# A Deterioration Model for Sewer Pipes Using CCTV and Artificial Intelligence

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## Abstract

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^{2}value for vitrified clay sewer pipes, concrete sewer pipes, and ductile iron sewer pipes are 71.18%, 71.47%, and 81.51%, respectively, and 73.69% for concrete stormwater pipes. To illustrate the impact of various factors on sewer pipes, sensitivity analyses under different scenarios are conducted. These analyses indicate that pipe diameter has a significant influence on sewer pipe deterioration, with little impact on stormwater pipes. These findings would guide decision makers in identifying critical pipes and taking necessary precautionary measures. Further, this provides a sound basis for prioritizing maintenance actions, which would pave the way for designing sustainable urban drainage systems for cities.

## 1. Introduction

- How can a prudent deterioration model be developed based on pipe age and structural grading?
- How can a predictive-based model be developed when there are inconsistencies with inspection data?

#### 1.1. Deterioration Models

#### 1.2. Weibull Analysis

#### 1.3. Point of Departure

## 2. Research Methods

#### 2.1. Phase A

#### 2.2. Phase B

#### 2.3. Phase C

## 3. Findings and Discussion

#### 3.1. Deterioration Model Using Weibull Analysis

- The newly installed pipes at t = 0 has an ICG of 0, which can be expressed as 1 on a scale from 0 to 1:

- 2.
- ICG = 5 at the end of the lifetime of the pipe, while ICG = 2 (critical performance index), which is presented as 0.25 on a scale from 0 to 1 and it represents the end of the useful service life (t):

- 3.
- The shape parameter 𝛿 = 3. 3 is chosen because it gives a better curve shape compared to 1, 2,3, 4, etc.

#### 3.2. Deterioration Models Using Unsupervised K-Means and Multilinear Regression

- 1.
- Clusters the data into k groups where k is predefined.
- 4.
- Select k points at random as cluster centers.
- 5.
- Assign objects to their closest cluster center according to the Euclidean distance function.
- 6.
- Calculate the centroid or mean of all objects in each cluster.
- 7.
- Repeat steps 2, 3, and 4 until the same points are assigned to each cluster in consecutive rounds.

^{2}and R

^{2}(adjusted) for vitrified clay sewer pipes are to be 71.18% and 71.11%, respectively. It indicates that the model fitted the data. Similarly, the values R2 and R2 (adjusted) for concrete sewer pipes were 71.47% and 70.92%. The ductile iron sewer pipes have a higher R

^{2}and R

^{2}(adjusted) value of 81.51% and 76.46% when compared to vitrified clay and concrete sewer pipes. It indicates that the model has a better fit. Furthermore, the concrete stormwater pipe had an R

^{2}and R

^{2}(adjusted) value of 73.69% and 73.64%. In general, the models showed good fit. R

^{2}shows that the predictors explain a certain percentage of the variance in the structural grade ICG, while the R

^{2}adjusted accounts for the number of predictors in the model.

_{0}) assumes that all regression coefficients are equal to zero. The alternate hypothesis (H

_{a}) assumes that not all of them are equal to zero. From the results, the p-value in the analysis of variance table is 0.000 for all material types. It implied that the null hypothesis is rejected, inferring that the model is significant—at a significance level of 0.05 hence—and at least one coefficient in the regression is not zero.

#### 3.3. Model Validation

#### 3.4. Sensitivity Analysis

#### 3.5. Model Summary

## 4. Practical Implications

- Having an understanding of the useful service life of the various pipe materials will help in making decisions on the best material to use while designing new sewer lines and replacing old ones.
- The Weibull deterioration curve will help professionals when planning for maintenance. The need to prioritize pipes that have exceeded their useful service life and the frequency of maintenance to be carried out on such pipes will be well planned. This will improve the lifespan of the pipes.
- The validation of CCTV inspection results through unsupervised learning will aid professionals to better understand the deterioration patterns given certain conditions and factors. Also, it helps them to ascertain the level of accuracy of inspection reports.
- The multilinear regression model developed in this study will be used in predicting the future condition state of pipes and when it is likely to fail. This will help in cost saving as measures are put in place to avoid such failure.
- One of the major impacts of sewer deterioration and failure is on the environment. This is because it can lead to the contamination of soil, drinking water sources, beaches, etc., thereby posing a risk to the health of the populace. The predictive model developed in this study would preclude such risks as a more proactive method of management and maintenance.

