Adaptive Particle Filtering for Fault Detection in Partially-Observed Boolean Dynamical Systems.

We propose a novel methodology for fault detection and diagnosis in partially-observed Boolean dynamical systems (POBDS). These are stochastic, highly nonlinear, and derivativeless systems, rendering difficult the application of classical fault detection and diagnosis methods. The methodology comprises two main approaches. The first addresses the case when the normal mode of operation is known but not the fault modes. It applies an innovations filter (IF) to detect deviations from the nominal normal mode of operation. The second approach is applicable when the set of possible fault models is finite and known, in which case we employ a multiple model adaptive estimation (MMAE) approach based on a likelihood-ratio (LR) statistic. Unknown system parameters are estimated by an adaptive expectation-maximization (EM) algorithm. Particle filtering techniques are used to reduce the computational complexity in the case of systems with large state-spaces. The efficacy of the proposed methodology is demonstrated by numerical experiments with a large gene regulatory network (GRN) with stuck-at faults observed through a single noisy time series of RNA-seq gene expression measurements.

Optimal Fault Detection and Diagnosis in Transcriptional Circuits Using Next-Generation Sequencing.

We propose a methodology for model-based fault detection and diagnosis for stochastic Boolean dynamical systems indirectly observed through a single time series of transcriptomic measurements using Next Generation Sequencing (NGS) data. The fault detection consists of an innovations filter followed by a fault certification step, and requires no knowledge about the possible system faults. The innovations filter uses the optimal Boolean state estimator, called the Boolean Kalman Filter (BKF). In the presence of knowledge about the possible system faults, we propose an additional step of fault diagnosis based on a multiple model adaptive estimation (MMAE) method consisting of a bank of BKFs running in parallel. Performance is assessed by means of false detection and misdiagnosis rates, as well as average times until correct detection and diagnosis. The efficacy of the proposed methodology is demonstrated via numerical experiments using a p53-MDM2 negative feedback loop Boolean network with stuck-at faults that model molecular events commonly found in cancer.