非線性熱傳導問題之未知時變熱源估測研究

The Research of the Unknown Time-Varying Heat Source Estimation in the Nonlinear Heat Conduction Problems

陳聰堅(Tsung-Chien Chen) ； 鄭中信(Chung-Hsin Cheng) ； 徐守仁(Shou-Jen Hsu) ； 張鴻源(Horng-Yuan Jang) ； 段伴虬(Pan-Chio Tuan)

《航空太空及民航學刊.系列B》 39卷2期 (2007/10) Pp. 83-91

https://doi.org/10.6124/JAAA.200710_39(2).04

摘要

當熱傳導係數和容積熱容量?溫度之二次函數時，此?複雜的非線性熱傳導問題。本文提出包括擴展型卡爾曼濾波器(EKF)和權重遞迴式最小平方估算器(WRLSE)之輸入估測法，在具對流之情況下，以邊界之溫度量測值即時逆向估算作用於此非線性熱傳導問題中之未知時變熱源及溫度場分布暫態響應，其中EKF可遞迴產生剩餘更新序列，WRLSE可辨識未知之時變熱源，並以估算之熱源求解溫度場之分布，由模擬之結果顯示，本法可即時準確旳估算未知時變熱源及溫度場分布，同時本文也證明若將非線性熱傳導問題視?線性熱傳導問題時，以線性估算法即卡爾曼濾波器(KF)結合權重遞迴式最小平方估算器(WRLSE)估算未知時變熱源時，會產生較大的誤差。

關鍵字

非線性熱傳導問題 ； 擴展型卡爾曼濾波器 ； 最小平方估算器

並列摘要

It is a complicated nonlinear heat conduction problem when the thermal conductivity and volumetric heat capacity are regarded as the quadratic temperature function. This research presents a methodology to estimate the time varying unknown heat source applied at this nonlinear heat conduction problem and the transient response of the temperature field distribution in the heat transfer condition by using the measurements of the boundary temperature. The algorithm is called input estimation (IE), it includes the extended Kalman filter (EKF) and weighted recursive least-square estimator (WRLSE). The purpose of EKF is to generate the recursive innovation sequence and WRLSE is used to identify the unknown time variant heat source. The simulation results show that the proposed algorithm can estimate the unknown time-varying heat source and temperature field distribution on-line with more accuracy in the nonlinear model. It also proves if the nonlinear heat conduction problem is regarded as linear heat conduction problem, the heat source estimated by Kalman filter and weighted recursive least-square estimator will cause more errors.

並列關鍵字

Nonlinear heat conduction problem ； Extended Kalman filter ； Weighted recursive least square estimator