System health monitoring and sensor placement are areas of great technical and scientific interest. Prognostics and health management of a complex system require multiple sensors to extract required information from the sensed environment, because no single sensor can obtain all the required information reliably at all times. The increasing costs of aging systems and infrastructures have become a major concern, and system health monitoring techniques can ensure increased safety and reliability of these systems. Similar concerns also exist for newly designed systems.

The main objectives of this research were: (1) to find an effective way for optimal functional sensor placement under uncertainty, and (2) to develop a system health monitoring approach with both prognostic and diagnostic capabilities with limited and uncertain information sensing and monitoring points. This dissertation provides a functional/information --based sensor placement methodology for monitoring the health (state of reliability) of a system and utilizes it in a new system health monitoring approach.

The developed sensor placement method is based on Bayesian techniques and is capable of functional sensor placement under uncertainty. It takes into account the uncertainty inherent in characteristics of sensors as well. It uses Bayesian networks for modeling and reasoning the uncertainties as well as for updating the state of knowledge for unknowns of interest and utilizes information metrics for sensor placement based on the amount of information each possible sensor placement scenario provides.

A new system health monitoring methodology is also developed which is: (1) capable of assessing current state of a system's health and can predict the remaining life of the system (prognosis), and (2) through appropriate data processing and interpretation can point to elements of the system that have or are likely to cause system failure or degradation (diagnosis). It can also be set up as a dynamic monitoring system such that through consecutive time steps, the system sensors perform observations and send data to the Bayesian network for continuous health assessment.

The proposed methodology is designed to answer important questions such as how to infer the health of a system based on limited number of monitoring points at certain subsystems (upward propagation); how to infer the health of a subsystem based on knowledge of the health of the main system (downward propagation); and how to infer the health of a subsystem based on knowledge of the health of other subsystems (distributed propagation).