arxiv: 2604.21839 · v1 · submitted 2026-04-23 · 📡 eess.SP

Recognition: unknown

A Hidden Markov Framework for Physically Interpretable Arc Stability Dynamics in Welding Systems

Hidir Selcuk Nogay

Authors on Pith no claims yet

Pith reviewed 2026-05-09 20:27 UTC · model grok-4.3

classification 📡 eess.SP

keywords arc weldingHidden Markov Modelspectral descriptorsarc stabilityShort-Time Fourier Transformstate persistencetemporal coherencewelding current

0 comments

The pith

Welding arc stability can be tracked as transitions between three regimes using a Hidden Markov Model on spectral features of the current signal.

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

Electric arc welding produces non-stationary current signals that are difficult to assess for stability with conventional frame-based methods. The paper models arc dynamics as a sequence of latent operational regimes in a probabilistic state-space framework. Spectral descriptors including energy, entropy, and centroid are extracted from the Short-Time Fourier Transform of the welding current to form the observations. A Hidden Markov Model then infers the evolution of states, revealing three dominant regimes—transient, stable, and extinction. These regimes show a monotonic rise in spectral energy and fall in entropy under stable conditions, along with high state persistence and low transition rates.

Core claim

Arc dynamics are modeled as a sequence of latent operational regimes within a probabilistic state-space framework. The welding current signal is transformed into a time-frequency domain using Short-Time Fourier Transform, and a set of physically meaningful spectral descriptors, including energy, entropy, and centroid, is extracted to construct the observation sequence. A Hidden Markov Model is employed to capture temporal dependencies and estimate the evolution of arc states. The analysis reveals three dominant regimes, transient, stable, and extinction, with a clear monotonic increase in spectral energy and a corresponding decrease in entropy, indicating reduced variability under stable 0.0

What carries the argument

Hidden Markov Model that uses spectral energy, entropy, and centroid features from the Short-Time Fourier Transform of the welding current signal as observations to infer latent arc regimes.

Load-bearing premise

The chosen spectral descriptors are sufficient to separate physically distinct arc regimes despite partial overlap in feature space, and the learned states correspond to meaningful operational regimes rather than artifacts of the model.

What would settle it

High-speed video of the arc during periods labeled transient, stable, or extinction by the model showing no visible differences in arc length, flicker, or stability would undermine the claim that the states are physically interpretable.

Figures

Figures reproduced from arXiv: 2604.21839 by Hidir Selcuk Nogay.

**Figure 1.** Figure 1: Proposed STFT–HMM framework for temporal arc stability modeling, including signal acquisition, feature extraction, observation sequence construction, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 3.** Figure 3: Temporal evolution of spectral features including energy-based index, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 5.** Figure 5: Silhouette analysis of clustering structure. Overlap regions indicate [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

**Figure 4.** Figure 4: PCA projection of feature vectors colored by inferred HMM states. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 6.** Figure 6: Temporal evolution of hidden states obtained via Viterbi decoding. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

read the original abstract

Electric arc welding (EAW) exhibits strongly non stationary and temporally evolving behavior, making reliable assessment of arc stability difficult using conventional frame based approaches. In this study, arc dynamics are modeled as a sequence of latent operational regimes within a probabilistic state-space framework. The welding current signal is transformed into a time-frequency domain using Short-Time Fourier Transform (STFT), and a set of physically meaningful spectral descriptors, including energy, entropy, and centroid, is extracted to construct the observation sequence. A Hidden Markov Model (HMM) is employed to capture temporal dependencies and estimate the evolution of arc states. The analysis reveals three dominant regimes, transient, stable, and extinction, with a clear monotonic increase in spectral energy and a corresponding decrease in entropy, indicating reduced variability under stable conditions. Despite partial overlap in the feature space, the inferred state sequence exhibits strong temporal coherence, supported by high state persistence and low transition rates. These findings highlight the limitations of static classification and emphasize the importance of temporal modeling. The proposed framework provides an interpretable and physically consistent representation of arc behavior, enabling more realistic monitoring and analysis of stability dynamics in welding processes.

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.

