Multi-level fuzzy comprehensive evaluation of the influence of reservoir sedimentation based on improved cloud model

The reservoir is the most basic project in water conservancy. While ensuring the safety and economic benefits of the project itself, it also protects the lives and property of people downstream (Liu 2018). However, to build a reservoir on a river would inevitably change the natural state of the river and causes issues like risen river water level, reduced flow rate, and sedimentary deposit, which result in sedimentation in the reservoir area, and cause unforeseeable disasters to the reservoir itself (Hu & Fang 2017). The problem of sedimentation brings about various influences on the reservoir, and the specific aspects of these influences are the research focus of many scholars. For example, in the existing influence evaluation of reservoir sedimentation, since the evaluation system does not give specific states to each influencing aspect, the subjectivity of experts increases significantly in the evaluation process. And the conclusion of the evaluation is difficult to accurately reflect the extent of the influences of reservoir sedimentation. The multi-level influence evaluation model of reservoir sedimentation using the improved cloud model could comprehensively evaluate the influence level of reservoir sedimentation, which provides insights regarding the future operation and management of the reservoir and the treatment of sedimentation deposits (Xie et al. 2012).

In recent years, with the development of the combination weighting method and cloud model, they have been gradually applied in different field. For example, Gao et al. (2019) combined the cloud model with combination weighting method was applied in coal mine safety risk evaluation, which provides a certain reference for coal mine safety management and risk prevention and control. Liu et al. (2020) applied cloud model and combination weighting method in the performance evaluation of train communication network, which provided theoretical reference for the performance evaluation in the field. Cui & Zheng (2019) applied combination weighting and improved cloud model to slope stability evaluation, and evaluated a road slope for reconstruction and expansion in Hunan Province and results were promising. Qiu et al. (2020) evaluated the effect of tunnel excavator based on cloud model and analytic hierarchy process. In the effectiveness of tunnelling machine, this method is considered to be reasonable scientific evaluation process which obtained objective and accurate evaluation results that could provide reference for similar research. Yan et al. (2019) found that the sedimentation of reservoir would influence water quality, which can be divided into three processes: the migration of sediment contains pollutants, the deposition and release of bottom silt pollutants, and the sedimentation treatment and discharge process. Xia et al. (2009) found that with the extension of operation time the severe sedimentation in reservoir area could lead to the further decline of flood control capacity of the reservoir. He et al. (2015) found that the effective storage capacity of the reservoir decreases due to sedimentation, causing the reservoir to be unable to function normally, and causing the residential and agricultural water demand in the downstream could not be met. Xie et al. (2012) quantified the influence of sedimentation on reservoirs, established an influence evaluation model of sedimentation on reservoirs, and applied the evaluation model to three typical reservoirs, namely Xiaolangdi, Danjiangkou and Sanmenxia, for preliminary evaluation and study, then calculated the influence degree of sedimentation on these reservoirs. Ge et al. (2021) studied the sedimentary characteristics of Lushui Reservoir and found that silt dredging is an effective way to extend the lifespan of reservoirs and relieve global sediment resource shortage problem, which has received widespread attention; Selek & Pınarlık (2019) found that the economic lifespan of the dam was controlled by water storage in reservoir. Also, dams are mostly destroyed by the dead volume of the reservoir which is filled by the sedimentation carried by the water that entered the reservoir; Choi et al. (2011) found that by additionally installing inspection dams, sedimentary deposits can be reduced, and the lifespan of reservoir increased by 60%. The study can also be used for reservoir management and design plans; Akar & Aksoy (2020) used stochastic time series models and analysis methods to study silt in river reservoirs, and the results showed that the expected value and difference of silt deposition in reservoirs can be estimated by analytic expression, and reduced the need for a comprehensive data generation mechanism. Also, the following research content provides reference for this article: Sahar Zinatloo-Ajabshir found that the prepared Dy₂Sn₂O₇ can effectively remove and destroy organic pollutants in water (Sahar et al. 2020). Seyed Ali Heidari-Asil et al. (2020) found that the ZC-C NSs product generated under phenylalanine showed excellent performance, and can be used to eliminate degradable organic pollutant acid blue 92. Nazari-Sharabian et al. (2019) studied the main limiting eutrophication factor of the total phosphorus (TP) concentration in the Mahabad dam reservoir in Iran. Li et al. (2021) proposed a numerical simulation method for fine-grained sediment deposition in the Sanxia reservoir area, which provides a reference for the prediction of sediment deposition in the reservoirs. Hou et al. (2021) analyzed the sedimentary discharge process of a reservoir under draining and different control water level conditions in the Sanmenxia reservoir; Zhu et al. (2021) calculated and proposed the basic conditions of suspended sediment removal in the river section based on prototype observation data, river bed composition analysis and a one-dimensional mathematical model.

