An Ensemble Learning Model for Forecasting Water-pipe Leakage

An Ensemble Learning Model for Forecasting Water-pipe Leakage | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article An Ensemble Learning Model for Forecasting Water-pipe Leakage Ahmed Ali Mohamed Warad, Khaled Wassif, Nagy Ramadan Darwish This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3892182/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 09 May, 2024 Read the published version in Scientific Reports → Version 1 posted 8 You are reading this latest preprint version Abstract Based on the benefits of different ensemble methods, such as bagging and boosting, which have been studied and adopted extensively in research and practice, where bagging and boosting focus more on reducing variance and bias, this paper presented an optimization ensemble learning-based model for a large pipe failure dataset of water pipe leakage forecasting, something that was not previously considered by others. It is known that tuning the hyperparameters of each base learned inside the ensemble weight optimization process can produce better-performing ensembles, so it effectively improves the accuracy of water pipe leakage forecasting based on the pipeline failure rate. To evaluate the proposed model, the results are compared with the results of the bagging ensemble and boosting ensemble models using the root-mean-square error (RMSE), the mean square error (MSE), the mean absolute error (MAE), and the coefficient of determination (R2) of the bagging ensemble technique, the boosting ensemble technique and optimizable ensemble technique are higher than other models. The experimental result shows that the optimizable ensemble model has better prediction accuracy. The optimizable ensemble model has achieved the best prediction of water pipe failure rate at the 14th iteration, with the least RMSE = 0.00231 and MAE = 0.00071513 when building the model that predicts water pipe leakage forecasting via pipeline failure rate. Physical sciences/Physics/Information theory and computation Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Mathematics and computing/Computational science Physical sciences/Mathematics and computing/Computer science Physical sciences/Mathematics and computing/Information technology Physical sciences/Mathematics and computing/Scientific data Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction In recent years, artificial intelligence (AI) and machine learning (ML) models have been suggested to be revolutionary innovations. 1 . ML is a branch of artificial intelligence that collects methods and algorithms for building experience-based learning systems. So, ML has been used to forecast failure rate of the water distribution network (WDN), with research on data validation and enhancement as well as investigations on the relationships between intervening factors that might explain the intricate process of pipe failure 2 . Water supply system leakage is a quiet problem that costs the globe billions of dollars each year. Because a large portion of the water supply pipelines are underground, leaks might go unnoticed and unreported for a long period of time 2 . Regarding water supply networks, there is a global trend among service management organizations to use machine learning to forecast pipe problems and breakages. Our previous work presented a systematic literature review (SLR) that employs ML models for water leakage problem 3 . Various studies have revealed the importance of water pipe leakage forecasting and presented machine learning algorithms for forecasting water pipe leakage and its failure rate. These studies include some of the most popular statistical models, such as linear regression (LR), poison regression (PR), and evolutionary polynomial regression (EPR). As machine-learning techniques, they use gradient boost trees (GB) 4–7 , Bayesian belief networks 8–10 , Support Vector Machines (SVMs) 11–13 and Artificial Neural Networks (ANNs) 11,14–19 . These studies have consistently found that ML models can provide valuable insights into the condition of these pipelines and help prioritize maintenance and repair efforts based on forecasting the failure rate of water pipes; however, ensemble approaches for water pipe leakage predictions have yet to be thoroughly investigated. Pipe failure is an essential instrument for water distribution network strategic restoration planning. Existing network data (physical data) and historical failure records (number of breaks) are used to make rehabilitation projections. 20 . Subsequently, pipe failure rate is an important measure to water pipe leakage forecasting. On the other hand, ensemble learning methods have been used widely in various applications and areas. To fit ensemble learning models into different problems, their hyperparameters must be tuned. Selecting the best hyperparameter configuration for ensemble learning models has a direct impact on the model’s performance. The application of ensemble learning methods 21 has become ubiquitous across various domains, from healthcare 22 , finance 23,24 , image recognition 25 , natural language processing 26–28 , enabling informed decision-making and predictive analytics 29,30 . However, the efficacy of ensemble learning models heavily relies on the careful selection of hyperparameters 31 , configuration setting that dictate the learning process and influence the model's generalization ability. Several ensemble models and approaches have been devised and widely utilized for classification and regression issues over the last two decades. In data analytics, ensemble models 32 are well-motivated, but not all ensembles are created equal. Specifically, different types of ensembles include bagging, and boosting. Each strategy has advantages and disadvantages. Bagging tends to decrease variance, not bias, to solve the over-fitting problem boosting aims to decrease bias, not variance by sequentially combining weak learners but is sensitive to noisy data and outliers and is prone to overfitting, as shown in Table 1. The aim of this paper is to suggest a new model in order to minimize the number of leakages for enhanced planning based on the pipe failure rate of water distribution networks (WDNs) by integrating the best hyperparameter tune of ensemble learning regression methods to predict water pipe leakage forecasting via pipeline failure rate, considering different lengths of water pipeline (100–2,000 mm) and different types of pipelines materials (thermoplastic, concrete pressure pipes, and ferrous); the data in this study is to be collected from Alexandria Water Company Egypt (AWCO). The proposed method involves collecting a dataset for water pipe leakage. This dataset includes several features linked to pipeline failures, such as pipeline material, age, etc. Pre-processing, feature selection, and descriptive statistical analysis are performed on the dataset. In this paper, the researchers focus on optimization ensemble weights and hyperparameter ensemble methods for our regression problem. However, determining the diversity of models to include is one challenging part of constructing an optimal ensemble. The proposed model will use Bayesian optimization method for optimizing the weights and hyperparameters of ensemble learning combined with a holdout-validation procedure for water pipe leakage using real data. Next, compare the optimization ensemble method, boosted tree ensemble learning, and bagged tree ensemble learning. Each model's performance varies based on the dataset and the model's base learner, with Bayesian parameter optimization producing the most accurate predictions. This paper is organized as follows: Section 2 discusses modelling techniques. In section 3, the proposed methodology and model development are discussed, along with the procedural details required for water pipe leakage forecasting. The proposed model's performance is compared to bagging and boosting models, as explained in Section 4. Finally, the paper's summary and recommendation for further research are provided in Section 5. Modelling Techniques Ensemble Learning 33,34 is, one of the hot topics, the integration of numerous learners (classification and regression models) to build a powerful learner (ensemble model). Unlike traditional learning methods, which attempt to build a single model from training data, ensemble learning methods attempt to build numerous models to tackle the same issue. Due to the availability of precise and diversified multiple models for integrating into a single solution, ensemble learning typically gives solutions with higher accuracy and/or resilience in most situations. Ensemble learning is often done in three phases: (1) development of base models, (2) selection of base models, and (3) aggregation of the selected base models utilizing certain combination methods. In the first step, a pool of basic models is formed, which might be homogeneous (same model types) or heterogeneous (various model types) (mixture of different model types). A base learning algorithm, such as decision trees, neural networks, or other approaches, is typically used to build base learners from training data. A selection of basic models is chosen in the second step. Finally, using a combination approach, the selected models are aggregated to produce a model. An ensemble's generalization capacity is frequently substantially stronger than that of basic learners. To obtain the final model with greater generalization, it is critical that the basic models be as precise and varied as feasible. Bagging Technique. Bagging 33,35 is an ensemble learning approach that is also known as Bootstrap aggregation. The same approach is used to train many models in parallel, each using a fraction of the training data created by bootstrap sampling. Bootstrap sampling is a sampling method in which a sample is formed by randomly picking items from a data collection and replacing them with replacement items. That is, after each selection, the item is returned to the data set. As a result, the same item may be picked more than once for the same sample. The metamodel is created by collecting the outcomes of many models by either voting (classification job) or averaging (regression task), as seen in Figure 1. Bagging is dependent on the varied training sizes of training data, which are referred to as bags, obtained from the training dataset. Each ensemble member is built using the tagging procedure. The prediction model is then constructed for each subset of bags, combining the values of several outputs by voting or averaging across the class label. The Bagging method