Sensor-only fault detection using pseudo transfer function identification

Motivated by passive health monitoring applications, we consider identification where only sensor measurements are available. The goal is to exploit unknown ambient disturbances and thus avoid the need for controlled actuation. To achieve this, we identify a pseudo transfer function (PTF) between sensor measurements. For the single-input case, one sensor is designated as the pseudo input to the system, while the second sensor measurements constitute the pseudo output. We show that the identified PTF is independent of the unknown initial state and unknown exogenous input. We demonstrate this method on two- and three-degree-of-freedom mass-spring-damper systems and validate the identified PTFs by comparing them with analytical results.