The influence evaluation of reservoir sedimentation is a complex and comprehensive problem, and the influence layer factors mainly include social, economic, ecological and environmental influences. At present, the sediment control problem has become an urgent matter, which seriously restricts the functional lifespan of reservoirs, but the evaluation process concerning the influence of sedimentation has not kept pace. To that purpose, this article combined the cloud model with the multi-level fuzzy comprehensive evaluation system to evaluate the effect of sedimentation on the reservoir. The model adopts precise numerical parameters with the cloud uncertainty parameters, and the optimized combination weighting method through genetic algorithm was used to improve the accuracy of the calculation results. The multi-level fuzzy comprehensive evaluation of reservoir sediment deposition turned out to be more reasonable and accurate, and could provide substantial benefits for solving reservoir sedimentation problems.

Subjective weight is determined based on analytic hierarchy process. The analytic hierarchy process (AHP) commonly used in systems engineering was proposed by American operations research scientist T.L.Saaty (Qi 2015). This method is widely used in solving multi-criterion decision-making problems, and it constructs a hierarchical structure according to the membership relationship among various factors. The relative importance of each level and element was determined by judging the comparative ranking, and then total ranking was obtained as the basis for making decisions (Zhao et al. 2003). The calculation steps to determine the weight are as follows:

• (1)

  Construct judgment matrix

In Equations (4) and (5), CI and CR are consistency index and consistency ratio respectively; is the maximum eigenvalue of matrix A; n is the number of rows and columns in the judgment matrix. When CR < 0.1, the judgment matrix passes the consistency test.

Grey correlation analysis determines whether different sequences are closely related or not by means of the set shape of sequence curves (Geng et al. 2018). This method can be used to determine the strength order of correlation between various influencing factors with the influence of reservoir sedimentation and their influencing degree. The variation trend and correlation degree are interrelated. If the variation trend is consistent, it indicates stronger correlation, whereas if the variation trend is inconsistent, it indicates weaker correlation (Yang et al. 2010). The calculation steps to determine the weight are as follows:

X_ij in the formula represents the actual data corresponding to the j evaluation index under the i evaluation unit; i = 1,2,3…, n. j = 1,2,3…, n.

(3) After adopting the above processing method, the correlation coefficient is calculated using the following formula:

Entropy weight method is a kind of objective weighting method, and can better distinguish the ability of various indicators, thus determining the weight (Luo et al. 2019). The definition of information entropy as the measurement standard, the dispersion degree of an index is judged by the magnitude of entropy value. The smaller the entropy value, the greater the dispersion degree of an index, and the greater the influence of this index will have on the comprehensive evaluation (Zhang et al. 2020). The basic steps to determine the weight through information entropy are as follows:

• (1)
  Data standardization:

  

  (11)
• (2)
  Dimensionless treatment:

  

  (12)

If ⁠, then ⁠, the information entropy of this index is 0.

• (3)
  Calculated entropy:

  

  (13)
• (4)
  Determine the weight of each indicator:

  

  (14)

Thus, the evaluation index weight matrix W = (w₁,w₂,…,w_n).

