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REVIEW 2 major objections 6 minor 25 references

Clock-linear RUL labels disagree with vibration; a three-stage degradation-state target fits the measured reference better and can be learned on held-out bearings.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-31 17:24 UTC pith:PBKIL375

load-bearing objection Honest target-vs-predictor separation with a real but descriptive IMS shape gain; useful hygiene, not a new RUL law. the 2 major comments →

arxiv 2607.28115 v1 pith:PBKIL375 submitted 2026-07-30 eess.SP cs.SYeess.SY

When Linear RUL Labels Disagree with Vibration Degradation: A Stage-Aware Target and Dual-Scale Predictor Evaluated on XJTU-SY and IMS

Behrad Mousaei Shir-Mohammad , Seyed Reza Tavakoli , Mohammad Mohammadi , Siavash Ahmadi , Babak Hossein Khalaj , Mohammad Hossein Rohban This is my paper
classification eess.SP cs.SYeess.SY
keywords bearing prognosticsremaining useful lifehealth indicatortarget designvibration measurementTransformerdata fusionstage-aware degradation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Bearing remaining-life work usually treats the training label as fixed, most often a straight line that falls with clock time. Vibration often stays nearly flat for a long stretch and then worsens quickly near failure, so that label can force a model to invent degradation the sensor has not yet shown. This paper splits the problem: first build a vibration-based health reference, mark early–middle–late stages, and fit a continuous linear–quadratic–exponential degradation-state target; then train compact sequence models to predict that target from past features only. On three official IMS failed-bearing runs the stage-aware curve beats the best anchored linear fit to the same reference by roughly 10% RMSE and 15% MAE on average. On a strict XJTU-SY hold-out the fused predictor reaches RMSE 0.0608 and R² 0.9617. The authors present this as a target-validity framework, not a universal physical law or a cure for cross-domain shift.

Core claim

For the evaluated vibration-derived degradation references, a continuous three-stage linear–quadratic–exponential target describes remaining-life state better than the strongest comparable global linear target, and that stage-aware target is learnable from causal feature sequences on bearings excluded from every fitted development step.

What carries the argument

The stage-aware degradation-state target: an oriented PCA health indicator is clustered into chronological early–middle–late stages, then fitted with a continuous linear–quadratic–exponential curve to the complementary normalized indicator, and compared against a best anchored linear fit to the same reference.

Load-bearing premise

The whole case rests on treating a smoothed, oriented first principal component of screened vibration features, forced into three contiguous stages, as a faithful enough picture of real degradation that fitting curves to it tests whether labels are adequate.

What would settle it

On additional complete failed-bearing runs from a different rig, check whether the same stage-aware curve still cuts RMSE and MAE versus the best anchored linear fit to that run’s vibration health reference, and whether blocked-bootstrap intervals for the squared-error gain stay above zero.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • RUL benchmarks should report target-shape checks against a vibration-derived reference, not only predictor error under a fixed clock-linear label.
  • Strong sequence models cannot fix a mismatched label; target design must be audited separately from architecture.
  • A better condition-consistent target still leaves cross-run and cross-fault shift unresolved, so transfer methods remain necessary.
  • Deployed systems should treat the output as a normalized degradation-state score that later needs machine-specific time calibration and uncertainty checks.

