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 analysis of composite channels using first order approximation and Monte Carlo simulations

Artificial open channels being costlier infrastructure, their design should ensure reliability along with optimality in project cost. This paper presents reliability analysis of composite channels, considering uncertainty associated with various design parameters such as friction factors, longitudinal slope, channel width, side slope, and flow depth. This study also considers uncertainties of watershed characteristics, rainfall intensity and drainage area to quantify the uncertainty of runoff. For uncertainty modeling, the advanced first order second moment method and Monte Carlo simulation are used and it is found that the results by both approaches show good agreement. Then, a reliability index that can be used to design a composite channel to convey design discharge for a specified risk or probability of failure is presented, and its sensitivity with different channel design parameters are analyzed. To validate the effectiveness of the present approach, the reliability values and safety factors for variable system loading scenario are obtained under static and dynamic environment. The sensitivity analysis shows that flow depth and bed width are the most influencing parameters that affect the safety factor and reliability.     

Optimization and uncertainty analysis of operational policies for multipurpose reservoir system

This paper presents optimization and uncertainty analysis of operation policies for Hirakud reservoir system in Orissa state, India. The Hirakud reservoir project serves multiple purposes such as flood control, irrigation and power generation in that order of priority. A 10-daily reservoir operation model is formulated to maximize annual hydropower production subjected to satisfying flood control restrictions, irrigation requirements, and various other physical and technical constraints. The reservoir operational model is solved by using elitist-mutated particle swarm optimization (EMPSO) method, and the uncertainty in release decisions and end-storages are analyzed. On comparing the annual hydropower production obtained by EMPSO method with historical annual hydropower, it is found that there is a greater chance of improving the system performance by optimally operating the reservoir system. The analysis also reveals that the inflow into reservoir is highly uncertain variable, which significantly influences the operational decisions for reservoir system. Hence, in order to account uncertainty in inflow, the reservoir operation model is solved for different exceedance probabilities of inflows. The uncertainty in inflows is represented through probability distributions such as normal, lognormal, exponential and generalized extreme value distributions; and the best fit model is selected to obtain inflows for different exceedance probabilities. Then the reservoir operation model is solved using EMPSO method to arrive at suitable operational policies corresponding to various inflow scenarios. The results show that the amount of annual hydropower generated decreases as the value of inflow exceedance probability increases. The obtained operational polices provides confidence in release decisions, therefore these could be useful for reservoir operation.     

Two solution methods for dynamic game in reservoir operation

During the last decade, a number of models have been developed to consider the conflict in dynamic reservoir operation. Most of these models are discrete dynamic models which are developed based on game theory. In this study, a continuous model of dynamic game and its corresponding solutions are developed for reservoir operation. Two solution methods are used to solve the model of continuous dynamic game, namely the Ricatti equations and collocation methods. The Ricatti equations method is a closed form solution, requiring less computational efforts compared with discrete models. The collocation solution method applies Newton's method or a quasi-Newton method to find the problem solution. These approaches are able to generate operating policies for dynamic reservoir operation. The Zayandeh-Rud river basin in central Iran is used as a case study and the results are compared with alternative water allocation models. The results show that the proposed solution methods are quite capable of providing appropriate reservoir operating policies, while requiring rather short computational times due to continuous formulation of state and decision variables. Reliability indices are used to compare the overall performance of the proposed models. Based on the results from this study, the collocation method leads to improved values of the reliability indices for total reservoir system and utility satisfaction of water users, compared to the Ricatti equations method. This is attributed to the flexible structure of the collocation model. When compared to alternative water allocation models, lower values of reliability indices are achieved by the collocation method.     

