12. State Estimation: A Model-Based Approach to Extend Test Data Exploitation

Design models can drastically improve the applicability of testing and allow measuring previously unmeasurable quantities and designing reduced test configurations. A common workflow is followed: a multiphysics system model provides a prediction of the system states which is corrected by the estimation algorithms using the measurement data. The model can then generate data of the non-measurable quantities (e.g. virtual sensors). A wide range of models can be used, including analytical, 1D lumped parameter and 3D distributed parameter models. Key is that they are easy to evaluate and have a small number of states, while capturing the dominant physics. Novel model order reduction techniques enable the use of more complex models. A wide range of state estimation approaches has been developed such as the (linear, extended, unscented, …) Kalman Filter and the Moving Horizon Estimator. All approaches require a trade-off between accuracy and computational load so that conventional estimators must be tailored to deal with high-fidelity nonlinear models of industrial complexity. The approach is illustrated with two cases: the estimation of hard-to-measure vehicle body forces using the extended Kalman filter and the application to an electro-mechanical drivetrain subject to unknown input forces. Methodological aspects are evaluated and different estimators are compared.