Modeling Unsteady Open-Channel Flow for Controller Design

An approximated linear model of unsteady open-channel flow is necessary to design the water-level controller for irrigation open channels. Toward this end, this paper presents the matrix approach to derive the linear model of open-channel system in analytical form mainly according to the Saint Venant equations and the backwater profile at the steady state of open channel. The hydraulic model of the check structure at the downstream end of open channel is also incorporated into the linear model. A practical example indicates that the frequency response of the open-channel system can be accurately analyzed with the linear model. The simulation results in the time domain show that the dynamic behavior of the linear model approximates to that of the nonlinear model of the open-channel system. Finally, the limitations of the linear model are discussed.     

Frequency Modeling of Open-Channel Flow

A good model is necessary to design automatic controllers for water distribution in an open-channel system. The frequency response of a canal governed by the Saint-Venant equations can be easily obtained in the uniform case. However, in realistic situations, open-channel systems are usually far from the uniform regime. This paper provides a new computational method to obtain a frequency domain model of the Saint-Venant equations linearized around any stationary regime (including backwater curves). The method computes the frequency response of the Saint-Venant transfer matrix, which can be used to design controllers with classical automatic control techniques. The precision and numerical efficiency of the proposed method compare favorably with classical numerical schemes (e.g., Runge–Kutta). The model is compared in nonuniform situations to the one given by a finite difference scheme applied to Saint-Venant equations (Preissmann scheme), first in the frequency domain, then in the time domain. The proposed scheme can be used, e.g., to validate finite difference schemes in the frequency domain.     

Backwater Prediction due to the Blockage Caused by a Single, Submerged Spur Dike in an Open Channel

A method is proposed for predicting the backwater effect due to a single, submerged spur dike located within an open channel flow. A theoretical analysis based on the momentum principle relates the backwater effect to the drag force exerted by the spur dike on the flow. Experimental data obtained in laboratory flumes having subcritical flow conditions throughout the flow field have been used in developing predictive relationships for the spur dike drag coefficient, which is found to be strongly correlated to the blockage created by the spur dike within the flow cross section. The predictive relationships provide a means of obtaining a first-level estimate of the backwater effect due to a single, submerged spur dike in an open channel flow.     

Energy and Momentum Velocity Coefficients for Calibrating Submerged Sluice Gates in Irrigation Canals

There is renewed interest in developing calibration methods for gates operating in submerged conditions in irrigation canals. In the present study, a new method based on a generalization of the standard energy-momentum method that accounts for variations in the energy and momentum velocity coefficients is proposed, for the following reasons. First, it was found that the assumption of uniform submerged jet velocity to account for the kinetic energy head and momentum flux is in reality equivalent to assuming a parabolic relationship between the Coriolis and Boussinesq coefficients. Second, literature investigations showed that the coefficients for the downstream side of submerged gates are notably greater than unity, and the implicit parabolic relationship between these coefficients in the standard energy-momentum method is inadequate, at least for high submergence conditions. The proposed energy-momentum method was evaluated using the data obtained from four gates operating in an irrigation canal in Southern Spain. Improvements in accuracy compared to the standard energy-momentum method (with a constant contraction coefficient Cc = 0.61) were obtained. The results indicate that the calibration of coefficient approach provides a means to improve the energy-momentum method by (indirectly) accounting more accurately for nonuniform velocity effects in the energy-momentum equations.     

Automatic Tuning of PI Controllers for an Irrigation Canal Pool

This paper presents a method to automatically tune decentralized proportional integral (PI) controllers for an irrigation canal pool. The auto tune variation (ATV) method is based on a relay experiment, which generates small amplitude oscillations of the canal pool. The ATV procedure can be used to get the integrator delay model parameters of a canal pool, which in turn can be used to tune a PI controller using classic rules, or other rules such as the ones proposed by Litrico and Fromion. This method does not require advanced automatic control knowledge and is implemented in the SIC software developed by Cemagref, which also incorporates a supervisory control and data acquisition module for real-time control. The ATV method is evaluated by simulations and experiments on a real irrigation canal located in the South of France, for local upstream, local downstream, and distant downstream controller tuning.     

