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Figure 3 displays a simple structure of the ANFIS-based model with two inputs. More details regarding the structure of this model are presented by Awan & Bae (2014). PSO was used as the optimizer. Figure 4 is a flowchart of the PSO-ANFIS approach. In brief, PSO was utilized to train the ANFIS-based model and find the optimal coefficients for connecting neurons in the network because evolutionary algorithms such as PSO can improve the predictive ability (Sedighkia et al. 2022). Table 1 displays the main characteristics of the ANFIS-based water temperature model. The water temperature depends on several factors and, hence, data-driven models are a good option to achieve a reasonable simulation of the thermal regime. This data-driven model can be directly applied to reservoir operation optimization. Two known indices – the Nash–Sutcliffe efficiency (NSE) index and root means square error (RMSE) – were applied to evaluate the goodness-of-fit of the hybrid machine-learning model (see Gupta et al. (2009) for more details).
Table 1

Main characteristics of the ANFIS-based downstream water temperature model

InputsNumber of MFs (inputs)Type of MFs (inputs)OutputsNumber of MFs (output)Type of MFs (output)Clustering method
Flow rate (m3/s); Wetted perimeter (m); Distance from the reservoir (m); Elevation from sea level (m); Water temperature at distance = 0 m (°C); Air temperature (°C) 10 Gaussian Water temperature at each cross-section 10 Linear Subtractive clustering 
InputsNumber of MFs (inputs)Type of MFs (inputs)OutputsNumber of MFs (output)Type of MFs (output)Clustering method
Flow rate (m3/s); Wetted perimeter (m); Distance from the reservoir (m); Elevation from sea level (m); Water temperature at distance = 0 m (°C); Air temperature (°C) 10 Gaussian Water temperature at each cross-section 10 Linear Subtractive clustering 

MFs, membership functions.

Figure 3

Simple structure of the ANFIS-based data-driven model.

Figure 3

Simple structure of the ANFIS-based data-driven model.

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Figure 4

The PSO-ANFIS flowchart.

Figure 4

The PSO-ANFIS flowchart.

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