CN106289568A - A kind of detonation flame temperature measurement system and the method for reconstructing of three-dimensional temperature field - Google Patents

Abstract

The present invention relates to a kind of detonation flame temperature measurement system and the method for reconstructing of three-dimensional temperature field, utilize some acoustic sensors and speaker that the detonation combustor temperature field at same position is measured.It is analyzed data processing, then utilizes cross-correlation technique to remain able to obtain time delay accurately in the case of signal to noise ratio is low and estimate.Disturb for combustion chamber environment reverberation, study the related algorithm processed based on cepstrum, improve Time delay Estimation Accuracy.Discrete region method based on LSQR algorithm (Least Squares QR Decomposition) is utilized to rebuild the temperature field in pulse-knocking engine combustor again in MATLAB.

Description

A kind of detonation flame temperature measurement system and the method for reconstructing of three-dimensional temperature field

Technical field

Present document relates to the measuring method of a kind of ignition temperature field distribution, especially the measurement side in detonation combustor temperature field Method, belongs to combustion diagnosis field.

Background technology

Document is " based on sonic sensor aeroengine combustor buring room Exit temperature distribution measurement Research, Shenyang aircraft industry Institute reports, Vol.26, No.2 " disclose and a kind of measure aeroengine combustor buring room Exit temperature distribution based on sonic sensor Method.The method is measured sound wave first with multiple acoustic sensors and is flown over the time used in this temperature field, then by the biography of sound wave Broadcast the relation of speed and medium temperature, draw the mean temperature of this propagation path, then utilize calculating based on method of least square Machine tomographic techniques (Computed Tomography) realizes the emulation of two-dimensional temperature field and rebuilds.Method described in document, the method is relatively Measure combustor exit temperature distribution accurately, preferably reflect the true temperature of flame.But due to combustor internal ring Border is severe, and outlet noise is very big, and sound wave has reflection, so combustor exit temperature distribution can not accurately be measured.And, This method only measures combustor exit temperature, it is impossible to research burning indoor temperature field feature respectively.Therefore, method described in document It is difficult to the combustor bulk temperature characteristic distributions in adverse circumstances is accurately measured.

Summary of the invention

Solve the technical problem that

Pulse-knocking engine (PDE, Pulse Detonation Engine) is a kind of new ideas based on detonating combustion Electromotor.The detonation wave that detonating combustion produces makes the pressure of detonation material, temperature to raise rapidly.In order to overcome adverse circumstances moderate heat Flame temperature is difficult to the difficult problem measured, and the present invention proposes a kind of detonation flame temperature measurement system and the reconstruction side of three-dimensional temperature field Method.

Technical scheme

The present invention utilizes some acoustic sensors and speaker to enter the detonation combustor temperature field at same position Row is measured.It is analyzed data processing, then utilizes cross-correlation technique to remain able to obtain standard in the case of signal to noise ratio is low True time delay is estimated.Disturb for combustion chamber environment reverberation, study the related algorithm processed based on cepstrum, improve time delay and estimate essence Degree.Discrete region method weight based on LSQR algorithm (Least Squares QR-Decomposition) is utilized again in MATLAB Build the temperature field in pulse-knocking engine combustor.

A kind of detonation flame temperature measurement system, it is characterised in that include band sound card and the main frame of display, power amplification Device, relay, number adopt card, terminal board, signal conditioner, speaker and mike；Speaker and mike are located at pinking combustion Burn indoor, band sound card and the main frame of display, power amplifier, relay, number to adopt card, terminal board and signal conditioner and be positioned at quick-fried Outside shake combustor, speaker is connected with relay, and mike is connected with signal conditioner；Sound wave thermometric software system in main frame Send digital sound wave signal, after sound card is converted to analogue signal, then arrive relay switch through power amplifier amplification output One end；Meanwhile, the sound wave thermometric software system on main frame is adopted digital I/O on card to number and is exported high level, high level by Adopt the terminal board extraction that card is connected with number, control cable deactivation relay through signal, the simulation letter that power amplifier is exported Number being transferred to speaker, analogue signal is converted into acoustic signals by speaker, and the acoustic signals received is converted to by mike Voltage signal, after signal conditioner amplifies, is adopted card by number and gathers, be then input to sound wave thermometric software system and carry out three-dimensional temperature The reconstruction of degree field.

