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.     

Simple Method for Quick Estimation of Leaky-Aquifer Parameters

Simple method and explicit equations are proposed for estimating the parameters of leaky aquifers from drawdown at an observation well, which avoid the curve matching or initial estimate of the parameter. The proposed method is computationally simple and the calculations can be performed even on a handheld calculator. The application of the methods is illustrated, using published data sets. The new method yields quick and accurate estimates of the leaky-aquifer parameters, if observed drawdowns do not contain large errors. The proposed method can also analyze the early drawdowns for accurate characteristics/parameters of a confined aquifer, if the conductance of the aquitard is assigned a zero value. It is hoped that the proposed method would be of help to field engineers and practitioners.     

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.     

Flow Depletion Induced by Pumping Well from Stream Perpendicularly Intersecting Impermeable/Recharge Boundary

Analytical solutions for rate and volume of flow depletion induced by pumping a well from a stream that intersects an impermeable or a recharge boundary at right angles are derived using the basic flow depletion factor defined earlier by the author. A new concept of directly obtaining stream flow depletion using the method of images is proposed. The solutions are derived for five different management cases of a stream and boundary intersecting at right-angles, assuming the aquifer to be confined with semi-infinite areal extent. A computationally simple function is proposed for accurately approximating the error function. The existing analytical solution in the case of a right-angle bend of stream given by Hantush was obtained for unconfined aquifers using a linearization of the governing partial differential equation. The solution for this case obtained using the proposed method for confined aquifer is the same as obtained by Hantush for unconfined aquifers, which shows that the linearization adopted by Hantush does not actually solve this problem for unconfined aquifers.     

Diagnostic Curve for Confined Aquifer Parameters from Early Drawdowns

A diagnostic curve of unimodal shape is developed for identifying the confined aquifer parameters from early drawdowns. A scaled well function is proposed for the diagnostic curve and computationally simple functions are developed for its accurate approximation. The diagnostic curve may be viewed as an alteration of the Theis’ curve or as the generalization of a previous approach proposed by the writer. Plotting the pumping test data in a convenient form and matching it to the diagnostic curve with a parallel shift of axes identify the aquifer parameters. The unimodal shape of the diagnostic curve facilitates matching and reduces the personal errors. The proposed method is simple, easy to apply, and yields accurate estimates of aquifer parameters from only early drawdowns, which would save considerable time and money involved in conducting a long-duration pumping test. The estimates obtained using the new method are as good as those obtained from much more complex methods. The new method does not require either the initial guess for the parameter values or repetitive evaluation of the well function.     

A double laser filtering approach to vibration noise rejection for hot-rolled strip flatness measurement

This paper proposes a new filtering method based on the Kalman filtering algorithm for hot-rolled strip flatness measurement system. The system involves processing slowly changing signal, which can be considered as a bounded random process, and its model parameters are completely unknown. The noise rejection strategy in double lasers can generate a compensation signal. Since the initial and accumulative error would lead to negative filter effect or even cause divergence, Kalman filter is integrated to effectively deal with the initial error and enhance convergence. In this setting, the noise rejection strategy is used as a prediction model to constitute a similar Kalman filter. The correlated error caused by measurement error is coped with by a compensation model based on the feature of correlated error to enhance the filter effect. Both theoretical analysis and simulations show that the new algorithm has a better filter effect than the traditional Kalman filtering algorithm for the system.     

Forecasting of Reference Evapotranspiration by Artificial Neural Networks

In recent years, artificial neural networks (ANNs) have been applied to forecasting in many areas of engineering. In this note, a sequentially adaptive radial basis function network is applied to the forecasting of reference evapotranspiration (ETo). The sequential adaptation of parameters and structure is achieved using an extended Kalman filter. The criterion for network growing is obtained from the Kalman filter’s consistency test, while the criteria for neuron/connection pruning are based on the statistical parameter significance test. The weather parameter data (air temperature, relative humidity, wind speed, and sunshine) were available at Nis, Serbia and Montenegro, from January 1977 to December 1996. The monthly reference evapotranspiration data were obtained by the Penman-Monteith method, which is proposed as the sole standard method for the computation of reference evapotranspiration. The network learned to forecast ETo,t+1 based on ETo,t?11 and ETo,t?23. The results show that ANNs can be used for forecasting reference evapotranspiration with high reliability.     

Simple Model for Analyzing Transient Pumping from Two Aquifers without Cross Flow

A computationally simple semianalytical model is proposed for calculating the drawdown due to pumping a well tapping two aquifers separated by an aquiclude with no cross flow. The new model can take into account the transient pumping discharge. Equations are proposed for calculating the transient contributions of the aquifers to the pumped discharge and drawdowns in aquifers. The residual drawdowns in the aquifers and the aquifer contributions during recovery period can also be obtained using the proposed model. Based upon a similar principle, another model is also developed that can consider the effect of the well storage. The proposed models can be used to calculate drawdowns neglecting or considering the well storage, in the case of transient pumping from two aquifers having different values of transmissivity and storage coefficient. It is hoped that the new models would be of help to the field engineers and practitioners.     