Desk Editor's Note private letter to a colleague

The HMM on STFT features from welding current produces coherent state sequences with sensible feature trends, but the physical labels for those states rest on post-hoc interpretation rather than independent checks.

read the letter

The paper fits a standard HMM to three spectral descriptors extracted from STFT of welding current signals and reports three regimes it labels transient, stable, and extinction. The states show high self-transition probabilities and the expected monotonic shifts in energy and entropy, which is consistent with reduced variability in stable arcs. That temporal structure is the main concrete result and it does improve on purely frame-by-frame classification by construction. The authors also note partial overlap in the feature space yet still recover usable persistence, which is a fair observation about why static classifiers fall short here. The work is a straightforward domain application rather than a methodological advance. The free choice of three states and the assignment of physical meanings after seeing the trends are the clear soft spots. No external anchor such as simultaneous voltage traces, high-speed video, or expert-labeled segments is mentioned to confirm that the inferred transitions match actual arc physics instead of the clustering induced by the observation model. The abstract supplies no accuracy numbers, cross-validation scores, or comparison against simpler baselines, so the strength of the physical-consistency claim stays qualitative. Readers working on process monitoring in manufacturing would find the pipeline useful as an example of bringing temporal models to arc signals. The paper is coherent on its own terms and shows honest engagement with the data, so it deserves a serious referee who can ask for the missing validation experiments and sensitivity checks on the number of states. I would send it out for review rather than desk-reject it.

Referee Report

3 major / 0 minor

Summary. The paper proposes a Hidden Markov Model (HMM) to model non-stationary arc dynamics in electric arc welding from the current signal. The signal is transformed via Short-Time Fourier Transform (STFT) and reduced to three spectral descriptors (energy, entropy, centroid) that form the observation sequence. An HMM with three hidden states is trained to infer a sequence of latent regimes labeled post hoc as transient, stable, and extinction. The central claims are that these regimes exhibit monotonic trends (increasing energy, decreasing entropy) consistent with reduced variability under stable conditions, that the state sequence shows high temporal coherence via high self-transition probabilities and low transition rates, and that the framework supplies a physically interpretable alternative to static classifiers.

Significance. If the physical correspondence of the inferred states can be independently verified, the work would demonstrate the utility of HMMs for capturing temporal structure in welding signals where frame-wise classifiers fail. The emphasis on monotonic feature trends and state persistence provides a concrete, falsifiable signature that could be tested against additional sensors. However, the absence of quantitative validation metrics, cross-validation, or external grounding currently limits the strength of these claims.

major comments (3)

[Abstract] Abstract: The assertion of three physically distinct regimes with 'clear monotonic increase in spectral energy and corresponding decrease in entropy' rests entirely on qualitative description. No quantitative metrics (e.g., Spearman rank correlation, p-values for trend tests, or effect sizes) or cross-validation results are supplied to support monotonicity or regime separation.
[Abstract] Abstract: The paper acknowledges 'partial overlap in the feature space' yet concludes that the HMM states capture operational regimes via temporal coherence. No overlap quantification (e.g., Bhattacharyya distance, confusion rates between states, or sensitivity to the choice of three states) is reported, leaving open the possibility that the observed persistence is an artifact of the HMM self-transition bias rather than arc physics.
[Abstract] Abstract: State labels (transient, stable, extinction) are assigned post hoc to the learned latent sequence without reference to independent physical anchors such as simultaneous voltage waveforms, high-speed video, or expert annotations. High self-transition probabilities are a direct modeling consequence and do not, by themselves, establish physical correspondence.

Simulated Author's Rebuttal

3 responses · 0 unresolved

Thank you for the constructive review. The comments highlight opportunities to strengthen the quantitative support and clarify the physical grounding of the inferred states. We address each point below and have revised the manuscript accordingly.

read point-by-point responses

Referee: [Abstract] Abstract: The assertion of three physically distinct regimes with 'clear monotonic increase in spectral energy and corresponding decrease in entropy' rests entirely on qualitative description. No quantitative metrics (e.g., Spearman rank correlation, p-values for trend tests, or effect sizes) or cross-validation results are supplied to support monotonicity or regime separation.

Authors: We agree that quantitative metrics strengthen the claims. The revised manuscript now includes Spearman rank correlation coefficients and p-values for the monotonic trends in spectral energy and entropy across the decoded state sequences. We have also added k-fold cross-validation results for the HMM to quantify the stability of the three-regime separation. revision: yes
Referee: [Abstract] Abstract: The paper acknowledges 'partial overlap in the feature space' yet concludes that the HMM states capture operational regimes via temporal coherence. No overlap quantification (e.g., Bhattacharyya distance, confusion rates between states, or sensitivity to the choice of three states) is reported, leaving open the possibility that the observed persistence is an artifact of the HMM self-transition bias rather than arc physics.

