Data-driven Kalman Filter-based Fault Detector
Although the data-driven methods based on PCA address the modelling issues of the model-based approaches, they work well when dealing with data that are generated by a system operating with linear dynamics. However, this is not usually the case of real complex systems. For this reason, new approaches are needed to take such issues into account. In particular, the DD-KFB takes into account such issues with 2 approaches:
- producing a switching system model by exploiting model identification techniques based on auto regressive (AR) system identification and regression trees (RTs) theory [DDKFB1,DDKFB2]. The main advantage of this methodology is that it provides a modelling framework that is both (i) simple from the computational complexity point of view (as it consists of a collection of linear models) and (ii) accurate in terms of damage detection performance;
- extending the classical PCA-based approach by means of the poly-exponential (PE) theory, and producing a nonlinear model. In particular, this is done by adding a PE correction term to the classical PCA-based model, and identifying its parameters.
In both cases, the modelling procedure is followed by the setup of a Kalman filter-based fault detection methodology, where the Kalman filter is used to check if the parameters describing the system move away from the nominal behaviour. The details of the methodology can be found in [DDKFB3], that is the publication of the method developed within VALU3S.
From a practitioner point of view, the above methods can be implemented in two steps:
- In the first step (training, off-line) a historical dataset is collected from the system of interest, and classical toolboxes (as detailed below) can be used to derive a mathematical model of the system;
- In the second step (fault detection, run-time) on-the-fly data are collected from the system of interest, and a Kalman filter, which requires very light computational resources, as it is only based on linear operations on (generally small) matrices, is run over a real-time board. A fault detection is raised when the Kalman filter output significantly deviates from the nominal expected behaviour.
- Fault detection performance in terms of number of faults detected
- Model identification with respect to nonlinear systems with high performance in terms of accuracy
- Resulting models are more complex, i.e. switching and nonlinear, thus the implementation complexity both from modelling and Kalman filter point of view is higher than the classical PCA-based method.
- [DDKFB1] Smarra F, Jain A, De Rubeis T, Ambrosini D, D’Innocenzo A, Mangharam R. (2018). Data-driven model predictive control using random forests for building energy optimization and climate control. Applied Energy, 226, 1252-1272.
- [DDKFB2] Smarra F, Di Girolamo GD, De Iuliis V, Jain A, Mangharam R, D’Innocenzo A. (2020). Data-driven switching modeling for MPC using regression trees and random forests. Nonlinear Analysis Hybrid Systems, 36, 100882.
- [DDKFB3] Smarra F. Tjen J., D’Innocenzo A. (2022). Learning methods for structural damage detection via entropy-based sensors selection. International Journal of Robust and Nonlinear Control, 1-33.