Defining Triangular Probability Distributions from Historical Cost Data

During the development of an automated cost estimating system, several factors led to the selection of the triangular probability-density function to model historical construction costs. The triangular-density function is customarily used when function parameters are directly estimated by experts. A typical example is for estimating activity durations by identifying a minimum value, a most likely value, and a maximum value. These values are then used to construct triangular-density functions to represent uncertain activity durations. For this work, however, it was necessary to estimate parameters of the triangular-density function using historical cost data. A methodology was developed to generate test data and compare three methods of parameter estimation—maximum likelihood, moment matching, and least-squares curve-fitting techniques. It is concluded that optimized moment matching and least-squares techniques produce more accurate parameter estimates, while maximum likelihood estimation yields less accurate results. It is further concluded that the least-squares minimization method always performed as well as or better than the optimized moment matching technique and was therefore selected as the method of choice for the project.     

Longitudinal Dispersion Coefficient in Single-Channel Streams

Using a new channel shape equation for straight channels and a more versatile channel shape or local flow depth equation for natural streams a method is developed for prediction of the longitudinal dispersion coefficient in single-channel natural streams, including straight and meandering ones. The method involves derivation of a new triple integral expression for the longitudinal dispersion coefficient and development of an analytical method for prediction of this coefficient in natural streams. The proposed method is verified using 70 sets of field data collected from 30 streams in the United States ranging from straight manmade canals to sinuous natural rivers. The new method predicts the longitudinal dispersion coefficient, where more than 90% calculated values range from 0.5 to 2 times the observed values. The advantage of the new method is that it is capable of accurately predicting the longitudinal dispersion coefficient in single-channel natural streams without using detailed dye concentration test data. A comparison between the new method and the existing methods shows that the new method significantly improves the prediction of the longitudinal dispersion coefficient.     

Diagnostic Curves for Identifying Leaky Aquifer Parameters with or without Aquitard Storage

Two sets of unimodal diagnostic curves, one set assumes no aquitard storage and the other set assumes aquitard storage, are developed for identifying the parameter of leaky aquifers from early drawdowns, which yields accurate estimates of the parameters and lessens the subjectivity due to personal errors. The proposed diagnostic curve method is simple, easy to apply, and is based on matching of the diagnostically plotted observed drawdowns to an appropriate diagnostic curve. The new method is simple, easy to apply, does not require either the initial guess for the parameter values or repetitive evaluation of the leaky aquifer well function, and outperforms the conventional curve-matching, optimization, extended Kalman filter, and artificial neural network methods. The proposed set of diagnostic curves has a good diagnostic property and is able to easily identify nonideal conditions. The new method suggests a shorter duration pumping test, which would save time, money, and water. It is hoped that the proposed method would be useful to the field engineers and practitioners.     

Finite element analysis of thermal stresses in functionally graded cemented carbides

Abstract

In this study, finite element method and X-ray diffraction measurement were used to determine the thermal stress distribution of functionally graded WC–Co composites. The calculated results show that high stress concentration occurs in the cobalt gradient zone, tensile stress pile-up occurs in the cobalt rich zone and compressive stress pile-up occurs in the surface zone. As the sintering time is increased, compressive residual stress in the surface zone has a tendency of decreasing. The maximum value of compressive stress in the surface zone is 250 MPa. The results are in good agreement with X-ray diffraction measurement results. For the purpose of this work, the material design method is achieved by changing the calculated parameters.     

Maximum likelihood estimation of aggregated Markov processes

We present a maximum likelihood method for the modelling of aggregated Markov processes. The method utilizes the joint probability density of the observed dwell time sequence as likelihood. A forward-backward recursive procedure is developed for efficient computation of the likelihood function and its derivatives with respect to the model parameters. Based on the calculated forward and backward vectors, analytical formulae for the derivatives of the likelihood function are derived. The method exploits the variable metric optimizer for search of the likelihood space. It converges rapidly and is numerically stable. Numerical examples are given to show the effectiveness of the method.     

Modeling Impact of Storage Zones on Stream Dissolved Oxygen

The Streeter-Phelps dissolved oxygen model is modified to incorporate storage zones. A dimensionless number reflecting enhanced decomposition caused by the increased residence time of the biochemical oxygen demand in the storage zone parameterizes the impact. This result provides a partial explanation for the high decomposition rates observed in shallow streams. An application suggests that the storage zone increases the critical oxygen deficit and moves it closer to the point source. It also indicates that the storage zone should have lower oxygen concentration than the main channel. An analysis of a dimensionless enhancement factor indicates that the biochemical oxygen demand decomposition in small streams could be up to two to three times more than anticipated based on the standard Streeter-Phelps model without storage zones. For larger rivers, enhancements of up to 1.5 could occur.     