Subjective weighting and objective weighting are two important methods to determine index weight. Subjective weighting refers to the weighting of indicators by experts in the field (Zhuang et al. 2006). It is characterized by strong subjectivity, but it can reflect the actual situation to a certain extent. Objective weighting refers to the weighting based on the digital characteristics of objective information, which avoids the interference of subjective factors. However, the weighting results cannot accurately reflect the correlation between indexes (Lu 2019). Both subjective and objective weights exist in evaluating the influence of reservoir sedimentation. The optimized combination weighting method by genetic algorithm can avoid the defect problem in the single method, and is suitable for the comprehensive analysis of the influence of reservoir sedimentation.

In the formula, ⁠; Z(j), Y(i,j) are the weight of randomly generated index j and the weight of index j determined by calculation method i, respectively; m and n are the number of weight calculation methods and the number of participating evaluation indexes, respectively.

Academician Li Deyi proposed cloud model theory on the basis of comprehensive probability theory and fuzzy mathematics (Li et al. 1995). Three numerical characteristics of the evaluation index are obtained through cloud model calculation, and the randomness and fuzziness of the system are linked mathematically.

Cloud model theory uses expectation, entropy and superentropy to characterize the digital characteristics of clouds, so as to realize the conversion of qualitative concepts to quantitative values, which can be expressed as (Zhou et al. 2014).

The cloud digital characteristic calculation equation of a certain index uses the following formula:

• (1)
  Mean value of cloud droplets in the computing cloud model:

  

  (17)
• (2)
  Discrete values of cloud droplets in the computing cloud model:

  

  (18)
• (3)
  Deviation value of cloud droplets in the computing cloud model:

  

  (19)

  where: n is the total number of cloud drops, which refers to the total number of standardized data for each indicator in the system; is the cloud drop value in the quantitative domain, which refers to the value of each data converted into [0,1] through standardization; is the mean value of cloud drops, which refers to the average value of each indicator after conversion.

In the cloud model, the cloud generator is a specific algorithm for converting qualitative concepts to quantitative values, which can be obtained through the input of digital eigenvalues and the number of cloud droplets, expressed as (Su et al. 2017), as shown in Figure 1. The reverse cloud generator can transform the quantitative value to a qualitative concept, which is a method based on statistical analysis of digital samples. The change of cloud droplet numbers in the cloud model is closely related to the accuracy of digital eigenvalues. When the number of cloud droplets is big enough, the accuracy of the calculation results can be guaranteed. The qualitative concept of converting accurate data into cloud digital characteristics (He 2016), is shown in Figure 2.

In order to quantitatively reveal the grade of the influence of reservoir sedimentation, the forward cloud generator was used. The evaluation level is the most critical level in the multi-level analysis system, and it demarcates the level limits for the evaluation objects, and many levels within the limits constitute the factor set of the evaluation level. The characteristic values of the cloud model were used to characterize comment set V of the multi-level index system of reservoir sedimentation influence evaluation. Among which, the reservoir sedimentation has a slight influence on V1, which is calculated by using a half-down normal cloud model; while the extremely severe influence on V4 was calculated using a half-liter normal cloud model. The moderate influence on V2 and the severe influence on V3 is calculated by using a complete normal cloud model. The calculation formula is as follows:

• (1)
  Half-down normal cloud model:

  

  (20)
• (2)
  Complete normal cloud model:

  

  (21)
• (3)
  Half-liter normal cloud model:

  

  (22)

In the formula, x₁ and x₂ are the upper and lower boundary values of each influence level in the evaluation layer, respectively, and the classification index of the influence level can be used as the boundary. E_x is the expectation of the corresponding influence level of the comment layer in the normal cloud model. E_n is the entropy of the comment layer corresponding to the normal cloud model. k is a constant, which mainly reflects the discrete range of entropy. In this paper, k is set as 0.02. through Equations (20)–(22), three characteristic values of the cloud model corresponding to the influence levels of sedimentation of each reservoir in the evaluation layer can be determined. The comment set V was divided into extremely severe influence (0.75, 0.0833, 0.02), severe influence (0.625, 0.0417, 0.02), moderate influence (0.375, 0.0417, 0.02) and slight influence (0.25, 0.0833, 0.02).

