Application of entropy-based fuzzy matter-element analysis in seepage monitoring of RCC dam

Abstract

Taking account of the fuzzy results of the seepage monitoring analysis of roller compacted concrete (RCC) dam and uncertainties of the individual indicator evaluation, the fuzzy matter-element model of seepage monitoring of RCC dam analysis has been established with the use of the fuzzy matter-element analysis theory and the concept of euclid approach degree. The use of entropy theory can calculate the weighting factor through the disorder utility values of the information reflected by the data itself, which can effectively avoid the problems of weight distribution and uncertainties of subjective judgments of the seepage monitoring analysis of roller compacted concrete dam. And further the example shows that the analysis of entropy-based fuzzy matter-element analysis model of the seepage monitoring of roller compacted concrete dam is in accordance with the actual situation, which verifies the effectiveness of the method.

Keywords

information entropy / fuzzy matter-element / roller compacted concrete (RCC) dam / seepage analysis

Introduction

The problem of roller compacted concrete (RCC) dam seepage is more complex because of its construction characteristics, which have been compacted in a construction process of a series of layer levels. The construction characteristics of the layers, as well as the dam itself and changes in the foundation of the dam will have considerable influence on seepage. To the analysis of the laws of RCC dam seepage, it is necessary to consider the comprehensive effect of the body and the layers in order to make the analysis be objective. At present, there have been many conventional concrete dam seepage monitoring models [1-5], which mainly apply the methods of conventional concrete dam, while there are rare safety monitoring models of roller compacted concrete dam because of its complexity. Given these above concerns, this paper has established the new safety monitoring models of roller compacted concrete dam with the use of matter-element analysis, fuzzy sets and the concept of euclid approach degree, and the information entropy theory in the calculation of weight. The fuzzy matter-element evaluation model is an effective evaluation criteria to avoid the impact of uncertainty and also a comprehensive objective assessment of the actual flow behavior of roller compacted concrete dam.

Seepage safety monitoring model of RCC dam

For the seepage monitoring of RCC dam, there are two methods, one is the pore water pressure monitoring, and the other is leakage monitoring. The established methods of the safety monitoring models are as follows.

Safety monitoring model of pore water pressure

The aim of pore water pressure safety monitoring of roller compacted concrete dam is to monitor the law of the pore water pressure of a certain point. Setting the piezometric water level corresponding to a certain point is h, and the expression of its safety monitoring model can be expressed as

(1)h=h_H+h_T+h_{\theta },

where h_H, h_T, and h_{\theta }, respectively, stand for the impact of water level, temperature, and aging changes on piezometric water level. Hereinafter, h_H is referred to the hydraulic components, h_T stands for the temperature component, and h_{\theta } is aging component.

1) Water pressure component

Water pressure is the comprehensive reflection of water level changes of the monitoring day and before, which means that the establishment of expression of h_H should consider the prelag effect. The expression of the hydraulic component h_H is established by the equivalent water depth, which is

(2)h_H={\displaystyle \sum _{i=\mathrm{1}}^{n_{\mathrm{1}}}{a}_{\mathrm{1}i}{H}_a^i},

where n_{\mathrm{1}} is the maximum power of H_a; a_{\mathrm{1}i} is the regression coefficient; and H_a is the equivalent water depth.

2) Temperature component

From a macro point of view, the temperature changes of the roller compacted concrete dam are similar to conventional concrete dam. The temperature component can be expressed as follows.

a) Situation considering dam body temperature monitoring data

If the dam body temperature monitoring data exist, then the monitoring values of the thermometers can be selected as the temperature impact factor, and the temperature component is

(3)h_T={\displaystyle \sum _{i=\mathrm{1}}^{n_{\mathrm{1}}}{b}_i{T}_i},

where b_i is the regression coefficient corresponding to the ith thermometer; T_i is the measured value of the ith thermometer; and n_{\mathrm{1}} stands for thermometer count.