#### Limitation and Future Works

## 5. Conclusions

- Use of Weibull deterioration curve for concrete and vitrified clay pipes based on the pipe age and structural grading. It is a good analysis tool for modeling deterioration when there is not enough data to develop a more detailed model. There is a need to develop a Weibull-based model that takes into account the impact of both pipe age and overall structural grade, i.e., Internal Condition Grade (ICG) of pipe.
- Utilize unsupervised-based learning of CCTV inspection data using K-means clustering. Most CCTV inspection reports are done based on the inspector’s observation and there is often a likelihood to experience human error. Thus, the use of unsupervised learning can overcome such rampant concern, since it identifies patterns and relationships in an unlabeled dataset where insufficient data are provided. With the help of unsupervised learning, the accuracy of these reports can be validated and ascertained, achieving a more reliable model.
- The results produced from this study give managers a good basis to make decisions and avert the risk that sewer failure would have on the environment.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Using an expected service life of 100 years for concrete pipes and 60 years for vitrified clay pipes.

**Figure 4.**Actual ICG and predicted ICG for different pipe types and materials: (

**a**) Vitrified clay sewer pipes, (

**b**) Concrete sewer pipes, and (

**c**) Concrete stormwater pipes.

**Figure 5.**Sensitivity analysis. (

**a**) Vitrified clay sewer pipes. (

**b**) Concrete sewer pipes. (

**c**) Ductile iron sewer pipes. (

**d**) Concrete stormwater pipes.

Pipe Type | Percentage of Similarity with Actual Data |
---|---|

Vitrified clay sewer pipes | 88% |

Concrete sewer pipes | 79% |

Ductile iron sewer pipes | 93% |

Concrete stormwater pipes | 90% |

Ductile iron storm water pipes | 95% |

Term | Coef | SE Coef | T-Value | p-Value | VIF |
---|---|---|---|---|---|

Constant | 1.4399 | 0.0193 | 74.53 | 0.000 | |

Diameter (m) | 0.7802 | 0.0213 | 36.62 | 0.000 | 1.22 |

AGE (year) | −0.6915 | 0.0194 | −35.62 | 0.000 | 1.01 |

Length (m) | 0.0696 | 0.0214 | 3.25 | 0.001 | 1.22 |

Model Summary | |||||

S | R-sq | R-sq(adj) | R-sq(pred) | ||

0.679996 | 71.18% | 71.11% | 70.94% | ||

Analysis of Variance | |||||

Source | DF | Adj SS | Adj MS | F-Value | p-Value |

Regression | 3 | 1410.21 | 470.071 | 1016.60 | 0.000 |

Diameter (m) | 1 | 620.12 | 620.125 | 1341.12 | 0.000 |

AGE (year) | 1 | 586.57 | 586.571 | 1268.55 | 0.000 |

Length (m) | 1 | 4.90 | 4.895 | 10.59 | 0.001 |

Error | 1235 | 571.06 | 0.462 | ||

Lack-of-Fit | 1227 | 571.06 | 0.465 | * | * |

Pure Error | 8 | 0.00 | 0.000 | ||

Total | 1238 | 1981.27 |

Term | Coef | SE Coef | T-Value | p-Value | VIF |
---|---|---|---|---|---|

Constant | 1.8239 | 0.0716 | 25.47 | 0.000 | |

Diameter (m) | 0.4233 | 0.0784 | 5.40 | 0.000 | 1.19 |

AGE (year) | −1.3519 | 0.0723 | −18.70 | 0.000 | 1.01 |

Length (m) | 0.0599 | 0.0786 | 0.76 | 0.447 | 1.20 |

Model Summary | |||||

S | R-sq | R-sq(adj) | R-sq(pred) | ||

