Mixed logical dynamical (MLD)-based Kalman filter for hybrid systems fault diagnosis

The Mixed Logical Dynamical (MLD) model framework is used in this paper to develop a novel algorithm for state estimation and fault diagnosis in hybrid systems. These systems, with both continuous and discrete dynamics, present challenges for accurate state estimation and timely fault detection. The proposed method integrates the constrained Kalman filter, MLD modeling, and mixed integer programming for robust state monitoring and fault diagnosis. It leverages the MLD model to represent system dynamics while handling discrete and continuous states, offering a flexible framework for hybrid system analysis. The constrained Kalman filter estimates the system state in real time, ensuring the estimation stays within constraints that reflect physical or operational limits. This enhances robustness, especially in noisy environments. Mixed integer programming efficiently manages discrete events and logical decisions, capturing the hybrid system's nature. The technique, called the Hybrid Kalman Filter (HKF), combines Kalman filtering with MLD models to detect and isolate sensor faults. A bank of HKFs monitors specific sensors or subsystems for precise fault isolation. When a fault occurs, the corresponding HKF detects it, providing critical information about its location and nature. The proposed method is tested on hybrid systems, both simulated and real-world, demonstrating its effectiveness in estimating system states and detecting sensor faults, even in complex environments. The results show its potential to improve hybrid system reliability and performance in industries such as automotive, aerospace, and industrial automation.