Where Pith is reading between the lines

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

  • If target audits become standard, many published RUL gains may shrink once models are scored against condition-consistent labels rather than 1−u alone.
  • Online stage detection without full-run hindsight is the practical bottleneck between this retrospective supervision recipe and live maintenance use.
  • Comparing LQE against monotone splines or change-point families on the same HI reference would show whether three fixed pieces are special or just one workable nonlinear family.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The manuscript argues that clock-linear RUL labels can disagree with vibration-observed degradation and therefore separates target construction from prediction. A development-only pipeline builds an oriented PCA health indicator, repairs k-means stages into chronological early–middle–late segments, and fits a continuous linear–quadratic–exponential degradation-state target Rb(u) to the complementary normalized HI reference zb. Causal CNN–LSTM and Transformer branches learn this target from feature sequences, with validation-fitted two-expert OWA fusion. On a bearing-wise XJTU-SY hold-out (Bearings 1–4 development, Bearing 5 test per condition, excluded from all fitted steps), fused RMSE/MAE/R² are 0.0608/0.0392/0.9617, dominated by the Transformer. Independently, on three documented IMS failed-bearing runs, the stage-aware curve reduces RMSE by 3.6–18.2% (mean 10.2%) and MAE by 3.1–31.1% (mean 15.0%) versus the best anchored linear fit to the same zb, with conservative ΔBIC 128.8–368.1 favoring LQE, while moving-block bootstrap intervals cross zero. The authors explicitly limit claims to descriptive target adequacy and learnability, not a universal nonlinear TTF law or robust cross-domain prediction.

Significance. If the bounded claims hold, the paper’s main value is methodological rather than architectural: it treats the RUL label as a testable measurement choice, compares stage-aware and fitted-linear representations against a shared vibration-derived reference on a second rig, and keeps target validity, held-out learnability, and transfer as separate research questions with matching claim boundaries (Table 3). Strengths include leakage-audited development-only preprocessing, Bearing-5 exclusion from normalization/screening/training/early-stopping/OWA, a stricter linear baseline than 1−u (Eqs. 14–15), conservative five-parameter BIC, dependence-aware bootstrap with open non-significance, and transparent negative exploratory IMS leave-one-run-out results. That honesty and protocol design are useful for Measurement/prognostics practice even though n=3 IMS runs and non-significant blocked bootstrap keep RQ1 descriptive. The dual-scale OWA predictor is secondary; the contribution is a target-validity framework, not SOTA architecture dominance.

major comments (2)
  1. [§2.4–2.6, Table 6, Fig. 8] §2.4–2.6 and Table 6: RQ1’s reference zb is built from the same pipeline’s oriented PCA-HI, smoothing, three-stage k-means with chronological repair, and end-of-run min–max normalization (Eqs. 7–10). Relative gains of LQE vs Rlin(a*) on that shared zb are well-specified and not tautological, but they still test functional form against a surrogate the authors define. Stagewise results already show non-uniform superiority (e.g., IMS2-B1 middle-stage RMSE worse by 14.5%). A load-bearing sensitivity check is needed: alternative HIs (e.g., RMS/kurtosis-only, different q, unsmoothed, or monotone composite), two- vs four-stage repairs, and at least one other parametric family (logistic/Gompertz/monotone spline) on the same three official runs, reporting whether mean RMSE/MAE gains and sign of ΔBIC persist. Without this, “stage-dependent targets better describe the evaluated vibration-derived de
  2. [§5 Limitations; Data Availability] §5 (Limitations) and Data Availability: the arXiv package omits final selected feature list, window/step, smoothing span, dropout/weight-decay, sequence length, seeds, and numerical OWA weights. For a measurement-oriented target-validity paper whose XJTU numbers and IMS fits are central evidence, these are not optional extras—they are part of the fitted model (§2.3). Either release a persistent-identifier artifact bundle with frozen preprocessing objects, stage boundaries, and exact configs, or demote quantitative XJTU/IMS point estimates to illustrative status until reproduction objects are available. This is fixable but currently load-bearing for verifiability.
minor comments (6)
  1. [§3.3, Table 9–10] Table 9 vs text: OWA MAE equals Transformer MAE at four decimals (0.0392) while MSE/R² improve only slightly; state explicitly that fusion gain is negligible on MAE and avoid language that could be read as strong ensemble benefit.
  2. [§2.7] §2.7: random 80/20 window-level validation within development bearings is correctly labeled optimistic; consider adding one blocked/group validation metric in the supplement so early-stopping behavior is auditable.
  3. [Figs. 10–12] Figs. 10–12: residual envelopes are descriptive only—add a one-line caption reminder that they are not calibrated prediction intervals (already noted in §5).
  4. [§2.5–2.6, Eq. (11)] Eq. (11): clarify whether u1, u2 are held fixed from clustering during least-squares for α,β,γ or jointly optimized; the conservative BIC counts five parameters, but the fitting paragraph should match that accounting exactly.
  5. [Table 5, Fig. 9] Table 5 / exploratory extended run: keep the strong 56.4% RMSE figure strictly out of abstract/confirmatory aggregates (already done); ensure Fig. 9 caption remains the sole home for that result.
  6. [§2.7–2.8] Minor prose: standardize “OWA” vs “OW A” spacing; fix “V alidation” line-break artifacts in §2.7–2.8.

