CN103884663B - Based on the 2-d reconstruction distribution of light optimization method of laser absorption spectroscopy - Google Patents

Based on the 2-d reconstruction distribution of light optimization method of laser absorption spectroscopy Download PDF

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CN103884663B
CN103884663B CN201410101835.6A CN201410101835A CN103884663B CN 103884663 B CN103884663 B CN 103884663B CN 201410101835 A CN201410101835 A CN 201410101835A CN 103884663 B CN103884663 B CN 103884663B
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洪延姬
王广宇
宋俊玲
石涛
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Peoples Liberation Army Strategic Support Force Aerospace Engineering University
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Abstract

The present invention is in conjunction with tunable diode laser absorption spectroscopy technology and computed tomography, provide a kind of for distribution of light optimization method during Combustion Flow Field 2-d reconstruction, the method comprises light matrix calculation procedure, Combustion Flow Field reconstruction procedures and distribution of light Optimization Steps.The first step, by tested discrete region, preset ray space distribution mode, compute ray, through the length in discretize region, obtains distribution of light matrix; Second step, selects suitable absorption line, calculates the ray cast result of initial gas distributed model, utilizes algebraic reconstruction algorithm to rebuild temperature and the concentration in tested flow field, calculates reconstruction error and standard deviation; 3rd step, adopts the global search of Adaptive simulated annealing method to obtain the distribution range of best light, then adopts sequential quadratic programming method Local Search to obtain best distribution of light.

