Reliability‐based control algorithms for nonlinear hysteretic systems based on enhanced stochastic averaging of energy envelope

Current reliability‐based control techniques have been successfully applied to linear systems; however, incorporation of stochastic nonlinear behavior of systems in such control designs remains a challenge. This paper presents two reliability‐based control algorithms that minimize failure probabilities of nonlinear hysteretic systems subjected to stochastic excitations. The proposed methods include constrained reliability‐based control (CRC) and unconstrained reliability‐based control (URC) algorithms. Accurate probabilistic estimates of nonlinear system responses to stochastic excitations are derived analytically using enhanced stochastic averaging of energy envelope proposed previously by the authors. Convolving these demand estimates with capacity models yields the reliability of nonlinear systems in the control design process. The CRC design employs the first‐level and second‐level optimizations sequentially where the first‐level optimization solves the Hamilton–Jacobi–Bellman equation and the second‐level optimization searches for optimal objective function parameters to minimize the probability of failure. In the URC design, a single optimization minimizes the probability of failure by directly searching for the optimal control gain. Application of the proposed control algorithms to a building on nonlinear foundation has shown noticeable improvements in system performance under various stochastic excitations. The URC design appears to be the most optimal method as it reduced the probability of slight damage to 8.7%, compared with 11.6% and 19.2% for the case of CRC and a stochastic linear quadratic regulator, respectively. Under the Kobe ground motion, the normalized peak drift displacement with respect to stochastic linear quadratic regulator is reduced to 0.78 and 0.81 for the URC and CRC cases, respectively, at comparable control force levels. Copyright © 2017 John Wiley & Sons, Ltd.     

Estimation of periodicities in hydrologic data

Periodicites in hydrologic data are frequently estimated and studied. In some cases the periodic components are subtracted from the data to obtain the stochastic components. In other cases the physical reasons for the occurrence of these periodicities are investigated. Apart from the annual cycle in the hydrologic data, periods corresponding to the 11 year sunspot cycle, the Hale cycle and others have been detected.The conclusions from most of these studies depend on the reliability and robustness of the methods used to detect these periodicities. Several spectral analysis methods have been proposed to investigate periodicities in time series data. Several of these have been compared to each other. The methods by Siddiqui and Wang and by Damsleth and Spjotvoll, which are stepwise procedures of spectrum estimation, have not been evaluated.     

Estimation of periodicities in hydrologic data

Periodicites in hydrologic data are frequently estimated and studied. In some cases the periodic components are subtracted from the data to obtain the stochastic components. In other cases the physical reasons for the occurrence of these periodicities are investigated. Apart from the annual cycle in the hydrologic data, periods corresponding to the 11 year sunspot cycle, the Hale cycle and others have been detected.The conclusions from most of these studies depend on the reliability and robustness of the methods used to detect these periodicities. Several spectral analysis methods have been proposed to investigate periodicities in time series data. Several of these have been compared to each other. The methods by Siddiqui and Wang and by Damsleth and Spjotvoll, which are stepwise procedures of spectrum estimation, have not been evaluated.Two of the methods of spectral analysis proposed by Siddiqui and Wang and by Damsleth and Spjotvoll are investigated in this study by using generated and observed data. Siddiqui and Wang's method is found to be superior to the Damsleth and Spjotvoll's method.     

A Dry Injection System for the Emplacement of Filter Packs and Annular Seals in Ground Water Monitoring Wells

The reliability of filter pack and annular seal emplacements, and the degree of integrity of installed seals, are two of the most important factors to be considered when both installing and later utilizing ground water monitoring wells.
Numerous, and often costly, problems of using existing methods of installing filter packs and annular seals during the construction of ground water monitoring wells have led to the development of a technique of installing these monitoring well components using a dry injection system.
The dry injection system has been used to construct monitoring wells in extremely complex overburden/bedrock environments with a variety of drilling techniques. The system has shown that a high degree of reliability in the, construction of monitoring wells and greater confidence in obtaining representative ground water samples can be achieved over existing methods of filter pack and annular seal emplacement. The system has also been more cost effective than existing methods, especially for deep boreholes and multilevel monitoring system installations.     

