Optimal experimental design for modeling the dynamic response of a pseudo-static moving load on a beam

Design, monitoring and control of complex structures require methods to accurately model the system dynamics. In this regard, parametric system identification techniques operating on experimental or operational data can potentially provide computationally efficient, compact, and accurate representations of the dynamics of complex systems. The success of the identification process depends on the quality of the available data together with an adequate model structure capable of representing the underlying dynamics of the structure. Yet, in practical application, the available vibration data is often insufficient to cover the full operational range of the system, which results in fractional and inaccurate modelling of the global structural dynamics. This is crucial especially for parameter- or configuration-dependent systems, whose behaviour changes according to the operational set-point.
In this work, we consider the problem of identifying the global response dynamics of a parameter-varying system based on a limited number of pseudo-static experiments. To this end, we use Linear Parameter Varying Vector Auto-Regressive with eXogenous input (LPV-VARX) models to represent the system’s response at each static configuration. The model parameters are then regressed across the configuration space with the help of non-linear regression.
As the main novelty, we introduce an adaptive design of experiments based on a Bayesian model identification framework, which aims at minimising the uncertainty of LPV-VARX model parameters across the configuration space of the system.
The resulting method facilitates the exploration of the configuration space of the system with a reduced number of experiments. The proposed method is assessed on the identification of a cart-beam system where the parameter-dependent dynamics are the outcome of the changing position of the cart across the beam.