# Prediction of Corroded Pipeline Failure Pressure Based on Empirical Knowledge and Machine Learning
## 1 Introduction  
Empirical formulae, such as ASME-B31G [1], DNV RP-F101 [2], and PCORRC [3], have been widely utilized for predicting the failure pressure of oil and gas defective pipelines due to their simplicity and ease of application. These formulae are primarily derived from theoretical analysis and burst test data, providing sufficient samples for practical engineering assessments. The ASME-B31G formula, for instance, offers a modified approach to address the over-conservatism of traditional standards by incorporating factors like defect depth and length [4]. Similarly, the DNV RP-F101 standard evaluates failure pressure based on sectional safety factors and allowable stress, demonstrating broader applicability and less conservative predictions [5]. The PCORRC formula, focusing on plastic collapse failure, is particularly suited for pipelines with moderate to high toughness. However, despite their widespread use, empirical formulae suffer from notable limitations. They often exhibit significant prediction errors, which can lead to either overly cautious or insufficiently conservative estimates. Additionally, these formulae may not accurately capture the complex interactions between various defect parameters and material properties, thereby compromising their reliability in certain scenarios. Consequently, while empirical formulae offer a rapid and convenient means of assessing pipeline integrity, their inherent inaccuracies necessitate the exploration of more sophisticated and precise methods. Artificial neural networks (ANNs) have emerged as powerful tools for predicting the failure pressure of pipelines with interacting corrosion defects, offering more accurate and less conservative results compared to traditional methods [6]. In recent studies, ANNs have been successfully integrated with finite element analysis (FEA) to develop empirical equations that account for complex interactions between corrosion defects and combined loadings [7]. Specifically, [PERSON] et al. utilized an ANN trained on extensive FEA data to derive an empirical equation for predicting the failure pressure of API 5L X52, X65, and X80 pipelines subjected to internal pressure and axial compressive stress [8]. The study demonstrated that defect depth has the most significant impact on failure pressure, followed by defect length and axial compressive stress. [PERSON] et al. utilized ANNs to predict the failure pressure of pipelines with interacting defects, achieving results that closely matched experimental burst pressures [9]. Similarly, [PERSON] et al. demonstrated the effectiveness of ANNs in predicting residual strength in pipelines subjected to internal pressure and axial compressive stress [10]. However, despite their advantages, ANN-based predictive methods often require substantial volumes of training data to achieve reliable performance, particularly in scenarios involving complex material behaviors or multi-variable interactions. In the field of predicting failure pressure in corroded pipelines, numerous methods have been developed to address the challenge of insufficient data. When faced with limited data availability, integrating multiple methodologies can effectively maximize the utility of available data resources. For instance, [PERSON] et al. combined data-driven models with statistical models to realize the prediction of oil and gas equipment failure rates [11]. Additionally, data reconfiguration techniques can be employed to augment the sample size when data are scarce. [PERSON] et al. introduced a transfer learning approach for corrosion prediction that leverages pre-existing knowledge from similar pipelines to compensate for the lack of direct supervisory information [12]. Moreover, it is crucial to develop comprehensive resilience assessment metrics and methodologies for structure systems, as demonstrated by [PERSON] et al., who proposed a novel resilience assessment approach based on dynamic Bayesian networks (DBNs) and Markov models [13].