Development of a fuzzy-queue-based stochastic quadratic program for water resources planning

In this study, a fuzzy-queue (FQ)-based inexact stochastic quadratic programming (SQP) method is developed through coupling FQ technique with inexact SQP. FQ-SQP improves upon the existing stochastic programming methods by considering the effects of queuing phenomenon during the water resources allocation process. FQ-SQP cannot only handle uncertainties expressed as interval values, random variables, and fuzzy sets, but also tackle nonlinearity in the objective function; more importantly, it can reflect the effects of FQ on water resources allocation and system benefit. The FQ-SQP model is applied to a case study of planning water resources management, where FM/FM/1 (fuzzy exponential interarrival time, fuzzy exponential service time, and one server) queue is incorporated within the SQP modeling framework. Based on α-cut analysis technique, interval solutions with fuzzy arrival and service rates have been generated, which result in different water resources allocation patterns as well as changed waiting water amounts and system benefits. Results indicate that consideration of queuing problem impacts on water resources allocation can provide more useful information for decision makers and gain in-depth insights into the effects of queuing problems for water resources allocation.     

Response uncertainty and time-variant reliability analysis for hysteretic MDF structures

Response uncertainty evaluation and dynamic reliability analysis corresponding to classical stochastic dynamic analysis are usually restricted to the uncertainties of the excitation. The inclusion of the parameter uncertainties contained in structural properties and excitation characteristics has become an increasingly important problem in many areas of dynamics. In the present paper, a point estimate procedure is proposed for the evaluation of stochastic response uncertainty, and a response surface approach procedure in standard normal space is proposed for analysis of time-variant reliability analysis for hysteretic MDF structures having parameter uncertainties. Using the proposed procedures, the response uncertainties and time-variant reliability can be easily obtained by several repetitions of stochastic response analysis under given parameters without conducting sensitivity analysis, which is considered to be one of the primary difficulties associated with conventional methods. In the time-variant reliability analysis, the failure probability can be readily obtained by improving the accuracy of the first-order reliability method using the empirical second-order reliability index. The random variables are divided into two groups, those with CDF and those without CDF. The latter are included via the high-order moment standardization technique. A numerical example of a 15F hysteretic MDF structure that takes into account uncertainties of four structural parameters and three excitation characteristics is performed, based on which the proposed procedures are investigated and the effects of parameter uncertainties are discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

钢框架结构的非线性静力抗震可靠性分析:Ⅰ有限元反应及其灵敏度

作为一种随机有限元方法,有限元可靠度方法通过有限元反应灵敏度分析将结构可靠度分析的近似解析方法与结构确定性分析的有限元方法结合起来,可以有效地处理结构反应是基本随机变量的隐式函数这一难题,因此成为大型复杂结构可靠度分析的有效工具。采用基于位移的非线性纤维梁柱单元对钢框架结构进行有限元建模,推导了单元与截面的基本方程。针对基于位移的纤维梁柱单元,采用逐级递进方式,分别推导了整体级、单元级、截面级和材料级的有限元反应灵敏度直接微分表达式。研究结果可为采用FORM或SORM等近似解析法进行钢框架结构的非线性静力有限元可靠性分析提供算法支持和编程依据。     

Grain yield reliability analysis with crop water demand uncertainty

A new method of reliability analysis for crop water production function is presented considering crop water demand uncertainty. The procedure uses an advanced first-order second moment (AFOSM) method in evaluating the crop yield failure probability. To determine the variance and the mean of actual evapotranspiration as the component of interest for AFOSM analysis, an explicit stochastic optimization model for optimal irrigation scheduling is developed based on the first and second-order moment analysis of the soil moisture state variables. As a result of the study, the violation probabilities of crop yield at different levels were computed from AFOSM method. Also using the optimization results and the double bounded density function estimation methodology, the weekly soil moisture density function is derived which can be used as a short term reliability index. The proposed approach does not involve any discretization of system variables. The results of reliability analysis and optimization model compare favorably with those obtained from simulation.     

