Quantification of Uncertainty in the Mathematical Modelling of a Multivariable Suspension Strut Using Bayesian Interval Hypothesis-Based Approach

Abstract

Mathematical models of a suspension strut such as an aircraft landing gear are utilized by engineers in order to predict its dynamic response under different boundary conditions. The prediction of the dynamic response, for example the external loads, the stress and the strength as well as the maximum compression in the spring-damper component aids engineers in early decision making to ensure its structural reliability under various operational conditions. However, the prediction of the dynamic response is influenced by model uncertainty. As far as the model uncertainty is concerned, the prediction of the dynamic behavior via different mathematical models depends upon various factors such as the model's complexity in terms of the degrees of freedom, material and geometrical assumptions, their boundary conditions and the governing functional relations between the model input and output parameters. The latter can be linear or nonlinear, axiomatic or empiric, time variant or time-invariant. Hence, the uncertainty that arises in the prediction of the dynamic response of the resulting different mathematical models needs to be quantified with suitable validation metrics, especially when the system is under structural risk and failure assessment. In this contribution, the authors utilize the Bayesian interval hypothesis-based method to quantify the uncertainty in the mathematical models of the suspension strut.

Types of Uncertainty

“…It is claimed that the method bridges the gap between the least-squares calibration and the Gaussian Process calibration and, thus, is an improvement of the method introduced in [22]. Furthermore, a Bayesian interval hypotheses-based approach [36] and a Bayesian inference-based approach [37] are used to compare different models based on their internal functional relations from axiomatic or empiric assumptions, see also Sect In order to apply the Bayesian methods, it is necessary to select prior distributions. Often, this is subjective and it is unclear how to choose them, which may lead to unrealistic assumptions.…”

Analysis, Quantification and Evaluation of Uncertainty

“…3.23. The structure is subject to gravitation g. For details on the derivation of the equations of motion see [107]. Regression studies on the stiffness and damping properties of the spring-damper system yielded several model candidates to describe the dynamic behaviour by combinations of linear, bilinear and power functions [105].…”

“…4. 25 Comparison of posterior probabilities P(H y,k,q |A ye,k ) for each hypothetical event k predicted by model q = 1 ( ), model q = 2 ( ), model q = 3 ( ), and model q = 4 ( ) according to [107] event constitutes an experimental output y and simulation model output η for the Q = 4 model candidates. For each k = 1, .…”