The quantity of speaker and mike is respectively 20, and a speaker and a mike form one group, and 20 groups equal On even each limit being distributed in cubic space.

A kind of voltage signal recording detonation flame temperature measurement system carries out the method for reconstructing of three-dimensional temperature field, and it is special Levy and be that step is as follows:

Step 1: use Cepstrum Method voltage signal that two Mikes are received to carry out Cepstrum Transform:

Wherein, the voltage signal received is:

x₁(t)=h₁(t)*s(t-τ₁)+n₁(t)

x₂(t)=h₂(t)*s(t-τ₂)+n₂(t)

Wherein, h₁(t)、h₂T () is the unit impulse response of combustor；n₁(t)、n₂T () is the noise letter that mike receives Number；s(t-τ₁)、s(t-τ₂) it is that two mikes receive the signal that sends of speakers；

Carrying out the voltage signal after Cepstrum Transform is:

x₁(t)=s (t-τ₁)+n₁(t)

x₂(t)=s (t-τ₂)+n₂(t)

Step 2: to the x after Cepstrum Transform₁(t) and x₂T () carries out computing cross-correlation:

$R_{x_1{x}_2}\left(\mathrm{\τ}\right)=\frac{1}{2\mathrm{\π}}\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\∫}}{x}_1(t-\mathrm{\τ})x_2\left(t\right)dt=\frac{1}{2\mathrm{\π}}\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\∫}}\[s_1(t-\mathrm{\τ})+n_1(t-\mathrm{\τ})\]\[{\mathrm{As}}_2\left(t\right)+n_2\left(t\right)\]dt$

Abbreviation can obtain:

$R_{x_1{x}_2}\left(\mathrm{\τ}\right)=R_{s_1{s}_2}\left(\mathrm{\τ}\right)+R_{s_1{n}_2}\left(\mathrm{\τ}\right)+R_{n_1{s}_2}\left(\mathrm{\τ}\right)+R_{n_1{n}_2}\left(\mathrm{\τ}\right)$

Wherein, A is the attenuation quotient in propagation process of sound wave,For the computing cross-correlation result of signal,It is respectively signal and the computing cross-correlation result of noise,It it is noise computing cross-correlation knot Really, it is apparent fromIt is zero, can be reduced to:

$R_{x_1{x}_2}\left(\mathrm{\τ}\right)=R_{s_1{s}_2}\left(\mathrm{\τ}\right)=\frac{1}{2\mathrm{\π}}\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\∫}}{s}_1(t-\mathrm{\τ})s_2\left(t\right)dt=\frac{1}{2\mathrm{\π}}\underset{-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\∫}}s(t+\mathrm{\Δ}t-\mathrm{\τ})s\left(t\right)dt=R_s(\mathrm{\τ}-\mathrm{\Δ}t)$

Wherein, Δ t is time delay, because R_s(τ-Δt)≤R_s(0), as τ=Δ t,Obtain maximum, Then by calculating, the moment that cross-correlation function peak value occurs is time delay Δ t and i.e. flies over time τ；

Step 3: employing LSQR algorithm reconstruction temperature field:

Three-dimensional Combustion room measurement space is divided into 3 × 3 × 3=27 space lattice, then

${\mathrm{\τ}}_i=\underset{j=1}{\overset{N}{\Σ}}{w}_{ij}{f}_j,i=1,2...,58$

In formula: w_ijIt is i-th paths length by jth space lattice；τ_iThe sound of i-th sound wave path for recording Ripple flies over the time；f_jFor the inverse of acoustic wave propagation velocity in region to be measured；

