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Utilizing cloud models to analyze the uncertainty and consequences of dam failure factors. Enhanced Analytic Hierarchy Process (AHP) with a scale criterion based on index scale and an expert score constraint mechanism. Focus on the downstream area of the Zipingpu Dam for assessing the uncertainty of dam comprehensive evaluation factors. The final outcome is represented by three numerical eigenvalues of the cloud model, determining the weights of each factor in the evaluation index system. This approach offers a novel method for the comprehensive evaluation of dam failure consequences.

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  • The consequences when a dam is breached must be fully assessed to understand the possible risks and impacts on the surrounding area.

  • A thorough assessment is essential to get a full picture and make informed decisions.

  • The cloud model provides a modern and efficient way to process data and compute processes so that they run in a virtual environment.

  • Scaling the cloud model properly is critical to ensuring optimal performance and cost-effectiveness for a variety of applications.

  • The Analytic Hierarchy Process (AHP) provides a structured way to make complex decisions by breaking problems down into a hierarchy.

AHP, cloud model scale, comprehensive assessment, dam failure consequences, the cloud model
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Most high dams and reservoirs built in southwestern China are located at the intersection of earthquake-prone plates, which often cause severe disasters downstream once a breach occurs under strong earthquake damage forces. For example, the Lower San Fernando Dam in California, USA (Bolton et al. 1977), and the Shigang Dam and Liyutan Dam in Taiwan Province, China have experienced more severe deformation of the dams under the destructive effects of earthquake loads, seriously threatening the safe and stable operation of the dams. The comprehensive assessment of the consequences of dam failure caused by earthquake damage can make the managers of relevant departments further realize the seriousness of the consequences of dam failure risk and formulate emergency management plans timely and appropriately to minimize losses, further understand the risk level of the dam, and improve the relevant management theory (Ye et al. 2011; Bharath et al. 2021; Ali et al. 2022; Xianqi et al. 2022).

At present, researchers have done a certain amount of research on the assessment of dam failure consequences. Generally, the comprehensive assessment of dam failure consequences is divided into four aspects: life loss, economic loss, social impact, and environmental impact (Xiong & Fangjin 2020; Sun et al. 2021). In terms of loss of life research, Wei et al. (Wei et al. 2022) studied the loss of life caused by a dam failure, put forward a new comprehensive assessment model, and determined the main impact factors and occurrence process of life loss caused by dam failure. Huang et al. (2017) selected 11 impact factors of life loss, calculated their weights, sorted them through further classification, and obtained the ranking of each impact factor. Ge et al. (2021) have proposed a method for calculating loss of life and determining the impacts of the influencing factors on the loss of life. In terms of economic loss research, through numerical simulation and calculation, Shen et al. (2013) selected impact factors to evaluate the economic losses caused by dam failure floods by using existing data. Garrote et al. (2016) systematically analyzed the economic risk of floods and summarized the impact of the flood on various economic losses. Ge et al. (2020a) selected the equivalent economic scale as the primary index to establish the economic risk standard. The industrial economic contribution index was introduced to determine the correction coefficient to modify the equivalent economic scale (EES) to reflect the potential economic loss of the area to be evaluated. In terms of social impact research, Gu et al. (2020) applied the fuzzy comprehensive assessment method to establish the assessment index system and criteria of the earth–rock dam failure impact on society and the environment. He et al. (2020) applied the modified variable fuzzy sets model method of gray system theory to evaluate the social impact caused by dam failure. In terms of environmental impact research, Wu et al. (2019) improved the traditional set pair analysis method by applying a degree of five grades and a generalized set, and combined with the index system, built the environmental impact assessment model of dam failure. Ge et al. (2020b) evaluated the environmental impact of dam failure by the calculation method combining the set pair analysis method and the cloud model. Ali et al. (Ali et al. 2022) used different indexes to evaluate the negative impacts of dam failure floods on the environment and applied a new method considering multiple assessment indexes to evaluate the negative impact combined with the proposed failure function. Li et al. (2021) evaluated geomorphic changes in dam failure flood areas considering geomorphic changes and land use types and verified appropriate calculation methods with examples. In terms of the comprehensive assessment of dam failure consequences, experts and scholars comprehensively assess the consequences of dam failure mainly through the analytic hierarchy process (AHP), matter element method, set pair analysis method, the cloud model method, entropy value method, disaster system management method, and mathematical model method (Li et al. 2021; Yanting et al. 2021).