Description

Based on the 2-d reconstruction distribution of light optimization method of laser absorption spectroscopy
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 Combustion Flow Field temperature/gas component concentrations 2-d reconstruction measurement.
Background technology
Tunable diode laser absorption spectroscopy technology (TDLAS) is when utilizing the laser of single-frequency through flow field regions to be measured, when 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 determine 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 being combined with computed tomography reconstruction technique, by measuring different angles light through the projection result behind flow field, utilizing inversion algorithm to obtain the Two dimensional Distribution in flow field.
In the flow field of reality 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 North Carolina University Lori A.Todd have studied different detector number and different distribution of light modes to the impact of concentration field reconstructed results at paper " Tomographicreconstruction of air pollutants evaluation of measurement geometries " (AppliedOptics, the 36th volume 20 phase 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 the situation that the result of 180 ° is better than that scanning angle is 90 °.
2. the people such as University of Virginia Kristin M.Busa is at paper " Measurements onNASA Langley Durable Combustor Rig by TDLAT Preliminary Results " (51stAIAA Aerospace Sciences Meeting including the New Horizons Forum andAerospace Exposition, AIAA-2013-0696) utilized filter back-projection algorithm to rebuild hypersonic combustor exit face temperature and H 2o concentration Two dimensional Distribution.Experiment adopts fan beam scanning, often organizes fan beam and comprises 21 light, gather 40 groups of fan beams totally 840 projection ray's data altogether, nearly one day consuming time of whole experiment in experiment.
3. the people such as Zhejiang University Wang Fei is at paper " Two-dimensional tomography for gasconcentration and temperature distributions based on tunable diode laserabsorption spectroscopy " (Measurement Science and Technology, 21 volumes the 4th phase in 2010) directly use 4 high-speed rotary turntables parallel running in research, the tested region of synchronous scanning, gather 400 data for projection altogether, realize flue cross section NH 3the 2-d reconstruction of temperature field and concentration field.
4. paper " Application ofDiode-Laser-Based Measurements in Hypersonic Flows " (the 50th AIAA AerospaceSciences Meeting including the New Horizons Forum and Aerospace Exposition of USAF laboratory Michael S.Bown, AIAA-2012-0555) ground experiment is carried out for HIFiRE2 combustor exit, 8 light paths are respectively arranged along horizontal and vertical directions respectively in experiment, algebraic reconstruction algorithm is utilized 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 demonstrates the feasibility of rebuilding Combustion Flow Field gas parameter based on TDLAS technology and computed tomography, but the projection ray's number more (being mostly greater than 100) adopted, 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 during combining adaptive simulated annealing optimization algorithm and seqential quadratic programming optimized algorithm optimize for TDLAS Combustion Flow Field distribution of light first.The optimization method of invention utilizes the ability of searching optimum of visual evoked potential estimation, for what a initial value sequential quadratic programming algorithm configures.Play the high advantage of sequential quadratic programming algorithm efficiency simultaneously, finally obtain optimum distribution of light mode.Utilize the method, light utilization ratio can be improved, obtain the best light distribution mode under certain projection ray number, for Combustion Flow Field 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 is measured.
According to an aspect of the present invention, provide a kind of for Combustion Flow Field 2-d reconstruction distribution of light optimization method, the method relates to light matrix computing module 1, Combustion Flow Field rebuilds module 2 and fiber distribution optimizes module 3, described light matrix computing module 1 comprises tested discrete region submodule 4, ray space distribution submodule 5 and projection ray's matrix submodule 6, described Combustion Flow Field is rebuild module 2 and is comprised absorption line information submodule 7, initial gas distributed model submodule 8, projection value calculating sub module 9, Combustion Flow Field temperature/concentration reestablishing submodule 10 and reconstruction error calculating sub module 11, described fiber distribution is optimized module 3 and is comprised Simulated Anneal Algorithm Optimize submodule 12 and seqential quadratic programming optimization submodule 13, described method comprises:
Step one, compute ray matrix
(1) tested discrete region is the net region of N × N by tested discrete region submodule 4, and hypothesis gas parameter character (as temperature, concentration of component and pressure etc.) in discrete net region is consistent;
(2) ray space distribution submodule 5 presets ray space distribution mode, and compute ray is apart from the distance s of tested regional center and the angle theta with x-axis, as the parameter describing ray space distribution;
(3) projection ray's matrix submodule 6 compute ray is through the length of each grid, sets 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 comprise 5 kinds of temperature and CONCENTRATION DISTRIBUTION in distribution of gas model, in conjunction with projection ray's matrix submodule 6 and absorption line information submodule 7, projection value calculating sub module 9 is utilized to calculate the projection value of every bar 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 obtained by Combustion Flow Field temperature/concentration reestablishing submodule 10 and the initial gas submodule 8 that distributes compares, and calculates 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, when the reconstruction error 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 that calculates and standard deviation and the front reconstruction error that once calculates and standard deviation, when the difference of twice, front and back reconstruction error and standard deviation is all less than 10 -8time, terminate Adaptive simulated annealing optimizer, export optimum results;
(2) result of Simulated Anneal Algorithm Optimize submodule 12 is optimized the initial value of submodule 13 as seqential quadratic programming, by objective function and reconstruction error and standard deviation with second order Taylor series expansion, and constraint condition linearization, obtain next design point by separating quadratic programming; Perform 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.
Wherein, the step one of aforementioned compute ray matrix describes ray space distribution, sets up the implementation of projection matrix.
The step 2 of previous combustion flow field temperature/CONCENTRATION DISTRIBUTION 2-d reconstruction is for setting up the Combustion Flow Field temperature/CONCENTRATION DISTRIBUTION 2-d reconstruction process based on algebraic reconstruction algorithm.
The step 3 of aforementioned distribution of light optimization is the distribution of light optimization method for setting up based on visual evoked potential estimation and sequential quadratic programming algorithm.
The advantage of Combustion Flow Field 2-d reconstruction distribution of light optimization method of the present invention is:
(1) improve light utilization ratio, improve reconstructed results quality.In projection ray's number one timing, adopt method of the present invention to be optimized distribution of light, the utilization ratio of projection ray can be improved, compare other projection patterns, effectively can improve Combustion Flow Field 2-d reconstruction outcome quality.
(2) optimization method search efficiency is high.Adaptive simulated annealing optimized algorithm and sequential quadratic programming algorithm combine by the present invention first, have played the advantage of visual evoked potential estimation ability of searching optimum, effectively prevent and are absorbed in local minimum and the dependence to initial value.Visual evoked potential estimation result is configured to the initial value of sequential quadratic programming algorithm, has played the advantage that sequential quadratic programming algorithm Local Search efficiency is high.
