CN104881535A - Improved thermal power plant boiler temperature field reconstruction temperature measuring algorithm - Google Patents

Abstract

The invention discloses an improved thermal power plant boiler temperature field reconstruction temperature measuring algorithm. The improved thermal power plant boiler temperature field reconstruction temperature measuring algorithm comprises the following steps that firstly, a sound wave propagation path ordinary differential equation mathematical model of sound waves in a non-uniform temperature field in a hearth is derived according to the target requirement and the propagation characteristic of the sound waves in the non-uniform temperature field, by means of the functional extremum problem and geodesic problem and on the basis of the Fermat principle; secondly, an ordinary differential equation is solved through a shooting method, the nonlinearity two-point boundary value problem of the sound wave propagation path mathematical model is converted into an ordinary initial value problem, approaching is achieved by setting different initial values in an iteration mode, and the numerical solution of the sound wave propagation path is worked out through the numerical value; thirdly, on the basis of sound wave propagation path correction, the acoustic CT algorithm is called, the sound wave propagation path in an original algorithm is improved according to a linear processing method, and the temperature field reconstruction and the like are carried out by introducing the actual sound wave propagation path bent through the effect of the non-uniform temperature field.

Description

The power plant boiler reconstruction of temperature field thermometric algorithm improved

Technical field

The present invention relates to a kind of power plant boiler reconstruction of temperature field thermometric algorithm of improvement, belong to thermal power plant's acoustic thermometry field.

Background technology

In the coal-burning boiler of large-size thermal power plant, the distribution in temperature field is one of important parameter of reflection combustion process and equipment state, not only boiler implosion and combustion diagnosis tool are of great significance, also directly have influence on the catching fire of coal dust, the economy of after-flame and boiler and security, have influence on the discharge capacity of pollutant simultaneously.The distribution of temperature field in furnace can reflect stove combustion ruuning situation, for the operation of operations staff provides reliable basis, and provides in-furnace temperature signal for the automation equipment of thermal control process.If the distribution of energy accurate reproduction temperature field in furnace, just can judge the combustion case of furnace flame in time, and carry out regulating and control, realize the optimization of burning.But, there is due to industrial combustion process self features such as transient changing, stochastic turbulence, bad environments, difficulty is brought to the on-line measurement about ermal physics amount field parameters, particularly the measurement of Temperature Distribution is more difficult, cause firing optimization not have reliable foundation like this, combustion optimisation is run and cannot be realized.

Acoustic thermometry is as a kind of novel temperature measurement technology of the boiler combustion on-line monitoring based on acoustic wave theory, not by the impact of external condition, adapt to the rugged surroundings of various high temperature, the many dirt of burn into, the each several part temperature data accurately of whole fire box temperature field can be provided, continuous coverage can be carried out to fire box temperature field, have that measuring accuracy is high, measurement range is wide, the plurality of advantages such as Real-Time Monitoring and Long-distance Control.Acoustic thermometry surface is the measurement to temperature, actually rebuilds temperature field, after obtaining the fly over time of sound wave in burner hearth, calls corresponding reconstruction of temperature field algorithm, can realize " measurement " to temperature.

Typical reconstruction of temperature field algorithm at present, such as acoustics CT method, parabola model method etc., all that acoustic wave propagation path is processed according to straight line when rebuilding temperature field, but under the boiler operatiopn operating mode of reality, by the impact of non-uniform temperature field in stove, acoustic wave propagation path will bend, and be called the buckling effect in temperature field.If still processed according to straight line during reconstruction of temperature field, the precision of reconstruction of temperature field will certainly be reduced, the inaccurate operation directly having influence on operations staff of temperature field measurement, and then affect economy and the security of boiler operatiopn.

Summary of the invention

Goal of the invention: for above-mentioned prior art Problems existing and deficiency, the object of this invention is to provide a kind of reconstruction of temperature field thermometric algorithm of improvement, for burner hearth inside thermometric difficulty, existing according to the inaccurate problem of acoustics reconstruction of temperature field algorithm calculating temperature-measuring results, the precision of further raising reconstruction of temperature field, thus measurement obtains thermo parameters method more accurately.