Authors: We have added explicit quantification of state overlap. The revision reports Bhattacharyya distances between the Gaussian emission distributions of the three states and includes a sensitivity analysis varying the number of states while tracking persistence metrics. To address potential self-transition bias, we compare the learned transition matrix against a null model with uniform random transitions. revision: yes
Referee: [Abstract] Abstract: State labels (transient, stable, extinction) are assigned post hoc to the learned latent sequence without reference to independent physical anchors such as simultaneous voltage waveforms, high-speed video, or expert annotations. High self-transition probabilities are a direct modeling consequence and do not, by themselves, establish physical correspondence.

Authors: Labeling is post hoc but is motivated by the observed feature trends aligning with established arc-welding physics (high variability at ignition, reduced variability in steady operation, and decay at extinction). The revised discussion section explicitly states this interpretive basis and the limitations of current-only data. Self-transition probabilities are data-estimated rather than imposed; their high values reflect the slow evolution of regimes. We acknowledge that multimodal anchors (voltage/video) were unavailable in the original experiments and have added a limitations paragraph on the need for such validation. revision: partial

Circularity Check

0 steps flagged

No circularity: standard HMM pipeline with post-hoc interpretation

full rationale

The paper extracts spectral features (energy, entropy, centroid) via STFT from the welding current, trains a standard HMM on the resulting observation sequence, infers the latent state sequence, and then reports observed trends (monotonic energy increase, entropy decrease) across the three states to assign labels (transient/stable/extinction). This chain contains no self-definitional equations, no fitted parameters renamed as predictions, and no load-bearing self-citations or ansatzes. The state labels and coherence claims are interpretive summaries of data-driven outputs rather than quantities forced by construction from the model inputs. The framework is therefore self-contained.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central claim rests on standard HMM assumptions plus the choice of three spectral features and three hidden states; the regimes themselves are data-derived rather than independently validated physical constructs.

free parameters (2)

Number of hidden states
Fixed at three to match the reported transient-stable-extinction regimes; value chosen to produce the described state sequence.
HMM transition and emission parameters
Learned from the observation sequences via standard Baum-Welch or Viterbi training; not reported as fixed a priori.

axioms (2)

domain assumption Arc dynamics obey the Markov property: future state depends only on current state, not on earlier history.
Core modeling assumption required for any HMM application.
domain assumption The three chosen spectral descriptors capture the physically relevant variability in arc behavior.
Invoked when mapping feature sequences to latent regimes.

invented entities (1)

Three latent arc regimes (transient, stable, extinction) no independent evidence
purpose: To label the hidden states discovered by the HMM
Postulated to give physical meaning to the inferred state sequence; no independent physical measurement or external validation cited in abstract.

pith-pipeline@v0.9.0 · 5496 in / 1588 out tokens · 48549 ms · 2026-05-09T20:27:06.674777+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

30 extracted references · 28 canonical work pages

[1]

Tukahiruwa and C

G. Tukahiruwa and C. Wandera, ”Influence of process parameters in gas- metal arc welding (GMAW) of carbon steels,” inWelding of Metallic Materials, IntechOpen, 2023, doi: 10.5772/intechopen.1002730

work page doi:10.5772/intechopen.1002730 2023
[2]

Zhang, L

L. Zhang, L. Chen, B. Jia, S. Yang, M. Pan, and H. Pan, ”Interpretable arc stability monitoring via Physics-Guided Data Programming in robotic gas metal arc welding,”Journal of Manufacturing Processes, vol. 166, pp. 352–369, May 2026, doi: 10.1016/j.jmapro.2026.03.049

work page doi:10.1016/j.jmapro.2026.03.049 2026
[3]

L. Chen, M. Liu, X. Liu, Z. Yu, P. Duan, Y . Liu, M. Fa, and B. Zheng, ”Bidirectional LSTM-based compensation of potential-asymmetry induced errors in double probe plasma diagnostics,”Journal of Physics D: Applied Physics, vol. 59, no. 3, p. 035206, Jan. 2026, doi: 10.1088/1361- 6463/ae357e

work page doi:10.1088/1361- 2026
[4]

T. C. Akinci, ”Time-frequency analysis of the current measurement by hall effect sensors for electric arc welding machine,”Mechanika, vol. 85, no. 5, pp. 66–71, 2010