Reliability constrained capacity expansion planning of water resource systems

Two questionable features of many existing studies of capacity expansion planning problems in water resources are (1) the modelling of the expansion as a deterministic process, and (2) the lack of control over the incidence of system failure. System failure, in this presentation, is related to the occurrence of shortfalls in water supply. A sequential decision model is used as a general framework for the formulation of stochastic demand capacity expansion problems subject to reliability constraints designed to regulate the incidence of system failure. Various different types of constraint are investigated and each is incorporated into a dynamic programming solution procedure by means of Lagrangian theory. Computational examples illustrate the potential importance of using such reliability constraints in the analysis of capacity expansion problems.     

Development of stochastic partial differential equations for subsurface hydrology

The use of stochastic models in subsurface hydrology is growing at a logistic pace. To tie together a number of different stochastic methodologies for deriving subsurface transport equations, we have put together a brief review of some of the more common techniques. Our attention is confined to a few select methodologies so that we might delve in detail into assumptions required by the various approaches and their strengths and weaknesses. The methods reviewed include: Martingale, stochastic-convective, stochastic-relativist, spectral-integral, perturbative, statistical-mechanical, and generalized hydrodynamics. Within this list, we also have included a few stochastic methodologies which have been used solely to develop expressions for the dispersion tensor.     

Advance first order second moment (AFOSM) method for single reservoir operation reliability analysis: a case study

Reservoir system reliability is the ability of reservoir to perform its required functions under stated conditions for a specified period of time. In classical method of reservoir system reliability analysis, the operation policy is used in a simple simulation model, considering the historical/synthetic inflow series and a number of physical bounds on a reservoir system. This type of reliability analysis assumes a reservoir system as fully failed or functioning, called binary state assumption. A number of researchers from various research backgrounds have shown that the binary state assumption in the traditional reliability theory is not extensively acceptable. Our approach to tackle the present problem space is to implement the algorithm of advance first order second moment (AFOSM) method. In this new method, the inflow and reservoir storage are considered as uncertain variables. The mean, variance and covariance of uncertain variables are determined using moment values of reservoir state variables. For this purpose, a stochastic optimization model developed based on the constraint state formulation is applied. The proposed model of reliability analysis is used to a real case study in Iran. As a result, monthly probabilities of water allocation were computed from AFOSM method, and the outputs were compared with those from Monte Carlo method. The comparison shows that the outputs from AFOSM method are similar to those from the Monte Carlo method. In term of practical use of this study, the proposed method is appropriate to determine the monthly probability of failure in water allocation without the aid of simulation.     

Assessing the reliability of probabilistic flood inundation model predictions

An ability to quantify the reliability of probabilistic flood inundation predictions is a requirement not only for guiding model development but also for their successful application. Probabilistic flood inundation predictions are usually produced by choosing a method of weighting the model parameter space, but previous study suggests that this choice leads to clear differences in inundation probabilities. This study aims to address the evaluation of the reliability of these probabilistic predictions. However, a lack of an adequate number of observations of flood inundation for a catchment limits the application of conventional methods of evaluating predictive reliability. Consequently, attempts have been made to assess the reliability of probabilistic predictions using multiple observations from a single flood event. Here, a LISFLOOD‐FP hydraulic model of an extreme (>1 in 1000 years) flood event in Cockermouth, UK, is constructed and calibrated using multiple performance measures from both peak flood wrack mark data and aerial photography captured post‐peak. These measures are used in weighting the parameter space to produce multiple probabilistic predictions for the event. Two methods of assessing the reliability of these probabilistic predictions using limited observations are utilized; an existing method assessing the binary pattern of flooding, and a method developed in this paper to assess predictions of water surface elevation. This study finds that the water surface elevation method has both a better diagnostic and discriminatory ability, but this result is likely to be sensitive to the unknown uncertainties in the upstream boundary condition. Copyright © 2015 John Wiley & Sons, Ltd.     

