Improved Channel Cross Section with Two-Segment Parabolic Sides and Horizontal Bottom

A channel cross section with parabolic sides and horizontal bottom has been recently published and proved to be more economical (provide lesser construction cost per unit length) than the trapezoidal cross section. This paper presents a new and improved cross section with two-segment parabolic sides and horizontal bottom. Each side of the cross section consists of two parabolic segments smoothly connected. Closed-form relationships for the cross-sectional area and perimeter are developed. For specific parameter conditions, the new cross section produces most of the common cross sections, including the parabolic sides—horizontal bottom and trapezoidal cross sections, as well as new cross-sectional shapes. It provides an additional degree of freedom in determining the optimal cross-sectional design. A spreadsheet-based optimization model for the new cross section that minimizes the total construction cost (excavation and composite linings) is developed. The constraints of the model include channel discharge and physical requirements, such as flow depth, top width, and side slope with fixed or depth-dependent freeboard. The model was validated and the cross-sectional performance was evaluated using different design scenarios. The optimization results show that the new cross section is more economical and more flexible than a cross section with (one-segment) parabolic sides. As such, it should be of interest to the irrigation and drainage engineers.     

Optimal Design of Composite Channels Using Genetic Algorithm

In the past, studies involving optimal design of composite channels have employed Horton’s equivalent roughness coefficient, which uses a lumped approach in assuming constant velocity across a composite channel cross section. In this paper, a new nonlinear optimization program (NLOP) is proposed based on a distributed approach that is equivalent to Lotter’s observations, which allows spatial variations in velocity across a composite channel cross section. The proposed NLOP, which consists of an objective function of minimizing total construction cost per unit length of a channel, is solved using genetic algorithm (GA). Several scenarios are evaluated, including no restrictions, restricted top width, and restricted channel side slopes, to account for certain site conditions. In addition, the proposed NLOP is modified to include constraints on maximum permissible velocities corresponding to different lining materials of the composite channel cross section, probably for the first time. The proposed methodology is applied to trapezoidal and triangular channel cross sections but can be easily extended to other shapes or compound channels. Optimal design graphs are presented to determine the channel dimensions of a composite trapezoidal channel cross section. The results obtained in this study indicate that cost savings up to 35% can be achieved for the unconstrained velocity case and up to 55% for the limiting velocity case when the proposed NLOP is solved using GA as compared with the existing NLOP solved using either the classical optimization solution technique or GA.     

Overtopping Probability Constrained Optimal Design of Composite Channels Using Swarm Intelligence Technique

In this paper swarm intelligence based methodology is proposed for optimal and reliable design of irrigation channels. The input parameters involved in channel design are prone to uncertainty and the solution of deterministic model may result in flooding risk and affect the stability of the channel. To provide reliability in the design, an overtopping probability constrained design is presented in this study. The deterministic equivalent of the probabilistic constraint is derived by following the principle of first order uncertainty analysis. In order to account for the uncertainty of design parameters in the objective function, a modified cost function is proposed. A methodology is propounded to solve it in a metaheuristic environment and solved it using elitist-mutated particle swarm optimization (EMPSO) method. The EMPSO based solutions are found to be quite successful and better than the classical optimization methods. Finally, it is concluded that the proposed methodology has a good potential for reliable design of composite channels for designer specified reliability values.     

Optimal Channel Cross Section with Composite Roughness

For channels with composite roughness, an equivalent uniform roughness coefficient and flow geometric elements are used in an optimal design method using the Manning equation. The optimal design problems are formulated in a nonlinear optimization framework with the objective function being a cost function per unit length of the canal. Constraints are the Manning equation, positive values for design variables, and specified values of side slopes or top width. The constrained problem is transformed into an unconstrained problem using the Lagrangian multipliers. To obtain an optimal solution for the resulting unconstrained problem, the first-order necessary conditions for optima are applied. The resulting simultaneous nonlinear equations are solved using the computational methodology developed. This technique is applied to illustrative numerical examples. The evaluations establish the potential applicability of the developed computational methodology for optimal design of open channel cross sections with composite roughness.     

Optimal Design of Channel Having Horizontal Bottom and Parabolic Sides

The cost of open channels can be minimized by using (1) the optimal design concept; (2) a new geometric shape to substitute for the trapezoidal channels, and/or (3) a composite channel. The channels in which the roughness along the wetted perimeter become distinctly different from part to part of the perimeter are called composite channels. The feasibility of a new cross-sectional shape that has a horizontal bed and two parabolic sides and lined as a composite channel is investigated to substitute for the trapezoidal cross section. The optimal design concept is used to establish the efficacy of the proposed new cross-sectional shape, because it gives the best and unique design of open channels. In optimal design concept, the geometric dimensions of a channel cross section are determined in a manner to minimize the total construction costs. The constraints are the given channel capacity and other imposed restrictions on geometric dimensions. The Lagrange multiplier technique is used to solve the resulting channel optimization models. The developed optimization models are applied to design the proposed and trapezoidal channels to convey a given design flow considering various design scenarios which include unrestricted, flow depth constrained, side slopes constrained, and top width constrained design. Each of these design scenarios again takes into account fixed freeboard, and depth-dependent freeboard cases of design. An analysis of the optimization results establishes the cost-saving capability of the proposed cross-sectional shape in comparison to a trapezoidal cross section.     

