer, but the NNLS algorithm embedded in the SA can ensure the non-negativity of the temperature reconstruction of each micro-element of the flame, and the search efficiency of the SA algorithm in the process of searching the minimum value of the target function is remarkably improved. Meanwhile, the SA algorithm has the advantages of high quality, strong initial value robustness, universality, easiness in implementation and the like, so that the NNLS-SA algorithm has good global search characteristics and is not easy to fall into a local optimal value, and has high precision and good convergence in the process of simultaneously solving the three-dimensional flame temperature and smoke black volume fraction distribution.
Drawings
FIG. 1 is a flow chart of an algorithm for simultaneous reconstruction of flame three-dimensional temperature and soot volume fraction distribution;
FIG. 2 is a comparison of reconstructed flame temperatures using the NNLS-SA and NNLS-PSO algorithms, respectively;
FIG. 3 is a comparison of the reconstructed flame soot volume fractions using the NNLS-SA and NNLS-PSO algorithms, respectively.
Detailed Description
The invention is further illustrated with reference to the following figures and specific examples. It is to be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention, which is to be given the full breadth of the appended claims and any and all equivalent modifications thereof which may occur to those skilled in the art upon reading the present specification.
Step one, setting flame parameters, inputting emergent spectral radiation intensity information of flame radiation rays in different directions, dispersing flame micro elements, and establishing a flame radiation transmission equation. Assuming a cylindrical flame model, the height H is 0.03m, the bottom radius R is 0.008m, and the flame internal temperature and soot volume fraction distribution obey equations (1) and (2). Divide the flame into
(V64) infinitesimals. Selecting 10000 emergent spectrum radiation intensity signals I of light rays in different directionsλ(R)(x, y, z, θ, ψ) and Iλ(G)(x, y, z, θ, ψ); wherein, (x, y, z) is the initial point coordinate of the light ray, x is-0.0160, the variation range of y is-0.0074, and the variation range of z is 0-0.03. (theta, psi) is the direction coordinate of the light, theta is the zenith angle, psi is the circumferential angle, theta is in the range of-5-1.2 deg., psi is in the range of 80-92 deg., lambda (R) and lambda (G) are respectively the wavelengths of R and G channels 610nm and 530 nm;
according to the input radiation intensity information, recording the length and the number of each light ray passing through different flame micro-elements, and establishing the following equation:
in the formula, nKRepresenting the total number of flame micro-elements penetrated by the light with the serial number K; k is the serial number of the ray; i isλK(s) is the radiation intensity of the lambda spectrum of the radiation ray with the serial number K in the s direction;
is serial number nKThe absorption coefficient of the infinitesimal body of (2); i.e. ip,jpRepresents the flame micro-element body through which the light passes along the transmission direction;
is the black body radiation intensity of lambda spectrum of flame radiation light with serial number K passing through the vn-th flame micro element,
the light ray has a serial number nKThe geometric length of the flame micro-elements of (a); λ is the wavelength of the flame radiation; wherein the absorption coefficient kappaλAnd volume fraction f of sootvSee formulas (4) - (6);
a＝1.811+0.1263lnλ+0.0217ln2λ+0.0417ln3λ (6)
b＝0.5821+0.1213lnλ+0.2309ln2λ+0.0011ln3λ
where e (m) is the complex refractive index m of soot as a function of wavelength, a-bi, where a and b are the real and imaginary parts of the complex refractive index m of soot, respectively.
The radiation transmission equation of all directions of light rays is combined to obtain the following equation:
Iλ＝A·Ibλ (7)
wherein, IλVector [ I ] formed by spectral emergent radiation intensity of flame in all directionsλ1,Iλ2,…,Iλm,…,IλK](ii) a A is a coefficient matrix formed by calculating coefficients A,
Ibλvector formed by black body radiation intensity of flame micro-element
V is the total number of flame control bodies (number of each infinitesimal body is 1,2, V, …, V), the total number of flame control bodies passing through is n for the flame radiation ray with the serial number K, and the number of each infinitesimal body passing through along the ray direction is V1, V2, vip，…，vn。
The detailed calculation formula of A is shown as formula (8),
step two: and setting an objective function, and carrying out iterative calculation by using the constructed simultaneous reconstruction algorithm, and reconstructing three-dimensional flame temperature and smoke black volume fraction distribution at the same time.
