Understanding rare safety and reliability events using forward-flux sampling

Abstract

This paper presents improvements upon methods that explore process trajectories leading to rare safety and reliability events. It applies the forward-flux sampling (FFS) method from the family of sampling algorithms developed to discover rare molecular dynamics pathways. For a relatively simple, dynamic exothermic CSTR model with noisy feed concentration, it shows how to apply the FFS algorithm to simulate and analyze rare trajectories between high- and low-conversion steady states. First, it compares results with a less efficient brute-force (BF) method, and then with a transition-path sampling (TPS) method. The effects of varying key process parameters; i.e., the residence time, τ, noise variance, ση2, and the controller gain, KC, which impact the rareness of an event, are investigated. Rates of rare-path transition between high- and low-conversion steady states, forward and backward, are shown to exhibit equilibrium ratios independent of ση2, with the forward rates decreasing with τ and KC, and the backward rates increasing with KC, whereas both increase with ση2. These unanticipated relationships should lead to improved alarm notifications being developed in this research work.