(3) optimization method highly versatile, is easy to improve.Leave self-editing function interface in optimized algorithm, may be used for the restrictive condition adding other distribution of light.The present invention may be used 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.
Accompanying drawing explanation
Fig. 1 is the system construction drawing realizing the method for the invention.
Fig. 2 is the system flowchart 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 change of iterations.
Fig. 5 is 36 distribution of light optimum results of the present invention.
Fig. 6 is the temperature and concentration Two dimensional Distribution that adopt distribution of light of the present invention to rebuild.
Embodiment
Now be used for Combustion Flow Field 2-d reconstruction distribution of light optimization method to the present invention to be in conjunction with the accompanying drawings and embodiments described in further detail.Fig. 1 gives 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: affect on basis on Combustion Flow Field 2-d reconstruction quality having analysed in depth distribution of light mode, propose 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, see Fig. 2:
Step one, 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) be the net region of 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) preset ray space distribution mode, to adopt 36 projection rays, calculate the distance of 36 light apart from tested regional center and with the angle of x-axis as the parameter describing ray space distribution;
(3) compute ray is through the length of each grid, sets 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) arrange initial 5 kinds of typical temperature and Modeling The Concentration Profiles, wherein assumed temperature is distributed as two Gauss and distributes and be superimposed upon on parabola, and temperature equation can be written as
T 0 = a 1 - a 2 * ( x 2 + y 2 ) + a 3 exp [ - ( x - x 1 ) 2 + ( y - y 1 ) 2 σ 1 ] + a 4 exp [ - ( x - x 2 ) 2 + ( y - y 2 ) 2 σ 2 ] - - - ( 1 )
By regulating a 1, a 2, a 3and a 4four coefficients, guarantee that temperature value is greater than 0, σ 1and σ 2determine the steep of Gauss distribution, x 1, y 1, x 2and y 2have impact on the center of Gauss distribution, choose 5 groups in literary composition and typically distribute as initial temperature distribution, as shown in Fig. 3 (a)-(e).CONCENTRATION DISTRIBUTION is Gauss distribution, and distribution range is 0.02-0.08, as shown in Fig. 3 (f).
(3) light matrix set up in integrating step one and absorption line information, calculate the projection value of every bar light, wherein projection value and integration absorption area can be expressed as
A j = Σ i p ( L i ) χ ( L i ) S v ( T , L i ) L i - - - ( 2 )
Wherein P is gas stagnation pressure, and χ is gas component concentrations to be measured, and L is the light path absorbing gas, S ν(T) be absorption line strengths, be the function of temperature T, can be written as
S v ( T ) = S v ( T 0 ) Q ( T 0 ) Q ( T ) T 0 T exp [ - hc E ″ k ( 1 T - 1 T 0 ) ] × [ 1 - exp ( - hcυ kT ) ] [ 1 - exp ( - hcυ k T 0 ) ] - 1 - - - ( 5 )
Wherein T 0for reference temperature, " be low-energy state energy level, h is Planck constant to E, and k is Boltzmann constant, and c is the light velocity, and Q (T) is partition function value during temperature T, and the partition function in certain temperature range can use polynomial repressentation.
Being write projection ray's matrix and projection result as matrix form is
L 11 L 12 . . . L 1 N L 21 L 21 . . . L 2 N . . . . . . . . . . . . L M 1 L M 1 . . . L MN · f 1 f 2 . . . f N v = A 1 A 2 . . . A M v - - - ( 6 )
Wherein N represents that tested region is by discrete lattice number, and M is the number of projection ray, A irepresent that centre frequency is the integration absorptivity of i-th light of v, f is flow field parameter to be measured, here f j=[PS (T) χ] j, L ijrepresent the length of i-th light through a jth 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
f → ( k ) = f → ( k - 1 ) - α ( L → i · f → ( k - 1 ) - A i ) L → i · L → i L → i - - - ( 7 )
Wherein k is iterations, and α is relaxation factor, due to temperature field and concentration field be on the occasion of, add in an iterative process nonnegativity restriction, meanwhile, for weaken reconstruction regions consecutive point sudden change response, adopt in process of reconstruction smoothing processing mechanism.
(4) reconstructed results is compared with original distribution mould, calculate reconstruction error and the standard deviation of five kinds of initial distribution.Wherein reconstruction error is expressed as
e T = Σ m = 1 M Σ n = 1 N | T cal m , n - T orig m , n | Σ m = 1 M Σ n = 1 N | T orig m , n | - - - ( 8 )
e X = Σ m = 1 M Σ n = 1 N | X cal m , n - X orig m , n | Σ m = 1 M Σ n = 1 N | X orig m , n | - - - ( 9 )
Wherein subscript ' cal ' represents result of calculation, and ' orig ' represents initial value.M and N represents line number and the columns of discrete grid block respectively.Using 5 kinds of temperature and concentration error mean value and standard deviation distributed as the objective function of optimized algorithm, be expressed as
e α ‾ = 1 n Σ i = 1 n e α
S α = ( 1 n - 1 Σ i = 1 n ( e α - e α ‾ ) 2 ) 1 2 - - - ( 10 )
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 setting projection ray number according to measurement, the locus of Mei Tiao projection ray by it apart from the distance s of tested regional center point with determine with x-axis angle theta, wherein projection ray's number is 36, set unit grids length as " 1 ", the scope of s is the scope of-4.5-4.5, θ is-90 °-90 °.Setting absorption line, sets up target system of equations;
(2) Adaptive simulated annealing: at temperature T x, produce new state j by current state i, both are respectively E by energy iand E jif, E j<E i, then 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 then still accepts new state j, otherwise reserved state i.Repeat certain number of times, until algorithm stop criterion meets.Arranging maximum iteration time is 500, and convergence inspection intervals is 5, and convergence residual error is 10 -8, initial temperature parameter is 1, and the relative ratios that temperature parameter declines, the decreasing ratio of temperature loss function, parameter quenching relative speed and loss function quenching relative speed are all taken as 1.
(3) seqential quadratic programming: by objective function with second order Taylor series expansion, and constraint condition linearization, obtain next design point by separating quadratic programming.Perform 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 visual evoked potential estimation and sequential quadratic programming algorithm, reconstruction error with iterations change as shown in Figure 4, wherein (a) is visual evoked potential estimation iteration result, and (b) is sequential quadratic programming algorithm result of calculation.As shown in Figure 5, wherein to distribution of light result after optimization coordinate axis represent with the unit length of grid division, and in figure, dotted line represents the grid of division.Temperature and the CONCENTRATION DISTRIBUTION result of Fig. 6 for adopting optimization distribution of light of the present invention to rebuild Fig. 3 (e).
Parallel beam and fan beam when adopting the distribution of light reconstructed results optimized identical with projection ray number are projected and calculates temperature field and concentration field reconstructed results compares.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 beam emissions end (summit) is 10 apart from tested regional center.As shown in the table, different light rays is divided and is planted temperature field and concentration field reconstructed results.When adopting fan beam projection, the reconstructed results relative deviation of temperature field and concentration field is maximum, and the reconstructed results adopting the distribution of light of Adaptive simulated annealing and sequential quadratic programming algorithm optimization to obtain is better than other 3 kinds of situations.When adopting fan beam and parallel beam projections, distribution of light is comparatively sparse, when adopting ART algorithm, supposes that gas parameter in each grid (temperature and concentration) is consistent, when there being light to pass tested grid, just can bringing this gridding information into iterative equation and calculating.Distribution of light after optimization compares parallel beam and fan beam projection, and light layout is more reasonable.
Table different light rays divides the e planted tand e x

