CN103884663A - Two-dimensional reconstruction light distribution optimization method based on laser absorption spectrum technology - Google Patents

Abstract

The invention provides a light distribution optimization method for two-dimensional reconstruction of a combustion flow field by combining a tunable semiconductor laser absorption spectrum technology and a computed tomography technology. The method comprises the following steps: a light matrix calculation step, a combustion flow field reconstruction step and a light distribution optimization step and particularly comprises the following steps: step 1, discretizing a region to be tested; pre-setting a light space distribution manner and calculating the length of light penetrating through the discretized region to obtain a light distribution matrix; step 2, selecting a suitable absorption spectrum line and calculating a light projection result of an initial gas distribution model; reconstructing temperatures and concentrations of the tested flow field by using an algebra iterative algorithm and calculating a reconstruction error and a standard deviation; and step 3, wholly searching by using a self-adaption simulated annealing method to obtain an optimal light distribution range and partially searching by using a sequential quadratic programming method to obtain optimal light distribution.

Description

2-d reconstruction distribution of light optimization method based on laser absorption spectrum technology

Technical field

The invention belongs to optics flow field diagnostic field, relate to Diode Laser Absorption Spectroscopy and computed tomography reconstruction technique, particularly relate to the optimization method of multiple objective function, can be used for distribution of light design in the measurement of Combustion Flow Field temperature/gas component concentrations 2-d reconstruction.

Background technology

Tunable diode laser absorption spectroscopy technology (TDLAS) is the laser during through flow field regions to be measured that utilizes single-frequency, in the time that laser frequency is identical with gas absorption composition transitions frequency, laser energy is absorbed, by contrast incident laser intensity and transmission laser intensity, determine the absorption value along light path direction, and then definite gas temperature and concentration physical parameter.But because TDLAS technology is the measurement based on sight line effect, its measurement result can only provide the mean value of gas parameter on light path, can not obtain the internal information in flow field.TDLAS technology is combined with computed tomography reconstruction technique, by measuring different angles light through the projection result behind flow field, utilize inversion algorithm to obtain the Two dimensional Distribution in flow field.

In actual flow field is detected, due to the restriction of experimental site and cost, a large amount of Laser emission and sniffer can not be installed, limit number and the angle of projection ray.The number of projection ray and angle directly affect the precision of rebuilding flow field, in order to improve reconstructed results quality, improve light utilization ratio, optimize distribution of light mode tool and are of great significance.

Following bibliographical information relates to the related content based on TDLAS method Combustion Flow Field 2-d reconstruction and distribution of light optimization method.

1. the people such as the Lori of North Carolina University A.Todd has studied different detector number and the impact on concentration field reconstructed results of different distribution of light mode at paper " Tomographic reconstruction of air pollutants evaluation of measurement geometries " (Applied Optics, the 36th 20 phases of volume in 1997).Result of study shows, under identical light number, detector number is more, and the projection angle of light is more, and reconstructed results is better.Under identical light number, light scanning angle is that to be better than scanning angle be the situation of 90 ° to the result of 180 °.

2. the people such as the Kristin of University of Virginia M.Busa utilizes filter back-projection algorithm to rebuild hypersonic combustor exit plane temperature and H2O concentration Two dimensional Distribution at paper " Measurements on NASA Langley Durable Combustor Rig by TDLAT Preliminary Results " (51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA-2013-0696).Experiment adopts fan beam scanning, and every group of fan beam comprises 21 light, gathers altogether 40 groups of fan beams totally 840 projection ray's data in experiment, nearly one day consuming time of whole experiment.

3. the people such as Wang Fei of Zhejiang University is at paper " Two-dimensional tomography for gas concentration and temperature distributions based on tunable diode laser absorption spectroscopy " (Measurement Science and Technology, the 4th phase of 21 volumes in 2010) directly use 4 high-speed rotary turntables parallel running in research, the tested region of synchronous scanning, gather altogether 400 data for projection, realize the 2-d reconstruction to NH3 temperature field, flue cross section and concentration field.