Circularity Check

2 steps flagged

RQ1 ‘target adequacy’ is largely goodness-of-fit of a stage-aligned LQE ansatz to a self-built HI reference (zb), not an independent degradation measurement—real GOF content remains, but the central shape claim is partly by construction.

specific steps
  1. self definitional [§2.4–2.6, Eqs. (7)–(11), (14)–(16); RQ1 / Table 6 / Fig. 8]
    "hb(t)=PCA1({fj(t)}q_j=1) ... ehb(u)=(hb(u)−min hb)/(max hb−min hb+ε), and define the complementary degradation reference zb(u)=1−ehb(u) ... Rb(u)=1−αu [S1]; 1−αu−β(u−u1)2 [S2]; Rb(u2)exp[−γ(u−u2)] [S3]. The transition locations u1 and u2 are obtained from the repaired stage sequence. Parameters α,β,γ≥0 are fitted by least squares to zb(u) ... The main target-shape comparison is therefore between Rlin(u;a⋆) and the three-stage curve in Eq. (11) ... Thus, stage-dependent targets better describe the evaluated vibration-derived degradation states"

    The ‘vibration-derived degradation reference’ zb is defined from the paper’s own oriented PCA-HI (and end-of-run min–max). Stage boundaries used inside Rb are obtained by clustering/repairing that same HI. Rb is then LS-fitted to zb. Claiming the stage-aware target better describes that reference is therefore largely claiming that a flexible, stage-tied fit to the pipeline’s surrogate is closer to the surrogate than a global line—i.e., the quantity being validated is constructed from the same objects that define the proposed target, not an external physical RUL or independent wear measurement. Relative GOF can still favor either form, so this is partial self-definitional circularity, not a full identity.

  2. fitted input called prediction [§2.5 Eq. (11); §2.6 Eqs. (14)–(15); Abstract / §3.2 IMS target-shape results]
    "Against the best anchored linear fit to the same vibration-derived reference, the stage-aware curve reduces RMSE by 3.6–18.2% and MAE by 3.1–31.1%; mean reductions are 10.2% and 15.0%. Conservative BIC differences of 128.8–368.1 favour the stage-aware representation"

    Both Rlin(a⋆) and Rb(α,β,γ,u1,u2) are fitted to the identical within-run zb; u1,u2 are taken from the HI stage procedure and BIC still assigns them as effective parameters. The reported ‘reductions’ and ΔBIC are in-sample descriptive superiority of a higher-capacity, stage-aligned parameterization over a one-parameter anchored line on a reference the authors built—not out-of-sample prediction of an independent label. The manuscript mostly labels this correctly as descriptive target-shape assessment, but the abstract’s ‘better describe … degradation states’ framing still presents fitted adequacy on a self-defined surrogate as the headline scientific result.