In the research contents of the above scholars, the causes of dam failure are mainly attributed to flood, project quality, and operation management, while further analysis of seismic load as the cause of dam failure is rarely conducted. In terms of research methods, the above research methods have certain limitations, and AHP, as the most widely used assessment method, has critical applications in many fields (Lv et al. 2022; Xiaoshen et al. 2022), but it has the disadvantage of being too strongly influenced by expert subjectivity, resulting in significant uncertainty and fuzziness of assessment results. The AHP is improved in this paper to improve the assessment system, which is greatly influenced by expert subjectivity. At present, the improvement of AHP is mainly aimed at improving scale. Although the improved scale can better solve the problem of inconsistency between experts' scoring results and actual cognition, it still reflects the scoring results by a numerical value, which cannot sufficiently reflect the uncertainty and fuzziness in the scoring process. The cloud model can fully reflect the ambiguity and randomness of the concept of uncertainty, so it is widely used in the analysis of ambiguity and uncertainty (Xiong & Fangjin 2020; Zou et al. 2020). For example, cloud model theory has essential applications in construction risk assessment, soil and water environment assessment, and hub transportation. Therefore, the cloud model is used in this paper to improve the traditional scaling criteria of AHP. Although it still relies on the experience of experts for scoring assessment, in essence, the expert scoring constraint mechanism based on the cloud model is introduced, and the improved AHP based on the cloud model is combined to conduct a comprehensive assessment of dam failure consequences, which can minimize the influence of expert subjectivity on assessment results.

Based on the above content, this paper takes the dam failure under the action of the earthquake as the premise, constructs the comprehensive assessment index system of dam failure consequences, introduces the expert scoring constraint mechanism based on the cloud model, and adopts the improved AHP based on the cloud model to analyze the uncertainty of the impact factors of dam failure consequences assessment, in order to provide a reference for the risk assessment of similar projects.

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By referring to the research content of literature (Li et al. 2021; Sun et al. 2021; Wei et al. 2022; Lian et al. 2023), this paper constructs a comprehensive assessment index system of dam failure consequences, which is divided into four categories: loss of life, economic loss, social impact, and environmental impact. Among them, in the analysis of loss of life, considering the powerful destructive effect of the earthquake, the impact on the loss of life is particularly significant, so the earthquake magnitude is emphasized in the analysis of loss of life. In this paper, the author believes that among the three analysis indexes of economic loss, social impact, and environmental impact, the destructive effect of earthquake and dam failure flood is more evident than that of earthquake and dam failure flood, so the earthquake magnitude is not considered as the factor under the corresponding index. The comprehensive assessment index system of dam failure consequences constructed in this paper is shown in Figure 1.
Figure 1
Comprehensive assessment index system of dam failure consequences.
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Comprehensive assessment index system of dam failure consequences.

Figure 1
Comprehensive assessment index system of dam failure consequences.
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Comprehensive assessment index system of dam failure consequences.

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Analytic hierarchy process

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AHP is a multi-criterion comprehensive decision analysis method that combines qualitative and quantitative analysis to deal with fuzzy or complex decision problems. The traditional AHP adopts the nine-scale criterion (Ali & Maryam 2014). When the nine-scale scale criterion is applied to analyze specific problems, there is a shortage of experts who are too influenced by subjectivity in the scoring process, and the scoring results often have a relatively sizeable discrete type. The root scale criterion is introduced into the traditional nine-scale construction criterion to reduce the discrete type and uncertainty of the calculation results. The root scale criterion can somewhat reduce the discreteness and uncertainty of expert grading results.

Based on Weber's law of psychology and guided by ‘equidistance grading and equitation assignment,’ the index scale criterion divides the gap of decision makers' judgment on the two factors into several levels (Zhang et al. 2020). The scale criterion has the consistency of judgment thinking and is equivalent to the consistency of objective difference judgment matrix, and the ranking between factors does not change due to the change of parameters. Flexible adjustment of parameters and ranking weights can further reduce the susceptibility of experts to subjective cognition. The index scale introduced in this paper is explained as follows: When parameter b is introduced into the judgment matrix, the index scale method still divides the judgment levels into 9. If b8 = 9, b1 = 1.3161 can be obtained. The three scaling criteria are shown in Table 1.

