To identify the transient and distributed internal surface heat flux of the slab mold in continuous casting process, a fuzzy inference method is proposed in this work. For temporal and spatial distribution characteristics of the internal surface heat flux of continuous casting mold, a decentralized fuzzy inference (DFI) identification scheme possessed of a decoupling characteristic in time and space is established. For each temperature measurement point, the fuzzy inference processes are, respectively, executed from the correspondingly observed temperature sequence through corresponding DFI units. In the time domain, according to sensitivity coefficients, the weighing and synthesizing processes for the decentralized inference results are performed to get the temporal compensation vector for the internal surface heat flux of mold. Then, in the space domain, according to the normal distribution function, the weighing and synthesizing processes for the temporal compensation vectors are performed to get the spatial compensation vector for the internal surface heat flux of mold. Numerical tests are carried out to research the influence of the number of thermocouples and measurement errors on the identification results, which prove the effectiveness of proposed scheme in this work.

References

References
1.
Zhang
,
L.
,
Shen
,
H.
,
Rong
,
Y.
, and
Huang
,
T.
,
2007
, “
Numerical Simulation on Solidification and Thermal Stress of Continuous Casting Billet in Mold Based on Meshless Methods
,”
Mater. Sci. Eng. A
,
466
(
1–2
), pp.
71
78
.
2.
Zhang
,
L.
,
Rong
,
Y.
,
Shen
,
H.
, and
Huang
,
T.
,
2007
, “
Solidification Modeling in Continuous Casting by Finite Point Method
,”
J. Mater. Process. Technol.
,
192–193
, pp.
511
517
.
3.
Louhenkilpi
,
S.
,
Mäkinen
,
M.
,
Vapalahti
,
S.
,
Räisänen
,
T.
, and
Laine
,
J.
,
2005
, “
3D Steady State and Transient Simulation Tools for Heat Transfer and Solidification in Continuous Casting
,”
Mater. Sci. Eng. A
,
413–414
, pp.
135
138
.
4.
Janik
,
M.
, and
Dyja
,
H.
,
2004
, “
Modelling of Three-Dimensional Temperature Field Inside the Mould During Continuous Casting of Steel
,”
J. Mater. Process. Technol.
,
157–158
, pp.
177
182
.
5.
Tsai
,
D. C.
, and
Hwang
,
W. S.
,
2012
, “
Numerical Simulation of the Solidification Processes of Copper During Vacuum Continuous Casting
,”
J. Cryst. Growth
,
343
(
1
), pp.
45
54
.
6.
Majchrzak
,
E.
,
1993
, “
Numerical Simulation of Continuous Casting Solidification by Boundary Element Method
,”
Eng. Anal. Bound. Elem.
,
11
(
2
), pp.
95
99
.
7.
Jolly
,
M.
,
2002
, “
Casting Simulation: How Well Do Reality and Virtual Casting Match? State of the Art Review
,”
Int. J. Cast Met. Res.
,
14
(
5
), pp.
303
313
.
8.
Nowak
,
I.
,
Smolka
,
J.
, and
Nowak
,
A. J.
,
2010
, “
An Effective 3D Inverse Procedure to Retrieve Cooling Conditions in an Aluminium Alloy Continuous Casting Problem
,”
Appl. Therm. Eng.
,
30
(
10
), pp.
1140
1151
.
9.
Gonzalez
,
M.
,
Goldschmit
,
M. B.
,
Assanelli
,
A. P.
,
Berdaguer
,
E. F.
, and
Dvorkin
,
E. N.
,
2003
, “
Modeling of the Solidification Process in a Continuous Casting Installation for Steel Slabs
,”
Metall. Mater. Trans. B
,
34
(
4
), pp.
455
473
.
10.
Pinheiro
,
C. A. M.
,
Samarasekera
,
I. V.
,
Brimacomb
,
J. K.
, and
Walker
,
B. N.
,
2000
, “
Mould Heat Transfer and Continuously Cast Billet Quality With Mould Flux Lubrication—Part 1: Mould Heat Transfer
,”
Ironmak. Steelmak
,
27
(
1
), pp.
37
54
.
11.
Li
,
G.
,
Liu
,
W.
, and
Xu
,
Y.
,
2007
, “
Application of Inverse Heat Conduction Problem in the Breakout Prediction
,”
Foundry Technol.
,
28
(5), pp.
702
704
(in Chinese).
12.
Ranut
,
P.
,
Nobile
,
E.
,
Persi
,
C.
, and
Spagnul
,
S.
,
2011
, “
Estimation of Heat Flux Distribution in a Continuous Casting Mould by Inverse Heat Transfer Algorithms
,”
ASME
Paper No. DETC2011-47435.
13.
Zhu
,
L. N.
,
Wang
,
G. J.
,
Chen
,
H.
, and
Luo
,
Z. M.
,
2011
, “
Inverse Estimation for Heat Flux Distribution at the Metal/Mold Interface Using Fuzzy Inference
,”
ASME J. Heat Transfer
,
133
(
8
), p.
081602
.
14.
Chen
,
H.
,
Su
,
L.
,
Wang
,
G.
,
Wan
,
S.
,
Zhang
,
L.
, and
Luo
,
Z.
,
2014
, “
Fuzzy Estimation for Heat Flux Distribution at the Slab Continuous Casting Mold Surface
,”
Int. J. Therm. Sci.
,
83
, pp.
80
88
.
15.
Wang
,
X.