If there are relatively more body temperature thermometers, the equivalent temperature factor could be selected as the temperature impact factor, of which the temperature component can be expressed as

(4)h_T={\displaystyle \sum _{i=\mathrm{1}}^{n_{\mathrm{2}}}{b}_{\mathrm{1}i}{\overline{T}}_i}+{\displaystyle \sum _{i=\mathrm{1}}^{n_{\mathrm{2}}}{b}_{\mathrm{2}i}{\beta }_i},

where b_{\mathrm{1}i}, b_{\mathrm{2}i}, respectively, stand for the equivalent average temperature measured by the thermometer of the ith layer and temperature load constant of temperature gradient; {\overline{T}}_i, {\beta }_i, respectively, stands for the equivalent average temperature measured by the thermometer of the ith layer and temperature gradient; and n_{\mathrm{2}} is the serial number of the thermometer layer.

b) Situation with no body temperature monitoring data

When there is no body temperature monitoring data, the temperature monitoring data can be selected as a temperature factor, of which the temperature component is as follows:

(5)h_T={\displaystyle \sum _{i=\mathrm{1}}^{n_{\mathrm{3}}}{b}_i{\overline{T}}_{ai}},

where b_i is the regression coefficient; {\overline{T}}_{ai} is the average temperature before monitoring day; n_{\mathrm{3}} is the number of time slots of the average temperature before monitoring day.

For the dam that has been operated for a long time, its temperature field changes in quasi-stable state, and the temperature factor may select simple harmonic form, and the temperature component is as follows:

(6)h_T={\displaystyle \sum _{i=\mathrm{1}}^{n_{\mathrm{4}}}\left(b_{\mathrm{3}i}\sin {\displaystyle \frac{\mathrm{2}\mathrm{\pi }it}{\mathrm{365}}}+b_{\mathrm{4}i}\cos {\displaystyle \frac{\mathrm{2}\mathrm{\pi }it}{\mathrm{365}}}\right)},

where t is the cumulative number of days from the initial value to monitoring value, and n_{\mathrm{4}} is the number of cycles.

3) Aging component

Aging component, which comprehensively reflects the process of dam seepage over time, is a complex one. Generally speaking, it grows quickly in the initial phase of water storage and becomes stable after the process. The aging component is

(7)h_{\theta }=c_{\mathrm{1}}\theta +c_{\mathrm{2}}\ln \theta ,

where c_i is the regression coefficient; and \theta is the cumulative number of days of the main monitoring value from the initial monitoring day divided by 100.

4) Pore water pressure safety monitoring model

Based upon the abovementioned study on the factor choices and expressions of hydraulic pressure component, temperature component and aging component, the pore water pressure safety monitoring model of roller compacted concrete dam is

(8)$$\begin{gathered} h=h_H+h_T+h_{\theta } \\ =a_{\mathrm{0}}+{\displaystyle \sum _{i=\mathrm{1}}^{n_{\mathrm{1}}}{a}_{\mathrm{1}i}{H}_a^i}+\{\begin{array}{c}{\displaystyle \sum b_i{T}_i}\\ {\displaystyle \sum \left(b_{\mathrm{1}i}{\overline{T}}_i+b_{\mathrm{2}i}{\beta }_i\right)}\\ {\displaystyle \sum b_i{\overline{T}}_{ai}}\\ {\displaystyle \sum \left(b_{\mathrm{3}i}\sin {\displaystyle \frac{\mathrm{2}\mathrm{\pi }it}{\mathrm{365}}}+b_{\mathrm{4}i}\cos {\displaystyle \frac{\mathrm{2}\mathrm{\pi }it}{\mathrm{365}}}\right)}\end{array}+c_{\mathrm{1}}\theta +c_{\mathrm{2}}\ln \theta \\ =a_{\mathrm{0}}+{\displaystyle \sum _{i=\mathrm{1}}^{n_{\mathrm{1}}}{a}_{\mathrm{1}i}}{\left[{\displaystyle \underset{-\infty }{\overset{t_{\mathrm{0}}}{\int }}{\displaystyle \frac{\mathrm{1}}{A\sqrt{\mathrm{2}\mathrm{\pi }}{x}_{\mathrm{2}}}}{\mathrm{e}}^{-\frac{{(t-x_{\mathrm{1}})}^{\mathrm{2}}}{\mathrm{2}{x}_{\mathrm{2}}^{\mathrm{2}}}}\mathrm{d}t}\right]}^i+\{\begin{array}{c}{\displaystyle \sum b_i{T}_i}\\ {\displaystyle \sum \left(b_{\mathrm{1}i}{\overline{T}}_i+b_{\mathrm{2}i}{\beta }_i\right)}\\ {\displaystyle \sum b_i{\overline{T}}_{ai}}\\ {\displaystyle \sum \left(b_{\mathrm{3}i}\sin {\displaystyle \frac{\mathrm{2}\mathrm{\pi }it}{\mathrm{365}}}+b_{\mathrm{4}i}\cos {\displaystyle \frac{\mathrm{2}\mathrm{\pi }it}{\mathrm{365}}}\right)}\end{array}+c_{\mathrm{1}}\theta +c_{\mathrm{2}}\ln \theta , \end{gathered}$$

where a_{\mathrm{0}} is the constant term.

