Nikolai B. Gorev

Noniterative Implementation of Pressure-Dependent Demands Using the Hydraulic Analysis Engine of EPANET 2

To analyze water distribution networks under pressure-deficient conditions, most of the available hydraulic simulators, including EPANET 2, must be either modified by embedding pressure-dependent demands in the governing network equations or run repeatedly with successive adjustments made to specific parameters until a sufficient hydraulic consistency is obtained. This paper presents and discusses a simple technique that implements the square root relationship between the nodal demand and the nodal pressure using EPANET 2 tools and allows a water distribution network with pressure-dependent demands to be solved in a single run of the unmodified snapshot hydraulic analysis engine of EPANET 2. In this technique, artificial strings made up of a flow control valve, a pipe with a check valve, and a reservoir are connected to the demand nodes before running the engine, and the pressure-dependent demands are determined as the flows in the strings. The resistance of the artificial pipes is chosen such that the demands are satisfied in full at a desired nodal pressure. The proposed technique shows reasonable convergence as evidenced by its testing on example networks.

Convergence of a Hydraulic Solver with Pressure-Dependent Demands

This paper analyzes the convergence of a pressure-driven analysis (PDA) model of a water distribution network solver based on Todini’s global gradient algorithm. The PDA model is constructed by embedding a pressure−demand relationship in the EPANET simulator code. To avoid spurious convergence, a residual-based convergence error was used. The introduction of pressure-dependent demands is shown to result in a far poorer convergence. The study of solver convergence as a function of the smoothness of the pressure−demand curve has demonstrated that, statistically, a smooth pressure−demand relationship gives a somewhat better convergence. To improve convergence, use was made of a quadratic approximation of the Hazen–Williams head loss−flow relationship in the vicinity of zero and the correct implementation of the Darcy−Weisbach formula in the solver. To further improve convergence, an iteration step control technique called the line search was used. The analysis of solver convergence for different line search variants has shown that the line search in its usual form is not efficient enough and may result in poorer convergence. A necessary error decrease algorithm, whose use in the line search improves solver convergence, is proposed. It is shown that due to the convergence improvement methods the convergence of the PDA solver is somewhat better than that of the demand-driven analysis solver and sufficient for direct problems such as design, for example.

Method to Cope with Zero Flows in Newton Solvers for Water Distribution Systems

AbstractThis paper presents and discusses a simple method to deal with zero flows in Newton solvers for water distribution systems, in particular in a previously published global gradient algorithm. The method consists in replacing the Hazen-Williams head loss–flow relationship for flows below a certain threshold with a linear relationship, which coincides with Hazen-Williams’ at zero, but has a nonzero derivative at that point, thus avoiding computational troubles associated with zero flows. Manual and automatic random testing of example networks shows that the proposed method compares well with both the algorithm adopted in water distribution modeling software and the recently proposed regularization method in convergence rate while outperforming them in computational veracity and applicability range.

Non-destructive deep trap diagnostics of epitaxial structures

Abstract A simple non-destructive method for determining the concentration of vacant deep traps in the vicinity of the film–substrate interface under extrinsic illumination is proposed and tested. The proposed technique relies on capacitance–voltage measurements under illumination. An increase in the width of the conductive channel under extrinsic illumination is expressed in terms of the structural parameters and the illumination-induced shift of the inflection point in the capacitance–voltage curve. The experimental results for GaAs epitaxial films are in satisfactory agreement with those obtained by an independent method based on sidegating measurements.

Determination of deep trap concentration at channel–substrate interface in GaAs MESFET using sidegating measurements

Abstract An analytical expression that describes the sidegating effect in a GaAs MESFET, (i.e. relates the drain current to the substrate voltage) is obtained. Based on this expression, a simple method for determining the concentration of vacant deep traps at the channel–substrate interface from sidegating measurements is proposed and applied for device characterization and parameter extraction.

Pseudotransient Continuation-Based Steady State Solver: Extension to Zero Flow Rates

This paper presents and discusses an extension of the pseudotransient continuation-based steady state solver for hydraulic networks proposed previously to the case of zero flow rates. The original solver, which reduces the solution of the governing nonlinear algebraic equations to the numerical integration of an initial-value problem, has problems in situations in which the head derivative of the flow rate tends to infinity, as is the case with zero flow rates. The extension is on the basis of the use of a model headloss-flow relationship that coincides with the true one at zero and has a finite head derivative at that point. This modified steady state solver is free from some convergence problems that occur in Newton-Raphson method-based solvers when analyzing a pipe network with control devices. The paper includes the results of the numerical analysis of test networks, which demonstrate the convergence of the modified steady state solver for cases in which existing steady state solvers have troubles.

HYDRAULIC SIMULATOR TESTING: METHODS,' TOOLS, AND RESULTS

This paper presents methods for automatic testing of static solvers of hydraulic simulators. The proposed methods are implemented in programs of evolutionary testing of solvers for convergence and the correctness of the converged solution. The programs search for network parameter combinations that result in divergence or incorrect solutions using genetic algorithms: divergences and incorrect but converged results are searched for by maximizing the number of iterations required to obtain a converged solution and the residual of the governing equations, respectively. The use of the methods is illustrated and the efficiency of the programs is shown by the example of the EPANET static solver. Examples of networks that present problems both for EPANET and for some commercial simulators are given. When making quantitative assessments and comparing the original version of the solver with its improved version, use was made of the random testing programs developed. A list of some unsolved problems in the simulation of water distribution systems is presented, and a solution to some of them is suggested.

Capacitance–voltage characteristics of selectively doped AlxGa1−xAs/GaAs heterostructures containing deep traps

The low- and high-frequency capacitance–voltage characteristics of a selectively doped AlxGa1−xAs/GaAs heterostructure containing deep traps in the AlxGa1−xAs layer are calculated. It is shown that the low-frequency capacitance–voltage characteristic features a rising portion when the deep traps are localized at the heterointerface, this rising portion being due to the onset of emptying of the deep traps. The calculated results agree with the experimental data.

DISPLACEMENT MEASUREMENT USING A TWO-PROBE IMPLEMENTATION OF MICROWAVE INTERFEROMETRY

This paper presents a two-probe implementation of microwave interferometry for displacement measurement at an unknown re∞ection coe-cient. Theoretically, the proposed technique gives the exact value of the displacement for re∞ection coe-cients (at the location of the probes) no greater than 1= p 2 and in the general case determines it to a worst-case accuracy of about 4.4% of the operating wavelength. Its experimental veriflcation has demonstrated reasonable measurement accuracy for displacements several times as great as the operating wavelength (in real-time measurements at a free-space wavelength of 3cm for a peak-to peak vibration amplitude of 15cm, the maximum error in the determination of the instantaneous relative displacement and the peak-to-peak amplitude was about 3mm and about 1mm, respectively).

Experimental Analysis of Hydraulic Solver Convergence with Genetic Algorithms

A procedure for the experimental convergence evaluation of a hydraulic-network solver is proposed, based on using genetic algorithms to search for network parameter values that maximize the number of iterations of the hydraulic-network solver under test. The efficiency of the method is demonstrated by the example of convergence evaluation for the EPANET hydraulic simulator. Examples of a pipe network and of combinations of parameter values for which the static solver of the simulator fails to converge in a reasonable number of iterations are given. The features of the EPANET 2.00.12 solver responsible for loss of convergence are discussed. New criteria for the automatic start of solution damping aimed at improving the convergence of the solver are proposed. The better convergence of the EPANET solver modified in accordance with these criteria is confirmed by the random and the proposed search-based testing method.