Investigation of a System Identification Methodology in the Context of the ASCE Benchmark Problem

This article briefly presents the theory for a system identification and damage detection algorithm for linear systems, and discusses the effectiveness of such a methodology in the context of a benchmark problem that was proposed by the ASCE Task Group in Health Monitoring. The proposed approach has two well-defined phases: (1) identification of a state space model using the Observer/Kalman filter identification algorithm, the eigensystem realization algorithm, and a nonlinear optimization approach based on sequential quadratic programming techniques, and (2) identification of the second-order dynamic model parameters from the realized state space model. Structural changes (damage) are characterized by investigating the changes in the second-order parameters of the “reference” and “damaged” models. An extensive numerical analysis, along with the underlying theory, is presented in order to assess the advantages and disadvantages of the proposed identification methodology.     

Structural Health Monitoring by Recursive Bayesian Filtering

A new vision of structural health monitoring (SHM) is presented, in which the ultimate goal of SHM is not limited to damage identification, but to describe the structure by a probabilistic model, whose parameters and uncertainty are periodically updated using measured data in a recursive Bayesian filtering (RBF) approach. Such a model of a structure is essential in evaluating its current condition and predicting its future performance in a probabilistic context. RBF is conventionally implemented by the extended Kalman filter, which suffers from its intrinsic drawbacks. Recent progress on high-fidelity propagation of a probability distribution through nonlinear functions has revived RBF as a promising tool for SHM. The central difference filter, as an example of the new versions of RBF, is implemented in this study, with the adaptation of a convergence and consistency improvement technique. Two numerical examples are presented to demonstrate the superior capacity of RBF for a SHM purpose. The proposed method is also validated by large-scale shake table tests on a reinforced concrete two-span three-bent bridge specimen.     

Kernel Method for Transient Rate and Volume of Well Discharge under Constant Drawdown

A kernel method is proposed for calculating transient rate and cumulative volume of well discharge under constant drawdown. The new method can also be used for obtaining the drawdown (in pressure head) in the aquifer at some distance away from the well. Employing the new method, an optimization method is used to estimate the aquifer parameters from transient well discharge or drawdown in the aquifer pressure head. The proposed method can also be used to model the recovery of drawdown (in aquifer pressure head) after the plug-in of the well.     

基于ELM和MCSCKF的锂离子电池SOC估计

为了减少噪声对锂离子电池荷电状态估计的影响,本文提出一种新颖的基于极限学习机和最大相关熵平方根容积卡尔曼滤波的SOC估计方法。首先,利用泛化性好、运行速度快的极限学习机作为卡尔曼滤波的测量方程;其次,基于灰狼优化算法,极限学习机的超参数被优化以提高电池荷电状态的估计精度;最后,基于最大相关熵平方根容积卡尔曼滤波,极限学习机的测量噪声被进一步减弱。所提方法可以简化极限学习机繁琐的调参过程,且为闭环的SOC估计方法。所提方法在多工况和宽温度范围内被测试以验证其泛化性能。测试结果显示,所提方法明显地提高了锂离子电池的荷电状态估计精度。同时,对比其他算法,所提方法的平均运行时间仅仅为长短时序列和循环门控单元网络的三分之一。当行驶工况复杂、温度变化区间较大时,所提方法的均方根误差小于1%,最大误差小于3%。当存在初始误差与环境噪声时,所提方法显示出了优越的鲁棒性。      

Modeling the Transient Pumping from Two Aquifers Using MODFLOW

A procedure is proposed for calculating the spatial and temporal variation of drawdown due to pumping a well tapping two aquifers separated by an aquitard, using convolution and MODFLOW. It can take into account the unsteady pumping discharge and cross flow through the intervening aquitard. A discrete pulse kernel method based on superposition/convolution is used to account for the unsteady pumping discharge. The discrete pulse kernels are calculated using MODFLOW. The contributions of the aquifers to the pumped discharge are accounted implicitly and not required to be specified explicitly. Available numerical models (e.g., MODFLOW) require the aquifer contributions that are implicitly controlled, to be specified explicitly. The use of the suggested procedure is illustrated using examples. The contributions of the aquifers are found not in proportion to their transmissivities but vary with time, when the diffusivities of the aquifers are not equal. Applying the new procedure, the numerical models, such as MODFLOW can be used to correctly model the transient pumping from two aquifers with cross flow; thus, it opens up the possibility of numerically accounting for the aquifer heterogeneity while dealing with the flow to a well tapping two aquifers under a transient pumping, which would be otherwise difficult to account for analytically.     