Tuning of Robust Distant Downstream PI Controllers for an Irrigation Canal Pool. I: Theory

The paper proposes a new method to tune robust distant downstream proportional integral (PI) controllers for an irrigation canal pool. The method emphasizes the role of gain and phase margins in the controller design, by linking the selection of these robustness indicators to the time domain specifications. This leads to link the frequency domain approach used by automatic control engineers to the time domain approach used by hydraulic engineers. The maximum error corresponding to an unpredicted perturbation is shown to be directly linked to the gain margin and the settling time to the phase margin of the controlled system. The tuning method gives analytical expressions for the controller parameters as function of physical parameters of the canal pool in order to satisfy desired performance requirements. The model is first expressed in terms of dimensionless variables, in order to get generic tuning formulas. The dimensionless PI coefficients are then expressed as functions of time-domain performance requirements. The PI tuning method is evaluated by simulation on a full nonlinear model for a canal pool taken from the ASCE test cases.     

Simple Optimal Downstream Feedback Canal Controllers: Theory

A new class of downstream water-level feedback controllers is proposed that can vary from a series of individual proportional-integral (PI) controllers (each gate adjusted based on one water level) to fully centralized controllers (each gate adjusted based on all water levels) that include the effects of lag time. The controller design method uses discrete-time state-feedback control with a quadratic penalty function, physically based states, and no state estimation. A simple, linear model of canal pool response, the integrator-delay model, is used to define the state transitions. All controllers within this class are tuned for the entire canal using optimization techniques. This avoids the tedious task of manually tuning simple controllers. The relative performance of the various controllers within this class can be directly compared without simulation, since the same objective function is used to tune each controller. An example is provided which suggests that the fully centralized controller will perform better than a series of local controllers. However, reasonably good performance can be obtained for some intermediate PI controllers that pass information to one additional check structure upstream and downstream. This should limit some of the difficulties reported for full optimal controllers where all check structures respond to water-level errors in all pools (e.g., saturation of inputs). The results of simulation studies of these controllers are provided in a companion paper.     

Simple Optimal Downstream Feedback Canal Controllers: ASCE Test Case Results

In a companion paper, a class of downstream-water-level feedback canal controllers was described. Within this class, a particular controller is chosen by selecting which controller coefficients to optimize (tune), the remaining coefficients being set to zero. These controllers range from a series of simple proportional-integral (PI) controllers to a single centralized controller that considers lag times. In this paper, several controllers within this class were tuned with the same quadratic performance criteria (i.e., identical penalty functions for optimization). The resulting controllers were then tested through unsteady-flow simulation with the ASCE canal automation test cases for canal 1. Differences between canal and gate properties, as simulated and as assumed for tuning, reduced controller performance in terms of both water-level errors and gate movements. The test case restrictions placed on minimum gate movement caused water levels to oscillate around their set points. This resulted in steady-state errors and much more gate movement (hunting). More centralized controllers handle unscheduled flow changes better than a series of local PI controllers. Controllers that explicitly account for pool wave travel times did not improve control as much as expected. Sending control actions within a given pool to upstream pools improved performance, but caused oscillations in some cases, unless control signals were also sent downstream. A good compromise between controller performance and complexity is provided by controllers that pass feedback from a given water level to the check structure at the upstream end of its pool (i.e., that used for downstream control of an individual pool) and to all upstream and one downstream check structures.     

A dental CT study for preoperative assessment of maxillary atrophy

According to a new technology in the planning of endo-osseous implantation, based on a new CT-software for evaluation of the bone structure of the jaws, anatomico-morphological changes after the loss of teeth are measured much more accurately than with conventional methods like the panoramic intraoral x-ray or conventional tomography. 30 mandibles and 22 maxillae of 36 patients were examined. Besides the topographic course of the mandibular canal and the location of the foramen mentale, the anatomic structures as the important aspects for planning endo-osseous implants are seen more accurately. It is now possible to recognise morphological changes with paraxial reconstructions in a very short time more clearly and precisely than with former techniques.     

