Physics-Informed Neural Networks Optimized by the Whale Optimization Algorithm for Cavitation Fault Detection in Centrifugal Pumps

Abstract Cavitation remains one of the most persistent and economically damaging failure mechanisms in centrifugal pumps, where violent vapor-bubble collapse inside the impeller generates localized shock pressures that progressively erode blade surfaces, induce broadband vibration, and reduce hydraulic efficiency by up to 30 %. Early-stage detection is extremely challenging due to highly nonlinear bubble dynamics, complex geometry, and scarcity of labelled operational data. This paper presents a novel data-efficient framework that embeds the extended Rayleigh–Plesset equation into a Physics-Informed Neural Network (PINN), with all five loss weights automatically tuned by the Whale Optimization Algorithm (WOA) using an unweighted fitness metric that avoids trivial weight collapse. Four key innovations enable superior performance: seven-dimensional Fourier feature encoding based on pump frequency and its first two harmonics to overcome spectral bias and resolve 50 Hz oscillations; dimensionless perturbation output around equilibrium radius guaranteeing physically bounded positive solutions; a five-component hybrid loss enforcing the PDE, initial conditions, positivity constraint, and sparse data fidelity using only 30 sensor measurements to break solution degeneracy; and WOA’s intelligent five-dimensional weight search. Evaluated over five independent random seeds, the WOA-PINN achieves a relative L₂ error of 0.46 ± 0.02 % against the analytical solution a 94.8 % improvement over the equal-weight baseline of 8.74 %. A dual-indicator detection module combining instantaneous cavitation number and bubble-collapse criterion delivers 100 % classification accuracy on cavitating and normal regimes. Sensitivity analysis over two orders of magnitude in equilibrium bubble radius (10 μm–1 mm) confirms sub-0.5 % error with variance below ±0.01 %, proving scale invariance, while architecture studies identify the 5×64 tanh network as Pareto-optimal. The critical advance lies in the fitness-function design and data-anchoring loss term, not the specific optimizer, as both WOA and PSO yield statistically equivalent gains exceeding 94 %.