Abstract Summary
Gantry robots, or cartesian manipulators, are popular choices for manufacturing due to their relatively simple control and movement precision. Currently, large gantry manipulators are being considered as part of the production of large structures, as in the case of wind turbine towers, offshore platforms, or vessels. Those gantry systems emerge as an excellent option to reduce manufacturing costs. However, their large size makes them susceptible to large vibrations which affect the precision of the end effector and overall fatigue life. The structural dynamics of flexible gantry manipulators comprise non-linear dynamics which are dependent on the position of the manipulator. This means that the structure will exhibit different modal characteristics depending on its configuration which makes this a challenging problem from a vibration control and fatigue life perspective. In this sense, a computationally simple modelling approach that can effectively represent the parameter-dependent dynamics could be of high value in the development of vibration control algorithms and as surrogate for fatigue-life estimation. In this work, we consider a simplified version of this problem featuring a beam with a moving mass, aiming at representing the constrained 1D horizontal motion of the manipulator and the resulting vertical vibration response. Our aim is to develop computationally efficient data-driven models for this simplified structure that could be easily generalized to the full range of motion of a gantry. To this end, we first consider a physics-based model of the structure, made up of an Euler-Bernoulli beam with a moving mass, where the inertial connection between the mass and the beam considers a random surface roughness. A finite element model of this system is built and is subsequently used to draw simulations of the vertical vibrations of the beam under different time-dependent mass trajectories. Next, we consider data-driven Linear Parameter Varying (LPV) Vector AutoRegressive (VAR) models to represent the vibration response of the beam. We consider various structures based on Bayesian non-linear regression and Gaussian Process regression of the LPV-VAR model coefficients. Due to the computational cost of model estimation, we introduce an input space sub-sampling method that reduces the size of the regression matrix, while preserving an even sample distribution over the input space. The proposed approach is evaluated on simulated data from the physics-based model. We compare the different modelling methodologies and assess their predictive accuracy, quality of the representation of the parameter-varying dynamics, and computational efficiency. While both modelling approaches lead to accurate representations of the beam’s vibration response the introduced input space sub-sampling method speeds up the estimation while preserving the modelling accuracy.
