# Failure Pressure Prediction of Corroded High-Strength Steel Pipe Elbow Subjected to Combined Loadings Using Artificial Neural Network

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## Abstract

**:**

## 1. Introduction

#### 1.1. High-Strength Steel Pipelines in the Oil and Gas Industry

#### 1.2. Pipeline Integrity Assessment Methods

#### 1.3. Artificial Neural Network as a Failure Pressure Prediction Tool

^{2}value of 0.99, and an ANN can be used for the failure pressure prediction of corroded pipes.

## 2. Methodology

#### 2.1. Geometric Parameters

#### 2.2. Pipe Material Properties

#### 2.3. Validation of the Finite Element Method

#### 2.4. Generation of Training Data Using Finite Element Method

#### 2.5. Development of Artificial Neural Network

^{2}value of 0.99 or greater.

## 3. Results and Discussion

#### 3.1. Development of Artificial Neural Network

#### 3.2. Development of Empirical Equation

#### 3.3. Failure Behaviour of Corroded High-Strength Steel Pipe Elbow

## 4. Conclusions

## 5. Recommendations for Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

$C$ | Cost function of an ANN using backpropagation algorithm |

$D$ | Diameter of pipe |

$d$ | Depth of defect |

$h$ | Hidden neuron of artificial neural network |

$i$ | Input variable of artificial neural network |

${i}_{n}$ | Normalised input variable of artificial neural network |

$l$ | Length of defect |

$o$ | Output variable of artificial neural network |

${P}_{f}$ | Failure pressure of a corroded pipe elbow |

${P}_{i}$ | Intact pressure of a pipe elbow |

$R$ | Bend radius of pipe elbow |

$s$ | Predicted output of an ANN |

${s}_{c}$ | Circumferential defect spacing |

${s}_{l}$ | Longitudinal defect spacing |

$t$ | Pipe wall thickness |

$UTS$ | Ultimate tensile strength |

$w$ | Defect width |

$y$ | Expected output of an ANN |

$UT{S}^{*}$ | True ultimate tensile strength |

${\sigma}_{c}$ | Axial compressive stress |

${\sigma}_{y}$ | Yield stress |

θ | Location of defect |

## Abbreviations

ANN | Artificial Neural Network |

FE | Finite Element |

FEA | Finite Element Analysis |

FEM | Finite Element Method |

FFNN | Feed Forward Neural Networks |

HSS | High-strength Steel |

## References

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**Figure 3.**Quarter model of a pipe elbow with (

**a**) no defects, (

**b**) a single defect, (

**c**) longitudinally aligned interacting defects (

**d**) circumferentially aligned interacting defects.

**Figure 4.**Application of axial compressive stress (normalised value of 0.5) and internal pressure during the transient analysis.

**Figure 8.**Normalised failure pressure of a corroded pipe elbow with a single defect of normalised defect length of 0.2 and subjected to a normalised axial compressive stress of 0.2.

**Figure 9.**Normalised failure pressures of corroded API 5L X80 pipe elbow with a normalised defect length of 0.5 and subjected to a normalised axial compressive stress of 0.2 for a single defect located at the (

**a**) intrados and (

**b**) extrados.

**Figure 10.**Normalised failure pressures of corroded API 5L X80 pipe elbow subjected to a normalised axial compressive stress of 0.2 for a single defect located at the intrados.

**Figure 11.**Normalised failure pressures of corroded (defect at the intrados) API 5L X80 pipe elbow with a normalised defect spacing (longitudinal) of 0.5 subjected to a normalised axial compressive stress of 0.2.

**Figure 12.**Normalised failure pressures of corroded (defect at the intrados) API 5L X80 pipe elbow with a normalised defect spacing (circumferential) of 0.5 subjected to a normalised axial compressive stress of 0.2.

Parameter | Value(s) |
---|---|

Diameter of pipe, $D$ | 300 mm |

Pipe wall thickness, $t$ | 10 mm |

Normalised pipe elbow bend radius, $R/D$ | 4.5 |

Defect location (θ) | −90°, 90° |

Normalised defect width, $w/t$ | 10 |

Normalised defect depth, $d/t$ | 0.0, 0.2, 0.4, 0.6, 0.8 |

Normalised defect length, $l/D$ | 0.0, 0.2, 0.5, 0.8, 1.1, 1.4 |

Normalised defect longitudinal spacing, ${s}_{l}/\sqrt{Dt}$ | 0.0, 0.5, 1.0, 2.0 |

Normalised defect circumferential spacing, ${s}_{c}/\sqrt{Dt}$ | 0.0, 0.5, 1.0, 2.0 |

Normalised axial compressive stress, ${\sigma}_{c}/{\sigma}_{y}$ | 0.0, 0.2, 0.4, 0.6, 0.8 |

Property | Value | |||
---|---|---|---|---|

API 5L X70 | API 5L X80 | API 5L X100 | Endplate | |

Modulus of elasticity, $E$ | 210 MPa | 210 MPa | 210 MPa | 210 TPa |

Poisson’s ratio, $v$ | 0.3 | |||

True ultimate tensile strength, $UT{S}^{*}$ (MPa) | 606.72 | 754.56 | 890.88 | - |

Yield stress, ${\sigma}_{y}$ (MPa) | 516.48 | 570.8 | 652.8 | - |

Author, Year | Shuai et al., 2022 [12] | Duan and Shen, 2006 [16] |

Pipe type | Elbow | Elbow |

Analysis type | FEM | Burst test |

Material | X80 | Based on published material properties |

Specimen | Convergence test model | Model 1 |

Burst Pressure (MPa) | 30.60 | 29.64 |

FEA failure pressure (MPa) | 29.74 | 28.86 |

Percentage Difference (%) | −2.81 | −2.63 |

Parameter | Value |
---|---|

Epoch | 2000 |

Minimum gradient | 1.023 × 10^{−10} |

Validation checks | 1500 |

Phase | Training | Validation | Test |
---|---|---|---|

R^{2} | 0.99 | 0.99 | 0.99 |

MSE | 0.0005 | 0.0004 | 0.0003 |

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## Share and Cite

**MDPI and ACS Style**

Vijaya Kumar, S.D.; Karuppanan, S.; Perumal, V.; Ovinis, M. Failure Pressure Prediction of Corroded High-Strength Steel Pipe Elbow Subjected to Combined Loadings Using Artificial Neural Network. *Mathematics* **2023**, *11*, 1615.
https://doi.org/10.3390/math11071615

**AMA Style**

Vijaya Kumar SD, Karuppanan S, Perumal V, Ovinis M. Failure Pressure Prediction of Corroded High-Strength Steel Pipe Elbow Subjected to Combined Loadings Using Artificial Neural Network. *Mathematics*. 2023; 11(7):1615.
https://doi.org/10.3390/math11071615

**Chicago/Turabian Style**

Vijaya Kumar, Suria Devi, Saravanan Karuppanan, Veeradasan Perumal, and Mark Ovinis. 2023. "Failure Pressure Prediction of Corroded High-Strength Steel Pipe Elbow Subjected to Combined Loadings Using Artificial Neural Network" *Mathematics* 11, no. 7: 1615.
https://doi.org/10.3390/math11071615