Failure Modes of Tearing and a Novel Robust Approach

Abstract

State-of-the-art Modelica implementations may fail in various ways when tearing is turned on: Completely incorrect results are returned without a warning, or the software fails with an obscure error message, or it hangs for several minutes although the problem is solvable in milliseconds without tearing. We give three detailed examples and an in-depth discussion why such failures are inherent in tearing and cannot be fixed within the traditional approach.Without compromising the advantages of tearing, these issues are resolved for the first time with staircase sampling. This is a non-tearing method capable of robustly finding all well-separated solutions of sparse systems of nonlinear equations without any initial guesses. Its robustness is demonstrated on the steady-state simulation of a particularly challenging distillation column. This column has three solutions, one of which is missed by most methods, including problem-specific tearing methods. All three solutions are found with staircase sampling.

Modelling, Simulation and Sensitivity Analysis of Generator Control Systems using Coexisting and Cooperative Tools

“…This is because when assembling multiple models in equations, there are multiple ways to decompose constraints into elementary equations. One of the most common decomposition methods is tearing which determines the computational time required to solve a given system of equations using sparsity patterns [26]. A typical implementation is triangular decomposition of the bottom block where only tearing is applied, which can lead to suboptimal results.…”