(21) Setting an objective function F, as shown in equation (9), and initializing an absorption coefficient vector k ═ k0The number of inner loop loops is 1, and the maximum number of inner loop iterations loopmax50, the Loop number Loop is 1, and the threshold value epsilon for whether the iteration process is terminated is 10-5Annealing planned initial temperature Ts,0＝2000K；
F＝||I′λ(G)-Iλ(G)|| (9)
Wherein, Iλ(G)、I′λ(G)The initial value vector kappa of the spectral radiation intensity and the absorption coefficient obtained by measurement and forward calculation respectively0Are vectors that are randomly and continuously distributed.
(22) Initializing a coefficient matrix a ═ a according to equation (8)0Calculating an initial objective function Fg，
Fg＝||A0Ibλ(G)-Iλ(G)|| (10)
Randomly selecting the p-th component kappa in the absorption coefficient vector kappapPerturbing by equations (11) and (12) to obtain a new absorption coefficient vector kappanewAnd updating the coefficient matrix A according to the formula (8) to obtain Anew:
κnew,p＝κp+delta (11)
Wherein delta follows a standard normal distribution of equation 12:
delta～N(0,1) (12)
by the updated coefficient matrix AnewAnd the radiation intensity I of the blackbody spectrum under the current iteration numberbλ(G)Calculating an estimate I 'of the radiation intensity vector at the flame G wavelength for the current iteration number'λ(G)(κnew)：
I′λ(G)(κnew)＝AnewIbλ(G) (13)
Calculating a current state objective function Fl：
Fl＝||I′λ(G)(κnew)-Iλ(G)|| (14)
The NNLS algorithm is realized by utilizing the lsqnanneg function of Matlab to solve the formula (7), and the blackbody spectral radiation intensity I of each infinitesimal body of the flame under the R wavelength is obtainedbλ(R)Solving the temperature value T of each infinitesimal body of the flame by the formula (15)f，
Tf＝c2/λ(R)ln{c1/[λ(R)5πIbλ(R)]+1} (15)
In the formula, c1Is a first radiation constant, c2Is a second radiation constant of 3.7418 × 10-16W·m2And 1.4388 × 10-2m·K；TfIs the temperature of each flame infinitesimal body, K; λ (R) is the R wavelength of the light;
the blackbody spectral radiant intensity I of each flame element at the G wavelength was calculated from the temperature of each flame element obtained by the formula (15) according to the Planck's law (formula (16))bλ(G)：
Wherein λ (G) is the G wavelength of light; according to the formula (7), the radiation intensity I is determined by the current coefficient matrix A and the blackbody spectrumbλ(G)Calculating an estimate I 'of the radiation intensity vector at the current flame G wavelength'λ(G)(κnew) Calculating the current state objective function F according to equation (14)l。
(24) Calculating Δ F ═ Fl－FgUpdating the objective function value FgAnd an absorption coefficient vector κ;
if Δ F<0, the state received by the annealing process is an important state, and the absorption coefficient vector k is equal to knewAn objective function Fg＝Fl；
If Δ F>If the state is 0 and the state is important, the determination is made based on the probability w that the solid is in the state, and the calculation of the probability function is shown in equation (17). Generating a [0,1 ] by a random data generator]Random number xi of interval, if w>Xi, the new state is the important state, and the updated absorption coefficient vector k is equal to knewAn objective function Fg＝Fl(ii) a Otherwise, the absorption coefficient vector and the target function are not updated;
w＝exp[-ΔF/(kbTs)] (17)
wherein k isbIs the Boltzmann constant, kb＝1.3806488×10-23，TsAn annealing temperature for an annealing plan;
(25) judging whether the inner circulation is stopped:
judging whether the iteration number k of the inner loop is less than the maximum iteration number k of the inner loopmaxAnd if so, looping to step (22); otherwise, stopping the inner loop and proceeding to the next step;
(26) judging whether the external circulation is stopped:
judging whether the iteration reaches the convergence condition according to the equation (18), if not, updating the outer Loop frequency Loop to Loop +1, and updating the annealing temperature T of the annealing plan according to the annealing mode of the equation (19)sLooping to step (22); otherwise, the circulation is stopped, and the next step is carried out;
Ts＝Ts,0·αLoop (19)
in the formula, α is a temperature decay rate, and is usually selected to be 0.7. ltoreq. α.ltoreq.1.0.
(27) Calculating the temperature and the volume fraction of the smoke black, and outputting the result:
calculating the temperature T of each micro element of the flame at the time of iteration termination according to the formula (18)endAnd absorption coefficient kappaendOutputting the temperature and the absorption coefficient, and calculating the volume fraction of the smoke black according to the following formula;
in the formula (f)vIs the volume fraction of soot of the flame micro-elements, ppm; kappaendIs the absorption coefficient of the flame infinitesimal body, m-1(ii) a E (m) is a function of the complex refractive index m of soot.
