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Prezentacja programu PowerPoint

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Technical University of Silesia, Gliwice, Poland. Inverse Problems in Engineering Symposium ... sensitivity analysis for geometry and boundary problems ... – PowerPoint PPT presentation

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Title: Prezentacja programu PowerPoint


1
Inverse Problems in Engineering
Symposium Tuscaloosa, June 2003
Application of Bezier splines and sensitivity
analysis in inverse geometry and boundary
problems
Iwona NOWAK, Andrzej J. NOWAK Institute of
Mathematics, Institute of Thermal
Technology, Technical University of Silesia,
Gliwice, Poland.
2
Scope of the Presentation
  • Problem formulation
  • Solution procedure
  • - sensitivity analysis for geometry and
    boundary problems
  • Numerical results
  • Conclusions

3
Continuous casting
4
Problem Formulation
y
A
B
liquid
C
F
D

solid
E
O
x
5
General Solution Strategy
make boundary problem well-posed
FDM FEM BEM
solve direct problem
best matching
modify assumed data
sensitivity coefficients
6
Sensitivity Coefficient
7
Main Set of Equations
8
Solution Algorithm
direct problem formulation -assumption of
vector Yy1,..., yn, q1,..., qm
freezing of heat fluxes
freezing of front location
end of calculations
9
Sensitivity Analysis - Boundary Part
10
Sensitivity Analysis Geometry Part
11
Sensitivity Analysis Geometry Part
Nowak I., Nowak A.J, Wrobel L.C Identification
of Phase Change Front by Bezier Splines and BEM,
International Journal of Thermal Sciences, vol.41
(2002) Elsevier Science, pp.492-499
12
Sensor Locations
y
A
B
liquid
C
all sensors are used
F
D
all sensors are used

solid
E
O
x
13
Numerical Results
phase change front location
heat flux distribution
measurements error 0.1 number of sensors 35
14
Numerical Results
measurements error 0.1 number of sensors 35
15
Sensor Locations
y
A
B
liquid
C
geometry sensors are used
F
D
geometry sensors are used

solid
E
O
x
16
Numerical Results
phase change front location
heat flux distribution
measurements error 0.1 number of sensors
35 sensors separated
17
Numerical Results
measurements error 0.1 number of sensors
35 sensors separated
18
Numerical Results
phase change front location
heat flux distribution
measurements error 2.0 number of sensors
35 sensors separated
19
Numerical Results
measurements error 2.0 number of sensors
35 sensors separated
20
Experiment
Drezet J.-M., Rappaz M., Grun G.-U.,Gremaud M.,
Determination of Thermophysical Properties and
Boundary Conditions of Direct Chill-Cast
Aluminium Alloys Using Inverse Methods,
Metallurgical and Materials Transactions A,
vol.31A, June 2000, pp.1627--1634
21
Numerical Results
Measured and predicted temperature in sensor
locations
22
Numerical Results
23
Numerical Results
24
Numerical Results
25
Conclusions
  • BEM based algorithms for solving inverse
    boundary and geometry problems
  • application of Bézier function and sensitivity
    coefficients
  • stabile results does not provide accurate
    solution
  • sensors separation permits to obtain encouraging
    results even with experimental measurements
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