基于特征正交分解的微波加热过程快速求解方法  

Rapid solution method for microwave heating processes based on proper orthogonal decomposition

作　　者：杨彪[1,2,3] 黄宏彬 杜庆治 吴照刚[1] 彭飞云 韩泽民 YANG Biao;HUANG Hong-bin;DU Qing-zhi;WU Zhao-gang;PENG Fei-yun;HAN Ze-min(Faculty of Information Engineering and Automation,Kunming University of Science and Technology,Kunming 650500,China;Yunnan Key Laboratory of Artificial Intelligence,Kunming University of Science and Technology,Kunming 650500,China;Key Laboratory of Unconventional Metallurgy of Ministry of Education,Kunming University of Science and Technology,Kunming 650093,China)

机构地区：[1]昆明理工大学信息工程与自动化学院,昆明650500 [2]昆明理工大学云南省人工智能重点实验室,昆明650500 [3]昆明理工大学非常规冶金教育部重点实验室,昆明650093

出　　处：《控制与决策》2024年第9期3059-3068,共10页Control and Decision

基　　金：国家自然科学基金项目(62363019,61863020)。

摘　　要：应用传统数值计算方法求解微波加热媒质过程的温度分布时,存在自由度数量大且无法快速获取温度分布的问题,为此开展如何平衡计算精度和求解速度的研究.一方面,推导微波加热模型有限元离散格式的高阶非线性方程组,并构建瞬像矩阵,在此基础上,引入特征正交分解(proper orthogonal decomposition, POD)方法获取最优POD基底,进一步降维得到低阶微波加热离散控制方程;另一方面,建立TE10波辐射下矩形波导中媒质内部显性耗散功率表达式,开展微波加热媒质全局温度分布的有效计算.数值计算结果表明:所提基于POD的微波加热求解方法不仅能够准确求得加热过程中媒质内部的温度分布,并且计算速度提升82.9%~85.5%;同时,该方法在加热边界条件或初始条件发生变化时,无需重新计算POD基底,用较少基底就能够描述高阶模型超99.9%以上能量,对微波加热媒质过程温度分布的实时控制和快速计算具有重要意义.This paper studies how to balance the accuracy of the calculation with the speed of the solution,as the number of freedom degrees is large and the temperature distribution cannot be obtained quickly when applying the traditional solution method of numerical calculation for the temperature distribution of the microwave heating medium process.For this reason,on the one hand,this paper derives a set of higher-order non-linear equations in finite element discrete format for the microwave heating model,and constructs a snapshot matrix.On the basis of this,the optimal proper orthogonal decomposition(POD)basis is obtained by introducing the POD method,which further reduces the dimensionality to obtain the low-order microwave heating discrete control equations.On the other hand,an expression for the explicit dissipated power inside the medium in a rectangular waveguide under TE10 mode wave radiation is developed,and an effective calculation of the global temperature distribution of the microwave heated medium is carried out.The numerical results show that the proposed method based on the POD can accurately calculate the temperature distribution inside the medium during the microwave heating process,and the computational speed is increased by 82.9%85.5%.At the same time,the method has the feature of not having to recalculate the POD basis when the heating boundary conditions or initial conditions change,and can describe the super 99.9%energy in the higher order model with less basis,which is very important for real-time control and fast calculation of the temperature distribution of the microwave heating medium process.

关 键 词：微波加热 温度分布 特征正交分解 有限元法 低阶模型 求解方法 

分 类 号：TN801[电子电信—信息与通信工程]