A hybrid of six soft models based on ANFIS for pipe failure rate forecasting and uncertainty analysis: a case study of Gorgan city water distribution network

The pipes as one of the main and important components of a water distribution network break during operation due to various factors. Developing models for pipes failure rate prediction can be one of the most important tools for managers and stakeholders during optimal operation of the water distribution network. In this study, the statistical and soft models such as Linear Regression, Generalized Linear Regression, Support Vector Machine, Feed Forward Neural Network (FFNN), Radial-Based Function Neural Network (RBFNN), and Adaptive Neuro-Fuzzy Inference System (ANFIS) were studied in order to predict the pipes failure rate based on the characteristics of Gorgan city water distribution network including diameter, length, age, installation depth, and number of failures of each pipe. In order to determine the optimal values of the parameters of each model, appropriate error indices including correlation coefficient (R), Mean Square Error (MSE), and Correlation Mean Square Error Ratio (CMSER) for training and test data were calculated, and the values of the parameters related to the model with the highest value of the CMSER index were considered as the model optimal values. Furthermore, in the validation stage, the values of R and MSE error indices for each of the above models were considered as a criterion for selecting the most appropriate model for predicting pipe failure rate. The findings show that among the soft and statistical models investigated, ANFIS with MSE of 0.071 and R of 0.92 can predict the failure rate of the studied network pipes more efficiently and more accurately than other models. Yet, despite the superiority of this model over other models, this model cannot accurately predict the failure rate of the studied network pipes due to its relatively high MSE value. Therefore, a new approach was developed based on the hybridization of trained models to provide a more efficient model for a more accurate prediction of the pipe failure rates of water distribution network. In this approach, the values of the network pipe failure rate predicted by each of the soft and statistical models are considered as independent input variables, and the observational failure rate values are considered as the dependent output variable of the ANFIS model. A comparison between the values of non-hybrid model validation data indices and the results of the proposed hybrid prediction model reveals that the use of the developed hybrid model increased the R error value from 8.1% (compared to the ANFIS model) to 260% (compared to the RBFNN model). It also decreased the MSE error value from 37% (compared to the FFNN model) to 58% (compared to the RBFNN model). Moreover, the hybrid model, compared to the superior non-hybrid ANFIS model, decreased MSE error rates by 45%. The findings show that the proposed model can significantly raise the accuracy of predicting the failure rate of pipes, compared to other existing models.

Automated summary

The study compared various statistical and soft models and found that the ANFIS model was the most efficient in predicting pipe failure rates. However, to further improve accuracy, a hybrid model was developed for prediction.