Stage level,volume and time‐frequency information content of Lake Tana using stochastic and wavelet analysis methods

Lake Tana is the largest fresh water body situated in the north‐western highlands of Ethiopia. In addition to its ecological services, it serves for local transport, electric power generation, fishing, recreational purposes, and source of dry season irrigation water supply. Evidence shows that the lake has dried at least once at about 15,000–17,000 before present owing to a combination of high evaporation and low precipitation events. Past attempts to understand and simulate historical fluctuation of Lake Tana based on simplistic water balance approach of inflow, outflow, and storage have failed to capture well‐known events of drawdown and rise of the lake that have happened in the last 44 years. This study tested different stochastic methods of lake level and volume simulation for supporting Lake Tana operational planning decision support. Three stochastic methods (perturbations approach, Monte Carlo methods, and wavelet analysis) were employed for lake level and volume simulation, and the results were compared with the stage level measurements. Forty‐four years of daily, monthly, and mean annual lake level data have shown a Gaussian variation with goodness of fit at 0.01 significant levels of the Kolmogorov–Smirnov test. The stochastic simulations predicted the lake stage level of the 1972, 1984, and 2002/2003 historical droughts 99% of the time. The information content (frequency) of fluctuation of Lake Tana for various periods was resolved using Wigner's Time‐Frequency Decomposition method. The wavelet analysis agreed with the perturbations and Monte Carlo simulations resolving the time (1970s, 1980s, and 2000s) in which low frequency and high spectral power fluctuation has occurred. The Monte Carlo method has shown its superiority for risk analysis over perturbation and deterministic method whereas wavelet analysis reconstructed historical record of lake stage level at daily and monthly time scales. Copyright © 2012 John Wiley & Sons, Ltd.     

CATCHMENT-WIDE, SECTIONAL AND LOCAL ASPECTS IN SEDIMENT TRANSPORT MODELLING AND MONITORING

1.INTRODUCTIONOVerthelastdecadesmuchprogresshasbeenmadeconcerningsedimenttransPOrtmodellingandmonitoring.Thedifferelltiationincatchmeflt-tvide,sectionalandlocalaspectsreflectsthefactthatmanysedimenttransportandpredictionmodelsaredealingwithspecialpartsofriverSystems,mainlydifferinginscale.Overthepastyears,scaleissuesinhydrologyhaverapidlyincreasedinimportance(BLoSCHL,1996).Onalargescaletheapplicationoffractals,self-similarityanalysistolandscapeorganizationandoptimalchannelnetlvorks(O…     

Predicting river water temperatures using stochastic models: case study of the Moisie River (Québec,Canada)

Successful applications of stochastic models for simulating and predicting daily stream temperature have been reported in the literature. These stochastic models have been generally tested on small rivers and have used only air temperature as an exogenous variable. This study investigates the stochastic modelling of daily mean stream water temperatures on the Moisie River, a relatively large unregulated river located in Québec, Canada. The objective of the study is to compare different stochastic approaches previously used on small streams to relate mean daily water temperatures to air temperatures and streamflow indices. Various stochastic approaches are used to model the water temperature residuals, representing short‐term variations, which were obtained by subtracting the seasonal components from water temperature time‐series. The first three models, a multiple regression, a second‐order autoregressive model, and a Box and Jenkins model, used only lagged air temperature residuals as exogenous variables. The root‐mean‐square error (RMSE) for these models varied between 0·53 and 1·70 °C and the second‐order autoregressive model provided the best results. A statistical methodology using best subsets regression is proposed to model the combined effect of discharge and air temperature on stream temperatures. Various streamflow indices were considered as additional independent variables, and models with different number of variables were tested. The results indicated that the best model included relative change in flow as the most important streamflow index. The RMSE for this model was of the order of 0·51 °C, which shows a small improvement over the first three models that did not include streamflow indices. The ridge regression was applied to this model to alleviate the potential statistical inadequacies associated with multicollinearity. The amplitude and sign of the ridge regression coefficients seem to be more in agreement with prior expectations (e.g. positive correlation between water temperature residuals of different lags) and make more physical sense. Copyright © 2006 John Wiley & Sons, Ltd.     