,
Tang
,
L.
,
Zang
,
X.
, and
Yao
,
M.
,
2012
, “
Mold Transient Heat Transfer Behavior Based on Measurement and Inverse Analysis of Slab Continuous Casting
,”
J. Mater. Process. Technol.
,
212
(
9
), pp.
1811
1818
.
16.
Du
,
F.
,
Wang
,
X.
,
Yao
,
M.
, and
Zhang
,
X.
,
2014
, “
Analysis of the Non-Uniform Thermal Behavior in Slab Continuous Casting Mold Based on the Inverse Finite-Element Model
,”
J. Mater. Process. Technol.
,
214
(
11
), pp.
2676
2683
.
17.
Badri
,
A.
,
Natarajan
,
T. T.
,
Snyder
,
C. C.
,
Powers
,
K. D.
,
Mannion
,
F. J.
, and
Cramb
,
A. W.
,
2005
, “
A Mold Simulator for the Continuous Casting of Steel—Part I: The Development of a Simulator
,”
Metall. Mater. Trans. B
,
36
(
3
), pp.
355
371
.
18.
Zhang
,
H.
,
Wang
,
W.
,
Zhou
,
D.
,
Ma
,
F.
,
Lu
,
B.
, and
Zhou
,
L.
,
2014
, “
A Study for Initial Solidification of Sn-Pb Alloy During Continuous Casting—Part I: The Development of the Technique
,”
Metall. Mater. Trans. B
,
45
(
3
), pp.
1038
1047
.
19.
Zhang
,
H.
,
Wang
,
W.
, and
Zhou
,
L.
,
2015
, “
Calculation of Heat Flux Across the Hot Surface of Continuous Casting Mold Through Two-Dimensional Inverse Heat Conduction Problem
,”
Metall. Mater. Trans. B
,
46
(
5
), pp.
2137
2152
.
20.
Udayraj
,
S.
,
Chakraborty
,
S.
,
Ganguly
,
E. Z.
,
Chacko
,
S. K.
,
Ajmani
,
P.
, and
Talukdar
,
2017
, “
Estimation of Surface Heat Flux in Continuous Casting Mould With Limited Measurement of Temperature
,”
Int. J. Therm. Sci.
,
118
, pp.
435
447
.
21.
Hadamard
,
J.
,
1923
,
Lectures on the Cauchy Problem in Linear Partial Differential Equations
,
Yale University Press
,
New Haven, CT
.
22.
Wang
,
G. J.
,
Luo
,
Z. M.
,
Zhu
,
L. N.
,
Chen
,
H.
, and
Zhang
,
L. H.
,
2012
, “
Fuzzy Estimation for Temperature Distribution of Furnace Inner Surface
,”
Int. J. Therm. Sci.
,
51
, pp.
84
90
.
23.
Wang
,
G.
,
Zhu
,
L.
, and
Chen
,
H.
,
2011
, “
A Decentralized Fuzzy Inference Method for Solving the Two-Dimensional Steady Inverse Heat Conduction Problem of Estimating Boundary Condition
,”
Int. J. Heat Mass Tranfer
,
54
(
13–14
), pp.
2782
2788
.
24.
Wang
,
K.
,
Wang
,
G.
,
Chen
,
H.
, and
Zhu
,
L.
,
2014
, “
Estimating Thermal Boundary Conditions of Boiler Membrane Water-Wall Using Decentralized Fuzzy Inference With Sensitivity Weighting
,”
Appl. Therm. Eng.
,
66
(
1–2
), pp.
309
317
.
25.
Chen
,
H.
,
Cao
,
D.
,
Wang
,
G.
,
Wan
,
S.
, and
Li
,
Y.
,
2016
, “
Fuzzy Estimation for Unknown Boundary Shape of Fluid-Solid Conjugate Heat Transfer Problem
,”
Int. J. Therm. Sci.
,
106
, pp.
112
121
.
26.
Wang
,
G.
,
Wan
,
S.
,
Chen
,
H.
,
Lv
,
C.
, and
Zhang
,
D.
,
2017
, “
A Double Decentralized Fuzzy Inference Method for Estimating the Time and Space-Dependent Thermal Boundary Condition
,”
Int. J. Heat Mass Transfer
,
109
, pp.
302
311
.
27.
Mahapatra
,
R. B.
,
Brimacombe
,
J. K.
,
Samarasekera
,
I. V.
,
Walker
,
N.
,
Paterson
,
E. A.
, and
Young
,
J. D.
,
1991
, “
Mold Behavior and Its Influence on Quality in the Continuous Casting of Steel Slabs—Part I: Industrial Trials, Mold Temperature Measurements, and Mathematical Modeling
,”
Metall. Trans. B
,
22
(
6
), pp.
861
874
.
28.
Sargolzaei
,
J.
,
Khoshnoodi
,
M.
,
Saghatoleslami
,
N.
, and
Mousavi
,
M.
,
2008
, “
Fuzzy Inference System to Modeling of Crossflow Milk Ultrafiltration
,”
Appl. Soft Comput.
,
8
(
1
), pp.
456
465
.
29.
Van Broekhoven
,
E.
, and
De Baets
,
B.
,
2006
, “
Fast and Accurate Center of Gravity Defuzzification of Fuzzy System Outputs Defined on Trapezoidal Fuzzy Partitions
,”
Fuzzy Set. Syst.
,
157
(
7
), pp.
904
918
.
You do not currently have access to this content.