Proposing multi-parameter identification of the system described by partial differential equations based on modified conjugate gradient method
Corressponding author's email:
tranthanhphong@tgu.edu.vnKeywords:
Heat source, identification, inverse problems, conjugate gradient method, partial differential equationsAbstract
The paper introduces the method of simultaneous identification of multi unknown parameters of the system described by the quadratic partial differential equation with the heat transfer equation as an example. Accordingly, a mobile heat source on the aluminium plate is considered with a fixed group of sensors located on the survey area to measure the evolution of temperature over time and space. Solving this inverse problem requires optimal input data to reduce computational time by eliminating the measurement values of useless sensors. A sensor selection algorithm is proposed in combination with the conjugate gradient method for effective identification. Moreover, the iterative algorithm is also corrected by proposing a flexible shutter and sliding window selection algorithm to optimize identification time. In order to help evaluate the effectiveness of the proposed method, the measured temperature value with the effect of disturbances follows the standard Gaussian distribution function. The results show that the proposed method has good ability to identify the function of heat flow density and trajectory with low latency and error to meet the requirements.
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