Detection of water leaks in supply pipes using continuous wave sensor operating at 2.45 GHz

An innovative sensor technique has been developed to detect water leaks in supply pipes, especially in cases where the existing prevailing methods do not offer reliable solution, such as in PVC pipelines or for minor leaks. The presented system uses a Continuous Wave (CW) Doppler sensing unit operating at 2.45 GHz, consisting of a low power transmitter, a homodyne receiver and a digital signal processing unit. The operation principle is the detection of the Doppler frequency shift of the reflected electromagnetic wave by slightly moving water that leaks out of a pipe. A first prototype has already been developed and tested in test sites as well as in real water leaking conditions. The system has additionally been compared to the commercially available water leaking methods, verifying its reliability and accuracy in the detection of water leaks.     

Seasonal Forecasts of Extreme Groundwater Levels

The need for the assessment of quality, reliability, and methods used for forecasting subsurface water levels, in particular, in the context of climate changes, is demonstrated. The role of individual factors that control the reliability of forecasts of extreme levels of subsurface water is estimated.     

Factorial two-stage stochastic programming for water resources management

This study presents a factorial two-stage stochastic programming (FTSP) approach for supporting water resource management under uncertainty. FTSP is developed through the integration of factorial analysis and two-stage stochastic programming (TSP) methods into a general modeling framework. It can handle uncertainties expressed as probability distributions and interval numbers. This approach has two advantages in comparison to conventional inexact TSP methods. Firstly, FTSP inherits merits of conventional inexact two-stage optimization approaches. Secondly, it can provide detailed effects of uncertain parameters and their interactions on the system performance. The developed FTSP method is applied to a hypothetical case study of water resources systems analysis. The results indicate that significant factors and their interactions can be identified. They can be further analyzed for generating water allocation decision alternatives in municipal, industrial and agricultural sectors. Reasonable water allocation schemes can thus be formulated based on the resulting information of detailed effects from various impact factors and their interactions. Consequently, maximized net system benefit can be achieved.     

The impact of upstream water abstractions on reservoir yield: the case of the Orós Reservoir in Brazil

Abstract

Water abstraction for irrigation upstream of a reservoir and its impact on reservoir yield and reliability are studied. Water demand and availability are strongly related in semi-arid environments where the irrigation sector is responsible for a large part of consumptive water use. Variations in water abstractions for irrigation depend on irrigation requirements per hectare and the size of the irrigated area. The Orós Reservoir in semi-arid Northeast Brazil has been taken as a case study. The results show that water abstracttion for irrigation is of significant importance for reservoir yield and reliability. Yield—reliability simulations for the study area show that taking into account upstream water abstraction for a reservoir yield of 20.0 m³/s results in a water-scarcity probability of 10% on an annual basis (90% reliability). This is only 5% if up-stream abstraction for irrigation is ignored. This study shows that observed land-use changes in the study area do have a significant impact on reservoir yield reliability. The variability of upstream water abstraction was found to be of low importance for reservoir yield and reliability.     

Identification of petroleum pollution sources of water bodies and streams

A three-level scheme is proposed for the identification of sources of fresh and old petroleum pollution of water bodies and streams, including an optimal complex of simple, available, and highly effective physicochemical techniques, criteria, and sample processing methods ensuring the reliability of conclusions derived from them. The efficiency of application of the proposed methods is illustrated in several water bodies and streams (the Bol’shaya Krepkaya, Tuzlov, Chitinka, and other rivers), which have experienced oil pollution.