full rationale

The paper’s strongest claim is descriptive: on three IMS runs, a continuous linear–quadratic–exponential curve fits the same vibration-HI-derived reference zb better than the best anchored linear fit (RMSE/MAE gains, ΔBIC). That comparison is not a pure tautology—both competitors are scored against identical zb, so a more flexible form can lose if zb is nearly linear, and the authors report blocked-bootstrap intervals that cross zero and limit the claim to descriptive target shape. Circularity is only partial: zb is defined as 1 minus min–max-normalized oriented PCA of the paper’s own screened features; chronological three-stage labels are obtained by k-means on that same HI; Rb is then least-squares-fitted to zb with transitions u1,u2 taken from those stages. Thus ‘stage-aware better describes the vibration-derived degradation state’ reduces largely to ‘a three-piece, stage-tied fit to our HI surrogate beats a one-parameter line on that same surrogate.’ RQ2 (XJTU held-out learnability of the constructed target) and OWA fusion are ordinary supervised evaluation against a retrospective label and are not circular in the strong sense. No load-bearing self-citation, uniqueness import, or renamed theorem chain supports the central claim. Score 4 reflects one structural fitted-input/self-definitional step around RQ1 while leaving independent GOF content and honest caveats intact.

Axiom & Free-Parameter Ledger

7 free parameters · 5 axioms · 2 invented entities

The load-bearing story rests on treating a constructed vibration health indicator and a three-stage phenomenological curve as the right reference for “degradation state,” then judging labels and predictors against that reference. Free parameters enter at feature screening, HI smoothing, stage cuts, LQE coefficients, linear anchor slope, network training, and OWA weights. Domain assumptions include three chronological stages, PCA orientation by Spearman time correlation, and retrospective full-run normalization being acceptable for supervision. The main invented object is the specific continuous LQE degradation-state target plus the audited development-only pipeline—not a new physical particle or force.

free parameters (7)
  • LQE coefficients α, β, γ (≥0) = Per-run LS fits (not globally tabulated)
    Least-squares fit per run to z_b with continuity and optional slope penalty; central shape comparison depends on these fitted values.
  • Stage boundaries u1, u2 = e.g. IMS1-B3: 0.074, 0.845; IMS1-B4: 0.077, 0.748; IMS2-B1: 0.584, 0.842
    From repaired k-means stages; counted as effective BIC parameters and define the piecewise target.
  • Anchored linear slope a* = Per-run (not listed numerically beyond resulting RMSE/MAE)
    Argmin of MSE of clip(1−a u) to z_b over a∈[0,2.5]; defines the strong linear baseline.
  • OWA weights w1*, w2* = Not numerically reported in manuscript
    Closed-form validation least squares on sorted branch predictions; frozen for test fusion metrics.
  • Feature-screening thresholds τvar, τρ, Crob threshold; q top features = IMS: 10 features, redundancy 0.98; others not fully specified
    Development-only filters determine the descriptor bank entering PCA-HI and models.
  • HI smoothing fraction / min stage fraction = 0.035 smoothing; 0.06 min stage fraction (IMS)
    Control stage geometry and reference smoothness; IMS uses 0.035 and 0.06.
  • Window length W, step S, sequence length L, training hyperparameters = Partial: Adam lr 0.001, batch 32, patience 10; W/S/L/dropout incomplete
    Affect features, temporal context, and reported XJTU errors; several left to “final experiment configuration.”
axioms (5)
  • domain assumption An oriented PCA1 health indicator from screened multi-domain vibration features is a valid monotone proxy for degradation state within a run.
    §2.3–2.4; all target comparisons and supervision derive from this HI and its normalization.
  • ad hoc to paper Bearing degradation is adequately summarized by exactly three chronological stages after k-means and contiguous repair.
    §2.4 explicitly calls this pragmatic, not mechanistic fault physics; the LQE target structure depends on it.
  • ad hoc to paper A continuous linear–quadratic–exponential piecewise map is an appropriate phenomenological form for the normalized remaining-life state.
    Eq. (11); chosen functional family for RQ1/RQ2 rather than derived from first principles.
  • domain assumption Retrospective full-run labels may supervise causal predictors if no future windows enter model inputs and test bearings are excluded from fitted development steps.
    §2.7 causality rules; standard in run-to-failure RUL but load-bearing for interpreting XJTU metrics as learnability only.
  • standard math Standard signal-processing and learning tools (Welch PSD, wavelets, PCA, k-means, CNN–LSTM, Transformer, Adam, OWA) behave as usual.
    Used throughout §2 without novel theoretical claims about these tools.
invented entities (2)
  • Continuous linear–quadratic–exponential degradation-state target Rb(u) no independent evidence
    purpose: Replace clock-linear RUL labels with a stage-dependent supervised surrogate aligned to vibration HI.
    Defined in Eq. (11) with continuity and clipping; central object of RQ1–RQ2.
  • Development-only stage-aware target + dual-scale OWA predictor pipeline no independent evidence
    purpose: Audit leakage, separate target validity from prediction, fuse local and long-context experts.
    End-to-end framework in §2 and Fig. 1/7; evaluation protocol is part of the contribution.