0.903053 | 71.47% | 70.92% | 69.58% | ||

Analysis of Variance | |||||

Source | DF | Adj SS | Adj MS | F-Value | p-Value |

Regression | 3 | 316.666 | 105.555 | 129.44 | 0.000 |

Diameter (m) | 1 | 23.781 | 23.781 | 29.16 | 0.000 |

AGE (year) | 1 | 285.156 | 285.156 | 349.67 | 0.000 |

Length (m) | 1 | 0.474 | 0.474 | 0.58 | 0.447 |

Error | 155 | 126.403 | 0.816 | ||

Total | 158 | 443.069 |

Term | Coef | SE Coef | T-Value | p-Value | VIF |
---|---|---|---|---|---|

Constant | 2.067 | 0.174 | 11.89 | 0.000 | |

Diameter (m) | −0.778 | 0.242 | −3.22 | 0.008 | 1.80 |

AGE (year) | 0.461 | 0.197 | 2.33 | 0.040 | 1.20 |

Length (m) | −0.345 | 0.224 | −1.54 | 0.152 | 1.55 |

Model Summary | |||||

S | R-sq | R-sq(adj) | R-sq(pred) | ||

0.672920 | 81.51% | 76.46% | 70.20% | ||

Analysis of Variance | |||||

Source | DF | Adj SS | Adj MS | F-Value | p-Value |

Regression | 3 | 21.952 | 7.3174 | 16.16 | 0.000 |

Diameter (m) | 1 | 4.694 | 4.6945 | 10.37 | 0.008 |

AGE (year) | 1 | 2.467 | 2.4673 | 5.45 | 0.040 |

Length (m) | 1 | 1.071 | 1.0706 | 2.36 | 0.152 |

Error | 11 | 4.981 | 0.4528 | ||

Total | 14 | 26.933 |

Term | Coef | SE Coef | T-Value | p-Value | VIF |
---|---|---|---|---|---|

Constant | 1.1298 | 0.0149 | 75.59 | 0.000 | |

Diameter (m) | 0.7252 | 0.0157 | 46.31 | 0.000 | 1.10 |

AGE (year) | 0.3100 | 0.0150 | 20.70 | 0.000 | 1.00 |

Length (m) | 0.3820 | 0.0156 | 24.43 | 0.000 | 1.09 |

Model Summary | |||||

S | R-sq | R-sq(adj) | R-sq(pred) | ||

0.568732 | 73.69% | 73.64% | 73.53% | ||

Analysis of Variance | |||||

Source | DF | Adj SS | Adj MS | F-Value | p-Value |

Regression | 3 | 1308.52 | 436.174 | 1348.48 | 0.000 |

Diameter (m) | 1 | 693.56 | 693.556 | 2144.21 | 0.000 |

AGE (year) | 1 | 138.54 | 138.538 | 428.31 | 0.000 |

Length (m) | 1 | 193.11 | 193.108 | 597.02 | 0.000 |

Error | 1444 | 467.07 | 0.323 | ||

Lack-of-Fit | 1441 | 467.07 | 0.324 | * | * |

Pure Error | 3 | 0.00 | 0.000 | ||

Total | 1447 | 1775.59 |

Descriptive Statistics | ||||
---|---|---|---|---|

Pipe Type | Mean | Standard Deviation | ||

Actual | Predicted | Actual | Predicted | |

Vitrified Clay Sewer pipes | 2 | 1 | 0.51 | 0.74 |

Concrete Sewer pipes | 3 | 2 | 1.42 | 1.62 |

Concrete Stormwater pipes | 3 | 3 | 1.31 | 1.02 |

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© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Salihu, C.; Mohandes, S.R.; Kineber, A.F.; Hosseini, M.R.; Elghaish, F.; Zayed, T.
A Deterioration Model for Sewer Pipes Using CCTV and Artificial Intelligence. *Buildings* **2023**, *13*, 952.
https://doi.org/10.3390/buildings13040952

**AMA Style**

Salihu C, Mohandes SR, Kineber AF, Hosseini MR, Elghaish F, Zayed T.
A Deterioration Model for Sewer Pipes Using CCTV and Artificial Intelligence. *Buildings*. 2023; 13(4):952.
https://doi.org/10.3390/buildings13040952

**Chicago/Turabian Style**

Salihu, Comfort, Saeed Reza Mohandes, Ahmed Farouk Kineber, M. Reza Hosseini, Faris Elghaish, and Tarek Zayed.
2023. "A Deterioration Model for Sewer Pipes Using CCTV and Artificial Intelligence" *Buildings* 13, no. 4: 952.
https://doi.org/10.3390/buildings13040952