1. Introduction
Pipelines are the most economical means of transport between gas wells, storage facilities, refinery plants and power plants. Failure of pipelines may pose catastrophic consequences to their surroundings, on top of economic losses from production interruption. Pipelines are susceptible to compressive longitudinal loads due to hoop stress from internal pressure and thermal stress induced by thermal expansion and pipe–soil friction resistance [
1]. Corrosion is a significant cause of pipeline failure as it thins the pipe wall, weakening the structural integrity of the pipeline by reducing the load-carrying capacity of the pipeline due to stress concentration at the corrosion region [
2].
Formation of corrosion in a pipeline is often irregular and unpredictable, with different types of corrosion formation having different structural effects on a pipeline. A corrosion defect disrupts the stress and strain field of a pipeline beyond the defect. A single corrosion defect has zero or negligible interactions with other corrosion defects, provided that the distance between these defects is outside of the interaction limit. Corrosion defects usually occur as clusters of corrosion pits, with a complex defect geometry rather than a single uniform defect. Interacting defects are more detrimental towards the structural integrity of a pipeline than single defects, as they may interact with each other and reduce the failure capacity of the pipeline [
3]. Therefore, they need to be considered differently when assessing corroded pipelines. Corrosion defects are commonly categorised and assessed by the type of interaction. For example, longitudinally aligned groups of corrosion defects have a Type 2 interaction, where defects lie on the same axial line and are separated by a length of pipe wall thickness. DNV defines the interaction limit of longitudinal interacting defects as per Equation (1), as a function of the outer diameter
D and thickness
t of a pipe [
4]. Defect spacing
s equal or greater than the interaction limit will be treated as a single defect, due to the negligible interaction effect [
5].
Residual strength assessment of a corroded pipeline can be assessed based on different complexities. ASME B31G classifies the complexity of assessment from Level 0 to Level 3 [
6]. Level 0 assessment relies on the tables of allowable defect depth and length. Level 1 assessment is a simple calculation based on defect depth and length, usually used by personnel in the field. The Level 2 assessment method is a calculation that incorporates a greater detail of information than Level 1 to produce a more accurate estimate of the failure pressure. It relies on detailed measurements of the corroded surface profile and involves repetitive calculations. The Level 3 assessment method requires the specifics of the corrosion defects such as their geometries, loadings, boundary conditions, material properties and failure criteria.
Considerable progress has been made recently to improve Level 2 and Level 3 assessments. It is known that Level 2 assessments based on established standards and codes, such as ASME B31G [
6], RSTRENG Effective Area [
7] and DNV RP-F101 [
4], are conservative in their estimation [
8]. These assessment standards are limited in their capabilities and most of them are applicable to a corroded straight pipeline with a single corrosion defect subjected to internal pressure only. Numerous works have been conducted to improve their predictions and expand their limited scope. Khalajestani et al. revised DNV’s equation and expanded its capability to assess single-defect corrosion at the intrados, crown and extrados of pipe elbows [
9]. FEA results from Level 3 assessment were utilised to develop a new assessment model that considered different defect geometries and configurations [
10,
11], boundary conditions and loadings [
12] and different material properties [
13]. The reliability of conventional assessment methods such as DNV was improved by redefining the defect depth of DNV’s equations [
14]. A new assessment model was developed by using numerical tools such as Monte Carlo simulation (MCS) to establish and solve limit state equations [
15]. A proprietary program, PIPEFLAW, is able to quickly assess the integrity of corroded pipelines. The programme is considered a Level 4 assessment method as it can automatically generate and analyse corroded pipeline models subjected to internal pressure and axial compressive force [
16,
17].
Of all the established residual strength assessment standards, DNV RP-F101 is the most comprehensive method, as it is applicable to corroded pipelines with a single defect (subjected to internal pressure and longitudinal compressive stress) and longitudinally interacting defects (subjected to internal pressure only). Equation (2) from the DNV guidelines is used to determine the failure pressure of a pipe with a single corrosion defect under combined loads of internal pressure and longitudinal compressive stress. Equation (2) is the product of Equations (3) and (4), where Equation (3) is used to determine the failure pressure of a pipe with a single corrosion defect under internal pressure only and Equation (4) gives the factor for longitudinal compressive stresses.
