A Data-Driven Approach to Fault Diagnosis Using Unknown-Input Observers

Core Concepts

The core message of this article is to propose a data-driven approach for designing a residual generator based on a dead-beat unknown-input observer (UIO) for linear time-invariant discrete-time state-space models affected by both disturbances and actuator faults. The authors derive necessary and sufficient conditions for the problem solvability using only the available data, without requiring knowledge of the original system matrices.

Abstract

The article presents a data-driven approach for designing a residual generator based on a dead-beat unknown-input observer (UIO) for linear time-invariant discrete-time state-space models affected by both disturbances and actuator faults.
Key highlights:

The authors first review the model-based conditions for the existence of such a residual generator.
They then prove that under suitable assumptions on the collected historical data, they can determine if the problem is solvable and identify the matrices of a possible residual generator.
An algorithm is proposed that, based only on the collected data (and not on the system description), is able to perform both tasks.
The data-driven conditions for the problem solvability are shown to be weaker than the conditions that guarantee the identifiability of the original system matrices.
The authors focus on dead-beat UIOs to provide a cleaner setup that allows for exact solutions, without needing to account for the contribution of the estimation error when trying to identify the fault.
The case of a residual generator based on an asymptotic UIO is discussed as a possible extension.

Stats

The state-space model of the system is described by the following equations:
x(k + 1) = Ax(k) + Bu(k) + Ed(k) + Bf(k)
y(k) = Cx(k)
where x(k) is the state, u(k) is the input, y(k) is the output, d(k) is the disturbance, and f(k) is the actuator fault.

Quotes

"Leveraging some recent results on data-driven unknown-input observer design, we propose a data-driven approach to the design of a residual generator, based on a dead-beat unknown input observer (UIO), for a generic linear time invariant state-space model, whose state equation is affected both by disturbances and by faults."
"Under a rather common assumption on the data (see Assumption 2), that can be related to the persistence of excitation of the system inputs, in Section IV we first provide data-based necessary and sufficient conditions for the problem solvability, and then, by resorting to a couple of technical results, we provide a simple Algorithm that allows to first check on data the problem solvability conditions, and then provides matrices of a dead-beat UIO-based residual generator."

Key Insights Distilled From

A data-driven approach to UIO-based fault diagnosis

by Giulio Fatto... at arxiv.org 04-10-2024

https://arxiv.org/pdf/2404.06158.pdf

Deeper Inquiries

How can the proposed data-driven approach be extended to handle more complex fault scenarios, such as multiple simultaneous actuator faults

To extend the proposed data-driven approach to handle more complex fault scenarios, such as multiple simultaneous actuator faults, a few modifications and enhancements can be made. One approach could be to implement a bank of residual generators, each designed to detect and identify a specific fault scenario. By utilizing multiple residual generators, each tailored to a particular fault condition, the system can effectively handle the detection and isolation of various fault combinations. Additionally, incorporating more sophisticated fault detection algorithms, such as pattern recognition or machine learning techniques, can enhance the system's ability to identify complex fault patterns. Furthermore, integrating redundancy and diversity in the sensor and actuator configurations can provide additional layers of fault tolerance and robustness to the system.

What are the potential limitations of the dead-beat UIO assumption, and how could the approach be adapted to work with asymptotic UIOs

The dead-beat UIO assumption, while simplifying the fault detection and identification process, may have limitations in certain scenarios. One potential limitation is the assumption of perfect state estimation, which may not always be achievable in practical systems due to modeling errors, noise, or uncertainties. To address this limitation, the approach could be adapted to work with asymptotic UIOs, which provide a more robust estimation of the system states over time. By incorporating asymptotic UIOs, the system can account for estimation errors and uncertainties, leading to more reliable fault detection and identification. This adaptation would involve adjusting the fault identification algorithm to accommodate the estimation error and ensure accurate fault isolation even in the presence of uncertainties.

Can the data-driven framework be further generalized to handle other types of faults, such as sensor faults or system parameter variations, in addition to actuator faults

The data-driven framework can be further generalized to handle other types of faults, such as sensor faults or system parameter variations, in addition to actuator faults. To extend the approach to address sensor faults, the system can be augmented with residual generators designed to detect anomalies in sensor measurements and identify faulty sensors. By analyzing the discrepancies between predicted and actual sensor readings, the system can pinpoint sensor faults and take corrective actions. Similarly, for handling system parameter variations, the data-driven approach can be enhanced to monitor and track changes in system parameters over time. By comparing the expected system behavior based on historical data with the actual system response, deviations due to parameter variations can be detected and mitigated. Incorporating adaptive algorithms that adjust the fault detection thresholds based on evolving system dynamics can improve the system's ability to handle a wide range of fault scenarios.