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

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.