(130a) Efficient Computation of Local Sensitivity Information for Nonsmooth Process Models

Discrete behavior may be introduced into an otherwise continuous process model to reflect changes in thermodynamic phase or flow regime, to represent discrete design decisions, or to represent closed-loop control actions. While discrete behavior is traditionally represented in process models using integer variables or disjunctions, these representations cannot preserve continuity between different discrete modes. Nonsmooth representations, on the other hand, provide a means to preserve this continuity information, and have been recently used to model discrete phenomena such as pinch analysis for heat integration, and flash drums that can handle different thermodynamic phases.

This presentation describes a recent improved branch-locking method [1] for computing local sensitivity information for these nonsmooth models, for use in overarching methods for simulation or optimization. This method borrows the computational benefits of the efficient reverse mode of automatic differentiation for smooth functions, even though the reverse mode does not apply directly to nonsmooth systems. The branch-locking method uses inexpensive probing steps to temporarily “lock” the nonsmooth model into a carefully-chosen smooth variant; this smooth model is then differentiated using standard efficient techniques. This method is accurate and automatable, and typically yields far superior computational performance to existing methods for nonsmooth sensitivity analysis. Implications and examples are discussed.

Reference

[1] KA Khan, Branch-locking AD techniques for nonsmooth composite functions and nonsmooth implicit functions, Optim. Methods Softw., in press, 2017