Development of stochastic dynamic Nash game model for reservoir operation. I. The symmetric stochastic model with perfect information

Increasing water demands, higher standards of living, depletion of resources of acceptable quality and excessive water pollution due to agricultural and industrial expansions have caused intense social and political predicaments, and conflicting issues among water consumers. The available techniques commonly used in reservoir optimization/operation do not consider interaction, behavior and preferences of water users, reservoir operator and their associated modeling procedures, within the stochastic modeling framework. In this paper, game theory is used to present the associated conflicts among different consumers due to limited water. Considering the game theory fundamentals, the Stochastic Dynamic Nash Game with perfect information (PSDNG) model is developed, which assumes that the decision maker has sufficient (perfect) information regarding the associated randomness of reservoir operation parameters. The simulated annealing approach (SA) is applied as a part of the proposed stochastic framework, which makes the PSDNG solution conceivable. As a case study, the proposed model is applied to the Zayandeh-Rud river basin in Iran with conflicting demands. The results are compared with alternative reservoir operation models, i.e., Bayesian stochastic dynamic programming (BSDP), sequential genetic algorithm (SGA) and classical dynamic programming regression (DPR). Results show that the proposed model has the ability to generate reservoir operating policies, considering interactions of water users, reservoir operator and their preferences.     

Development of stochastic dynamic Nash game model for reservoir operation II. The value of players’ information availability and cooperative behaviors

Stochastic dynamic game models can be applied to derive optimal reservoir operation policies by considering interactions among water users and reservoir operator, their preferences, their levels of information availability and cooperative behaviors. The stochastic dynamic game model with perfect information (PSDNG) has been developed by [Ganji A, Khalili D, Karamouz M. Development of stochastic dynamic Nash game model for reservoir operation. I. The symmetric stochastic model with perfect information. Adv Water Resour, this issue]. This paper develops four additional versions of stochastic dynamic game model of water users interactions based on the cooperative behavior and hydrologic information availability of beneficiary sectors of reservoir systems. It is shown that the proposed models are quite capable of providing appropriate reservoir operating policies when compared with alternative operating models, as indicated by several reservoir performance characteristics. Among the proposed models, the selected model by considering cooperative behavior and additional hydrologic information (about the randomness nature of reservoir operation parameters), as exercised by reservoir operator, provides the highest attained level of performance and efficiency. Furthermore, the selected model is more realistic since it also considers actual behavior of water users and reservoir operator in the analysis.     

A Monte-Carlo game theoretic approach for Multi-Criteria Decision Making under uncertainty

Game theory provides a useful framework for studying Multi-Criteria Decision Making problems. This paper suggests modeling Multi-Criteria Decision Making problems as strategic games and solving them using non-cooperative game theory concepts. The suggested method can be used to prescribe non-dominated solutions and also can be used as a method to predict the outcome of a decision making problem. Non-cooperative stability definitions for solving the games allow consideration of non-cooperative behaviors, often neglected by other methods which assume perfect cooperation among decision makers. To deal with the uncertainty in input variables a Monte-Carlo Game Theory (MCGT) approach is suggested which maps the stochastic problem into many deterministic strategic games. The games are solved using non-cooperative stability definitions and the results include possible effects of uncertainty in input variables on outcomes. The method can handle multi-criteria multi-decision-maker problems with uncertainty. The suggested method does not require criteria weighting, developing a compound decision objective, and accurate quantitative (cardinal) information as it simplifies the decision analysis by solving problems based on qualitative (ordinal) information, reducing the computational burden substantially. The MCGT method is applied to analyze California’s Sacramento-San Joaquin Delta problem. The suggested method provides insights, identifies non-dominated alternatives, and predicts likely decision outcomes.     

Probabilistic reservoir operation using Bayesian stochastic model and support vector machine

Available water resources are often not sufficient or too polluted to satisfy the needs of all water users. Therefore, allocating water to meet water demands with better quality is a major challenge in reservoir operation. In this paper, a methodology to develop operating strategies for water release from a reservoir with acceptable quality and quantity is presented. The proposed model includes a genetic algorithm (GA)-based optimization model linked with a reservoir water quality simulation model. The objective function of the optimization model is based on the Nash bargaining theory to maximize the reliability of supplying the downstream demands with acceptable quality, maintaining a high reservoir storage level, and preventing quality degradation of the reservoir. In order to reduce the run time of the GA-based optimization model, the main optimization model is divided into a stochastic and a deterministic optimization model for reservoir operation considering water quality issues.The operating policies resulted from the reservoir operation model with the water quantity objective are used to determine the released water ranges (permissible lower and upper bounds of release policies) during the planning horizon. Then, certain values of release and the optimal releases from each reservoir outlet are determined utilizing the optimization model with water quality objectives. The support vector machine (SVM) model is used to generate the operating rules for the selective withdrawal from the reservoir for real-time operation. The results show that the SVM model can be effectively used in determining water release from the reservoir. Finally, the copula function was used to estimate the joint probability of supplying the water demand with desirable quality as an evaluation index of the system reliability. The proposed method was applied to the Satarkhan reservoir in the north-western part of Iran. The results of the proposed models are compared with the alternative models. The results show that the proposed models could be used as effective tools in reservoir operation.     