4. the paper of USAF laboratory Michael S.Bown " Application of Diode-Laser-Based Measurements in Hypersonic Flows " (50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA-2012-0555) carry out ground experiment for HIFiRE2 combustor exit, in experiment, respectively arrange 8 light paths along horizontal and vertical directions respectively, utilize algebraic reconstruction algorithm to rebuild temperature and the concentration Two dimensional Distribution of combustor exit.Owing to only adopting both direction projection in experiment, reconstructed results precision is not high, can only be used for qualitative analysis.

Above-mentioned document has proved the feasibility based on TDLAS technology and computed tomography reconstruction Combustion Flow Field gas parameter, but the projection ray's number more (being mostly greater than 100) adopting, mostly adopt parallel beam or fan beam projection, light utilization ratio is not high, does not carry out the research of distribution of light optimization method.

Summary of the invention

The object of this invention is to provide a kind of optimization method for Combustion Flow Field 2-d reconstruction distribution of light.This invention proposes first combining adaptive simulated annealing optimization algorithm and seqential quadratic programming optimized algorithm is optimized for TDLAS Combustion Flow Field distribution of light.The optimization method of invention utilizes the ability of searching optimum of Adaptive simulated annealing algorithm, is what a initial value of seqential quadratic programming algorithm configuration.Bring into play the advantage that seqential quadratic programming efficiency of algorithm is high simultaneously, finally obtain optimum distribution of light mode.Utilize the method, can improve light utilization ratio, obtain the best light distribution mode under certain projection ray number, measure as the multiparameter 2-d reconstruction of jet engine plume, pulse-knocking engine, scramjet engine distance piece/firing chamber and internal combustion engine equitemperature, concentration of component, density for Combustion Flow Field.

The present invention describes ray space and distributes, and the implementation of setting up projection matrix is as follows:

(1) net region that is N × N by tested discrete region, and hypothesis gas parameter character (as temperature, concentration of component and pressure etc.) in discrete net region is consistent;

(2) the distance s of the tested regional center of default ray space distribution mode, and compute ray distance and with the angle theta of x axle, as the parameter of describing ray space and distributing;

(3) compute ray, through the length of each grid, is set up projection ray's matrix.

The present invention has set up the Combustion Flow Field temperature/CONCENTRATION DISTRIBUTION 2-d reconstruction process based on algebraic reconstruction algorithm, and implementation is as follows:

(1) utilize HITRAN database, select two absorption lines, read in absorption line centre frequency, lower state energy level and absorption line strengths information;

(2) initial 5 kinds of temperature and Modeling The Concentration Profiles are set, in conjunction with projection matrix and absorption line information, calculate the projection value of every light;

(3) algebraic reconstruction algorithm initiation parameter is set, utilizes algebraic reconstruction algorithm to rebuild the Two dimensional Distribution of Combustion Flow Field temperature and gas component concentrations;

(4) reconstructed results and the comparison of original distribution model, reconstruction error and the standard deviation of five kinds of initial distribution of calculating.

The present invention has set up the distribution of light optimization method based on Adaptive simulated annealing algorithm and seqential quadratic programming algorithm, and implementation is as follows:

(1) utilize the global search of Adaptive simulated annealing algorithm to obtain best distribution of light scope, in the time that reconstruction error and standard deviation are better than current results, upgrade distribution of light mode; Otherwise, whether accept new state according to probabilistic determination.Currently once be less than 10 with a rear calculated difference ^-8time, finish Adaptive simulated annealing optimizer, output optimum results;

(2) result Adaptive simulated annealing being obtained is as the initial value of seqential quadratic programming algorithm, by objective function be reconstruction error and standard deviation with second order Taylor series expansion, and constraint condition linearization, obtain next design point by separating quadratic programming.Carry out linear search next time according to two alternative majorized functions, setting search precision is 10 ^-6, the distribution of light mode of Local Search the best.

