Weight analysis of dam break risk consequences influencing factors

There are numerous influencing factors of the risk consequences of dam break. Scientific and reasonable index 5 system and its weight distribution is one of the key element for comprehensive evaluation of the dam-break risk. Taking into consideration of 20 factors , including hazards, exposure and vulnerability factors, the evaluation index system of the consequences of the dam break risk is constructed. Using the Statistical Cloud Model (SCM) to improve the entropy method, we establish the weight calculation model of the influencing factors of the dam break risk consequences. The results shows that the top 5 factors with the highest weight are risk population, flood intensity , alert time, risk understanding and distance 10 from the dam. Compared to the traditional algebraic weight calcu lation methods, the result is basically consistent with the algebraic weight distribution, and increases the range by 2.03 t imes, supporting a more scientific basis for recognizing and evaluating the dam break risk consequences.


Introduction
Co mprehensive evaluation of the risk consequences of dam break is the overall description of the severity of the consequences of the dam failure (Ling et al., 2009).The factors that can influence the risk consequences of dam break are usually co mposed of 3 factors, namely, hazards, exposure and vulnerability ( Okada, 2004;Smith, 2013).The vulnerab ility factors can be further divided into 4 aspects: loss of life, economic loss, social impact and environmental impact.Fro m the point of v iew of system science, dam break flood d isaster system is a dynamic system with high di mension, co mp lexity and uncertainty.It accords with the development trend of risk assessment research "from low d imensional linearity to comp lex high-dimensional nonlinearity", "fro m single scale to mult i-d imensional space-time scale", "fro m single scenario to combined scenario", "from certainty to uncertainty" (Zou et al., 2013).
The previous research on the index system of risk consequences and its weight is not sufficient.The uncertainty of the impact of dam failure is exp lored, and suggestions for research index system are given ( Lee and Noh, 2003;Wagenaar et al., 2016).The relationship between the hazard influencing factors and relationship between exposure and vulnerability factors is very comp licated and the different types of flood including dam break flood can cause different degree of life loss (Jonkman et al., 2018;W isner and Uitto, 2009).The indirect loss index for nature d isasters is introduced and their weight is calculated by the traditional algebraic method (Dan iell et al., 2018).The DAMBREAK co mputer programme is utilized to analysis the to analyze the regional water safety systems, but is not co mbine with the weight calculation (Ren et al., 2017).In the quantitative evaluation of risk consequences, we need to consider the comb ined effects of various factors, in which weight is a key part of it.The function of weight is to coordinate and balance the difference between the indexes.It is a measure t o unify each index without considering the dimension difference between the indexes.In order to evaluate the risk consequences more co mp rehensively and objectively, many influencing factors are needed.However, too many indicators, more than 9 for examp le, will b ring such problems like the difficulty in expert scoring and consistency test, and too average weight distribution.
In the course of calculat ing the weights, different methods have their own emphasis.For examp le, entropy weight method as one of the important methods of weight calcu lation, does not adequately consider the subjective opinions of experts.The analytic hierarchy process (AHP) is faced with the difficu lty of consistency checking when dealing with the conditions of mu ltip le factors (>9) (Su et al., 2016).When previous studies used the data of Statistical Cloud Model (SCM) to calcu late weights, they had neglected the entropy when applied the SCM to convert the subjective opinions, resulting in the imperfection of informat ion utilization (Mithas et al., 2011;Wan et al., 2015).These mentioned defects all lead to lack of scientificity in the calculation of weight.This manuscript introduces the SCM, which can reflect the fuzziness and randomness, to improve the entropy method for analy zing the weight of influencing factors of dam break risk consequences.
The scientific influencing factors' weight will provide an impo rtant basis for further research on the dam-break risk comprehensive evaluation and for the establishment and improvement of d am risk management theory.

Risk index system
The establishment of evaluation index system is a systematic process.Scientific and reasonable evaluation index system is the guarantee for accurate risk assessment of dam failure, and the evaluation result is helpful for later research.Influencing factors of dam-break risk consequences are many and complicated in both quality and quantity, direct and indirect contribution, natural and social ways (Zhou et al., 2014).We choose the representative indicators as much as possible to reduce the mutual influence and derivative of the indicators.For examp le, the risk population is the most direct factor of l ife loss, we only set it in the life bearing bodies, even though it is influencing the eco nomic and social aspects, but in indirect and less crucial way (Dutta et al., 2003).In the selection of the economic impact factors, the selection of GDP(Gross Do mestic Product) per cap ita can better reflect the economic situation of the dam area.Co mpared with the GDP of the area, it is more accurate.Similarly, the co mprehensive ability of water environ ment, soil environ ment and social carrying capacity is also selected.Whether the established index system is scientific and reasonable is directly related to whether it can objectively reflect the nature of the vulnerab ility itself.On the basis of aforementioned factors and characteristic of dam- break flood system, we establish the risk influencing factor index system scientifically and reasonably as shown in Fig. 1.

Figure 1．Index
of dam-break risk consequences influencing factors .