first chooses a random sample with replacement from the original training dataset, and then generates numerous learner algorithm outputs (bags). Boosting Technique. Boosting 34,36 is a sequential ensemble method for converting low-accuracy models (weak learners) into strong ensemble models. After training a basic model with poor accuracy, the next generation of the model focuses on the instances in the training data set that were wrongly identified. Each succeeding model version is trained using the whole training data set to create an aggregated predictor, which reduces the likelihood of overfitting the data. Finally, using the weighted majority vote (classification task) or weighted sum, the predictions from each model are integrated into a single final forecast (regression task). Boosting, as seen in Figure 2. Hyperparameter Optimization Model Hyperparameter optimization 32 37 is one of the major challenges in the ML industry. This stage includes identifying an effective hyperparameter configuration that enhances the model’s performance for a particular dataset. Usually, these hyperparameters are identified before beginning the learning process that are tuned based on the performance of the selected hyperparameter and a validation set performance as an objective. There are different hyperparameter optimization algorithms, such as (1) grid search is considered expensive from computationally side because require searching for all possible defined hyperparameter configurations to identify and select the optimal model, and (2) random search that try to overcome the limitations of the grid search by optimizing the model in a randomly selected hyperparameter configuration, however, its stochastic nature may result in a bad hyperparameter configuration, but (3) Bayesian optimization provide a surrogate solution by developing a probabilistic model and using an acquisition function that helps to identify the most probability hyperparameters incorporating the previous evaluations from the search space, as seen in Figure 3. In each iteration, Bayesian optimization seeks to gather observations with the maximum amount of information by striking a balance between exploitation and exploration (i.e., investigating unknown hyperparameters) (gathering observations from hyperparameters close to the optimum). Proposed Methodology for Model Development The proposed methodology is to develop a predictive model for water pipe leakage via pipeline failure rate using ensemble learning methods. Our method consists of the subsequent stages: (1) Dataset generation stage based on Alexandria Water Company (ACWA) as water supply systems in Alexandria, Egypt, and (2) the proposed model has developed three models including Bagging, Boosting, and optimizable ensemble methods in order to select the one with satisfactory performance for water leakage forecasting, and evaluated by RMSE, MSE, MAE, and R2. In addition, validated based on the real data collected. These stages will be explained more in the following sections. Dataset Generation (Case study: City of Alexandria) Data is definitely the most vital element of machine learning. If there is no data, there is no common purpose. So, the aim of the collected data is to define the problem. Also, the way data is stored and organized is important based on the type of variable. Using data from our research collected from water supply systems in Alexandria, Egypt, the cadastral base investigated has 1951913 water service connections and a length of distribution network of 9373 kilometers (Km) ‎, consisting of different types of materials such as "high-density polyethylene", "cast iron", and "polyvinyl chloride". Since the 1960s, the city of Alexandria has developed its water distribution network as part of its infrastructure, that is shown in Figure. 4 . Real data from the water supply network of Alexandria, a city in the north of Egypt, are used to illustrate and evaluate the models. This dataset was extracted from the Geographic Information System (GIS) office of Alexandria Water Company and was included in the Excel workbooks. It consists of 63423 data points, which cover the city of Alexandria with a total length of 3545206 m. The researchers preprocessed the data by replacing categorical variables like pipe material are encoded into numerical formats and replacing all missing values of attributes with the mean of the values because the most values in this case from a kind of numerical class attribute, the benefit of this pre-processing is to enhance the results of predictions for the predictive model and facility extract desired information from the dataset, as shown in Table 2. Model Development Ensemble Learning Regression (ELR) is an ML approach that combines several models to improve prediction performance for nonlinear regression problems 36 . In our study, we investigated three ensemble learning models: (A) Bootstrap Bagging (Bag) with Regression Trees (RT) Learners; (B) Least Square Boosting (LS Boost) with RT Learners; and (C) an optimizable ensemble method using Bayesian optimization. The model aims to improve the prediction performance by finding optimal values of "the minimum leaf size", "learning rate", "number of learners", and "number of predictors to sample" for the ensemble models’ optimizable hyperparameters. Models were developed to forecast the water pipe leakage on the basis of failure rate as the target based on more factors, such as "material", "diameter", and "length", etc. by using MATLAB version R2020a software 38 . The entire ensemble learning model process, which is represented using the flowchart in Figure 5 and its stepwise implementation using MATLAB, is outlined as follows in the algorithm structure: Load the data into the MATLAB software environment. Preprocess the dataset. Explore the dataset to get correlated features and types of variables. Represented the correlated features. Exitance: missing values and outliers. Preprocess the missing values of data and categorical types of variables. Modeling the dataset Transform the dataset into an ensemble learning model format. Identify the data set variable and the response. Identify the percent of held-out using the holdout-validation process. Apply the default Bagged and Boosting Ensemble tool in MATLAB for the data set. Evaluate bagged and boosted ensemble methods fitting through the dataset. Apply the Bayesian optimization process to identify the most relevant ensemble learning hyperparameters based on MSE values. Build the final model by optimizing the LS-Boosted tree and bagged tree algorithm with Bayesian optimization. Apply the resultant model to the entire throughout quality dataset. Evaluate and report the predictive performance of the model. Experimental Procedures The researchers used three ensemble techniques, as presented in section 3. The experiment results were implemented on an Intel (R) Core (TM) i7-10510U CPU @ 1.80 GHz and 2.30 GHz and the Windows 10 operating system. MATLAB software environment 38 version R2020a software has been used for regression as a machine learning toolbox. Configure using holdout-validation: 25%, because the dataset is large enough to avoid sample bias problems that will use previous research to focus the search space on the most promising values. Next, experiment using the boosting ensemble learning and bagged ensemble learning models. Configure the optimizable ensemble learning to use the maximum number of estimators at which the algorithm is ended ("number of learners": 8, and "a learning rate": 0.1). Following that, we will examine what the algorithms have done, intending to determine which method is more likely to be efficient and how this efficiency varies by hyperparameter tuning, utilizing ensemble learning on our problem., finally, repeat the experiment in the optimizable ensemble to determine the optimal convergence with 30 iterations scoring: 'Mean Squared Error', as shown in Table 3. Evaluation Measurements The efficacy of evaluation depends on which measure metrics are used; thus, it is essential to select metrics. Several metrics are often used to evaluate the performance of forecasting models.: root-mean-square-error (RMSE) given in (1), mean absolute error (MAE) given in (2), coefficient of determination (R2) given in (3), and mean square error (MSE) given in (4) are four evaluation metrics used in this paper to examine and evaluate the performance of the used machine learning methods 39–42 , shown in Table 4. The model with the fewest average deviations for the same data are often chosen to use the fundamental assessment technique known as mean absolute error (MAE). However, because they both amplify values with significant variances, the MSE and RMSE are susceptible to outliers. They are therefore appropriate for assessing stability. Results and Discussion The ELR was used for water pipe leakage forecasting via pipeline failure rate to assist in the decision-making process for the prioritization of water distribution networks rehabilitation measures. The researchers configured using the holdout-validation technique for large datasets to avoid sample bias problems by using 25% present held out-validation. The final model is trained using the full data set. The researchers conducted three sets of experiments as bagging ensemble technique, the boosting ensemble technique, and optimizable ensemble techniques as the Bayesian optimization approach was employed to fine-tune the hyperparameters of these ELR models, according to table 5. The number of input predictors and samples is the range of optimizable hyperparameters for the ensemble model. The ideal hyperparameters for our study were chosen to use the Bayesian optimization technique from the ranges displayed in Table 5. In this investigation, the loss function was the mean square error (MSE) between the objective values that were predicted and the actual values. The acquisition function used by the Bayesian optimizer is the expected improvement per second plus 37 to ascertain the hyperparameter set for the following iteration. Water pipe leakage was predicted using the appropriate model, which had its set of hyperparameters optimized to minimize the upper-per-confidence interval of the MSE objective function. The tuning process patterns and optimum hyperparameter values found using Bayesian optimization search are shown in Figure 6, the curves in the figure represent the minimal hold-validated mean square error that results from identifying the ideal hyperparameter values, and shows that the best prediction of water pipe failure rate can be achieved by selecting the MSE function in