# Explainable Ensemble Learning Model for Residual Strength Forecasting of Defective Pipelines
## 1 Introduction  
As a means of transporting oil and natural gas, pipelines have become the primary mode of oil and gas transportation due to their large-scale transportation capacity, reliable and safe transportation process, low cost, and environmental \"friendliness\" [1]. Duringtheir entire life cycle, pipelines are affected by many factors, such as improper construction and operation [2], design flaws [3], mechanical damage [4], material ageing [5], and corrosion [6; 7]; as a result, the remaining strength of pipelines decreases, thus affecting the service life of pipelines. Nearly half of the world's operational oil and gas pipelines have entered the ageing phase. Taking the United States as an illustration, approximately half of the pipelines currently in service were commissioned before the 1960s. Statistical data indicate that, due to ageing pipeline infrastructure corrosion defects and other problems, the annual failure rate of oil and gas pipelines has escalated from 0.04 incidents per 10\({}^{3}\) km to 0.14 incidents per 10\({}^{3}\) km. Since 2010, statistics show that 670 oil and gas pipeline accidents have occurred in the United States. Factors such as defects are the primary causes of pipeline failures for these ageing pipelines. Precisely predicting residual strength in defective pipelines is critical for assessing their remaining service life, guaranteeing operational safety, and facilitating proactive maintenance measures. Consequently, it is essential to employ appropriate methods to forecast the remaining strength of pipelines with defects, thereby enabling the pre-emptive prevention of failure accidents [8]. According to different calculation methods, the commonly used prediction methods for pipeline remaining strength include empirical formulas, finite elements, and machine learning approaches. The widely used methods are shown in Figure 1. Due to their convenience in calculation and simplicity in operation, empirical formulas have been commonly applied in predicting the remaining strength of defective pipelines. A series of typical formulas, such as ASME B31G-2009, BS 7910-2005, PCORRC, and API 579-1/AMSE FFS-1-2007, are applied to calculate remaining strength [9; 10; 11; 12; 13]. Among them, when calculating the remaining strength, BS 7910-2005 and PCORRC can yield similar curves. ASME B31G-2009 shows a certain conservatism in evaluating the pipeline's remaining strength. API 579-1/AMSE FFS-1-2007 exhibits significant conservatism in evaluating medium- and high-grade pipeline steels, resulting in inaccurate evaluation results. The above-mentioned empirical formulas are relatively conservative, have poor adaptability, limited application scope, and the prediction errors cannot be ignored. With the advancement of computer technology, researchers have gradually applied the finite element method to the numerical simulation of pipeline remaining strength, and relatively good prediction results have been obtained. For instance, [PERSON] et al. proposed a variable-strength material damage model with damage accumulation, achieving the coupled analysis of structural damage and material fatigue residual strength, and enabling the calculation of the strength of nonlinear damage cross-sections, which has essential practical engineering application value [14]. [PERSON] et al. considered the influence of different defect sizes on pipeline residual strength, established a finite-element model of an X80 pipeline with grouped corrosion defects using ABAQUS 6.14.2, and verified the accuracy of the finite-element model through burst tests. The research results provide theoretical support for the safety management of X80 pipelines [9]. [PERSON] et al. analyzed the residual strength of buried pipelines with corrosion defects under different defect parameters using the finite-element elastic-plastic method, and the research can provide valuable references for the simulation real-time monitoring and safety analysis during the pipeline operation stage [15]. [PERSON] et al.