Temperature Field Reconstruction by Acoustic Based on Newton-Raphson Regularization Iteration
The principle of three-dimensional temperature field reconstruction by acoustic is introduced. In order to realize the three-dimensional temperature field reconstruction by acoustic, the Newton-Raphson method based on the least square method is developed. Three-dimensional temperature field is reconstructed by regularization iteration method that the regularization term is added according to the features of temperature field distribution. It is shown that the algorithm of Newton-Raphson and regularization iteration can realize the reconstruction of the temperature field. INTRODUCTION Acoustic pyrometry technology is very important in many real industrial needs and applications because of the advantages as non-contact acoustic temperature measurement, without interference to measurement objects, easy to realize visual measurement[1-5]. It is the key problem to obtain the quick and accuracy reconstruction algorithm to realize temperature field reconstruction in the region being measured. The main algorithms in two dimensional temperature field reconstruction are least squares, gaussian function and regularization algorithm, algebraic reconstruction algorithm and so on. The algorithms of three dimensional temperature field reconstruction main include the least square and SVD algorithm [6], CGLS and LSQR [7] etc..It is a important research subject to improve the accuracy of the threedimensional temperature field reconstruction, this paper presents Newton Raphson and regularization iteration method to reconstruct the three-dimensional temperature field, the simulation results show that this method is suitable for the reconstruction of temperature field, that satisfy the requirement of temperature measurement. _____________ Yanqiu Li, Shi Liu, H. Inaki Schlaberg, Jiye Zhang. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China 132 THE PRINCIPLE OF ACOUSTIC PYROMETRY The basic principle of acoustic pyrometry is based on that the propagation speed in gas medium is the function of gas temperature[8]. RT v Z T M    (1) where v is the propagation speed of acoustic wave in gas medium, m/s; R is molar gas constant, J/mol•k; γ is gas specific heat ratio, T is the absolute temperature of gas, K, M is molar mass of gas, kg/mol, Z = / R M  , it is a constant to specified gas. Time of Flight(TOF) that acoustic wave is propagated along a sound ray is represented 1 ( , , ) ( , , ) i i i i j i j L L b dl n a x y z dl n v x y z       (2) in which, bi represents the time of flight of the wave along the ith sound path; Li is the ith sound wave ray transmission path; (x,y,z) is the location of units, vj(x,y,z) is the sound speed of the jth imaging unit; aj(x,y,z) is the slowness of the jth pixel units (i.e., the reciprocal of velocity), ni is the measurement noise. When the number of reconstructed pixel unit and the grid size is small, it can be considered that aj(x,y,z) in each imaging unit is approximately constant, then the formula (2) can be simplified as reconstruction model in the form of a matrix equation: B LA n   (3) in which, L M N R   represents the line segment length, M B R  is the TOF vector measured practically, N A R  represents the space state factor, i.e. the reciprocal of velocity. M stands for the total of independent TOF measured across the temperature field, N is the number of pixels, M n R  represents the noise vector in TOF measurement data. A is calculated by proper reconstruction algorithm, and then the temperature T(x,y,z) is obtained according to (4). 2 2 1 ( , , ) ( , , ) T x y z A x y z Z  (4) TEMPERATURE FIELD RECONSTRUCTION BY NEWTON-RAPHSON METHOD In reconstruction algorithm, the modified Newton-Raphson method based on the least squares technique is most widely used. Newton-Raphson algorithm is an iterative approximation algorithm which is used to find a solution of nonlinear function originally. For the three-dimensional temperature field reconstruction by acoustic