بهینه‌سازی مقطع و ارتفاع آزاد کانال‌های ذوزنقه‌ای براساس حداقل احتمال سرریز و هزینه‌های خاکبرداری و پوشش

در حالت عمومی بازدهی کانال های آبرسانی معمولا کمتر از حد قابل قبول می باشد یکی از دلایل آن عدم استفاده از روش های بهینه سازی مناسب در طراحی کانال ها است. هدف از بهینه سازی مقطع کانال، طراحی کانال در مطلوب ترین حالت هیدرولیکی با اقتصادی ترین حالت ممکن است. در طراحی کانال ها توجه به حداقل سازی احتمال سرریز نیز ضروری می باشد. در تحقیق حاضر، هدف، حداقل سازی مجموع هزینه های خاکبرداری و پوشش به همراه حداقل سازی احتمال سرریز شدن جریان از کانال برای کانال با مقطع ذوزنقه ای در دبی های مختلف بوده است. در ادامه، تاثیر تغییر دبی بر بهینه سازی ابعاد کانال مورد بررسی قرار گرفته است. ارتفاع آزاد و دبی جریان به عنوان متغیر طراحی لحاظ گردیده است. فرمول بندی مسئله با توجه به وجود قید برقراری معادله مانینگ، منجر به یک بهینه سازی غیرخطی می شود که با استفاده از نرم افزار ولفرام متمتیکا حل شده است. نتایج نشان داد که با افزایش دبی، مقدار بهینه عمق و عرض کف افزایش می یابد به دنبال آن هزینه های ساخت نیز افزایش یافته است ولی با افزایش دبی، ارتفاع آزاد کانال کاهش داشته است.

optimization of the cross-section and free board of trapezoidal channels based on the minimum probability of overflow and excavation and covering costs

introductionin general, the efficiency of water supply channels is usually less than acceptable, one of the reasons for this is the lack of appropriate optimization methods in channel design. the goal of optimizing the channel cross-section is to design the channel in the most favorable hydraulic state with the most economical possible. in channel design, it is also necessary to pay attention to minimizing the possibility of overflowing. in the present study, the goal was to minimize the total costs of excavation and covering along with minimizing the possibility of overflow from the channel for a channel with a trapezoidal cross-section at different discharges. in the following, the effect of changing the discharge on optimizing the channel dimensions has been investigated.materials and methodthe effect of flow change on the optimization of channel dimensions has been investigated in addition, minimizing the possibility of overflow is also considered as a goal. therefore, free bord and flow rate are also considered as design variables. problem formulation leads to nonlinear optimization due to the manning equation constraint. in single-objective optimization, the feasible set is determined entirely based on the objective function, and for each set of answers, the best answer is determined based on the value of the objective function. in multi-objective optimization problems, there is not only one answer, but a set of optimal answers is obtained according to the objectives of the problem. in this research, the constrained method of multi-objective programming technique is used. in this method, the vector optimization problem is converted into a numerical optimization. the conversion of the vector form to a numerical one is done in such a way that one of the objectives (here, minimizing the construction cost) is considered as the only objective of the model, and the second objective (here, minimizing the overflow probability) is considered as a constraint. as a result, the resulting model is the numerical and deterministic form of the previous vector and stochastic model.results and discussionthe results showed that as the discharge value increases, construction cost increases. also, the construction cost for all discharges decreases with the increase in the probability of overflow up to a probability of overflow of 0.5 and then increases. in other words, for all discharges, the construction cost is at its minimum when the probability of overflow is 0.5. with increasing discharge, the optimal channel width increased. also, the optimal width for all discharges decreased with an increase in overflow probability up to a value of 0.5 and then increased. in other words, for all discharges, the optimal width has a minimum value at a probability of overflow equal to 0.5. with the increase in the discharge value, the flow depth increased. also, the flow depth for all discharges increased with the increase in the probability of overflow up to the value of the probability of overflow equal to 0.5 and then had a decreasing trend. in other words, for all discharges, the flow depth has a maximum value at the probability of overflow equal to 0.5. with the increase in the discharge value, the optimal free height decreased. also, the optimal free height for all discharges has a decreasing trend with the increase in the probability of overflow up to the overflow probability value of 0.5 and then has an increasing trend. in other words, for all discharges, the optimal free height has a minimum value at the overflow probability of 0.5.conclusionthe results of this study showed that in a trapezoidal channel, if optimization is performed to minimize the cost of channel construction, including the total cost of excavation and channel lining, as well as minimizing the probability of overflow from the channel, with an increase in the discharge amount at a specific (fixed) probability, the width of the channel bottom, the depth of the flow, and the cost of channel construction have increased. in other words, with an increase in the discharge, the dimensions of the channel cross-section have increased, which has brought about higher costs, but with an increase in the optimal depth, the need for free head of the channel has decreased, so with an increase in the flow discharge, the optimal free head has decreased. also, for all discharges at an overflow probability of 0.5, the cost of channel construction, the optimal width, and the optimal free head have a minimum value, and the flow depth has a maximum value.