Lightweight Fatigue Estimation Method

• The method integrates cycle counting, stochastic modeling, and ML surrogates to deliver accurate fatigue life predictions with minimal computational overhead.
• It reduces hardware and memory demands, enabling real-time implementation in embedded systems for applications like structural health monitoring and fatigue warning.
• Practical implementations in wind turbines, automotive systems, and robotics demonstrate its effectiveness in optimizing design and prolonging component life.

A lightweight fatigue estimation method is an algorithmic, analytic, or machine learning-based framework that achieves accurate fatigue or fatigue-life assessment with minimized computational cost, memory footprint, hardware requirements, and model complexity. Such methods are essential for real-time structural health monitoring, embedded control systems, in-vehicle fatigue warning, and rapid engineering design optimization where exhaustive high-fidelity simulation or extensive experimental campaigns are prohibitive or unnecessary. The following sections review the principal classes of lightweight fatigue estimation, representative modern implementations, algorithmic structures, mathematical formulations, performance metrics, and recommended practices based on recent literature.

1. Foundational Algorithms and Modeling Approaches

Lightweight fatigue estimators are structurally diverse, falling into several methodological archetypes:

• Cycle-counting and stress-life analytics: Based on the stress–life (S–N) curves and the Palmgren–Miner rule, fatigue damage is linearly accumulated per detected cycle (from rainflow or peak-valley counting), yielding $D = \sum_{i} \frac{n_i}{N_i}$ where $n_i$ is the number of cycles and $N_i$ the cycles-to-failure at amplitude $\Delta\sigma_i$ (Ribeiro et al., 4 Jan 2026).
• Statistical-moment and probabilistic metrics: Fatigue is assessed by extracting higher-order statistics (mean, skewness, kurtosis) from time-series windows of sensor or physiological signals (e.g., heart rate, accelerometer data), and mapping deviations from reference distributions into fatigue scores or distances on the Pearson diagram (Stirenko et al., 2018, Gordienko, 2016).
• Stochastic and Markovian reconstruction: Fatigue loading in complex systems is estimated by fitting stochastic differential equations (SDEs) or Markov chains from measured data at one location and simulating torque or stress histories for others, with follow-up cycle-counting and damage summation (Lind et al., 2014, Berglind et al., 2014).
• Physics-based machine learning surrogates: Networks are trained as surrogates for physics-based damage models, often with embedded physical constraints to capture load-sequence effects. Fatigue lifetime is predicted under arbitrary, non-uniform loading (Baktheer et al., 7 Mar 2025).
• Vision-based and activity-based detectors: In contexts such as driver monitoring or wearable fatigue analytics, lightweight neural architectures (e.g., YOLO variants, graph neural networks, shallow CNNs) process video, image, or sensor data to infer states associated with fatigue, adapting feature selection and architecture design for low-latency, low-memory deployment (Jin et al., 16 Aug 2025, Ren et al., 29 Jul 2025).
• Machine learning pipelines for high-dimensional operational histories: Certifiable ML-based workflows replace classical simulation and cycle-count protocols by modular ML models that predict stress, segment-wise damage, and fatigue life directly from operational parameter sets (Ladrón et al., 12 Sep 2025).

These approaches share a focus on reducing hardware, computation, and experimental cost, enabling deployment on embedded platforms or within iterative optimization loops where only conservative or relative fatigue estimation is required.

2. Mathematical Formulations and System Architectures

Lightweight fatigue estimation frameworks instantiate a range of mathematical and computational strategies:

• Stress–life accumulation:

$D = \sum_{i}\frac{n_i}{N_i}$

with $$N_i(\Delta\sigma_i)=\bar{a}[\Delta\sigma_i(\frac{t}{t_{\mathrm{ref}}})^k]^{-m}$$ for classic S–N curves, applied to structures such as floating wind-turbine towers via analytic geometry scaling calibrated against a reference simulation (Ribeiro et al., 4 Jan 2026).

