control//fault diagnosis

Fault diagnosis is the task of using a system's observations to distinguish a malfunction from its expected behaviour and, when the evidence permits it, to identify the malfunction's source and size; in a loop that senses, estimates and acts, it is the stage that notices the system itself has changed (how its state evolves, or how its sensors see it). It runs in every modern car, whose **on-board diagnostics** (OBD) are a dense set of model checks, in avionics, chemical plants and power grids, and in a drone's autopilot each time it rejects a GPS fix that disagrees with its prediction.

Fault diagnosis is the task of using a system's observations to distinguish a malfunction from its expected behaviour and, when the evidence permits it, to identify the malfunction's source and size; in a loop that senses, estimates and acts, it is the stage that notices the system itself has changed (how its state evolves, or how its sensors see it). It runs in every modern car, whose on-board diagnostics (OBD) are a dense set of model checks, in avionics, chemical plants and power grids, and in a drone's autopilot each time it rejects a GPS fix that disagrees with its prediction.

The work has three steps: detect that something is wrong, isolate what it is, estimate how large it is. All three rest on the residual, what is measured minus what a trusted source says should be measured. The trusted source is either a second sensor or a model acting as one (analytical redundancy); a fault model says how each fault enters the equations; a detection threshold or a change detection test such as CUSUM decides when the residual stops being noise; and fault isolation designs residuals whose pattern of reactions, the fault signature matrix, points at one culprit.

The model isolates and explains; data scale and see the unforeseen.

Model-based fault detection and isolation builds residuals from physics or an identified model, each with a meaning (the pressure does not match the pump curve); it needs little data and much knowledge of the equipment, and it isolates by design. Data-driven anomaly detection learns normal behaviour from months of healthy operation, scales to five hundred signals and flags what nobody foresaw, but says this is odd rather than this is the bearing. In production the hybrid wins: physical relations turned into features for a data model, or a black box trained on healthy data acting as the expected value, its residual watched by a CUSUM.

A supervised classifier trained on examples of each fault rarely works, because faults are exactly what a well-maintained plant does not have, and defects provoked on a test bench look little like natural ones. It pays off with large fleets of identical units or a credible fault simulator.

An adaptive controller is already a diagnostic system. Its adapted parameters are symptoms: a drone whose estimated thrust efficiency sits 15 % below the rest of the fleet has a propeller or a motor to inspect. Comparing parameters across identical units, or against the unit's own history, is one of the cheapest diagnostics there is.

A residual can reveal an inconsistency without naming the failed component. In a two-tank system several faults produce overlapping signatures, and only enough independent measurements separate them, a limit set by the sensors and studied under controllability and observability.

What happens after detection is the subject of fault-tolerant control (keep working with the fault) and maintenance (decide when to repair it); an attacker who knows the detector is a fault of a different kind, treated in cyber-physical security.