Sensor-Based Bayesian Inference and Placement: Review and Examples

Systems, complex or otherwise, can be monitored through sensors placed at various functional levels to infer information about system reliability parameters (and by extension, reliability characteristics). Sensor placement directly affects the quantity and utility of inferred information, and need to be judiciously located throughout the relevant system. Sensors can be embedded or attached upon components, sub-systems or the entire system itself. Functional sensors can detect levels of functionality (including levels of degraded performance) and time to failure of the elements of the system they are monitoring. Data gathered from multiple system sensors will be ‘overlapping’ in that they are drawn from the same process or system at the same time. Overlapping data requires specific consideration for subsequent inference – system states observed by all sensors contextualize the data of all others. This paper is a review of how overlapping sensor data is analyzed in a Bayesian framework, and form part of a sensor placement optimization process to maximize information. This is particularly useful in scenarios where sensors are expensive to install with various resource constraints (such as volume and weight) limiting their use. The paper also presents review of a method of measuring the information utility of various sensor placement arrangements in a Bayesian construct of both on-demand and time-based continuous systems. Prior information is used to simulate evidence sets, which are then used to simulate posterior distribution of reliability metrics of interest. Information utility is derived from these posterior distributions, and an expected information utility is then attributed to sensor placement. Finally, examples of applying the methodologies discussed will be presented.