For nonlinear transient heat transfer system, a fuzzy adaptive predictive inverse method (FAPIM) is proposed to inverse transient boundary heat flux. The influence relationship matrix is utilized to establish time-varying linear prediction model of the temperatures at measurement point. Then, the predictive and measurement temperatures are used to inverse the heat flux at current moment by rolling optimization. A decentralized fuzzy inference (DFI) mechanism is established. The deviation vector of the predictive temperature is adopted to conduct decentralized inference by a set of fuzzy inference units, and then, the influence relationship matrix is updated online to guarantee the adaptive ability of the prediction model by weighting fuzzy inference components. FAPIM is utilized to inverse the unknown heat flux of a heat transfer system with temperature-dependent thermal properties, which has shown that the inverse method has better adaptive ability for the inverse problems of nonlinear heat transfer system.

References

1.
Kim
,
T.-G.
, and
Lee
,
Z.-H.
,
1997
, “
Time-Varying Heat Transfer Coefficients Between Tube-Shaped Casting and Metal Mold
,”
Int. J. Heat Mass Transfer
,
40
(
15
), pp.
3513
3525
.
2.
Hills
,
R. G.
, and
Hensel
,
E. C.
, Jr.
,
1986
, “
One-Dimensional Nonlinear Inverse Heat Conduction Technique
,”
Numer. Heat Transfer
,
10
(
4
), pp.
369
393
.
3.
Lou
,
C.
,
Li
,
W.-H.
,
Zhou
,
H.-C.
, and
Salinas
,
C. T.
,
2011
, “
Experimental Investigation on Simultaneous Measurement of Temperature Distributions and Radiative Properties in an Oil-Fired Tunnel Furnace by Radiation Analysis
,”
Int. J. Heat Mass Transfer
,
54
(
1–3
), pp.
1
8
.
4.
Duda
,
P.
, and
Taler
,
J.
,
2009
, “
A New Method for Identification of Thermal Boundary Conditions in Water-Wall Tubes of Boiler Furnaces
,”
Int. J. Heat Mass Transfer
,
52
(
5–6
), pp.
1517
1524
.
5.
Liu
,
L. H.
, and
Tan
,
H. P.
,
2001
, “
Inverse Radiation Problem in Three-Dimensional Complicated Geometric Systems With Opaque Boundaries
,”
J. Quant. Spectrosc. Radiat. Transfer
,
68
(
5
), pp.
559
573
.
6.
Beck
,
J. V.
,
Blackwell
,
B.
, and
St. Clair
,
C. R.
, Jr.
,
1985
,
Inverse Heat Conduction: III-Posed Problems
,
Wiley-Interscience
,
New York
.
7.
Pourgholi
,
R.
, and
Rostamian
,
M.
,
2010
, “
A Numerical Technique for Solving IHCPs Using Tikhonov Regularization Method
,”
Appl. Math. Model.
,
34
(
8
), pp.
2102
2110
.
8.
Yang
,
F.
, and
Fu
,
C. L.
,
2010
, “
The Method of Simplified Tikhonov Regularization for Dealing With the Inverse Time-Dependent Heat Source Problem
,”
Comput. Math. Appl.
,
60
(
5
), pp.
1228
1236
.
9.
Wang
,
G. J.
,
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 Transfer
,
54
(
13–14
), pp.
2782
2788
.
10.
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
.
11.
Zhu
,
L. N.
,
Wang
,
G. J.
,
Chen
,
H.
, and Luo, Z.,
2011
, “
Inverse Estimation for Heat Flux Distribution at the Metal-Mold Interface Using Fuzzy Inference
,”
ASME J. Heat Transfer
,
133
(
8
), p.
081602
.
12.
Beck
,
J. V.
,
Litkouhi
,
B.
, and
St. Clair
,
C. R.
, Jr.
,
1982
, “
Efficient Sequential Solution of the Nonlinear Inverse Heat Conduction Problem
,”
Numer. Heat Transfer
,
5
(3), pp.
275
286
.
13.
Beck
,
J. V.
,
1970
, “
Nonlinear Estimation Applied to the Nonlinear Inverse Heat Conduction Problem
,”
Int. J. Heat Mass Transfer
,
13
(
4
), pp.
703
716
.
14.
Huang
,
C.-H.
, and Tsai, C.-C.,
1998
, “
An Inverse Heat Conduction Problem of Estimating Boundary Fluxes in an Irregular Domain With Conjugate Gradient Method
,”
Int. J. Heat Mass Transfer
,
34
(
1
), pp.
