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.

scholarly journals Cable force estimation of cables with small sag considering inclination angle effect

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Wen-Yu He ◽  
Fan-Cheng Meng ◽  
Wei-Xin Ren
Keyword(s):  
Boundary Conditions ◽  
Inclination Angle ◽  
Estimation Methods ◽  
Unknown Boundary ◽  
Force Estimation ◽  
Numerical Examples ◽  
Cable Force ◽  
Angle Effect ◽  
Unknown Boundary Conditions ◽  
Cable Force Estimation

AbstractCable force estimation is essential for security assessment of cable-stayed bridges. Cable force estimation methods based on the relationship between cable force and frequency have been extensively studied and used during both construction phase and service phase. However, the effect induced by inclination angle of the cable is not included in the establishment of frequency-cable force relationship as horizontal cable model is normally employed. This study aims to investigate the influence of the inclination angle on vibration based cable force estimation and provide practical formulas accordingly. Firstly numerical examples of fixed-fixed and hinged-hinged cables are simulated to illustrate the necessity of considering the inclination angle effect on the modal parameters and cable force estimation for inclined cables with small sag. Then practical formulas considering the inclination angle effect to estimate the cable force of fixed-fixed and hinged-hinged cables via the fundamental frequency are established accordingly. For the inclined cables with unknown boundary conditions, the coefficients reflecting boundary condition are predicted via the practical formulas for fixed-fixed and hinged-hinged cables. And the cable force considering the influence of inclination angle and unknown boundary conditions is obtained by iteration method. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed method.

INVERSE RECONSTRUCTION OF THERMAL AND MECHANICAL BOUNDARY CONDITIONS IN COUPLED NONLINEAR THERMO-ELASTIC PROBLEMS

2014 ◽  
Vol 06 (02) ◽  
pp. 1450014 ◽  
Author(s):  
S. KHAJEHPOUR ◽  
M. R. HEMATIYAN
Keyword(s):  
Boundary Conditions ◽  
Time Domain ◽  
Inverse Analysis ◽  
Optimization Method ◽  
Elastic Problem ◽  
Unknown Boundary ◽  
The Finite Element Method ◽  
Inverse Reconstruction ◽  
The Time Domain ◽  
Unknown Boundary Conditions

A stable technique based on the finite element method for inverse analysis of coupled nonlinear thermo-elastic problems is presented. Not only the time-domain is divided into small intervals, but also the space-domain is divided into several sub-domains. The inverse problem is solved in each sub-domain subsequently. For the inverse analysis in each sub-domain, the unknown boundary conditions are found by using an optimization method and also by employing the information obtained in the previous sub-domain. The method is sufficiently stable to be used for inverse analysis of a thermo-elastic problem under a thermal shock. Three numerical examples are provided to demonstrate the efficiency of the proposed method. The effects of the number of sub-domains are investigated in the examples.

A Least-Squares Finite Element Formulation for Inverse Detection of Unknown Boundary Conditions in Steady Heat Conduction

2008 ◽  
Author(s):  
Brian H. Dennis
Keyword(s):  
Finite Element Method ◽  
Heat Flux ◽  
Finite Element ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Unknown Boundary ◽  
Unknown Boundary Conditions ◽  
Steady Heat Conduction ◽  
Steady Heat ◽  
Element Method

A Least Squares Finite Element Method (LSFEM) formulation for the detection of unknown boundary conditions in steady heat conduction is presented. The method is capable of determining temperatures and heat fluxes in locations where such quantities are unknown provided such quantities are sufficiently overspecified in other locations. In several finite element and boundary element inverse implementations, the resulting system of equations becomes become rectangular if the number of overspecified conditions exceeds the number of unknown conditions. In the case of the finite element method, these rectangular matrices are sparse and can be difficult to solve efficiently. Often we must resort to the use of direct factorizations that require large amounts of core memory for realistic geometries. This difficulty has prevented the solution of large-scale inverse problems that require fine meshes to resolve complex 3-D geometries and material interfaces. In addition, the Galerkin finite element method (GFEM) does not provide the same level of accuracy for both temperature and heat flux. In this paper, an alternative finite element approach based on LSFEM will be shown. The LSFEM formulation always results in a symmetric positivedefinite matrix that can be readily treated with standard sparse matrix solvers. In this approach, the differential equation is cast in first-order form so equal order basis functions can be used for both temperature and heat flux. Enforcement of the overspecified boundary conditions is straightforward in the proposed formulation. The methods allows for direct treatment of complex geometries composed of heterogeneous materials.

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