Table 1

Three scaling criteria of AHP

Paired comparisonImportance degreeTraditional scaleRoot scaleIndex scale
Xi is more important than Yj Absolutely 9  b8 
Strongly 7  b6 
Obviously 5  b4 
Slightly 3  b2 
Xi and Yj are equally important  1 1 b0 
Xi is not as important as Yj Slightly 1/3  1/b2 
Obviously 1/5  1/b4 
Strongly 1/7  1/b6 
Absolutely 1/9  1/b8 
Paired comparisonImportance degreeTraditional scaleRoot scaleIndex scale
Xi is more important than Yj Absolutely 9  b8 
Strongly 7  b6 
Obviously 5  b4 
Slightly 3  b2 
Xi and Yj are equally important  1 1 b0 
Xi is not as important as Yj Slightly 1/3  1/b2 
Obviously 1/5  1/b4 
Strongly 1/7  1/b6 
Absolutely 1/9  1/b8 
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Cloud model theory

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Uncertainty cloud model

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The cloud model theory is a qualitative and quantitative conversion model proposed by academician Deyi Li in 1995, which uses three numerical eigenvalues expectation Ex, entropy En, and hyper entropy He to represent its characteristics, namely C (Ex, En, He). Ex is the most representative point in the cloud model, reflecting the expectation of the distribution of cloud droplets in the quantitative domain, reflecting the qualitative concept, and representing the central value of the numerical distribution. En is a value that measures the degree of ambiguity of qualitative concepts and represents the range of acceptable qualitative concepts, the degree of fuzziness and discreteness of cloud droplet distribution, and the degree of expected uncertainty. He is a measure of entropy, reflecting the degree of uncertainty of entropy, namely the entropy of entropy, representing the condensation of the uncertainty of cloud droplets in the domain of discussion, and expressed as the thickness of cloud droplets in the cloud image. Gaussian cloud, as the most critical cloud model, is a quantitative domain in which C (Ex, En, He) is a qualitative concept on the quantitative domain, and x is a random realization of the qualitative concept obeying a Gaussian distribution ⁠, where obeys a Gaussian distribution ⁠. Thus, the determinacy of x on the qualitative concept satisfies:
(1)
There is A one-dimensional discourse domain U, where the cloud droplet group over any cell in U is represented by Δx, where Δx's contribution ΔA to the qualitative concept C is:
(2)
The total contribution A of all elements on U to C is:
(3)
Li Deyi et al. (Zhang et al. 2020) proposed the cloud drops that contribute to the qualitative concept in the domain of the theory mainly fall in the interval [Ex − 3En, Ex + 3En], and the approximation can ignore the cloud drops outside the interval [Ex − 3En, Ex + 3En], which is the 3 En principle of Gaussian clouds. The numerical characteristics of the cloud model are shown schematically in Figure 2 (Huang et al. 2017). If two cloud models C1 (Ex1, En1, He1) and C2 (Ex2, En2, He2) exist in the same domain, after calculating the algebraic sum of C1 and C2 resulting in C (Ex, En, He), for C = C1/C2, the following equation can be used to calculate the three numerical eigenvalues of the cloud models:
(4)
(5)
(6)
Figure 2
The digital characteristics of the cloud model.
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The digital characteristics of the cloud model.

Figure 2
The digital characteristics of the cloud model.
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The digital characteristics of the cloud model.

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Scale criterion of the cloud model

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In this paper, based on the index scale and combined with the cloud model, the cloud model scale criterion was constructed according to the 3En principle of normal distribution and relevant reference articles, as shown in Table 2.

