Real-world engineering problems: Two surrogate methods for robust vibration control of moving mass-beam coupling systems with epistemic uncertainty

The dynamic responses and the vibration control of the moving mass-beam coupling systems are one of the real-world problems in engineering fields including vehicle-bridge coupling systems and missile-gun systems. There are many uncertainty factors in the real-world engineering applications. Analyzing the effects of uncertainty on the state trajectory of the system is significant to realize the safe operation of the system. This paper develops two surrogate methods to research the evidence-theory-based robust adaptive fuzzy sliding mode control (ET-RAFSMC) of the moving mass-beam coupling systems. For the first approach, the active learning Kriging (ALK) is combined with the ET-RAFSMC to perform the evidence response analysis through an interval Monte Carlo simulation, and then a Karush-Kuhn-Tucker condition is utilized to alleviate the burden of searching the extreme responses. The other surrogate method is the Lobatto polynomial function, which integrates with a spare sampling method for improving the computational efficiency and accuracy when running the extreme value analysis of the ET-RAFSMC. The accuracy and the efficiency of the proposed methods are studied by comparing with Monte Carlo simulations as well as Legendre expansion model. Finally, the performance of the ET-RAFSMC is studied through comparing with the traditional sliding mode control.