the optimizable ensemble model, as shown in Table 5. This table shows the "Learning Rate", "Minimum leaf Size", and "Number of predictors to simples". In order to develop the proposed method, the optimizable ensemble-based model was over the Bayesian optimization method, as it has the lowest MSE. Figures 7 showed response plots for the three models: the bagged tree ensemble technique, the boosted tree ensemble technique, and the optimizable ensemble technique, respectively. Figure 8 presents the Residuals plot of each model. Figures 9 demonstrates the predicted values comparing with actual plot of failure rate: (a) bagged tree; (b) LSboosted tree; and (c) optimizable ensemble. In Figures 9, shown the predicted values versus actual response have been plotted, showing that most of the values match, except for a few data points where the true and expected values diverge significantly. The breadth of the band for residual values in the residuals plot, as shown in Figure 8, is constant with a few exceptions. The model gains are stable across all regression models due to the performance of test data in the same. In Figure 7, versus actual values of water pipe leakage forecasting via pipeline failure rate and demonstrates that all the developed models scored high R. The results also show that there is no high variation between predicted and actual values, and there are no outliers. The study used a set of mathematical validation equations to evaluate each model's performance. The evaluation matrices demonstrated that bagged trees has RMSE 0.03195, MAE 0.0041853, and R2 0.98. However, LS boosted trees has RMSE 0.022654, MAE 0.014829, and R2 0.99. Optimizable Ensemble, on the other hand, has RMSE 0.00231, MAE 0.00071513, and R2 as 1, presented in Table 6. The results showed that all models could forecast the failure rate of water pipes. Table 6 compares the RMSE, 𝑅2, MSE, and MAE of the minimum correlation bagged ensemble learning model, LS boosted ensemble learning model, and optimizable ensemble learning model by hyperparameters. Experiments show that the maximal correlation optimizable ensemble learning model can achieve the best prediction effect, and RMSE, 𝑅2, MSE, and MAE are 0.00231, 1, 5.34E-06, and 0.00071513 respectively. Compared with the bagged tree and LS boosed tree ensemble learning method and optimizable ensemble model combination, the proposed model also achieved better results. Conclusion Using artificial intelligence-based techniques for solving decision support and engineering issues are common in today's world. This work presents a thorough and insightful investigation of the use of ensemble models on real dataset in water pipe leaking. Several common ensemble models and hyperparameter tuning strategies are being investigated to help researchers and practitioners use ensemble learning methods for data-driven predictions. Specifically, three ensemble models were studied.; optimization ensemble method, boosted tree ensemble learning and bagged tree ensemble learning, while evaluating the model performance using the RMSE, MSE, MAE, and R2 values for the failure rate as evaluating parameters. This paper presented a hyperparameter tuning optimization for models of Bayesian optimization-based ensemble learning real-world dataset is used in experiments to evaluate the effectiveness of various ensemble models and optimizable ensemble methods, as well as to offer useful examples of hyperparameter optimization. In light of the approach outlined in "dataset generation" and "ensemble learning algorithms development", the generated dataset is entered into various ensemble learning models, including the bagging ensemble technique, and the boosting ensemble technique as homogeneous ensemble, and the optimizable ensemble technique. Hyperparameter tuning methods are employed to enhance the learning procedures to predict water pipe leakage based on the failure rate. This study was conducted to develop an optimization-based ensemble learning model with Bayesian optimization for water pipe leakage forecasting via pipeline failure rate. The developed model applied to a real dataset of water pipe leakage from AWCO in Egypt and compared it to state-of-the-art ensemble learning methods. In light of the outcomes that were achieved, it was shown the three models had shown acceptable performances, the optimizable ensemble model was the most efficient, showing an RMSE of 0.00231 and an R2 of 1. These parameters were calculated by comparing actual and predicted cases during hold-validation. Our study demonstrates that the proposed model has excellent accuracy and high application value and shows unique advantages. This paper will help decision-makers in the decision-making process, through developing an optimization-based ensemble learning method that can optimize weights and tuning hyperparameters of ensemble learning methods in water pipe leakage forecasting as pipeline failure rate. For future research, the researchers will integrate this model that developed into an internet of things (IoT) system. Declarations Author Contribution All authors have contributed equally to this study and reviewed and approved the final version of the manuscript. Acknowledgements The authors acknowledge AWCO for providing the help and data described during this study. The research data was processed using the MATLAB software environment. Data Availability The data that supports the findings of this study is available from Alexandria Water Company. Restrictions apply to the availability of these data, which were used under license for the current study and are not publicly available. However, data are available from the corresponding author upon reasonable request and with permission from Alexandria Water Company. References Jan, Z. et al. Artificial intelligence for industry 4.0: Systematic review of applications, challenges, and opportunities. Expert Syst. Appl. 216, 119456 (2023). Islam, M. R., Azam, S., Shanmugam, B. & Mathur, D. 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Tables Table 1 Comparation between Boosting and Bagging techinque Boosting Bagging The aim of the model to decrease bias, not variance to decrease variance not bias, to solve the over-fitting problem Type of combing predictions different types the same type of prediction The weight of layer models according to their performance. Each model has the same weightage Training data subsets Every new data subset contains the elements were misclassified by previous models randomly drawn with replacement from the entire training dataset. The independent between the models New Models are influenced by the accuracy of previous Models (sequential) Each model is independent of each other (parallel) Table 2 Data description Variable Type description Input Factors Length Numerical The length of the pipe in meters(m) Diameter Numerical The diameter of pipe in millimeters Material Numerical The material of the pipe section, categorized as Numerical type Hazen-Williams C Numerical The relationship which relates the flow of water in a pipe with the physical properties of the pipe and the pressure Flow (m³/h) Numerical The average of flow of the pipe Velocity (m/s) Numerical The average of velocity of the pipe Head loss Gradient (m/km) Numerical result of head loss calculated using Hazen-William's formula divided by total length of the pipe Installation Year Numerical The Installation Year of pipe Age (years) Numerical The age of pipes in years Number of breaks Numerical The number of total damages recorded on the pipe Target Failure rate Numerical The rate of water pipe failure Table 3 Performance of different decision tree-based models based on validation error Bagged Trees Boosted Trees Optimizable Ensemble Minimum Leaf Size 8 8 29 Number of Leaners 30 30 272 Learning Rate _ 0.1 0.85188 Optimized Options disabled Disabled Auto validation holdout-validation: 25% Table 4 Statistical Performance Metrics Description Table 5 Configuration of constructed optimizable ensemble models Optimizable Hyperparameters Range Ensemble Methods [Bag, LS Boost] Optimizer Bayesian Optimizer Acquisition Function Expected improvement per second plus Minimum leaf Size [1-31711] Number of Learners [10-500] Learning Rate [0.001,1] Number of predictors to simples [1-10] Iterations 30 Table 6 Comparison of the Three Intelligent Models Results Bagged Trees Boosted Trees Optimizable Ensemble RMSE 0.03195 0.022654 0.00231 R2 0.98 0.99 1 MSE 0.0010208 0.00051322 5.34E-06 MAE 0.0041853 0.014829 0.00071513 Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3892182","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":271148595,"identity":"8669f98e-845f-42ad-a65d-b1ce6fdb2381","order_by":0,"name":"Ahmed Ali Mohamed Warad","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABEUlEQVRIiWNgGAWjYDACCSDmAbMSGB8kGEjIgZgHHhCphdngQ4GNMVhLApFa2CRnfEhLbACz8ejgn92d+OBtm10+f3sCgzSPweH0+WGHHwJtsZPTbcBhyZ2zmw3ntiVbzjjzgMEYqCV34+00A6CWZGOzAzisuZG7TZp3G7MBww2gMrCW2QkgLQcSt+HQIn8jd/tv3m31BvJALYdBDjOcnf4BrxYDoC3MvNsOGxjcSGBsnGGQliAvnYPfFsMbuZsl5/47bmB45mEzwwcDG8MN0jkFBxIMcPtF7kbuxg9vzlQbyB1PPv4j4Y+EvPzs9M0fPlTYyeH0PgIwNkCcClZpQFA5EpBvIEX1KBgFo2AUjAQAAJoVaJ2Pdzd2AAAAAElFTkSuQmCC","orcid":"","institution":"Cairo University","correspondingAuthor":true,"prefix":"","firstName":"Ahmed","middleName":"Ali Mohamed","lastName":"Warad","suffix":""},{"id":271148596,"identity":"9745b165-4c9b-47b2-b6bf-ba0b351c970b","order_by":1,"name":"Khaled Wassif","email":"","orcid":"","institution":"Cairo 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1","display":"","copyAsset":false,"role":"figure","size":110112,"visible":true,"origin":"","legend":"\u003cp\u003eBagging Ensemble Technique\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3892182/v1/4fa02a07a13776579d0cfe0f.png"},{"id":50756918,"identity":"533408a1-2ccd-480e-b3a1-8e774bac68d3","added_by":"auto","created_at":"2024-02-06 19:43:37","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":229607,"visible":true,"origin":"","legend":"\u003cp\u003eBoosting Ensemble Technique\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3892182/v1/1bcc6f2f88b2d1184cdde5a0.png"},{"id":50757286,"identity":"d04751cb-bb75-4ff0-9f1e-e6f3903b2b5f","added_by":"auto","created_at":"2024-02-06 19:51:37","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":81466,"visible":true,"origin":"","legend":"\u003cp\u003eEnsemble Model with internally tuned hyperparameters\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-3892182/v1/d7f9833d244c8bddc3f0f421.png"},{"id":50757561,"identity":"8205e481-5f6a-4c55-8027-d73eb832b7b9","added_by":"auto","created_at":"2024-02-06 