2010
[5]

de Alteriis, R

G. de Alteriis, R. Schiano Lo Moriello, A. Astarita, and A. T. Silvestri, ”A coherence-driven method for instability frequency identification and uncertainty evaluation in friction stir welding,”Measurement, vol. 275, p. 121385, May 2026, doi: 10.1016/j.measurement.2026.121385

work page doi:10.1016/j.measurement.2026.121385 2026
[6]

S. Kang, T. Yang, S. Jeon, M. Kang, and J. Shin, ”Accurate real-time weld shape monitoring in laser welding using spectral features and a deep neural network,”Measurement, vol. 270, p. 120903, Apr. 2026, doi: 10.1016/j.measurement.2026.120903

work page doi:10.1016/j.measurement.2026.120903 2026
[7]

Akgun, A

O. Akgun, A. Akan, H. Demir, and T. C. Akinci, ”Analysis of Gait Dy- namics of ALS Disease and Classification of Artificial Neural Networks,” Tehniˇcki vjesnik, vol. 25, no. S1, pp. 183–187, 2018. doi: 10.17559/TV- 20171011153544

work page doi:10.17559/tv- 2018
[8]

Taskin, S

S. Taskin, S. Seker, M. Karahan, and T. C. Akinci, ”Spectral analysis for current and temperature measurements in power cables,”Electric Power Components and Systems, vol. 37, no. 4, pp. 415–426, 2009. doi: 10.1080/15325000802599383

work page doi:10.1080/15325000802599383 2009
[9]

Khoshnaw, I

F. Khoshnaw, I. Krivtsun, and V . Korzhyk, ”Arc welding methods,” in Welding of Metallic Materials: Methods, Metallurgy, and Performance, Elsevier, 2023, pp. 37–71, doi: 10.1016/B978-0-323-90552-7.00004-3

work page doi:10.1016/b978-0-323-90552-7.00004-3 2023
[10]

Swierczynska, A

A. Swierczynska, A. Janeczek, C. Pandey, et al., ”A bibliometric review of A-TIG welding: unveiling global research trends,”International Journal of Advanced Manufacturing Technology, vol. 143, pp. 1367–1387, Mar. 2026, doi: 10.1007/s00170-026-17474-2

work page doi:10.1007/s00170-026-17474-2 2026
[11]

T. C. Akinci, H. S. Nogay, and G. Gokmen, ”Determination of optimum operation cases in electric arc welding machine using neural network,” Journal of Mechanical Science and Technology, vol. 25, no. 4, pp. 1003– 1010, 2011. doi: 10.1007/s12206-011-0202-9

work page doi:10.1007/s12206-011-0202-9 2011
[12]

H. S. Nogay and T. C. Akinci, ”Classification of operation cases in electric arc welding machine by using deep convolutional neural networks,”Neural Computing and Applications, vol. 33, pp. 6657–6670,
[13]

doi: 10.1007/s00521-020-05443-4

work page doi:10.1007/s00521-020-05443-4
[14]

Garc ´ıa Rodr´ıguez, C

A. Garc ´ıa Rodr´ıguez, C. C. Barriga Castellanos, J. E. Rocha-Gonzalez, and E. B ´arcenas, ”Time–frequency and spectral analysis of welding arc sound for automated SMAW quality classification,”Sensors, vol. 26, no. 8, p. 2357, 2026, doi: 10.3390/s26082357

work page doi:10.3390/s26082357 2026
[15]

P. Kah, G. O. Edigbe, B. Ndiwe, et al., ”Assessment of arc stability features for selected gas metal arc welding conditions,”SN Applied Sciences, vol. 4, p. 268, 2022, doi: 10.1007/s42452-022-05150-5

work page doi:10.1007/s42452-022-05150-5 2022
[16]

Capezza, A

C. Capezza, A. Lepore, and K. Paynabar, ”Stream-based active learning for process monitoring,”Technometrics, vol. 68, no. 1, pp. 159–171, 2026, doi: 10.1080/00401706.2025.2561744

work page doi:10.1080/00401706.2025.2561744 2026
[17]

Z. Wang, S. He, X. Zhao, and M. Zhen, ”Condition-based maintenance for production systems: Inferring degradation states from quality charac- teristics,”IISE Transactions, 2026, doi: 10.1080/24725854.2026.2628678

work page doi:10.1080/24725854.2026.2628678 2026
[18]