城市供水管网在地震时的连通可靠性分析

考虑地震作用效应和管道抗力的随机特性,建立了埋地管道单元的概率预测模型,评估其在地震时的震害状态。把供水管网系统简化为边权有向网络图,通过Monte Carlo随机模拟过程,近似再现管网中各管段的破坏状态,进而分别结合图论理论方法和模糊关系矩阵法,对管网进行连通可靠性分析。由于Monte Carlo模拟算法是以管网各节点与水源点处于连通状态的近似频率计算来代替精确概率分析,为获得稳定的计算结果,对所用算例进行了5000次模拟。算例分析表明,基于图论方法和模糊关系矩阵法得到的管网连通可靠性结果基本相等。     

Reliability analysis of a rangeland system: the application of Profust theory

Reliability is the ability of a system to perform its required functions under stated conditions for a specified period of time. A number of researchers from various research backgrounds have shown that the binary state assumption in the traditional reliability theory (e.g., defining a natural system as fully failed or functioning) is not extensively acceptable, and thus the fuzzy state assumption should be used to replace the binary state assumption. In the present paper, the concept of profust reliability theory is introduced and a conceptual model of profust reliability for reliability analysis of a rangeland system, on the basis of the fuzzy state and the probability assumptions, is developed. This model is consisted of two parts, the fuzzy part which considers the vagueness in the system failure and the probabilistic part that incorporates the failure randomness in the reliability analysis. The ability of this model in reliability analysis of a natural system is illustrated for a real case study of rangeland system. For this purpose, the failure is defined as the rangeland system’s transition from its normal state. Generally, such transitions take place as a result of drought events. Furthermore, to determine the randomness in failure a conditional probability formulation is developed. This formulation determines the probability of the next drought duration, given the amount of severity in the present state. The result shows that the rangeland system reliability has been increased by 22% after constructing eight floodwater spreading systems.     

Building more realistic reservoir optimization models using data mining - A case study of Shelbyville Reservoir

In this paper, we promote a novel approach to develop reservoir operation routines by learning from historical hydrologic information and reservoir operations. The proposed framework involves a knowledge discovery step to learn the real drivers of reservoir decision making and to subsequently build a more realistic (enhanced) model formulation using stochastic dynamic programming (SDP). The enhanced SDP model is compared to two classic SDP formulations using Lake Shelbyville, a reservoir on the Kaskaskia River in Illinois, as a case study. From a data mining procedure with monthly data, the past month’s inflow (Q_t−1), current month’s inflow (Q_t), past month’s release (R_t−1), and past month’s Palmer drought severity index (PDSI_t−1) are identified as important state variables in the enhanced SDP model for Shelbyville Reservoir. When compared to a weekly enhanced SDP model of the same case study, a different set of state variables and constraints are extracted. Thus different time scales for the model require different information. We demonstrate that adding additional state variables improves the solution by shifting the Pareto front as expected while using new constraints and the correct objective function can significantly reduce the difference between derived policies and historical practices. The study indicates that the monthly enhanced SDP model resembles historical records more closely and yet provides lower expected average annual costs than either of the two classic formulations (25.4% and 4.5% reductions, respectively). The weekly enhanced SDP model is compared to the monthly enhanced SDP, and it shows that acquiring the correct temporal scale is crucial to model reservoir operation for particular objectives.     

A stochastic model for optimal operation of inter-basin water allocation systems: a case study

This paper presents a new methodology for optimal operation of inter-basin water transfer systems by conjunctive use of surface water resources in water donor basin and groundwater resources in water receiving basin. To incorporate the streamflow uncertainty, an integrated stochastic dynamic programming (ISDP) model is developed. In the ISDP, the monthly inflow to the reservoir in the water donor basin, the water storage of the reservoir, and the water storage of the aquifer in the water receiving basin are considered as state variables. A water allocation optimization model is embedded in the main structure of ISDP and a new ensemble streamflow prediction model based on K-nearest-neighbourhood algorithm is also developed and linked to the ISDP. By using a new reoptimization process, the ISDP model provides monthly policies for water allocation to users in water donor and receiving basins. As water users can form a coalition to increase their benefits, several solution concepts in cooperative game theory, namely Nash–Harsanyi, Shapley, Nucleolus, Weak Nucleolus, Proportional Nucleolus, Separable Costs Remaining Benefits (SCRBs) and Minimum Costs Remaining Savings are utilized to determine the profit of each water user. In the last step, stakeholders make negotiation over these solution concepts using the Fallback bargaining theory to reach a unanimous agreement on the final distribution of the total benefit. The methodology is applied to an inter-basin water transfer project and the results show that the Shapley and SCRB solutions concepts can provide better distributions for the total benefit and the total benefit of water users is increased by a factor of 1.6 when they participate in a grand coalition.     