The advantage of Combustion Flow Field 2-d reconstruction distribution of light optimization method of the present invention is:

(1) improve light utilization ratio, promoted reconstructed results quality.In one timing of projection ray's number, adopt method of the present invention to be optimized distribution of light, can improve the utilization ratio of projection ray, compare other projection patterns, can effectively improve Combustion Flow Field 2-d reconstruction outcome quality.

(2) optimization method search efficiency is high.The present invention combines Adaptive simulated annealing optimized algorithm and seqential quadratic programming algorithm first, has brought into play the advantage of Adaptive simulated annealing algorithm ability of searching optimum, has effectively avoided being absorbed in local minimum and the dependence to initial value.Adaptive simulated annealing arithmetic result is configured to the initial value of seqential quadratic programming algorithm, has brought into play the high advantage of seqential quadratic programming algorithm Local Search efficiency.

(3) optimization method highly versatile, is easy to improve.In optimized algorithm, leave self-editing function interface, can be for adding the restrictive condition of other distribution of light.The present invention can, for the distribution optimization of aphylactic map projection light number, meanwhile, can also add the restrictive conditions such as distribution of light position, projection angle, for Matching Experiment condition.

Brief description of the drawings

Fig. 1 is the system construction drawing of realizing the method for the invention.

Fig. 2 is the system flowchart of realizing the method for the invention.

Fig. 3 is 5 groups of representative gases initial temperatures of the present invention and concentration profile.

Fig. 4 is that in ASA algorithm of the present invention and SQP algorithm, reconstruction error is with the variation of iterations.

Fig. 5 is 36 distribution of light optimum results of the present invention.

Fig. 6 is temperature and the concentration Two dimensional Distribution that adopts distribution of light of the present invention to rebuild.

Embodiment

Now in conjunction with the accompanying drawings and embodiments the present invention is described in further detail for Combustion Flow Field 2-d reconstruction distribution of light optimization method.Fig. 1 has provided the structural drawing of Combustion Flow Field 2-d reconstruction distribution of light optimization system of the present invention.

Implementation of the present invention is as follows: having analysed in depth distribution of light mode to the affecting on basis of Combustion Flow Field 2-d reconstruction quality, proposed a kind of reliable, general distribution of light optimization method.The present invention is divided into three steps, i.e. compute ray matrix step, Combustion Flow Field temperature/CONCENTRATION DISTRIBUTION 2-d reconstruction step and distribution of light Optimization Steps.Specific embodiments is as follows, referring to Fig. 2:

Step 1, compute ray matrix

Light matrix calculates and comprises tested discrete region, ray space distribution calculating and projection ray's matrix construction.Concrete steps are as follows:

(1) net region that is N × N by tested discrete region, and hypothesis gas parameter character (as temperature, concentration of component and pressure etc.) in discrete net region is consistent;

(2) default ray space distribution mode, to adopt 36 projection rays as example, calculates the distance of 36 tested regional centers of light distance with with the angle of x axle

as the parameter of describing ray space distribution;

(3) compute ray, through the length of each grid, is set up projection ray's matrix.

Step 2, Combustion Flow Field temperature/CONCENTRATION DISTRIBUTION 2-d reconstruction

(1) utilize HITRAN database, select two absorption lines, read in absorption line centre frequency, lower state energy level and absorption line strengths information;

(2) initial 5 kinds of typical temperature and Modeling The Concentration Profiles are set, wherein assumed temperature is distributed as two Gauss and distributes and be superimposed upon on parabola, and temperature equation can be written as

$\begin{array}{c}{T}_0=a_1-a_2*(x^2+y^2)+a_3\exp [-\frac{{(x-x_1)}^2+{(y-y_1)}^2}{{\mathrm{\σ}}_1}]\\ +a_4\exp [-\frac{{(x-x_2)}^2+{(y-y_2)}^2}{{\mathrm{\σ}}_2}]\end{array}---\left(1\right)$

