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Data-Driven Sensor Fault Diagnosis with Proven Guarantees using Incrementally Stable Recurrent Neural Networks

Farhad Ghanipoor, Carlos Murguia, Giancarlo Ferrari Trecate, Nathan van de Wouw

TL;DR

This manuscript constructs a data-driven Fault Detection and Isolation method for sensor faults with proven performance guarantees and demonstrates the effectiveness and practical applicability of the proposed methodology on a roll-plane model of a vehicle.

Abstract

Robust Recurrent Neural Networks (R-RENs) are a class of neural networks that have built-in system-theoretic robustness and incremental stability properties. In this manuscript, we leverage these properties to construct a data-driven Fault Detection and Isolation (FDI) method for sensor faults with proven performance guarantees. The underlying idea behind the scheme is to construct a bank of multiple R-RENs (acting as fault isolation filters), each with different levels of sensitivity (increased or decreased) to faults at different sensors. That is, each R-REN is designed to be specifically sensitive to faults occurring in a particular sensor and robust against faults in all the others. The latter is guaranteed using the built-in incremental stability properties of R-RENs. The proposed method is unsupervised (as it does not require labeled data from faulty sensors) and data-driven (because it exploits available fault-free input-output system trajectories and does not rely on dynamic models of the system under study). Numerical simulations on a roll-plane model of a vehicle demonstrate the effectiveness and practical applicability of the proposed methodology.

Data-Driven Sensor Fault Diagnosis with Proven Guarantees using Incrementally Stable Recurrent Neural Networks

TL;DR

This manuscript constructs a data-driven Fault Detection and Isolation method for sensor faults with proven performance guarantees and demonstrates the effectiveness and practical applicability of the proposed methodology on a roll-plane model of a vehicle.

Abstract

Robust Recurrent Neural Networks (R-RENs) are a class of neural networks that have built-in system-theoretic robustness and incremental stability properties. In this manuscript, we leverage these properties to construct a data-driven Fault Detection and Isolation (FDI) method for sensor faults with proven performance guarantees. The underlying idea behind the scheme is to construct a bank of multiple R-RENs (acting as fault isolation filters), each with different levels of sensitivity (increased or decreased) to faults at different sensors. That is, each R-REN is designed to be specifically sensitive to faults occurring in a particular sensor and robust against faults in all the others. The latter is guaranteed using the built-in incremental stability properties of R-RENs. The proposed method is unsupervised (as it does not require labeled data from faulty sensors) and data-driven (because it exploits available fault-free input-output system trajectories and does not rely on dynamic models of the system under study). Numerical simulations on a roll-plane model of a vehicle demonstrate the effectiveness and practical applicability of the proposed methodology.
Paper Structure (11 sections, 2 theorems, 36 equations, 2 figures, 2 tables)

This paper contains 11 sections, 2 theorems, 36 equations, 2 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. Problem Formulation
  3. Robust REN-Based Fault Detector Filters
  4. Illustrative Example
  5. Training and Test Data-Sets
  6. Performance of Fault Detector Filters
  7. Conclusion
  8. Appendices
  9. Direct Parameterization of R-aRENs
  10. Proof of Theorem \ref{['theorem']}
  11. Roll Plane System Description

Key Result

Theorem 1

(Direct FDI Filter Design with Performance Guarantees) Consider the data-generating system eq:sys, $s_f$ data-sets of input-output signals, $u$ and $y$, and $s_f$ synthetic data-sets of sensors faults. Moreover, consider the R-aREN fault detection filters eq:REN_filter with given design parameters $ where $\delta{r_i}^{s_{12}} := r_i^{s_2} - r_i^{s_1},$ with $r_i^{s_2}$ representing the residual

Figures (2)

  • Figure 1: Roll plane system schematic.
  • Figure 2: Residual signals of fault detectors for a test scenario with fault in the first sensor.

Theorems & Definitions (4)

  • Definition 1
  • Theorem 1
  • Remark 1
  • Lemma 1