However, Level 2 assessment methods have varying degrees of accuracy in their prediction of the failure pressure when compared to Level 3 assessment methods such as numerical analysis using the finite element method [
18]. Level 3 assessment methods involve advance analysis techniques and require a higher level of information such as boundary conditions and material properties for the analysis. Numerical methods such as the finite element method (FEM) have been widely employed to verify and validate the failure behaviour and failure pressure of corroded pipelines [
17,
19,
20,
21]. FEM is especially useful for parametric studies with varying corrosion geometries, which otherwise would be too costly to be carried out experimentally. Despite the advantages of Level 3 assessment methods, numerical methods are computationally expensive. One FEM simulation with upwards of thirty thousand nodes in a model may take up to two to three hours. A comprehensive parametric study for varying corrosion defect geometries through FEM can be computationally and time-intensive.
Machine learning has been increasingly adopted for assessing the integrity and reliability of corroded pipelines. Machine learning models have been developed to predict the burst pressure of corroded pipelines, trained with a database of corroded pipeline burst pressures determined experimentally [
22,
23,
24]. Machine learning techniques could be used to develop a new assessment method that combines the advantages of both Level 2 and Level 3 assessment methods. Data-driven machine learning frameworks such as artificial neural networks (ANNs) have been used in the past to predict the failure pressure of straight pipes and pipe bends with a single corrosion defect [
9,
25], as well as interacting corrosion defects [
5,
10]. The dataset used to train the ANN models was derived from the FEM and full-scale burst test of pipelines with machined defects. These ANN models were used to understand the non-linear relationship between the corrosion geometries and failure pressure of corroded pipelines when subjected to internal pressure only. Tohidi and Sharifi [
26] found that the weights and biases from a trained ANN can be used to formulate an equation for the ultimate strength of locally corroded plate girder ends. The formula has a high degree of accuracy and can be used readily.
This paper proposes the application of an ANN together with the FEM to formulate an equation to predict the failure pressure of a corroded pipeline with varying longitudinally interacting corrosion defect geometries, subjected to internal pressure and longitudinal compressive stress.
4. Conclusions
An equation for the failure pressure prediction of a corroded pipeline subjected to combined loads was formulated from an ANN trained with a database generated by FEA. FEA was performed on an API 5L X65 grade steel pipe with longitudinal interacting corrosion defects and subjected to internal pressure and longitudinal compressive stress. The pipe was considered to have failed when the von Mises stress of its wall exceeded the true UTS in the FEA. The FEM was validated with burst tests to ensure an accurate representation of an actual pipeline failure pressure. Preliminary FEA was conducted to better understand the influence of the corrosion defect parameters and loading applied on the failure pressure of a pipe. The results from this preliminary FEA were compared with the DNV method, which revealed conservative failure pressure estimations by the DNV method. Further FEA was carried out in full factorial design for significant parameters only. Defect depth limits of 0.2 and 0.8 d/t; defect length limits of 0.2 and 1.2 l/D; defect spacing limits of 0 to 3 ; and longitudinal compressive stress limits of 0 to 0.7 were considered. In the full factorial design FEA, the interaction limit of longitudinally interacting defects was found to be 2.0 .
The results from FEA were used to train an ANN to formulate a failure pressure prediction equation. The training of the ANN was stopped when the error of its predictions achieved a satisfactory level of MSE < 1 × 10−5. The weights and biases from the trained ANN were expressed in mathematical form to formulate the failure pressure prediction equations. The failure pressure equations were compared with the DNV method and tested with an unseen FEA dataset. The predictions from the failure pressure prediction equations were accurate with an R2 value of 0.9921, an MSE of 4.746 × 10−4 and an MAE of 1.374 × 10−2, with the percentage error ranging from −9.39% to 4.63%, with a standard deviation of 2.83. All factors should be considered when assessing the failure pressure of a corroded pipeline, and the equations should complement, rather than replace, an established assessment method for a comprehensive and rigorous pipeline assessment.