Technical scheme: for achieving the above object, the technical solution used in the present invention is the power plant boiler reconstruction of temperature field thermometric algorithm improved, and comprises the following steps:

1) according to the propagation characteristic of sound wave in non-uniform temperature field, utilize extreme-value problem and the brachistochrone problem of functional, on the basis of Fermat principle, derive sound wave ordinary differential equation mathematical model of acoustic wave propagation path in non-uniform temperature field in burner hearth;

2) shooting method is utilized to solve ordinary differential equation, the nonlinear two point boundary value prob lems of described acoustic wave propagation path mathematical model is converted into general initial-value problem, and approach in an iterative manner by arranging different initial values, numerical evaluation goes out the numerical solution of acoustic wave propagation path;

3) on the basis to acoustic wave propagation path correction, call acoustics CT algorithm, and by former algorithm, the mode of acoustic wave propagation path according to line processing is improved, introduce actual affecting by non-uniform temperature field and produce bending acoustic wave propagation path, carry out reconstruction of temperature field;

4) utilize the trimming algorithm in computer graphics, calculate the actual path of sound wave crooked route in each grid division, for improvement of after reconstruction of temperature field;

5) sound wave that experimentally indoor theory calculate or the actual measurement of field experiment obtain flies over the estimated value of time, calls the reconstruction of temperature field algorithm after described improvement, based on revised acoustic wave propagation path, rebuilds temperature field.

Further, described step 1) according to the propagation characteristic of sound wave in non-uniform temperature field, utilize extreme-value problem and the brachistochrone problem of functional, on the basis of Fermat principle, derive sound wave in burner hearth in non-uniform temperature field the ordinary differential equation mathematical model of acoustic wave propagation path be specially:

Brachistochrone problem can be expressed as

$\left\{\begin{array}{c}y=y\left(x\right),(0\≤x\≤a)\\ y\left(a\right)=\mathrm{\α}\\ y\left(b\right)=\mathrm{\β}\end{array}\right.---\left(18\right)$

In formula, (a, α) and (b, β) is respectively the initial point position of brachistochrone, and y represents studied brachistochrone, and x is corresponding horizontal ordinate;

In burner hearth, sound wave trajectory can be expressed as:

y＝y(x) (19)

Length differential along this travel path can be expressed as:

$\mathrm{ds}=\sqrt{(1+{\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2)}\mathrm{dx}---\left(20\right)$

The pass of known acoustic wave propagation velocity and medium temperature is again

$v=\sqrt{\frac{\mathrm{\γRT}}{m}}=z\sqrt{T}---\left(21\right)$

In formula, v represents sound velocity of wave propagation; γ is the ratio of gas medium specific heat at constant pressure and specific heat at constant volume; R is mol gas constant; M is gas molar quality; T represents gas absolute temperature; Z is constant, only relevant with above-mentioned dielectric property;

So sound wave propagate from launching site position (x1, y1) to acceptance point position (x2, y2) required for time be:

$t={\∫}_{x_1}^{x_2}\frac{\mathrm{ds}}{\mathrm{dv}}=\frac{1}{z}{\∫}_{x_1}^{x_2}\sqrt{\frac{1+y^{\′2}}{T(x,y)}}\mathrm{dx}---\left(22\right)$

According to Fermat principle, sound wave arrives acceptance point position and necessarily propagates according to the path that acoustic transit time is the shortest from launching site position, so the variation of formula (5) is 0, i.e. δ t=0, according to Euler equation following equation can be derived:

$y^{\′\′}=\frac{1+y^{\′2}}{2T(x,y)}(y^{\′}\frac{\∂T(x,y)}{\∂x}-\frac{\∂T(x,t)}{\∂y})---\left(23\right)$

Ordinary differential equation (6) is exactly the mathematical model of acoustic wave propagation path, and its boundary condition is respectively:

$\left\{\begin{array}{c}y\left(x_1\right)=y_1\\ y\left(x_2\right)=y_2\end{array}\right.$ Or $\left\{\begin{array}{c}y\left(x_1\right)=y_1\\ y^{\′}\left(x_1\right)=y_1^{\′}\end{array}\right.---\left(24\right)$

I.e. known launching site (x1, and acceptance point position (x2, y2), or known launching site (x1 y1), y1) position and exit direction thereof, just can obtain the actual propagation path of sound wave by the boundary value problem solving ordinary differential equation.

