A fixed-lag smoother for solving joint input and state estimation problems in structural dynamics

Abstract: In this thesis we have investigated different numerical filters for joint input and state estimation, with the aim of designing a robust algorithm capable of monitoring the continuous motion and loading in a truck chassis. The algorithm has to be able to use sparse measurements of the motion on different parts of the truck as it is excited by road induced vibrations, and transform this data into knowledge of the state in the entire system. To do this, the algorithm has to be supplied with information about the dynamic properties of the current system.In Paper A we have developed and implemented a fixed-lag smoother for joint input and state estimation in linear time-invariant dynamic structures. A fixed-lag smoother maximizes the use of information available in the measurements by allowing a small time lag in the estimation. As input, external forces as well as support motions can be computed. Furthermore, both measurement noise and model errors are accounted for and simulated as stochastic processes. The filter is firstly verified with straightforward numerical simulations of a simply supported beam, followed by a more involved simulation of a truck fuel tank. It is shown that the fixed-lag smoother performs very well, it estimates both input and states with a high accuracy even though the signals are contaminated with noise and the model contains errors.In Paper B the fixed-lag smoother is applied on real measurements. We investigate the capabilities of the proposed filter by analysing acceleration measurements from a truck side skirt excited by road induced vibrations. In this study, we focus on estimating the state in the side skirt body from a minimum number of measurement sensors. The dynamic properties of the side skirt are obtained experimentally from an operational modal analysis. It is shown that the fixed-lag smoother estimates the state very well. The results also shows that the smoothing effect is larger when fewer measurement sensors are used.