It should be noted that x_{\mathrm{1}} and x_{\mathrm{2}} of Eq. (8) are unknown, and therefore in the process of establishing pore water pressure safety analysis model of RCC dam, the definition of x_{\mathrm{1}}, x_{\mathrm{2}} and their corresponding constant terms and regression coefficients should aim at the optimal target of regression.

Safety monitoring model of leakage

For roller compacted concrete dam, its leakage mainly comes from the body of roller compacted layer and construction layer, of which the law of leakage of body is similar to conventional concrete dam. While the leakage of the construction layer is the major part of leakage of RCC dam, and its law is special. Setting the leakage of roller compacted layer of RCC dam is Q_{\mathrm{1}}, then

(9)Q_{\mathrm{1}}=Q_{\mathrm{2}}+Q_{\mathrm{3}},

where Q_{\mathrm{2}}, Q_{\mathrm{3}} is leakage of the roller compacted layer and the construction layer, respectively; the impact factors and corresponding expressions of Q_{\mathrm{2}} and Q_{\mathrm{3}} are shown as follows:

1) Leakage impact factor of roller compacted layer and its expression

a) Hydraulic components

The law of leakage of roller compacted layer of RCC dam is similar to conventional concrete dam leakage. Therefore, in the process of establishment of the law of leakage of roller compacted layer of RCC dam, the choice of impact factors is similar to conventional concrete dam, that is, leakage is 1-3 power-related to water depth, which means that the expression of hydraulic components is

(10)Q_{\mathrm{2}H}={\displaystyle \sum _{i=\mathrm{1}}^{m_{\mathrm{1}}}{a}_i^{\prime }}{H}_s^i,

where a_i^{\prime } is the regression coefficient; m_{\mathrm{1}} is the maximum power of the water depth, which is generally selected as 3; and H_s is upstream water depth.

b) Temperature component Q_{\mathrm{2}T} and aging component Q_{\mathrm{2}\theta }

The law of leakage of roller compacted layer of RCC dam, which is affected by temperature changes and aging, is similar to conventional concrete dam; thus similar to conventional concrete dam, the expression of impact factor is the same as the corresponding part of pore water pressure safety monitoring model, that is, the temperature component Q_{\mathrm{2}T} accords with Eqs. (3)-(6) and aging component accords with Eq. (7).

2) Impact factor of leakage of roller compacted layer and its expressionβ

a) Hydraulic components

Based on the characteristic of layer seepage of construction layer of RCC dam, the cubic law of rock cracks seepage can be used to simulate the changes of layers in the analysis of leakage law, that is, leakage of the construction layer of roller compacted layers caused by change of water level can be expressed as

(11)Q_{\mathrm{3}H}=D{b}^{\mathrm{3}}J,

where D is the impact coefficient, which is related with flowing viscosity of construction layer of RCC dam; b is width of construction layer of the RCC dam; J is the hydraulic gradient of construction layer.

For dam, the water has generally seeped into the corridors of the gullies through the pool. Thus, the leakage path of the construction layer can be seemed as a constant value. The hydraulic gradient J of Eq. (11) is mainly related with upstream water depth H_s. Therefore, Eq. (11) can be changed as

(12)Q_{\mathrm{3}H}=G{b}^{\mathrm{3}}{H}_s,

where G is the impact coefficient, which relates to the flowing viscosity of construction layer of RCC dam and leakage path.

b) Temperature component Q_{\mathrm{3}T} and aging component Q_{\mathrm{3}\theta }

As a result of changes in the body, on one hand, the width of the construction layer changes, and on the other hand, viscous properties of seepage rises; at the same time, the pore of the construction layer will also change, which leads to change of law of leakage of the construction layer. During the establishment of leakage safety monitoring model of construction layer, the changes of dam structure deformation behavior have been caused by the changes of the body temperature, which will also cause the changes of the leakage of the construction layer, is called temperature component that is expressed as Q_{\mathrm{3}T}, of which the expression is shown in Eqs. (4)-(7). Moreover, changes of seepage viscosity caused by changes of temperature and the change of seepage cause by the change of the pore of the construction layer is called aging component, and this component is expressed as Q_{\mathrm{3}\theta }, of which the expression refers to Eq. (8).