Further, described step 2) utilize shooting method to solve ordinary differential equation, the nonlinear two point boundary value prob lems of acoustic wave propagation path mathematical model is converted into general initial-value problem, and approach in an iterative manner by arranging different initial values, the numerical solution that numerical evaluation goes out acoustic wave propagation path is specially:

If

y′(x ₁)＝t ₀(25)

At this moment the boundary condition of the differential equation becomes

$\left\{\begin{array}{c}y\left(x_1\right)=y_1\\ y^{\′}\left(x_1\right)=t_0\end{array}\right.---\left(26\right)$

In formula, x1 is starting point horizontal ordinate, and y1 is corresponding ordinate, and y ' is the first order derivative of corresponding ordinate, represents with t0;

Utilize shooting method that above-mentioned nonlinear two-point boundary value problem is converted into the initial-value problem of equation below

$\left\{\begin{array}{c}{y}^{\′\′}=f(x,y,y^{\′})\\ y^{\′}\left(x_1\right)=t_0\\ y\left(x_1\right)=y_1\end{array}\right.---\left(27\right)$

When solving, first to select a step-length h according to accuracy requirement, obtain the approximate value of each Nodes, if exitance is suitable, then have y (x2, t0)=y2; If obtain y (x2, t0) >y2, separately establish a value t1 being less than t0, again solve; If obtain y (x2, t1) <y2, next time should value between to and tl, can adopt linear interpolation

$t_2=t_1+\frac{(t_1-t_0)(y_2-y(x_2,t_1))}{y(x_2,t_1)-y(x_2,t_0)}---\left(28\right)$

Iteration is gone down and is finally made in this format

limy(x ₂,t _k)＝y ₂(29)

Only need meet in practical application

|y(x ₂,t _k)-y ₂|＜ε (30)

Time, stop iteration.

Further, described step 3) on the basis to acoustic wave propagation path correction, call acoustics CT algorithm, and by former algorithm, the mode of acoustic wave propagation path according to line processing is improved, introduce actual affecting by non-uniform temperature field and produce bending acoustic wave propagation path, carry out reconstruction of temperature field, be specially:

If the temperature on acoustic wave propagation path is uneven, path can be divided into some sections along the direction of propagation, the length in each section of path be li (i=1,2, n).The medial temperature of each section is Ti, and acoustic transit time is τ i; For the measurement of two-dimensional cross sectional Temperature Distribution, needing plane by stress and strain model is n unit, in unit the medial temperature of gas be respectively Ti (i=1,2, n); For solving Ti, need to arrange multiple acoustic emission and receiving trap, if they define altogether m bar acoustic wave propagation path.For wherein jth bar travel path (j=1,2, m), have following equation:

${\mathrm{\&tau;}}_j=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}_{\mathrm{ji}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ji}}^{\&prime;}{x}_{\mathrm{ji}}---\left(31\right)$

In formula, τ j is the travel-time of sound wave along jth paths, a ' _ji=l ' _ji/ z, l ' _jijth bar sound wave crooked route for reality passes the length of i-th unit grid, equally, a ' _jifor to be measured, represent the temperature funtion characteristic in grid; Write as matrix form, obtained system of linear equations:

A′x＝t (32)

T=(τ in formula ₁τ _m) ^t; X=(x ₁x _n) ^t; $A^{\&prime;}=\left[\begin{array}{ccc}{a}_{11}^{\&prime;}& ...& a_{1n}^{\&prime;}\\ ...& ...& ...\\ a_{m1}^{\&prime;}& ...& a_{\mathrm{mn}}^{\&prime;}\end{array}\right].$

Solved in the hope of variable x, can so just have been obtained the inverse of sound wave velocity of propagation in each grid division by least square method, utilize the relational expression of speed and temperature, can temperature field be rebuild:

$T_i={\left(\frac{1}{x_i}\right)}^2---\left(33\right)$

Further, described step 4) utilize trimming algorithm in computer graphics, calculate the actual path of sound wave crooked route in each grid division, for improvement of after reconstruction of temperature field be specially:

Reconstruction of temperature field algorithm after improvement and the key distinction of former algorithm are, owing to being subject to the impact of non-uniform temperature field buckling effect, acoustic wave propagation path is no longer straight line, do not calculate the diffusion path length in each grid by simple geometric relationship, key issue is the sound wave path length l ' how obtained in each grid _ji; In emulation experiment, can Modling model temperature field T (x, y), utilize step 2) ordinary differential equation of acoustic wave propagation path derived, sound wave crooked route is obtained by the numerical solution emulation of series of points on shooting method solution path, to the trimming algorithm of these numerical solution application X-Y schemes, can try to achieve under the effect of temperature field buckling effect, the actual sound wave path length l ' in each grid _ji, thus obtain a ' _ji, then solve variable x by least square method, utilize the relational expression of speed and temperature to rebuild temperature field.

