By Philipp Limbourg
Mechatronic layout tactics became shorter and extra parallelized, precipitated by way of growing to be time-to-market strain. tools that allow quantitative research in early layout phases are required, may still dependability analyses goal to steer the layout. as a result of restricted quantity of information during this part, the extent of uncertainty is excessive and specific modeling of those uncertainties turns into necessary.
This paintings introduces new uncertainty-preserving dependability equipment for early layout levels. those comprise the propagation of uncertainty via dependability versions, the activation of information from related parts for analyses and the mixing of doubtful dependability predictions into an optimization framework. it really is proven that Dempster-Shafer concept may be a substitute for likelihood conception in early layout degree dependability predictions. professional estimates might be represented, enter uncertainty is propagated throughout the process and prediction uncertainty could be measured and interpreted. The ensuing coherent technique might be utilized to symbolize the uncertainty in dependability models.
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Additional info for Dependability Modelling under Uncertainty: An Imprecise Probabilistic Approach
All include C− , C+ and CP as special cases. Examples for the family of Archimedean copulas are the Frank  and the Mardia copula . Archimedean copulas are popular in case of two variables, but can’t be readily extended to the multivariate case . The most commonly used copula for more than two dimensions is the Gaussian copula. Its big advantage is the easy communicability. The set of parameters for estimating the dependencies is a n × n correlation matrix ρ . 20) −1 is an inverse standard normal distribution (mean zero, standard deviation 1) and FGauss n,ρ FGauss a multivariate standard normal distribution with correlation matrix ρ .
3) Thus, the vector p represents the input parameter of the system dependability model in a probabilistic representation. In real life, p is never accurately known and in fact there are uncertainties on a large scale that disturb the exact knowledge on p. This thesis will therefore illustrate how to form an uncertainty model around p and project this uncertainty onto the output. 3 Representation and Propagation of Uncertainty Using the Dempster-Shafer Theory of Evidence This chapter collects fragments from current research to form a coherent framework for uncertainty representation and propagation in the Dempster-Shafer theory of evidence (DST).
In a probabilistic framework, PDFs or CDFs can be considered as measures of uncertainty, in the DST framework, a mass distribution plays this role. Uncertainty modeling and Propagation The main part of the framework comprises of the uncertainty modeling and propagation phases. Depending on the measures of uncertainty and the quantities of interest chosen, uncertainties can be modeled in different ways. In a probabilistic representation, they may be represented by a joint PDF on x. The joint PDF is commonly simplified either by using independence assumptions or dependency models to break down the multivariate PDF to univariate distributions, which are often represented by parametric functions such as Gaussian or Weibull distributions.
Dependability Modelling under Uncertainty: An Imprecise Probabilistic Approach by Philipp Limbourg