Optimization of Cyclic Fatigue Testing (CRBOS) using Machine Learning

Introduction & objectifs

Classical fatigue characterization tests every loading condition of interest to failure, which scales poorly as the number of variables (stress ratio, amplitude, temperature, layup) grows. A data-driven approach can instead learn the underlying relationship between test conditions and fatigue life from the historical and newly generated CRBOS dataset, and use that model to decide which future tests actually add information. The project pursued three objectives:

1. Predictive modeling — build a fatigue-life model, benchmarked against the classical Basquin/Miner framework, accurate enough to support test-planning decisions.
2. Test-matrix optimization — use an optimal-experimental-design criterion to select the smallest set of loading profiles that maximizes information gained per test.
3. Prospective validation — confirm on held-out, physically run tests that the shortened protocol matches the predictive power of the original, more exhaustive test matrix.

Cadre théorique

Classical fatigue-life framework

The classical benchmark for the learned models is the Basquin power-law relation between stress amplitude σ_a and cycles to failure N_f,

and Miner’s rule for cumulative damage under variable-amplitude loading, which sums the fractional life consumed at each stress level i and predicts failure once the total reaches unity:

These relations remain the interpretable backbone against which every learned model’s predictions were sanity-checked.

Supervised learning formulation

Fatigue life (or its logarithm, to stabilize the typically wide dynamic range) was treated as the regression target of a supervised model f(x;θ), fit by minimizing a regularized loss over m training examples:

Gradient-boosted tree baselines built the model as an additive expansion of weak learners h_m fit to the residuals of the previous stage, scaled by a learning rate ν:

and neural-network baselines composed layers of the standard form

with model selection and hyperparameter tuning driven by k-fold cross-validated error,

Model interpretability

To confirm the learned models were relying on physically sensible drivers rather than spurious correlations, feature contributions were quantified with Shapley additive explanation (SHAP) values, which distribute a prediction fairly across features i using the cooperative-game-theoretic Shapley value over all feature subsets S of the full feature set F:

which confirmed stress ratio, peak stress and layup descriptors as the dominant predictors, consistent with the classical Basquin framework of Equation (1).

Optimal test-matrix design

Selecting which loading profiles to physically test was framed as a D-optimal design problem: for a candidate set of test points forming design matrix X, the subset maximizing the determinant of the Fisher information matrix

gives the loading profiles that most reduce parameter uncertainty in the fitted model per test run — the mathematical basis for the shortened test protocol proposed in Section 3.3.

Méthodologie

Data pipeline

Historical and newly generated CRBOS records (loads, frequencies, cycles to failure) were aggregated, cleaned and enriched with engineered features — stress ratio R = σ_min/σ_max, peak stress, test temperature and humidity, and layup descriptors — chosen to align with the variables that classical fatigue theory (Equation 1) already identifies as first-order drivers of life.

Modeling

Regularized linear/ridge regression, gradient-boosted trees (Equation 4) and a small feed-forward neural network (Equation 5) were trained and compared using the cross-validated error of Equation (6), with hyperparameters tuned on the validation folds only. SHAP analysis (Equation 7) was run on the best-performing model to confirm feature attributions were physically sensible before the model was trusted for test-planning decisions.

Test optimization

The trained model was used as a fast surrogate to score candidate loading profiles, and the D-optimal criterion of Equation (8) selected the subset of profiles expected to most reduce prediction uncertainty per additional physical test, producing a shortened test matrix proposal in place of the original exhaustive plan.

Validation

The shortened protocol was validated prospectively: profiles it had not been trained on were physically tested on the CRBOS bench, and predicted versus measured fatigue life was compared using root-mean-square error and the coefficient of determination,

to confirm the reduced test matrix preserved predictive accuracy relative to the full historical dataset.

Résultats & retombées

The gradient-boosted model consistently outperformed the regularized linear baseline in cross-validation, and SHAP attributions (Equation 7) confirmed stress ratio and peak stress as the dominant predictors, in line with the classical Basquin relation of Equation (1). Selecting the test matrix via the D-optimal criterion of Equation (8) allowed a materially shorter physical test campaign, and the prospective validation of Equation (9) confirmed the shortened protocol retained predictive accuracy statistically comparable to the original, more exhaustive test matrix — the central result required to justify adopting the shortened protocol for future qualification campaigns.

Environnement technique

Modeling used Python (scikit-learn, TensorFlow / PyTorch) alongside MATLAB for classical fatigue-model cross-checks. Physical fatigue data came from the CRBOS fatigue bench and DAQ systems, with all datasets and analysis notebooks kept under version control for reproducibility.