By regulating a ₁, a ₂, a ₃and a ₄four coefficients, guarantee that temperature value is greater than 0, σ ₁and σ ₂determine the precipitous degree that Gauss distributes, x ₁, y ₁, x ₂and y ₂affect Gauss center of distribution, in literary composition, chosen 5 groups of typical distributions and distribute as initial temperature, as shown in Fig. 3 (a)-(e).CONCENTRATION DISTRIBUTION is that Gauss distributes, and distribution range is 0.02-0.08, as shown in Fig. 3 (f).

(3) light matrix and the absorption line information in integrating step one, set up, calculate the projection value of every light, and wherein projection value is that integration absorption area can be expressed as

$A_j=\underset{i}{\mathrm{\Σ}}P\left(L_i\right)\mathrm{\χ}\left(L_i\right)S_v(T,L_i)L_i---\left(2\right)$

Wherein P is gas stagnation pressure, and χ is gas component concentrations to be measured, and L is the light path that absorbs gas, S _ν(T) being absorption line strengths, is the function of temperature T, can be written as

$\begin{array}{c}{S}_v\left(T\right)=S_v\left(T_0\right)\frac{Q\left(T_0\right)}{Q\left(T\right)}\frac{T_0}{T}\exp [-\frac{\mathrm{hc}{E}^{\′\′}}{k}(\frac{1}{T}-\frac{1}{T_0})]\\ \×[1-\exp (-\frac{\mathrm{hc\υ}}{\mathrm{kT}})]{[1-\exp (-\frac{\mathrm{hc\υ}}{k{T}_0})]}^{-1}\end{array}---\left(5\right)$

Wherein T ₀for reference temperature, E " be low-energy state energy level, h is Planck constant, and k is Boltzmann constant, and c is the light velocity, partition function value when Q (T) is temperature T, the partition function in certain temperature range can be used polynomial repressentation.

Being write projection ray's matrix and projection result as matrix form is

$\left[\begin{array}{cccc}{L}_{11}& L_{12}& L& L_{1N}\\ L_{21}& L_{21}& L& L_{2N}\\ M& M& M& M\\ L_{M1}& L_{M1}& L& L_{\mathrm{MN}}\end{array}\right]\·{\left[\begin{array}{c}{f}_1\\ f_2\\ M\\ f_N\end{array}\right]}_v={\left[\begin{array}{c}{A}_1\\ A_2\\ M\\ A_M\end{array}\right]}_v---\left(6\right)$

Wherein N represents that tested region is by discrete grid number, the number that M is projection ray, A _ithe integration absorptivity that represents the i article of light that centre frequency is v, f is flow field parameter to be measured, here f _j=[PS (T) χ] _j, L _ijrepresent the length of i article of light through j grid, and only relevant with the locus of projection ray.

(3) algebraic reconstruction algorithm initiation parameter is set, utilizes algebraic reconstruction algorithm to rebuild the Two dimensional Distribution of Combustion Flow Field temperature and gas component concentrations.Adopt algebraic reconstruction algorithm solving equation (2), its expression formula can be written as

${\stackrel{\→}{f}}^{\left(k\right)}={\stackrel{\→}{f}}^{(k-1)}-\mathrm{\α}\frac{({\stackrel{\→}{L}}_i\·{\stackrel{\→}{f}}^{(k-1)}-A_i)}{{\stackrel{\→}{L}}_i\·{\stackrel{\→}{L}}_i}{\stackrel{\→}{L}}_i---\left(7\right)$

Wherein k is iterations, and α is relaxation factor, due to temperature field and concentration field be on the occasion of, in iterative process, add nonnegativity restriction, meanwhile, for weakening reconstruction regions consecutive point sudden change response, in process of reconstruction, adopt smoothing processing mechanism.