Further, described step 5) sound wave that obtains of the actual measurement of experimentally indoor theory calculate or field experiment flies over the estimated value of time, call the reconstruction of temperature field algorithm after improvement, based on revised acoustic wave propagation path, reconstruction carried out to temperature field and is specially:

The key parameter of reconstruction of temperature field is that sound wave flies over the time, therefore before reconstruction, first to determine that the sound wave of each paths flies over the time, in laboratory simulations, sound wave cannot be obtained by direct measurement to fly over the time, but can Modling model temperature field T (x, y) be passed through, by carrying out integration along acoustic wave propagation path to acoustic wave propagation velocity, directly can calculate and trying to achieve sound wave and to fly over time TOF data:

$\mathrm{TOF}={\&Integral;}_k\frac{1}{v(x,y)}{\mathrm{dl}}_k---\left(34\right)$

In engineering practice, can by arranging that in boiler setting surrounding some pingers and receiver carry out actual measurement and obtain sound wave and fly over the time, obtain sound wave and fly over after the time, the reconstruction of temperature field algorithm that just can call after improvement carries out reconstruction of temperature field.

Beneficial effect: compared with prior art, the present invention has the following advantages: utilize shooting method by the ordinary differential equation mathematical model of numerical evaluation acoustic wave propagation path, obtain the actual acoustic wave propagation path bent in non-uniform temperature field, call acoustics CT algorithm and its mode by line processing is improved, temperature field is rebuild, further improve the precision of rebuilding temperature field, thus obtain thermo parameters method more accurately.

Accompanying drawing explanation

Fig. 1 is the power plant boiler reconstruction of temperature field thermometric algorithm flow chart that the present invention improves;

Fig. 2 is that shooting method solves schematic diagram;

Fig. 3 is stress and strain model and path profile schematic diagram;

Fig. 4 is model and rebuilds temperature field schematic diagram.

Embodiment

Below in conjunction with the drawings and specific embodiments, illustrate the present invention further, these examples should be understood only be not used in for number the present invention and limit the scope of the invention, after reading this disclosure, the amendment of those skilled in the art to the various equivalent form of value of the present invention all falls within the application's claims limited range.

1) acoustic wave propagation path modeling.

In fact the mathematical model of acoustic wave propagation path belongs to extreme-value problem and the brachistochrone problem of functional.The extreme-value problem of functional is one of basic problem of the variational method; Brachistochrone problem refers to asks the curve that between two point of fixity, acoustic transit time is the shortest, is exactly the brachistochrone between two points, can be expressed as

$\left\{\begin{array}{c}y=y\left(x\right),(0\&le;x\&le;a)\\ y\left(a\right)=\mathrm{\&alpha;}\\ y\left(b\right)=\mathrm{\&beta;}\end{array}\right.---\left(35\right)$

In burner hearth, sound wave trajectory can be expressed as:

y＝y(x) (36)

Length differential along this travel path can be expressed as:

$\mathrm{ds}=\sqrt{(1+{\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2)}\mathrm{dx}---\left(37\right)$

The pass of known acoustic wave propagation velocity and medium temperature is again

$v=\sqrt{\frac{\mathrm{\&gamma;RT}}{m}}=z\sqrt{T}---\left(38\right)$

In formula, z is constant, only relevant with dielectric property.

So sound wave propagate from launching site position (x1, y1) to acceptance point position (x2, y2) required for time be:

$t={\&Integral;}_{x_1}^{x_2}\frac{\mathrm{ds}}{\mathrm{dv}}=\frac{1}{z}{\&Integral;}_{x_1}^{x_2}\sqrt{\frac{1+y^{\&prime;2}}{T(x,y)}}\mathrm{dx}---\left(39\right)$

According to Fermat principle, sound wave arrives acceptance point position and necessarily propagates according to the path that acoustic transit time is the shortest from launching site position.So the variation of formula (5) is 0, i.e. δ t=0, according to Euler equation following equation can be derived:

$y^{\&prime;\&prime;}=\frac{1+y^{\&prime;2}}{2T(x,y)}(y^{\&prime;}\frac{\&PartialD;T(x,y)}{\&PartialD;x}-\frac{\&PartialD;T(x,t)}{\&PartialD;y})---\left(40\right)$

Ordinary differential equation (6) is exactly the mathematical model of acoustic wave propagation path, and its boundary condition is respectively:

$\left\{\begin{array}{c}y\left(x_1\right)=y_1\\ y\left(x_2\right)=y_2\end{array}\right.$ Or $\left\{\begin{array}{c}y\left(x_1\right)=y_1\\ y^{\&prime;}\left(x_1\right)=y_1^{\&prime;}\end{array}\right.---\left(41\right)$

I.e. known launching site (x1, and acceptance point position (x2, y2), or known launching site (x1 y1), y1) position and exit direction thereof, just can obtain the actual propagation path of sound wave by the boundary value problem solving ordinary differential equation.

