control//fault diagnosis//analytical redundancy

Analytical redundancy is the use of a mathematical model as a second sensor: a relation between measured quantities predicts what one of them should read, so that its disagreement with the real reading becomes a residual. It is how fault diagnosis gets a trusted comparison without paying for duplicate hardware, and it is the heart of model-based diagnosis in cars, aircraft and process plants.

Analytical redundancy is the use of a mathematical model as a second sensor: a relation between measured quantities predicts what one of them should read, so that its disagreement with the real reading becomes a residual. It is how fault diagnosis gets a trusted comparison without paying for duplicate hardware, and it is the heart of model-based diagnosis in cars, aircraft and process plants.

The alternative is physical redundancy: two or three identical sensors on the same quantity, compared or voted (redundancy). It is robust and needs no model, and it costs money, weight, wiring and power, which is why airliners carry it for the few measurements that matter most and almost nothing else does. Analytical redundancy reuses sensors that are already there. Take a centrifugal pump: from the shaft speed and the flow, the pump's characteristic curve predicts the pressure rise; a pressure reading that disagrees by more than the curve's uncertainty says that either the pressure sensor, the flow sensor or the impeller is no longer what the model assumed (centrifugal pump).

There are three common ways to build the model side:

An observer predicts the output from the inputs and its own state estimate; the innovation of a running Kalman filter is such a residual, already scaled by its expected spread, which is why a filter in an autopilot doubles as a sensor watchdog.

Parity relations are combinations of measurements that must sum to zero when everything is healthy. A tank's mass balance is the classic one: inflow minus outflow minus the rate of change of the stored mass, all measured, should be noise around zero, and a persistent offset is a leak or a drifting flowmeter (balance equation).

A physical parameter estimated online, a pump's efficiency or a motor's resistance tracked by recursive least squares, is compared with its nominal value; the parameter drifting is the residual, and its direction often names the cause.

The price of a model as a sensor is its error. A real residual contains model error alongside the fault, so the model's accuracy sets the smallest fault that can be told from normal operation; a crude model is a wide threshold. Physical redundancy catches a sensor failure regardless of the plant, while analytical redundancy can also see faults of the process itself (a worn impeller, a blocked pipe) that duplicate sensors would agree about.