Fig. 5

The steps in the error curve corresponding to the static reduced model reflect the changes in the latent parameter. Changing the latent parameter from \({\varvec{\eta }}_0\) (no damage) to \({\varvec{\eta }}_9\) (20 % decrease of thickness) increases the error of the static reduced model by three orders of magnitude. The adaptive reduced model uses the incomplete sensor samples to adapt to changes in the latent parameters. The gappy POD basis is derived from complete sensor samples (i.e., \(\rho ^{\text {basis}}= 100~\%\)), the sensor rate \(\rho ^{\text {update}}\) for deriving the updates to the reduced model is set to \(\rho ^{\text {update}}= 0.6~\%\) (a) and to \(\rho ^{\text {update}}= 0.8~\%\) (b). The dimension of the reconstruction basis is set to \(r= 30\). For \(\rho ^{\text {update}}= 0.6~\)%, the number of known components in the incomplete sensor samples is \(k^{\text {update}}= 29 < r\) and therefore the regression problem underlying gappy POD becomes underdetermined, see “Deriving the gappy POD basis” section. This leads to large errors. Increasing the sensor rate to \(\rho ^{\text {update}}= 0.8~\%\) leads to an overdetermined regression problem and therefore to lower errors of the adapted reduced model