This paper presents a novel efficient method of estimating the joint probability distribution of continuous random variables with arbitrary (nonmonotonic or monotonic) relationships. As the backbone of the method is a set of monotonization transformations that "roll out" the relationships, the method is named the rolling pin method. The method allows one to estimate joint probability distributions when the actual causal structure of the attributes is unknown or extremely intricate to be determined accurately. Once the relationships are monotonized by the transformations, an appropriate parametric copula function is used to describe the joint distribution of the transformed variables. The copula function allows modeling the joint distribution of the transformed variables with a few parameters. The monotonization transformations empower standard parametric copulas to (i) capture complicated unknown dependence structures, (ii) model multivariate joint probability distributions with different pairwise dependence structures using the same parametric copula, and (iii) model nonmonotonicity. The application and performance of the method are shown using two examples.

A method of designing model-predictive safety systems that can detect operation hazards proactively is presented. Such a proactive safety system has two major components: a set of operability constraints and a robust state estimator. The safety system triggers alarm(s) in real time when the process is unable to satisfy an operability constraint over a receding time-horizon into the future. In other words, the system uses a process model to project the process operability status and to generate alarm signals indicating the presence of a present or future operation hazard. Unlike typical existing safety systems, it systematically accounts for nonlinearities and interactions among process variables to generate alarm signals; it provides alarm signals tied to unmeasurable, but detectable, state variables; and it generates alarm signals before an actual operation hazard occurs. The application and performance of the method are shown using a polymerization reactor example.

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