Effects of uncertainty in rock-physics models on reservoir parameter estimation using seismic amplitude variation with angle and controlled-source electromagnetics data

This paper investigates the effects of uncertainty in rock-physics models on reservoir parameter estimation using seismic amplitude variation with angle and controlled-source electromagnetics data. The reservoir parameters are related to electrical resistivity by the Poupon model and to elastic moduli and density by the Xu-White model. To handle uncertainty in the rock-physics models, we consider their outputs to be random functions with modes or means given by the predictions of those rock-physics models and we consider the parameters of the rock-physics models to be random variables defined by specified probability distributions. Using a Bayesian framework and Markov Chain Monte Carlo sampling methods, we are able to obtain estimates of reservoir parameters and information on the uncertainty in the estimation. The developed method is applied to a synthetic case study based on a layered reservoir model and the results show that uncertainty in both rock-physics models and in their parameters may have significant effects on reservoir parameter estimation. When the biases in rock-physics models and in their associated parameters are unknown, conventional joint inversion approaches, which consider rock-physics models as deterministic functions and the model parameters as fixed values, may produce misleading results. The developed stochastic method in this study provides an integrated approach for quantifying how uncertainty and biases in rock-physics models and in their associated parameters affect the estimates of reservoir parameters and therefore is a more robust method for reservoir parameter estimation.     

Modeling river/reservoir system management, water allocation, and supply reliability

The state of Texas has implemented a modeling system for assessing the availability and reliability of water resources that consists of a generalized simulation model called the Water Rights Analysis Package (WRAP) and input datasets for the state's 23 river basins. Reservoir/river system management and water allocation practices are simulated using historical naturalized monthly streamflow sequences to represent basin hydrology. Institutional systems for allocating streamflow and reservoir storage resources among numerous water users are considered in detail in evaluating basinwide impacts of water management decisions. The generalized WRAP model is a flexible tool that may be applied to river basins anywhere. The Texas experience in implementing a statewide modeling system illustrates issues that are relevant to water management in many other regions of the world.     

Performance evaluation of implicit stochastic reservoir operation optimization supported by long-term mean inflow forecast

This study applies implicit stochastic optimization (ISO) to develop monthly operating rules for a reservoir located in Northeast Brazil. The proposed model differs from typical ISO applications as it uses the forecast of the mean inflow for a future horizon instead of the current-month inflow. Initially, a hundred different 100-year monthly inflow scenarios are synthetically generated and employed as input to a deterministic operation optimization model in order to build a database of optimal operating data. Later, such database is used to fit monthly reservoir rule curves by means of nonlinear regression analysis. Finally, the established rule curves are validated by operating the system under 100 new inflow ensembles. The performance of the proposed technique is compared with those provided by the standard reservoir operating policy (SOP), stochastic dynamic programming (SDP) and perfect-forecast deterministic optimization (PFDO). Different forecasting horizons are tested. For all of them, the results indicate the feasibility of using ISO in view of its lower vulnerability in contrast to the SOP as well as the proximity of its operations with those by PFDO. The results also reveal that there is an optimal choice for the forecasting horizon. The comparison between ISO and SDP shows small differences between both, justifying the adoption of ISO for its simplified mathematics as opposed to SDP.     

Assessing traffic noise impact based on probabilistic and fuzzy approaches under uncertainty

Traffic noise can cause severe sound pollution for human communities. This paper proposes a hybrid approach to assess traffic noise impact under uncertainty. There are many factors influencing traffic noise level, but only three traffic parameters, namely, traffic flow, traffic speed and traffic component, are highly uncertain. These uncertain parameters are represented by probability distributions, and Monte Carlo simulations are performed to generate a noise distribution after considering about other certain influencing factors. Fuzzy set and binary fuzzy relations as well as probability analysis method are applied to identify the predicted traffic noise impacts in qualitatively and quantitatively. The applicability of this proposed technique is demonstrated using a case study.     