Control 20 speakers and launch acoustic signals successively, form one and measure the cycle, then obtain 58 sound wave paths, phase The system of linear equations answered is:

$\begin{array}{c}{w}_{11}{f}_1+w_{12}{f}_2+\mathrm{...}+w_{1,27}{f}_{27}={\mathrm{\τ}}_1\\ w_{21}{f}_1+w_{22}{f}_2+\mathrm{...}+w_{2,27}{f}_{27}={\mathrm{\τ}}_2\\ .\\ .\\ .\\ w_{58,1}{f}_1+w_{58,2}{f}_2+\mathrm{...}{w}_{58,27}{f}_{27}={\mathrm{\τ}}_{58}\end{array}$

Equation group is expressed in matrix as

Ax=b, is the mathematical model of three dimensional displacement fields

In formula:It is 58 × 27 right-safeguarding factor matrixs, reflects jth space lattice to i-th sound The contribution of wave path: x=(f₁,f₂,…,f₂₇)^T, it is 27 dimension temperature field vectors；B=(τ₁,τ₂,…,τ₅₈)^T, obtain for step 2 58 dimensions fly over measure of time data vector；

Obtain matrix x=(f₁,f₂,…,f₂₇)^T, by x=(f₁,f₂,…,f₂₇)^TBring intoWherein Z For acoustic constants, i.e. solve the mean temperature in each grid, using this temperature as the temperature of each mesh space geometric center Degree, then in MATLAB, call cubic spline interpolation method can draw the three-dimensional temperature field of whole area of space to be measured.

Beneficial effect

A kind of detonation flame temperature measurement system of present invention proposition and the method for reconstructing of three-dimensional temperature field, use acoustics to survey It is fast that temperature has the speed of response, is not affected the advantages such as radiation by extraneous wall temperature.When the time of acquisition, owing to have employed cross-correlation skill Art, can obtain accurate time delay in the environment of low signal-to-noise ratio and estimate.It addition, use the method for cepstrum that reverberation is carried out Process, decrease the acoustic reflection impact on measuring.In reconstruction of temperature field, have employed discrete region based on LSQR algorithm Method, it is possible to achieve the three-dimensional structure in temperature field, measures and monitoring in real time continuously.Finally realize high temperature, the pinking of high spread speed Flame transient temperature field analysis.

Accompanying drawing explanation

Fig. 1 is the method for the present invention experiment schematic diagram to detonation combustor temperature field measurement

Fig. 2 is sensor mounting location schematic diagram

During Fig. 3, the present invention proposes the flow chart of method

Detailed description of the invention

In conjunction with embodiment, accompanying drawing, the invention will be further described:

The step of described detonation flame image temp measuring method is as follows:

Step 1: building of pinking laboratory table.With reference to Fig. 1, for a certain pulse-knocking engine model machine, fire in pinking (speaker and mike have collectively constituted sound wave sensing to be respectively mounted 20 mikes and speaker in burning some space of room Device), connect computer by data collecting card；First digital sound wave signal is sent by the sound wave thermometric software system in main frame, After sound card is converted to analogue signal, then export through power amplifier amplification, one end of arrival relay switch, meanwhile, Sound wave thermometric software system on main frame is adopted digital I/O on card to number and is exported high level, and this high level is connected by adopting card with number Terminal board draw, through control signal cable deactivation relay, the analogue signal that power amplifier is exported and speaker phase Connection, makes speaker launch acoustic signals.The acoustic signals of arrival is converted to voltage signal by mike, through signal conditioner After amplification, being adopted card by number and gather, voltage signal is called in by the sound wave thermometric software on main frame.

Step 2: the time obtains.