pith-pipeline@v1.2.0-daily-grok45 · 22235 in / 4510 out tokens · 91457 ms · 2026-07-31T17:24:02.973002+00:00 · methodology

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read the original abstract

Remaining useful life (RUL) studies commonly treat the label as fixed, although clock-linear labels may decline while measured vibration remains nearly stable and then changes rapidly near failure. We separate target design from prediction. A development-only pipeline constructs an oriented vibration health indicator, identifies chronological early, middle, and late stages, and fits a continuous linear-quadratic-exponential degradation-state target. A compact CNN-LSTM and Transformer learn the target from causal feature sequences, and validation-fitted Ordered Weighted Averaging combines their outputs. In a bearing-wise XJTU-SY hold-out, all bearings ending in 5 are excluded from fitted preprocessing, training, early stopping, and fusion. The fused predictor obtains an RMSE of 0.0608, an MAE of 0.0392, and an R-squared value of 0.9617, with the Transformer providing most of the accuracy. Target shape is assessed independently on three documented IMS failed-bearing trajectories. Against the best anchored linear fit to the same vibration-derived reference, the stage-aware curve reduces RMSE by 3.6-18.2% and MAE by 3.1-31.1%; the mean reductions are 10.2% and 15.0%, respectively. Conservative BIC differences of 128.8-368.1 favor the stage-aware representation, whereas moving-block bootstrap intervals cross zero. Thus, stage-dependent targets better describe the evaluated vibration-derived degradation states, but the evidence remains descriptive because only three official IMS runs are available. The study establishes a measurement-oriented target-validity framework, not a universal nonlinear law for physical time-to-failure or robust cross-domain prediction.

Figures

Figures reproduced from arXiv: 2607.28115 by Babak Hossein Khalaj, Behrad Mousaei Shir-Mohammad, Mohammad Hossein Rohban, Mohammad Mohammadi, Seyed Reza Tavakoli, Siavash Ahmadi.

Figure 1
Figure 1. Figure 1: Study logic from raw vibration to evidence. Development bearings determine preprocessing, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Example horizontal and vertical vibration signals from the XJTU-SY bearing dataset. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Example retained feature with a monotone, stage-consistent trend after smoothing. [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Chronologically ordered life-stage segmentation obtained from the oriented, smoothed [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Continuous degradation-informed target with linear, quadratic, and exponential segments. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Illustration of the trade-off between local feature noise and trend smoothness for different [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Validation-based OWA fusion procedure for combining the CNN-LSTM and Transformer [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: External IMS target-shape assessment on the three documented failed-bearing trajectories. [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Exploratory analysis of the 6,324-snapshot extended directory. The result strongly favours [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: RUL prediction for Bearing1 5 with empirical residual envelope and stage-boundary markers. 3.4 RQ3: Added Value of Fusion and Limits Under Distribution Shift Exploratory cross-run target-training ablation To test whether target choice affects prediction rather than curve fitting alone, a leave-one-run-out experiment trained the same CNN–LSTM/Transformer/OWA pipeline with either the stage-aware target or t… view at source ↗
Figure 11
Figure 11. Figure 11: RUL prediction for Bearing2 5 with empirical residual envelope and stage-boundary markers [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: RUL prediction for Bearing3 5 with empirical residual envelope and stage-boundary markers. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗

