Distributed Parameter Systems Modeling Of Large-scale Vertical Quench Furnace Based On Haar Wavelet Transform

Large-scale vertical quench furnace is a kind of critical equipment for thermal treatment of high-strength aluminum alloy forgings widely used in aerospace industry. It is very difficult to establish an accurately temperature field model because the structure of large-scale vertical quenching furnace is complex; many different types of heat transfer are combined; temperature distribution was distributed parameter characteristically. This paper used mechaismsim-parameters modeling method to establish a mathematical model of temperature filed and a distributed parameter systems dynamic model of large-scale vertical quench for the study of its control methods. The main research results of this paper are as follows:(1) It established a distributed parameter systems model of temperature fields and determined the system dynamic model structure by analysising the furnace heat transfer process and in accordance with the principles of the heat balance in the cylindrical coordinate system.(2) It proposed an identification algorithm based on Haar wavelets approximation transform. The detail method was:choosing Haar orthogonal wavelets as basic function and using its differential operational matrix and its properties, transferring the partial differential equation describing distributed parameter system control model to matrix algebra equation. On this basis the parameter on-line identification algorithm for temperature distributed parameter systems of large-scale vertical quench furnace was deduced according to method of Least Square. The proposed method doesn’t need to consider the initial conditions and boundary conditions and it was much simpler than other methods which made use of the integrated operational matrix.(3) Simulation experiments were carried on by MATLAB. Through analyzing simulation results, characteristic of influence on parameter identification precision from space and time step was obtained. The simulation result indicated that this parameter estimation algorithm was effective, easy to compute and could undermine the characteristics of the nosise.It could get the model paramenters.by using that identification algorithm. It got the model parameters by choosing the Haar wavelet of8-order and using the identification algorithm, and finished establishing the distributed parameter systems model.