Number adopts the Guan Bi of 20 relays having 20 radical word I/O output lead correspondences to control on relay switch plate on card, Thus realize the programme-control that acoustic signals is launched.Speaker and mike are arranged in a space of combustor, ginseng According to Fig. 2, being numbered in the direction of the clock, respectively No. 1-20, each only one of which speaker launches acoustic signals, when No. 1 When speaker launches acoustic signals, the data that the data gathered with the mike of No. 1 gather with other 19 mikes numbered Carrying out computing cross-correlation, correspondence show that on 19 paths, sound wave flies over the time, and 1-20 speaker launches acoustic signals successively, composition Measure the cycle for one.The voltage signal recorded is called in sound wave thermometric software, then with cross correlation algorithm, when available sound wave flies over Between.Calculating process is:

Step 2.1: reverberation process-Cepstrum Method.

When there is reverberation in combustor, it is assumed that the voltage signal that the acoustic signals that two Mikes receive is converted into can represent For:

x₁(t)=h₁(t)*s(t-τ₁)+n₁(t)

x₂(t)=h₂(t)*s(t-τ₂)+n₂(t)

Wherein, h₁(t) and h₂The unit impulse response of (t) combustor；n₁(t), n₂T () is the noise letter that mike receives Number；s(t-τ₁), s (t-τ₂) it is the signal that sends of the speaker that two mikes receive.

Above formula is done Cepstrum Transform:

$\stackrel{\‾}{X}\left(k\right)=\stackrel{\‾}{h}\left(k\right)+\stackrel{\‾}{s}\left(k\right)+\stackrel{\‾}{\mathrm{\ϵ}}\left(k\right)$

Wherein,It is x (t), h (t) respectively, s) cepstrum t).

The Fourier transform of unit impulse response h (t) is H (ω), and it can be divided into minimum phase part H_ap(ω), and entirely Logical part H_min(ω), such as following formula:

H (ω)=H_ap(ω)H_min(ω)

Wherein, | H_ap(ω) |=1.

The cepstrum of unit impulse response h (t) is:

$\stackrel{\‾}{h}\left(k\right)={\stackrel{\‾}{h}}_{ap}\left(k\right)+{\stackrel{\‾}{h}}_{min}\left(k\right)$

WhereinThe most corresponding all-pass sections and the cepstrum of minimum phase part, by the property of minimum phase Matter can obtain the minimum phase part of cepstrum:

${\stackrel{\&OverBar;}{h}}_{min}\left(k\right)=\left\{\begin{array}{c}0,k<0\\ \stackrel{\&OverBar;}{h}\left(k\right),k=0\\ \stackrel{\&OverBar;}{h}\left(k\right)+\stackrel{\&OverBar;}{h}(-k),k>0\end{array}\right.$

${\stackrel{\&OverBar;}{h}}_{ap}\left(k\right)=\left\{\begin{array}{c}\stackrel{\&OverBar;}{h}\left(k\right),k<0\\ \stackrel{\&OverBar;}{h}\left(0\right),k=0\\ -\stackrel{\&OverBar;}{h}(-k),k>0\end{array}\right.$

Because the cepstrum of input signal x (t) can be expressed as:

$\stackrel{\&OverBar;}{X}\left(k\right)={\stackrel{\&OverBar;}{h}}_{ap}\left(k\right)+{\stackrel{\&OverBar;}{h}}_{min}\left(k\right)+\stackrel{\&OverBar;}{s}\left(k\right)+\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}\left(k\right)$

Delay, τ is converted into e at frequency domain^jωrForm, it will only affect all-pass sections, and not produce minimum phase part Impact, from signal cepstrumIn deductPart:

$X\left(k\right)={\stackrel{\&OverBar;}{h}}_{ap}\left(k\right)+\stackrel{\&OverBar;}{s}\left(k\right)+\stackrel{\&OverBar;}{\mathrm{\&epsiv;}}\left(k\right)$

X (k) is changed to time domain:

X (t)=s (t-τ)+n (t)

Step 2.2: correlation time-delay estimate method

Signal step 2.1 processed, is x (t), carries out computing cross-correlation:

$R_{x_1{x}_2}\left(\mathrm{\&tau;}\right)=\frac{1}{2\mathrm{\&pi;}}\underset{-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Integral;}}{x}_1(t-\mathrm{\&tau;})x_2\left(t\right)dt=\frac{1}{2\mathrm{\&pi;}}\underset{-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Integral;}}\&lsqb;s_1(t-\mathrm{\&tau;})+n_1(t-\mathrm{\&tau;})\&rsqb;\&lsqb;{\mathrm{As}}_2\left(t\right)+n_2\left(t\right)\&rsqb;dt$

Abbreviation can obtain:

$R_{x_1{x}_2}\left(\mathrm{\&tau;}\right)=R_{s_1{s}_2}\left(\mathrm{\&tau;}\right)+R_{s_1{n}_2}\left(\mathrm{\&tau;}\right)+R_{n_1{s}_2}\left(\mathrm{\&tau;}\right)+R_{n_1{n}_2}\left(\mathrm{\&tau;}\right)$

Wherein,For the computing cross-correlation result of signal,It is respectively signal and noise Computing cross-correlation result,It it is noise computing cross-correlation result.It is apparent from It is zero.Can be reduced to:

$R_{x_1{x}_2}\left(\mathrm{\&tau;}\right)=R_{s_1{s}_2}\left(\mathrm{\&tau;}\right)=\frac{1}{2\mathrm{\&pi;}}\underset{-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Integral;}}{s}_1(t-\mathrm{\&tau;})s_2\left(t\right)dt=\frac{1}{2\mathrm{\&pi;}}\underset{-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Integral;}}s(t+\mathrm{\&Delta;}t-\mathrm{\&tau;})s\left(t\right)dt=R_s(\mathrm{\&tau;}-\mathrm{\&Delta;}t)$

Wherein, Δ t is time delay, because R_s(τ-Δt)≤R_s(0), as τ=Δ t,Obtain maximum, Then by calculating, the moment that cross-correlation function peak value occurs is time delay Δ t.

Abscissa corresponding to correlation function maximum of points is exactly time delay.

Can effectively be suppressed the interference of combustor noise by cross-correlation technique, obtain more in the environment of low signal-to-noise ratio Time delay is estimated accurately.

Step 3: experimental calibration.

Setting D is the distance between speaker and mike, and unit is m；τ is that sound wave flies over the time, and unit is that ms, T are Temperature, unit is degree Celsius.Then hygrometric formula:

$T=\frac{D^2}{{\mathrm{Z\&tau;}}^2}\&times;{10}^6-273.16---\left(1\right)$

Wherein, Z is acoustic constants, unit m²/(s²K), released by hygrometric formula is counter

$Z=\frac{D^2}{(T+273.16){\mathrm{\&tau;}}^2}\&times;{10}^6---\left(2\right)$

Terminate at Thermal-state test, when flue-gas temperature is cooled to room temperature, record room temperature.According to formula (2), calculate 10 groups of numbers According to, try to achieve Z, average, obtaining Z is 20.19m²/(s²K)。

Step 4: the foundation in detonation combustor temperature field.It is as follows that LSQR algorithm rebuilds temperature field:

Make L_iIt is i-th sound wave path, τ_iSound wave for recording in step 2 flies over the time, has a formula:

${\mathrm{\&tau;}}_i={\&Integral;}_{L_i}\frac{1}{v(x,y,z)}dl={\&Integral;}_{L_i}f(x,y,z)dl---\left(3\right)$

In formula: (x, y, z) be acoustic wave propagation velocity in region to be measured to v, and (x, y z) are v (x, y, inverse z) to f.

Detonation combustor typically has a size of 10 × 10 × 100cm, chooses a measurement at combustor exit to 10cm Space (10 × 10 × 10cm).Acoustic thermometry space has 58 sound wave paths (remove and overlap and on wall), three-dimensional is fired Burn room measurement space and be divided into 3 × 3 × 3=27 space lattice, then can obtain according to formula (3):

${\mathrm{\&tau;}}_i=\underset{j=1}{\overset{N}{\&Sigma;}}{w}_{ij}{f}_j,i=1,2...,58$

In formula: w_ijIt is i-th paths length by jth space lattice.