19:59:37","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":792823,"visible":true,"origin":"","legend":"\u003cp\u003eThe water network of the city of Alexandria\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-3892182/v1/d072851dce6103d1e81d27d3.png"},{"id":50757285,"identity":"c30c4817-de3b-4516-9615-61a19b2b217f","added_by":"auto","created_at":"2024-02-06 19:51:37","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":362097,"visible":true,"origin":"","legend":"\u003cp\u003eProposed Framework\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-3892182/v1/91da469e3bec5ea97b265a80.png"},{"id":50756921,"identity":"de27e3a6-0021-44c5-9c36-4b768f8136e3","added_by":"auto","created_at":"2024-02-06 19:43:37","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":93756,"visible":true,"origin":"","legend":"\u003cp\u003ePerformance curve of optimizable ensemble model\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-3892182/v1/0e7549f4d39c46ec0d271c53.png"},{"id":50756925,"identity":"f04bf7d8-3104-40a4-99ed-92b061d1f21a","added_by":"auto","created_at":"2024-02-06 19:43:37","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":392739,"visible":true,"origin":"","legend":"\u003cp\u003eresponse plots of failure rate: (a) bagged tree; (b) LSboosted tree; and (c) optimizable ensemble\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-3892182/v1/3dfdad420483e51199bea9d5.png"},{"id":50756923,"identity":"10d35e7f-7534-4549-9733-46644a4f892a","added_by":"auto","created_at":"2024-02-06 19:43:37","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":200112,"visible":true,"origin":"","legend":"\u003cp\u003ethe Residuals plot of failure rate: (a) bagged tree; (b) LSboosted tree; and (c) optimizable ensemble\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-3892182/v1/f9c1a47e8ff24b3680c4866b.png"},{"id":50757287,"identity":"aecc7ce5-9769-4b65-b11b-d7c3965da7f0","added_by":"auto","created_at":"2024-02-06 19:51:37","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":46540,"visible":true,"origin":"","legend":"\u003cp\u003epredicted vs actuall plot of failure rate: (a) bagged tree; (b) LSboosted tree; and (c) optimizable ensemble\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-3892182/v1/380e733050a00b9ab99ae265.png"},{"id":56488305,"identity":"37e08bb5-976b-46bc-a8fc-0553b78af16b","added_by":"auto","created_at":"2024-05-14 21:31:45","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2554851,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3892182/v1/77196c3b-0ae7-4e3b-90d6-a4d6f5c3d986.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"An Ensemble Learning Model for Forecasting Water-pipe Leakage","fulltext":[{"header":"Introduction","content":"\u003cp\u003eIn recent years, artificial intelligence (AI) and machine learning (ML) models have been suggested to be revolutionary innovations.\u003csup\u003e1\u003c/sup\u003e. ML is a branch of artificial intelligence that collects methods and algorithms for building experience-based learning systems. So, ML has been used to forecast failure rate of the water distribution network (WDN), with research on data validation and enhancement as well as investigations on the relationships between intervening factors that might explain the intricate process of pipe failure\u0026nbsp;\u003csup\u003e2\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWater supply system leakage is a quiet problem that costs the globe billions of dollars each year. Because a large portion of the water supply pipelines are underground, leaks might go unnoticed and unreported for a long period of time\u0026nbsp;\u003csup\u003e2\u003c/sup\u003e. Regarding water supply networks, there is a global trend among service management organizations to use machine learning to forecast pipe problems and breakages. Our previous work presented a systematic literature review (SLR) that employs ML models for water leakage problem\u0026nbsp;\u003csup\u003e3\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eVarious studies have revealed the importance of water pipe leakage forecasting and presented machine learning algorithms for forecasting water pipe leakage and its failure rate. These studies include some of the most popular statistical models, such as linear regression (LR), poison regression (PR), and evolutionary polynomial regression (EPR). As machine-learning techniques, they use gradient boost trees (GB)\u0026nbsp;\u003csup\u003e4\u0026ndash;7\u003c/sup\u003e, Bayesian belief networks\u003csup\u003e8\u0026ndash;10\u003c/sup\u003e, Support Vector Machines (SVMs)\u0026nbsp;\u003csup\u003e11\u0026ndash;13\u003c/sup\u003e and Artificial Neural Networks (ANNs)\u0026nbsp;\u003csup\u003e11,14\u0026ndash;19\u003c/sup\u003e. These studies have consistently found that ML models can provide valuable insights into the condition of these pipelines and help prioritize maintenance and repair efforts based on forecasting the failure rate of water pipes; however, ensemble approaches for water pipe leakage predictions have yet to be thoroughly investigated.\u003c/p\u003e\n\u003cp\u003ePipe failure is an essential instrument for water distribution network strategic restoration planning. Existing network data (physical data) and historical failure records (number of breaks) are used to make rehabilitation projections.\u0026nbsp;\u003csup\u003e20\u003c/sup\u003e. Subsequently, pipe failure rate is an important measure to water pipe leakage forecasting. On the other hand, ensemble learning methods have been used widely in various applications and areas. To fit ensemble learning models into different problems, their hyperparameters must be tuned. Selecting the best hyperparameter configuration for ensemble learning models has a direct impact on the model\u0026rsquo;s performance.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe application of ensemble learning methods\u0026nbsp;\u003csup\u003e21\u003c/sup\u003e has become ubiquitous across various domains, from healthcare\u0026nbsp;\u003csup\u003e22\u003c/sup\u003e, finance\u0026nbsp;\u003csup\u003e23,24\u003c/sup\u003e, image recognition\u0026nbsp;\u003csup\u003e25\u003c/sup\u003e, natural language processing\u003csup\u003e26\u0026ndash;28\u003c/sup\u003e, enabling informed decision-making and predictive analytics\u0026nbsp;\u003csup\u003e29,30\u003c/sup\u003e. However, the efficacy of ensemble learning models heavily relies on the careful selection of hyperparameters\u003csup\u003e31\u003c/sup\u003e, configuration setting that dictate the learning process and influence the model\u0026apos;s generalization ability.\u003c/p\u003e\n\u003cp\u003eSeveral ensemble models and approaches have been devised and widely utilized for classification and regression issues over the last two decades. In data analytics, ensemble models\u003csup\u003e32\u003c/sup\u003e are well-motivated, but not all ensembles are created equal. Specifically, different types of ensembles include bagging, and boosting. Each strategy has advantages and disadvantages. Bagging tends to decrease variance, not bias, to solve the over-fitting problem boosting aims to decrease bias, not variance by sequentially combining weak learners but is sensitive to noisy data and outliers and is prone to overfitting, as shown in Table 1.\u003c/p\u003e\n\u003cp\u003eThe aim of this paper is to suggest a new model in order to minimize the number of leakages for enhanced planning based on the pipe failure rate of water distribution networks (WDNs) by integrating the best hyperparameter tune of ensemble learning regression methods to predict water pipe leakage forecasting via pipeline failure rate, considering different lengths of water pipeline (100\u0026ndash;2,000 mm) and different types of pipelines materials (thermoplastic, concrete pressure pipes, and ferrous); the data in this study is to be collected from Alexandria Water Company Egypt (AWCO). The proposed method involves collecting a dataset for water pipe leakage. This dataset includes several features\u0026nbsp;linked to pipeline failures, such as pipeline material, age, etc. Pre-processing, feature selection, and descriptive statistical analysis are performed on the dataset.\u003c/p\u003e\n\u003cp\u003eIn this paper, the researchers focus on optimization ensemble weights and hyperparameter ensemble methods for our regression problem. However, determining the diversity of models to include is one challenging part of constructing an optimal ensemble. The proposed model will use Bayesian optimization method for optimizing the weights and hyperparameters of ensemble learning combined with a holdout-validation procedure for water pipe leakage using real data. Next, compare the optimization ensemble method, boosted tree ensemble learning, and bagged tree ensemble learning. Each model\u0026apos;s performance varies based on the dataset and the model\u0026apos;s base learner, with Bayesian parameter optimization producing the most accurate predictions.\u003c/p\u003e\n\u003cp\u003eThis paper is organized as follows: Section 2 discusses modelling techniques. In section 3, the proposed methodology and model development are discussed, along with the procedural details required for water pipe leakage forecasting. The proposed model\u0026apos;s performance is compared to bagging and boosting models, as explained in Section 4. Finally, the paper\u0026apos;s summary and recommendation for further research are provided in Section 5.\u003c/p\u003e"},{"header":"Modelling Techniques","content":"\u003cp\u003eEnsemble Learning\u0026nbsp;\u003csup\u003e33,34\u003c/sup\u003e is, one of the hot topics, the integration of numerous learners (classification and regression models) to build a powerful learner (ensemble model). Unlike traditional learning methods, which attempt to build a single model from training data, ensemble learning methods attempt to build numerous models to tackle the same issue. Due to the availability of precise and diversified multiple models for integrating into a single solution, ensemble learning typically gives solutions with higher accuracy and/or resilience in most situations. Ensemble learning is often done in three phases: (1) development of base models, (2) selection of base models, and (3) aggregation of the selected base models utilizing certain combination methods. In the first step, a pool of basic models is formed, which might be homogeneous (same model types) or heterogeneous (various model types) (mixture of different model types). A base learning algorithm, such as decision trees, neural networks, or other approaches, is typically used to build base learners from training data. A selection of basic models is chosen in the second step. Finally, using a combination approach, the selected models are aggregated to produce a model. An ensemble\u0026apos;s generalization capacity is frequently substantially stronger than that of basic learners. To obtain the final model with greater generalization, it is critical that the basic models be as precise and varied as feasible.