Critical Flow Section in Collector Channel

This paper shows how the critical flow section in a collector channel can be located by solving the dynamic equation of spatially varied flow, Manning's equation, and making use of the singular-point concept. In addition to channel length and tailwater elevation, the occurrence of a critical flow section in a spatially varied flow also depends on the combination of channel cross-sectional geometry, roughness, slope, and inflow rate. When the critical flow section is necessary to be developed in a collector channel, the two dimensionless parameters (Fq∕S0 representing the design capacity and N∕S0 representing the channel roughness) derived in this study guide selection of channel cross-sectional parameters. A set of design charts is provided for trapezoidal channels with a side slope of 1V:1H, 0.5V:1H, or 0V:1H.     

Optimal Design of Open Channel Section Incorporating Critical Flow Condition

The flow at critical condition of an open channel is unstable. At critical condition, a small change in specific energy will cause abrupt fluctuation in water depth of the channel. This is because the specific energy curve is almost vertical at critical state. Therefore, if the design depth of the channel is near or equal to critical depth of the channel, the shape of the channel must be altered to avoid a large fluctuation in water depth. In the present study, a nonlinear optimization model is presented for designing an optimal channel section incorporating the critical flow condition of the channel. The optimization model derives the optimal channel section at a desirable difference from the critical condition of the channel so that a small change in the specific energy of the channel will not cause an abrupt change in flow depth. The objective of the optimization model is to minimize the total construction costs of the channel. Manning’s equation is used to specify the uniform flow condition in the channel. The developed optimization model is solved by sequential quadratic programming using MATLAB. Applicability of the model is demonstrated for a trapezoidal channel section with composite roughness. However, it also can be extended to other shapes of channel.     

Optimal Control of Open-Channel Flow Using Adjoint Sensitivity Analysis

An optimal flow control methodology based on adjoint sensitivity analysis for controlling nonlinear open channel flows with complex geometries is presented. The adjoint equations, derived from the nonlinear Saint-Venant equations, are generally capable of evaluating the time-dependent sensitivities with respect to a variety of control variables under complex flow conditions and cross-section shapes. The internal boundary conditions of the adjoint equations at a confluence (junction) derived by the variational approach make the flow control model applicable to solve optimal flow control problems in a channel network over a watershed. As a result, an optimal flow control software package has been developed, in which two basic modules, i.e., a hydrodynamic module and a bound constrained optimization module using the limited-memory quasi-Newton algorithm, are integrated. The effectiveness and applicability of this integrated optimal control tool are demonstrated thoroughly by implementing flood diversion controls in rivers, from one reach with a single or multiple floodgates (with or without constraints), to a channel network with multiple floodgates. This new optimal flow control model can be generally applied to make optimal decisions in real-time flood control and water resource management in a watershed.     

Simplified Design of Hydraulically Efficient Power-Law Channels with Freeboard

A power-law channel section is very versatile. It can model a wide range of familiar man-made or natural channel shapes. However estimating the wetted perimeter of a power-law channel section is difficult. The problem gets complicated further when considering the freeboard in the design process. In this paper, the wetted perimeter is estimated using the isoperimetric theorem which results in a simple and accurate expression for the wetted perimeter that does not lead to discontinuity in the optimal solution. For unconstrained optimum power-law channels, it is shown that the exponent and side slope at the water surface have values of 0.314 and 0.352, respectively, independent of either the maximum side slope or the relative freeboard. The analyses have also shown that the most hydraulically efficient power-law channel sections come closest to the semicircle. They tend to be U shaped and narrow with small relative freeboard ( ? 0.30). A design procedure and two design charts are presented together with two illustrative examples to demonstrate the simplicity of the method.     

Diffusion Wave Model for Simulating Storm-Water Runoff on Highway Pavement Surfaces at Superelevation Transition

On a curved section of highway, the cross slope of the road is often designed to be superelevated to balance the centrifugal force and gravity applied on vehicles. The accumulation of storm-water runoff (sheet flow) near superelevation transitions may significantly increase due to the extended flow path and converging flow lines. A two-dimensional finite-volume-based diffusion wave model is developed to simulate the sheet flow on these geometrically complex surfaces. Both Dirichlet- and Neumann-type boundary conditions are developed for open boundaries based on kinematic wave theory. Results show that the distribution of sheet flow is closely related to the cross slope, longitudinal slope, rainfall intensity, and the width of the road. The analysis of sheet flow characteristics on superelevation transition areas suggests that the optimal longitudinal slope in the range of 0.3–0.4% minimizes the depth of storm-water runoff on the road surface.     

