Kısıtlı veri ile yorulma çatlağı ilerleme hızı tahmini: Yapay ve fizik bilgili sinir ağlarının karşılaştırmalı analizi
Fatigue crack growth rate prediction with limited data: A comparative analysis of artificial and physics-informed neural networks
- Tez No: 1022080
- Danışmanlar: PROF. DR. MESUT KIRCA
- Tez Türü: Yüksek Lisans
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2026
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Lisansüstü Eğitim Enstitüsü
- Ana Bilim Dalı: Makine Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Malzeme ve İmalat Bilim Dalı
- Sayfa Sayısı: Belirtilmemiş.
Özet
Bu tez çalışmasında, S35C çeliğinde eğilme ve burulma yüklemesi altında küçük yorulma çatlaklarının ilerleme hızının tahmini için geleneksel Yapay Sinir Ağı ile Fizik Bilgili Sinir Ağı karşılaştırılmıştır. Fizik Bilgili Sinir Ağı, McEvily çatlak ilerleme modelini kayıp fonksiyonuna fizik kısıtı olarak dahil etmektedir. Referans alınan çalışmadan elde edilen beş deneysel veri seti (her biri 9-17 veri noktası, toplam 67 nokta), Birini Dışarıda Bırak Çapraz Doğrulama (LOOCV) yöntemiyle değerlendirilmiştir. Her iki model de aynı mimari yapıda (3 girdi, 8-8 gizli nöron, Tanh aktivasyon, 113 parametre) tasarlanmış olup aralarındaki tek fark Fizik Bilgili Sinir Ağı'nın kayıp fonksiyonuna eklenen fizik kısıtlarıdır. Bu tasarım, performans farklarının yalnızca fizik bilgisinden kaynaklanmasını garanti etmektedir. Sonuçlar, Fizik Bilgili Sinir Ağı'nın gürültülü eğilme verilerinde Yapay Sinir Ağı'ndan üstün performans sergilediğini göstermektedir: Eğilme σ=220 MPa veri setinde Fizik Bilgili Sinir Ağı R²=0,8910, Yapay Sinir Ağı R²=0,8753 (+0,0157); Eğilme σ=240 MPa veri setinde Fizik Bilgili Sinir Ağı R²=0,8415, YSA R²=0,8332 (+0,0083). Yapay Sinir Ağı ise düzgün trendli burulma verilerinde daha yüksek R² elde etmiştir (fark 0,003-0,037). Ortalama LOOCV R² değerleri açısından iki model arasındaki fark yalnızca 0,007'dir (YSA: 0,9062, FBSA: 0,8992). Monotonluk analizi, bu çalışmanın en güçlü bulgusunu ortaya koymuştur: Yapay Sinir Ağı, Eğilme σ=220 MPa veri setinde tahminlerinin %6,1'inde fiziksel monotonluğu ihlal etmiş — gerilme şiddeti faktörü aralığı artarken çatlak ilerleme hızının azaldığını tahmin etmiştir. Fizik Bilgili Sinir Ağı ise beş veri setinin tamamında sıfır monotonluk ihlali göstermiştir. Ayrıca Fizik Bilgili Sinir Ağı, beş veri setinin üçünde daha düşük aşırı öğrenme farkı göstermiştir (ortalama: YSA 0,0422, FBSA 0,0369). Bu çalışma, McEvily çatlak ilerleme denklemini fizik bilgili sinir ağı çerçevesine entegre eden ilk araştırmadır. Ayrıca literatürdeki en küçük veri setlerinden biriyle (veri seti başına 9-17 nokta) elde edilen sonuçlar, farklı çalışmaların bulgularıyla tutarlılık göstermiştir. Bu bulgular, fizik kısıtlarının özellikle deneysel verinin kısıtlı olduğu durumlarda hem genelleme kapasitesini hem de fiziksel tutarlılığı artırdığını göstermektedir.
Özet (Çeviri)
Within the scope of this specific academic thesis study, a rigorous and systematic comparative analysis is conducted between a conventional Artificial Neural Network (ANN) and a Physics-Informed Neural Network (PINN) to accurately evaluate their respective capabilities in predicting the propagation and growth rate of small, short fatigue cracks in S35C carbon steel components that are subjected to both bending and torsional mechanical loading conditions. Fatigue crack growth prediction remains one of the most critical challenges in structural integrity assessment, as small cracks exhibit highly stochastic behavior that deviates significantly from the long-crack regime described by classical fracture mechanics. The ability to accurately predict crack propagation rates at this stage is essential for ensuring the safety and reliability of engineering components subjected to cyclic loading throughout their service life. The Physics-Informed Neural Network developed in this work incorporates the McEvily crack growth model as a physics constraint directly into its loss function. The McEvily model, which describes the crack growth rate as a function of the effective stress intensity factor range and accounts for crack closure and threshold effects, provides a physically meaningful framework that guides the neural network's learning process. By embedding this established fracture mechanics formulation into the training procedure, the PINN is designed to produce predictions that are not only data-driven but also consistent with the underlying physical mechanisms governing fatigue crack propagation. In addition to improving prediction reliability, the integration of physical laws into the optimization process reduces the likelihood of the network converging toward mathematically acceptable yet physically unrealistic solutions. This characteristic is particularly valuable in engineering applications where extrapolation beyond the available experimental data is often unavoidable. Consequently, the proposed framework seeks to balance predictive accuracy with engineering interpretability, providing a model whose outputs remain consistent with well-established fracture mechanics principles. Five experimental datasets obtained from the reference study were used for model evaluation. These datasets encompass two bending loading conditions (stress amplitudes of σ = 220 MPa with 11 data points and σ = 240 MPa with 17 data points) and three torsional loading conditions (stress amplitudes of σ = 140 MPa with 14 data points, σ = 165 MPa with 16 data points, and σ = 175 MPa with 9 data points), yielding a combined total of 67 experimental observations. Given the extremely limited size of each individual dataset, the Leave-One-Out Cross-Validation (LOOCV) method was employed as the evaluation strategy. LOOCV is particularly well-suited for small-sample problems because it maximizes the use of available data for both training and validation, providing an unbiased estimate of model generalization performance without requiring a separate held-out test set. This validation strategy also ensures that every experimental observation contributes to both model training and performance assessment, thereby maximizing the value extracted from the limited experimental measurements. Such an approach is especially important in fatigue research, where generating additional crack growth data is both time-intensive