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Reference graph

Works this paper leans on

25 extracted references · 8 canonical work pages · 1 internal anchor

  1. [1]

    Conformal prediction: A gentle introduction,

    A. N. Angelopoulos and S. Bates, “Conformal prediction: A gentle introduction,”Foundations and Trends in Machine Learning, vol. 16, no. 4, pp. 494–591, 2023, doi: 10.1561/2200000101

    doi:10.1561/2200000101 2023

  2. [2]

    Feature learning for bearing prognos- tics: A comprehensive review of machine/deep learning methods, challenges, and opportunities,

    A. Ayman, A. Onsy, O. Attallah, H. Brooks, and I. Morsi, “Feature learning for bearing prognos- tics: A comprehensive review of machine/deep learning methods, challenges, and opportunities,” Measurement, vol. 245, art. 116589, 2025, doi: 10.1016/j.measurement.2024.116589

    arXiv 2025

  3. [3]

    Uncertainty-aware prognostics of ball bearings using physics-based simulation and conditional normalizing flows,

    A. Bott, B. Liu, L. Nuding, J. Wachsmuth, A. Puchta, and J. Fleischer, “Uncertainty-aware prognostics of ball bearings using physics-based simulation and conditional normalizing flows,” IEEE Access, vol. 14, pp. 20100–20110, 2026, doi: 10.1109/ACCESS.2026.3661174

    arXiv 2026

  4. [4]

    Prognostics and remaining useful life prediction of machinery: Advances, opportunities and challenges,

    N. Gebraeel, Y. Lei, N. Li, X. Si, and E. Zio, “Prognostics and remaining useful life prediction of machinery: Advances, opportunities and challenges,”Journal of Dynamics, Monitoring and Diagnostics, vol. 2, no. 1, pp. 1–12, 2023, doi: 10.37965/jdmd.2023.148

    work page doi:10.37965/jdmd.2023.148 2023

  5. [5]

    A hybrid prognosis scheme for rolling bearings based on a novel health indicator and nonlinear Wiener process,

    J. Guo, Z. Wang, H. Li, Y. Yang, C.-G. Huang, M. Yazdi, and H. S. Kang, “A hybrid prognosis scheme for rolling bearings based on a novel health indicator and nonlinear Wiener process,”Reli- ability Engineering & System Safety, vol. 245, art. 110014, 2024, doi: 10.1016/j.ress.2024.110014. 26

    arXiv 2024

  6. [6]

    Bearing Data Set,

    J. Lee, H. Qiu, G. Yu, J. Lin, and Rexnord Technical Services, “Bearing Data Set,” IMS, University of Cincinnati, NASA Prognostics Data Repository, NASA Ames Research Center, Moffett Field, CA, USA, 2007. [Online]. Available: NASA PCoE Data Repository. Accessed: Jul. 21, 2026

    2007

  7. [7]

    XJTU-SY rolling element bearing accelerated life test datasets: A tutorial,

    Y. Lei, T. Han, B. Wang, N. P. Li, T. Yan, and J. Yang, “XJTU-SY rolling element bearing accelerated life test datasets: A tutorial,”Journal of Mechanical Engineering, vol. 55, no. 16, pp. 1–6, 2019, doi: 10.3901/JME.2019.16.001

    doi:10.3901/jme.2019.16.001 2019

  8. [8]

    A review on physics-informed data-driven remaining useful life prediction: Challenges and opportunities,

    H. Li, Z. Zhang, T. Li, and X. Si, “A review on physics-informed data-driven remaining useful life prediction: Challenges and opportunities,”Mechanical Systems and Signal Processing, vol. 209, art. 111120, 2024, doi: 10.1016/j.ymssp.2024.111120

    arXiv 2024

  9. [9]