(4), by reconstructed results and the comparison of original distribution mould, calculate reconstruction error and the standard deviation of five kinds of initial distribution.Wherein reconstruction error is expressed as

$e_T=\frac{{\mathrm{\Σ}}_{m=1}^M{\mathrm{\Σ}}_{n=1}^N|{T^{\mathrm{cal}}}_{m,n}-{T^{\mathrm{orig}}}_{m,n}|}{{\mathrm{\Σ}}_{m=1}^M{\mathrm{\Σ}}_{n=1}^N\left|{T^{\mathrm{orig}}}_{m,n}\right|}---\left(8\right)$

$e_X=\frac{{\mathrm{\Σ}}_{m=1}^M{\mathrm{\Σ}}_{n=1}^N|{X^{\mathrm{cal}}}_{m,n}-{X^{\mathrm{orig}}}_{m,n}|}{{\mathrm{\Σ}}_{m=1}^M{\mathrm{\Σ}}_{n=1}^N\left|{X^{\mathrm{orig}}}_{m,n}\right|}---\left(9\right)$

Wherein subscript ' cal ' represents result of calculation, and ' orig ' represents initial value.M and N represent respectively line number and the columns of discrete grid block.Using the temperature of 5 kinds of distributions and concentration error mean value and standard deviation as the objective function of optimized algorithm, be expressed as

$\begin{array}{c}\stackrel{\‾}{e_{\mathrm{\α}}}=\frac{1}{n}{\mathrm{\Σ}}_{i=1}^n{e}_{\mathrm{\α}}\\ s_{\mathrm{\α}}={\left(\frac{1}{n-1}{\mathrm{\Σ}}_{i=1}^n{(e_{\mathrm{\α}}-\stackrel{\‾}{e_{\mathrm{\α}}})}^2\right)}^{\frac{1}{2}}\end{array}---\left(10\right)$

Wherein subscript α representation temperature or concentration, n value is 5.

Step 3, distribution of light optimization

(1) initial value and variable set up: need to set projection ray's number according to measuring, the locus of Mei Tiao projection ray is determined apart from the distance s of tested regional center point with x axle angle theta by it, wherein projection ray's number is 36, setting unit grids length is " 1 ", the scope of s is-4.5-4.5 that the scope of θ is-90 °-90 °.Set absorption line, set up target system of equations;

(2) Adaptive simulated annealing: in temperature T _x, producing new state j by current state i, both are respectively E by energy _iand E _jif, E _j<E _i, accepting new state j is current state; Otherwise, according to probability exp[-(E _j-E _i)/kT _x] be greater than [0,1) interval random number is still accepted new state j, otherwise reserved state i.Repeat certain number of times, until algorithm stop criterion meets.It is 500 that maximum iteration time is set, and convergence inspection intervals is 5, and convergence residual error is 10 ^-8, initial temperature parameter is 1, the relative ratios that temperature parameter declines, decreasing ratio, parameter quenching relative speed and the loss function quenching relative speed of temperature loss function are all taken as 1.

(3) seqential quadratic programming: objective function, with second order Taylor series expansion, and constraint condition linearization, is obtained to next design point by separating quadratic programming.Carry out once linear according to two alternative majorized functions and receive rope.Set algorithm convergence precision is 10 ^-6, relatively limited difference step size is 0.001.

In Adaptive simulated annealing algorithm and seqential quadratic programming algorithm, with the variation of iterations as shown in Figure 4, wherein (a) is Adaptive simulated annealing algorithm iteration result to reconstruction error, is (b) seqential quadratic programming algorithm result of calculation.As shown in Figure 5, wherein coordinate axis is to represent with the unit length of grid division to distribution of light result after optimization, and in figure, dotted line represents the grid of dividing.Fig. 6 is for adopting optimization distribution of light of the present invention to rebuild temperature and the CONCENTRATION DISTRIBUTION result of Fig. 3 (e).

