طراحی بهینه نمونه‌برداری فشار در شبکه‌های توزیع آب برای کالیبراسیون مدل‎های هیدرولیکی

یکی از مهم‌ترین کاربردهای مدل‌های هیدرولیکی شبکه‌های توزیع آب، شبیه‌سازی و درک شرایط غیرنرمال شبکه است. لذا وجود مدل‌های کالیبره شده برای ایجاد درک واقعی از رفتار شبکه ضروری است. انجام این فرایند نیازمند جمع‌آوری داده‌های میدانی از شبکه است تا با مقایسه رفتار پیش‌بینی‌شده به‌وسیله مدل با داده‌های واقعی، عملکرد مدل اصلاح شود. نمونه‌برداری از شبکه محدودیت‌های مختلفی دارد. بنابراین فرآیند طراحی نمونه‎برداری، جنبه‌های مختلف نمونه‌برداری نظیر مکان، تعداد و تناوب را به‎صورت بهینه تعیین می‎کند. در این مقاله به‌منظور طراحی نمونه‎برداری، تمرکز روی مکان‌های اندازه‌گیری فشار به‌منظور کالیبراسیون مدل هیدرولیکی است. برای اجرای طراحی نمونه‎برداری، ابتدا با انجام تحلیل حساسیت، عدم‌قطعیت در فشار هر گره میان پارامترهای ورودی مدل تقسیم می‌شود. در این مقاله از روش تحلیل حساسیت عمومی سوبول و الگوریتم ژنتیک چندهدفه عدد صحیح تحت عنوان الگوریتم minsgaii با دو معیار هزینه‌های نمونه‌برداری کمینه و آنتروپی بیشینه برای انتخاب نقاط نمونه‌برداری بهینه استفاده شده است. بررسی سناریوهای مختلف، بیانگر تاثیر نوع پارامتر بر موقعیت نقاط منتخب است. در این میان میزان مشابهت نتایج سناریوهای ترکیبی با سناریوهای مجزا از حالات شامل زبری، به حالات شامل تقاضا کاهش پیدا می‌کند که بیانگر نقش موثرتر زبری در انتخاب نقاط در سناریوهای ترکیبی است. هم‌چنین بررسی حالات ترکیبی پارامترها نشان داد که اندرکنش‌های میان پارامترها در انتخاب نقاط موثر است.

Optimal Design of Pressure Sampling in Water Distribution Networks for Calibration of Hydraulic Models

Introduction Simulating and understanding of abnormal conditions is one of the most important applications of hydraulic models of water distribution networks. Hence, existence of calibrated models is essential to network behavior realization. This process requires field data collection to improve model’s performance by comparing predicted and actual data. Sampling from network has different constraints. Therefore the sampling design process is performed in order to optimize it, which includes different aspects of sampling, such as location, number and frequency. This paper focuses on pressure sampling nodes for hydraulic model calibration. To implement sampling design, first by sensitivity analysis, uncertainty of each nodal pressure is divided between model inputs. Methodology In this paper, a global sensitivity analysis method, Sobol, is used which divides the variance of model into model inputs and their interactions. Then, two criteria for selecting sampling points are defined. The first criterion maximizes the entropy and magnitude of sensitivity values of each parameter for the set of sampling design points. The second criterion, by replacing number of points with sampling costs, follows minimization of sampling costs. To solve the integer multiobjective optimization problem, the multiobjective integer genetic algorithm called MINSGAII is employed. Results and Discussion Investigating different scenarios demonstrates effect of parameter type on the position of selected points. In the meantime, similarity between the results of combinatorial and individual scenarios decreases from cases including roughness to cases involving demand. This indicates effective role of roughness in selecting points in combinatorial scenarios. Also, analysis of combinatorial scenarios suggests that parameter interactions are effective in selecting points. Conclusion The results showed that the developed approach offers good performance in selecting sampling points with different scenarios. The MINSGAII algorithm has a good ability to find the solutions of the integer multiobjective optimization problem. The use of pressure driven simulation method is effective on the results of sensitivity analysis and sampling design. Introduction Simulating and understanding of abnormal conditions is one of the most important applications of hydraulic models of water distribution networks. Hence, existence of calibrated models is essential to network behavior realization. This process requires field data collection to improve model’s performance by comparing predicted and actual data. Sampling from network has different constraints. Therefore the sampling design process is performed in order to optimize it, which includes different aspects of sampling, such as location, number and frequency. This paper focuses on pressure sampling nodes for hydraulic model calibration. To implement sampling design, first by sensitivity analysis, uncertainty of each nodal pressure is divided between model inputs. Methodology In this paper, a global sensitivity analysis method, Sobol, is used which divides the variance of model into model inputs and their interactions. Then, two criteria for selecting sampling points are defined. The first criterion maximizes the entropy and magnitude of sensitivity values of each parameter for the set of sampling design points. The second criterion, by replacing number of points with sampling costs, follows minimization of sampling costs. To solve the integer multiobjective optimization problem, the multiobjective integer genetic algorithm called MINSGAII is employed. Results and Discussion Investigating different scenarios demonstrates effect of parameter type on the position of selected points. In the meantime, similarity between the results of combinatorial and individual scenarios decreases from cases including roughness to cases involving demand. This indicates effective role of roughness in selecting points in combinatorial scenarios. Also, analysis of combinatorial scenarios suggests that parameter interactions are effective in selecting points. Conclusion The results showed that the developed approach offers good performance in selecting sampling points with different scenarios. The MINSGAII algorithm has a good ability to find the solutions of the integer multiobjective optimization problem. The use of pressure driven simulation method is effective on the results of sensitivity analysis and sampling design. Introduction Simulating and understanding of abnormal conditions is one of the most important applications of hydraulic models of water distribution networks. Hence, existence of calibrated models is essential to network behavior realization. This process requires field data collection to improve model’s performance by comparing predicted and actual data. Sampling from network has different constraints. Therefore the sampling design process is performed in order to optimize it, which includes different aspects of sampling, such as location, number and frequency. This paper focuses on pressure sampling nodes for hydraulic model calibration. To implement sampling design, first by sensitivity analysis, uncertainty of each nodal pressure is divided between model inputs. Methodology In this paper, a global sensitivity analysis method, Sobol, is used which divides the variance of model into model inputs and their interactions. Then, two criteria for selecting sampling points are defined. The first criterion maximizes the entropy and magnitude of sensitivity values of each parameter for the set of sampling design points. The second criterion, by replacing number of points with sampling costs, follows minimization of sampling costs. To solve the integer multiobjective optimization problem, the multiobjective integer genetic algorithm called MINSGAII is employed. Results and Discussion Investigating different scenarios demonstrates effect of parameter type on the position of selected points. In the meantime, similarity between the results of combinatorial and individual scenarios decreases from cases including roughness to cases involving demand. This indicates effective role of roughness in selecting points in combinatorial scenarios. Also, analysis of combinatorial scenarios suggests that parameter interactions are effective in selecting points. Conclusion The results showed that the developed approach offers good performance in selecting sampling points with different scenarios. The MINSGAII algorithm has a good ability to find the solutions of the integer multiobjective optimization problem. The use of pressure driven simulation method is effective on the results of sensitivity analysis and sampling design.