Bayesian Physics-Informed Neural Networks With MIQPSO-Backstepping Control for Vibration Suppression in Nonuniform Quay Cranes

This article proposes a trajectory tracking strategy for nonuniform quay cranes to suppress flexible cable vibration and attenuate payload swing and rotation, thereby improving tracking accuracy and transport efficiency. To address the challenges posed by time-varying and spatially distributed partial differential equation models, we propose a Bayesian physics-informed neural network (BPINN) framework that integrates tension constraints into the loss function to suppress flexible cable vibrations. In the Bayesian setting, the BPINN acts as a prior model, and Hamiltonian Monte Carlo (HMC) sampling is employed to infer the posterior distribution of the system states. To handle the underactuated nature of the quay crane, differential flatness is exploited to map BPINN-predicted states into a flat output space, where an adaptive backstepping controller is designed to guarantee global uniform ultimate boundedness. Moreover, a multistrategy improved quantum-behaved particle swarm optimization (MIQPSO) scheme is introduced for online tuning of control parameters, achieving a favorable tradeoff between global exploration and fast convergence. Lyapunov analysis establishes closed-loop stability, and simulations and experiments demonstrate fast and accurate tracking as well as robust vibration suppression under external disturbances.