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Analysis on mass flow rate of R22 and R407C through coiled adiabatic capillary tubes with GA and PSO optimized BP networks

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Abstract

R22 and R407C mass flow rates through straight and coiled adiabatic capillary tubes are analyzed with three ANN models, i.e., the feed forward network with back propagation (BP) algorithm, GA-BP (genetic algorithm optimized BP network) and PSO-BP (BP algorithm combined with particle swarm optimization). The modelled outputs by these ANN methods are compared with experimental data. The results showed that the predicted mass flow rates with the three models of BP, GA-BP and PSO-BP agree quite well with the experimental data with the mean relative error of 3.82 %, 3.14 % and 2.3 % for R22, and 3.17 %, 2.66 % and 2.46 % for R407C, respectively. PSO-BP network is then employed to predict the coiling effect of capillary tubes on the mass flow rate. It is shown that the mass flow rates with coiled diameter between 0.04 m and 0.6 m are about 4 %–13 % lower than that of the straight capillary tube.

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Abbreviations

a :

Half width of possible measured value interval

c 1 :

Self-adjustment weight

c 2 :

Social-adjustment weight

D :

Coiled diameter (m)

d :

Inner diameter (mm)

f :

Activation function

Gbest :

Global best position

k u :

Coverage factor for uniform distribution assumption

L :

Length (m)

m :

Mass flow rate (kg h−)

mxgen :

Largest iteration number

n :

Total number of test samples

P :

Pressure (bar)

Pbest :

Particle best position

r1, r2 :

Uniformly (0, 1) distributed pseudorandom numbers

t :

Current iteration number

T cn :

Condensation temperature (°C)

T e :

Evaporation temperature (°C)

T suc :

Suction vapor temperature (°C)

W :

Connection weight

u′b(m):

Relative standard uncertainty of mass flow rate

u′E(m):

Relative expanded uncertainty of mass flow rate

v :

Particle velocity

V th :

Theoretical displacement volume (m3·h−1)

x :

Input of the neuron

X :

Particle position

y :

Output of the neuron

y p :

Predicted output

α :

Learning rate

θ :

Threshold (bias)

ΔT sub :

Degree of inlet subcooling (°C)

ε :

Inertia weight

λ :

Volumetric efficiency of the compressor

ρ suc :

Density of suction vapor (kg m−3)

cn:

Condensation

e:

Evaporation

ei:

Experimental value of a test sample

i:

The neuron number of input layer

in:

Inlet

j :

The neuron number of hidden layer

k:

The neuron number of output layer

out:

Outlet

pi:

Predicted value of a test sample

sub:

Subcooling

suc:

Suction

I:

Total number of output layer neurons

new:

New value

old:

Old value

ANN:

Artificial neural network

ANFIS:

Adaptive neuro-fuzzy inference system

BP:

Back propagation

Eq.:

Equation

GA:

Genetic algorithm

MAPE:

Mean absolute percentage error

MRE:

Mean relative error

MSE:

Mean square error

PSO:

Particle swarm optimization

RE:

Relative error

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Acknowledgments

This work was supported in part by Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (No. 2012940), China and Beijing Natural Science Foundation (No. 3192034), China.

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Authors and Affiliations

  1. School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing, 102206, China

    Guobing Zhou

  2. School of Software Engineering, South China University of Technology, Guangzhou, 510006, China

    Yuchen Zhou

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  1. Guobing Zhou
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Correspondence to Guobing Zhou.

Additional information

Recommended by Editor Yong Tae Kang

Guobing Zhou is a Professor of the School of Energy, Power and Mechanical Engineering, North China Electric Power University, Beijing, China. He received his Ph.D. in Thermal Engineering from Tianjin University. His research interests include micro-channel flow and heat transfer, HVAC&R, solar thermal storage and applications.

Yuchen Zhou is currently working toward the Bachlor’s degree with the School of Software Engineering, South China University of Technology, Guangzhou, China. Her current research interests include swarm intelligence, machine learning, and natural language processing.

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Zhou, G., Zhou, Y. Analysis on mass flow rate of R22 and R407C through coiled adiabatic capillary tubes with GA and PSO optimized BP networks. J Mech Sci Technol 34, 3445–3455 (2020). https://doi.org/10.1007/s12206-020-0737-8

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  • DOI: https://doi.org/10.1007/s12206-020-0737-8

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