In order to evaluate the performance of the NNLS-SA algorithm, the NNLS-PSO algorithm is introduced for comparison, the temperature of flames and the volume fraction of soot are respectively reconstructed by using the NNLS-SA algorithm and the NNLS-PSO algorithm, wherein a Particle Swarm Optimization algorithm (PSO) is proposed according to the Swarm foraging behavior of birds, and is also an intelligent Optimization algorithm based on random search.
The reconstruction relative error of the flame soot volume fraction is calculated according to equation (21), the reconstruction relative error of the flame temperature is calculated according to equation (22), and the reconstruction results are shown in fig. 2 and 3.
In the formula (f)v,rstFor the reconstructed volume fraction of soot, fv,setFor a set volume fraction of soot, TrstFor reconstructed flame temperature values, TsetIs a set flame temperature value.
The NNLS-PSO algorithm mainly utilizes a Monte Carlo method, updates the whole value of the absorption coefficient vector kappa every time of iteration, searches a solution space through a particle group, and obtains the optimal values of the volume fraction of the smoke black and the temperature by comparing the historical optimal values of the objective function. In each iteration process of the NNLS-SA algorithm, the absorption coefficient values of one or more micro-elements are only updated, and then the change of the objective function before and after updating is compared to obtain the optimal value of the volume fraction of the smoke black and the temperature.
The NNLS-SA algorithm embeds the NNLS algorithm in the SA algorithm, guarantees the temperature property of temperature field solving, and meanwhile solves the volume fraction of the smoke black by utilizing the good global search characteristic of the SA algorithm to the nonlinear problem. Compared with the NNLS-PSO algorithm, the algorithm does not blindly update the absorption coefficients of all the infinitesimal bodies at random, but selects the absorption coefficients of one or more infinitesimal bodies to update, so that the algorithm has higher precision, is not easy to fall into a local extreme value, has better stability, and has higher solving precision of the NNLS-SA algorithm under the same iteration times. From the reconstruction results of the flame temperatures in fig. 2, it can be seen that in grids 46 to 48, the true values of the temperatures are 901K, the temperatures reconstructed using the NNLS-SA algorithm are 894K, 894K and 901K, respectively, and the temperatures reconstructed using the NNLS-PSO algorithm are 863K, 862K and 863K, respectively, and it can be seen that the flame temperatures reconstructed using the NNLS-SA algorithm are more accurate. It can also be seen from the reconstructed results of the volume fractions of the soot in fig. 3 that in grids No. 10 to 12, the true values of the volume fractions of the soot are 0.8031ppm, the volume fractions of the flame soot reconstructed by the NNLS-SA algorithm are 0.8197ppm, 0.8042ppm and 0.8082ppm, respectively, and the volume fractions of the flame soot reconstructed by the NNLS-PSO algorithm are 0.7283ppm, 0.9224ppm and 1.3466ppm, respectively, and the reconstructed results of the NNLS-SA algorithm on the volume fractions of the soot are more accurate than those reconstructed by the NNLS-PSO algorithm. Meanwhile, the average relative errors of the reconstructed temperature and the volume fraction of the smoke black of the two algorithms are calculated, the average relative errors of the reconstructed temperature and the volume fraction of the smoke black of the NNLS-SA algorithm are respectively 0.7% and 6.05%, and the average relative errors of the reconstructed temperature and the volume fraction of the smoke black of the NNLS-PSO algorithm are respectively 10.87% and 43.85%. In conclusion, the NNLS-SA algorithm has higher reconstruction precision no matter the reconstruction of the temperature or the volume fraction of the smoke black.
Claims (7)
1. An algorithm for simultaneously reconstructing three-dimensional flame temperature and smoke black volume fraction distribution is characterized by comprising the following steps:
firstly, inputting emergent spectral radiation intensity information of flame radiation rays in different directions, dispersing flame micro-elements, and establishing a flame radiation transmission equation;
and step two, setting a target function, performing iterative calculation by using a constructed simultaneous reconstruction algorithm, and reconstructing to obtain flame three-dimensional temperature and smoke black volume fraction distribution.