\u003c/p\u003e\n\u003cp\u003eBagging Technique.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBagging\u0026nbsp;\u003csup\u003e33,35\u003c/sup\u003e is an ensemble learning approach that is also known as Bootstrap aggregation. The same approach is used to train many models in parallel, each using a fraction of the training data created by bootstrap sampling. Bootstrap sampling is a sampling method in which a sample is formed by randomly picking items from a data collection and replacing them with replacement items. That is, after each selection, the item is returned to the data set. As a result, the same item may be picked more than once for the same sample. The metamodel is created by collecting the outcomes of many models by either voting (classification job) or averaging (regression task), as seen in Figure 1.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBagging is dependent on the varied training sizes of training data, which are referred to as bags, obtained from the training dataset. Each ensemble member is built using the tagging procedure. The prediction model is then constructed for each subset of bags, combining the values of several outputs by voting or averaging across the class label. The Bagging method first chooses a random sample with replacement from the original training dataset, and then generates numerous learner algorithm outputs (bags).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBoosting Technique.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eBoosting\u0026nbsp;\u003csup\u003e34,36\u003c/sup\u003e is a sequential ensemble method for converting low-accuracy models (weak learners) into strong ensemble models. After training a basic model with poor accuracy, the next generation of the model focuses on the instances in the training data set that were wrongly identified. Each succeeding model version is trained using the whole training data set to create an aggregated predictor, which reduces the likelihood of overfitting the data. Finally, using the weighted majority vote (classification task) or weighted sum, the predictions from each model are integrated into a single final forecast (regression task). Boosting, as seen in Figure 2.\u003c/p\u003e\n\u003cp\u003eHyperparameter Optimization Model\u003c/p\u003e\n\u003cp\u003eHyperparameter optimization\u003csup\u003e32\u003c/sup\u003e \u003csup\u003e37\u003c/sup\u003e is \u0026nbsp; one of the major challenges in the ML industry. This stage includes identifying an effective hyperparameter configuration that enhances the model\u0026rsquo;s performance for a particular dataset. Usually, these hyperparameters are identified before beginning the learning process that are tuned based on the performance of the selected hyperparameter and a validation set performance as an objective.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThere are different hyperparameter optimization algorithms, such as (1) grid search is considered expensive from computationally side because require searching for all possible defined hyperparameter configurations to identify and select the optimal model, and (2) random search that try to overcome the limitations of the grid search by optimizing the model in a randomly selected hyperparameter configuration, however, its stochastic nature may result in a bad hyperparameter configuration, but (3) Bayesian optimization provide a surrogate solution by developing a probabilistic model and using an acquisition function that helps to identify the most probability hyperparameters incorporating the previous evaluations from the search space, as seen in Figure 3.\u003c/p\u003e\n\u003cp\u003eIn each iteration, Bayesian optimization seeks to gather observations with the maximum amount of information by striking a balance between exploitation and exploration (i.e., investigating unknown hyperparameters) (gathering observations from hyperparameters close to the optimum).\u003c/p\u003e"},{"header":"Proposed Methodology for Model Development ","content":"\u003cp\u003eThe proposed methodology is to develop a predictive model for water pipe leakage via pipeline failure rate using ensemble learning methods. Our method consists of the subsequent stages: (1) Dataset generation stage based on Alexandria Water Company (ACWA) as water supply systems in Alexandria, Egypt, and (2) the proposed model has developed three models including Bagging, Boosting, and optimizable ensemble methods in order to select the one with satisfactory performance for water leakage forecasting, and evaluated by RMSE, MSE, MAE, and R2. In addition, validated based on the real data collected. These stages will be explained more in the following sections.\u003c/p\u003e\n\u003cp\u003eDataset Generation (Case study: City of Alexandria)\u003c/p\u003e\n\u003cp\u003eData is definitely the most vital element of machine learning. If there is no data, there is no common purpose. So, the aim of the collected data is to define the problem. Also, the way data is stored and organized is important based on the type of variable.\u003c/p\u003e\n\u003cp\u003eUsing data from our research collected from water supply systems in Alexandria, Egypt, the cadastral base investigated has 1951913 water service connections and a length of distribution network of 9373 kilometers (Km)\u0026nbsp;\u0026lrm;, consisting of different types of materials such as \u0026quot;high-density polyethylene\u0026quot;, \u0026quot;cast iron\u0026quot;, and \u0026quot;polyvinyl chloride\u0026quot;. Since the 1960s, the city of Alexandria has developed its water distribution network as part of its infrastructure, that is shown in Figure. 4\u003cspan dir=\"RTL\"\u003e.\u003c/span\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eReal data from the water supply network of Alexandria, a city in the north of Egypt, are used to illustrate and evaluate the models. This dataset was extracted from the Geographic Information System (GIS) office of Alexandria Water Company and was included in the Excel workbooks. It consists of 63423 data points, which cover the city of Alexandria with a total length of 3545206 m. The researchers preprocessed the data by replacing categorical variables like pipe material are encoded into numerical formats and replacing all missing values of attributes with the mean of the values because the most values in this case from a kind of numerical class attribute, the benefit of this pre-processing is to enhance the results of predictions for the predictive model and facility extract desired information from the dataset, as shown in\u0026nbsp;Table 2.\u003c/p\u003e\n\u003cp\u003eModel Development\u003c/p\u003e\n\u003cp\u003eEnsemble Learning Regression (ELR) is an ML approach that combines several models to improve prediction performance for nonlinear regression problems\u003csup\u003e36\u003c/sup\u003e. In our study, we investigated three ensemble learning models: (A) Bootstrap Bagging (Bag) with Regression Trees (RT) Learners; (B) Least Square Boosting (LS Boost) with RT Learners; and (C) an optimizable ensemble method using Bayesian optimization. The model aims to improve the prediction performance by finding optimal values of \u0026quot;the minimum leaf size\u0026quot;, \u0026quot;learning rate\u0026quot;, \u0026quot;number of learners\u0026quot;, and \u0026quot;number of predictors to sample\u0026quot; for the ensemble models\u0026rsquo; optimizable hyperparameters.\u003c/p\u003e\n\u003cp\u003eModels were developed to forecast the water pipe leakage on the basis of failure rate as the target based on more factors, such as \u0026quot;material\u0026quot;, \u0026quot;diameter\u0026quot;, and \u0026quot;length\u0026quot;, etc. by using MATLAB version R2020a software\u0026nbsp;\u003csup\u003e38\u003c/sup\u003e. The entire ensemble learning model process, which is represented using the flowchart in Figure 5 and its stepwise implementation using MATLAB, is outlined as follows in the algorithm structure:\u003c/p\u003e\n\u003col\u003e\n \u003cli\u003eLoad the data into the MATLAB software environment.\u003c/li\u003e\n \u003cli\u003ePreprocess the dataset.\u003col style=\"list-style-type: lower-alpha;\"\u003e\n \u003cli\u003eExplore the dataset to get correlated features and types of variables.\u003c/li\u003e\n \u003cli\u003eRepresented the correlated features.\u003c/li\u003e\n \u003cli\u003eExitance: missing values and outliers.\u003c/li\u003e\n \u003cli\u003ePreprocess the missing values of data and categorical types of variables.\u003c/li\u003e\n \u003c/ol\u003e\n \u003c/li\u003e\n \u003cli\u003eModeling the dataset\u003col style=\"list-style-type: lower-alpha;\"\u003e\n \u003cli\u003eTransform the dataset into an ensemble learning model format.\u003c/li\u003e\n \u003cli\u003eIdentify the data set variable and the response.\u003c/li\u003e\n \u003cli\u003eIdentify the percent of held-out using the holdout-validation process.\u003c/li\u003e\n \u003c/ol\u003e\n \u003c/li\u003e\n \u003cli\u003eApply the default Bagged and Boosting Ensemble tool in MATLAB for the data set.\u003c/li\u003e\n \u003cli\u003eEvaluate bagged and boosted ensemble methods fitting through the dataset.\u003c/li\u003e\n \u003cli\u003eApply the Bayesian optimization process to identify the most relevant ensemble learning hyperparameters based on MSE values.\u003c/li\u003e\n \u003cli\u003eBuild the final model by optimizing the LS-Boosted tree and bagged tree algorithm with Bayesian optimization.\u003c/li\u003e\n \u003cli\u003eApply the resultant model to the entire throughout quality dataset.\u003c/li\u003e\n \u003cli\u003eEvaluate and report the predictive performance of the model.\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp\u003eExperimental Procedures\u003c/p\u003e\n\u003cp\u003eThe researchers used three ensemble techniques, as presented in section 3. The experiment results were implemented on an Intel (R) Core (TM) i7-10510U CPU @ 1.80 GHz and 2.30 GHz and the Windows 10 operating system. MATLAB software environment\u0026nbsp;\u003csup\u003e38\u003c/sup\u003e version R2020a software has been used for regression as a machine learning toolbox.