Analyzing Propagation of Model Form Uncertainty for Different Suspension Strut Models

Model form uncertainty often arises in structural engineering problems when simplifications and assumptions in the mathematical modelling process admit multiple possible models. It is well known that all models incorporate a model error that is captured by a discrepancy due to missing or incomplete physics in the mathematical model. As an example, this discrepancy can be modelled as a function based upon Gaussian processes and its confidence bounds can be seen as a measure of adequacy for the respective model. Assessment of model form uncertainty can be conducted by comparing the confidence bounds of competing discrepancy functions. In this paper, a modular active spring-damper system is considered that was designed to resemble a suspension strut as part of an aircraft landing gear and is excited by dynamic drop tests. In previous research about the suspension strut, different mathematical system models with respect to different linear and non-linear assumptions for damping and stiffness properties to describe the dynamic system behaviour of the suspension strut were compared by means of the confidence intervals of their discrepancy functions. The results indicated that the initial conditions used for exciting the system model were inadequate. The initial conditions themselves constitute a mathematical model, so that model form uncertainty inherent to the initial condition model can effect the system model. The propagation of model form uncertainty within the model will be analysed in this paper by considering two cases: In the first case, the system model is excited with an inadequate initial condition model, while in the second case, experimentally measured initial conditions will be employed that represent the true value except for measurement errors. The comparison of both shows how model form uncertainty propagates through the model chain from the initial condition model to the system model.