2) numerical evaluation acoustic wave propagation path.

Equation (6) is the nonlinear boundary value problem of a second order differential equation, does not solve by the general method changing into two initial-value problems, can only approach in an iterative manner by arranging different initial values.Acoustic wave propagation path can regard a trajectory as, and guided missile is launched from starting point, just in time gets to terminal through curve, and its key issue is exactly that guided missile is launched along what direction could finally be hit the mark, and namely the initial value of y ' (x1) is how many.

If

y′(x ₁)＝t ₀(42)

At this moment the boundary condition of the differential equation becomes

$\left\{\begin{array}{c}y\left(x_1\right)=y_1\\ y^{\&prime;}\left(x_1\right)=t_0\end{array}\right.---\left(43\right)$

This is a general initial-value problem, and its solution is relevant with t0, and method for solving has a lot, and such as imperial lattice-storehouse tower algorithm, can obtain the series of values solution of acoustic wave propagation path.The essence of shooting method is exactly the initial-value problem nonlinear two-point boundary value problem being converted into equation below

$\left\{\begin{array}{c}{y}^{\&prime;\&prime;}=f(x,y,y^{\&prime;})\\ y^{\&prime;}\left(x_1\right)=t_0\\ y\left(x_1\right)=y_1\end{array}\right.---\left(44\right)$

When solving, first to select a step-length h according to accuracy requirement, obtain the approximate value of each Nodes, if exitance is suitable, then have y (x2, t0)=y2.If obtain y (x2, t0) >y2, separately establish a value t1 being less than t0, again solve; If obtain y (x2, t1) <y2, next time should value between to and tl, can adopt linear interpolation

$t_2=t_1+\frac{(t_1-t_0)(y_2-y(x_2,t_1))}{y(x_2,t_1)-y(x_2,t_0)}---\left(45\right)$

Iteration is gone down and is finally made in this format

limy(x ₂,t _k)＝y ₂(46)

Only need meet in practical application

|y(x ₂,t _k)-y ₂|＜ε (47)

Time, stop iteration.Shooting method implementation procedure is see Fig. 2.

3) improvement of reconstruction of temperature field algorithm.

Consider that non-uniform temperature field causes the actual propagation path of buckling effect to be the series of values solution of the travel path obtained by the method for numerical evaluation, be difficult to the approximate temperature distribution function obtaining each travel path, and then the reconstruction algorithm such as parabola model method cannot be utilized.Therefore, the reconstruction of temperature field algorithm based on correction rear path improves to obtain on the basis of acoustics CT method.

If the temperature on acoustic wave propagation path is uneven, path can be divided into some sections along the direction of propagation, the length in each section of path be li (i=1,2 ..., n).The medial temperature of each section is Ti, and acoustic transit time is τ i.For the measurement of two-dimensional cross sectional Temperature Distribution, needing plane by stress and strain model is n unit, as shown in Fig. 3 (a); In unit the medial temperature of gas be respectively Ti (i=1,2 ..., n).For solving Ti, need to arrange multiple acoustic emission and receiving trap, if they define altogether m bar acoustic wave propagation path.For wherein jth bar travel path (j=1,2 ..., m), there is following equation:

${\mathrm{\&tau;}}_j=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}_{\mathrm{ji}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ji}}^{\&prime;}{x}_{\mathrm{ji}}---\left(48\right)$

In formula, τ j is the travel-time of sound wave along jth paths, a ' _ji=l ' _ji/ z, l ' _jijth bar sound wave crooked route for reality passes the length of i-th unit grid, equally, a ' _jifor to be measured, represent the temperature funtion characteristic in grid.Write as matrix form, obtained system of linear equations:

A′x＝t (49)

T=(τ in formula ₁τ _m) ^t; X=(x ₁x _n) ^t; $A^{\&prime;}=\left[\begin{array}{ccc}{a}_{11}^{\&prime;}& ...& a_{1n}^{\&prime;}\\ ...& ...& ...\\ a_{m1}^{\&prime;}& ...& a_{\mathrm{mn}}^{\&prime;}\end{array}\right].$

Solved in the hope of variable x, can so just have been obtained the inverse of sound wave velocity of propagation in each grid division by least square method, utilize the relational expression of speed and temperature, can temperature field be rebuild:

$T_i={\left(\frac{1}{x_i}\right)}^2---\left(50\right)$

4) path in each grid is calculated.