In the formula, is the combined weight corresponding to each index in the factor layer; j = 1,2,3, corresponding to the evaluation indexes of the three influence layers.

In the formula, is the combined weight corresponding to each index of the influence layer.

In this paper, the influence evaluation of reservoir sedimentation is divided into four steps. The evaluation process is shown in Figure 3.

Step 1: Combined with the actual conditions of the reservoir, the influencing factors of reservoir sedimentation were analyzed and a multi-level fuzzy comprehensive evaluation index system were established for evaluating the influence of reservoir sedimentation

Step 2: Calculate the subjective weight using analytic hierarchy process, calculate the objective weight using grey correlation analysis method and entropy weight method, and calculate the combined weight using genetic algorithm (Zheng 2017)

Step 3: Calculate the membership of each sediment influence indicator through the cloud model

Step 4: Obtain the overall evaluation results of the indicator system according to the improved cloud model

The reservoir was built on a sandy river, and its designed irrigation area and total storage capacities are 2.13 × 10⁵hm² and 6.4 × 10⁸m³, respectively. It is a large Type I water conservancy project with comprehensive benefits including agricultural irrigation function, downstream flood control function and power generation function. The reservoir is mainly responsible for the downstream agricultural irrigation and water supply and urban flood control tasks. It mainly supports the agricultural economy, including cotton, wheat, corn and other economic forest and fruit industries. The completion of the reservoir not only contributed to the local economic and social development, but also played an important role in the regional microclimate, biodiversity protection and artificial landscape construction around the reservoir area. The reservoir is located deep in the mid-latitude continent, surrounded by mountains, and is far from the ocean. The main source of water in the reservoir is the upstream glacier melt water and the mixed recharge of precipitation. The inter-annual change of the water and sediment in the reservoir is small, but distributes unevenly during the year. Sediment is mainly concentrated in the flood season, which is from June to August.

By the end of 2017, the amount of sedimentation in the reservoir under normal water level had reached 3.212 × 10⁸m³, and the storage capacity loss rate was 52.92%, of which the deposition of dead storage capacity is 1.306 × 10⁸m³, accounting for 98.94% of the dead storage capacity. The sedimentation storage is 1.91 × 10⁸m³, accounting for 40.05% of utilizable storage capacity. The deposition storage is 0.0979 × 10⁸m³, accounting for 3.71% of flood control storage capacity. According to the evaluation system for the sedimentation of the reservoir, the specific state data of the reservoir are compared according to the evaluation system, as shown in Table 1.

Professor Wang Peizhuang first proposed the fuzzy comprehensive evaluation model in the 1980s. After more than 40 years of development, great improvements have taken place in the evaluation methods. The original single comprehensive evaluation could not meet the needs of evaluation, so the multi-level fuzzy comprehensive evaluation was created (Xu et al. 2017). Multi-level fuzzy comprehensive evaluation adopt multiple factors and multiple objective decision making technology. One of the widely used technologies is the fusion of the analytic hierarchy process and fuzzy evaluation method (Ma 2010). The advantages of the evaluation index system are divided into multilevel hierarchy, the analytic hierarchy process was used to determine the index weight of each factor, the fuzzy hierarchy fuzzy matrix was then used to determine the relationships between the various levels of fuzzy evaluation, and finally the evaluation result was obtained (Zhang 2000). The evaluation of the influence of reservoir sedimentation is a complex comprehensive fuzzy evaluation system. The multi-stage fuzzy comprehensive evaluation method is used to evaluate the influence of reservoir sedimentation.

Set U contains the composition of the reservoir sedimentation influence factor; according to Figure 4, there are: U = {U1 (social influence), U2 (economic influence), U3 (ecological environmental influence)}, in which: U1 = {F (flood protection), D (dam safety), R (channel form)}, U2 = {S (shipping), I (irrigation), W (water supply), T (tourism), P (power generation), A (reservoir breeding), Dr (upstream flooding)}, U3 = {Q (water quality) and B (biodiversity), L (land salinization)}, respectively. The indicators in the factor layer are summarized by analyzing various types of reservoirs and combined with the research cases in this article. The indicators are mutually independent and there is no intersection, therefore, the indicators in the factor layer were determined. The factor layer in the evaluation system is to comprehensively evaluate the various functions of the reservoir for classification and determination, which can more accurately reflect the functionality of the reservoir, and the index of the factor layer can accurately reflect the actual siltation situation of the reservoir. The impact layer in the evaluation system is classified and summarized according to various indicators of the factor layer, and is divided into three major impacts, reflecting the impact level of reservoir sedimentation in these aspects.

