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This research presents the condition prediction of sewer pipes using a linear regression approach. The analysis is based on data obtained via Closed Circuit Television (CCTV) inspection over a sewer system. Information such as pipe material and pipe age is collected. The regression approach is developed to evaluate factors which are important and predict the condition using available information. The analysis reveals that the method can be successfully used to predict pipe condition. The specific model obtained can be used to assess the pipes for the given sewer system. For other sewer systems, the method can be directly applied to predict the condition. The results from this research are able to assist municipalities to forecast the condition of sewer pipe mains in an effort to schedule inspection, allocate budget and make decisions.

Sewer pipelines are built to transport sewerage from all areas to the treatment plant eventually. The pipes are designed for a given life span, however the pipe deterioration usually follows no specific trend line. It is always challenging to predict the deteriorating process due to various involved factors, which are usually difficult to obtain relevant data. Those factors are categorized into three groups by Chughtai and Zayed [

The pipe conditions are obtained via various approaches. Some of available inspection techniques include: man-walk though, ultrasonic, focused electrode leak location (FELL), sewer scanner and evaluation technology (SSET), laser-based scanning system, and CCTV. The most popular method is the CCTV application. For the data used in this study, the condition data are primarily based on information obtained via CCTV. During the condition determination process, experts’ opinions are often adopted to rate a pipe section’s condition by combining all information. For the data used in this study, the pipe conditions are classified into 5 categories, as shown in

Research regarding the sewer pipe condition deterioration has been widely studied in recent years. There are various models applied and developed in the condition prediction. For example, Moselhi and Shehab [

This study aims to evaluate the significance of variables related to sewer mains. It also tends to predict the pipe condition using the linear regression approach.

The first step is the initial analysis of the data. The descriptive information includes pipe material, pipe diameter, pipe age, pipe installation depth. The pipe material includes concrete pipe and clay pipe. The pipe diameter ranges between 45 cm to 180 cm. The installation depth ranges between 65 cm to 213 cm. Additional data analysis will be presented in the results section

The second step is the application of regression approach. The general linear model is a linear model specifies the relationship between a dependent variable Y, and as set of predictor variables Xi, therefore, we have

In the equation, β_{0} is the regression coefficient for the intercept and β_{i} are the coefficients for the variable X_{i}. The β_{i} values are obtained by the maximum likelihood (ML) estimation, which is an iterative computational procedure. There are multiple method for the Ml estimate, such as Newton-Raphson and Fisher-Scoring methods [

In terms of statistical significance testing, the test are usually performed via Wald statistic, the likelihood ratio (LR), or a score statistic. Detailed information can be found in McCullagh and Nelder [

Index | State condition | Description |
---|---|---|

1 | Excellent | No defects |

2 | Good | Damage initiation |

3 | Fair | Multiple damages, possibly serious |

4 | Poor | Advanced damages |

5 | Bad | Damages threatening safety and functionality |

Pipe material | |||||||
---|---|---|---|---|---|---|---|

1. Pipe index = 0.657119 + 0.0926041 pipe age + 3.66928e−005 pipe diameter + 0.000892305 pipe depth | |||||||

2. Pipe index = 0.702251 + 0.0926041 pipe age + 3.66928e−005 pipe diameter + 0.000892305 pipe depth | |||||||

Coefficients | |||||||

Term | Coef | SE Coef | T | P | |||

Constant | 0.679685 | 0.181897 | 3.7367 | 0.000 | |||

Pipe age | 0.092604 | 0.002947 | 31.4209 | 0.000 | |||

Pipe diameter | 0.000037 | 0.000954 | 0.0385 | 0.969 | |||

Pipe material | |||||||

1 | −0.022566 | 0.035253 | −0.6401 | 0.523 | |||

Pipe depth | 0.000892 | 0.000847 | 1.0538 | 0.294 | |||

Summary of model | |||||||

S = 0.431973 | R-Sq = 86.99% | R-Sq(adj) = 86.64% | |||||

PRESS = 29.8366 | R-Sq(pred) = 86.13% | ||||||

In the following analysis, the constant and pipe age are included in the model. Although the pipe diameter does not seem to be a very significant variable, considering the P value (0.294) is not very great, it is also included in the model. The new fitting results are shown in

Therefore, based on the available data, the model generated is

Regression equation | ||||||
---|---|---|---|---|---|---|

Pipe index = 0.6775 + 0.0924892 | Pipe age + 0.000950407 | Pipe depth | ||||

Coefficients | ||||||

Term | Coef | SE Coef | T | P | ||

Constant | 0.677500 | 0.145722 | 4.6493 | 0.000 | ||

pipe age | 0.092489 | 0.002918 | 31.6969 | 0.000 | ||

pipe depth | 0.000950 | 0.000833 | 1.1406 | 0.256 | ||

Summary of model | ||||||

S = 0.429708 | R-Sq = 86.95% | R-Sq(adj) = 86.78% | ||||

PRESS = 29.1550 | R-Sq(pred) = 86.44% | |||||

Analysis of variance | ||||||
---|---|---|---|---|---|---|

Source | DF | Seq SS | Adj SS | Adj MS | F | P |

Regression | 2 | 187.004 | 187.004 | 93.502 | 506.38 | 0.000000 |

pipe age | 1 | 186.764 | 185.516 | 185.516 | 1004.70 | 0.000000 |

pipe depth | 1 | 0.240 | 0.240 | 0.240 | 1.30 | 0.255839 |

Error | 152 | 28.067 | 28.067 | 0.185 | ||

Total | 154 | 215.071 |

This paper develops a model to predict the condition of sewer mains. Based on the available data, it shows that among all available variables, the pipe age is the most significant factor. The pipe installation depth also has an impact in the regression analysis. The pipe material and pipe diameter are found to be less important. The regression generates a very decent model, with R square of 0.87 obtained. The ANOVA analysis re-emphasizes the importance of the pipe age variable. The residual analysis shows that the normality assumption of applying the linear model is valid. Although sewer mains are impacted by various factors which also differ significantly from municipality to municipality. The derived equation may not be directly used in other sewer systems. However, the method used and developed can be applied in the analysis of other sewer mains condition when relevant data are available.

Ali Gedam,Suraj Mangulkar,Bal Gandhi, (2016) Prediction of Sewer Pipe Main Condition Using the Linear Regression Approach. Journal of Geoscience and Environment Protection,04,100-105. doi: 10.4236/gep.2016.45010