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eConfigure using holdout-validation: 25%, because the dataset is large enough to avoid sample bias problems that will use previous research to focus the search space on the most promising values. Next, experiment using the boosting ensemble learning and bagged ensemble learning models. Configure the optimizable ensemble learning to use the maximum number of estimators at which the algorithm is ended (\u0026quot;number of learners\u0026quot;: 8, and \u0026quot;a learning rate\u0026quot;: 0.1). Following that, we will examine what the algorithms have done, intending to determine which method is more likely to be efficient and how this efficiency varies by hyperparameter tuning, utilizing ensemble learning on our problem., finally, repeat the experiment in the optimizable ensemble to determine the optimal convergence with 30 iterations scoring: \u0026apos;Mean Squared Error\u0026apos;, as shown in\u0026nbsp;Table 3. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eEvaluation Measurements\u003c/p\u003e\n\u003cp\u003eThe efficacy of evaluation depends on which measure metrics are used; thus, it is essential to select metrics. Several metrics are often used to evaluate the performance of forecasting models.: root-mean-square-error (RMSE) given in (1), mean absolute error (MAE) given in (2), coefficient of determination (R2) given in (3), and mean square error (MSE) given in (4) are four evaluation metrics used in this paper to examine and evaluate the performance of the used machine learning methods\u0026nbsp;\u003csup\u003e39\u0026ndash;42\u003c/sup\u003e, shown in Table 4.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe model with the fewest average deviations for the same data are often chosen to use the fundamental assessment technique known as mean absolute error (MAE). However, because they both amplify values with significant variances, the MSE and RMSE are susceptible to outliers. They are therefore appropriate for assessing stability.\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cp\u003eThe ELR was used for water pipe leakage forecasting via pipeline failure rate to assist in the decision-making process for the prioritization of water distribution networks rehabilitation measures. The researchers configured using the holdout-validation technique for large datasets to avoid sample bias problems by using 25% present held out-validation. The final model is trained using the full data set. The researchers conducted three sets of experiments as bagging ensemble technique, the boosting ensemble technique, and optimizable ensemble techniques as the Bayesian optimization approach was employed to fine-tune the hyperparameters of these ELR models, according to table 5.\u003c/p\u003e\n\u003cp\u003eThe number of input predictors and samples is the range of optimizable hyperparameters for the ensemble model. The ideal hyperparameters for our study were chosen to use the Bayesian optimization technique from the ranges displayed in Table 5.\u003c/p\u003e\n\u003cp\u003eIn this investigation, the loss function was the mean square error (MSE) between the objective values that were predicted and the actual values. The acquisition function used by the Bayesian optimizer is the expected improvement per second plus\u003csup\u003e37\u003c/sup\u003e to ascertain the hyperparameter set for the following iteration. Water pipe leakage was predicted using the appropriate model, which had its set of hyperparameters optimized to minimize the upper-per-confidence interval of the MSE objective function.\u003c/p\u003e\n\u003cp\u003eThe tuning process patterns and optimum hyperparameter values found using Bayesian optimization search are shown in Figure 6, the curves in the figure represent the minimal hold-validated mean square error that results from identifying the ideal hyperparameter values, and shows that the best prediction of water pipe failure rate can be achieved by selecting the MSE function in the optimizable ensemble model, as shown in\u0026nbsp;Table 5. This table shows the \u0026quot;Learning Rate\u0026quot;, \u0026quot;Minimum leaf Size\u0026quot;, and \u0026quot;Number of predictors to simples\u0026quot;. In order to develop the proposed method, the optimizable ensemble-based model was over the Bayesian optimization method, as it has the lowest MSE.\u003c/p\u003e\n\u003cp\u003eFigures 7 showed response plots for the three models: the bagged tree ensemble technique, the boosted tree ensemble technique, and the optimizable ensemble technique, respectively. Figure 8 presents the Residuals plot of each model. Figures 9 demonstrates the predicted values comparing with actual plot of failure rate: (a) bagged tree; (b) LSboosted tree; and (c) optimizable ensemble.\u003c/p\u003e\n\u003cp\u003eIn Figures 9, shown the predicted values versus actual response have been plotted, showing that most of the values match, except for a few data points where the true and expected values diverge significantly. The breadth of the band for residual values in the residuals plot, as shown in Figure 8, is constant with a few exceptions. The model gains are stable across all regression models due to the performance of test data in the same. In Figure 7, versus actual values of water pipe leakage forecasting via pipeline failure rate and demonstrates that all the developed models scored high R. The results also show that there is no high variation between predicted and actual values, and there are no outliers.\u003c/p\u003e\n\u003cp\u003eThe study used a set of mathematical validation equations to evaluate each model\u0026apos;s performance. The evaluation matrices demonstrated that bagged trees has RMSE 0.03195, MAE 0.0041853, and R2 0.98. However, LS boosted trees has RMSE 0.022654, MAE 0.014829, and R2 0.99. Optimizable Ensemble, on the other hand, has RMSE 0.00231, MAE 0.00071513, and R2 as 1, presented in Table 6. The results showed that all models could forecast the failure rate of water pipes.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTable 6 compares the RMSE, 𝑅2, MSE, and MAE of the minimum correlation bagged ensemble learning model, LS boosted ensemble learning model, and optimizable ensemble learning model by hyperparameters. Experiments show that the maximal correlation optimizable ensemble learning model can achieve the best prediction effect, and RMSE, 𝑅2, MSE, and MAE are 0.00231, 1, 5.34E-06, and 0.00071513 respectively. Compared with the bagged tree and LS boosed tree ensemble learning method and optimizable ensemble model combination, the proposed model also achieved better results. \u0026nbsp;\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eUsing artificial intelligence-based techniques for solving decision support and engineering issues are common in today's world. This work presents a thorough and insightful investigation of the use of ensemble models on real dataset in water pipe leaking. Several common ensemble models and hyperparameter tuning strategies are being investigated to help researchers and practitioners use ensemble learning methods for data-driven predictions. Specifically, three ensemble models were studied.; optimization ensemble method, boosted tree ensemble learning and bagged tree ensemble learning, while evaluating the model performance using the RMSE, MSE, MAE, and R2 values for the failure rate as evaluating parameters.\u003c/p\u003e \u003cp\u003eThis paper presented a hyperparameter tuning optimization for models of Bayesian optimization-based ensemble learning real-world dataset is used in experiments to evaluate the effectiveness of various ensemble models and optimizable ensemble methods, as well as to offer useful examples of hyperparameter optimization. In light of the approach outlined in \"dataset generation\" and \"ensemble learning algorithms development\", the generated dataset is entered into various ensemble learning models, including the bagging ensemble technique, and the boosting ensemble technique as homogeneous ensemble, and the optimizable ensemble technique. Hyperparameter tuning methods are employed to enhance the learning procedures to predict water pipe leakage based on the failure rate.\u003c/p\u003e \u003cp\u003eThis study was conducted to develop an optimization-based ensemble learning model with Bayesian optimization for water pipe leakage forecasting via pipeline failure rate. The developed model applied to a real dataset of water pipe leakage from AWCO in Egypt and compared it to state-of-the-art ensemble learning methods. In light of the outcomes that were achieved, it was shown the three models had shown acceptable performances, the optimizable ensemble model was the most efficient, showing an RMSE of 0.00231 and an R2 of 1. These parameters were calculated by comparing actual and predicted cases during hold-validation. Our study demonstrates that the proposed model has excellent accuracy and high application value and shows unique advantages.\u003c/p\u003e \u003cp\u003eThis paper will help decision-makers in the decision-making process, through developing an optimization-based ensemble learning method that can optimize weights and tuning hyperparameters of ensemble learning methods in water pipe leakage forecasting as pipeline failure rate. For future research, the researchers will integrate this model that developed into an internet of things (IoT) system.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAll authors have contributed equally to this study and reviewed and approved the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThe authors acknowledge AWCO for providing the help and data described during this study. The research data was processed using the MATLAB software environment.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e \u003cp\u003eThe data that supports the findings of this study is available from Alexandria Water Company. Restrictions apply to the availability of these data, which were used under license for the current study and are not publicly available. 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Optimizing ensemble weights and hyperparameters of machine learning models for regression problems. Mach. Learn. with Appl. 7, 100251 (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGanaie, M. A., Hu, M., Malik, A. K., Tanveer, M. \u0026amp; Suganthan, P. N. Ensemble deep learning: A review. Eng. Appl. Artif. Intell. 115, (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eThomas Rincy, N. \u0026amp; Gupta, R. Ensemble learning techniques and its efficiency in machine learning: A survey. \u003cem\u003e2nd Int. Conf. Data, Eng. Appl. IDEA 2020\u003c/em\u003e (2020) doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1109/IDEA49133.2020.9170675\u003c/span\u003e\u003cspan address=\"10.1109/IDEA49133.2020.9170675\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKhoshgoftaar, T. M., Van Hulse, J. \u0026amp; Napolitano, A. Comparing boosting and bagging techniques with noisy and imbalanced data. IEEE Trans. Syst. Man, Cybern. Part ASystems Humans 41, 552\u0026ndash;568 (2011).