Using measurement data for subspace system identification results in parameter estimates to be afflicted with statistical uncertainty due to finite sample size, (most often) unknown inputs and sensor noise properties. To quantify this uncertainty, the idea is to propagate the covariance of structural responses (accelerations, velocities, displacements or strains) and structural inputs (if available) onto the estimates of transfer function, modal parameters and modal indicators (MAC and MPC). The propagation is based on Delta method, where the sensitivity matrices are obtained with the perturbation theory. Below are two plots from our most recent paper about uncertainty quantification of the transfer function. Along the same lines, one can also check our quadratic framework for uncertainty quantification of MAC and MPC.

In Operational Modal Analysis (OMA) the ambient excitation is assumed to be stationary noise which is sometimes violated, in particular in the presence of periodic movement of rotating machinery on a structure during its operation. Then both ambient and unmeasured periodic forces act on the structure, and the outputs of the corresponding system are described by both the structural system dynamics as well as the dynamics of the periodic excitation. This might render OMA difficult in practice, since the identified eigenstructure then contains a mix of periodic and structural modes. In this work we conceive an output-only subspace identification algorithm where the (unknown) periodic components are consistently rejected from the raw measurements. This is particularly useful when the periodic modes are close to structural modes, or when they are of high energy and then may mask the system response to the random part of the input. Below are two figures showing application of the proposed approach on experimental data from a plate. More detailed explanation of this method can be found in our paper. The proposed approach was transferred to ARTeMIS Modal Pro.

The premise of damage detection is to take a decision whether the state of a currently monitored structure is statistically different from its nominal behaviour. Such decision indicates only whether the damage has occurred, or not. In data-driven decision making, damage-sensitive features are computed directly from the data and are evaluated in a residual which is tested for damages in statistical hypothesis tests. Such residual is dependent on the natural changes of the ambient excitation, which poses a major challenge in its evaluation, since excitation conditions are in principle unknown and unmeasured. Therefore any important change therein may be falsely classified as a damage and raise false alarms. A solution to that problem lies in the design of a damage detection residual, whose mean value must be independent of such changes. We've conceived such robust residual in our work here. Below are two figures from its statistical hypothesis testing, evaluated on a numerical damage campaign of an offshore foundation.