# The Influence of Axial Compressive Stress and Internal Pressure on a Pipeline Network: A Review
## 3 Pipeline Residual Strength Assessment Methods
### Artificial Neural Networks  
An Artificial Neural Network (ANN) is a powerful prediction tool in machine learning that can result in highly accurate predictions [3]. They are nonlinear systems modelled efficiently using an interconnected complex assembly of nodes that utilize supervised learning algorithms to learn from a training database by recognizing and inferring from patterns without requiring an explicit set of instructions [50]. Over the past decade, the use of ANN in pipe integrity assessment has become increasingly popular. [PERSON] and [PERSON] [45] developed a back-propagation neural network (BPNN) with three layers for the assessment of residual load bearing capacity of steel plate girder ends with local corrosion using data generated from FEA. This approach resulted in accurate structural integrity assessments with a minimal error margin (within 2%). Based on the developed BPNN, an empirical equation was established for the assessment of the structure. Following this approach, [PERSON] et al. [42] developed an ANN for the vulnerability assessment of underground urban gas pipelines. In this study, the application of ANN was assessed against a support vector machine (SVM). Although it was concluded that SVM resulted in a more accurate assessment of the structure, the ANN also resulted in an acceptable error percentage of 8.64%. This error percentage can be drastically reduced by increasing the number of training data. [PERSON] et al. [11] developed an ANN for the failure pressure assessment of corroded pipes with a single corrosion defect subjected to internal pressure only based on burst test results of corroded pipe grades ranging from API 5L X42 to X100. A total of 71 datasets were utilized for the training of the developed ANN with 1 hidden layer (with 30 neurons). Based on the results of this study, it was revealed that the ANN predicts the failure pressures with a R-squared value of 0.99. In line with these approaches, various researchers have developed ANNs for the integrity assessment of steel structures. In this approach, new assessment methods have been developed by integrating FEM and ANN. As ANNs require a large set of training data, FEM is used as a data generation tool. The data from the FEA is then used to train the ANN, which results in highly accurate results for assessing corroded pipes subjected to internal pressure and axial compressive stress [3]. [PERSON] et al. [2; 9; 12; 43; 44] developed an empirical failure pressure assessment method for the failure pressure of corroded mid- to high-strength steel straight pipes with single defects [12], and longitudinally [43] as well as circumferentially [9] aligned the interacting defects subjected to internal pressure and axial compressive stress utilizing training data generated by FEA. In their assessment, the failure pressure was assessed as a function of the defect geometry and axial compressive stress acting on the pipe. For single corrosion defects, the developed empirical failure pressure equations were as a function of the defect depth and length and the axial compressive stress acting on the pipe. As for corroded pipes with interacting corrosion defects, the developed empirical failure pressure equations were as a function of the defect depth, length, and spacing, and the axial compressive stress acting on the pipe. The developed equations resulted in failure pressure predictions that were highly accurate with a R-squared value of 0.99. Following this approach, [PERSON] et al. [8] studied the application of ANN for the failure pressure prediction of underground high-strength steel (HSS) pipes that developed stray current corrosion defects. [PERSON] et al. [51] developed an ANN to assess the failure pressure of corroded mid- to high-strength steel straight pipes with a single defect subjected to internal pressure and axial compressive stress utilizing training data generated by FEA. The developed ANN resulted in failure pressure predictions with an R-squared value of 0.99.