High-Resolution Method for Modeling Hydraulic Regime Changes at Canal Gate Structures

A method for modeling flow regime changes at gate structures in canal reaches is presented. The methodology consists of using an approximate Riemann solver at the internal computational nodes, along with the simultaneous solution of the characteristic equations with a gate structure equation at the upstream and downstream boundaries of each reach. The conservative form of the unsteady shallow-water equations is solved in the one-dimensional form using an explicit second-order weighted-average—flux upwind total variation diminishing (TVD) method and a Preissmann implicit scheme method. Four types of TVD limiters are integrated into the explicit solution of the governing hydraulic equations, and the results of the different schemes were compared. Twelve possible cases of flow regime change in a two-reach canal with a gate downstream of the first reach and a weir downstream of the second reach, were considered. While the implicit method gave smoother results, the high-resolution scheme—characteristic method coupling approach at the gate structure was found to be robust in terms of minimizing oscillations generated during changing flow regimes. The complete method developed in this study was able to successfully resolve numerical instabilities due to intersecting shock waves.     

Structure of Flow Upstream of Vertical Angled Screens in Open Channels

This paper presents the results of a laboratory study of the structure of flow in a diversion structure with a vertical angled wedge-wire fish screen. This screen had a 10×25?mm mesh and was tested at three angles of 10.4, 17.5, and 26.8°, to the direction of the approaching flow, for two mean velocities of 0.5 and 0.8?m/s, with a depth of flow of about 0.75?m. In this water and fish diversion (channel or) structure, it was found that the depth of flow at any section is approximately constant with a drop at the screen on the side of the canal and decreased towards the bypass located at the downstream end. The distribution of the velocity component u in the direction of the approaching flow as well as the perpendicular component w and the resultant velocity V was uniform in the vertical direction. The depth averaged mean velocity for different verticals at any section in the diversion structure increased with the longitudinal distance x and was correlated with the relative width, bs/b (in the diversion structure) for all five experiments. Correlations have been found for the depth averaged transport velocity and the impinging velocity on the screen in terms of the approach velocity U. A general relation has also been developed for the attack angle of the flow on the screen. The downstream part of the screen carried more flow into the canal compared to the upstream part as a result of the uniform mesh size used in this study. The results of this hydraulic study should be useful, particularly for freshwater adult fish, in designing screens in irrigation canals and for micro-hydro sites that use diversion canals.     

程序化计算端面移动量在多楔模具参数化设计上的应用

精确地计算出楔横轧轧制过程中轧件端面移动量 ,对于楔横轧多楔模具设计合理确定楔与楔之间的相对位置起着至关重要的作用。在综合楔横轧轧制过程不同阶段端面移动量计算规律的基础上 ,开发并编制出楔横轧端面移动量计算机源程序 ,并应用于楔横轧多楔模具参数化设计。通过实际轧制实验证明 ,该程序计算结果正确、计算效率高 ,为楔横轧多楔模具参数化设计提供了良好的前处理通用程序     

Bottom Slot Discharge Outlet for Combined Sewer Diversion Structure

The concept of a bottom slot outlet was developed to serve as a combined sewer overflow diversion structure to convey flow to deep tunnel storage under free discharge conditions and pass the remaining volume once storage capacity is exceeded with minimum backwater effects. In order to test the concept, a 1:19.5 scale model was constructed and tested over a range of discharges in order to determine the required slot length to pass a certain discharge. Different bottom slopes and slot widths were tested. For subcritical approach flow, the flow in the structure passed through critical depth at the upstream end of the slot, eliminating the possibility of backwater effects. The results were found to be nearly independent of the bottom slope for typical small slopes in sewer systems, and a simple dimensionless relation was developed to relate the slot length to other parameters. A mathematical model combining continuity and energy relations for the remaining flow in the structure with an orifice relation for flow through the slot was capable of reproducing the observed experimental results.     

