A Quantitative Performance Index for Observer-Based Monitoring Systems

Model-based monitoring systems based on state observer theory are attractive for machine monitoring because practical, inexpensive, and reliable sensors can be located remote to the signal(s) of interest. Then, a model of the machine plus an estimation algorithm are utilized to convert the output of the remote sensors to signals representing the desired local behavior. While this type of monitoring system has shown much promise in the laboratory, it has not been widely accepted by industry because, in practice, these systems often have poor performance with respect to accuracy, bandwidth, reliability (false alarms), and robustness. In this paper, the limitations of the deterministic state observer are investigated quantitatively from the machine monitoring viewpoint. The limitations in the transient and steady-state observer performance are quantified based on the estimation error bounds, and from these error bounds, performance indices are selected. Then, based on the relationships between the indices, a main index is determined in order to represent the overall observer performance. The index is the condition number of the observer eigenvectors in L₂ norm. It is shown that observers with small condition numbers are guaranteed to have small error bounds. This index can be utilized as a quality condition for any linear observer regardless of how it is designed as well as form the basis for an observer design methodology for high performance observer-based monitoring systems.