3) Q_{\theta }

As seen from the abovementioned analysis, leakage of roller compacted layer and construction later of RCC dam is mainly affected by the water level, temperature, and aging, and therefore, leakage safety monitoring model of RCC dam can be expressed as

(13)Q=Q_H+Q_T+Q_{\theta },

where Q is leakage of the RCC dam body; Q_H is hydraulic component of body leakage; Q_T is temperature component of body leakage; and Q_{\theta } is aging component of body leakage.

Based on the above analysis, leakage safety monitoring model of RCC dam body is

(14)Q=a_{\mathrm{0}}+{\displaystyle \sum _{i=\mathrm{1}}^{m_{\mathrm{1}}}{a}_i{H}_a^i+d{b}^{\mathrm{3}}}{H}_a+\{\begin{array}{c}{\displaystyle \sum b_i{T}_i}\\ {\displaystyle \sum \left(b_{\mathrm{1}i}{\overline{T}}_i+b_{\mathrm{2}i}{\beta }_i\right)}\\ {\displaystyle \sum b_i{\overline{T}}_{ai}}\\ {\displaystyle \sum \left(b_{\mathrm{1}i}\sin {\displaystyle \frac{\mathrm{2}\mathrm{\pi }it}{\mathrm{365}}}+b_{\mathrm{2}i}\cos {\displaystyle \frac{\mathrm{2}\mathrm{\pi }it}{\mathrm{365}}}\right)}\end{array}+c_{\mathrm{1}}\theta +c_{\mathrm{2}}\ln \theta ,

where a_{\mathrm{0}} is the constant term; a_i, d, b_i, b_{\mathrm{1}i}, b_{\mathrm{2}i}, c_{\mathrm{1}}, and c_{\mathrm{2}} is the corresponding regression coefficient of each factor, respectively; b is width of roller compacted construction layer of RCC dam; and d{b}^{\mathrm{3}}{H}_a comprehensively reflects the impact of dam leakage of the construction layer of RCC dam under the changes of water depth.

Fuzzy matter-element analysisβadding weight of information entropy

Fuzzy matter-element analysis

Matter M, its characteristic C and value x, which are described by fuzzy element analysis [6,7], are called three elements of matter that consist of matter R=(M,C,C(M)). If value x of the element model is ambiguity, R is known as the fuzzy element. If there are m characteristics of matter \mathit{M}, C_{\mathrm{1}},…, C_m and the corresponding value x_{\mathrm{1}},…, x_m, then R is fuzzy element. The combination of m dimensional element of n matters constitutes the m dimensional comprehensive fuzzy element {\mathit{R}}_{mn} of n matters, which is

(15){\mathit{R}}_{mn}=\begin{array}{cc}& \begin{array}{ccc}{M}_1& \cdots & M_n\end{array}\\ \begin{array}{c}{C}_1\\ ⋮\\ C_m\end{array}& \left[\begin{array}{ccc}{x}_{11}& \cdots & x_{1n}\\ ⋮& & ⋮\\ x_{m1}& \cdots & x_{mn}\end{array}\right]\end{array},

where {\mathit{R}}_{mn} is the m dimensional comprehensive fuzzy element of n matters; M_j is the jth matter (j＝1, 2,…, n) ; C_i is ith characteristic (i＝1, 2,…, m) ; and x_{ij} is the fuzzy value corresponding to ith characteristic of jth matter.

Evaluation factors set

Roller compacted concrete dam is a large-scale complex system, which can be affected by many factors. Various types of data (including designing, construction, monitoring records, etc.), as well as the monitoring data of the laid-bit fixed-point equipment (such as seepage) are information sources of evaluations of state of the layers, which can be used to judge the operation sate.

The measured data can directly reflect dam operation state. The operation behavior of the dam can be judged based on the analysis of monitoring data such as seepage. Therefore, the evaluation factors can be chosen as

(16)U=\{U_{\mathrm{1}},U_{\mathrm{2}}\},

\begin{array}{ll}{U}_{\mathrm{1}}=\{u_{\mathrm{11}},u_{\mathrm{12}},\cdots ,u_{\mathrm{1}n}\},& U_{\mathrm{2}}=\{u_{\mathrm{21}},u_{\mathrm{22}},\cdots ,u_{\mathrm{2}n}\},\end{array}

where U_{\mathrm{1}} is the relevant parameter of RCC layer impact area such as seepage; and U_{\mathrm{2}} is changes of the trend of relevant parameter of RCC layer impact area, which is aging.

