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ECO DRIVE - 858018;info:eu-repo/grantAgreement/EC/H2020/858018, INNTERESTING - 851245;info:eu-repo/grantAgreement/EC/H2020/851245

Abstract:

Within the context of wind turbine component design, there is an interest to develop novel, advanced virtual test approaches using Digital Twins of both components and test bench setups. More specifically, virtual testing of novel pitch ball bearing designs is of interest, as these typically require large scale test setups. In this work, the use of a Smart Virtual Sensing (SVS) Digital Twin [1] is proposed to estimate pitch ball bearing parameters, as well the overall system states and inputs. A multibody model of a pitch bearing test setup, including a parametrized analytical ball bearing model representing the pitch ball bearing, is combined with a Kalman Filter. A multibody formulation typically yields a set of Differential Algebraic Equations (DAEs) due to the presence of kinematic equality constraints. Recently, several approaches have been proposed in literature to combine these DAEs with a Kalman Filter ([1], [2] and references therein) for combined state and input estimation by relaxing the constraint definition leading to a set of non-linear Ordinary Differential Equations (ODEs). Rodriguez et al. [3] have recently presented an approach for multibody model parameter estimation. While these approaches cover equality constraints in different approximated ways, they do not in general consider inequality constraints. It is shown in this work that these approaches can lead to unstable behaviour of the Kalman Filter for bearing parameter estimation, as these parameters represent physical quantities, which in general have to be bounded (e.g. non- negative values) via inequality constraints. Without these constraints, the estimated parameter values can be out of bound and lead to unstable behaviour. This work therefore further proposes an active set approach to enforce inequality constraints, stabilizing the Kalman Filter and allowing for robust bearing parameter estimation. The proposed approach is validated numerically and the necessity of including the inequality constraints to stabilize the Kalman Filter is highlighted. REFERENCES [1] Risaliti, E., Tamarozzi, T., Vermaut, M., Cornelis, B. and Desmet, W. Multibody model based estimation of multiple loads and strain field on a vehicle suspension system. Mechanical Systems and Signal Processing. (2019) 123: 1-25. [2] Adduci, R., Vermaut, M., Naets, F., Croes J. and Desmet, W. A Discrete-Time Extended Kalman Filter Approach Tailored for Multibody Models: State-Input Estimation. Sensors. (2021) 21: 4495 [3] Rodríguez, A.J., Sanjurjo, E., Pastorino, R. and Naya, M.Á. State, parameter and input observers based on multibody models and Kalman filters for vehicle dynamics. Mechanical Systems and Signal Processing. (2021) 155: 107544.