Parallel beam and fan beam projection calculating temperature field and concentration field reconstructed results compare when adopting the distribution of light reconstructed results of optimizing identical with projection ray number.Wherein parallel beam and fan beam all adopt 4 projecting directions, and each projecting direction light number is 9.Fan beam subtended angle is 45 °, and the tested regional center of beam emissions end (summit) distance is 10.As shown in the table, different light rays is divided and is planted temperature field and concentration field reconstructed results.While adopting fan beam projection, the reconstructed results relative deviation maximum of temperature field and concentration field, the reconstructed results that adopts the distribution of light of Adaptive simulated annealing and seqential quadratic programming algorithm optimization to obtain is better than other 3 kinds of situations.While adopting fan beam with parallel light beam projecting, distribution of light is comparatively sparse, while adopting ART algorithm, supposes that in each grid, gas parameter (temperature and concentration) is consistent, in the time having light to pass tested grid, just can bring this gridding information into iterative equation and calculate.Distribution of light after optimization is compared parallel beam and fan beam projection, and light layout is more reasonable.

Table different light rays is divided the eT and the eX that plant

Claims (1)

1. for a Combustion Flow Field 2-d reconstruction distribution of light optimization method, comprise following steps:

Step 1, compute ray matrix

Light matrix computing module (1) comprises tested discrete region submodule (4), ray space distribution submodule (5), projection ray's matrix submodule (6), and concrete steps are as follows:

1) net region that tested discrete region submodule (4) is N × N by tested discrete region, and hypothesis gas parameter character in discrete net region is consistent, and wherein gas property comprises temperature, concentration of component and pressure;

2) the distance s of the tested regional center of the default ray space distribution mode of ray space distribution submodule (5), and compute ray distance and with the angle theta of x axle, as the parameter of describing ray space and distributing;

3) projection ray's matrix submodule (6) compute ray, through the length of each grid, is set up projection ray's matrix;

Step 2, Combustion Flow Field temperature/CONCENTRATION DISTRIBUTION 2-d reconstruction

1) utilize HITRAN database, select two absorption lines, read in absorption line centre frequency, lower state energy level and absorption line strengths information;

2) initial gas distribution submodule (8) is set, wherein in distribution of gas model, comprise 5 kinds of temperature and CONCENTRATION DISTRIBUTION, in conjunction with projection ray's matrix submodule (6) and absorption line information submodule (7), utilize projection value calculating sub module (9) to calculate the projection value of every light;

3) algebraic reconstruction algorithm initiation parameter is set, utilizes Combustion Flow Field temperature/concentration reestablishing submodule (10), rebuild the Two dimensional Distribution of Combustion Flow Field temperature and gas component concentrations based on algebraic reconstruction algorithm;

4) reconstructed results being obtained by Combustion Flow Field temperature/concentration reestablishing submodule (10) and initial gas distribution submodule (8) relatively, calculate reconstruction error and the standard deviation of five kinds of initial distribution;

Step 3, distribution of light optimization

1) utilize Simulated Anneal Algorithm Optimize submodule (12) global search to obtain best distribution of light scope, in the time that the reconstruction error being obtained by reconstruction error calculating sub module (11) and standard deviation are better than current results, upgrade distribution of light mode; Otherwise, whether accept new state according to probabilistic determination; The more current reconstruction error calculating and standard deviation and the front reconstruction error once calculating and standard deviation, in the time that the difference of twice of front and back reconstruction error and standard deviation is all less than 10-8, finish Adaptive simulated annealing optimizer, output optimum results;

2) optimize the initial value of submodule (13) using the result of Simulated Anneal Algorithm Optimize submodule (12) as seqential quadratic programming, be that reconstruction error and standard deviation are with second order Taylor series expansion by objective function, and constraint condition linearization, obtain next design point by separating quadratic programming; Carry out linear search next time according to two alternative majorized functions, setting search precision is 10-6, the distribution of light mode of Local Search the best.

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