Uncertainty quantification in the mathematical modelling of a suspension strut using Bayesian inference

In the field of structural engineering, mathematical models are utilized to predict thedynamic response of systems such as a suspension strut under different boundary andloading conditions. However, different mathematical models exist based on their govern-ing functional relations between the model input and state output parameters. For exam-ple, the spring-damper component of a suspension strut is considered. Its mathematicalmodel can be represented by linear, nonlinear, axiomatic or empiric relations resultingin different vibrational behaviour. The uncertainty that arises in the prediction of thedynamic response from the resulting different approaches in mathematical modellingmay be quantified withBAYESIANinference approach especially when the system is understructural risk and failure assessment. As the dynamic output of the suspension strut,the spring-damper compression and the spring-damper forces as well as the ground impactforce are considered in this contribution that are taken as the criteria for uncertaintyevaluation due to different functional relations of models. The system is excited by initialvelocities that depend on a drop height of the suspension strut during drop tests. The sus-pension strut is a multi-variable system with the payload and the drop height as its variedinput variables in this investigation. As a new approach, the authors present a way toadequately compare different models based on axiomatic or empiric assumptions offunctional relations using the posterior probabilities of competing mathematical models.The posterior probabilities of different mathematical models are used as a metric toevaluate the model uncertainty of a suspension strut system with similar specificationsas actual suspension struts in automotive or aerospace applications for decision makingin early design stage. The posterior probabilities are estimated from the likelihood func-tion, which is estimated from the cartesian vector distances between the predicted outputand the experimental output.