Table 2

Scale criterion of the cloud model

Paired comparisonImportance degreeCloud modelCloud model scale
Xi is more important than Yj Absolutely C1 (Ex1, En1, He1) C1 (1.7321, 0.33, 0.02) 
Strongly C2 (Ex2, En2, He2) C2 (3, 0.33, 0.02) 
Obviously C3 (Ex3, En3, He3) C3 (5.1966, 0.33, 0.02) 
Slightly C4 (Ex4, En4, He4) C4 (9, 0.33, 0.02) 
Xi and Yj are equally important  C0 (Ex0, En0, He0) C0 (1, 0, 0) 
Xi is not as important as Yj Slightly C5 (Ex5, En5, He5) C5 (1/1.7321, 0.33/(1.7321)2, 0.02/(1.7321)2) 
Obviously C6 (Ex6, En6, He6) C6 (1/3, 0.33/(3)2, 0.02/(3)2) 
Strongly C5 (Ex7, En7, He7) C7 (1/5.1966, 0.33/(5.1966)2, 0.02/(5.1966)2) 
Absolutely C5 (Ex8, En8, He8) C8 (1/9, 0.33/(9)2, 0.02/(9)2) 
Paired comparisonImportance degreeCloud modelCloud model scale
Xi is more important than Yj Absolutely C1 (Ex1, En1, He1) C1 (1.7321, 0.33, 0.02) 
Strongly C2 (Ex2, En2, He2) C2 (3, 0.33, 0.02) 
Obviously C3 (Ex3, En3, He3) C3 (5.1966, 0.33, 0.02) 
Slightly C4 (Ex4, En4, He4) C4 (9, 0.33, 0.02) 
Xi and Yj are equally important  C0 (Ex0, En0, He0) C0 (1, 0, 0) 
Xi is not as important as Yj Slightly C5 (Ex5, En5, He5) C5 (1/1.7321, 0.33/(1.7321)2, 0.02/(1.7321)2) 
Obviously C6 (Ex6, En6, He6) C6 (1/3, 0.33/(3)2, 0.02/(3)2) 
Strongly C5 (Ex7, En7, He7) C7 (1/5.1966, 0.33/(5.1966)2, 0.02/(5.1966)2) 
Absolutely C5 (Ex8, En8, He8) C8 (1/9, 0.33/(9)2, 0.02/(9)2) 
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Expert scoring constraint mechanism

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The atomization property of cloud theory is as follows: when He = 1/3En, cloud droplets with Gaussian distribution are more dispersed, and cloud droplets no longer converge to form clouds, presenting an atomization state, indicating that experts cannot reach a consensus on the importance of two influence factors at this time, so He = 1/3En is taken as the atomization point of the cloud model. The following example illustrates the expert scoring mechanism. There are two assessment indicators, C1 and C2, of the same layer. Experts are asked to score them, and the cloud model scale criterion is applied to calculate the scoring results. The cloud model weight is calculated as (2.00, 0.3, 0.12). The generated figure is shown in Figure 3(a). This indicates that there are significant problems with the assessment data. Due to the influence of subjective factors, the dispersion of the data is large, the generated digital eigenvalues lose significance, and the effectiveness of the assessment results is low. Will give feedback on the information to the experts, and experts to fully communicate with each other to exchange ideas and scores again until the cloud model weight is calculated by scoring results generated by the cloud that meet the requirements and think about the results effectively. Such as the cloud model weight calculated by scoring results for (2.00, 0.2, 0.02), the generated figure as shown in Figure 3(b). The distribution of the cloud droplets is tight, and the results are valid.
Figure 3
Cloud chart of expert scoring results: (a) before the adjustment and (b) after the adjustment.
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Cloud chart of expert scoring results: (a) before the adjustment and (b) after the adjustment.

Figure 3
Cloud chart of expert scoring results: (a) before the adjustment and (b) after the adjustment.
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Cloud chart of expert scoring results: (a) before the adjustment and (b) after the adjustment.

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Calculation of weight of each impact factor

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The cloud model criterion is used to score the factors of the same layer and construct the judgment matrix. The root method is used to calculate the weight ωi (Exi, Eni, Hei) of the cloud model, and the equation of ωi is:
(7)
(8)
(9)
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Study area overview

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The Zipingpu Water Conservancy Project is situated in Chengdu, Sichuan Province, China, in the upper reaches of the Minjiang River and the lower reaches of the Chengdu Plain. It is a large-scale project that provides comprehensive benefits to the region. The main structure of the project is a reinforced concrete-face rockfill dam, standing at a maximum height of 156.0 m. With a total storage capacity of 1.112 billion cubic meters and controlling a basin area of 22,662 square km, it plays a crucial role in water resource management.