2. The algorithm for simultaneously reconstructing flame three-dimensional temperature and soot volume fraction distribution according to claim 1, wherein the first step comprises:
(11) the emergent spectral radiation intensity information of the input flame radiation rays in different directions comprises emergent spectral radiation intensity Iλ(R)(x, y, z, theta, psi) and the intensity of the emergent spectral radiation Iλ(G)(x,y,z,θ,ψ)；
Wherein, Iλ(R)(x, y, z, theta, psi) as a starting point coordinate (x, y, z), a zenith angle of a direction coordinate theta, and a circumferential angle psi; i isλ(G)(x, y, z, theta, psi) as initial point coordinates (x, y, z), zenith angle of direction coordinates theta, and circumferential angle psi;
(12) dispersing the flame micro-elements, and performing three-dimensional grid division on the flame micro-elements;
(13) recording the length and the number of each light ray passing through different flame micro-elements according to the radiation intensity information input in the step (11), and establishing the following equation:
in the formula, nKRepresenting the total number of flame micro-elements penetrated by the light with the serial number K; k is the serial number of the ray; i isλK(s) is the lambda spectral radiation intensity of the radiation ray with sequence number K in the s direction;
is serial number nKThe absorption coefficient of the infinitesimal body of (2); i.e. ip,jpRepresents the flame micro-element body through which the light passes along the transmission direction;
the black body radiation intensity of the lambda spectrum of the flame radiation light with the serial number K passing through the vn-th flame micro element body;
the light ray has a serial number nKThe geometric length of the flame micro-elements of (a); λ is the wavelength of the flame radiation;
the radiation transmission equation of all directions of light rays is combined to obtain the following equation:
Iλ＝AIbλ (2)
wherein, IλVector [ I ] formed by spectral emergent radiation intensity of flame in all directionsλ1,Iλ2,…,Iλm,…,IλK](ii) a A is a coefficient matrix formed by calculating coefficients A,
Ibλvector formed by black body radiation intensity of flame micro-element
V is the total number of flame control bodies, each infinitesimal body is numbered 1,2, V, …, V, for the flame radiation ray with the serial number K, the total number of the penetrated flame control bodies is n, and the number of the penetrated infinitesimal bodies along the ray direction is V1, V2, vip，…，vn。
3. The algorithm for simultaneously reconstructing three-dimensional flame temperature and smoke black volume fraction distribution according to claim 1, wherein the coefficient A is calculated as follows:
4. the algorithm for simultaneously reconstructing flame three-dimensional temperature and soot volume fraction distribution according to claim 3, wherein the second step comprises:
(21) setting an objective function F, and initializing an absorption coefficient vector k ═ k0Inner loop maximum iteration number loopmaxThe threshold epsilon for whether the iteration process is terminated, the number of initialization inner loops Loop is 1, the number of outer loops Loop is 1, and the initial annealing temperature T of the annealing plans,0；
F＝||I′λ(G)-Iλ(G)|| (4)
Wherein, Iλ(G)、I′λ(G)Respectively the measured and calculated spectral radiation intensity of G wavelength and the initial value vector kappa of the absorption coefficient0Is a vector which is randomly and continuously distributed;
(22) initializing a coefficient matrix a ═ a according to equation (3)0Calculating an initial objective function Fg，
Fg＝||A0Ibλ(G)-Iλ(G)|| (5)
Randomly selecting the p-th component kappa in the absorption coefficient vector kappapDisturbing by using the formulas (6) and (7) to obtain a new absorption coefficient vector kappanewAnd updating the coefficient matrix A according to the formula (3) to obtain Anew:
κnew,p＝κp+delta (6)
Wherein delta follows a standard normal distribution of equation 7:
delta～N(0,1) (7)
by the updated coefficient matrix AnewAnd the radiation intensity I of the blackbody spectrum under the current iteration numberbλ(G)Calculating an estimate I 'of the radiation intensity vector at the flame G wavelength for the current iteration number'λ(G)(κnew)：
I′λ(G)(κnew)＝AnewIbλ(G) (8)
Calculating a current state objective function Fl：
Fl＝||I′λ(G)(κnew)-Iλ(G)|| (9)
Wherein I in the iterative processbλ(G)Obtained by the following method:
firstly, the spectral radiation intensity vector I of the measured R wavelength is utilizedλ(R)The vector kappa of the absorption coefficient updated in the iterative processnewCoefficient matrix AnewSolving the formula (2) by using a non-negative least square algorithm to obtain the blackbody spectral radiation intensity I of each infinitesimal body of the flame under the R wavelengthbλ(R)By the formula (10),solving the temperature value T of each infinitesimal body of the flamef；
Tf＝c2/λ(R)ln{c1/[λ(R)5πIbλ(R)]+1} (10)