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGalar, M., Fernandez, A., Barrenechea, E., Bustince, H. \u0026amp; Herrera, F. A review on ensembles for the class imbalance problem: Bagging-, boosting-, and hybrid-based approaches. IEEE Trans. Syst. Man Cybern. Part C Appl. Rev. 42, 463\u0026ndash;484 (2012).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIsabona, J., Imoize, A. L. \u0026amp; Kim, Y. Machine Learning-Based Boosted Regression Ensemble Combined with Hyperparameter Tuning for Optimal Adaptive Learning. \u003cem\u003eSensors\u003c/em\u003e 22, (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMathworks. Statistics and Machine Learning Toolbox\u0026trade; User\u0026rsquo;s Guide R2020a. \u003cem\u003eMATLAB Mathworks Inc\u003c/em\u003e 2020a, 7984 (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOzor, P. A., Onyedeke, S. O. \u0026amp; Mbohwa, C. Application of artificial neural network to analysis of campus water pipe failure. \u003cem\u003eProc. Int. Conf. Ind. Eng. Oper. Manag.\u003c/em\u003e 2018, 2014\u0026ndash;2022 (2018).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRobles-Velasco, A., Mu\u0026ntilde;uzuri, J., Onieva, L. \u0026amp; Rodr\u0026iacute;guez-Palero, M. Trends and applications of machine learning in water supply networks management. J. Ind. Eng. Manag. 14, 45\u0026ndash;54 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJafari, S. M., Zahiri, A. R., Bozorg Hadad, O. \u0026amp; Mohammad Rezapour Tabari, M. 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. Soft Comput. 25, 7459\u0026ndash;7478 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWarad, A. A. M., Wassif, K. \u0026amp; Darwish, N. R. Intelligent Models for Forecasting Repair Timing of Leakage Water Pipelines. in \u003cem\u003e3rd International Mobile, Intelligent, and Ubiquitous Computing Conference, MIUCC\u003c/em\u003e 2023 255\u0026ndash;260 (Institute of Electrical and Electronics Engineers Inc., 2023). doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1109/MIUCC58832.2023.10278375\u003c/span\u003e\u003cspan address=\"10.1109/MIUCC58832.2023.10278375\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTable \u003cspan dir=\"RTL\"\u003e1\u003c/span\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eComparation between Boosting and Bagging techinque\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"601\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.5%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003e\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"36.666666666666664%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eBoosting\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"38.833333333333336%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eBagging\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.5%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eThe aim of the model\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"36.666666666666664%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eto decrease bias, not variance \u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"38.833333333333336%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eto decrease variance not bias,\u0026nbsp;to solve the over-fitting problem\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.5%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eType of combing predictions\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"36.666666666666664%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003edifferent types\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"38.833333333333336%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003ethe same type of prediction\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.5%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eThe weight of layer models\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"36.666666666666664%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eaccording to their performance.\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"38.833333333333336%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eEach model has the same weightage\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.5%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eTraining data subsets\u0026nbsp;\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"36.666666666666664%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eEvery new data subset contains the elements were misclassified by previous models\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"38.833333333333336%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003erandomly drawn with replacement from the entire training dataset.\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"24.5%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eThe independent between the models\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"36.666666666666664%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eNew Models are influenced by the accuracy of previous Models (sequential)\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"38.833333333333336%\" valign=\"top\"\u003e\n \u003cp dir=\"RTL\"\u003e\u003cspan dir=\"LTR\"\u003eEach model is independent of each other (parallel)\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eTable \u003cspan dir=\"RTL\"\u003e2\u003c/span\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eData description\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"633\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"15.189873417721518%\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"24.050632911392405%\"\u003e\n \u003cp\u003e\u003cstrong\u003eVariable \u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.196202531645568%\"\u003e\n \u003cp\u003e\u003cstrong\u003eType \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"42.563291139240505%\"\u003e\n \u003cp\u003e\u003cstrong\u003edescription\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"15.189873417721518%\" rowspan=\"10\"\u003e\n \u003cp\u003e\u003cstrong\u003eInput\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eFactors\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"24.050632911392405%\"\u003e\n \u003cp\u003eLength\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.196202531645568%\"\u003e\n \u003cp\u003eNumerical\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"42.563291139240505%\"\u003e\n \u003cp\u003eThe length of the pipe in meters(m)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"28.35820895522388%\"\u003e\n \u003cp\u003eDiameter\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.455223880597014%\"\u003e\n \u003cp\u003eNumerical\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"50.1865671641791%\"\u003e\n \u003cp\u003eThe diameter of pipe in millimeters\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"28.35820895522388%\"\u003e\n \u003cp\u003eMaterial\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.455223880597014%\"\u003e\n \u003cp\u003eNumerical\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"50.1865671641791%\"\u003e\n \u003cp\u003eThe material of the pipe section, categorized\u0026nbsp;as Numerical type\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"28.35820895522388%\"\u003e\n \u003cp\u003eHazen-Williams C\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.455223880597014%\"\u003e\n \u003cp\u003eNumerical\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"50.1865671641791%\"\u003e\n \u003cp\u003eThe relationship which relates the flow of water in a pipe with the physical properties of the pipe and the pressure\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"28.35820895522388%\"\u003e\n \u003cp\u003eFlow (m\u0026sup3;/h)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.455223880597014%\"\u003e\n \u003cp\u003eNumerical\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"50.1865671641791%\"\u003e\n \u003cp\u003eThe average of flow of the pipe\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"28.35820895522388%\"\u003e\n \u003cp\u003eVelocity (m/s)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.455223880597014%\"\u003e\n \u003cp\u003eNumerical\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"50.1865671641791%\"\u003e\n \u003cp\u003eThe average of velocity of the pipe\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"28.35820895522388%\"\u003e\n \u003cp\u003eHead loss Gradient (m/km)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.455223880597014%\"\u003e\n \u003cp\u003eNumerical\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"50.1865671641791%\"\u003e\n \u003cp\u003eresult of head loss calculated using Hazen-William\u0026apos;s formula divided by total length of the pipe\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"28.35820895522388%\"\u003e\n \u003cp\u003eInstallation Year\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.455223880597014%\"\u003e\n \u003cp\u003eNumerical\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"50.1865671641791%\"\u003e\n \u003cp\u003eThe Installation Year of pipe\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"28.35820895522388%\"\u003e\n \u003cp\u003eAge (years) \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.455223880597014%\"\u003e\n \u003cp\u003eNumerical\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"50.1865671641791%\"\u003e\n \u003cp\u003eThe age of pipes in years\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"28.35820895522388%\"\u003e\n \u003cp\u003eNumber of breaks\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.455223880597014%\"\u003e\n \u003cp\u003eNumerical\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"50.1865671641791%\"\u003e\n \u003cp\u003eThe number of total damages recorded on the pipe\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"15.189873417721518%\"\u003e\n \u003cp\u003e\u003cstrong\u003eTarget\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"24.050632911392405%\"\u003e\n \u003cp\u003eFailure rate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"18.196202531645568%\"\u003e\n \u003cp\u003eNumerical\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"42.563291139240505%\"\u003e\n \u003cp\u003eThe rate of water pipe failure\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eTable 3\u003c/p\u003e\n\u003cp\u003ePerformance of different decision tree-based models based on validation