Set V is composed of the influence levels of reservoir sediment accumulation. As shown in Figure 3, V = {slight influence V1 (0–0.25), moderate influence V2 (0.25–0.5), severe influence V3 (0.5–0.75), and extremely severe influence V4 (0.75–1)}. The factors of the indicator system are shown in Table 2, and the evaluation factors and classification criteria of sedimentation influence are shown in Table 3.

The degree of sedimentation various in different reservoir operating time, and its influences on reservoir are also different. At the beginning of the design, the reservoir was set with reserved dead storage capacity. With the increase of the running time, the amount of sediment deposition in the reservoir area increases, which gradually increases the impact of sedimentation on the reservoir. The state of each factor changes from the slight influence at the beginning to the extreme influence at the end, affecting the service lifespan and long-term benefits of the reservoir.

In the above evaluation process, the fuzziness of the evaluation system has been fully considered, but the fuzzy nature of its randomness and volatility has not been well reflected. Cloud models can transform qualitative concepts and quantitative values, and have advantages in describing the randomness and uncertainty of the evaluation system. Based on the advantages of cloud model theory, this paper combines the multi-level fuzzy comprehensive evaluation model with cloud theory to improve the accuracy of the influence evaluation of reservoir sedimentation.

Based on their engineering experience, experts in this field first compare various influence factors in the influence layer to prioritise the influence factors, and the analytic hierarchy method was used to determine the subjective weight of each index in the influence layer. Then, the various factors in the factor layer were evaluated and the importance of each factor was determined, and the analytic hierarchy process was used to determine the subjective weight of each index in the factor layer. Based on objective information, the various indicators affecting reservoir sedimentation were standardized. First, the gray correlation analysis and the entropy weight method were used to analyze the objective weights of the indicators in the impact layer, and then the gray correlation analysis and entropy method was used to analyze the objective weight of each factor in the factor layer. The weights obtained by the above three methods are combined using genetic algorithm, and the minimum weight of the square of the weight difference of each method was calculated through generating randomly population, and the influence layer and the index of the factor layer was obtained using the optimized combination weighting method through genetic algorithm. The index weights of the influence layer are shown in Table 4, and the index weights of the factor layer are shown in Table 5.

From Tables 4 and 5, the combination weights of the influence layer are 0.5118, 0.2561, 0.2321, respectively. the combination weights of the factor layer are 0.1161, 0.1562, 0.0391, 0.0734, 0.0409, 0.0702, 0.0880, 0.1196, 0.0106, 0.1205, 0.0599, 0.0526, 0.0530, respectively.

Each index data of the influence evaluation of reservoir sedimentation is analyzed using the backward cloud generator, and three digital characteristics of the cloud model for each index were obtained. Formula (11) was used to standardize the data. According to the processed data, formulas (17)-formula (19) and formula (23)-formula (25) were used to calculate the values of 13 evaluation indicators for factor levels and values of 3 indicators for influence levels, respectively. The cloud digital characteristics of the evaluation indicators are shown in Table 6. The numerical characteristics of the comment stratigraphic cloud obtained by formulas (26)-(28) are (0.6372, 0.0664, 0.0795).

According to the results of the comment layer and the cloud model rear sight, the formula (29) and Matlab software were used to generate the comprehensive evaluation cloud, and the cloud model rear sight of reservoir sedimentation is shown in Figure 5. It can be inferred that the cloud droplets are concentrated in the evaluation value Ex = 0.625–0.75, indicating that the influence level of sedimentation in the reservoir is between the severe influence level and the extremely severe influence level. According to the upper and lower limits of the comment stratigraphic model scale, the degree of sedimentation influence is under severe influence level.

