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Inverse Identification of Temperature-Dependent Thermal Properties Using Improved Krill Herd Algorithm

  • S. C. Sun
  • H. Qi
  • X. Y. Yu
  • Y. T. Ren
  • L. M. Ruan
Article
  • 65 Downloads

Abstract

A novel intelligent algorithm, krill herd (KH), is firstly introduced to solve the inverse identification of temperature-dependent thermal properties of materials. To promote the searching ability and accelerate the convergence velocity, three improved KH (IKH) algorithms are proposed and developed for solving the optimization tasks. The temperature-dependent thermal conductivity and specific heat of a building material are estimated by using the KH algorithms, and the IKHs achieve better performance than the original KHs. Moreover, the functional forms of thermal conductivity of insulating and refractory materials are also reconstructed. The IKH algorithm is proved to be more accurate than other algorithms. Finally, a two-dimensional nonhomogeneous heat conduction model is investigated and the thermal conductivities of materials at specified temperatures are reconstructed, in which no prior information is needed for the expressions of the thermal conductivity to be identified. All the retrieval results show that IKH algorithm is robust and effective for solving the inverse heat conduction problems.

Keywords

Improved KH algorithm Inverse identification Temperature-dependent thermal property Inverse heat conduction Thermal conductivity 

List of symbols

a

Coefficient of thermal conductivity of steel

b

Constant term of energy equation or coefficient of specific heat of steel

c

Coefficient of thermal conductivity of slag wool, foam brick and silica brick

cp

Specific heat, J/(kg·°C)

C

Volume specific heat, J/(m3·°C)

Cbest

Effect coefficient of the best krill individual

Cr

Crossover probability

Ct

Coefficient of search step

D

Random movement

F

Foraging movement

Fobj

Fitness function

I

Iteration number

k

Coefficient of thermal conductivity of carbon steel and aluminum

K

Fitness value

L

Length of medium

LB

Lower boundary

m

Measured signal

M

Population size

Mu

Mutation probability

n

The number of boundary

N

Induced movement

R

A uniformly distributed random number

q

Heat flux, W/m2

rand()

A uniformly distributed random number

t

Temperature, °C

UB

Upper boundary

V

Total speed

Vf

Foraging speed

x

x-coordinate, m

X

Position of krill individual

Y

Value of estimation parameters

y

y-coordinate, m

Greeks symbols

α

Local or target effect

β

Effect provided by the food or the individual best position

Δ

A fluctuation

Δt

Search step size

ε

Computational accuracy

εrel

Relative error

γ

Measurement error

λ

Thermal conductivity, W/(m·°C)

μ

Control number

ρ

Density, kg/m3

σ

Standard deviation

τ

Time, s

ω

Inertia weight

ς

A normally distributed random number

Ψ

Sensitivity coefficient

Subscripts

best

The best value

est

Estimated parameter

exa

Exact parameter

f

Foraging motion

food

Imaginary food position

in

Incident value

max

The maximum value

mea

Measurement value

min

The minimum value

n

Induced movement

new

The current iteration

old

The last iteration

out

Outgoing value

r

Random number

Notes

Acknowledgements

The supports of this work by the National Natural Science Foundation of China (No. 51576053) and the Major National Scientific Instruments and Equipment Development Special Foundation of China (No. 51327803) are gratefully acknowledged. A very special acknowledgment is made to the editors and referees who make important comments to improve this paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • S. C. Sun
    • 1
  • H. Qi
    • 1
  • X. Y. Yu
    • 1
  • Y. T. Ren
    • 1
  • L. M. Ruan
    • 1
  1. 1.School of Energy Science and EngineeringHarbin Institute of TechnologyHarbinPeople’s Republic of China

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