Reconstruction of temperature field algorithm after improvement and the key distinction of former algorithm are, owing to being subject to the impact of non-uniform temperature field buckling effect, acoustic wave propagation path is no longer straight line, do not calculate the diffusion path length in each grid by simple geometric relationship, key issue is the sound wave path length l ' how obtained in each grid _ji.In emulation experiment, can Modling model temperature field T (x, y), the ordinary differential equation of the acoustic wave propagation path utilizing chapter 2 to derive, sound wave crooked route is obtained by the numerical solution emulation of series of points on shooting method solution path, to the trimming algorithm of these numerical solution application X-Y schemes, can try to achieve under the effect of temperature field buckling effect, the actual sound wave path length l ' in each grid _ji, see Fig. 3 (b), thus obtain a ' _ji, then solve variable x by least square method, utilize the relational expression of speed and temperature to rebuild temperature field.

5) reconstruction of temperature field.

The key parameter of reconstruction of temperature field is that sound wave flies over the time, therefore before reconstruction, first to determine that the sound wave of each paths flies over the time, in laboratory simulations, sound wave cannot be obtained by direct measurement to fly over the time, but can Modling model temperature field T (x, y) be passed through, by carrying out integration along acoustic wave propagation path to acoustic wave propagation velocity, directly can calculate and trying to achieve sound wave and to fly over time TOF data:

$\mathrm{TOF}={\&Integral;}_k\frac{1}{v(x,y)}{\mathrm{dl}}_k---\left(51\right)$

In engineering practice, can by arranging that in boiler setting surrounding some pingers and receiver carry out actual measurement and obtain sound wave and fly over the time.Obtaining sound wave flies over after the time, and the reconstruction of temperature field algorithm that just can call after improvement carries out reconstruction of temperature field.Model temperature field and innovatory algorithm rebuild the two-dimension temperature field distribution that obtains see Fig. 4.

As mentioned above, although represented with reference to specific preferred embodiment and described the present invention, it shall not be construed as the restriction to the present invention self.Under the spirit and scope of the present invention prerequisite not departing from claims definition, various change can be made in the form and details to it.

Claims (6)

1. the power plant boiler reconstruction of temperature field thermometric algorithm improved, is characterized in that, comprise the following steps:

1) according to the propagation characteristic of sound wave in non-uniform temperature field, utilize extreme-value problem and the brachistochrone problem of functional, on the basis of Fermat principle, derive sound wave ordinary differential equation mathematical model of acoustic wave propagation path in non-uniform temperature field in burner hearth;

2) shooting method is utilized to solve ordinary differential equation, the nonlinear two point boundary value prob lems of described acoustic wave propagation path mathematical model is converted into general initial-value problem, and approach in an iterative manner by arranging different initial values, numerical evaluation goes out the numerical solution of acoustic wave propagation path;

3) on the basis to acoustic wave propagation path correction, call acoustics CT algorithm, and by former algorithm, the mode of acoustic wave propagation path according to line processing is improved, introduce actual affecting by non-uniform temperature field and produce bending acoustic wave propagation path, carry out reconstruction of temperature field;

4) utilize the trimming algorithm in computer graphics, calculate the actual path of sound wave crooked route in each grid division, for improvement of after reconstruction of temperature field;

5) sound wave that experimentally indoor theory calculate or the actual measurement of field experiment obtain flies over the estimated value of time, calls the reconstruction of temperature field algorithm after described improvement, based on revised acoustic wave propagation path, rebuilds temperature field.

2. the power plant boiler reconstruction of temperature field thermometric algorithm improved according to claim 1, is characterized in that,

Described step 1) according to the propagation characteristic of sound wave in non-uniform temperature field, utilize extreme-value problem and the brachistochrone problem of functional, on the basis of Fermat principle, derive sound wave in burner hearth in non-uniform temperature field the ordinary differential equation mathematical model of acoustic wave propagation path be specially:

Brachistochrone problem can be expressed as

$\left\{\begin{array}{c}y=y\left(x\right),(0\&le;x\&le;a)\\ y\left(a\right)=\mathrm{\&alpha;}\\ y\left(b\right)=\mathrm{\&beta;}\end{array}\right.---\left(1\right)$

