Integration of Stochastic Effects and Data Uncertainties into the Design of Process Equipment

Stochastic effects and data uncertainties are present in any engineering calculation. Their impact may be particularly important if they concern the design of process equipment. A calculation model for the dynamic behavior of a heat exchanger and procedures to deal with the related uncertainties are presented. Their propagation through the calculation by means of a Monte Carlo approach is shown. The temperature at the heat exchanger outlet and the step response of a sudden variation in the heat exchanger inlet temperature are simulated and evaluated by way of example. It is demonstrated that the inclusion of stochastic effects and uncertainties provides a more reliable basis for design decisions and hence reduces the probability of errors.     

Obtaining efficient estimates of park use and testing for the structural adequacy of models

This paper provides an examination of the problem of heteroscedasticity as it relates to estimating park use, although the results can also be applied to a wide variety of flow problems involving traffic, people or commodities. The major issue is that estimates of flows obtained using ordinary least squares, OLS, often yield statistically significant results while still giving rise to large differences between observed and predicted flows (residuals). The paper presents results which show that for the flow estimation problem of concern, more accurate use estimates may be obtained by using generalized least squares, GLS, rather than using OLS. Weights to use in GLS regression are developed taking into account the variance to be expected in origin-destination flows. It is shown that deriving the correct weights, estimates of variances, to use in a regression analysis results in an ‘absolute’ test for the structural appropriateness of the regression model. Tests related to the ‘absolute’ adequacy test are introduced and their use to identify specific structural problems with a model is illustrated.