A fuzzy-Markov-chain-based analysis method for reservoir operation

Abstract

In this study, a fuzzy-Markov-chain-based stochastic dynamic programming (FM-SDP) method is developed for tackling uncertainties expressed as fuzzy sets and distributions with fuzzy probability (DFPs) in reservoir operation. The concept of DFPs used in Markov chain is presented as an extended form for expressing uncertainties including both stochastic and fuzzy characteristics. A fuzzy dominance index analysis approach is proposed for solving multiple fuzzy sets and DPFs in the proposed FM-SDP model. Solutions under a set of a-cut levels and fuzzy dominance indices can be generated by solving a series of deterministic submodels. The developed method is applied to a case study of a reservoir operation system. Solutions from FM-SDP provide a range of desired water-release policies under various system conditions for reservoir operation decision makers, reflecting dynamic and dual uncertain features of water availability simultaneously. The results indicate that the FM-SDP method could be applicable to practical problems for decision makers to obtain insight regarding the tradeoffs between economic and system reliability criteria. Willingness to obtain a lower benefit may guarantee meeting system-constraint demands; conversely, a desire to acquire a higher benefit could run into a higher risk of violating system constraints.

Risk analysis methods of water supply systems: comprehensive review from source to tap

“…Data like types of component malfunctions, failure sequence and availability of replacement parts can also be included in the Markov analysis to determine how safe and reliable a component is which can indicate the rates of transition. This method was developed at the beginning of the twentieth century (Fu, Li, and Huang 2012). The Markov technique is named after the Russian mathematician Andrei Andreyevich Markov who undertook the study of stochastic processes, i.e.…”

“…This analysis has made it possible to define a new sequence of random but related facts that will resemble the original sequence. Markov analysis is a probabilistic technique that facilitates the decision-making process by providing a probabilistic description of various outcomes (Fu, Li, and Huang 2012). As a management tool, Markov analysis has been satisfactorily applied to a number of different industrial processes with great results, thanks to its versatility and accuracy.…”

“…As in any of the models we presented before there is a need to collect as much appropriate data as possible. Note that if we are considering to analysing several changes of state, say 3 or 4, a data management tool would be advisable in such cases as the collection and arrangement process can, at times, be time-consuming and a tad tedious (Fu, Li, and Huang 2012). Sempewo and Kyokaali (2016) applied a Markov analysis a tool to the decision-making process and to foresee the actual and probable state of a distribution water supply.…”

Application of risk analysis in the liquefied natural gas (LNG) sector: An overview

“…Over the years, fuzzy set theory has been combined with classical risk assessment tools to produce fuzzy based risk assessment methodologies for assessing the risk and reliability of complex systems in safety critical industries. Fuzzy ETA (Kenarangui, 1991;Fu et al, 2018), fuzzy FTA (Yuhua and Datao, 2005;Yazdi et al, 2017;Moeinedini et al, 2018;Piadeh et al, 2018), fuzzy FMEA (Baykasoğlu and Gölcük, 2017; Karatop and Sinan, 2017;Orouei and Jahan, 2017), fuzzy BN, fuzzy PN (Chang et al, 2018; and fuzzy Markov chain (Fu et al, 2012) are examples of the common fuzzy based risk assessment tools.…”

Application of Markov chain on daily rainfall data in Paraíba-Brazil from 1995-2015

“…Markov chain models have been widely used for simulating discrete time series. Some applications include vegetation dynamics (Balzter, 2000), hydrological processes (Schoof & Pryor, 2008;Fu, Li, & Huang, 2012), wind speed (Shamshad, Bawadi, Hussin, Majid, & Sanusi, 2005) and urban growth (Le Gallo & Chasco, 2008). Markov chain models can vary in two properties: the number of states (different values that the variable can assume) and the order (number of previous values used to determine the state-to-state transition probabilities) (Schoof & Pryor, 2008).…”