Application of ANFIS and LSSVM strategies for estimating thermal conductivity enhancement of metal and metal oxide based nanofluids

Figures & data

Figure 1. Construction of typical ANFIS.

Figure 2. Schematic diagram of proposed PSO-LSSVM model.

Figure 3. Schematic diagram of proposed PSO-ANFIS model.

Table 1. Details of trained LSSVM and ANFIS algorithms.

Type	Comment/ value	Type	Comment/ value
LSSVM		ANFIS
Kernel function	RBF	Membership function	Gaussian
σ^2	0.4326	No. of membership function parameters	120
ϒ	10626.6529	No. of clusters	10
Optimization method	PSO	Optimization method	PSO
Number of data utilized for training	961	Number of data utilized for training	961
Number of data utilized for testing	320	Number of data utilized for testing	320
Population size	110	Population size	80
Maximum Iteration	1500	Maximum Iteration	1000
C1	1	C1	1
C2	2	C2	2

Figure 4. Regression plots between experimental and estimated thermal conductivity by LSSVM for: (a) training data, (b) testing data (c) total data.

Figure 5. Regression plots between experimental and estimated thermal conductivity by ANFIS for: (a) training data, (b) testing data (c) total data.

Figure 6. Absolute deviation of suggested models: (a) LSSVM, (b) ANFIS.

Figure 7. Relative deviation of suggested models: (a) LSSVM, (b) ANFIS.

Table 2. Statistical analyses obtained from the models.

	LSSVM			ANFIS
Analysis	Total	Training	Testing	Total	Training	Testing
R^2	0.994	0.995	0.991	0.984	0.992	0.983
AARD (%)	2.621	2.462	3.098	5.736	3.278	6.057
MSE	0.001	0.001	0.001	0.001	0.001	0.001
RMSE	0.02	0.019	0.023	0.034	0.025	0.032
STD	0.015	0.014	0.017	0.024	0.019	0.020

Figure 8. Comparison of LSSVM and ANFIS models with different models to estimate dimensionless thermal conductivity of Al₂O₃-water nanofluid.

Figure 9. Comparison of LSSVM and ANFIS models with different models to estimate dimensionless thermal conductivity of Ag-water nanofluid.

Figure 10. Comparison of LSSVM and ANFIS models with Thang et al. model to estimate dimensionless thermal conductivity of CNT-water nanofluid at different temperatures.

Figure 11. Comparison of LSSVM and ANFIS models with Thang et al. model to estimate dimensionless thermal conductivity of CNT-water nanofluid for different particle sizes.

Figure 12. Comparison of LSSVM and ANFIS models with different models to estimate dimensionless thermal conductivity of CuO-water nanofluid.

Figure 13. Comparison of LSSVM and ANFIS models with Jang et al. models to estimate dimensionless thermal conductivity of TiO₂-EG nanofluid for different volume void fractions and size particles.

Figure 14. Residual plots for: (a) ANFIS (b) LSSVM models.

Figure 15. Outlier analysis of the suggested (a) LSSVM and (b) ANFIS models.

Figure 16. Sensitivity analysis of parameters used for developing model.