结构-地基动力相互作用时域数值计算模型研究

完全在时域数值分析范畴内，本文对结构一地基动力相互作用系统运动方程进行了深入推导，给出了统一的基本表达形式，简化可获得目前应用的各类主要时域模型。其中，基于结构一地基交界面的位移协调条件及作用力与反作用力平衡方程，推导了动力相互作用分析子结构法模式的时域基本方程。从结构的一般动力平衡方程出发，推导了相互作用直接法模式的基本平衡方程，并基于有限元模型对两类模式间的等价性条件进行了理论验证。     

Comparison of capability of time integration methods in capturing dynamic loading

Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method (AAM) for linear elastic systems, except that the capability to capture dynamic loading was not explored. It was found that there were different quadrature equations to predict the next step displacement increment. A modified quadrature equation of this method was derived so that the equation to determine the next step displacement was numerically equivalent to the equation used in the constant AAM. It was verified that the original form of this method, in general, had a better capability to capture dynamic loadings than the constant AAM. This excellent property, in addition to computational efficiency, will help to make this method competitive with general secondorder accurate integration methods.     

复阻尼多自由度系统动力分析的模态叠加法

工程实际中,复阻尼多自由度系统的瞬态响应过去一直是通过频域方法求解的。频域方法的一个突出问题是求传递函数矩阵的计算工作量过大。本文给出一种有效而实用的时域解法———实模态叠加法,此外还介绍了复模态叠加法。实模态叠加法是基于一个事实,即n维复向量空间中的复向量可以在n维实向量空间中的一组线性无关的实向量构成的基下表出;另外,就此方法还讨论了复阻尼多自由度系统初始运动条件的给出和转换问题。复模态叠加法则是通过变量替换的方法,变其中的复特征值问题为形式上的一个实特征值问题来解决的。     

Adaptive neuro-fuzzy inference system for prediction of water level in reservoir

Accurate prediction of the water level in a reservoir is crucial to optimizing the management of water resources. A neuro-fuzzy hybrid approach was used to construct a water level forecasting system during flood periods. In particular, we used the adaptive network-based fuzzy inference system (ANFIS) to build a prediction model for reservoir management. To illustrate the applicability and capability of the ANFIS, the Shihmen reservoir, Taiwan, was used as a case study. A large number (132) of typhoon and heavy rainfall events with 8640 hourly data sets collected in past 31 years were used. To investigate whether this neuro-fuzzy model can be cleverer (accurate) if human knowledge, i.e. current reservoir operation outflow, is provided, we developed two ANFIS models: one with human decision as input, another without. The results demonstrate that the ANFIS can be applied successfully and provide high accuracy and reliability for reservoir water level forecasting in the next three hours. Furthermore, the model with human decision as input variable has consistently superior performance with regard to all used indexes than the model without this input.     

Rule reduction in fuzzy logic for better interpretability in reservoir operation

Decision‐making in reservoir operation has become easy and understandable with the use of fuzzy logic models, which represent the knowledge in terms of interpretable linguistic rules. However, the improvement in interpretability with increase in number of fuzzy sets (‘low’, ‘high’, etc) comes with the disadvantage of increase in number of rules that are difficult to comprehend by decision makers. In this study, a clustering‐based novel approach is suggested to provide the operators with a limited number of most meaningful operating rules. A single triangular fuzzy set is adopted for different variables in each cluster, which are fine‐tuned with genetic algorithm (GA) to meet the desired objective. The results are compared with the multi fuzzy set fuzzy logic model through a case study in the Pilavakkal reservoir system in Tamilnadu State, India. The results obtained are highly encouraging with a smaller set of rules representing the actual fuzzy logic system. Copyright © 2007 John Wiley & Sons, Ltd.     

