Virtual sensing of structural vibrations using dynamic substructuring

• Replacing the mode shapes of the full structure with component modes in analytical virtual sensing.
• Estimation of system states or full-field strain data of a structural part under unknown excitation using a limited set of physical sensors.
• Substructuring saves a lot of work, because only part of the structure is modelled. The unmodelled part may include modelling uncertainties, non-linearity, or structural variability, which can be ignored.
• Interface reduction makes it possible to apply dynamic substructuring also when the number of interface degrees of freedom is large.
• Combined empirical and analytical virtual sensing can be applied to reduce the estimation error due to noisy signals.

Virtual sensing techniques use information available from a limited set of physical sensors together with the finite element model to calculate an estimate of the quantity of interest. In structural dynamics applications, analytical mode shapes from the finite element model are typically used as a basis to estimate the response at unmeasured locations by an expansion algorithm. An alternative is to model only the interesting part of the structure using substructuring techniques, in which the natural modes are replaced by component modes consisting of a selected number of fixed interface modes plus the interface constraint modes. They are mutually independent and compose a valid subspace for estimating the unmeasured response. If the number of interface degrees of freedom is large, interface reduction is applied. The main advantage of the proposed approach is that the modelling effort can be substantially decreased, because only part of the structure is modelled and the modelling uncertainties, non-linearities, or changes in the omitted structure can be ignored. The method is validated by numerical simulations of three different structures under unknown excitation. Different types and locations of virtual sensors are studied. Also, the effects of noise and model errors are investigated. The most accurate estimation is obtained if the virtual sensor is located away from the interface and close to a physical sensor.