Reviews setting

The state of operation behavior of RCC dam layer is divided into five grades. In addition, the setting isβV=\{v_{\mathrm{1}},v_{\mathrm{2}},v_{\mathrm{3}},v_{\mathrm{4}},v_{\mathrm{5}}\} = (normal, normal, mildly abnormal, severely abnormal, malignant disorders).

Favorably membership degree

The degree that fuzzy value of each individual indicator subordinates to the corresponding fuzzy value of evaluation indicator of the standard project is called the favorably membership degree.

Evaluation indicator value can be divided into five regions. In monitoring projects, situations that the values of the horizontal displacement, vertical displacement, etc, are either too large or too small are abnormal. It is better to set \widehat{y} (\widehat{y}=f(x) as the fitting value calculated in accordance with the mathematical model) as the center, and divide the region considering the deviation of the observed value. y is observation value of effect, and S is the residual standard deviation of model. Moreover, we have the following:

A district:

y_{\min }\le y\le y_{\max },\mathrm{a}\mathrm{n}\mathrm{d}\stackrel{\wedge }{y}-\mathrm{2}S\le y\le \stackrel{\wedge }{y}+\mathrm{2}S.

B district:

y_{\min }\le y\le y_{\max },\mathrm{a}\mathrm{n}\mathrm{d}\stackrel{\wedge }{y}+\mathrm{2}S\le y\le \stackrel{\wedge }{y}+\mathrm{3}S\mathrm{o}\mathrm{r}\stackrel{\wedge }{y}-\mathrm{3}S\le y\le \stackrel{\wedge }{y}-\mathrm{2}S.

C district:

y_{\min }\le y\le y_{\max },\mathrm{a}\mathrm{n}\mathrm{d}y\ge \stackrel{\wedge }{y}+\mathrm{3}S\mathrm{o}\mathrm{r}y\le \stackrel{\wedge }{y}-\mathrm{3}S.

D district:

E district:

The trend term of evaluation indicators refers to the change process that the measured effect value generates aging component with time arising. Aging component is not reversible. Therefore, the change of aging component is an important indicator of the operation state of RCC dam. Aging component may be carried out through the separation from the establishment of mathematical model of water pressure and temperature (or rainfall). Generally speaking, there are five kinds of expressions of aging component as follows, which are shown in Fig. 1.

The abovementioned five areas of A, B, C, D, and E are, respectively, corresponding to five evaluation grades v_l, v₂, v₃, v₄, v₅ divided according to evaluation indicator characteristics. If threshold values of these five trends are expressed by figures, their membership degrees are correspondingly 0.2, 0.4, 0.6, 0.8, and 1.0.

For the eigenvalues of the evaluation indicators of the evaluation of the program, some are bigger and more excellent, while the others are smaller and more excellent. Therefore, different formulas should be applied. This paper uses the following equation:

Situation about the smaller and the more excellent:

(17){\mu }_{ij}=\min x_i/x_{ij},

where {\mu }_{ij} is favorably membership degree; \min x_i is the maximum and minimum values of the ith (i＝1, 2,..., m) evaluation indicator. In addition, based on this, we can establish a favorable membership degree matrix {\tilde{\mathit{R}}}_{mn}.

Standard fuzzy element and difference square matrix

Standard fuzzy element R_{\mathrm{0}n} favorably refers to the maximum or minimum value of favorably membership degree of each evaluation indicator of favorably membership fuzzy element {\tilde{\mathit{R}}}_{mn}. In this paper, the maximum value is optimal, that is, favorably membership degrees of all indicators are 1. If {\mathit{\Delta }}_{ij} (i＝1, 2,…, m, j＝1, 2,…, n) stands for the square of element difference between the standard fuzzy element R_{\mathrm{0}n} and favorable membership matrix {\tilde{\mathit{R}}}_{mn}, the difference square matrix {\mathit{R}}_{\mathit{\Delta }} is as follows:

(19){\mathit{\Delta }}_{ij}={({\mu }_{\mathrm{0}j}-{\mu }_{ij})}^{\mathrm{2}},

(20){\mathit{R}}_{\mathit{\Delta }}=\left[\begin{array}{lll}{\mathit{\Delta }}_{\mathrm{11}}& \cdots & {\mathit{\Delta }}_{\mathrm{1}n}\\ ⋮& & ⋮\\ {\mathit{\Delta }}_{m\mathrm{1}}& \cdots & {\mathit{\Delta }}_{mn}\end{array}\right].

