Ensemble learning model for water pipe leakage prediction

Water pipe leakage prediction

In other literature, the kilometers in which the leak occurred can be used to calculate the failure rate. In this case study, this option is not selected because that information is not found. Multiple failures may have occurred on the same pipe. However, the age of construction is considered as the difference between the year the pipe was installed and a certain year. Finally, we used a dataset with dimension 63423 × 10. The information considered is shown in Table 3. In Table 6, the input variables and methodologies used are compared with other common inputs and methodologies considered in the reviewed literature.

Regarding Table 1, Hazen-Williams C is a relationship that relates the flow of water in a pipe to the physical properties of the pipe and pressure. In WDS, it is very common to divide the system into segments based on pipeline (material) type. Cities are not at the same altitude. This factor is also called height or depth in other papers. This option is not selected because that information is not found in this document. Another factor that must be accounted for is the number of breaks. In this case, all breaks in the pipe are calculated together. It is important to explain that the number of breaks, once the break in the pipe is repaired, the resistance of the pipe will be different than before. Therefore, this study attempts to provide basic patterns for defining predictive models for WDS, depending on the initial considerations for the problem. .

Ensemble learning model results

In this section, detailed information about the tested models will be published. ELR was used for water pipe leakage prediction with pipeline failure rates to support the decision-making process for prioritizing water network remediation actions. The researchers set out to use a holdout validation technique on a large dataset to avoid sample bias issues by using a current holdout validation of 25%. The final model is trained using the complete dataset. The researchers reported that a Bayesian optimization approach was adopted to fine-tune the hyperparameters of these ELR models according to Table 7, and three sets were used as bagging ensemble method, boosting ensemble method, and optimizable ensemble method. We conducted an experiment.

The number of input predictors and samples is a range of optimizable hyperparameters for the ensemble model. The ideal hyperparameters for our study were selected using Bayesian optimization techniques from the range shown in Table 7.

In this study, the loss function was the mean squared error (MSE) between the predicted target value and the actual value. The acquisition function used by the Bayesian optimizer is the expected improvement per second plus the value.³⁷ Check the hyperparameters set for the next iteration. Water pipe leakage was predicted using an appropriate model in which the set of hyperparameters was optimized to minimize the upper bound of the confidence interval of the MSE objective function.

The tuning process patterns and optimal hyperparameter values ​​found using the Bayesian optimization search are shown in Figure 6. The curve in the figure represents the minimum hold-validated mean squared error resulting from identifying the ideal hyperparameter values, indicating that an optimal prediction is made. The water pipe failure rate can be achieved by selecting the MSE function in an optimizable ensemble model, as shown in Table 7. This table shows the Learning Rate, Minimum Leaf Size, and Number of Predictors to Simple. To develop the proposed method, the optimizable ensemble-based model with the lowest MSE was preferred over the Bayesian optimization method.

Figure 7 shows the response plots for three models: the bagged tree ensemble method, the boosted tree ensemble method, and the optimizable ensemble method, respectively. Figure 8 shows the residual plots for each model. Figure 9 shows the predicted values ​​compared to the actual plot of failure rates. (a) Bagged tree. (b) LS boost tree. (c) Optimizable ensemble.

Figure 9 plots the predicted values ​​and the actual response and shows that most of the values ​​are in good agreement, except for a few data points where the true and expected values ​​are significantly different. As shown in Figure 8, the width of the band of residual values ​​in the residual plot is constant with a few exceptions. The model gains are stable across all regression models due to the performance of the test data within the same regression model. Figure 7 compares the actual values ​​of water pipe leakage prediction by pipeline failure rate and shows that all developed models have high R2 scores. This result also shows that there is no significant variation between the predicted and actual values ​​and there are no outliers.

In this study, we evaluated the performance of each model using a set of mathematical validation equations. The evaluation matrix showed that the bagged tree had an RMSE of 0.03195, MAE of 0.0041853, and R2 of 0.98. However, the RMSE of the LS boosted tree is 0.022654, MAE is 0.014829, and R2 is 0.99. On the other hand, Optimizable Ensemble has RMSE of 0.00231, MAE of 0.00071513, and R2 of 1, as shown in Table 8. The results showed that all models were able to predict the failure rate of water pipes.

Table 8 compares the RMSE. RMinimum Correlation Bagged Ensemble Learning Model, LS Boost Ensemble Learning Model, Hyperparameter Optimizable Ensemble Learning Model 2, MSE, MAE. Experiments show that the maximum correlation optimizable ensemble learning model can achieve the best prediction effectiveness and RMSE. R2, MSE, and MAE are 0.00231, 1, 5.34E-06, and 0.00071513, respectively. Compared to the combination of bagging tree and LS boosted tree ensemble learning methods and optimizable ensemble models, the proposed model also achieved better results. It is observed that his developed ELR model is satisfactory.

computational complexity

The computational complexity of ensemble approaches is an additional important aspect to consider. The main drawback of optimizable ensembles through hyperparameter tuning is their complexity. It takes significantly more time to train (training time) than a boosted or bagged tree. It also requires more computational resources. It also provides the time complexity (observations/second) of the method in terms of predicted speed. The predicted speed measurement in (obs/s) refers to the number of observations processed per second. Conversely, it represents the time taken for one prediction in seconds.

The complexity of each algorithm is shown in Figure 10. The vertical axis represents complexity on the algorithm scale due to prediction speed and training time. The results show that Boosted Tree provides the best results in terms of prediction speed (280000 Obs/s) compared to Bagging Tree (72000 Obs/s) and Optimizable Ensemble (22000 Obs/s). I did. The researchers observed that the optimizable ensemble model had the highest predictive power. However, due to their high complexity, the prediction speed of optimizable ensemble models is highly dependent on the hardware used.

According to Table 9 and Figure 10, the proposed algorithm has the highest prediction rate among all methods with reverse order complexity. The complexity of the optimizable ensemble for hyperparameter tuning achieves the highest accuracy and is number one in the order of training time complexity. Of course, the complexity of ensemble learning methods increases with the optimization of hyperparameter tuning. Therefore, the training time of the boosted tree method and the bagging tree method is shorter than that of the proposed method. Therefore, the prediction process using optimizable ensembles takes more time than other algorithms. This can be a problem for large datasets.

Comparison of different machine learning models

According to Table 6, we found that SVM, ANN, and LR use more methods to compare and apply our problem in the reviewed literature. Further evaluation of the developed ELR model was performed and the results are shown in Table 4. Although the ELR model is considered to be superior, we compared it with several ML techniques to improve the applicability of the model and found it to have good predictive ability.

Model settings for machine learning models

Regarding SVM, capacitance (C), gamma (γ), and epsilon (ε) are the parameters that need to be defined and are shown in Table 10 for the SVM-L model and in Table 11 for the SVM-RBF model .

Regarding the ANN, the number of input layers, number of hidden layers, neurons in the hidden layer, training cycle, learning rate, and activation function are the parameters that need to be defined and are listed in Table 12 for the ANN model. parameter.

Comparing results of different machine learning models

We now consider the performance of the developed ELR model in comparison with other machine learning techniques, namely Support Vector Machine (SVM), Artificial Neural Network (ANN), and Linear Regression (LR), as shown in Table 13. Let's look at. The developed ELR model is: Better performance than other machine learning models applied to the same dataset in terms of RMSE, MSE, MAE, and R2 values. All testing of the various machine learning models was completed on Orange Data Mining using an Intel(R) Core (TM) i7-10510U. CPU @ 1.80 GHz 2.30 GHz, 16 GBRAM, PC.