基于迭代算法的炉膛三维温度场声学重建

Research on Reconstruction of Three-dimensional Temperature Field in Furnace by Acoustics Based on Iterative Algorithms

针对电站锅炉炉内三维温度场重建问题,基于声学理论构建了数学模型。求解大型病态矩阵方程是重建问题的关键,一般的求解方法无法得到满意的结果。采用CGLS(Conjugate Gradient Least Squares)算法和LSQR(Least Squares QR-Decomposition)算法对三维温度场重建中的病态矩阵方程进行求解,对炉膛火焰分布的几种典型模型进行了仿真重建。重建结果表明,2种迭代算法都能解决三维温度场重建问题,与CGLS算法相比,LSQR算法具有更好的数值稳定性和更强的抗噪声能力,适用于燃烧情况复杂的大型电站锅炉温度场重建。

In order to solve reconstruction problem of three-dimensional temperature field in furnace of power plant boiler,a mathematical model was constructed based on acoustic theory. The problem of solving a large ill-posed matrix equation is key to the reconstruction problem,and general methods can not obtain satisfying solutions. The matrix equation was solved by CGLS（ Conjugate Gradient Least Squares） algorithm and LSQR（ Least Squares QR-Decomposition） algorithm. Three typical temperature field models were simulated. Simulation results indicate that these two iterative algorithms are able to solve three-dimensional temperature field reconstruction problem. Compared with CGLS algorithm,LSQR algorithm has better numerical stability and better anti-noise ability. LSQR algorithm is suitable for reconstruction problem in large-scale power plant with complicated combustion.