• Stochastic modeling and fatigue-load reconstruction:

$dT(t) = A(T(t),v(t))dt + B(T(t),v(t))dW(t)$

where $A,B$ are drift/diffusion functions extracted from conditional empirical moments, supporting synthetic time-series generation for turbines without direct load sensors (Lind et al., 2014).

• Statistical-moment fatigue metrics:

$$E_{\mathrm{inst}}(t) = \sqrt{\left(s^2_{\mathrm{inst}}(t) - s^2_{\mathrm{ref}}\right)^2 + \left(K_{\mathrm{inst}}(t) - K_{\mathrm{ref}}\right)^2}$$

where $s^2,S,K$ are skewness, kurtosis, and their squared forms, estimated over sliding windows; fatigue is reported as distance from physiological rest reference (Stirenko et al., 2018).

• Machine learning surrogates and pipelines:
  • Physics-informed FFNN surrogates, e.g.,

  $$\text{Input: } S^{\mathrm{max}}_1, \Delta S^{\mathrm{max}}, \eta^{\mathrm{cons}} \rightarrow \text{Output: } \sum\eta$$

  with sequence-effect penalties and constraint terms in custom loss functions; generalization achieved for multi-level loading (Baktheer et al., 7 Mar 2025). - Certifiable ML pipelines, comprising MLP modules for stress prediction, segment-wise damage, and global fatigue life, combining time-weighted averages and modular regression (Ladrón et al., 12 Sep 2025).

• Vision-based object detection for fatigue cues:

  • Efficient CNN-attention fusion modules (CAFM), spatial context-calibrators (RCM), and PAN-style multi-scale feature heads, with explicit mathematical branches for channel and axial reasoning, enabling YOLO11-CR to achieve $88.09\%$ mAP@50 at $106.4$FPS with $2.691$M parameters (Jin et al., 16 Aug 2025).

3. Implementation, Optimization, and Resource Constraints

Lightweight methods are distinguished by their implementability on constrained devices and efficiency in operational loops:

Method Type	Typical Parameters	Compute/Memory Profile
Analytic damage scaling	$C$, $r$, $t$, $m$, $k$	$O(n)$ per design, $<1$ms
Stochastic SDE	$A_{ij}$, $B_{ij}$ tables	$O(n_{\text{bins}}N)$, minutes offline; $<1$s
Statistical-moment	mean, skewness, kurtosis	$O(1)$ update/beat, $<10$kB
ML surrogates	FFNN (10x16), MLP (64x2)	$<1$s inference, $<100$k parameters
Vision pipelines	$2.7$M params, $3.3$GFlops	$11$MB weights, $50$MB activations, $25$–$100$FPS

Standard strategies to further optimize include weight quantization (INT8), pruning of low-salience channels/layers, use of ring buffers or online moment algorithms, and modularization of model phases. Validation frequently relies on comparison to high-fidelity simulations (e.g., OpenFAST, FEM), with typical mean relative errors $<10\%$ in deployment regimes (Ribeiro et al., 4 Jan 2026, Ladrón et al., 12 Sep 2025). In addition, embedded implementations on microcontrollers (MCUs) or edge platforms are practical for statistical and low-parameter ML methods (Stirenko et al., 2018, Jin et al., 16 Aug 2025).

4. Comparative Performance, Robustness, and Adaptation

Performance characteristics of lightweight methods have been quantified across domains:

