Parameter identification for stochastic diffusion equations with unknown boundary conditions

1988 ◽  
Vol 17 (1) ◽  
pp. 15-36 ◽  
Author(s):  
Shin-Ichi Aihara ◽  
Arunabha Bagchi
Keyword(s):  
Boundary Conditions ◽  
Parameter Identification ◽  
Diffusion Equations ◽  
Unknown Boundary ◽  
Stochastic Diffusion ◽  
Unknown Boundary Conditions ◽  
Stochastic Diffusion Equations

An Inverse Method for Simultaneous Estimation of the Center and Surface Thermal Behavior of a Heated Cylinder Normal to a Turbulent Air Stream

2002 ◽  
Vol 124 (4) ◽  
pp. 601-608 ◽  
Author(s):  
Jiin-Hong Lin ◽  
Cha’o-Kuang Chen ◽  
Yue-Tzu Yang
Keyword(s):  
Boundary Conditions ◽  
Thermal Behavior ◽  
Measurement Errors ◽  
Boundary Behavior ◽  
Traditional Approach ◽  
Simultaneous Estimation ◽  
Unknown Boundary ◽  
Heated Cylinder ◽  
Air Stream ◽  
Unknown Boundary Conditions

A two-dimensional inverse analysis utilizes a different perspective to simultaneously estimate the center and surface thermal behavior of a heated cylinder normal to a turbulent air stream. A finite-difference method is used to discretize the governing equations and then a linear inverse model is constructed to identify the unknown boundary conditions. The present approach is to rearrange the matrix forms of the governing differential equations and estimate the unknown boundary conditions of the heated cylinder. Then, the linear least-squares-error method is adopted to find the solutions. The results show that only a few measuring points inside the cylinder are needed to estimate the unknown quantities of the thermal boundary behavior, even when measurement errors are considered. In contrast to the traditional approach, the advantages of this method are that no prior information is needed on the functional form of the unknown quantities, no initial guesses are required, no iterations in the calculating process are necessary, and the inverse problem can be solved in a linear domain. Furthermore, the existence and uniqueness of the solutions can easily be identified.

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