and economically demanding. Both models were deliberately designed with identical architectural configurations to ensure a fair and rigorous comparison. Each network receives three input features — the stress intensity factor range (ΔK), the stress ratio (R), and the applied stress amplitude (σ) — processes them through two hidden layers of 8 neurons each with hyperbolic tangent (Tanh) activation functions, and produces a single output representing the predicted crack growth rate (da/dN). This configuration results in exactly 113 trainable parameters for each model. The sole difference between the two architectures lies in the PINN's augmented loss function, which includes two additional physics-based penalty terms beyond the standard mean squared error: a McEvily equation consistency term weighted at 0.5 and a monotonicity gradient penalty term weighted at 0.1. This carefully controlled experimental design ensures that any observed differences in predictive performance can be attributed exclusively to the incorporation of physics knowledge, rather than to differences in model capacity, complexity, or optimization strategy. Accordingly, the comparative analysis isolates the influence of the embedded physical constraints while eliminating potential sources of bias associated with differing network structures or hyperparameter choices. The results reveal a nuanced and dataset-dependent performance pattern. The Physics-Informed Neural Network demonstrated superior predictive accuracy on the noisy bending datasets, where experimental scatter is more pronounced and the data exhibits greater variability. Specifically, for the bending dataset at σ = 220 MPa, the PINN achieved an R² value of 0.8910 compared to the ANN's R² of 0.8753, representing an improvement of +0.0157. For the bending dataset at σ = 240 MPa, the PINN attained R² = 0.8415 versus the ANN's R² of 0.8332, an improvement of +0.0083. Conversely, the ANN achieved marginally higher R² values on the torsional datasets, which exhibit smoother and more regular trends, with performance differences ranging from 0.003 to 0.037. When considering the overall mean LOOCV R² across all five datasets, the two models perform nearly identically, with the ANN achieving 0.9062 and the PINN achieving 0.8992 — a negligible difference of merely 0.007 that falls well within the bounds of statistical uncertainty. These findings indicate that incorporating physics constraints does not necessarily guarantee higher numerical accuracy under every loading condition, but instead provides a more balanced trade-off between predictive performance and adherence to known physical behavior. Such behavior is particularly desirable in engineering practice, where physically consistent predictions are often more valuable than marginal improvements in statistical metrics alone. The monotonicity analysis constitutes the most compelling and significant finding of this research. A physically valid crack growth model must predict monotonically increasing growth rates with increasing stress intensity factor ranges, as this relationship is a fundamental requirement dictated by fracture mechanics principles. The conventional ANN violated this physical monotonicity constraint in 6.1% of its predictions for the bending σ = 220 MPa dataset, erroneously predicting decreasing crack growth rates despite increasing stress intensity factor ranges. Such non-physical predictions, while potentially achieving acceptable numerical accuracy metrics, are fundamentally unreliable from an engineering standpoint and could lead to dangerous underestimation of crack growth in safety-critical applications. In stark contrast, the Physics-Informed Neural Network maintained perfect monotonicity compliance across all five datasets with zero violations, demonstrating that the embedded physics constraints effectively prevent the model from learning spurious non-physical patterns present in the training data. Furthermore, the PINN exhibited lower overfitting gaps in three out of five datasets, with average overfitting gaps of 0.0422 for the ANN and 0.0369 for the PINN, indicating improved generalization capability attributable to the regularizing effect of the physics-based loss terms. These observations suggest that the physics-informed formulation serves not only as a mechanism for enforcing physical consistency but also as an implicit regularization strategy that enhances model robustness under limited-data conditions. The elimination of physically inconsistent predictions further increases confidence in the applicability of the proposed framework to engineering decision-making processes involving structural integrity assessment. This study represents the first research effort to integrate the McEvily crack growth equation within a physics-informed neural network framework, establishing a novel methodology for physics-constrained fatigue life prediction. Moreover, the results obtained from what constitutes one of the smallest datasets reported in the PINN literature (9 to 17 data points per dataset) demonstrate remarkable consistency with findings from 10 independent studies in the broader physics-informed machine learning domain, reinforcing the validity and generalizability of the proposed approach. These findings collectively demonstrate that physics constraints enhance both generalization capacity and physical consistency of neural network predictions, particularly in scenarios where experimental data is scarce — a condition that is ubiquitous in fatigue testing due to the time-consuming and costly nature of crack growth experiments. The proposed methodology therefore provides a promising foundation for future studies involving physics-guided machine learning models applied to fracture mechanics and structural health monitoring. Future investigations may extend this framework to different materials, loading conditions, and crack growth formulations while also exploring more advanced physics-informed architectures capable of incorporating additional fracture mechanics principles. Such developments have the potential to further improve the reliability, interpretability, and practical applicability of artificial intelligence techniques for fatigue life assessment in safety-critical engineering systems.
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