PSI - Issue 64

Philipp Kähler et al. / Procedia Structural Integrity 64 (2024) 1248–1255 Kähler / Petryna / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 6. (a) Laboratory structure with measurement equipment and initial mass, (b) model sketch.

A finite element model of the system was created and dynamically validated using the Operational Modal Analysis methods. A simplified surrogate model with only five degrees of freedom in vertical direction was then generated from the FE model using model reduction algorithms. The displacement, velocity, and acceleration for each degree of freedom were then calculated by the Newmark algorithm. When an update is initiated, the data assimilation techniques should not only update the state parameters, but also correct the mass matrix of the surrogate model. Furthermore, the KF should be able to detect, localize, and possibly quantify the implemented system changes in real time. Multiple parameter variations in the KF were investigated, such as the ensemble size, the number of time steps between the system updates or the magnitude of the model noise in order to assess their influence on the quality of the Kalman update. At the beginning, an ensemble of =50 different models were initialized, with different entries in their mass matrices. The entries were sampled according to a gaussian distribution with the mean values ̅ from the reduced surrogate model and a standard deviation of = 0.2 ⋅ ̅ . Since the load identification process using CNNs is not perfect, but subjected to uncertainties, a variation in the applied initial mass was additionally introduced to simulate the imprecise load identification, resulting in different initial displacements. In Fig. 7 (a), an exemplary plot of the time evolution of the five mass matrix entries during the experiment can be seen. At first, the system was in its initial state. The model parameter update took a short duration to converge the mass matrix entries of all ensemble members towards the initial values. After the system was altered at time = sv by an additional mass of Δ 3 = 300 g at point 3, a clear jump in the ensemble mean of mass matrix entry ̅ 3 ≈ 327 g is visible, while the other mass matrix entries remain almost constant. This indicates that the algorithm can detect, localize, and quantify the induced system change. Fig. 7 (b) displays the results of the detected mass changes for all ensemble means Δ ̅ after a corresponding system change was induced. It can be observed that small system changes (Δ = 100 g) can be detected, however, due to the magnitude of the model noise used, they could not be clearly located. This is indicated by the red numbers in the heatmap, which illustrate the detected changes in mass values, that are not negligibly small with respect to the induced system change. The bigger mass changes of Δ = 300 g and Δ = 500 g were correctly detected, localized and quantified.