A new methodology for water resources multicriteria decision making under uncertainty

A multiciteria decision making problem in water resource is addressed through the generation of fuzzy Pareto optimal set. Methodology is using positive and negative ideal solutions (Lai, Y.-J., Liu, T.-Y., Hwang, C.L. (1994). TOPSIS for MODM. European Journal of Operational Research 76, 486-500) and a set of weights assigned to the objective functions in fuzzy triangular form. Solution of the problem is obtained by transforming each objective function into a set of three objective functions. A planning problem of multicriteria waste water treatment from the literature is used as an illustrative example to demonstrate the utility of the proposed methodology. The obtained fuzzy Pareto solution set has been compared with the deterministic solution set. It is shown that the proposed approach can: (a) capture the uncertainty associated with the assignment of weights; and (b) provide the decision makers with a wider range of solutions to select from.     

Risk assessment for optimal freshwater inflow in response to sustainability indicators in semi-arid coastal bay

Coastal zones are the primary interface for the exchange of natural and man-made materials between terrestrial and coastal ecosystems. While continuous industrial development and population growth in the coastal region promote unprecedented economic prosperity, water resource management in bay and estuary areas turns out to be a crucial challenge. Therefore, local, state, and federal water planning groups are attempting to manage the supply of freshwater inflow based on sustainability goals, especially for semi-arid coastal regions like South Texas. Surface and ground water management practices in this semi-arid coastal region are implemented to ensure an ever-lasting water supply on one hand and to maintain ecosystem integrity in the bay and estuary system on the other hand. The aim of this study is to apply a stochastic compromise programming model to identify a compromise solution under uncertainty in terms of two competing objectives: minimizing freshwater release from a coastal reservoir and maximizing fishery harvest in its associated bay—Corpus Christi Bay, South Texas. The global criterion method used in the solution procedure seeks to select a compromise solution that possesses the shortest distance from a positive ideal solution (PIS) and the farthest distance from a negative ideal solution (NIS). Solutions were found using three distance-based functions in conjunction with stochastic constraints reflecting the risk levels involved in decision-making. Results indicate that current flows in the mouth of the Nueces River are not sufficient to maintain the salinity level and to satisfy harvest requirements in the Corpus Christi Bay if water supply goal in the city has higher priority. Therefore, a sustainable management plan of exploring the structure of demand and supply is highly desirable in this fast growing urban region.     

Evaluation of the Ross fast solution of Richards’ equation in unfavourable conditions for standard finite element methods

Ross [Ross PJ. Modeling soil water and solute transport – fast, simplified numerical solutions. Agron J 2003;95:1352–61] developed a fast, simplified method for solving Richards’ equation. This non-iterative 1D approach, using Brooks and Corey [Brooks RH, Corey AT. Hydraulic properties of porous media. Hydrol. papers, Colorado St. Univ., Fort Collins; 1964] hydraulic functions, allows a significant reduction in computing time while maintaining the accuracy of the results. The first aim of this work is to confirm these results in a more extensive set of problems, including those that would lead to serious numerical difficulties for the standard numerical method. The second aim is to validate a generalisation of the Ross method to other mathematical representations of hydraulic functions.     

An inexact programming method for agricultural irrigation systems under parameter uncertainty

Rapid population growth and economy development have led to increasing reliance on water resources. It is even aggravated for agricultural irrigation systems where more water is necessary to support the increasing population. In this study, an inexact programming method based on two-stage stochastic programming and interval-parameter programming is developed to obtain optimal water-allocation strategies for agricultural irrigation systems. It is capable of handling such problems where two-stage decisions need to be suggested under random- and interval-parameter inputs. An interactive solving procedure derived from conventional interval-parameter programming makes it possible for the impact of lower and upper bounds of interval inputs to be well reflected in the resulting solutions. An agricultural irrigation management problem is then provided to demonstrate the applicability, and reasonable solutions are obtained. Compared to the solutions from a representative interval-parameter programming model where only one decision-stage exists, the interval of optimized objective-function value is narrow, indicating more alternatives could be provided when water-allocation targets are rather high. However, chances of obtaining more benefits exist in association with a risk of paying more penalties; such a relationship becomes apparent when the variation of water availability is much intensive.     

Stochastic and statistical methods in hydrology and environmental engineering

Recent developments in stochastic and statistical methods in hydrology and environmental engineering presented in the upcoming sequence of research papers are evaluated, compared and put into proper perspective. These papers are being published as a memorial to Professor T. E. Unny who was a founding Editor of the journalStochastic Hydrology and Hydraulics. As explained in this introductory paper, other activities that took place to celebrate Professor Unny's lifetime academic accomplishments include an international conference held in his honor at the University of Waterloo in June, 1993 and the publication of a four-volume conference proceedings in 1994.     