重轨端部淬火温度场与相变的计算机模拟

运用有限元法对U71Mn钢(%:0.65～0.76C、0.15～0.35Si、1.10～1.40Mn、≤0.030V、≤0.025Ti)重轨端部电磁感应加热55 s,空冷8 s,喷风冷却42 s,空冷至常温的热处理过程进行了计算机模拟分析,计算机图形学理论动态显示轨端内部任意时刻的温度分布、组织分布。模拟结果表明,在该冷却条件下淬火后端部横断面组织为细片状珠光体(索氏体+托氏体),无马氏体、贝氏体等组织,与实验结果相吻合。     

Case Study: Delayed Sedimentation Response to Inflow and Operations at Sanmenxia Dam

This paper presents a study on the reservoir sedimentation processes in response to changes in incoming flow at the upstream and changes in the pool level at the downstream for Sanmenxia Reservoir, which is located on the middle reach of the Yellow River in China and has experienced serious sedimentation problems even since its impoundment in 1960. The hysteresis effect in reservoir sedimentation was used as the basis for analysis and its behavior was fully investigated throughout this study. The research found that the rise in the elevation of Tongguan, which is located in the backwater region at a distance of 113.5?km upstream of the Sanmenxia Dam, had a time delay of about 2?years compared with the sediment deposition in the reservoir area downstream of Tongguan. Moreover the accumulated sediment deposition in the reservoir area was closely related not only to the current year’s flow and dam operational conditions, but also to the preceding 3–4?years’ flow and dam operational conditions. Likewise the variation of Tongguan’s elevation was a function of 6?years’ linearly superimposed runoff, and the channel bed slope in the vicinity of Tongguan was determined by a moving average pool level over a 7?year period. The research results are of practical importance in particular for optimizing the operation of Sanmenxia Dam, and the finding of the hysteresis phenomenon in the sedimentation process of the reservoir is of merit to the advancement of sedimentation science.     

Examination of Level of Analysis Accuracy for Curved I-Girder Bridges through Comparisons to Field Data

To evaluate the accuracy of different levels of analysis used to predict horizontally curved steel I-girder bridge response, a field test was performed on a three-span structure. Collected strain data were reduced to determine girder vertical and bottom flange lateral bending moments. Experimental moments were compared to numerical moments obtained from three commonly employed levels of analysis. Level 1 analysis includes two manual calculation methods: a line girder analysis method described in the AASHTO Guide Specification for Horizontally Curved Highway Bridges, and the V-load method. Grillage models represent Level 2 and were created using three commercially available computer programs: SAP2000, MDX, and DESCUS. Level 3 consists of three-dimensional (3D) finite element models created using SAP2000 and the BSDI 3D system. Responses obtained from each level are compared and discussed for a single radial cross section of the structure, and the compared results involve truck loads and placement schemes that do not represent those used for bridge design. The field test and numerical data presented are used solely to determine the accuracy of each level of analysis for predicting structure response to a specific live load at a specific cross section. Results showed that Level 2 and Level 3 analyses predict girder vertical bending moment distributions more accurately than Level 1 analyses throughout the tested cross section. The comparisons indicate that Level 3 girder vertical bending moment distributions offered no appreciable increase in accuracy over Level 2 analyses. The study also indicates that both Level 1 and Level 3 analyses provide bottom flange lateral bending moment distributions that do not correlate well with field test results for the studied bridge cross section.     

Hydrostatic, Temperature, Time-Displacement Model for Concrete Dams

This paper presents frequency domain solution algorithms of the one-dimensional transient heat transfer equation that describes temperature variations in arch dam cross sections. Algorithms are developed to compute the temperature T(x,t), spatial distribution, and time evolution for the “direct” problem, where the temperature variations are specified at the upstream and downstream faces, and for the “inverse” problem, where temperatures have been measured at thermometers located inside instrumented dam sections. The resulting nonlinear temperature field is decomposed in an effective average temperature, Tm(t), and a linear temperature difference, Tg(x,t), from which the dam thermal displacement response can be deducted. The proposed frequency domain solution procedures are able to reproduce an arbitrary transient heat response by appending trailing temperatures at the end of thermal signals, thus transforming a periodic heat transfer problem in a transient one. The frequency domain solution procedures are used to develop the HTT (hydrostatic, temperature, time) statistical model to interpret concrete dam-recorded pendulum displacements. In the HTT model, the thermal loads are arbitrary and can contain temperature drift or unusual temperature conditions. The explicit use of Tm(t) and Tg(x,t) in the HTT dam displacement model allows extrapolation for temperature conditions that have never been experienced by the dam before (within the assumption of elastic behavior). The HTT model is applied to the 131-m-high Schlegeis arch dam, and the results are compared with the HST (hydrostatic, seasonal, time) displacement model that is widely used in practice.     