Weight calculating model based on SCM-improved entropy method
Uncertainty is an intrinsic property of the objective world.The most important and most common uncertainties include fuzziness and randomness (Regas et al., 2010).The in fluencing factor system of the dam failure risk consequence is a mult ilevel and mu lti-index system with uncertainties (Li et al., 1995).In determining the importance of each risk factor to the comprehensive evaluation of the consequence, it needs a "quantitative conversion" of the uncertainty of the indicator.In the process of conversion, the expert's judgment makes a choice between ma ny different factors that mutually affect each other and will absolutely lead to the amb iguity of boundaries, which is the fuzziness.On the other hand, the risk factors of dam break involve many aspects of life, economic loss, environmental and social imp acts.In order to avoid the impact of expert's personal experience and subjective factors on the evaluation results, the risk factors of dam break need to adopt the method of group decision-making process.When an expert judged diverse risk factors, other experts must have some d ifferent opinions, reflecting in the rando mness of judg ments.Therefore, dam-break risk assessment system is a co mplex system integrating fuzziness and randomness.The SCM is invented under this context of the random and fu zzy feature of the dam break risk system.It describes the notions by the concept of clouds, reflects the randomness and fuzziness of concepts in natural language, and realizes the conversion between qualitative and quantitative information (Wang et al., 2016;Liu et al., 2018).In the process of group decision-making, the traditional method is only a simple algebraic operation of expert's rat ings, which could not reflect the disagreements of d ifferent experts and the concentration of opinions.In fact, the experts' opinion is actually a rounded value that focuses on a certain degree of swing, which is using a stable tendency of the random number instead of the exact value, basically consistent with the central idea of SCM and the concept of entropy (Yari and

SCM Theory
The SCM , wh ich was proposed by Li Dey i, is a model of uncertainty transformation between a qualitative concept and quantitative numerical representation (Li et al., 1995;Li et al., 2014).It main ly reflects the fuzziness and randomness of the concept of things or human knowledge in the objective world and integrates these two together.Constituting the mutual mapping between qualitative and quantitative, cloud generator is the key to its practical application.
Membership cloud: Suppose a universe U={x}, L is the language value of the link in U.The membership degree RL (x) of the element x in U to the qualitative concept expressed by L is a stable random number.The membership degree distributed in the universe of discourse is called the membership cloud as shown in Fig. 2. Hyper-entropy (He): The measure of En uncertainty, entropy of entropy, reflects the discreteness of cloud drops.When the He is larger, the dispersion of cloud droplets is greater, that is, the greater the randomness of the membership value is, and the greater the "thickness" of the cloud can be.When it is closer to the concept centre or away fro m the centre, the randomness is relatively small, which is similar to a person's subjective feelings.
Cloud Generator: Generator is the most basic cloud algorith m, which can achieve quantitative range and distribution rules fro m the qualitative information exp ressed in language value.Cloud generators are main ly div ided into the forward cloud generator and the backward cloud generator.The conversion process from qualitative concept to quantitative representation is conducted the forward cloud generator, the conversion process fro m quantitative representation to qualitative concept is produced by the backward cloud generator.

Entropy Method
The subjective weight analysis method is mo re dependent on the experts' opinions, and the consistency test under many factors is very d ifficult (Yari and Chaji, 2012).Therefo re, this manuscript introduces entropy weight method as an objective weight calcu lation method.Entropy is a measure of uncertainty or randomness in informat ion theory (Ouyang and Shi, 2013).
In general, the mo re uncertain or random the event is, the more informat ion it will contain, so the bigger entropy is.
Therefore, the most important part of the entropy method is to obtain the differences in information, wh ich is the degree of variation (Wang and Chen, 2016).According to the degree of variation of each index, we can calculate the entropy of each factor, and then use the entropy to adjust the weight of it, and finally, the objective weight value of the factors in the sy stem is obtained.
The contribution of the numerical value in h igh-frequency or common consensus factor to the qualitative concept is greater than that of the numerical value in low-frequency (Yang and Nataliani, 2017).The En in the SCM could coincide with the idea of the entropy method in essence (Sheng et al., 2016;Dong et al., 2010).Th is manuscript makes use of the similar connotations of the SCM and entropy method.The objective advantages of entropy method need to be based on large amounts of score samp les, which can be produced by the SCM cloud generator to get enough samples fro m limited experts' opinions.This manuscript attempts to use the SCM of qualitative-quantitative conversion model to improve the entropy method and make a scientific and objective response to the weight of risk factor.

Improved entropy method based on SCM
Suppose there are n indicators (colu mn vectors) and m experts (ro w vectors).Each indicator co mputes the expectation and variance according to the cloud model.Statistical equation for calculating the jth indicator is as follow (Li et al., 1995): (2) The weight equation for the indicator calculated with the use of the conventional algebraic method is as follow: This algebraic method is easy to use, but it does not make any use of the changes of En in the SCM and may be mislead ing.
For examp le, when the average scores of all indicators are the same, the weight of each indicator will calcu late the same result.However, Enj and Hej could change greatly, but will not make enough reflection of the change in original equation, so an improved model is needed to replace this equation, as follow: If the Enj is not equal to 0, the equation of the weight is revised and the cloud entropy is involved in the calculation.The larger the cloud entropy, the more divergence of opinions the expert has on the index, so the weight of the index should be reduced.The sma ller the entropy is, the smaller the expert's d isagreement on the indicator, so the weight of the indicator should be increased.When the minimu m entropy Enj is equal to 0, indicating that the indicators of the experts have the same score, and then the weight of the equation remained unchanged.