Simple Model for Analyzing Transient Pumping from Two Aquifers with Cross Flow

A simple semianalytical model is proposed for calculating the drawdown due to pumping a well tapping two aquifers. The new model can take into account the transient pumping discharge and cross flow between the aquifers. The transient contributions of the aquifers to the pumped discharge can also be implicitly obtained using the model.     

Bayesian State Estimation Method for Nonlinear Systems and Its Application to Recorded Seismic Response

The focus of this paper is to demonstrate the application of a recently developed Bayesian state estimation method to the recorded seismic response of a building and to discuss the issue of model selection. The method, known as the particle filter, is based on stochastic simulation. Unlike the well-known extended Kalman filter, it is applicable to highly nonlinear systems with non-Gaussian uncertainties. The particle filter is applied to strong motion data recorded in the 1994 Northridge earthquake in a seven-story hotel whose structural system consists of nonductile reinforced-concrete moment frames, two of which were severely damaged during the earthquake. We address the issue of model selection. Two identification models are proposed: a time-varying linear model and a simplified time-varying nonlinear degradation model. The latter is derived from a nonlinear finite-element model of the building previously developed at Caltech. For the former model, the resulting performance is poor since the parameters need to vary significantly with time in order to capture the structural degradation of the building during the earthquake. The latter model performs better because it is able to characterize this degradation to a certain extent even with its parameters fixed. For this case study, the particle filter provides consistent state and parameter estimates, in contrast to the extended Kalman filter, which provides inconsistent estimates. It is concluded that for a state estimation procedure to be successful, at least two factors are essential: an appropriate estimation algorithm and a suitable identification model.     

Genetic Algorithms for the Calibration of Constitutive Models for Soils

This paper presents a study that uses an innovative numerical method called the “genetic algorithm” for material parameter optimization in constitutive modeling. The paper introduces a new scheme, a fitness function, to estimate the error of predicted behavior due to a given set of material parameters. Optimization efficiency of the proposed fitness function is analyzed by changing the selected genetic algorithm parameters. The genetic algorithm and the new fitness function were found to be capable of optimizing material parameters of complex constitutive models.     

Least-Squares Estimation with Unknown Excitations for Damage Identification of Structures

System identification and damage detection for structural health monitoring of civil infrastructures have received considerable attention recently. Time domain analysis methodologies based on measured vibration data, such as the least-squares estimation and the extended Kalman filter, have been studied and shown to be useful. The traditional least-squares estimation method requires that all the external excitation data (input data) be available, which may not be the case for many structures. In this paper, a recursive least-squares estimation with unknown inputs (RLSE-UI) approach is proposed to identify the structural parameters, such as the stiffness, damping, and other nonlinear parameters, as well as the unmeasured excitations. Analytical recursive solutions for the proposed RLSE-UI are derived and presented. This analytical recursive solution for RLSE-UI is not available in the previous literature. An adaptive tracking technique recently developed is also implemented in the proposed approach to track the variations of structural parameters due to damages. Simulation results demonstrate that the proposed approach is capable of identifying the structural parameters, their variations due to damages, and unknown excitations.     

Approximation of M Function for Partially Penetrating Wells

A computationally simple approximation of the Hantush M function is proposed. Using this approximation, an optimization method is proposed for identifying the aquifer parameters from early drawdowns around partially penetrating wells. The aquifer parameters are hydraulic conductivity and specific storage. The application of the method is illustrated using a field example. The proposed method results in a 120-fold saving in time when compared to the prior method. It is hoped that the proposed approximation and method will be of help to the field engineers and practitioners.     

Thermal Ice Growth: Real-Time Estimation

The quasi-steady thermal ice growth model was recast in state-space form and used with the Kalman filter to estimate ice thickness and to recursively estimate the model parameters for thermal ice growth. This approach was appropriate at locations where measurements of the ice thickness were made during the study. The model was applied to two widely separated sites from which ice thickness measurements were available for a number of winters: Post Pond, N.H., and Snowshoe Lake, Alaska. The parameters required by the Kalman filter were estimated through numerical experiments and were consistent between both locations. The Kalman filter was able to produce better results, as measured by a least-squares criterion, than a model using parameter values that had been determined using all data at each location.     

Well Loss Estimation: Variable Pumping Replacing Step Drawdown Test

An optimization method is presented for simultaneous estimation of aquifer parameters and well loss parameters utilizing all the drawdowns observed during a variable rate pumping or multiple step pumping test. The proposed method does not require any graphical analysis. It is shown that a variable rate pumping test is a better substitute for the conventional step drawdown test to estimate well loss parameters. It suggests that the pumping rate may be changed frequently without waiting for a near steady state to be reached (or a selected duration, say 60 min) in each step of a conventional step drawdown test. This can result in a substantial saving of time and money involved in conducting a step drawdown test with a view to estimate well loss parameters. This gives a greater number of distinct discharges, which improves the estimates of the well loss parameters. Application of the method is demonstrated on published data sets, the results of which show that the parameters estimated using the new method are more reliable as compared to those obtained using prior methods.