# Fault Detection for Dynamical Systems using Differential Geometric and Concurrent Learning Approach

## Abstract

This paper presents a fault identification and estimation approach that brings together the differential geometric concept of observability codistribution with data driven concurrent learning. In order to identify faults in presence of unknown disturbances, we utilize the differential geometric approach to design a coordinate transformation, to find a subspace in which the effect of disturbances and system faults can be segregated. We then use concurrent learning to estimate magnitude of the constant fault. We illustrate the approach to fault isolation for a linear helicopter dynamics and a spherical pendulum dynamics. We use Lyapunov stability analysis to show that the fault estimate by concurrent learning converges to the actual fault value, and then illustrate the design of a recovery controller.

- Authors:

- Publication Date:

- Research Org.:
- Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1507533

- Report Number(s):
- PNNL-SA-129423

Journal ID: ISSN 2405-8963

- DOE Contract Number:
- AC05-76RL01830

- Resource Type:
- Journal Article

- Journal Name:
- IFAC-PapersOnLine

- Additional Journal Information:
- Journal Volume: 51; Journal Issue: 24; Journal ID: ISSN 2405-8963

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Fault detection and diagnosis

### Citation Formats

```
Chakraborty, I., and Vrabie, D.
```*Fault Detection for Dynamical Systems using Differential Geometric and Concurrent Learning Approach*. United States: N. p., 2018.
Web. doi:10.1016/j.ifacol.2018.09.552.

```
Chakraborty, I., & Vrabie, D.
```*Fault Detection for Dynamical Systems using Differential Geometric and Concurrent Learning Approach*. United States. doi:10.1016/j.ifacol.2018.09.552.

```
Chakraborty, I., and Vrabie, D. Mon .
"Fault Detection for Dynamical Systems using Differential Geometric and Concurrent Learning Approach". United States. doi:10.1016/j.ifacol.2018.09.552.
```

```
@article{osti_1507533,
```

title = {Fault Detection for Dynamical Systems using Differential Geometric and Concurrent Learning Approach},

author = {Chakraborty, I. and Vrabie, D.},

abstractNote = {This paper presents a fault identification and estimation approach that brings together the differential geometric concept of observability codistribution with data driven concurrent learning. In order to identify faults in presence of unknown disturbances, we utilize the differential geometric approach to design a coordinate transformation, to find a subspace in which the effect of disturbances and system faults can be segregated. We then use concurrent learning to estimate magnitude of the constant fault. We illustrate the approach to fault isolation for a linear helicopter dynamics and a spherical pendulum dynamics. We use Lyapunov stability analysis to show that the fault estimate by concurrent learning converges to the actual fault value, and then illustrate the design of a recovery controller.},

doi = {10.1016/j.ifacol.2018.09.552},

journal = {IFAC-PapersOnLine},

issn = {2405-8963},

number = 24,

volume = 51,

place = {United States},

year = {2018},

month = {1}

}