辽河坳陷大民屯凹陷三台子地区下第三系碎屑岩储层预测研究

针对目标区下第三系储层横向变化快,沉积特征不明显等特点,为提高滚动探井、开发井的钻探成功率,本文研制形成一套具有针对性的油气藏勘探预测研究方法.即运用多井约束波阻抗地震反演方法来预测砂体展布,同时对生成的地震波阻抗反演数据体中的振幅、厚度等暗含的有效信息进行提取,对砂体的分布范围及厚度变化进行准确而精细的描述和预测,最终依据此法优选有利相带,部署井位,取得了很好的勘探开发效果.     

物探方法在水库坝基渗漏勘探中的应用

近年来物探方法在坝基勘探、活断层探测、溶洞探测和基础检测等工程中得到广泛应用,并取得了令人瞩目的成绩。本文介绍了在某水库坝基渗漏勘探开展物探工作的情况,取得了满意的结果,表明应用多种物探方法对解决工程问题具有较好的效果。     

Evaluating suspended sediment and turbidity reduction projects in a glacially conditioned catchment through dynamic regression and fluvial process-based modelling

Elevated turbidity (T_n) and suspended sediment concentrations (SSC) during and following flood events can degrade water supply quality and aquatic ecosystem integrity. Streams draining glacially conditioned mountainous terrain, such as those in the Catskill Mountains of New York State, are particularly susceptible to high levels of T_n and SSC sourced from erosional contact with glacial-related sediment. This study forwards a novel approach to evaluate the effectiveness of stream restoration best management practices (BMPs) meant to reduce stream T_n and SSC, and demonstrates the approach within the Stony Clove sub-basin of the Catskills, a water supply source for New York City. The proposed approach is designed to isolate BMP effects from natural trends in T_n and SSC caused by trends in discharge and shifts in average T_n or SSC per unit discharge (Q) following large flood events. We develop Dynamic Linear Models (DLMs) to quantify how T_n-Q and SSC-Q relationships change over time at monitoring stations upstream and downstream of BMPs within the Stony Clove and in three other sub-basins without BMPs, providing observational evidence of BMP effectiveness. A process-based model, the River Erosion Model, is then developed to simulate natural, hydrology-driven SSC-Q dynamics in the Stony Clove sub-basin (absent of BMP effects). We use DLMs to compare the modelled and observed SSC-Q dynamics and isolate the influence of the BMPs. Results suggest that observed reductions in SSC and T_n in the Stony Clove sub-basin have been driven by a combination of declining streamflow and the installed BMPs, confirming the utility of the BMPs for the monitored hydrologic conditions.     

Multi‐objective particle swarm optimization for generating optimal trade‐offs in reservoir operation

A multi‐objective particle swarm optimization (MOPSO) approach is presented for generating Pareto‐optimal solutions for reservoir operation problems. This method is developed by integrating Pareto dominance principles into particle swarm optimization (PSO) algorithm. In addition, a variable size external repository and an efficient elitist‐mutation (EM) operator are introduced. The proposed EM‐MOPSO approach is first tested for few test problems taken from the literature and evaluated with standard performance measures. It is found that the EM‐MOPSO yields efficient solutions in terms of giving a wide spread of solutions with good convergence to true Pareto optimal solutions. On achieving good results for test cases, the approach was applied to a case study of multi‐objective reservoir operation problem, namely the Bhadra reservoir system in India. The solutions of EM‐MOPSOs yield a trade‐off curve/surface, identifying a set of alternatives that define optimal solutions to the problem. Finally, to facilitate easy implementation for the reservoir operator, a simple but effective decision‐making approach was presented. The results obtained show that the proposed approach is a viable alternative to solve multi‐objective water resources and hydrology problems. Copyright © 2007 John Wiley & Sons, Ltd.     

Stochastic-fuzzy multi criteria decision making for robust water resources management

All realistic Multi Criteria Decision Making (MCDM) problems in water resources management face various kinds of uncertainty. In this study the evaluations of the alternatives with respect to the criteria will be assumed to be stochastic. Fuzzy linguistic quantifiers will be used to obtain the uncertain optimism degree of the Decision Maker (DM). A new approach for stochastic-fuzzy modeling of MCDM problems will be then introduced by merging the stochastic and fuzzy approaches into the Ordered Weighted Averaging (OWA) operator. The results of the new approach, entitled SFOWA, give the expected value and the variance of the combined goodness measure for each alternative, which are essential for robust decision making. In order to combine these two characteristics, a composite goodness measure will be defined. By using this measure the model will give more sensitive decisions to the stakeholders whose optimism degrees are different than that of the decision maker. The methodology will be illustrated by using a water resources management problem in the Central Tisza River in Hungary. Finally, SFOWA will be compared to other methods known from the literature to show its suitability for MCDM problems under uncertainty.