Seismic fragility assessment of highway bridges using support vector machines

Seismic fragility curves provide a powerful tool to assess the reliability of structures. However, conventional fragility analysis of structures comprising a large number of components requires enormous computational efforts. In this paper, the application of probabilistic support vector machines (PSVM) for the system fragility analysis of existing structures is proposed. It is demonstrated that support vector machine based fragility curves provide accurate predictions compared to rigorous methodologies such as component based fragilities developed by Monte Carlo simulations. The proposed method is applied to an existing bridge structure in order to develop fragility curves for serviceability and collapse limit states. In addition, the efficiency of using the PSVM method in the application of vector-valued ground motion intensity measures (IM) as well as traditional single-valued IM are investigated. The results obtained from an incremental dynamic analysis of the structure are used to train PSVMs. The application of PSVM in binary and multi-class classifications is used for the fragility analysis and reliability assessment of the bridge structure.     

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.     

Risk analysis for flood control operation of seasonal flood-limited water level incorporating inflow forecasting error

Abstract

The seasonal flood-limited water level (FLWL), which reflects the seasonal flood information, plays an important role in governing the trade-off between reservoir flood control and conservation. A risk analysis model for flood control operation of seasonal FLWL incorporating the inflow forecasting error was proposed and developed. The variable kernel estimation is implemented for deriving the inflow forecasting error density. The synthetic inflow incorporating forecasting error is simulated by Monte Carlo simulation (MCS) according to the inflow forecasting error density. The risk analysis for seasonal FLWL control was estimated by MCS based on a combination of the forecasting inflow lead-time, seasonal design flood hydrographs and seasonal operation rules. The Three Gorges reservoir is selected as a case study. The application results indicate that the seasonal FLWL control can effectively enhance flood water utilization rate without lowering the annual flood control standard.

Editor D. Koutsoyiannis; Associate editor A. Viglione

Citation Zhou, Y.-L. and Guo, S.-L., 2014. Risk analysis for flood control operation of seasonal flood-limited water level incorporating inflow forecasting error. Hydrological Sciences Journal, 59 (5), 1006–1019.     

Time-dependent reliability analysis using Bayesian MCMC on the reduction of reservoir storage by sedimentation

Currently, an operational strategy for the maintenance of reservoirs is an important issue because of the reduction of reservoir storage from sedimentation. However, relatively few studies have addressed the reliability analysis including uncertainty on the decrease of the reservoir storage by the sedimentation. Therefore, it is necessary that the reduction of the reservoir storage by the sedimentation should be assessed by a probabilistic viewpoint because the natural uncertainty is embedded in the process of the sedimentation. The objective of this study is to advance the maintenance procedures, especially the assessment of future reservoir storage, using the time-dependent reliability analysis with the Bayesian approach. The stochastic gamma process is applied to estimate the reduction of the Soyang dam reservoir storage in South Korea. In estimating the parameters of the stochastic gamma process, the Bayesian Markov chain Monte Carlo (MCMC) scheme using the informative prior distribution through the empirical Bayes method is applied. The Metropolis–Hastings algorithm is constructed and its convergence is checked by the various diagnostics. The range of the expected life time of the Soyang dam reservoir by the Bayesian MCMC is estimated from 111 to 172 years at a 5 % significance level. Finally, it is suggested that improving the assessment strategy in this study can provide valuable information to the decision makers who are in charge of the maintenance of a reservoir or a dam.     

Tracer relations in mixed lakes in non-steady state

Tracer concentration in mixed lakes was usually calculated under assumption of steady hydrologic state, i.e., constant input, output, and volume. Departures from steady state were treated by the use of average flow or weighting the concentration by inflow values. An exact analytical solution indicates the limits of validity of the above approximations. The exact solution can be adapted for multiple inputs and outputs, exchange with atmospheric moisture, evaporation with isotope fractionation and formation of epilimnion. The solution is simplified for certain types of connection between outflow and volume.     

