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A novel technique based on the improved firefly algorithm coupled with extreme learning machine (ELM-IFF) for predicting the thermal conductivity of soil

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Abstract

Thermal conductivity is a specific thermal property of soil which controls the exchange of thermal energy. If predicted accurately, the thermal conductivity of soil has a significant effect on geothermal applications. Since the thermal conductivity is influenced by multiple variables including soil type and mineralogy, dry density, and water content, its precise prediction becomes a challenging problem. In this study, novel computational approaches including hybridisation of two metaheuristic optimisation algorithms, i.e. firefly algorithm (FF) and improved firefly algorithm (IFF), with conventional machine learning techniques including extreme learning machine (ELM), adaptive neuro-fuzzy interface system (ANFIS) and artificial neural network (ANN), are proposed to predict the thermal conductivity of unsaturated soils. FF and IFF are used to optimise the internal parameters of the ELM, ANFIS and ANN. These six hybrid models are applied to the dataset of 257 soil cases considering six influential variables for predicting the thermal conductivity of unsaturated soils. Several performance parameters are used to verify the predictive performance and generalisation capability of the developed hybrid models. The obtained results from the computational process confirmed that ELM-IFF attained the best predictive performance with a coefficient of determination = 0.9615, variance account for = 96.06%, root mean square error = 0.0428, and mean absolute error = 0.0316 on the testing dataset (validation phase). The results of the models are also visualised and analysed through different approaches using Taylor diagrams, regression error characteristic curves and area under curve scores, rank analysis and a novel method called accuracy matrix. It was found that all the proposed hybrid models have a great ability to be considered as alternatives for empirical relevant models. The developed ELM-IFF model can be employed in the initial stages of any engineering projects for fast determination of thermal conductivity.

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Abbreviations

SVR:

Support vector regression

GPR:

Gaussian process regression

CNN:

Convolutional neural network

ANN:

Artificial neural network

adj.R 2 :

Adjusted Coefficient Of Determination

MAE:

Mean absolute error

MAPE:

Mean absolute percentage error

NS:

Nash–Sutcliffe efficiency

PI:

Performance Index

R 2 :

Coefficient of determination

VAF:

Variance account for

WI:

Willmott's Index of agreement

WMAPE:

Weighted mean absolute percentage error

S :

Saturation degree

n :

Porosity

γ d :

Dry density

QC:

Quartz content

CC:

Clay content

SC:

Sand content

GSHPs:

Ground source heat pumps

k r :

Normalised thermal conductivity

BTES:

Borehole thermal energy storage

TDR:

Time domain reflectometry

MLAs:

Machine learning algorithms

ANFIS:

Adaptive neuro-fuzzy interface system

DNN:

Deep neural network

OAs:

Optimisation algorithms

MOA:

Metaheuristic optimisation algorithm

PE:

Processing element

FIS:

Fuzzy inference system

FF:

Firefly algorithm

IFF:

Improved firefly algorithm

ELM:

Extreme learning machine

MFs:

Membership functions

SLFN:

Single-layer feed-forward network

m :

Population size

itr:

Maximum number of iterations

N :

Number of neurons

RMSE:

Root mean square error

ROC:

Receiver operating characteristic

REC:

Regression error characteristic

SE:

Squared error

AD:

Absolute deviation

AUC:

Area under the curve

TR:

Training

TS:

Testing

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Authors and Affiliations

  1. Discipline of Civil and Infrastructure Engineering, School of Engineering, Royal Melbourne Institute of Technology (RMIT), Melbourne, VIC, 3001, Australia

    Navid Kardani, Majidreza Nazem & Annan Zhou

  2. Department of Civil Engineering, National Institute of Technology Patna, Patna, 800005, India

    Abidhan Bardhan & Pijush Samui

  3. Department of Civil Engineering, Faculty of Engineering, University of Malaya, 50603, Kuala Lumpur, Malaysia

    Danial Jahed Armaghani

Authors
  1. Navid Kardani
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  2. Abidhan Bardhan
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  3. Pijush Samui
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  4. Majidreza Nazem
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  5. Annan Zhou
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  6. Danial Jahed Armaghani
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Correspondence to Navid Kardani or Annan Zhou.

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Kardani, N., Bardhan, A., Samui, P. et al. A novel technique based on the improved firefly algorithm coupled with extreme learning machine (ELM-IFF) for predicting the thermal conductivity of soil. Engineering with Computers 38, 3321–3340 (2022). https://doi.org/10.1007/s00366-021-01329-3

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