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arxiv: 2509.01347 · v1 · pith:M2IAG3ETnew · submitted 2025-09-01 · 📡 eess.SY · cs.SY

Data-Driven Fault Isolation in Linear Time-Invariant Systems: A Subspace Classification Approach

Mohammad Amin Sheikhi , Gabriel de Albuquerque Gleizer , Peyman Mohajerin Esfahani , Tam\'as Keviczky This is my paper

Pith reviewed 2026-05-25 08:01 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords data-driven fault isolationbehavioral frameworknullspace-based filtersubspace classificationlinear time-invariant systemsactuator and sensor faultsmodel-free design
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The pith

Reparameterizing the fault isolation problem in a behavioral framework yields a direct, model-independent filter design from fault-free data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a data-driven method for isolating actuator and sensor faults in linear time-invariant systems. It builds a nullspace-based filter solely from input-output data collected under noise, without requiring an explicit system model. The approach reparameterizes the problem inside a behavioral framework and treats the underlying classification geometrically. This yields conditions for when faults are mutually discernible, expressed via fundamental system properties in the noise-free case, and those conditions are checkable directly from the data. A simulation example illustrates the filter's performance.

Core claim

By reparameterizing the problem within a behavioral framework, the authors achieve a direct fault isolation filter design that is independent of any explicit system model, using only fault-free input-output data collected under process and measurement noises.

What carries the argument

Nullspace-based filter obtained via subspace classification after behavioral reparameterization of the isolation task.

If this is right

  • Fault isolation becomes possible without first identifying or using an explicit state-space model.
  • Discernibility between any pair of faults reduces to a check on rank or subspace relations that can be computed from data matrices alone.
  • The same data set used to build the filter also suffices to verify the discernibility conditions.
  • The method accounts for both process noise and measurement noise during data collection.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The geometric view may connect the method to other data-driven techniques that operate on Hankel matrices or kernel representations.
  • Because the filter is built from a single batch of fault-free data, it could support periodic redesign when new operating data arrives.
  • Extending the noise-free discernibility test to noisy data would require quantifying how noise perturbs the relevant subspaces.

Load-bearing premise

The characterization of mutual fault discernibility in terms of fundamental system properties in a noise-free setting can be evaluated using only the available data.

What would settle it

Apply the filter to a linear system where the geometric test on the data matrix predicts two faults are indiscernible, then observe whether the filter output still separates them correctly under the same noise-free data.

Figures

Figures reproduced from arXiv: 2509.01347 by Gabriel de Albuquerque Gleizer, Mohammad Amin Sheikhi, Peyman Mohajerin Esfahani, Tam\'as Keviczky.

Figure 1
Figure 1. Figure 1: Geometric interpretation of the fault isolation problem. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: A noise-free actuator fault scenario. The fault magnitude is indicated [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The proposed FI performance in the presence of noise with different types of faults. (Left) The left y-axis represents fault signals in different [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
read the original abstract

We study the problem of fault isolation in linear systems with actuator and sensor faults within a data-driven framework. We propose a nullspace-based filter that uses solely fault-free input-output data collected under process and measurement noises. By reparameterizing the problem within a behavioral framework, we achieve a direct fault isolation filter design that is independent of any explicit system model. The underlying classification problem is approached from a geometric perspective, enabling a characterization of mutual fault discernibility in terms of fundamental system properties given a noise-free setting. In addition, the provided conditions can be evaluated using only the available data. Finally, a simulation study is conducted to demonstrate the effectiveness of the proposed method.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The paper proposes a data-driven fault isolation method for LTI systems subject to actuator and sensor faults. It constructs a nullspace-based isolation filter directly from noisy fault-free input-output data by reparameterizing the problem in the behavioral framework, yielding a design independent of any explicit system model. Mutual fault discernibility is characterized geometrically in the noise-free case in terms of fundamental system properties, with the resulting conditions shown to be evaluable from the available data alone; effectiveness is illustrated via simulation.

Significance. If the central derivations hold, the work advances model-free fault diagnosis by integrating behavioral systems theory with subspace methods to produce a direct, data-only isolation filter. The geometric characterization of discernibility and its data-driven test constitute a concrete, falsifiable contribution that could reduce reliance on identified models in noisy environments.

minor comments (3)
  1. [§3.2] §3.2: the transition from the noise-free geometric rank condition (Eq. (17)) to the noisy-data test statistic is stated without an explicit bound on the perturbation induced by process/measurement noise; a short remark on the required signal-to-noise ratio would clarify applicability.
  2. [Fig. 4] Fig. 4 caption: the legend uses symbols that do not match the plotted lines; this is a minor but distracting inconsistency.
  3. [§5] The simulation section reports detection rates but does not tabulate the numerical values of the data-driven discernibility test for each fault pair; adding these values would strengthen the claim that the conditions are evaluable from data.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the constructive review and the recommendation of minor revision. No major comments were raised in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper's central derivation reparameterizes the fault isolation problem in the behavioral framework to obtain a nullspace-based filter directly from fault-free input-output data, followed by a geometric characterization of mutual fault discernibility in the noise-free case whose conditions are stated to be evaluable from data. These steps rely on standard external tools (behavioral systems theory and geometric control) rather than reducing by construction to fitted parameters, self-definitions, or self-citation chains within the manuscript. No load-bearing step equates a claimed prediction or result to its own inputs; the simulation study serves only as validation. The approach is therefore independent and non-circular.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Review performed on abstract only; ledger entries reflect the high-level claims stated in the abstract.

axioms (2)
  • domain assumption The plant is linear time-invariant.
    Explicit in the title and abstract.
  • domain assumption Fault-free input-output trajectories are available under process and measurement noise.
    Stated as the sole data source for filter design.

pith-pipeline@v0.9.0 · 5658 in / 1180 out tokens · 65964 ms · 2026-05-25T08:01:23.628438+00:00 · methodology

discussion (0)

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Reference graph

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