# Geoadditive Quantile Regression Model for Sewer Pipes Deterioration Using Boosting Optimization Algorithm

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Mathematical Formulation

- First, collection of the available data including inspection data (e.g., observed defects, their severity, their orientation and their location), pipe characteristics (e.g., length, diameter, material type, buried depth and slope) and maintenance data (e.g., number of previous flushes, number of previous reported backups). If available, the operational data (e.g., dry weather flow, wet weather flow, inflow infiltration) are also collected.
- Second, data processing where variables are classified into categorical (e.g., material) and continuous (e.g., diameter). The response variable is the internal condition of the pipe that is expressed in terms of score obtained after rating the observed defects following a grading protocol (e.g., Water Resource Center: WRc). The model equation is developed, and the base learners’ priors are selected.
- Third, the last step is simulation and model performance evaluation. The number of iterations and step-length are set to the same values in both quantiles. The validated models are used for predictions and the effect of the selected covariates are examined.

#### 2.1. Geoadditive Quantile Regression

#### 2.2. Boosting Algorithm

Algorithm 1: Component-wise functional gradient descent boosting algorithm for structured additive quantile regression. | |

## 3. Case Study

#### 3.1. Inspection Data Collection and Processing

#### 3.2. Factors Selection and Model Development

#### 3.3. Response Variable

## 4. Results and Discussion

#### 4.1. Model Selected Covariates

#### 4.2. Covariates’ Effects on the Response Variable

#### 4.3. Spatial Effects

_{2}S) that reacts with the cementitious pipes and reduces their thickness. An in-depth investigation will likely reveal the main causes of the obtained high deterioration rate in the airport area. However, on the decision-making side, early decision making recommends an increase of inspection frequency in this area. The south west districts, where there are a mix of cementitious and plastic pipes, present also high deterioration rates for both 50% and 95% quantiles (Figure 12b,c).

#### 4.4. Discussion

## 5. Conclusions

## 6. Future Research Needs

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

SQRM | Structured Quantile Regression model |

GMRF | Gaussian Markov Random Filed |

ICG | Internal Condition Grading |

EPA | Environmental Protection Agency |

AC | Asbestos Cement |

CON | Concrete |

BR | Brick |

VCT | Vitrified clay |

ST | Steel |

CI | Cast iron |

CMP | Corrugated metal pipes |

PVC | Polyvinyl chloride |

PE | Polyethylene |

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**Figure 6.**(

**a**) Linear effect of the diameter on the 95% quantile; (

**b**) nonlinear effects of the length covariate on the 5% quantile.

**Figure 10.**Physical characteristics covariates fitting to the response variables (

**a**) age, (

**b**) length, (

**c**) diameter, (

**d**) material.

**Figure 11.**Example of maintenance covariates fitting to the output response (

**a**) number of previous backups, (

**b**) number of previous repairs.

Covariates (Physical) | Description |
---|---|

Material | Designed material of pipes (categorical: 1 = cementitious, 2 = clay, 3 = metallic, 4 = plastic) |

Age | The difference between the inspection date and the installation date (continuous) |

Length | The manhole to manhole distance inspected (continuous) |

Diameter | size of the pipes (continuous) |

Depth | mean distance from the crown of the pipe to the ground surface (continuous) |

Slope | Angle between the pipes axis with the horizontal (continuous) |

rservs | Number of residential connections to the pipe (continuous) |

cservs | Number of commercial buildings connected to the pipe (continuous) |

Covariates (Maintenance) | |

Flushes | Number of flushes done previously on the sewer pipe (continuous) |

repairs | Number of previous repairs on the sewer pipe (continuous) |

Rcuts | Number of times, the roots have been cut from inside the pipe (continuous) |

Backups | Number of times, there have been water backups in the sewers (continuous) |

Degrease | Number of time, the maintenance team have degreased the sewer pipe (continuous) |

Cleaning | Number of time, the sewer pipes have been cleaned (continuous) |

Covariates (Environmental) | |

Geospatial location | The geographic location of the sewer pipe. While it is widely accepted that pipes having the same characteristics deteriorates at the same pace, there is a variation in the deterioration across pipes in the same cohort but affected by different environmental covariates such as the nature of the soil they are buried in, the groundwater fluctuation, soil compaction, traffic on the ground, activities in the vicinity. These unobserved and unknown data have correlated and uncorrelated effects on the structural response |

Covariates | 5th Percentile | 50th Percentile | 95th Percentile | |||
---|---|---|---|---|---|---|

Linear | Nonlinear | Linear | Nonlinear | Linear | Nonlinear | |

Age | - | - | x | x | x | x |

rservs | - | x | x | x | x | |

cservs | - | x | x | - | x | - |

Length | - | x | - | - | - | - |

Diameter | - | - | - | - | x | - |

Material | x | - | x | - | x | - |

Flushes | - | x | x | x | - | x |

Cleaning | - | x | - | x | - | - |

Degrease | - | x | - | x | - | - |

Backups | - | x | - | x | - | - |

Roots | - | x | - | x | - | - |

repairs | x | x | x | x | x | x |

Replaced | - | - | X | - | x | - |

Slope | - | x | - | x | - | - |

Depth | - | x | - | x | - | - |

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**MDPI and ACS Style**

Balekelayi, N.; Tesfamariam, S.
Geoadditive Quantile Regression Model for Sewer Pipes Deterioration Using Boosting Optimization Algorithm. *Sustainability* **2020**, *12*, 8733.
https://doi.org/10.3390/su12208733

**AMA Style**

Balekelayi N, Tesfamariam S.
Geoadditive Quantile Regression Model for Sewer Pipes Deterioration Using Boosting Optimization Algorithm. *Sustainability*. 2020; 12(20):8733.
https://doi.org/10.3390/su12208733

**Chicago/Turabian Style**

Balekelayi, Ngandu, and Solomon Tesfamariam.
2020. "Geoadditive Quantile Regression Model for Sewer Pipes Deterioration Using Boosting Optimization Algorithm" *Sustainability* 12, no. 20: 8733.
https://doi.org/10.3390/su12208733