Through the measurement in a cycle, a system of linear equations can be obtained:

$\begin{array}{c}{w}_{11}{f}_1+w_{12}{f}_2+\mathrm{...}+w_{1,27}{f}_{27}={\mathrm{\&tau;}}_1\\ w_{21}{f}_1+w_{22}{f}_2+\mathrm{...}+w_{2,27}{f}_{27}={\mathrm{\&tau;}}_2\\ .\\ .\\ .\\ w_{58,1}{f}_1+w_{58,2}{f}_2+\mathrm{...}{w}_{58,27}{f}_{27}={\mathrm{\&tau;}}_{58}\end{array}$

Equation group matrix is represented by

Ax=b, is the mathematical model of three dimensional displacement fields

In formula:It is 58 × 27 right-safeguarding factor matrixs, reflects jth space lattice to i-th sound wave The contribution in path: x=(f₁,f₂,…,f₂₇)^T, x is 27 dimension speed inverse vectors: b=(τ₁,τ₂,…,τ₅₈)^T, it is that 58 dimensions fly over Measure of time data vector.

Obtain matrix x, i.e. carry it into formula (1), utilize step 3 to draw to obtain Z, temperature can be obtainedI.e. solve the mean temperature in each grid, using this temperature as in each mesh space geometry The temperature of the heart, then in MATLAB, call cubic spline interpolation method can draw the three dimensional temperature of whole area of space to be measured ?.

Claims (3)

1. a detonation flame temperature measurement system, it is characterised in that include band sound card and the main frame of display, power amplifier, Relay, number adopt card, terminal board, signal conditioner, speaker and mike；Speaker and mike are located at detonation combustor In, band sound card and the main frame of display, power amplifier, relay, number are adopted card, terminal board and signal conditioner and are positioned at pinking combustion Burning outdoor, speaker is connected with relay, and mike is connected with signal conditioner；Sound wave thermometric software system in main frame sends Digital sound wave signal, after sound card is converted to analogue signal, then amplifies output one end to relay switch through power amplifier； Meanwhile, the sound wave thermometric software system on main frame is adopted the digital I/O on card to number and is exported high level, and high level is adopted by with number The terminal board that card is connected is drawn, and controls cable deactivation relay through signal, the analogue signal transmission exported by power amplifier To speaker, analogue signal is converted into acoustic signals by speaker, and the acoustic signals received is converted to voltage letter by mike Number, after signal conditioner amplifies, adopted card by number and gather, be then input to sound wave thermometric software system and carry out three-dimensional temperature field Rebuild.

A kind of detonation flame temperature measurement system the most according to claim 1, it is characterised in that speaker and mike Quantity is respectively 20, and a speaker and a mike form one group, and 20 groups are evenly distributed in each of cubic space On individual limit.

3. the voltage signal recording the detonation flame temperature measurement system described in claim 2 carries out three-dimensional temperature field Method for reconstructing, it is characterised in that step is as follows:

Step 1: use Cepstrum Method voltage signal that two Mikes are received to carry out Cepstrum Transform:

Wherein, the voltage signal received is:

x₁(t)=h₁(t)*s(t-τ₁)+n₁(t)

x₂(t)=h₂(t)*s(t-τ₂)+n₂(t)

Wherein, h₁(t)、h₂T () is the unit impulse response of combustor；n₁(t)、n₂T () is the noise signal that mike receives；s (t-τ₁)、s(t-τ₂) it is that two mikes receive the signal that sends of speakers；

Carrying out the voltage signal after Cepstrum Transform is:

x₁(t)=s (t-τ₁)+n₁(t)

x₂(t)=s (t-τ₂)+n₂(t)

Step 2: to the x after Cepstrum Transform₁(t) and x₂T () carries out computing cross-correlation:

$R_{x_1{x}_2}\left(\mathrm{\&tau;}\right)=\frac{1}{2\mathrm{\&pi;}}\underset{-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Integral;}}{x}_1(t-\mathrm{\&tau;})x_2\left(t\right)\mathrm{\&omega;}=\frac{1}{2\mathrm{\&pi;}}\underset{-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Integral;}}\&lsqb;s_1(t-\mathrm{\&tau;})+n_1(t-\mathrm{\&tau;})\&rsqb;\&lsqb;{\mathrm{As}}_2\left(t\right)+n_2\left(t\right)\&rsqb;dt$

Abbreviation can obtain:

$R_{x_1{x}_2}\left(\mathrm{\&tau;}\right)=R_{s_1{s}_2}\left(\mathrm{\&tau;}\right)+R_{s_1{n}_2}\left(\mathrm{\&tau;}\right)+R_{n_1{s}_2}\left(\mathrm{\&tau;}\right)+R_{n_1{n}_2}\left(\mathrm{\&tau;}\right)$

Wherein, A is the attenuation quotient in propagation process of sound wave,For the computing cross-correlation result of signal,It is respectively signal and the computing cross-correlation result of noise,It it is noise computing cross-correlation knot Really, it is apparent fromIt is zero, can be reduced to:

$R_{x_1{x}_2}\left(\mathrm{\&tau;}\right)=R_{s_1{s}_2}\left(\mathrm{\&tau;}\right)=\frac{1}{2\mathrm{\&pi;}}\underset{-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Integral;}}{s}_1(t-\mathrm{\&tau;})s_2\left(t\right)dt=\frac{1}{2\mathrm{\&pi;}}\underset{-\mathrm{\&infin;}}{\overset{\mathrm{\&infin;}}{\&Integral;}}s(t+\mathrm{\&Delta;}t-\mathrm{\&tau;})s\left(t\right)dt=R_s(\mathrm{\&tau;}-\mathrm{\&Delta;}t)$

Wherein, Δ t is time delay, because R_s(τ-Δt)≤R_s(0), as τ=Δ t,Obtain maximum, then lead to Crossing calculating, the moment that cross-correlation function peak value occurs is time delay Δ t and i.e. flies over time τ；

Step 3: employing LSQR algorithm reconstruction temperature field:

Three-dimensional Combustion room measurement space is divided into 3 × 3 × 3=27 space lattice, then

${\mathrm{\&tau;}}_i=\underset{j=1}{\overset{N}{\&Sigma;}}{w}_{ij}{f}_j,i=1,2...,58$

In formula: w_ijIt is i-th paths length by jth space lattice；τ_iThe sound wave of i-th sound wave path for recording flies Cross the time；f_jFor the inverse of acoustic wave propagation velocity in region to be measured；

Control 20 speakers and launch acoustic signals successively, form one and measure the cycle, then obtain 58 sound wave paths, accordingly System of linear equations is:

w₁₁f₁+w₁₂f₂+…w_1,27f₂₇=τ₁

w₂₁f₁+w₂₂f₂+…w_2,27f₂₇=τ₂

w_58,1f₁+w_58,2f₂+…w_58,27f₂₇=τ₅₈

Equation group is expressed in matrix as

Ax=b, is the mathematical model of three dimensional displacement fields

In formula:It is 58 × 27 right-safeguarding factor matrixs, reflects jth space lattice to i-th sound wave path Contribution: x=(f₁,f₂,...,f₂₇)^T, it is 27 dimension temperature field vectors；B=(τ₁,τ₂,…,τ₅₈)^T, for step 2 obtain 58 dimension Fly over measure of time data vector；

Obtain matrix x=(f₁,f₂,…,f₂₇)^T, by x=(f₁,f₂,…,f₂₇)^TBring intoWherein Z is sound Learn constant, i.e. solve the mean temperature in each grid, using this temperature as the temperature of each mesh space geometric center, then In MATLAB, call cubic spline interpolation method can draw the three-dimensional temperature field of whole area of space to be measured.