Claims (1)

1., for a Combustion Flow Field 2-d reconstruction distribution of light optimization method, comprise following steps:
Step one, 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) tested discrete region is the net region of N × N by tested discrete region submodule (4), and hypothesis gas parameter character in discrete net region is consistent, and wherein gas property comprises temperature, concentration of component and pressure;
2) ray space distribution submodule (5) presets ray space distribution mode, and compute ray is apart from the distance s of tested regional center and the angle theta with x-axis, as the parameter describing ray space distribution;
3) projection ray's matrix submodule (6) compute ray is through the length of each grid, sets 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 comprise 5 kinds of temperature and CONCENTRATION DISTRIBUTION in distribution of gas model, in conjunction with projection ray's matrix submodule (6) and absorption line information submodule (7), projection value calculating sub module (9) is utilized to calculate the projection value of every bar 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 obtained by Combustion Flow Field temperature/concentration reestablishing submodule (10) and the initial gas submodule (8) that distributes compares, and calculates 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, when the reconstruction error 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 that calculates and standard deviation and the front reconstruction error that once calculates and standard deviation, when the difference of twice, front and back reconstruction error and standard deviation is all less than 10-8, terminates Adaptive simulated annealing optimizer, export optimum results;
2) result of Simulated Anneal Algorithm Optimize submodule (12) is optimized the initial value of submodule (13) as seqential quadratic programming, by objective function and reconstruction error and standard deviation with second order Taylor series expansion, and constraint condition linearization, obtain next design point by separating quadratic programming; Perform 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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