01
Residual Generator
Primary diagnostic signal.
Module computing residuals r(t) = y(t) - ŷ(t) from the nominal model or observer.
Fault Detection and Isolation
Systematic methodology for fault detection, isolation, and identification in dynamic systems by comparing observed signals against a nominal model.
Category
Abstraction level
FDI module in Active FTCPredictive maintenanceMonitoring aircraft enginesFault detection in robot sensorsMonitoring autonomous vehiclesSafety instrumented systems for chemical processes (SIS)Detection of faults in multirotor drones
Generate residuals: r(t) = y(t) - ŷ(t), where ŷ(t) is the model/observer output. Apply a statistical test or threshold: r > γ → detection. Use an observer bank (each sensitive to a single component) or parity equations for isolation. Identification: online adaptive methods (e.g., least squares) to estimate fault magnitude.
How to automatically detect, localize, and characterize faults in a dynamic system based on input and output signals, without operator intervention.
02
Residual Evaluator / Decision Logic
Fault detection and isolation.
Module comparing residuals against thresholds or applying statistical tests (CUSUM, GLR, χ²) to make fault decisions.
03
Observer Bank
Isolation — locating the faulty component.
Set of observers (Luenberger, KF) designed for different fault scenarios — each generating residuals sensitive to one fault type.
04
Fault Identification Module
Detection and identification — entry point to the FTC reconfiguration mechanism.
Estimates the magnitude and character of the fault (adaptive parameter estimation, LS, Bayesian methods) after isolation.
Common pitfalls
False Alarm Rate vs Missed Detection RateHIGH
Lowering the detection threshold increases FAR; raising it increases MDR. Application-dependent trade-off is required.
Receiver Operating Characteristic (ROC), adaptive thresholds, Bayesian decision theory.
Fault–Disturbance IndistinguishabilityHIGH
Observer-based FDI may confuse external disturbances with faults (lack of robustness).
Robust FDI methods (unknown input observers, H∞ observers) separate disturbances from faults through observer design.
Isolation Under Simultaneous FaultsMEDIUM
Standard observer bank schemes designed for single faults fail with two simultaneous faults.
Combinatorial methods, machine learning, and generalized likelihood ratio tests.
1971
Beard — first formal FDI
breakthroughR. V. Beard (MIT) formalises fault accommodation — the beginning of model-based FDI.
1984
Frank — observer-based FDI survey
P. M. Frank systematises observer-based FDI methods; Dedicated Observer Scheme (DOS) and GOS.
1991
Gertler — parity equations
J. Gertler formalises the parity equations approach to FDI as an alternative to observers.
1993
IFAC SAFEPROCESS — dedicated conference
breakthroughFirst IFAC SAFEPROCESS conference — FDI/FTC becomes a distinct subdiscipline.
2010
Data-driven FDI — ML classifiers
Rise of SVM, random forests, and neural networks for data-driven FDI on industrial data (predictive diagnostics).
2020
Deep learning FDI
Autoencoders, LSTM, and Transformer-based anomaly detection applied to FDI in robotics and Industry 4.0.
CPU AVXPRIMARY
FDI runs on the RT CPU in the control loop (typically the same platform as the controller).
GPU Tensor CoresPOSSIBLE
Deep learning FDI (autoencoders, LSTM) may use GPU for offline training or inference in non-hard-RT systems.
Hardware agnosticGOOD
Model-based FDI is hardware-agnostic; a deterministic RT scheduler is the key requirement.
EXTENDS
KF
The Kalman Filter (KF) is a recursive state estimator proposed by Rudolf E. Kálmán in 1960. It operates in two steps: prediction (propagating state and covariance through the dynamics model) and correction (updating with a new measurement, weighted by the Kalman gain matrix). It is optimal in the MMSE sense for linear systems with Gaussian noise. In robotics and control, the KF is the foundation of localization, object tracking, sensor fusion (IMU + GPS + LiDAR), fault detection, and state prediction for MPC. The Extended Kalman Filter (EKF) linearises the nonlinear model at the operating point; the Unscented Kalman Filter (UKF) propagates deterministic sigma points instead; the Particle Filter uses Monte Carlo approximation for arbitrary distributions. The Kalman Filter is a building block of virtually every modern FDI and FTC system — the residuals it generates (differences between predicted and observed output) are the primary signal for fault detection.
GO TO CONCEPT| Title | Publisher | Type |
|---|---|---|
| Diagnosis and Fault-Tolerant Control (Blanke et al., 3rd ed.) Chapters 3–7: model-based FDI, observers, parity equations. | Springer | documentation |
| Fault Diagnosis in Dynamic Systems: Theory and Application (Patton, Frank, Clark) Classic FDI textbook (1989). | Prentice Hall | documentation |
| IFAC SAFEPROCESS — Safety of Computer Control Systems IFAC Technical Committee TC 6.4 — the central FDI/FTC community hub. | IFAC | official website |
Diagnosis and Fault-Tolerant Control (Blanke et al., 3rd ed.)
Chapters 3–7: model-based FDI, observers, parity equations.
documentationSpringer
Fault Diagnosis in Dynamic Systems: Theory and Application (Patton, Frank, Clark)
Classic FDI textbook (1989).
documentationPrentice Hall
IFAC SAFEPROCESS — Safety of Computer Control Systems
IFAC Technical Committee TC 6.4 — the central FDI/FTC community hub.
official websiteIFAC