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arxiv: 2606.17347 · v1 · pith:D5RUDYNW · submitted 2026-06-15 · eess.SY · cs.SY

Classifying Transient Regimes in Dynamic Systems through Properties of Spatial Curves and Stochastic Processes: A Data-Driven Approach

Cristian Puerto-Santana , Javier Diaz-Rozo , Carlos Puerto-Santana , Carlos Ocampo-Martinez This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-06-27 02:01 UTCgrok-4.3pith:D5RUDYNWrecord.jsonopen to challenge →

classification eess.SY cs.SY
keywords regime classificationtransient regimesspatial curvesarc lengthdynamic systemsstochastic processesstability theorymultivariate systems
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The pith

A spatial curve from sample moments classifies transient regimes in multivariate dynamic systems using its arc length.

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

The paper introduces a representation of dynamic systems as spatial curves constructed from sample mathematical moments. It then links geometrical properties of these curves to stability theory and stationary stochastic processes to create two classifiers, one based on arc length and one on curvatures. These classifiers identify behaviors including multivariate asymptotic stability, marginal stability, and cyclostationarity. The arc length version is shown to outperform existing techniques on simulated linear, nonlinear, and discontinuous systems while avoiding the need for multiple parameters. This targets limitations in current sensor-based regime classification methods for complex multivariate cases that may include periodic signals.

Core claim

Connecting sample mathematical moments into a spatial curve and applying stability theory along with properties of stationary stochastic processes allows arc-length and curvature classifiers to describe and detect transient regimes such as asymptotic stability, marginal stability, and cyclostationarity in multivariate systems.

What carries the argument

The spatial curve representation of the system based on its sample mathematical moments, where arc length serves as the main distinguishing feature for regime classification.

If this is right

  • The classifiers apply to linear, nonlinear, and discontinuous multivariate systems under the studied conditions.
  • No additional parameters or post-hoc tuning are required for the proposed classifiers.
  • The method handles systems containing periodic signals where other sensor-based solutions may fail.
  • The arc length classifier uses fewer computation resources than some existing alternatives while achieving better classification performance.

Where Pith is reading between the lines

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

  • The geometric representation could be tested on experimental rather than only simulated data to check real-world robustness.
  • Curvature-based classification might be combined with the arc length version for hybrid detection in systems with mixed behaviors.
  • This moment-curve approach might connect to other time-series geometry methods for regime detection in control applications.

Load-bearing premise

That a spatial curve built from sample mathematical moments, combined with stability theory and properties of stationary stochastic processes, is sufficient to distinguish transient behaviors such as asymptotic stability, marginal stability, and cyclostationarity without additional parameters or post-hoc tuning.

What would settle it

Apply both the arc length classifier and a competing method to a new simulated multivariate cyclostationary system; if the arc length method consistently misclassifies the regime while the competitor succeeds, the outperformance claim is falsified.

Figures

Figures reproduced from arXiv: 2606.17347 by Carlos Ocampo-Martinez, Carlos Puerto-Santana, Cristian Puerto-Santana, Javier Diaz-Rozo.

Figure 1
Figure 1. Figure 1: Scheme of the proposed methodology for transient regimes and stationary regime classification. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Results of the simulated linear dynamic system. (a) Input and output signals of the simulated linear dynamical system. (b) [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Results of the simulated non-linear dynamic system. (a) Input and output signals of the simulated non-linear dynamical [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Results of the simulated discontinuous dynamic system. (a) Input signals of the simulated discontinuous dynamical [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
read the original abstract

This article proposes a novel methodology for the classification of transient and stationary regimes in dynamic systems. Several sensor-based solutions for regime classification in the literature require the setting of several parameters, or are not suitable for scenarios involving multivariate systems that may contain periodic signals. The proposed method introduces a spatial curve representation of the considered system based on its sample mathematical moments. Then, by connecting concepts of stability theory, geometrical properties of spatial curves and stationary stochastic processes, two regime classifiers are designed using the arc length and the curvatures of the proposed curve. Both classifiers are capable of describing and detecting transient regimes, considering behaviors such as: multivariate asymptotically, marginally stability, and cyclostationarity. Furthermore, a quantitative comparison in performance and computation resources of the proposed classifiers against existing classifiers in the literature illustrates that the proposed regime classifier based on the arc length outperforms other techniques in classifying transient regimes for simulated linear, non-linear, and discontinuous multivariate systems under the specified studied conditions.

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 / 2 minor

Summary. The paper proposes a data-driven methodology for classifying transient and stationary regimes in dynamic systems. It constructs a spatial curve representation based on sample mathematical moments of the system outputs, then applies concepts from stability theory, geometrical properties of spatial curves, and stationary stochastic processes to design two classifiers: one based on arc length and one based on curvature. Both are intended to detect behaviors including multivariate asymptotic stability, marginal stability, and cyclostationarity. A quantitative comparison on simulated linear, nonlinear, and discontinuous multivariate systems claims that the arc-length classifier outperforms existing techniques under the specified studied conditions, while also comparing computational resources.

Significance. If the central claims hold with supporting derivations and validation, the work would offer a parameter-free classifier grounded in stability theory and stochastic process properties, addressing limitations of sensor-based methods that require parameter tuning or struggle with multivariate periodic signals. The geometric framing via moments-based curves is a distinctive contribution that could enable new tools for regime detection in control applications, provided the simulations demonstrate generalizability beyond the studied cases.

minor comments (2)
  1. [Abstract] Abstract: the performance claim is scoped to 'specified studied conditions' without enumerating the system dimensions, noise levels, sampling rates, or exact comparison baselines; this should be expanded for reproducibility even in the abstract.
  2. [Abstract] The abstract states the method is suitable for scenarios involving periodic signals, but does not indicate how cyclostationarity is quantitatively distinguished from marginal stability in the curve properties; a brief clarification would strengthen the claim.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the accurate summary of our manuscript and for acknowledging the potential significance of a parameter-free, geometrically grounded classifier for transient regimes. The recommendation of 'uncertain' appears to stem from the absence of listed major comments; we therefore provide no point-by-point responses below and stand ready to address any specific concerns the referee may wish to raise in a subsequent round.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper defines a spatial curve from sample mathematical moments, then applies arc length and curvature classifiers grounded in stability theory and stationary stochastic process properties. These steps are presented as direct constructions from the data and external mathematical concepts, with performance evaluated on simulated systems under explicitly stated conditions. No equation or claim reduces by construction to a fitted input renamed as prediction, no self-citation chain is load-bearing for the central result, and no ansatz or uniqueness theorem is smuggled in. The method is scoped without hidden tuning or self-referential definitions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Abstract-only review; the central claim rests on the unverified assumption that moment-derived spatial curves plus geometric and stochastic concepts suffice for regime detection. No free parameters, axioms, or invented entities can be audited in detail.

axioms (1)
  • domain assumption Stability theory, geometrical properties of spatial curves, and stationary stochastic processes can be connected to design regime classifiers
    Invoked in the abstract to justify the two classifiers.
invented entities (1)
  • spatial curve representation based on sample mathematical moments no independent evidence
    purpose: To encode system behavior for arc-length and curvature-based regime classification
    New representation introduced as the foundation of the method; no independent evidence supplied in abstract.

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discussion (0)

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Reference graph

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