Decomposition algorithms for system reliability estimation with applications to interdependent lifeline networks

Reliability and risk assessment of lifeline systems call for efficient methods that integrate hazard and interdependencies. Such methods are computationally challenged when the probabilistic response of systems is tied to multiple events, as performance quantification requires a large catalog of ground motions. Available methods to address this issue use catalog reductions and importance sampling. However, besides comparisons against baseline Monte Carlo trials in select cases, there is no guarantee that such methods will perform or scale well in practice. This paper proposes a new efficient method for reliability assessment of interdependent lifeline systems, termed RAILS, that considers systemic performance and is particularly effective when dealing with large catalogs of events. RAILS uses the state‐space partition method to estimate systemic reliability with theoretical bounds and, for the first time, supports cyclic interdependencies among lifeline systems. Recycling computations across an entire seismic catalog with RAILS considerably reduces the number of system performance evaluations in seismic performance studies. Also, when performance estimate bounds are not tight, we adopt an importance and stratified sampling method that in our computational experiments is various orders of magnitude more efficient than crude Monte Carlo. We assess the efficiency of RAILS using synthetic networks and illustrate its application to quantify the seismic risk of realistic yet streamlined systems hypothetically located in the San Francisco Bay Region.     

Incremental dynamic analysis for estimating seismic performance sensitivity and uncertainty

Incremental dynamic analysis (IDA) is presented as a powerful tool to evaluate the variability in the seismic demand and capacity of non‐deterministic structural models, building upon existing methodologies of Monte Carlo simulation and approximate moment‐estimation. A nine‐story steel moment‐resisting frame is used as a testbed, employing parameterized moment‐rotation relationships with non‐deterministic quadrilinear backbones for the beam plastic‐hinges. The uncertain properties of the backbones include the yield moment, the post‐yield hardening ratio, the end‐of‐hardening rotation, the slope of the descending branch, the residual moment capacity and the ultimate rotation reached. IDA is employed to accurately assess the seismic performance of the model for any combination of the parameters by performing multiple nonlinear timehistory analyses for a suite of ground motion records. Sensitivity analyses on both the IDA and the static pushover level reveal the yield moment and the two rotational‐ductility parameters to be the most influential for the frame behavior. To propagate the parametric uncertainty to the actual seismic performance we employ (a) Monte Carlo simulation with latin hypercube sampling, (b) point‐estimate and (c) first‐order second‐moment techniques, thus offering competing methods that represent different compromises between speed and accuracy. The final results provide firm ground for challenging current assumptions in seismic guidelines on using a median‐parameter model to estimate the median seismic performance and employing the well‐known square‐root‐sum‐of‐squares rule to combine aleatory randomness and epistemic uncertainty. Copyright © 2009 John Wiley & Sons, Ltd.     

Surrogate accelerated sampling of reservoir models with complex structures using sparse polynomial chaos expansion

Markov Chain Monte Carlo (MCMC) methods are often used to probe the posterior probability distribution in inverse problems. This allows for computation of estimates of uncertain system responses conditioned on given observational data by means of approximate integration. However, MCMC methods suffer from the computational complexities in the case of expensive models as in the case of subsurface flow models. Hence, it is of great interest to develop alterative efficient methods utilizing emulators, that are cheap to evaluate, in order to replace the full physics simulator. In the current work, we develop a technique based on sparse response surfaces to represent the flow response within a subsurface reservoir and thus enable efficient exploration of the posterior probability density function and the conditional expectations given the data.Polynomial Chaos Expansion (PCE) is a powerful tool to quantify uncertainty in dynamical systems when there is probabilistic uncertainty in the system parameters. In the context of subsurface flow model, it has been shown to be more accurate and efficient compared with traditional experimental design (ED). PCEs have a significant advantage over other response surfaces as the convergence to the true probability distribution when the order of the PCE is increased can be proved for the random variables with finite variances. However, the major drawback of PCE is related to the curse of dimensionality as the number of terms to be estimated grows drastically with the number of the input random variables. This renders the computational cost of classical PCE schemes unaffordable for reservoir simulation purposes when the deterministic finite element model is expensive to evaluate. To address this issue, we propose the reduced-terms polynomial chaos representation which uses an impact factor to only retain the most relevant terms of the PCE decomposition. Accordingly, the reduced-terms polynomial chaos proxy can be used as the pseudo-simulator for efficient sampling of the probability density function of the uncertain variables.The reduced-terms PCE is evaluated on a two dimensional subsurface flow model with fluvial channels to demonstrate that with a few hundred trial runs of the actual reservoir simulator, it is feasible to construct a polynomial chaos proxy which accurately approximates the posterior distribution of the high permeability zones, in an analytical form. We show that the proxy precision improves with increasing the order of PCE and corresponding increase of the number of initial runs used to estimate the PCE coefficient.