Keywords: deterioration model, probabilistic neural networks, stormwater pipes, discriminant analysis.

This paper shows an application of probabilistic neural networks in modeling the serviceability deterioration of stormwater pipes. The deteriorating condition of a pipe is often assessed and graded using grading schemes and CCTV inspection data. The deterioration process of each pipe is considered following an independent pattern that is determined by the pipe's attributes. The pipes' attributes include design, construction and operation factors. The probabilistic neural networks model (PNNM) was then applied to the classsification of that individual pattern. Hence, it can predict the future condition of a pipe given its attributes. A case study was used in order to illustrate the performance of the proposed PNNM when comparing with the classical model using discrimiant analysis. In the case study, a new proposed threshold values for the existing grading scheme of the Water Service Australia Association [1] was also suggested and tested using the PNNM. Finally the effect of factors on serviceability deterioration was also investigated.

Two datasets from the case study were valid for the analysis. The first was developed using an existing grading scheme and the second used the new proposed threshold values. Furthermore, two extra factors, soil type and climatic classification (TMI) were added to both datasets because they might be contributing factors. They were inferred from the depth factor. In summary, nine input factors were used for both models. The datasets were further divided into a calibration dataset (75%) and a validation dataset (25%)

In determining the structure of the PNNM, a Bayesian classifier was adopted. For simplicity, the prior knowledge and mis-classification consequence were not used for Bayesian classifiers. In other words, all pipes were treated as equally important. Hence, a pipe is classified for a serviceability condition if its probability has the highest value compared to the ones of other conditions. The probability was estimated using a Gaussian distribution which is the most commonly used. The variance (smoothing parameter) of Guassian distribution is also an important element affecting the PNNM performance. It was selected using a trial and error search. It was concluded with a value equal to 2.5 for the implementation of the probabilistic neural network tool of the MATLAB software. The training process (calibrating model parameters) was actually assigning the pattern values from the calibration datasets to the weights connecting the neurons.

Similarly, a discriminant model was developed with the aid of the SPSS statistical software. The software provides all statistical tests and data processing. The model parameters were calibrated using calibration datasets.

Both models were then tested using validation dataset. The model's performance was evaluated using performance rate which is the percentage of correctly classified pattern over all input patterns. The results showed that PNNM outperformed discriminant model and there was a small drop in performance of 'proposed' dataset compared to 'existing' dataset. However, this small drop was considered ignorable.

The effects of a number of different factors on the deterioration of stormwater pipe networks were analysed. However, the key factors for prediction in the PNN model were found to be difficult to interpret, suggesting that besides prediction accuracy, the model interpretation is an important issue for further investigation. When using the discriminant model, pipe size, slope and climatic condition (TMI) were found significant factors affecting the pipe deterioration. However, when marginally statistical tests were used instead, only pipe size, age and slope were found to be marginally significant factors.

1

WSAA, Sewer Inspection Reporting Code of Australia: Water Service Association of Australia (WSAA), 2002.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £105 +P&P)