• Rainflow–Miner estimators remain gold-standard for offline fatigue; however, spectral and hysteresis (Preisach) methods offer sub-second, online damage rate estimation with configurable accuracy, often exceeding 80–95% correlation to rainflow at $M=3$–$10$ relays (Berglind et al., 2014).
• ML pipelines achieve competitive or superior accuracy vs. classical cycle-counting, often with 3–10% error in practical domains of fatigue life, accompanied by calibrated uncertainty quantification (e.g., bootstrapped intervals, GPR layers) (Ladrón et al., 12 Sep 2025, Farid, 2021).
• Active learning and Bayesian inference reduce costly experimentation: Bayesian acquisition with GP priors for fatigue strength estimation achieves sub-Newton point estimates with up to 60% reduction in specimen count compared to staircase protocols—even under significant prior misspecification and quantized load settings (Weichert et al., 2022).
• Continuous self-monitoring and adaptation: Methods for in-situ calibration (e.g., torque–stiffness mapping in continuum robots (Chen et al., 11 Sep 2025)), periodic retraining, and domain adaptation pipelines are standard, maintaining robustness to changing operational conditions, sensor drift, and demographic diversity (Jin et al., 16 Aug 2025).

5. Domain Applications and Future Engineering Directions

Lightweight fatigue estimators are widely deployed across such domains as wind energy, automotive safety, robotic health awareness, structural design, and physical activity monitoring:

• Wind turbines: Online fatigue estimation enables real-time control and lifetime management with minimal instrumentation, using SDE or Preisach relay-based methods (Lind et al., 2014, Berglind et al., 2014, Ribeiro et al., 4 Jan 2026).
• Driver fatigue detection: Efficient convolution-attention or spatio-temporal graph networks (LiteFat, YOLO11-CR) allow embedded, high-throughput inference from video data, critical for intelligent vehicle safety (Ren et al., 29 Jul 2025, Jin et al., 16 Aug 2025).
• Robotics and adaptive structures: Smart continuum robots leverage joint torque and hybrid hinge mechanisms to self-sense and mitigate fatigue, achieving up to $49\%$ accumulation reduction over conventional designs (Chen et al., 11 Sep 2025).
• Aircraft structures and certification: ML pipelines deliver rapid, uncertainty-quantified fatigue life predictions, expediting design iteration and supporting compliance with industry standards (Ladrón et al., 12 Sep 2025).
• Personal fatigue monitoring: Statistical-moment and bootstrapped clustering techniques from commonplace sensors enable cross-activity classification and individualized fatigue tracking, suitable for both professional and lay populations (Gordienko, 2016).

Anticipated extensions include temporal modeling of fatigue cues, deeper 3D mesh analysis, integration with domain-adaptive semi-supervised learning, AI-assisted digital twins, and continuous retraining with sensor fusion.

6. Practical Implementation and Limitations

Effective lightweight fatigue estimation demands consideration of specific boundary conditions, underlying assumptions, and integration protocols:

• Assumption checks: Markovianity and stationarity in stochastic models, sufficiency of descriptors in GP-based approaches, robustness of learned adjacency in vision graph models, and domain generality in ML pipelines require empirical validation and periodic recalibration (Lind et al., 2014, Weichert et al., 2022, Ren et al., 29 Jul 2025).
• Calibration points and transferability: Estimators based on analytic geometry scaling, S–N curves, or ML surrogates often require recalibrating constants or retraining network weights when designs, material batches, or environmental regimes change significantly (Ribeiro et al., 4 Jan 2026, Baktheer et al., 7 Mar 2025).
• Limitations in extreme or multimodal scenarios: Nonlinear hydrodynamic effects, rare event loadings, extreme sensor noise, and out-of-domain operational states may degrade estimator fidelity, thus necessitating occasional fallback to high-fidelity simulation or lab measurement (Ribeiro et al., 4 Jan 2026, Zhao et al., 2023, Ladrón et al., 12 Sep 2025).
• Recommended practices: Modular phase design (stress → damage → lifetime), ongoing uncertainty evaluation, and hybrid analytic/ML integration are favored for certifiable, interpretable deployment.

In summary, lightweight fatigue estimation methods—spanning analytics, statistical modeling, and modern ML architectures—are rapidly advancing as standard tools for fatigue-aware control, health monitoring, and design optimization, balancing accuracy and resource efficiency, and adapting to continually evolving operational demands (Jin et al., 16 Aug 2025, Baktheer et al., 7 Mar 2025, Ladrón et al., 12 Sep 2025).