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arxiv: 2410.10830 · v3 · submitted 2024-09-28 · 💻 cs.CE

A framework for probabilistic prediction of remaining useful life in structural materials

Victor Maudonet , Carlos Frederico Trotta Matt , Americo Cunha Jr This is my paper

Pith reviewed 2026-05-23 21:08 UTC · model grok-4.3

classification 💻 cs.CE
keywords modelframeworklifepredictionremainingusefulcreepcriteria
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The pith

A probabilistic framework combining robust regression, Sobol indices, Monte Carlo propagation, and AIC/BIC model selection for uncertainty-aware creep remaining useful life prediction.

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

Creep failure occurs when materials slowly deform and eventually break under sustained high-temperature stress. Standard prediction models treat this as a fixed equation and ignore the scatter seen in real test data. The described framework first fits a model while down-weighting outliers, then ranks which input variables drive most of the prediction spread using Sobol indices, runs many random simulations to build a distribution of possible rupture times, and finally picks the best model according to Akaike and Bayesian information criteria. The output is not a single number but a probability distribution that can be turned into safe operating windows with stated confidence. The authors note the same steps could apply to fatigue or combined creep-fatigue problems.

Core claim

The proposed framework enables the definition of safe operational limits with quantifiable confidence levels and is general and extensible to other time-dependent degradation phenomena such as fatigue and creep-fatigue interaction.

Load-bearing premise

That the variability present in experimental creep rupture data is adequately captured by the chosen parametric models and can be propagated without introducing bias through the sequence of robust regression, Sobol analysis, and Monte Carlo sampling.

Figures

Figures reproduced from arXiv: 2410.10830 by Americo Cunha Jr, Carlos Frederico Trotta Matt, Victor Maudonet.

Figure 1
Figure 1. Figure 1: Schematic illustration of the probabilistic uncertainty quantification framework [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Larson-Miller model’s first-order (left) and total (right) Sobol indices. [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: First-order (left) and total (right) Sobol indices for the Orr-Sherby-Dorn model. [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Manson-Succop model’s first-order (top) and total (bottm) Sobol indices. [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Rupture time histogram for Larson-Miller model for the four operational condi [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Rupture time histogram for Orr-Sherby-Dorn model for the four operational [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Rupture time histogram for Manson-Succop model for the four operational [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
read the original abstract

Accurate prediction of remaining useful life under creep conditions is essential for the structural reliability of high-temperature components in critical engineering systems. Traditional approaches based on deterministic parametric models often overlook the substantial variability inherent in experimental data, compromising the accuracy and robustness of long-term predictions. This study introduces a probabilistic framework to quantify uncertainties in creep rupture time prediction. Robust regression techniques are first applied to mitigate the influence of outliers and enhance the stability of model estimates. Global sensitivity analysis using Sobol indices is then employed to identify the dominant contributors to model uncertainty, followed by Monte Carlo simulations to propagate these uncertainties and estimate the distribution of the remaining useful life. Finally, model selection is guided by statistical criteria, including the Akaike and Bayesian information criteria, to identify the most reliable predictive model. The proposed framework not only enables the definition of safe operational limits with quantifiable confidence levels but is also general and extensible to other time-dependent degradation phenomena, such as fatigue and creep-fatigue interaction.

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

2 major / 2 minor

Summary. The paper introduces a probabilistic framework for remaining useful life (RUL) prediction under creep conditions. It applies robust regression to experimental creep rupture data, performs global sensitivity analysis via Sobol indices to rank uncertainty sources, uses Monte Carlo sampling to propagate uncertainties into RUL distributions, and selects models via AIC/BIC. The central claim is that this workflow yields reliable probabilistic RUL predictions that support definition of safe operational limits with quantifiable confidence and is extensible to fatigue and creep-fatigue.

