Quantification and Evaluation of Parameter and Model Uncertainty for Passive and Active Vibration Isolation

Abstract

Vibration isolation is a common method used for minimizing the vibration of dynamic load-bearing structures in a region past the resonance frequency, when excited by disturbances. The vibration reduction mainly results from the tuning of stiffness and damping during the early design stage. High vibration reduction over a broad bandwidth can be achieved with additional and controlled forces, the active vibration isolation. In this context, “active” does not mean the common understanding that the surroundings are isolated against the machine vibrations. Also in this context, “passive” means that no additional and controlled force is present, other than the common understanding that the machine is isolated against the surroundings. For active vibration isolation, a signal processing chain and an actuator are included in the system. Typically, a controller is designed to enable a force of an actuator that reduces the system’s excitation response. In both passive and active vibration isolation, uncertainty is an issue for adequate tuning of stiffness and damping in early design stage. The two types of uncertainty investigated in this contribution are parametric uncertainty, i.e. the variation of model parameters resulting in the variation of the systems output, and model uncertainty, the uncertainty from discrepancies between model output and experimentally measured output. For this investigation, a simple one mass oscillator under displacement excitation is used to quantify the parameter and model uncertainty in passive and active vibration isolation. A linear mathematical model of the one mass oscillator is used to numerically simulate the transfer behavior for both passive and active vibration isolation, thus predicting the behavior of an experimental test rig of the one mass oscillator under displacement excitation. The models’ parameters that are assumed to be uncertain are mass and stiffness as well as damping for the passive vibration isolation and an additional gain factor for the velocity feedback control in case of active vibration isolation. Stochastic uncertainty is assumed for the parameter uncertainty when conducting a Monte Carlo Simulation to investigate the variation of the numerically simulated transfer functions. The experimental test rig enables purposefully adjustable insertion of parameter uncertainty in the assumed value range of the model parameters in order to validate the model. The discrepancy between model and system output results from model uncertainty and is quantified by the Area Validation Metric and an Bayesian model validation approach. The novelty of this contribution is the application of the Area Validation Metric and Bayes’ approach to evaluate and to compare the two different passive and active approaches for vibration isolation numerically and experimentally. Furthermore, both model validation approaches are compared.