On 12 May 2008, a devastating earthquake with a magnitude of 8.0 on the Richter scale struck Wenchuan County, located approximately 17 km away from the Zipingpu dam. The earthquake's epicenter reached an intensity of 11°, resulting in significant damage to the dam structure due to the powerful seismic forces. Despite the high magnitude and intensity of the earthquake, the dam body did not fail or breach. However, it is important to note that the strong earthquake had apparent effects on the dam, raising concerns about its long-term stability.

The safety and integrity of the Zipingpu dam are of utmost importance due to the potentially catastrophic consequences downstream in the event of a failure. Therefore, it is imperative to conduct a thorough and timely risk assessment to evaluate the dam's stability and the potential risks it poses. This assessment should consider factors such as the dam's structural condition (Bharath et al. 2021), geological characteristics of the area, seismic activity, and the effects of the 2008 Wenchuan earthquake.

The schematic figure of the study area is shown in Figure 4.
Figure 4
Schematic figure of the study area.
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Schematic figure of the study area.

Figure 4
Schematic figure of the study area.
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Schematic figure of the study area.

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Results and comparative analysis

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Calculation results of improved AHP based on the cloud model

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Invite experts to score the impact factors in the assessment index system. According to Equations (2)–(7), the cloud model eigenvalues of each impact factor are calculated, and the expert scoring mechanism is used to test the scoring results continuously. After repeated adjustments, the results meet the expected requirements. According to the calculated synthetic weight, Ex is the first-ranking factor, En is the second-ranking factor, and He is the third for the total ranking. The results are shown in Table 3.