    Dynamic normalized health indicator construction and Bayesian recurrent state estimation for remaining useful life prediction of high-speed bearings in wind turbine drivetrain,

    X. Li, W. Teng, Y. Zhang, D. Peng, and Y. Liu, “Dynamic normalized health indicator construction and Bayesian recurrent state estimation for remaining useful life prediction of high-speed bearings in wind turbine drivetrain,”Measurement, vol. 246, art. 116725, 2025, doi: 10.1016/j.measurement.2025.116725

    arXiv 2025

  10. [10]

    RULSurv: A probabilistic survival-based method for early censoring-aware prediction of remaining useful life in ball bearings

    C. M. Lillelund, F. Pannullo, M. O. Jakobsen, M. Morante, and C. F. Pedersen, “RULSurv: A probabilistic survival-based method for early censoring-aware prediction of remaining useful life in ball bearings,” arXiv:2405.01614v3 [cs.LG], 2025, doi: 10.48550/arXiv.2405.01614

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2405.01614 2025

  11. [11]

    Topology-aware hybrid Wi- Fi/BLE fingerprinting via evidence-theoretic fusion and persistent homology,

    B. Mousaei Shir-Mohammad, B. Moshiri, and A. Yaghmaei, “Topology-aware hybrid Wi- Fi/BLE fingerprinting via evidence-theoretic fusion and persistent homology,” arXiv preprint arXiv:2510.16557, 2025, doi: 10.48550/arXiv.2510.16557

    work page doi:10.48550/arxiv.2510.16557 2025

  12. [12]

    Data-driven prognostic scheme for bearings based on a novel health indicator and gated recurrent unit network,

    Q. Ni, J. C. Ji, and K. Feng, “Data-driven prognostic scheme for bearings based on a novel health indicator and gated recurrent unit network,”IEEE Transactions on Industrial Informatics, vol. 19, no. 2, pp. 1301–1311, 2023, doi: 10.1109/TII.2022.3169465

    arXiv 2023

  13. [13]

    Local enhancing Transformer with temporal con- volutional attention mechanism for bearings remaining useful life prediction,

    H. Peng, B. Jiang, Z. Mao, and S. Liu, “Local enhancing Transformer with temporal con- volutional attention mechanism for bearings remaining useful life prediction,”IEEE Trans- actions on Instrumentation and Measurement, vol. 72, art. 3522312, pp. 1–12, 2023, doi: 10.1109/TIM.2023.3291787

    arXiv 2023

  14. [14]

    A piecewise method for bearing remaining useful life estimation using temporal convolutional networks,

    H. Qiu, Y. Niu, J. Shang, L. Gao, and D. Xu, “A piecewise method for bearing remaining useful life estimation using temporal convolutional networks,”Journal of Manufacturing Systems, vol. 68, pp. 227–241, 2023, doi: 10.1016/j.jmsy.2023.04.002

    work page doi:10.1016/j.jmsy.2023.04.002 2023

  15. [15]

    Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics,

    H. Qiu, J. Lee, J. Lin, and G. Yu, “Wavelet filter-based weak signature detection method and its application on rolling element bearing prognostics,”Journal of Sound and Vibration, vol. 289, no. 4–5, pp. 1066–1090, 2006, doi: 10.1016/j.jsv.2005.03.007

    doi:10.1016/j.jsv.2005.03.007 2006

  16. [16]

    Bearings remaining useful life prediction across equipment-operating conditions based on multisource-multitarget domain adaptation,

    L. Shuang, X. Shen, J. Zhou, H. Miao, Y. Qiao, and G. Lei, “Bearings remaining useful life prediction across equipment-operating conditions based on multisource-multitarget domain adaptation,”Measurement, vol. 236, art. 115026, 2024, doi: 10.1016/j.measurement.2024.115026

    arXiv 2024

  17. [17]

    Remaining useful life prognostics of bearings based on convolution attention networks and enhanced transformer,

