Comparative modelling of reaction and impulse turbines using ANN, ANFIS, and PSO-enhanced neural networks

Turbomachines are broadly classified into impulse and reaction turbines, each governed by distinct energy conversion mechanisms. Conventional performance evaluation of turbines is experimentally intensive and limited in scalability. This study develops and benchmarks three intelligent modelling techniques (artificial neural networks (ANN), adaptive neuro-fuzzy inference systems (ANFIS), and a hybrid ANN enhanced with particle swarm optimization (ANN-PSO)) to predict the hydraulic power output of FM60 impulse and FM61 reaction turbines. A total of 197 experimental data points were analyzed, comprising 120 samples from reaction turbines and 77 from impulse turbines, with flow rate, pressure, and torque used as input parameters. The comparative results demonstrate that the ANN achieved the highest predictive accuracy for impulse turbines, attaining a regression coefficient of determination $$({R}^{2})$$ of $$0.99973$$ with a mean squared error (MSE) of 1.99 × 10−4, corresponding to an average prediction error below 1.5%. For reaction turbines, the ANN-PSO model delivered the best performance, reaching an $${R}^{2}$$ of $$0.99720$$ and reducing deviation from experimental values to within $$6.0\text{\%}$$. ANFIS also produced strong correlations, with $${R}^{2}$$ values above $$0.984$$ for both turbine types, but exhibited higher maximum deviations of up to $$13.36\text{\%}$$ in the reaction turbine case. These findings show that hybrid optimization improves ANN robustness for complex fluid–mechanical interactions, whereas standalone ANN architectures are sufficient for smoother input–output relationships. By offering predictive accuracies above $$99\text{\%}$$ across both turbine types, the proposed models provide a reliable and cost-effective alternative to traditional performance testing. The outcomes highlight practical opportunities for integrating intelligent modelling into turbine design, monitoring, and optimization frameworks, while also identifying the need for expanded datasets, additional structural features, and advanced validation strategies to enhance generalizability.