Estimation of the Longitudinal Dispersion Coefficient Using the Velocity Profile in Natural Streams

In this study, a theoretical method for predicting the longitudinal dispersion coefficient is developed based on the transverse velocity distribution in natural streams. Equations of the transverse velocity profile for irregular cross sections of the natural streams are analyzed. Among the velocity profile equations tested in this study, the beta distribution equation, which is a probability density function, is considered to be the most appropriate model for explaining the complex behavior of the transverse velocity structure of irregular natural streams. The new equation for the longitudinal dispersion coefficient that is based on the beta function for the transverse velocity profile is developed. A comparison of the proposed equation with existing equations and the observed longitudinal dispersion coefficient reveals that the proposed equation shows better agreement with the observed data compared to other existing equations.     

New Methods for Aquifer Parameters from Slug Test Data

An objective method and a diagnostic curve method are developed for estimating the aquifer parameters (storage coefficient and transmissivity) from slug test data on a fully penetrating well. In the objective method, explicit equations are developed for estimating the aquifer parameters. In the diagnostic curve method, a set of unimodal diagnostic curves is developed along with a guiding straight line. The rise or fall in water level of the well is plotted diagnostically on a double logarithmic graph and matched to one of the diagnostic curves plotted on the same scale with a parallel shift of axes, to estimate the aquifer parameters from the dual coordinates of a selected point on the matched portion of the graphs. The unimodal shape of the diagnostic curves and the guiding straight line facilitate the matching and limit the subjectivity. The proposed methods can easily identify a nonideal condition. The estimates of the aquifer parameters obtained using the proposed methods are more accurate than those obtained using the prior curve matching methods. The proposed methods are also able to identify nonideal conditions. It is hoped that the new methods will be of help to field and practicing engineers.     

Pile Behavior due to Excavation-Induced Soil Movement in Clay. I: Stable Wall

A series of centrifuge model tests has been conducted to investigate the behavior of a single pile subjected to excavation-induced soil movements behind a stable retaining wall in clay. The results reveal that after the completion of soil excavation, the wall and the soil continue to move and such movement induces further bending moment and deflection on an adjacent pile. For a pile located within 3?m behind the wall where the soil experiences large shear strain (>2%) due to stress relief as a result of the excavation, the induced pile bending moment and deflection reach their maximum values sometime after soil excavation and thereafter decrease slightly with time. For a pile located 3?m beyond the wall, the induced pile bending moment and deflection continue to increase slightly with time after excavation until the end of the test. A numerical model developed at the National University of Singapore is used to back-analyze the centrifuge test data. The method gives a reasonably good prediction of the induced bending moment and deflection on a pile located at 3?m or beyond the wall. For a pile located at 1?m behind the wall where the soil experiences large shear strain (>2%) due to stress relief resulting from the excavation, the calculated pile response is in good agreement with the measured data if the correct soil shear strength obtained from postexcavation is used in the analysis. However, if the original soil shear strength prior to excavation is used in the analysis, this leads to an overestimation of the maximum bending moment of about 25%. The practical implications of the findings are also discussed in this paper.     

Sorption Behavior and Long-Term Retention of Reactive Solutes in the Hyporheic Zone of Streams

This paper analyzes the transport of sorbing solutes by extending the advective storage path model developed for longitudinal transport of inert solutes in streams coupled with flow-induced uptake in the hyporheic zone. Independent observations of a conservative (3H) and a reactive (51Cr) tracer in both the stream water and the hyporheic zone were used to differentiate between hydraulic and sorption processes. The method of temporal moments was found to be inadequate for parameter determination, whereas fitting versus the entire tracer breakthrough curves with special emphasis on the tail indicates that the proposed model could be used to represent both conservative and reactive transport. Information on the tracer inventory of the conservative tracer in the hyporheic zone was found to be of vital importance to the evaluation of the hydraulic exchange. A model evaluation based on stream water data alone can yield predictions of a wash-out in the hyporheic zone that deviates markedly from the observed wash-out. This prohibits long-term predictions of the wash-out from the hyporheic zone as well as the evaluation of sorption properties. The sorption in the hyporheic zone was found to follow a two-step model, where the first step is instantaneous and the second kinetic. A model with a single-step sorption process could not reproduce the observed breakthrough curves. An evaluation of the relative importance of including sorption kinetics in solute stream transport models is elucidated by means of the analytical expressions for the temporal moments. The omission of the kinetics in the second sorption step in the hyporheic zone will result in relative errors in the moments of second order or higher. The error will increase with decreasing residence time in the hyporheic zone. Especially, long-term predictions of the wash-out from the hyporheic zone require consideration of the rate-limited sorption.     

