FDI
How it works
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.
Problem solved
How to automatically detect, localize, and characterize faults in a dynamic system based on input and output signals, without operator intervention.
Components
Module computing residuals r(t) = y(t) - ŷ(t) from the nominal model or observer.
Module comparing residuals against thresholds or applying statistical tests (CUSUM, GLR, χ²) to make fault decisions.
Set of observers (Luenberger, KF) designed for different fault scenarios — each generating residuals sensitive to one fault type.
Estimates the magnitude and character of the fault (adaptive parameter estimation, LS, Bayesian methods) after isolation.
Implementation
Lowering the detection threshold increases FAR; raising it increases MDR. Application-dependent trade-off is required.
Observer-based FDI may confuse external disturbances with faults (lack of robustness).
Standard observer bank schemes designed for single faults fail with two simultaneous faults.
Evolution
R. V. Beard (MIT) formalises fault accommodation — the beginning of model-based FDI.
P. M. Frank systematises observer-based FDI methods; Dedicated Observer Scheme (DOS) and GOS.
J. Gertler formalises the parity equations approach to FDI as an alternative to observers.
First IFAC SAFEPROCESS conference — FDI/FTC becomes a distinct subdiscipline.
Rise of SVM, random forests, and neural networks for data-driven FDI on industrial data (predictive diagnostics).
Autoencoders, LSTM, and Transformer-based anomaly detection applied to FDI in robotics and Industry 4.0.
Hardware requirements
FDI runs on the RT CPU in the control loop (typically the same platform as the controller).
Deep learning FDI (autoencoders, LSTM) may use GPU for offline training or inference in non-hard-RT systems.
Model-based FDI is hardware-agnostic; a deterministic RT scheduler is the key requirement.