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

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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.

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Abbreviations

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

c p :

Specific heat, J/(kg·°C)

C :

Volume specific heat, J/(m3·°C)

C best :

Effect coefficient of the best krill individual

C r :

Crossover probability

C t :

Coefficient of search step

D :

Random movement

F :

Foraging movement

F obj :

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

V f :

Foraging speed

x :

x-coordinate, m

X :

Position of krill individual

Y :

Value of estimation parameters

y :

y-coordinate, m

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

ε rel :

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

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

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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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Authors and Affiliations

  1. School of Energy Science and Engineering, Harbin Institute of Technology, 92, West Dazhi Street, Harbin, 150001, People’s Republic of China

    S. C. Sun, H. Qi, X. Y. Yu, Y. T. Ren & L. M. Ruan

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  1. S. C. Sun
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  2. H. Qi
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Correspondence to H. Qi.

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Sun, S.C., Qi, H., Yu, X.Y. et al. Inverse Identification of Temperature-Dependent Thermal Properties Using Improved Krill Herd Algorithm. Int J Thermophys 39, 121 (2018). https://doi.org/10.1007/s10765-018-2442-8

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