Determination of weight of information entropy

Information entropy of information system is a degree of disorder of information that is the smaller the entropy and the smaller degree of system disorder. Therefore, it is the information entropy that can be used to evaluate the order degree and its effectiveness of obtained system information [8,9]. The matrix composed by evaluation indicator values can be used to determine the weight of indicators, and subjective disturbance should be eliminated as rare as possible. Calculation of entropy weight is expressed as follows:

1) To build an assessment matrix of n things and m evaluation indicators,

R={(x_{ij})}_{mn},i=\mathrm{1},\mathrm{2},\cdots ,m;j=\mathrm{1},\mathrm{2},\cdots ,n.

2) To determine the regulation of a matrix of processing, using the following formula has been a normalized matrix to determine the following expressions:

b_{ij}=(x_{ij}-\min x_i)/(\max x_i-\min x_i).

3) According to the definition of entropy, the entropyβof n things and m evaluation indicators is

(21)H_i=-{\displaystyle \frac{\mathrm{1}}{\ln n}}\left[{\displaystyle \sum _{j=\mathrm{1}}^n(f_{ij}l\ln f_{ij})}\right],

where f_{ij}=b_{ij}/{\displaystyle \sum _{j=\mathrm{1}}^n{b}_{ij}}.

4) Calculate the entropy weight of the evaluation indicator W={(w_i)}_{\mathrm{1}\times m}, where

(22)w_i=(\mathrm{1}-H_i)/\left(m-{\displaystyle \sum _{i=\mathrm{1}}^m{H}_i}\right).

As seen from the above, the use entropy method to calculate the weight of each indicator is actually to use the difference between the information order degrees contained in each indicator. The greater different between sample values in indicators, the greater the weight of indicator.

Calculations of neartude

Neartude refers to the close level between the evaluated sample and standard sample. The greater it is, the closer; otherwise, it is the farther. Therefore, various options can be sorted according to the neartude, while the standard value can also be carried out the category of neartude. Fuzzy operator can be used to calculate and build the neartude fuzzy element matrix {\mathit{R}}_{\rho H}.

(23){\mathit{R}}_{\rho H}=\left[\begin{array}{llll}& M_{\mathrm{1}}& \cdots & M_n\\ \rho H_j& \rho H_{\mathrm{1}}& \cdots & \rho H_n\end{array}\right],

where \rho H_j is the jth neartude of the neartude fuzzy element matrix {\mathit{R}}_{\rho H}.

(24)\rho H_j=\mathrm{1}-\sqrt{{\displaystyle \sum _{i=\mathrm{1}}^m{w}_i{\mathit{\Delta }}_{ij}}},j=\mathrm{1},2,\cdots ,n.

Then, the evaluation of the sample can be determined, and the neartude of each corresponding grade of the review set can be judged according to Eq. (24).

Based on the above steps, entropy-based fuzzy element analysis model of seepage monitoring of RCC dam can be established. The model will evaluate the seepage situation of the dam according to the neartude of each corresponding grade of the review setting.

Example

Take some RCC dam project for instance, where three uplift measuring points are chosen. According to the osmometer measuring point of the dam, P1, P2, and P3 are selected for analysis.

Analysis of seepage pressure monitoring model

Based on the above seepage analysis and the measured data of the dam, the calculation results are shown in Table 1.

The aging trend component is shown in Fig. 2, which can be seen from the chart, P2 and P3 decrease, while P1 gradually increases but slowly.

According to the analysis, the comprehensive evaluation system of roller compacted concrete dam seepage behavior is shown in Table 2.

Information entropy weight fuzzy element analysis

Having done the fuzzy element analysis on the data in Table 2 and calculated the entropy weights of each indicator are shown in Table 3, respectively. Table 4 is the final calculation of the neartude.

As shown in Table 4, compared with other grades, the neartude of the maximum value of 2006 is the closest to the normal grade indicators, which demonstrates that the dam seepage pressure is in the normal range in 2006.

Conclusion

In this paper, roller compacted concrete dam seepage monitoring model, based on the comprehensive analysis method of the information entropy theory and the fuzzy matter-element analysis theory, has been carefully studied. Constructing the corresponding evaluation factors sets and review sets, the entropy-based fuzzy element comprehensive analysis model of the roller compacted concrete dam seepage monitoring has been put forward and verified by the example. The model may be more complex in theory, but its calculation process is simple, convenient, practical, and reasonable, which has been verified by the results of the example. The use of entropy theory can calculate the weighting factor through the disorder utility values of the information reflected by the data itself and then effectively reduce the subjectivity of the calculation, improve its interoperability. The model provides another way to analyze the roller compacted concrete dam seepage behavior.

References

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