    N. Sun, J. Tang, X. Ye, C. Zhang, S. Zhu, S. Wang, and Y. Sun, “Remaining useful life prognostics of bearings based on convolution attention networks and enhanced transformer,” Heliyon, vol. 10, no. 19, art. e38317, 2024, doi: 10.1016/j.heliyon.2024.e38317. 27

    work page doi:10.1016/j.heliyon.2024.e38317 2024

  18. [18]

    Remaining useful life prediction of rolling bearings based on time convolutional network and Transformer in parallel,

    Y. Tang, R. Liu, C. Li, and N. Lei, “Remaining useful life prediction of rolling bearings based on time convolutional network and Transformer in parallel,”Measurement Science and Technology, vol. 35, no. 12, art. 126102, 2024, doi: 10.1088/1361-6501/ad73ee

    work page doi:10.1088/1361-6501/ad73ee 2024

  19. [19]

    Knowledge informed machine learning using a Weibull- based loss function,

    T. von Hahn and C. K. Mechefske, “Knowledge informed machine learning using a Weibull- based loss function,”Journal of Prognostics and Health Management, vol. 2, no. 1, pp. 9–44, 2022, doi: 10.22215/jphm.v2i1.3162

    work page doi:10.22215/jphm.v2i1.3162 2022

  20. [20]

    A hybrid prognostics approach for estimating remaining useful life of rolling element bearings,

    B. Wang, Y. Lei, N. P. Li, and N. B. Li, “A hybrid prognostics approach for estimating remaining useful life of rolling element bearings,”IEEE Transactions on Reliability, vol. 69, no. 1, pp. 401–412, 2020, doi: 10.1109/TR.2018.2882682

    arXiv 2020

  21. [21]

    Research on a remaining useful life prediction method for degradation angle identification two-stage degradation process,

    Z. Wang, Y. Ta, W. Cai, and Y. Li, “Research on a remaining useful life prediction method for degradation angle identification two-stage degradation process,”Mechanical Systems and Signal Processing, vol. 184, art. 109747, 2023, doi: 10.1016/j.ymssp.2022.109747

    arXiv 2023

  22. [22]

    Remaining useful life prediction across conditions based on a health indicator-weighted subdomain alignment network,

    Z. Xu, C. W. K. Chow, M. M. Rahman, R. Rameezdeen, and Y. W. Law, “Remaining useful life prediction across conditions based on a health indicator-weighted subdomain alignment network,”Sensors, vol. 25, no. 15, art. 4536, 2025, doi: 10.3390/s25154536

    work page doi:10.3390/s25154536 2025

  23. [23]

    On ordered weighted averaging aggregation operators in multicriteria decision- making,

    R. R. Yager, “On ordered weighted averaging aggregation operators in multicriteria decision- making,”IEEE Transactions on Systems, Man, and Cybernetics, vol. 18, no. 1, pp. 183–190, 1988, doi: 10.1109/21.87068

    doi:10.1109/21.87068 1988

  24. [24]

    Cross-domain remaining useful life prediction for rolling bearings based on wavelet decomposition and dynamic calibrated domain adaptive networks,

    Y. Zhang, X. Zhao, Z. Peng, R. Xu, and Y. Hui, “Cross-domain remaining useful life prediction for rolling bearings based on wavelet decomposition and dynamic calibrated domain adaptive networks,”Measurement, vol. 251, art. 117278, 2025, doi: 10.1016/j.measurement.2025.117278

    arXiv 2025

  25. [25]

    Construction of health indicators for condition monitoring of rotating machinery: A review of the research,

    H. Zhou, X. Huang, G. Wen, Z. Lei, S. Dong, P. Zhang, and X. Chen, “Construction of health indicators for condition monitoring of rotating machinery: A review of the research,”Expert Systems with Applications, vol. 203, art. 117297, 2022, doi: 10.1016/j.eswa.2022.117297. 28

    arXiv 2022