Robust Information Entropy

The optimal sensor configuration, obtained by minimizing Equation (3.70), depends on the designer s choice of the nominal model determined by the nominal parameter vector 0. One way to account for the uncertainty in the nominal model is to use a prescribed PDF p(0 C) for 0. In this case, the optimal sensor configuration becomes the one that minimizes the robust information entropy Eg/lHeiAlSf, 0, C)] which is a measure of the overall uncertainty in both 0 and 0  

The information entropy He(A S, 0 , C) given by Equation (3.70) is a special case of the robust information entropy [fl (A 5, O, C)] in Equation (3.71) and it corresponds to the choice p 0 C) = 5(0 - 0 ), where 5(.) denotes the Dirac delta function. The multi-dimensional integration over 0 involved in Equation (3.71) can be carried out by Monte Carlo simulation or by an asymptotic expansion developed for these types of integrals [197]. 

The present formulation for optimal sensor placement in terms of the information entropy provides a rational procedure for comparing the uncertainty of the estimates of the parameter values for different sensor configurations. Specifically, a direct measure of the uncertainty reduction is provided by the change of the information entropy  

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Keywords asymptotic expansion evidence information entropy Markov Chain Monte Carlo simulation modal identification Ockham factor regression problem robustness seismic attenuation... 

The probabilistic reliability systems of events are analysed by Ziba (2000). The analysis is based on the concepts of entropy as defined in information theory and applied to probability theory. The recommended approach allows concentrating the system analysis only on important failure modes and connects uncertainty, redundancy and robustness of systems of events. Despite this approach, the system analysis leads to complicated computations. 

The general optimization task is to compute optimal connection device parameters for a robust structure. Therefore, the robustness measure, Eq. 48, is evaluated for the three load cases. The uncertainty is assessed by applying the information reducing measure entropy for fuzzy quantities (Eq. 61). The weighting factors and penalty functions of the robustness measure are here not considered. For the design d, it yields... 

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