In formula, (a, α) and (b, β) is respectively the initial point position of brachistochrone, and y represents studied brachistochrone, and x is corresponding horizontal ordinate;

In burner hearth, sound wave trajectory can be expressed as:

y＝y(x) (2)

Length differential along this travel path can be expressed as:

$\mathrm{ds}=\sqrt{(1+{\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2)}\mathrm{dx}---\left(3\right)$

The pass of known acoustic wave propagation velocity and medium temperature is again

$v=\sqrt{\frac{\mathrm{\&gamma;RT}}{m}}=z\sqrt{T}---\left(4\right)$

In formula, v represents sound velocity of wave propagation; γ is the ratio of gas medium specific heat at constant pressure and specific heat at constant volume; R is mol gas constant; M is gas molar quality; T represents gas absolute temperature; Z is constant, only relevant with above-mentioned dielectric property;

So sound wave propagate from launching site position (x1, y1) to acceptance point position (x2, y2) required for time be:

$t={\&Integral;}_{x_1}^{x_2}\frac{\mathrm{ds}}{\mathrm{dv}}=\frac{1}{z}{\&Integral;}_{x_1}^{x_2}\sqrt{\frac{1+y^{\&prime;2}}{T(x,y)}}\mathrm{dx}---\left(5\right)$

According to Fermat principle, sound wave arrives acceptance point position and necessarily propagates according to the path that acoustic transit time is the shortest from launching site position, so the variation of formula (5) is 0, i.e. δ t=0, according to Euler equation following equation can be derived:

$y^{\&prime;\&prime;}=\frac{1+y^{\&prime;2}}{2T(x,y)}(y^{\&prime;}\frac{\&PartialD;T(x,y)}{\&PartialD;x}-\frac{\&PartialD;T(x,y)}{\&PartialD;y})---\left(6\right)$

Ordinary differential equation (6) is exactly the mathematical model of acoustic wave propagation path, and its boundary condition is respectively:

$\left\{\begin{array}{c}y\left(x_1\right)=y_1\\ y\left(x_2\right)=y_2\end{array}\right.$ Or $\left\{\begin{array}{c}y\left(x_1\right)=y_1\\ y^{\&prime;}\left(x_1\right)=y_1^{\&prime;}\end{array}\right.---\left(7\right)$

I.e. known launching site (x1, and acceptance point position (x2, y2), or known launching site (x1 y1), y1) position and exit direction thereof, just can obtain the actual propagation path of sound wave by the boundary value problem solving ordinary differential equation.

3. the power plant boiler reconstruction of temperature field thermometric algorithm improved according to claim 1, is characterized in that:

Described step 2) utilize shooting method to solve ordinary differential equation, the nonlinear two point boundary value prob lems of acoustic wave propagation path mathematical model is converted into general initial-value problem, and approach in an iterative manner by arranging different initial values, the numerical solution that numerical evaluation goes out acoustic wave propagation path is specially:

If

y′(x ₁)＝t ₀(8)

At this moment the boundary condition of the differential equation becomes

$\left\{\begin{array}{c}y\left(x_1\right)=y_1\\ y^{\&prime;}\left(x_1\right)=t_0\end{array}\right.---\left(9\right)$

In formula, x1 is starting point horizontal ordinate, and y1 is corresponding ordinate, and y ' is the first order derivative of corresponding ordinate, represents with t0;

Utilize shooting method that above-mentioned nonlinear two-point boundary value problem is converted into the initial-value problem of equation below

$\left\{\begin{array}{c}{y}^{\&prime;\&prime;}=f(x,y,y^{\&prime;})\\ y^{\&prime;}\left(x_1\right)=t_0\\ y\left(x_1\right)=y_1\end{array}\right.---\left(10\right)$

When solving, first to select a step-length h according to accuracy requirement, obtain the approximate value of each Nodes, if exitance is suitable, then have y (x2, t0)=y2; If obtain y (x2, t0) >y2, separately establish a value t1 being less than t0, again solve; If obtain y (x2, t1) <y2, next time should value between to and tl, can adopt linear interpolation

$t_2=t_1+\frac{(t_1-t_0)(y_2-y(x_2,t_1))}{y(x_2,t_1)-y(x_2,t_0)}---\left(11\right)$

Iteration is gone down and is finally made in this format

lim y(x ₂,t _k)＝y ₂(12)

Only need meet in practical application

|y(x ₂,t _k)-y ₂|＜ε (13)

Time, stop iteration.