In the formula, c1Is a first radiation constant, c2Is a second radiation constant; t isfIs the temperature of each flame infinitesimal body; λ (R) is the R wavelength of the light;
then, the temperature of each flame infinitesimal body obtained by the formula (10) is used for calculating the blackbody spectral radiation intensity I of each flame infinitesimal body under the G wavelength according to the formula (11)bλ(G)；
Wherein λ (G) is the G wavelength of light;
(23) calculating Δ F ═ Fl－FgUpdating the objective function value FgAnd an absorption coefficient vector κ;
if Δ F<0, the state received by the annealing process is an important state, and the absorption coefficient vector k is equal to knewAn objective function Fg＝Fl；
If Δ F>0, judging whether the solid is accepted as an important state according to the probability w of the solid in the state; generating a [0,1 ] by a random data generator]Random number xi of interval, if w>Xi, the new state is the important state, and the updated absorption coefficient vector k is equal to knewAn objective function Fg＝Fl(ii) a Otherwise, the absorption coefficient vector and the target function are not updated;
(24) judging whether the inner circulation is stopped:
judging whether the loop of the iteration times of the internal loop is less than the loop of the maximum iteration times of the internal loopmaxAnd if so, looping to step (22); otherwise, stopping the internal circulation and carrying out the next step;
(25) judging whether the external circulation is stopped:
judging whether the iteration reaches the convergence condition according to the formula (12), and if not, updating the outer loop timesThe Loop +1 is set to the Loop, and the annealing temperature T of the annealing plan is updated in accordance with the annealing method of the formula (13)sLooping to step (22); otherwise, the circulation is stopped, and the next step is carried out;
Ts＝Ts,0·αLoop (13)
wherein α is a temperature decay rate;
(26) calculating the temperature and the volume fraction of the smoke black, and outputting the result:
calculating the temperature T of each micro element of the flame when the iteration is stopped according to the formula (12)endAnd absorption coefficient kappaendOutputting the temperature and the absorption coefficient, and calculating the volume fraction of the smoke black according to the following formula;
in the formula (f)vIs the soot volume fraction of the flame infinitesimal body; kappaendIs the absorption coefficient of the flame infinitesimal body; and E (m) is the complex refractive index m of the soot varying with the wavelength, which is a function of a-bi, wherein a and b are the real part and the imaginary part of the complex refractive index m of the soot, respectively.
5. The algorithm for simultaneous reconstruction of flame three-dimensional temperature and soot volume fraction distribution according to claim 4, wherein the probability function w is:
w＝exp[-ΔF/(kbTs)] (17)
wherein k isbIs the Boltzmann constant, TsThe annealing temperature for the annealing plan.
6. The algorithm for simultaneously reconstructing three-dimensional flame temperature and soot volume fraction distribution according to claim 4, wherein the temperature decay rate α is a value: alpha is more than or equal to 0.7 and less than or equal to 1.0.
7. The algorithm for simultaneous reconstruction of flame three-dimensional temperature and soot volume fraction distribution according to claim 4, wherein the solving of the non-negative least squares algorithm comprises the following steps:
the method comprises the following steps: setting the sequence gamma as an empty set, and setting the sequence Z as [1,2,3 …, M]And I isbλ＝0；
Step two: calculating M-dimensional vector, eta ═ AT(Iλ-AIbλ)；
Step three: if the sequence Z is an empty set or for all sequences i e Z, ω is satisfiediTurning to the step eleven if the temperature is less than or equal to 0, otherwise, carrying out the next step;
step four: find the exponent q, so that ηq＝max{ωi:i∈Z}；
Step five: moving the exponent q from the sequence Z into the sequence Γ;
step six: a. theΓDenoted as an S M matrix. If i ∈ Γ, the ith column of matrix A is the new matrix AΓColumn i. If i ∈ Z, then the new matrix AΓIs a zero vector and calculates a least squares problem
Defines only the solution Z satisfying the correspondence of the element i in the sequence ΓiZ corresponding to element i in the sequence ZiIs a zero solution;
step seven: if all Z corresponding to the element i in the sequence gamma are satisfiediAre both greater than 0, then IbλZ, and go to step two, otherwise go to the next step;
step eight: finding the exponent u in the sequence Γ elements such that it satisfies the following relationship:
step nine: is provided with
Let Ibλ＝Ibλ+β(Z-Ibλ)；
Step ten: index of all satisfactions
Moves from sequence Γ into sequence Z, and goes to step six;
step eleven: and finishing the calculation.
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