Abstract
Thermal conductivity is the unique thermal characteristic of soil that regulates the flow of heat energy. A significant impact on geothermal applications is caused by the heat conductivity of the soil. Generally thermal conductivity of soil depends on quartz content, degree of saturation, porosity, dry density, weather condition, and some topographical factors. In this study, four major factors are considered on which thermal conductivity of soil depends, viz., quartz content (QC), degree of saturation (S), porosity (η), and dry density (γ) of soil. In this study, three machine learning models, namely, adaptive neuro fuzzy inference system (ANFIS), extreme learning machine (ELM), and extreme gradient boosting (XGBoost) are used to predict thermal conductivity of soil more accurately and errorless. A total of 110 datasets have been used, where 70% (77 cases) of the dataset are used in the training phase and the rest 30% (33 cases) are used in the testing phase. Models’ performances are judged using various performance parameters like R2, a-20 index, VAF, WI, NS RMSE, MAE, SI, RSR, and WMAPE. Proposed models are also judged with the help of regression curve, error matrix, rank analysis, radar diagram, and William’s plot. Reliability index (β) and failure probability (Pf) are computed with the help of FOSM (first-order second moment) approach. The overall performance of ANFIS model is superior as compared to the other models, and ELM performs worst. To know the influence of each input parameters on the output, sensitivity analysis is performed.
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Data availability
The data presented in this study are available on request from the corresponding author.
Abbreviations
- ML:
-
Machine learning
- Qc :
-
Quartz content
- η:
-
Porosity
- ELM:
-
Extreme learning machine
- R2 :
-
Coefficient of determination
- WI:
-
Willmott’s index of agreement
- RMSE:
-
Root mean square error
- SI:
-
Scatter index
- FOSM:
-
First-order second moment method
- Pf :
-
Probability of failure
- TMP:
-
Trend measuring parameters
- TR:
-
Training
- µ:
-
Average value
- Ee :
-
Error for EMP
- SOR:
-
Strength of relation
- ANFIS:
-
Adaptive neuro fuzzy inference system
- S:
-
Degree of saturation
- γ:
-
Dry density
- XGBoost:
-
Extreme gradient boosting
- VAF:
-
Variance account factor
- NS:
-
Nash Sutcliffe efficiency
- MAE:
-
Mean absolute error
- RSR:
-
RMSE-observation standard deviation ratio
- β:
-
Reliability index
- TC:
-
Thermal conductivity
- EMP:
-
Error measuring parameters
- TS:
-
Testing
- σ:
-
Standard deviation
- Et :
-
Error for TMP
- I:
-
Ideal value of EMP and TMP
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RM: Conceptualization, formal analysis, investigation, software, validation, visualization. KK: Writing—original draft. SK: Formal analysis, data curation. GK: Methodology. PS: Writing—review and editing.
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Mustafa, R., Kumari, K., Kumari, S. et al. Probabilistic analysis of thermal conductivity of soil. Arab J Geosci 17, 22 (2024). https://doi.org/10.1007/s12517-023-11831-1
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DOI: https://doi.org/10.1007/s12517-023-11831-1