• 1.

  The reservoir sedimentation impact evaluation model constructed in this paper was applied to the target study area. The results showed that the numerical characteristics of the comment stratigraphic cloud model for the evaluation of the reservoir sedimentation impact are 0.6372, 0.0664, 0.0795, respectively. The impact of the sedimentation on the reservoir is severe. If no precautions are taken to reduce reservoir sedimentation and slow down the sedimentation rate, the lifespan and function of the reservoir will inevitably be compromised. According to global reservoir statistics, the total storage capacity loss of reservoirs caused by sedimentation is 0.5%–1.0% every year. Accurate evaluation of the impact of siltation of reservoirs provides a useful reference for the safety management of reservoirs and the treatment of silt deposition.

• 2.

  Predecessors have also done similar studies. For example, Xie Jinming established a sediment deposition impact evaluation model using the analytic hierarchy process, and the model was used to quantitatively evaluate the impact of sediment deposition on the reservoir. The results showed that the model is basically reliable. Liu Sihai established a multi-level fuzzy comprehensive evaluation model based on analytic hierarchy process, fuzzy mathematics theory and cloud model theory for studying the impact of reservoir sedimentation. The model was applied to Kizil reservoir to evaluated the impact level of reservoir sedimentation. In this paper, an improved cloud model and combination weighting method were used to analyze the sedimentation problems of reservoirs. Based on previous study, optimization and improvement were carried out, and combination weighting method was adopted. First, the analytic hierarchy process was used to analyze the subjective weights, and then the gray relational analysis and entropy weighting methods were used to analyze the objective weights. Finally, the optimized combination weighting method using genetic algorithm was used to determine the comprehensive weights, which fully considers the subjective and objective factors of the evaluation indicators.

• 3.

  The study method in this article also has some limitations. The reservoir sedimentation impact evaluation model is to analyze the impact degree of reservoir sedimentation. This article analyzes the actual conditions of each influencing factor from a qualitative point of view. In future studies, if the actual conditions could be transformed into quantitative analysis, the accuracy of the results might be better. As for the research methods, this article adopts the cloud model and combination weighting method. Future studies could also adopt cutting-edge technologies and the latest mathematical theories to solve issues in water conservancy engineering. The problems that we encountered in water conservancy engineering sometimes need outside the box thinking, taking advantage of scientific method from other disciplines might just do.

• 1.

  This article adopts the analytic hierarchy process in a comprehensive evaluation model to study the impact of reservoir sedimentation. The target layer, comment layer, influence layer, factor layer, and status layer were constructed from top to bottom, and the sedimentation impact evaluation index of the target reservoir was established. The reservoir sedimentation impact evaluation model based on the improved cloud model realizes the conversion of qualitative concepts and quantitative values between indicators, and overcomes the defects of the multi-level fuzzy comprehensive evaluation model.

• 2.

  The reservoir sedimentation impact evaluation model based on the cloud model and the combination weighting method not only could obtain accurate target layer evaluation results, but also describes the specific impact of the reservoir sedimentation. The model could analyze the impact of each sedimentation indicator in depth, and concludes the main factors that affect reservoir sedimentation. From the combination weight of the influencing layer factors perspective, the degree of sedimentation is most affected by the social factors. While considering the combination weight of the factor layer, the degree of sedimentation is affected by the safety of the dam and that is the biggest impact factor.

• 3.

  Combining the cloud model and genetic algorithm in computing to evaluate the impact of reservoir sedimentation, the calculation results were much more accurate than that of the traditional methods, and is more in line with the actual needs of the project. The multi-level fuzzy comprehensive evaluation model is applied to the evaluation of the sedimentation impact in a certain reservoir, and concluded that the impact level of the sedimentation in the reservoir is severe. The evaluation result is consistent with the actual sedimentation situation of the reservoir, therefore the evaluation model constructed in this paper was verified.

The authors acknowledge the Water Resources Science and Technology Special Fund Project (No. T201801).

No conflict of interest exists.

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