Hybrid-Cells-in-Series Model for Solute Transport in Streams and Relation of Its Parameters with Bulk Flow Characteristics

The conceptualized hybrid-cells-in-series model, consists of a plug flow zone and two thoroughly mixed unequal reservoirs, all connected in series, has three time parameters, namely: (1) residence time of solute in the plug flow zone; and (2) residence times of solute in the two thoroughly mixed reservoirs. The model simulates closely advection-dispersion solute transport in natural streams. The resident time parameters are related to the velocity of flow, width of water surface, and depth of flow in the stream. Through the Péclet number, defined as Pe = (Δxu)/DL (in which Δx=process unit size; u=mean flow velocity; and DL=longitudinal dispersion coefficient), the relations of the model parameters with the longitudinal dispersion coefficient and with the bulk stream flow characteristics have been established. For a given reach of a stream, the parameters are inversely proportional to the flow velocity. By decoupling of pure advection by the plug flow component and dispersion of tracer by the two thoroughly mixed reservoir components, a robust fitting to the observed concentration-time data in natural streams was achieved.     

Theoretical Elastic-Plastic Solution for Laterally Loaded Piles

In this paper, the theoretical solutions of maximum deflection and moment for laterally loaded long piles in a uniform subgrade reaction modulus linear-plastic soil are presented. These solutions are in the form of normalized results and enable easy and exact calculation of the deflection or moment for three head loading conditions. Comparisons between the theoretical solution and a numerical solution established previously showed good agreement.     

Estimating Aquifer Parameters from Early Drawdowns in Large-Diameter Wells

The existing equation applicable for large diameter wells in confined aquifers is transformed into a convenient form and a set of semilogarithmic diagnostic curves is developed for identifying the aquifer parameters (storage coefficient and transmissivity) from early drawdowns in large diameter wells. A scaled well function is proposed for the diagnostic curves. The aquifer parameters are estimated by matching the diagnostically plotted drawdowns to one of the diagnostic curves by a parallel shift of only one axis. The substantial curvature of the diagnostic curves and shifting of only one axis facilitate matching and reduce subjectivity. The proposed method is an improvement over the existing matching methods. The new method can reliably identify the aquifer parameters from only early drawdowns and would result in a 100-fold saving in time and money. It is hoped that this method would be helpful to field engineers and practitioners.     

Analysis of liquid flow through ceramic porous media used for molten metal filtration

A two-dimensional mathematical model has been developed to study fluid flow inside ceramic foam filters, used for molten metal filtration, as a function of their structural characteristics. The model is based on the selection of a unit cell, geometric model, formed by two interconnected half-pores. The good agreement between experimental and computed permeabilities showed that the unit cell model approximates very well the effect of filter structure on the flow conditions inside the filter. The validity of the model is supported by the fact that permeabilities are calculated from directly measured structural parameters,i.e., without the introduction of any fitting variable, such as tortuosity. The laminar flow solutions for the Navier-Stokes equation, in steady state, were obtained numerically using the control-volume method. The boundary of the unit cell was represented through axisymmetrical, body-fitted coordinates to obtain a better representation of the complex pore shape. The generality of the model, to study fluid flow in reticulated media, was tested by comparing the computed specific permeabilities with values measured for ceramic foam filters and for the new ceramic filter of lost packed bed (CEFILPB). Such a comparison shows good agreement and discloses a fundamental property of the last kind of porous medium: the critical porosity. The model indicates how porosity and pore dimensions of reticulated filters may be tailored to meet specific fluid flow requirements.     

鱼雷罐喷粉铁水预处理脱磷动力学模型

在分析了铁水喷粉脱磷预处理过程机理的基础上，同时考虑熔池的均混时间、粉剂穿透比和停留时间，开发了鱼雷罐喷粉铁水预处理脱磷动力学模型，应用模型计算分析了改变不同工艺条件对脱磷速率的影响，并对实际生产过程进行了模型分析，取得了较好的效果。     

Modelling of flow curves for hot deformation

A new mathematical model for hot deformation flow curves is presented. The developed expression can be used for austenite or ferrite deformation, for monotonically increasing flow curves as well as for those with a maximum or with oscillating shape. By experimental determination of 4 flow curves, the parameters for the flow curve field can be calculated. Experiments have been carried out using aluminium- killed mild steels in hot compression tests with a range of deformation temperature between 700 and 1250°C and of strain rate between 0.1 and 20 s^-1. The accuracy of the new approach and the ability to meet the different flow curve shapes proved to be very good.     

