Optimal input design for guaranteed fault diagnosis of nonlinear systems: An active deep learning approach

Abstract

The trend toward increasing complexity in many industries has made component malfunctions and other abnormal events increasingly frequent. These events, often referred to as faults, must be quickly and accurately diagnosed in order to ensure safe and reliable system operation. Active fault diagnosis (AFD) refers to methods that design particular input signals to be injected into a system that improve detectability of faults. In this work, we present a novel optimal AFD strategy focused on the design of minimally invasive input signals that guarantee safety (i.e., state constraints are not violated) while also providing a complete fault diagnosis (i.e., measurements are consistent with at most one model) for general nonlinear systems under uncertainty. Our approach is inspired from taking a data-driven perspective to this problem wherein we aim to learn its solution by querying an oracle that certifies if a given input sequence satisfies separability and safety constraints or not. Since the oracle is expensive to query in many cases, we develop an efficient active learning method that uses deep neural network models to sequentially identify a batch of informative input sequences to query at every iteration. We discuss strategies for practically evaluating upper and lower bounds on the oracle using over- and under-approximations of reachable state and output sets for the dynamic system. The effectiveness and generality of our proposed approach is demonstrated through multiple case studies including linear and nonlinear systems.