error\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"41.39344262295082%\" valign=\"top\"\u003e\u003cbr\u003e\u003c/td\u003e\n \u003ctd width=\"19.057377049180328%\" valign=\"top\"\u003e\n \u003cp\u003eBagged Trees\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.057377049180328%\" valign=\"top\"\u003e\n \u003cp\u003eBoosted Trees\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.491803278688526%\" valign=\"top\"\u003e\n \u003cp\u003eOptimizable Ensemble\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"41.39344262295082%\" valign=\"top\"\u003e\n \u003cp\u003eMinimum Leaf Size\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.057377049180328%\" valign=\"top\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.057377049180328%\" valign=\"top\"\u003e\n \u003cp\u003e8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.491803278688526%\" valign=\"top\"\u003e\n \u003cp\u003e29\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"41.39344262295082%\" valign=\"top\"\u003e\n \u003cp\u003eNumber of Leaners\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.057377049180328%\" valign=\"top\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.057377049180328%\" valign=\"top\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.491803278688526%\" valign=\"top\"\u003e\n \u003cp\u003e272\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"41.39344262295082%\" valign=\"top\"\u003e\n \u003cp\u003eLearning Rate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.057377049180328%\" valign=\"top\"\u003e\n \u003cp\u003e_\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.057377049180328%\" valign=\"top\"\u003e\n \u003cp\u003e0.1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.491803278688526%\" valign=\"top\"\u003e\n \u003cp\u003e0.85188\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"41.39344262295082%\" valign=\"top\"\u003e\n \u003cp\u003eOptimized Options\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.057377049180328%\" valign=\"top\"\u003e\n \u003cp\u003edisabled\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"19.057377049180328%\" valign=\"top\"\u003e\n \u003cp\u003eDisabled\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"20.491803278688526%\" valign=\"top\"\u003e\n \u003cp\u003eAuto\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"41.39344262295082%\" valign=\"top\"\u003e\n \u003cp\u003evalidation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"58.60655737704918%\" colspan=\"3\" valign=\"top\"\u003e\n \u003cp\u003eholdout-validation: 25%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eTable 4\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;Statistical Performance Metrics Description\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" style=\"width: 1032px;\" width=\"1032\" height=\"357\"\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003eTable 5\u003c/p\u003e\n\u003cp\u003eConfiguration of constructed optimizable ensemble models\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"546\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eOptimizable Hyperparameters\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eRange\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eEnsemble Methods\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e[Bag, LS Boost]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eOptimizer\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eBayesian Optimizer\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eAcquisition Function\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eExpected improvement per second plus\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eMinimum leaf Size\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e[1-31711]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eNumber of Learners\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e[10-500]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eLearning Rate\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e[0.001,1]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eNumber of predictors to simples\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e[1-10]\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003eIterations\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTable \u003cspan dir=\"RTL\"\u003e6\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003eComparison of the Three Intelligent Models\u003c/p\u003e\n\u003cdiv align=\"\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"458\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd width=\"31.728665207877462%\" valign=\"top\"\u003e\n \u003cp\u003eResults\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.00656455142232%\" valign=\"top\"\u003e\n \u003cp\u003eBagged Trees\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.632385120350108%\" valign=\"top\"\u003e\n \u003cp\u003eBoosted Trees\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.632385120350108%\" valign=\"top\"\u003e\n \u003cp\u003eOptimizable Ensemble\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"31.728665207877462%\" valign=\"top\"\u003e\n \u003cp\u003eRMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.00656455142232%\" valign=\"top\"\u003e\n \u003cp\u003e0.03195\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.632385120350108%\" valign=\"top\"\u003e\n \u003cp\u003e0.022654\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.632385120350108%\" valign=\"top\"\u003e\n \u003cp\u003e0.00231\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"31.728665207877462%\" valign=\"top\"\u003e\n \u003cp\u003eR2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.00656455142232%\" valign=\"top\"\u003e\n \u003cp\u003e0.98\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.632385120350108%\" valign=\"top\"\u003e\n \u003cp\u003e0.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.632385120350108%\" valign=\"top\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"31.728665207877462%\" valign=\"top\"\u003e\n \u003cp\u003eMSE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.00656455142232%\" valign=\"top\"\u003e\n \u003cp\u003e0.0010208\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.632385120350108%\" valign=\"top\"\u003e\n \u003cp\u003e0.00051322\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.632385120350108%\" valign=\"top\"\u003e\n \u003cp\u003e5.34E-06\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd width=\"31.728665207877462%\" valign=\"top\"\u003e\n \u003cp\u003eMAE\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"21.00656455142232%\" valign=\"top\"\u003e\n \u003cp\u003e0.0041853\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.632385120350108%\" valign=\"top\"\u003e\n \u003cp\u003e0.014829\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd width=\"23.632385120350108%\" valign=\"top\"\u003e\n \u003cp\u003e0.00071513\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-3892182/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3892182/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eBased on the benefits of different ensemble methods, such as bagging and boosting, which have been studied and adopted extensively in research and practice, where bagging and boosting focus more on reducing variance and bias, this paper presented an optimization ensemble learning-based model for a large pipe failure dataset of water pipe leakage forecasting, something that was not previously considered by others. It is known that tuning the hyperparameters of each base learned inside the ensemble weight optimization process can produce better-performing ensembles, so it effectively improves the accuracy of water pipe leakage forecasting based on the pipeline failure rate. To evaluate the proposed model, the results are compared with the results of the bagging ensemble and boosting ensemble models using the root-mean-square error (RMSE), the mean square error (MSE), the mean absolute error (MAE), and the coefficient of determination (R2) of the bagging ensemble technique, the boosting ensemble technique and optimizable ensemble technique are higher than other models. The experimental result shows that the optimizable ensemble model has better prediction accuracy. The optimizable ensemble model has achieved the best prediction of water pipe failure rate at the 14th iteration, with the least RMSE\u0026thinsp;=\u0026thinsp;0.00231 and MAE\u0026thinsp;=\u0026thinsp;0.00071513 when building the model that predicts water pipe leakage forecasting via pipeline failure rate.\u003c/p\u003e","manuscriptTitle":"An Ensemble Learning Model for Forecasting Water-pipe Leakage","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-06 19:43:32","doi":"10.21203/rs.3.rs-3892182/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-03-01T02:10:05+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-02-23T21:40:13+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"09d1550d-b0d9-44b7-958c-5bba5cfa9336","date":"2024-02-05T14:15:25+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-02-04T18:55:44+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-02-04T18:53:21+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-02-04T18:20:13+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-02-04T16:07:57+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-01-23T21:57:41+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"cdf12808-9c61-43ba-b870-c9bb1e6d9dd9","owner":[],"postedDate":"February 6th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":28578049,"name":"Physical sciences/Physics/Information theory and computation"},{"id":28578050,"name":"Physical sciences/Engineering"},{"id":28578051,"name":"Physical sciences/Mathematics and computing"},{"id":28578052,"name":"Physical sciences/Mathematics and computing/Computational science"},{"id":28578053,"name":"Physical sciences/Mathematics and computing/Computer science"},{"id":28578054,"name":"Physical sciences/Mathematics and computing/Information technology"},{"id":28578055,"name":"Physical sciences/Mathematics and computing/Scientific data"}],"tags":[],"updatedAt":"2024-05-14T21:27:23+00:00","versionOfRecord":{"articleIdentity":"rs-3892182","link":"https://doi.org/10.1038/s41598-024-60840-x","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-05-09 21:18:07","publishedOnDateReadable":"May 9th, 2024"},"versionCreatedAt":"2024-02-06 19:43:32","video":"","vorDoi":"10.1038/s41598-024-60840-x","vorDoiUrl":"https://doi.org/10.1038/s41598-024-60840-x","workflowStages":[]},"version":"v1","identity":"rs-3892182","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3892182","identity":"rs-3892182","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}