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Research Papers: Melting and Solidification

Fuzzy Identification of the Time- and Space-Dependent Internal Surface Heat Flux of Slab Continuous Casting Mold

[+] Author and Article Information
Guangjun Wang

School of Power Engineering,
Chongqing University,
Chongqing 400044, China;
Key Laboratory of Low-grade Energy Utilization
Technologies and Systems,
Ministry of Education,
Chongqing University,
Chongqing 400044, China

Shibin Wan, Kun Wang, Cai Lv

School of Power Engineering,
Chongqing University,
Chongqing 400044, China

Hong Chen

School of Power Engineering,
Chongqing University,
Chongqing 400044, China;
Key Laboratory of Low-grade Energy Utilization
Technologies and Systems,
Ministry of Education,
Chongqing University,
Chongqing 400044, China
e-mail: chenh@cqu.edu.cn

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 4, 2017; final manuscript received July 16, 2018; published online August 28, 2018. Assoc. Editor: Ali Khounsary.

J. Heat Transfer 140(12), 122301 (Aug 28, 2018) (9 pages) Paper No: HT-17-1658; doi: 10.1115/1.4040955 History: Received November 04, 2017; Revised July 16, 2018

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.

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Figures

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Fig. 1

Schematic diagram of the horizontal cross section of the slab continuous casting mold

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Fig. 2

Space mesh of the slab continuous casting mold

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Fig. 3

Decentralized fuzzy inference module DFIMm

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Fig. 4

Decentralized fuzzy inference unit DFIUr in the DFI module DFIMm

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Fig. 5

Membership of fuzzy sets Al

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Fig. 6

Membership of fuzzy sets Bl

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Fig. 7

Temporal and spatial weighting of the results of the DFI

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Fig. 12

Actual heat flux G2

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Fig. 15

Identification result (a) and errors (b) of DFI when the standard deviation of the measurement errors σ=0.5

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Fig. 16

Identification result (a) and errors (b) of DFI when the standard deviation of the measurement errors σ = 1.0

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Fig. 13

Estimated heat flux G2 (a) and its error (b) by the DFI

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Fig. 8

Temperature distribution of the measurement plane with different space meshes when t = 40 s

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Fig. 9

The temperature history at the measurement point (x = 790 mm, y = 18 mm) with different time-step sizes

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Fig. 10

Actual heat flux G1

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Fig. 11

Estimated heat flux G1 (a) and its error (b) by the DFI

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Fig. 14

Identification result (a) and errors (b) of DFI when the number of measurement points M = 9

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