Nonlinear Identification of Lumped-Mass Buildings Using Empirical Mode Decomposition and Incomplete Measurement

Most structures exhibit some degrees of nonlinearity such as hysteretic behavior especially under damage. It is necessary to develop applicable methods that can be used to characterize these nonlinear behaviors in structures. In this paper, one such method based on the empirical mode decomposition (EMD) technique is proposed for identifying and quantifying nonlinearity in damaged structures using incomplete measurement. The method expresses nonlinear restoring forces in semireduced-order models in which a modal coordinate approach is used for the linear part while a physical coordinate representation is retained for the nonlinear part. The method allows the identification of parameters from nonlinear models through linear least-squares. It has been shown that the intrinsic mode functions (IMFs) obtained from the EMD of a response measured from a nonlinear structure are numerically close to its nonlinear modal responses. Hence, these IMFs can be used as modal coordinates as well as provide estimates for responses at unmeasured locations if the mode shapes of the structure are known. Two procedures are developed for identifying nonlinear damage in the form of nonhysteresis and hysteresis in a structure. A numerical study on a seven-story shear-beam building model with cubic stiffness and hysteretic nonlinearity and an experimental study on a three-story building model with frictional magnetoreological dampers are performed to illustrate the proposed method. Results show that the method can quite accurately identify the presence as well as the severity of different types of nonlinearity in the structure.     

Dynamic Soil Stiffnesses at Side of Embedded Structures with Rectangular Base

Soil behavior at the side of an embedded structure with rectangular base area is formulated. The soil medium is idealized as a stack of horizontal sheets interconnected by distributed vertical springs. Each sheet is made of a previously proposed column-spring system. The computed results indicate that, at frequencies higher than the fundamental natural frequency of the soil medium, the vertical springs can be eliminated and each sheet can be treated as an independent sheet in the plane strain condition. This approximation and Galerkin’s method for weighted residuals lead to very simple expressions for the soil stiffnesses per depth at the side of a structure with rectangular cross section. The formulations developed are computationally very convenient and confirmed to produce results close to those computed by a far more rigorous method. The dynamic soil stiffnesses at the side of a structure are computed for various cases. The dynamic response analyses of partially embedded structures are presented to demonstrate the application of the approach and formulations developed.     

Surface Loading of a Multilayered Viscoelastic Pavement: Semianalytical Solution

In this paper a new method is proposed to analyze the mechanical response of a linear viscoelastic pavement. The material parameters of the asphalt concrete are characterized by the relaxation modulus and creep compliance, which are further represented by the Prony series. By virtue of the Laplace transform and the correspondence principle, the solution in the Laplace domain is first derived. The interconversion between the relaxation modulus and creep compliance is then applied to treat the complicated inverse Laplace transform. The displacement, strain, and stress fields are represented concisely in terms of the convolution integral in the time domain, which is subsequently solved analytically. Therefore, responses of the viscoelastic pavement are finally expressed analytically in the time domain and numerically in space domain, called a semianalytical approach. Since both the relaxation modulus and creep compliance are used simultaneously, instead of only one parameter in the conventional methods, the present method is also called a dual-parameter method. The present formulation is verified at both the short- and long-term time limits analytically and at the other finite time numerically, as compared to the conventional numerical methods. We clearly show that the present dual-parameter and semianalytical method can predict accurately the time-dependent responses of the viscoelastic pavement, especially at the long-term time. The present formulation could also be employed to validate the widely used collocation method.