47
54
.
15.
Huang
,
C.-H.
, and
Chen
,
C.-W.
,
1998
, “
A Boundary Element-Based Inverse Problem in Estimating Transient Boundary Conditions With Conjugate Gradient Method
,”
Int. J. Numer. Methods Eng.
,
42
(
5
), pp.
943
965
.
16.
Rouquette
,
S.
,
Guo
,
J.
, and
Le Masson
,
P.
,
2007
, “
Estimation of the Parameters of a Gaussian Heat Source by the Levenberg–Marquardt Method: Application to the Electron Beam Welding
,”
Int. J. Therm. Sci.
,
46
(
2
), pp.
128
138
.
17.
Liu
,
F.-B.
,
2011
, “
A Hybrid Method for the Inverse Heat Transfer of Estimating Fluid Thermal Conductivity and Heat Capacity
,”
Int. J. Therm. Sci.
,
50
(
5
), pp.
718
724
.
18.
Yang
,
Y.-C.
,
Chen
,
W.-L.
, and
Lee
,
H.-L.
,
2011
, “
A Nonlinear Inverse Problem in Estimating the Heat Generation in Rotary Friction Welding
,”
Numer. Heat Transfer Part A
,
59
(
2
), pp.
130
149
.
19.
Yang
,
Y.-C.
, and
Chen
,
W.-L.
,
2011
, “
A Nonlinear Inverse Problem in Estimating the Heat Flux of the Disc in a Disc Brake System
,”
Appl. Therm. Eng.
,
31
(
14–15
), pp.
2439
2448
.
20.
Mohammadiun
,
H.
,
Molavi
,
H.
,
Bahrami
,
H. R. T.
, and
Mohammadiun
,
M.
,
2012
, “
Real-Time Evaluation of Severe Heat Load Over Moving Interface of Decomposing Composites
,”
ASME J. Heat Transfer
,
134
(
11
), p.
111202
.
21.
Khajehpour
,
S.
,
Hematiyan
,
M. R.
, and
Marin
,
L.
,
2013
, “
A Domain Decomposition Method for the Stable Analysis of Inverse Nonlinear Transient Heat Conduction Problems
,”
Int. J. Heat Mass Transfer
,
58
(
1–2
), pp.
125
134
.
22.
Cui
,
M.
,
Duan
,
W.-W.
, and
Gao
,
X.-W.
,
2015
, “
A New Inverse Analysis Method Based on a Relaxation Factor Optimization Technique for Solving Transient Nonlinear Inverse Heat Conduction Problems
,”
Int. J. Heat Mass Transfer
,
90
, pp.
491
498
.
23.
Daouas
,
N.
, and
Radhouani
,
M.-S.
,
2004
, “
A New Approach of the Kalman Filter Using Future Temperature Measurements for Nonlinear Inverse Heat Conduction Problems
,”
Numer. Heat Transfer Part B
,
45
(
6
), pp.
565
585
.
24.
Liu
,
C.-S.
,
2014
, “
On-Line Detecting Heat Source of a Nonlinear Heat Conduction Equation by a Differential Algebraic Equation Method
,”
Int. J. Heat Mass Transfer
,
76
, pp.
153
161
.
25.
Li
,
Y.
,
Wang
,
G.
, and
Chen
,
H.
,
2015
, “
Simultaneously Regular Inversion of Unsteady Heating Boundary Conditions Based on Dynamic Matrix Control
,”
Int. J. Therm. Sci.
,
88
, pp.
148
157
.
26.
Li
,
Y.
,
Wang
,
G.
, and
Chen
,
H.
,
2015
, “
Simultaneously Estimation for Surface Heat Fluxes of Steel Slab in a Reheating Furnace Based on DMC Predictive Control
,”
Appl. Therm. Eng.
,
80
, pp.
396
403
.
27.
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
.
28.
Broekhoven
,
E. V.
, and
Baets
,
B. D.
,
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
.
29.
Duda
,
P.
,
2016
, “
A Method for Transient Thermal Load Estimation and Its Application to Identification of Aerodynamic Heating on Atmospheric Reentry Capsule
,”
Aerosp. Sci. Technol.
,
51
, pp.
26
33
.
30.
Duda
,
P.
,
2015
, “
Numerical and Experimental Verification of Two Methods for Solving an Inverse Heat Conduction Problem
,”
Int. J. Heat Mass Transfer
,
84
, pp.
1101
1112
.
You do not currently have access to this content.