Table 3

Total ranking of impact factor weights

IndicatorExEnHeExEnHeExEnHeExEnHeComposite weight
Rank
ωi (Ex, En, He)
A1 0.626 0.600 0.600            
A2    0.085 0.090 0.090         
A3       0.128 0.136 0.136      
A4          0.161 0.174 0.174   
A11 0.263 0.262 0.262          (0.164, 0.171, 0.166) 1 
A12 0.130 0.131 0.131          (0.081, 0.095, 0.092) 4 
A13 0.178 0.178 0.178          (0.111, 0.099, 0.096) 3 
A14 0.208 0.209 0.209          (0.130, 0.115, 0.115) 2 
A15 0.095 0.095 0.095          (0.059, 0.062, 0.062) 6 
A16 0.069 0.069 0.069          (0.044, 0.053, 0.053) 7 
A17 0.057 0.056 0.056          (0.036, 0.027, 0.027) 9 
A21    0.148 0.147 0.147       (0.013, 0.017, 0.017) 17 
A22    0.076 0.077 0.077       (0.006, 0.005, 0.005) 25 
A23    0.336 0.335 0.335       (0.028, 0.033, 0.031) 12 
A24    0.213 0.218 0.218       (0.018, 0.016, 0.016) 15 
A25    0.107 0.107 0.107       (0.009, 0.008, 0.008) 23 
A26    0.120 0.116 0.116       (0.010, 0.013, 0.013) 22 
A31       0.105 0.108 0.108    (0.013, 0.011, 0.011) 18 
A32       0.224 0.220 0.220    (0.030, 0.032, 0.035) 11 
A33       0.246 0.248 0.248    (0.031, 0.038, 0.038) 10 
A34       0.156 0.157 0.157    (0.020, 0.018, 0.018) 14 
A35       0.086 0.088 0.088    (0.011, 0.007, 0.013) 20 
A36       0.183 0.179 0.179    (0.023, 0.027, 0.027) 13 
A41          0.067 0.070 0.070 (0.011, 0.015, 0.015) 19 
A42          0.245 0.248 0.248 (0.039, 0.034, 0.038) 8 
A43          0.476 0.468 0.468 (0.078, 0.089, 0.089) 5 
A44          0.088 0.089 0.089 (0.014, 0.018, 0.018) 16 
A45          0.060 0.061 0.061 (0.010, 0.014, 0.014) 21 
A46          0.031 0.031 0.031 (0.005, 0.007, 0.007) 26 
A47          0.033 0.033 0.033 (0.006, 0.008, 0.008) 24 
IndicatorExEnHeExEnHeExEnHeExEnHeComposite weight
Rank
ωi (Ex, En, He)
A1 0.626 0.600 0.600            
A2    0.085 0.090 0.090         
A3       0.128 0.136 0.136      
A4          0.161 0.174 0.174   
A11 0.263 0.262 0.262          (0.164, 0.171, 0.166) 1 
A12 0.130 0.131 0.131          (0.081, 0.095, 0.092) 4 
A13 0.178 0.178 0.178          (0.111, 0.099, 0.096) 3 
A14 0.208 0.209 0.209          (0.130, 0.115, 0.115) 2 
A15 0.095 0.095 0.095          (0.059, 0.062, 0.062) 6 
A16 0.069 0.069 0.069          (0.044, 0.053, 0.053) 7 
A17 0.057 0.056 0.056          (0.036, 0.027, 0.027) 9 
A21    0.148 0.147 0.147       (0.013, 0.017, 0.017) 17 
A22    0.076 0.077 0.077       (0.006, 0.005, 0.005) 25 
A23    0.336 0.335 0.335       (0.028, 0.033, 0.031) 12 
A24    0.213 0.218 0.218       (0.018, 0.016, 0.016) 15 
A25    0.107 0.107 0.107       (0.009, 0.008, 0.008) 23 
A26    0.120 0.116 0.116       (0.010, 0.013, 0.013) 22 
A31       0.105 0.108 0.108    (0.013, 0.011, 0.011) 18 
A32       0.224 0.220 0.220    (0.030, 0.032, 0.035) 11 
A33       0.246 0.248 0.248    (0.031, 0.038, 0.038) 10 
A34       0.156 0.157 0.157    (0.020, 0.018, 0.018) 14 
A35       0.086 0.088 0.088    (0.011, 0.007, 0.013) 20 
A36       0.183 0.179 0.179    (0.023, 0.027, 0.027) 13 
A41          0.067 0.070 0.070 (0.011, 0.015, 0.015) 19 
A42          0.245 0.248 0.248 (0.039, 0.034, 0.038) 8 
A43          0.476 0.468 0.468 (0.078, 0.089, 0.089) 5 
A44          0.088 0.089 0.089 (0.014, 0.018, 0.018) 16 
A45          0.060 0.061 0.061 (0.010, 0.014, 0.014) 21 
A46          0.031 0.031 0.031 (0.005, 0.007, 0.007) 26 
A47          0.033 0.033 0.033 (0.006, 0.008, 0.008) 24 
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It can be seen from Table 3 that the value ranges of Ex, En, and He of 26 impact factors in the response layer are (0.005–0.164), (0.005–0.171), and (0.005–0.166), respectively. The numerical distribution of the calculation results is relatively concentrated, indicating that a single factor has little impact on the comprehensive assessment of dam failure consequences, and it is the joint action of many factors, as shown in Figure 5(a). En/He are all less than 1/3, which indicates that the comprehensive assessment cloud atomization degree is low, the distribution of cloud droplets is concentrated, and the uncertainty of the calculation results is well handled. Risk population A11, alarm time A14, the severity of dam failure flood A13, and earthquake magnitude A12, these four factors had a more significant impact on the comprehensive assessment of dam failure consequences, both impact factors for life loss. This is due to the earthquake load and the dam under the flood risk area's dual role in the vast population's lower reaches. Most of the population, due to the damage of the earthquake, was trapped in the rubble at the same time; the alarm time was short, communication was inconvenient, the dam failure flood was fierce, and the people could not evacuate in time, resulting in the above impact factors in the comprehensive assessment of dam failure consequences accounting for a large proportion. The change of these impact factors will have a qualitative impact on the comprehensive assessment of dam failure consequences. However, the comprehensive assessment of dam failure consequences results from the joint action of many factors, and the impact degree of the 26 impact factors of the response layer on the comprehensive assessment of dam failure consequences cannot be ignored. The state layer of the cloud model weights are four calculation results, as shown in Figure 5(b), loss of life > environmental impact > social impact > economic loss. This is because the dam failure consequences caused by the life loss are priceless and immeasurable. There are secondary disasters brought about by the dam, and impaired social influence also does not allow us to ignore the importance of reconstructing disaster areas. Compared with other indicators, the economic loss has recoverability.
Figure 5
The cloud model synthesizes weight: (a) state layer and (b) response layer.
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The cloud model synthesizes weight: (a) state layer and (b) response layer.