Significance. If the framework were shown to produce well-calibrated predictive distributions on held-out creep data and to avoid bias from unmodeled mechanism transitions, it would offer a practical, extensible template for uncertainty-aware life prediction in high-temperature components. The approach assembles standard statistical tools (robust regression, Sobol, Monte Carlo, information criteria) rather than introducing parameter-free derivations or machine-checked proofs, so its significance would rest on demonstrated empirical performance rather than methodological novelty.

major comments (2)
  1. [Abstract / Results] No Results or Validation section supplies experimental data, fitted parameters, residual plots, hold-out prediction intervals, or calibration metrics (e.g., coverage of 95 % intervals). Without these, the claim that the framework produces reliable probabilistic RUL predictions usable for safe limits cannot be evaluated.
  2. [Methodology] The workflow assumes the chosen parametric creep-rupture models (standard time-temperature parameters) adequately capture observed scatter without bias. No residual diagnostics, comparison to nonparametric alternatives, or sensitivity to mechanism transitions are reported; this assumption is load-bearing for unbiased Monte Carlo propagation of RUL distributions.
minor comments (2)
  1. [Introduction] Notation for the creep-rupture models and the precise definition of the RUL random variable should be introduced with equations in a dedicated section.
  2. [Abstract] The abstract states the framework is 'general and extensible' but provides no concrete illustration or pseudocode for adaptation to fatigue; a short worked example would strengthen the claim.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which correctly identify gaps in empirical demonstration and model validation. We address each point below and commit to revisions that will strengthen the manuscript's claims with concrete results and diagnostics.

read point-by-point responses

  1. Referee: [Abstract / Results] No Results or Validation section supplies experimental data, fitted parameters, residual plots, hold-out prediction intervals, or calibration metrics (e.g., coverage of 95 % intervals). Without these, the claim that the framework produces reliable probabilistic RUL predictions usable for safe limits cannot be evaluated.

    Authors: We agree that the current manuscript, which emphasizes the methodological workflow, lacks the requested empirical elements. In the revised version we will add a dedicated Results and Validation section that applies the framework to experimental creep-rupture datasets. This section will report fitted parameters from the robust regression, residual plots, hold-out prediction intervals, and calibration metrics including the observed coverage rate of nominal 95 % intervals. These additions will allow direct assessment of whether the probabilistic RUL predictions are well-calibrated and suitable for defining safe limits. revision: yes

  2. Referee: [Methodology] The workflow assumes the chosen parametric creep-rupture models (standard time-temperature parameters) adequately capture observed scatter without bias. No residual diagnostics, comparison to nonparametric alternatives, or sensitivity to mechanism transitions are reported; this assumption is load-bearing for unbiased Monte Carlo propagation of RUL distributions.

    Authors: We acknowledge that the parametric-model assumption is central and currently unexamined. The revision will incorporate residual diagnostics to quantify any systematic bias and will include a sensitivity study examining how RUL distributions change under plausible mechanism transitions. While a full benchmark against nonparametric alternatives lies outside the paper's intended scope, we will explicitly discuss this limitation and justify the parametric choice on the basis of the added diagnostics and information-criteria results. revision: partial

Circularity Check

0 steps flagged

No circularity: standard uncertainty propagation on external data

full rationale

The described workflow applies robust regression to fit parametric creep-rupture models to experimental data, uses Sobol indices for sensitivity, then Monte Carlo sampling to obtain RUL distributions, followed by AIC/BIC model selection. None of these steps reduce a claimed prediction to a quantity defined by the same fitted parameters by construction, nor do they rely on self-citations or imported uniqueness theorems. The central claim of quantifiable confidence levels for safe limits rests on external experimental data and conventional statistical tools, rendering the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; no specific free parameters, axioms, or invented entities are extractable beyond the general domain assumption that experimental variability can be modeled probabilistically.

axioms (1)
  • domain assumption Experimental creep rupture data exhibits substantial variability that deterministic parametric models overlook.
    Explicitly stated in the abstract as the motivation for the probabilistic approach.

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