Sensor Placement for Damage Localization in Sensor Networks

The objective of this thesis is to formulate and solve the sensor placement problem for damage localization in a sensor network. A Bayesian estimation problem is formulated with the time-of-flight (ToF) measurements. In this model, ToF of lamb waves, which are generated and received by piezoelectric sensors, is the total time for each wave to be transmitted, reflected by the target, and received by the sensor. The ToF of the scattered lamb wave has characteristic information about the target location. By using the measurement model and prior information, the target location is estimated in a centralized sensor network with a Monte Carlo approach. Then we derive the Bayesian Fisher information matrix (B-FIM) and based on that posterior Cramer-Rao lower bound (PCRLB), which sets a limit on the mean squared error (MSE) of any Bayesian estimator. In addition, we develop an optimal sensor placement approach to achieve more accurate damage localization, which is based on minimizing the PCRLB. Simulation results show that the optimal sensor placement solutions lead to much lower estimation errors than some sub-optimal sensor placement solutions

Fast Bayesian experimental design: Laplace-based importance sampling for the expected information gain

In calculating expected information gain in optimal Bayesian experimental design, the computation of the inner loop in the classical double-loop Monte Carlo requires a large number of samples and suffers from underflow if the number of samples is small. These drawbacks can be avoided by using an importance sampling approach. We present a computationally efficient method for optimal Bayesian experimental design that introduces importance sampling based on the Laplace method to the inner loop. We derive the optimal values for the method parameters in which the average computational cost is minimized according to the desired error tolerance. We use three numerical examples to demonstrate the computational efficiency of our method compared with the classical double-loop Monte Carlo, and a more recent single-loop Monte Carlo method that uses the Laplace method as an approximation of the return value of the inner loop. The first example is a scalar problem that is linear in the uncertain parameter. The second example is a nonlinear scalar problem. The third example deals with the optimal sensor placement for an electrical impedance tomography experiment to recover the fiber orientation in laminate composites.Comment: 42 pages, 35 figure

A Bayesian Approach to Sensor Placement and System Health Monitoring

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)