Figure 5
The cloud model synthesizes weight: (a) state layer and (b) response layer.
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The cloud model synthesizes weight: (a) state layer and (b) response layer.

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Comparison of calculation results using different scale criteria

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The calculation results using different scale criteria are compared and analyzed, and the analysis results are shown in Tables 4 and 5.

Table 4

Comparison of weight calculation results using different scale criteria

IndicatorTraditionalRoot scaleIndex scaleCloud model scale
A1 0.691 0.465 0.617 0.626 
A2 0.068 0.146 0.091 0.085 
A3 0.112 0.187 0.132 0.128 
A4 0.129 0.202 0.159 0.161 
A11 0.206 0.101 0.166 0.164 
A12 0.084 0.065 0.079 0.081 
A13 0.126 0.079 0.108 0.111 
A14 0.153 0.087 0.129 0.130 
A15 0.056 0.053 0.061 0.059 
A16 0.037 0.043 0.042 0.044 
A17 0.029 0.038 0.032 0.036 
A21 0.009 0.023 0.016 0.013 
A22 0.004 0.015 0.006 0.006 
A23 0.026 0.039 0.031 0.028 
A24 0.015 0.029 0.016 0.018 
A25 0.006 0.019 0.008 0.009 
A26 0.007 0.018 0.014 0.010 
A31 0.010 0.023 0.011 0.013 
A32 0.027 0.039 0.032 0.030 
A33 0.03 0.041 0.033 0.031 
A34 0.017 0.030 0.022 0.020 
A35 0.008 0.020 0.013 0.011 
A36 0.021 0.034 0.021 0.023 
A41 0.009 0.023 0.009 0.011 
A42 0.033 0.044 0.037 0.039 
A43 0.061 0.060 0.075 0.078 
A44 0.012 0.026 0.018 0.014 
A45 0.007 0.021 0.011 0.010 
A46 0.003 0.014 0.004 0.005 
A47 0.004 0.015 0.005 0.006 
IndicatorTraditionalRoot scaleIndex scaleCloud model scale
A1 0.691 0.465 0.617 0.626 
A2 0.068 0.146 0.091 0.085 
A3 0.112 0.187 0.132 0.128 
A4 0.129 0.202 0.159 0.161 
A11 0.206 0.101 0.166 0.164 
A12 0.084 0.065 0.079 0.081 
A13 0.126 0.079 0.108 0.111 
A14 0.153 0.087 0.129 0.130 
A15 0.056 0.053 0.061 0.059 
A16 0.037 0.043 0.042 0.044 
A17 0.029 0.038 0.032 0.036 
A21 0.009 0.023 0.016 0.013 
A22 0.004 0.015 0.006 0.006 
A23 0.026 0.039 0.031 0.028 
A24 0.015 0.029 0.016 0.018 
A25 0.006 0.019 0.008 0.009 
A26 0.007 0.018 0.014 0.010 
A31 0.010 0.023 0.011 0.013 
A32 0.027 0.039 0.032 0.030 
A33 0.03 0.041 0.033 0.031 
A34 0.017 0.030 0.022 0.020 
A35 0.008 0.020 0.013 0.011 
A36 0.021 0.034 0.021 0.023 
A41 0.009 0.023 0.009 0.011 
A42 0.033 0.044 0.037 0.039 
A43 0.061 0.060 0.075 0.078 
A44 0.012 0.026 0.018 0.014 
A45 0.007 0.021 0.011 0.010 
A46 0.003 0.014 0.004 0.005 
A47 0.004 0.015 0.005 0.006 
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Table 5

Range of weight calculation results using different scale criteria

Traditional scaleRoot scaleIndex scaleImprovement of cloud theory
ExEnHe
State layer 0.068–0.691 0.146–0.465 0.091–0.617 0.085–0.626 0.090–0.600 0.090–0.600 
Response layer 0.003–0.206 0.014–0.101 0.004–0.166 0.005–0.164 0.005–0.171 0.005–0.166 
Traditional scaleRoot scaleIndex scaleImprovement of cloud theory
ExEnHe
State layer 0.068–0.691 0.146–0.465 0.091–0.617 0.085–0.626 0.090–0.600 0.090–0.600 
Response layer 0.003–0.206 0.014–0.101 0.004–0.166 0.005–0.164 0.005–0.171 0.005–0.166 
View Large

