Keywords: imprecise probability, probability density function with bounded parameters, maximum entropy distributions, inequality constraints, sparse data, parametric and non-parametric probabilistic uncertainty model, fatigue failure, vibro-acoustic analysis, failure analysis..

This paper is concerned with the application of a recently developed imprecise probability description to problems in mechanics. This uncertainty model expresses the probability density function of vaguely known variables as the exponential of a linear combination of functions of the uncertain variable and bounded parameters. The bounded parameters are established by using statistical expectation inequality constraints specified on the functions of the uncertain variable(s), which may arise by analysing a small data set or can be provided by an expert who is not confident enough to specify a single value. Starting from these bounded parameters, a family of probability density functions is constructed. Employing this uncertainty model enables us to investigate how imprecision in the probabilistic assignment can affect the prediction of engineering systems performance with respect to safety, quality or design constraints. In particular, the effects of using this imprecise model in the evaluation of the fatigue failure of a structural joint and of the failure probability are investigated. Moreover, this uncertain description is combined with parametric and non-parametric probabilistic uncertainty models, within the context of the hybrid finite element or statistical energy analysis approach to the analysis of mid- and high-frequency vibration analysis, for establishing bounds on the failure probability.

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