Data-driven formulation of steel fiber pull-out force in cementitious composites using genetic programming
Bibliographic record
Abstract
Abstract This study aims to develop a data-driven approach for predicting and formulating the pull-out force of steel fibers in cementitious composites using a genetic programming variant, gene expression programming (GEP). A comprehensive dataset of 437 experimental data was collected from previous studies, including key variables such as embedment length, fiber inclination angle, tensile strength of fibers, aspect ratio, loading rate, water-to-cement ratio, compressive strength of matrix, and fiber geometry. The GEP model developed in this study demonstrated notable accuracy in predicting pull-out force, with an R 2 of 0.93. Model performance was evaluated using multiple statistical criteria, confirming its satisfactory predictive ability. Furthermore, a k-fold cross-validation was performed, and the results confirmed the model’s robustness and capability for generalizing to new data. Sensitivity analysis using SHAP interpretation revealed that the fibers’ tensile strength and the embedment length are the most influential factors affecting the pull-out force. The GEP method was adopted for its ability to generate accurate and interpretable mathematical formulas. Accordingly, a mathematical formula for the pull-out force is proposed, providing an efficient and interpretable tool for future studies. Overall, the GEP approach can significantly reduce reliance on costly and time-consuming experimental procedures while ensuring reliable performance predictions and practical formulations.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".