Leaky One-Dimensional Flow with Storage and Skin Effect in Finite-Width Sink

One-dimensional horizontal flow in a semiinfinite confined aquifer can be described in terms of mathematical solutions that relate drawdown in the aquifer to aquifer parameters and flow into or out of a line sink. A new solution that considers the effects of a low-permeability skin along with storage in a finite-width sink is developed for the leaky-aquifer case. A coefficient Sk is defined to represent the skin effect for one-dimensional flow. The transient solution, which is obtained by inverting the Laplace-space solution using the Stehfest numerical algorithm, calculates drawdowns in the sink as well as in the aquifer. A nondimensional drain function D(u,x/B,A/x,Sk/x)q is defined based on the solution. Selected type curves for the drain function are plotted, and a match-point procedure is described that is based on matching observed drawdowns at observation wells to an appropriate type curve. The match-point procedure is illustrated by fitting simulated drawdown data to a type curve and determining the aquifer parameters. The drawdown solution is also represented by dimensional time–drawdown plots, which can be used to determine aquifer parameters by adjusting the parameters until model-calculated drawdowns match observed values. This new solution can be used to analyze drawdowns that result from a canal pumping test in which the discharge from the canal is derived from water stored in the canal and from a leaky aquifer and in which the drawdowns are affected by storage and a low-permeability skin in the canal.     

Dynamic Routing Model with Real-Time Roughness Updating for Flood Forecasting

A flood routing model with time-varying roughness updating was developed to simulate flows through natural channels based on the dynamic wave theory. Taking observed stages as the targets, a roughness updating technique was developed using the Gauss-Newton method to update the Manning n in each time step of the routing processes. The technique provides a reasonable roughness coefficient estimate and reliable initialization of stage profile for the forecast. The examinations including the initialization of stage profile, conservation of mass, iteration convergence, effectiveness evaluation, and convergence with different initial values were conducted to verify the predictive capability of the roughness updating technique. The forecasting results show that the stage recalculated by updating the Manning n in current time has a good agreement with the observed stage. The presented model can improve the forecast for a lead time up to 6?h in the Tanshui River of northern Taiwan.     

Alkylimidazolium Bromides as Corrosion Inhibitors for Mild Steel in Acidic Medium

Inhibition of mild steel corrosion in 1 M HCl solution by 1-alkyl-3-methylimidazolium bromides was investigated using electrochemical and weight loss methods. The studied ionic liquids showed appreciable inhibition efficiencies. Polarization measurements proved that the studied compounds were mixed-type inhibitors with predominantly anodic inhibition. The inhibition efficiency increased with the ionic liquid concentration and with the length of the alkyl chain. The values obtained from the polarization curves and weight loss measurements were in good agreement. The highest inhibition efficiency reached for the 1-octyl-3-methylimidazolium bromide was 94%. The Gibbs energy of adsorption was calculated by means of the Langmuir and Flory–Huggins isotherm and El-Awady thermodynamic-kinetic model.     

超高强钢冷轧过程轧制力计算的改进模型

 为了解决采用圆弧模型计算超高强钢冷轧过程轧制变形区轧辊压扁曲线误差较大的问题,充分考虑到超高强钢的轧制特点,通过分析不同压扁半径下轧辊压扁曲线的变化规律,构造出新型轧辊压扁曲线函数模型,给出了该函数中轧制变形区接触弧长特性参数与轧辊压扁曲线特性参数的求解方法。基于此,根据弹塑性理论中的变形与应力关系,推导了入口弹性变形区、塑性压下变形区以及出口弹性变形区单位轧制压力分布计算过程,建立了超高强钢冷轧过程总轧制力计算模型。并将其推广应用到某钢厂2030冷连轧机组,验证了该模型的计算准确度。结果表明,超高强钢冷轧过程轧辊压扁曲线用二次函数表示,更能准确反映轧辊压扁状态,其计算结果与实际值具有较高的吻合度。同时,为冷连轧机组生产超高强钢产品极限轧制能力的评估与轧制规程的制定提供了理论依据。