Optimal Spacing of Shallow Tube Wells in Relation to Conveyance Losses

A mathematical model is developed to determine the optimal spacing of shallow tube wells and the optimal length of field channel lining to minimize the total cost. The model takes into account the monthly varying crop water requirements. The optimization model is also applied to a set of basic data pertaining to North Bihar, India.     

Flooding Probability-Based Optimal Design of Trapezoidal Open Channel Using Freeboard as a Design Variable

A flooding probability based cost effective design of open channel section has been proposed using freeboard as an additional design variable. The freeboard of the channel is calculated based on the flooding probability value. The proposed model is solved using classical optimization techniques as well as a nondominated sorting genetic algorithm. The results of the model are compared with an earlier reported model to demonstrate its superiority and field applicability.     

New Strategy for Optimizing Water Application under Trickle Irrigation

The determination of water application parameters for creating an optimal soil moisture profile represents a complex nonlinear optimization problem which renders traditional optimization into a cumbersome procedure. For this reason, an alternative methodology is proposed which combines a numerical subsurface flow model and artificial neural networks (ANN) for solving the problem in two, fully separate steps. The first step employs the flow model for calculating a large number of wetting profiles (output), obtained from a systematic variation of both water application and initial soil moisture (input). The resulting matrix of corresponding input/output values is used for training the ANN. The second step, the application of the fully trained ANN, then provides the irrigation parameters which range from a specified initial soil moisture to a desired crop-specific soil moisture profile. In order to avoid substantial disadvantages associated with the common feedforward backpropagation approach, a self-organizing topological feature map is implemented to perform this task. After a comprehensive sensitivity analysis, the new methodology is applied to the outcome of an irrigation experiment. The convincing results recommend the new methodology as a positive contribution towards an improved irrigation efficiency.     

A Methodology For Design And Operation Of Heap Leaching Systems

Leaching is a hydrometallurgical activity widely used in mineral processing, both for metallic and non-metallic ores, and in soil remediation. The dissolution of valuable species by heap leaching is strongly dependent on the design and operating variables, so the study of the influence of these variables on recovery and their optimization for the best performance are attractive tasks for the development of the mining industry. In this work, a methodology is developed that enables the planning and design of leaching systems. This methodology uses a proposed superstructure and a mathematical model to analyze the system behavior and determine the optimal design and operating conditions. The model was generated with a Mixed Integer Nonlinear Programming (MINLP) approach and solved by different solvers under GAMS® software (General Algebraic Modelling System). The Spatial Branch-and-Bound (SBB) solver obtained the global optimum in the shortest times. Based on a case of study for copper leaching, it is demonstrated that the procedure allows achieving optimal design and operational conditions.     

Efficient Probabilistic Back-Analysis of Slope Stability Model Parameters

Back-analysis of slope failure is often performed to improve one’s knowledge on parameters of a slope stability analysis model. In a failed slope, the slip surface may pass through several layers of soil. Therefore, several sets of model parameters need to be back-analyzed. To back-analyze multiple sets of slope stability parameters simultaneously under uncertainty, the back-analysis can be implemented in a probabilistic way, in which uncertain parameters are modeled as random variables, and their distributions are improved based on the observed slope failure information. In this paper, two methods are presented for probabilistic back-analysis of slope failure. For a general slope stability model, its uncertain parameters can be back-analyzed with an optimization procedure that can be implemented in a spreadsheet. When the slope stability model is approximately linear, its parameters can be back-analyzed with sensitivity analysis instead. A feature of these two methods is that they are easy to apply. Two case studies are used to illustrate the proposed methods. The case studies show that the degrees of improvement achieved by the back-analysis are different for different parameters, and that the parameter contributing most to the uncertainty in factor of safety is updated most.     

Optimal Design and Operation of Irrigation Pumping Stations

A methodology based on solving a large-scale nonlinear programming problem is presented for the optimal design and operation of pumping stations. Optimum design and operation refers to the selection of pump type, capacity, and number of units as well as scheduling the operation of irrigation pumps that results in minimum design and operating cost for a given set of demand curves. The design criteria for such pumping stations are based fundamentally on some important and critical parameters, such as pump capacity, number of units, types of pumps, and civil works. The optimization process consists of three main steps: (1) determination of minimum yearly consumed energy; (2) minimization of the total cost for all sets of pumping stations; and (3) selection of the least-cost set among the feasible sets of pumping stations, recognizing a combination of the cited criteria. The computational analysis is based upon one major objective function and a computer program, which is developed to solve the generated equations. Application of the model to the Farabi Agricultural and Industrial Project, Iran, shows considerable savings, about 25% in total annual cost of the pumping station.     