It can be seen from Tables 4 and 5 and Figure 6 that the weight calculation results using the traditional scale have a wide range and strong dispersion. Although the weight calculation results using the square root scale reduce the range of weight value, its importance is still determined by a single numerical value, which cannot eliminate the inherent shortcomings of AHP. The weight calculation results using the index scale and the cloud model scale are slightly different, but a single value still describes their importance, the calculation result is still a single value, and the calculation result is still subjective and cannot objectively reflect the opinions of experts. Using the cloud model scale weight calculation results show that the experts in the process of grading are no longer dependent on a single value, can more accurately describe the relative importance of each impact factor, reflect the integrity of the analysis process through the expert scoring, the intervention of constraint mechanisms, effectively limits the expert scoring, and is influenced by subjective factors. Guarantee the objectivity of the assessment results, this method describes the qualitative and quantitative transformations well, and the calculation results are more reliable.
Figure 6
Comparison of weight calculation results using different scale criteria: (a) A1:A11 ∼ A17, (b) A2: A21 ∼ A26, (c) A3: A31 ∼ A36, (d) A4: A41 ∼ A47, (e) A1i ∼ A4i, and (f) A1 ∼ A4.
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Comparison of weight calculation results using different scale criteria: (a) A1:A11 ∼ A17, (b) A2: A21 ∼ A26, (c) A3: A31 ∼ A36, (d) A4: A41 ∼ A47, (e) A1i ∼ A4i, and (f) A1 ∼ A4.

Figure 6
Comparison of weight calculation results using different scale criteria: (a) A1:A11 ∼ A17, (b) A2: A21 ∼ A26, (c) A3: A31 ∼ A36, (d) A4: A41 ∼ A47, (e) A1i ∼ A4i, and (f) A1 ∼ A4.
View largeDownload slide

Comparison of weight calculation results using different scale criteria: (a) A1:A11 ∼ A17, (b) A2: A21 ∼ A26, (c) A3: A31 ∼ A36, (d) A4: A41 ∼ A47, (e) A1i ∼ A4i, and (f) A1 ∼ A4.

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  • (1) The earthquake damage is taken as the inducing condition of dam failure. Furthermore, considering the earthquake's damage, the impact factors of the comprehensive assessment of dam failure consequences are selected. The uncertainty analysis of the impact factors of the comprehensive assessment of dam failure consequences is carried out using the improved AHP based on the cloud model. Relative to the individual value of assessment results of traditional AHP, this paper uses three digital characteristics of the cloud model, Ex, En, and He. The results in the characterization will be discrete, combining the characteristics of randomness and fuzziness uncertainty. At the same time, introducing an expert scoring constraint mechanism better solved the scoring process, the influence of experts' subjective factors on the assessment results, and the calculation results show richer information, more objectivity, and more credibility.

  • (2) The analysis results show that the life loss indicators in the assessment of the weight proportion are highest, the risk population and alarm time, severity of dam failure flood, and earthquake magnitude. These four factors impact the comprehensive assessment of dam failure consequences. Relative to other impact factors that are more apparent and impact factors for life loss, the weight of other impact factors' numerical distribution is relatively small and concentrated, but its role cannot be ignored.

  • (3) The rationality and authenticity of the calculation results in this paper need to be further demonstrated. Considering the induced conditions of dam failure from different perspectives, this paper can provide a reference for relevant managers to make scientific and reasonable decisions and further improve the risk management theory. At the same time, it can provide a new way of thinking for the comprehensive assessment of dam failure consequences.

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This study was supported by the National Natural Science Foundation of China (No. 51609087) and the Key Scientific Research Projects of Colleges and Universities in Henan Province in 2021 (No. 21A570001).

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All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for submission. The authors are grateful for the support provided by the National Natural Science Foundation of China (No. 51609087 and No .51709114), the Key Scientific Research Projects of Colleges and Universities in Henan Province in 2021 (No. 21A570001) and the Collaborative Innovation Center for Efficient Utilization of Water Resources in Yellow River Basin.

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All relevant data are included in the paper or its Supplementary Information.

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The authors declare there is no conflict.

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