Griffin and J

D. Griffin and J. Lim, ”Signal estimation from modified short- time Fourier transform,”IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. 32, no. 2, pp. 236–243, Apr. 1984, doi: 10.1109/TASSP.1984.1164317

work page doi:10.1109/tassp.1984.1164317 1984
[19]

J. K. Hammond and P. R. White, ”The analysis of non-stationary signals using time-frequency methods,”Journal of Sound and Vibration, vol. 190, no. 3, pp. 419–447, 1996, doi: 10.1006/jsvi.1996.0072

work page doi:10.1006/jsvi.1996.0072 1996
[20]

Sucic, N

V . Sucic, N. Saulig, and B. Boashash, ”Analysis of local time-frequency entropy features for nonstationary signal components time supports de- tection,”Digital Signal Processing, vol. 34, pp. 56–66, Nov. 2014, doi: 10.1016/j.dsp.2014.07.013

work page doi:10.1016/j.dsp.2014.07.013 2014
[21]

G. Luo, D. Zhang, Y . Koh, K. Ng, and W. Leong, ”Time–frequency entropy-based partial-discharge extraction for nonintrusive measurement,” IEEE Transactions on Power Delivery, vol. 27, no. 4, pp. 1919–1927, Oct. 2012, doi: 10.1109/TPWRD.2012.2200911

work page doi:10.1109/tpwrd.2012.2200911 1919
[22]

Eric Wong, Vidroha Debroy, and Dianxiang Xu

B. Ghoraani and S. Krishnan, ”Time–frequency matrix feature extraction and classification of environmental audio signals,”IEEE Transactions on Audio, Speech, and Language Processing, vol. 19, no. 7, pp. 2197–2209, Sep. 2011, doi: 10.1109/TASL.2011.2118753

work page doi:10.1109/tasl.2011.2118753 2011
[23]

L. R. Rabiner, ”A tutorial on hidden Markov models and selected applications in speech recognition,”Proceedings of the IEEE, vol. 77, no. 2, pp. 257–286, Feb. 1989, doi: 10.1109/5.18626

work page doi:10.1109/5.18626 1989
[24]

P. J. Rousseeuw, ”Silhouettes: A graphical aid to the interpretation and validation of cluster analysis,”Journal of Computational and Ap- plied Mathematics, vol. 20, pp. 53–65, Nov. 1987, doi: 10.1016/0377- 0427(87)90125-7

work page doi:10.1016/0377- 1987
[25]

Pavlovic, B

V . Pavlovic, B. J. Frey, and T. S. Huang, ”Time-series classification using mixed-state dynamic Bayesian networks,” inProc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR), Fort Collins, CO, USA, 1999, pp. 609–615, doi: 10.1109/CVPR.1999.784983. 11

work page doi:10.1109/cvpr.1999.784983 1999
[26]

Haykin and D

S. Haykin and D. J. Thomson, ”Signal detection in a nonstationary environment reformulated as an adaptive pattern classification problem,” Proceedings of the IEEE, vol. 86, no. 11, pp. 2325–2344, Nov. 1998, doi: 10.1109/5.726792

work page doi:10.1109/5.726792 1998
[27]

S. H. Holan and N. Ravishanker, ”Time series clustering and classifi- cation via frequency domain methods,”WIREs Computational Statistics, vol. 10, no. 6, p. e1444, 2018, doi: 10.1002/wics.1444

work page doi:10.1002/wics.1444 2018
[28]

Kohlmorgen, ”Tracking and visualization of changes in high- dimensional non-parametric distributions,” inProc

J. Kohlmorgen, ”Tracking and visualization of changes in high- dimensional non-parametric distributions,” inProc. IEEE Workshop on Machine Learning for Signal Processing (MLSP), Sao Luis, Brazil, 2004, pp. 203–212, doi: 10.1109/MLSP.2004.1422975

work page doi:10.1109/mlsp.2004.1422975 2004
[29]

Sin and J

B. Sin and J. H. Kim, ”Nonstationary hidden Markov model,”Signal Processing, vol. 46, no. 1, pp. 31–46, Sep. 1995, doi: 10.1016/0165- 1684(95)00070-T

work page doi:10.1016/0165- 1995
[30]

Basseville and A

M. Basseville and A. Benveniste, ”Sequential segmentation of nonsta- tionary digital signals using spectral analysis,”Information Sciences, vol. 29, no. 1, pp. 57–73, Feb. 1983, doi: 10.1016/0020-0255(83)90009-9

work page doi:10.1016/0020-0255(83)90009-9 1983