Investigation on the Dimensions and Shape of a Submerged Vane for Sediment Management in Alluvial Channels

A submerged vane is a flow-training facility mounted vertically on the channel bed to control the sediment movement in the channel cross section, and has been utilized in various applications, such as prevention of bank erosion, sediment exclusion at water intakes, and deepening channels for navigation. The performance of a submerged vane is related to its dimensions and shape. This study aims to investigate a vane’s sediment control effectiveness as a function of its size and shape, with the expectation of an optimal combination of dimensions and shape. A model for the calculation of the transverse bed profile in a cross section of a straight alluvial channel induced by a single submerged vane is developed. The model is utilized to investigate the performances for three types of vanes: (1) rectangular plates with various height and length; (2) tapered plates with linear decreasing in length from the base to the top; and (3) plates of parallelogram with the top of the plates swept forward or backward. Design guidelines and suggestions on the dimensions and shape of the vane are provided based on the results.     

混沌人工鱼群的鲁棒保性能控制权值矩阵优化方法

针对鲁棒保性能控制中的权值矩阵依赖经验选取,无法最大限度的减小系统保守性的问题,提出了一种基于混沌人工鱼群算法的鲁棒保性能控制权值矩阵优化方法.该方法中,将保性能控制鲁棒界作为优化的目标函数来寻找最优权值矩阵是整个算法实现的关键.该种改进的人工鱼群优化算法融合了混沌搜索与自适应步长和视野的人工鱼群优化算法,有效的解决了基本人工鱼群算法的后期收敛速度慢、易陷入局部最优等缺点.通过测试函数对比验证了该种改进人工鱼群优化算法的优越性,并通过应用实例验证了该权值矩阵优化方法的有效性.      

A GENETIC ALGORITHMS BASED MULTI-OBJECTIVE OPTIMIZATION APPROACH APPLIED TO A HYDROMETALLURGICAL CIRCUIT FOR OCEAN NODULES

Several hydrometallurgical processes have been studied for the extraction of metals from lean ores utilizing various flow sheet options. Of particular significance is the grade of the ore being treated, the energy consumed and associated costs, options for byproduct recovery, and the relative price of the products. A process scheme needs to be optimized for simultaneously maximizing metal throughput and minimizing the direct operating costs incurred within constraints set for the operating variables. This leads to a multi-objective optimization problem. The range of input grades for raw material, which a flowsheet can handle, needs to be worked out based on an optimization exercise. A lean manganese-bearing resource such as polymetallic sea nodules has been chosen in this article for the development of an optimization approach based on which the input raw nodules grades are to be treated by a particular flowsheet. Only the chemical consumption costs have been adopted in this article as a measure of direct operating costs. A linear simulation model for the flowsheet has been developed, keeping a set of design parameters constant. The solutions generated by using a sequential modular approach become inputs to an optimization procedure based on a multi-objective genetic algorithm belonging to the differential evolution family. The variables considered in the optimization task are the grade of nodules and reactivity of different species inside the reactor. A nickel equivalent (t/h function) has been suggested as a measure of productivity, as it indirectly enhances the input manganese ore grade through a price ratio effect. This productivity function was maximized with the simultaneous minimization of direct chemical costs. Pareto optimal solutions were generated with grades of nodules and reactivity in the leach reactor as decision variables. The effect of the price ratio on the Pareto optimal solutions was also investigated. The various cases investigated clarifies the methodology for choosing an appropriate ore grade range for a given process flowsheet. Appropriate decisions regarding the nature of raw material to be used for a given flowsheet are then found on the basis of the Pareto optimal solutions.     

Stability Analyses of Rainfall Induced Landslides

The slope stability issues concerning rainfall induced slope failures are investigated and presented. Specifically, the effect of both negative and positive pore water pressures on the stability of initially unsaturated slopes are carefully explained and coupled with infinite slope analysis methods in order to present a predictive formulation of slope failures that occur as a result of rainfall events. The formulation serves as a baseline analysis method for evaluating potentially unstable soil slopes that are subject to surface infiltration and explains the various triggering mechanisms that may occur based on individual combinations of the slope geometry, soil strength, and infiltration parameters. A procedural method is outlined for utilizing the analytical formulation to predict the change in the factor of safety for a slope subject to infiltration and a detailed analysis of a case study is presented to verify the method. Quantitative statements are made concerning the time and depth of failure in relationship to the soil, slope, and rainfall parameters.