A semi-empirical approach and uncertainty analysis to pipes under hydrogen embrittlement degradation

The Hydrogen Embrittlement (HE) appearance is the main reason for the desire to evaluate the burst pressure of pipes. Several existing models predict burst pressure of hydrogen-induced pre-cracking pipes with the fracture mechanics criterion (fracture toughness, Jcr). Still, none of them has taken into account the model uncertainty. In this paper, we propose a surrogated model associated with molecular models. The discrete values of the dimensionless influence functions presented for elastic and plastic components of J are connected by machine learning (Random Forest Regression, RFR) and third-order polynomial functions with optimized factors to avoid the inconvenience of using the lookup table. The molecular empirical models are obtained by the up-to-date Balancing Composite Motion Optimization (BCMO) algorithm. Because samples of elastic and plastic databases are limited and the final output, Pb, is not directly derived from molecular models, all databases are used for training without the conventional data splitting to train and test sets. Consequently, the proposed approaches (RFR model and Empirical model) are validated based on the experiments collected globally. The final models are accounted for the residual distribution as the unavoidable component. The efficiency of the Random Forest and empirical models is validated by experiments or simulations from the literature when the evaluation metrics (i.e., R-square, Mean Absolute Error) are (0.9666, 0.8695 MPa) and (0.9701, 0.7996 MPa), respectively. The drawbacks of the proposed models, heavily dependent on databases, are also illustrated and discussed for further development. Strict boundaries of input and output, especially the fracture toughness, which is commonly degraded due to the effect of HE, from the test set combined with the uncertainty of the models based on the analysis of model residuals are also proposed for validation.