Experts' scoring
According to the requirement of data volu me based on entropy method, we invite 20 experts to score the index system.Each index scoring adopts 100 integral points system, accord ing to the importance without any comparison between each other.
Scoring points should be scored from the perspective of comprehensive assessment of the risk consequences of the dam break.This scoring way can reveal the experts' opin ion properly without imp ly any preference of the factors, and makes the of the axis, the higher the expert's score.The En of Lv3 is larger than that of Lv1, we can find the cloud is wider, and the He of E4 is larger than that of E2, so the distribution of the cloud is obviously "thicker" than E2.In a word, the membership cloud can obviously reflect the degree of divergence and randomness of expert opinions.

Weight calculation
After the result of the scoring is processed by the backward cloud generator according fro m the Eq. ( 1) to ( 3) and ( 5), the 5 improved weight distribution result and result comparing the algebraic is shown in Table 1:

Discussion
In order to verify the validity o f the method, the results of the distribution contrast of the original and improved ones are drawn as Fig. 4.  According to the Fig. 3, Fig. 4 and Table 1, the analysis of figures shows following: (1) The top rankings have not changed after the adjustment, and still maintain the consistency of ranking.All o f these top ranking factors are scored higher and the opinions are concentrated, which is in line with the objective situation.At the same time, the range increased by 2.04 times.
(2) The distribution of weights is basically corresponding to the numerical value of Ex, reflecting the opinions of experts.
At the same time, accord ing to the adjustment of En, wh ich reflects the difference of expert opinion, the weight of opinion unified index is further enlarged.Several factors are reduced the weight due to the large differences in opinions and the further reduction in adjusted weights.It reflects the validity of the entropy method in handling the weight distribution through the differences in opinions.
Thus, it can be seen that the SCM-imp roved entropy weight model is more in keeping with the general cognition of the people while ensuring the objective and fair data.

Conclusions
Dam break is a kind of low probability and high loss risk event with uncertainties.In this manuscript, risk factors are d ivided into hazards, exposure and vulnerability factors, and 20 factors are be selected as the main influencing factors of dam break risk consequences.We used SCM to imp rove the entropy method, based on the same ideas that these two methods are dealing with the divergence.The fuzziness index of the information is generated by the backward cloud generator, and then Nat. Hazards Earth Syst.Sci.Discuss., https://doi.org/10.5194/nhess-2018-265Manuscript under review for journal Nat.Hazards Earth Syst.Sci. Discussion started: 20 September 2018 c Author(s) 2018.CC BY 4.0 License.downstream environmental impact and present 21 influence receptors, but the weight distribution of them is too average (Co lo mer and Gallardo, 2008).The Statistical Cloud Model (SCM) is used on the qualitative and quantitative transformation Nat. Hazards Earth Syst.Sci.Discuss., https://doi.org/10.5194/nhess-2018-265Manuscript under review for journal Nat.Hazards Earth Syst.Sci. Discussion started: 20 September 2018 c Author(s) 2018.CC BY 4.0 License.

Figure
Figure 2．Sketch map of a Membership Cloud.The x and y axes are for the expectation number and probability of distribution respectively.RL (x) takes a value between 0 and 1, whereas the cloud represents the mapping fro m the universe U to the interval [0,1], that is:RL (x): U→[0,1],∀x∈U, x→RL (x)It can be seen that the qualitative concept to the quantitative value on the universe U is a one-to-many mapping relat ion, rather than a one-to-one relationship on the traditional fuzzy function.The degree of membership of x to L is a probability distribution, not a fixed value.SCM uses the expectation (Ex), entropy (En) and hyper entropy (He ) as a whole to characterize an uncertain concept.Expectation(Ex): The mathemat ical expectation of cloud drop distribution in the universe of discourse, that is, the domain value corresponding to the centric of the area under the coverage of the membership cloud, wh ich is the domain value x of the degree of membership.Generally, it is the point most capable of characterizing the qualitative concept, reflecting the information centre value of the corresponding fuzzy concept.Entropy (En): En is a measure of the ambiguity of a qualitative concept, reflect ing the range of va lues that can be accepted . Hazards Earth Syst.Sci.Discuss., https://doi.org/10.5194/nhess-2018-265Manuscript under review for journal Nat.Hazards Earth Syst.Sci. Discussion started: 20 September 2018 c Author(s) 2018.CC BY 4.0 License.

Figure 3 .
Figure 3. Sketch map of 20 indexes' membership cloud.As shown in the Fig. 3, the centre vertex of the cloud is Ex, En represents the width of the cloud, and He represents the degree of dispersion of cloud distribution, that is, the thickness of cloud lines.For instance, the closer the Ex to the right side

Table 1 .
Results comparison of the weight distribution.