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Frontiers of Agricultural Science and Engineering

ISSN 2095-7505

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Front. Agr. Sci. Eng.    2015, Vol. 2 Issue (3) : 205-215    https://doi.org/10.15302/J-FASE-2015073
REVIEW
Risk analysis methods of the water resources system under uncertainty
Zeying GUI,Chenglong ZHANG,Mo Li,Ping GUO()
Centre for Agricultural Water Research in China, China Agricultural University, Beijing 100083, China
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Abstract

The main characteristic of the water resources system (WRS) is its great complexity and uncertainty, which makes it highly desirable to carry out a risk analysis of the WRS. The natural environmental, social economic conditions as well as limitations of human cognitive ability are possible sources of the uncertainties that need to be taken into account in the risk analysis process. In this paper the inherent stochastic uncertainty and cognitive subjective uncertainty of the WRS are discussed first, from both objective and subjective perspectives. Then the quantitative characterization methods of risk analysis are introduced, including three criteria (reliability, resiliency and vulnerability) and five basic optimization models (the expected risk value model, conditional value at risk model, chance-constrained risk model, minimizing probability of risk events model, and the multi-objective optimization model). Finally, this paper focuses on the various methods of risk analysis under uncertainty, which are summarized as random, fuzzy and mixed methods. A more comprehensive risk analysis methodology for the WRS is proposed based on the comparison of the advantages, disadvantages and applicable conditions of these three methods. This paper provides a decision support of risk analysis for researchers, policy makers and stakeholders of the WRS.
Keywords water resources system      evaluation criterion      optimization model      risk analysis method      uncertainty     
Corresponding Author(s): Ping GUO   
Just Accepted Date: 22 October 2015   Online First Date: 03 November 2015    Issue Date: 10 November 2015
 Cite this article:   
Zeying GUI,Chenglong ZHANG,Mo Li, et al. Risk analysis methods of the water resources system under uncertainty[J]. Front. Agr. Sci. Eng. , 2015, 2(3): 205-215.
 URL:  
https://academic.hep.com.cn/fase/EN/10.15302/J-FASE-2015073
https://academic.hep.com.cn/fase/EN/Y2015/V2/I3/205
Fig.1  The framework of water resources system (WRS) risk analysis
Fig.2  Conceptual model for identifying the risk factors in the risk of water shortages
Evaluation criteria (RRV)Sub-criteriaFormulaeInterrelationshipFeaturesApplicable conditions
ReliabilityReliabilityα=P(Xt⊂S)α + r = 1Reliability and risk rate is relativeIf α = 1(r = 0), then the system is in a normal state and high stability; otherwise, the system is in an unsatisfactory stateUncertaintyFocusing to describe the probabilities of a failure, but the magnitude and the consequences caused by risk cannot be given
Risk rater=P(Xt⊂F)
ResiliencyResiliencyβ=P(Xt⊂S|Xt−1⊂F)=P(Xt−1⊂F,Xt⊂S)P(Xt−1⊂F)The longer recurrence cycle last, the resiliency is smaller, i.e. after a long recurrence cycle, it is more difficult to back to normalIf β = 1(or β = 0), then the system is in a normal state.If 0<β<1, then the system sometimes an unsatisfactory state, but it is possible to return to normalSensitivityNow that the system is in an unsatisfactory state, how long does the state return to normal
Recurrence cycleT=1N−1∑n=1N−1d(μ,n)
VulnerabilityVulnerabilityχ=E(S)=∑t=1NFPiSiGenerally it can be described by expected value, standard deviation and coefficient of variation0≤χ≤1, if χ = 1, than the system has be in a vulnerable state; if χ = 0, it is always in the normal stateSeverityHow much the severity and consequences resulted from a failure
Risk levelσ=D(X)=∑i=1n(Xt−E(X))2·P(Xt)Cv=σ/E(X)=σ/μ
Tab.1  The risk evaluation criteria of the WRS
Optimization modelsObjective functionsConstraintsReferences
The expected risk value modelmin⁡E[f(x;ξ)]E[gj(x;ξ)]≤0[38−42]
The conditional value at risk modelmin⁡φα(x;ξ)gj(x;ξ)≤0[43−45]
The chance-constrained risk modelmin⁡f(x;ξ){Pr⁡{f(x;ξ)≤f}≥αPr⁡{gj(x;ξ)≤f}≥β[46−49]
The minimizing probability of risk event modelmin⁡Pr⁡{hk(x;ξ)}gj(x;ξ)≤0−
The multi-objective optimization modelmin⁡[f1(x;ξ),f2(x;ξ),⋯,fm(x;ξ)]gj(x;ξ)≤0[50−52]
Tab.2  The risk optimization models of the WRS
MethodsFeaturesApplicable conditionsAn overview of the application
AdvantagesDisadvantages
Stochastic 1. Sensitivity to hypothesis, depending on sample size and the number of sample1. The number of samples is relatively sufficient.1. The description of the “probability” of risk is more realistic.1. The gap between the assumption and the practice.
2. High precision, sufficient results.2. Probability distribution obtained by an empirical or theoretical estimation.2. Mature development.2. Heavy workload and complex computation.
FuzzyDescribing the probability distribution is unknown and the sample size is pretty small.1. Data are relatively insufficient.1. Subjective evaluation can be involved.1. The membership function construction is inconsistent standard yet.
2. Focus on the magnitude of the risk of relativity.2. Widely used in the risk evaluation indices.2. The principles of selecting the indices are inconsistent.
MixedCombination of the above two methods.Describing fuzziness and risk random probability distribution.Accurately reflect the actual characteristics of risk assessment in the WRS1. The workload of processing data will increase worrisomely
2. The mathematical model used for processing variables and its coupling relationship will be more complicated.
Tab.3  Comparison among the three methods of risk analysis in the WRS
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