This paper presents a validation of a recently developed joint input-state estimation algorithm for force identification and response estimation in structural dynamics, using data obtained from in situ experiments on a footbridge. First, the algorithm is used to identify two impact forces applied to the bridge deck. Next, the algorithm is used to extrapolate measured accelerations due to wind loading to unmeasured locations in the structure. The dynamic model of the footbridge used in the system inversion is obtained from a detailed finite element model, that is calibrated using a set of experimental modal characteristics. The quality of the estimated forces and accelerations is assessed by comparison with the corresponding measured quantities. In both cases, a very good overall agreement is obtained.@en

An existing joint input-state estimation algorithm is extended for applications in structural dynamics. The estimation of the input and the system states is performed in a minimum-variance unbiased way, based on a limited number of response measurements and a system model. The noise statistics are estimated, as they are essential for the joint input-state estimation and can be used to quantify the uncertainty on the estimated forces and system states. The methodology is illustrated using data from an in situ experiment on a footbridge.@en

This paper presents a verification of a state-of-the-art joint input-state estimation algorithm using data obtained from in situ experiments on a footbridge. A dynamic model of the footbridge is based on a detailed finite element model that is calibrated using a set of experimental modal characteristics. The joint input-state estimation algorithm is used for the identification of two impact, harmonic, and swept sine forces applied to the bridge deck. In addition to these forces, unknown stochastic forces, such as wind loads, are acting on the structure. These forces, as well as measurement errors, give rise to uncertainty in the estimated forces and system states. Quantification of the uncertainty requires determination of the power spectral density of the unknown stochastic excitation, which is identified from the structural response under ambient loading. The verification involves comparing the estimated forces with the actual, measured forces. Although a good overall agreement is obtained between the estimated and measured forces, modeling errors prohibit a proper distinction between multiple forces applied to the structure for the case of harmonic and swept sine excitation.@en

In structural dynamics, the forces acting on a structure are in many cases not well known. System inversion techniques may then be used to estimate these forces from the measured response of the structure. This paper presents conditions for the invertibility of linear system models, that apply generally to any instantaneous input estimation algorithm. The conditions ensure the identifiability of the dynamic forces, the stability of the system inversion and the uniqueness of the identified quantities. For the specific case of modally reduced order models, which can be obtained either from first principle models or from experimental data using system identification techniques, the conditions can be directly expressed in terms of the modal properties of the structure. This physical insight can then be used to design vibration experiments that aim for system inversion. Each of the conditions is derived and illustrated by a conceptual example. @en