4. the power plant boiler reconstruction of temperature field thermometric algorithm improved according to claim 1, is characterized in that:

Described step 3) on the basis to acoustic wave propagation path correction, call acoustics CT algorithm, and by former algorithm, the mode of acoustic wave propagation path according to line processing is improved, introduce actual affecting by non-uniform temperature field and produce bending acoustic wave propagation path, carry out reconstruction of temperature field, be specially:

If the temperature on acoustic wave propagation path is uneven, path can be divided into some sections along the direction of propagation, the length in each section of path be li (i=1,2, n).The medial temperature of each section is Ti, and acoustic transit time is τ i; For the measurement of two-dimensional cross sectional Temperature Distribution, needing plane by stress and strain model is n unit, in unit the medial temperature of gas be respectively Ti (i=1,2, n); For solving Ti, need to arrange multiple acoustic emission and receiving trap, if they define altogether m bar acoustic wave propagation path.For wherein jth bar travel path (j=1,2, m), have following equation:

${\mathrm{\&tau;}}_j=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&tau;}}_{\mathrm{ji}}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ji}}^{\&prime;}{x}_{\mathrm{ji}}---\left(14\right)$

In formula, τ j is the travel-time of sound wave along jth paths, a ' _ji=l ' _ji/ z, l ' _jijth bar sound wave crooked route for reality passes the length of i-th unit grid, equally, a ' _jifor to be measured, represent the temperature funtion characteristic in grid; Write as matrix form, obtained system of linear equations:

A′x＝t (15)

T=(τ in formula ₁τ _m) ^t; X=(x ₁x _n) ^t; $A^{\&prime;}=\left[\begin{array}{ccc}{a}_{11}^{\&prime;}& ...& a_{1n}^{\&prime;}\\ ...& ...& ...\\ a_{m1}^{\&prime;}& ...& a_{\mathrm{mn}}^{\&prime;}\end{array}\right].$

Solved in the hope of variable x, can so just have been obtained the inverse of sound wave velocity of propagation in each grid division by least square method, utilize the relational expression of speed and temperature, can temperature field be rebuild:

$T_i={\left(\frac{1}{x_i}\right)}^2---\left(16\right).$

5. the power plant boiler reconstruction of temperature field thermometric algorithm improved according to claim 1, is characterized in that:

Described step 4) utilize trimming algorithm in computer graphics, calculate the actual path of sound wave crooked route in each grid division, for improvement of after reconstruction of temperature field be specially:

Reconstruction of temperature field algorithm after improvement and the key distinction of former algorithm are, owing to being subject to the impact of non-uniform temperature field buckling effect, acoustic wave propagation path is no longer straight line, do not calculate the diffusion path length in each grid by simple geometric relationship, key issue is the sound wave path length l ' how obtained in each grid _ji; In emulation experiment, can Modling model temperature field T (x, y), utilize step 2) ordinary differential equation of acoustic wave propagation path derived, sound wave crooked route is obtained by the numerical solution emulation of series of points on shooting method solution path, to the trimming algorithm of these numerical solution application X-Y schemes, can try to achieve under the effect of temperature field buckling effect, the actual sound wave path length l ' in each grid _ji, thus obtain a ' _ji, then solve variable x by least square method, utilize the relational expression of speed and temperature to rebuild temperature field.

6. the power plant boiler reconstruction of temperature field thermometric algorithm improved according to claim 1, is characterized in that,

Described step 5) sound wave that obtains of the actual measurement of experimentally indoor theory calculate or field experiment flies over the estimated value of time, call the reconstruction of temperature field algorithm after improvement, based on revised acoustic wave propagation path, reconstruction is carried out to temperature field and is specially:

The key parameter of reconstruction of temperature field is that sound wave flies over the time, therefore before reconstruction, first to determine that the sound wave of each paths flies over the time, in laboratory simulations, sound wave cannot be obtained by direct measurement to fly over the time, but can Modling model temperature field T (x, y) be passed through, by carrying out integration along acoustic wave propagation path to acoustic wave propagation velocity, directly can calculate and trying to achieve sound wave and to fly over time TOF data:

$\mathrm{TOF}={\&Integral;}_k\frac{1}{v(x,y)}d{l}_k---\left(17\right)$

In engineering practice, can by arranging that in boiler setting surrounding some pingers and receiver carry out actual measurement and obtain sound wave and fly over the time, obtain sound wave and fly over after the time, the reconstruction of temperature field algorithm that just can call after improvement carries out reconstruction of temperature field.