Engineering Overview

The Lhasa River originates at the southern foot of the Nyenchen Tanglha Mountains at the Poncho la Kongma trench in Lhari County, Tibet, China. It is bounded by the Salween River valley in the north and northeast; in the east, it joins Palomzangbo and Nyang Rivers. Its south is the mainstream of the Yarlung Tsangpo River. Its western and northwestern parts are the inner stream system of northern Tibet; its location is plotted in Fig. 1. The inlet is 3580 meters above sea level with a total drop of 1620 meters, the length of river basin is 551 km, and it covers an area of 32471 km² and accounts for 13.5% of the Yarlung Tsangpo River valley. The mountain peaks in the northern part of the basin are 5000-5500 meters above sea level, and the valley floor is 4000-4500 meters above sea level. The Lhasa River basin has a mild climate, flat terrain, thick soil, and abundant water resources, it is one of the major grain-producing areas in Tibet, so it significantly impacts the economic development of Lhasa.

Fig. 1.

The location of the Lhasa River Basin.

The Determination of the Evaluation Index

In this paper, the monitoring point in Maizhokunggar County, Yangbajain, Duilong Deqing County, Lhasa City, and Dagzê County of the Lhasa River basin are adopted as the investigation object. The data were collected from the 2011 water quality monitoring data at the Tibetan Autonomous Region Sha Tsui Environmental Monitoring Centre station; eight routine monitoring items of water quality at each monitoring point were analyzed, it including PH (X₁), DO (X₂), COD (X₃), COD_Mn (X₄), Ammonia nitrogen (X₅), Total cyanide (X₆), Total phosphorus (X₇) and Fluoride (X₈); their average value of monitoring index at the A₁-A₅classic cross sections are shown in Table 1. And according to ''Environmental Quality Standard of surface water'', the seven assessment indices of water quality can be classified as five levels as shown in Table 2, level I (very good), level II (good), level III (common), level IV (bad) and level IV (worse).

The Evidence Theory

It is assumed that questions to be assessed is q, a collection of all possible results is Θ = {F₁, F₂, F₃, ..., F_d}; where, Θ is identification framework; the set of factors that determine the result is E = {E₁, E₂, E₃, ..., E_d}, E_i is the evidence body; assuming that a set function m:2^Θ→[0,1] meet with 𝐦(Φ)=0,∑A⊆Θ𝐦(F)=1 and Bel(F)=∑B⊆Fm(B), then m is defined as a basic probability distribution function. m(F) is the basic reliability of proposition F; Bel(F) is called as the reliability of proposition F.

So the basic reliability m(F) of F under the action of all body of evidence is [17]:

Where, k is normalization coefficient.

Construction of Basic Reliability Distribution Function

The reliability of the evidence body is influenced by the reliability of the information source and its value. The reliability of the information source can be reflected based on its certainty reliability s_i and uncertainty reliability m_i(δ); among them, the certainty reliability represents the probability that the object is identified. The greater the certainty reliability is, the more reliable the information source is, and the higher the reliability is. The evidence body is divided into the positive index and negative index; the characteristic of positive index demonstrates that with the increase of index value, the probability of event is greater, and the reliability is higher; the inverse index has the opposite characteristic, as the likelihood of the event is smaller, the reliability becomes lower.

Suppose that there are n categories of a problem, and the results of the classification are influenced by d-type evidence. R(+) is a matrix composed of upper limits of evaluation index intervals corresponding to different classifications, R(–) is the matrix of the lower limit of the evaluation index interval, their expression is listed as follows:

Let P_i be the reliability generated by evidence x_i, and the basic reliability distribution is

Where, the corresponding positive indicator is

The corresponding inverse index is

The Construction of Assessment Systems

By substituting the corresponding indexes at the critical points of the classification grades in Equations (3) and (4) into Equation (5), the reliability of the classification limits of the indexes M is obtained as follows [18]:

All row vectors and uncertainty reliability {m₁(δ), m₂(δ), m₃(δ), ..., m_d(δ)} in matrix M are substituted into formula (1), the critical reliability of each grade is obtained as follows:

Finally, the subjects were classified according to the different intervals of the synthetic reliability of q.

The Calculation of Determination Reliability Based on the Entropy Weight Gray Correlation Method

In order to determine its reliability objectively and reasonably, the entropy weight gray correlation method is used. Firstly, the weight of each index is calculated by entropy theory, and then the reliability of each index is determined by gray correlation method.

(1) The determination of weight coefficients

The membership index g_ij of target i under index j is first determined, and objective membership degree matrix G = (g_ij)_m×n is constructed; the normalized target membership matrix G = (g_ij)_m×n is obtained as [19]:

The entropy of index j is

The weight of indicator j is

Where, 0≤ω_j≤1 and ∑j=1nωj=1, then the weight ω_j(j = 1, 2, ..., n) of index j is substituted into (y_ij)_m×n, the weighted membership degree matrix is obtained as follows:

(2) Determination of basic reliability distribution function

Let R_ij be the comprehensive gray correlation coefficient. In this paper, the comprehensive correlation method is used to calculate the correlation coefficient to avoid the distortion results obtained by using the optimal and the worst correlation alone. The calculation of r_ij is listed as follows:

The optimal correlation coefficient r_ij⁺ is [20]

The worst correlation coefficient r_ij^– is

Where, X+=max1≤i≤m1≤j≤nxij={x1+,…,xn+} is the ideal optimal sequence; X−=max1≤i≤m1≤j≤nxij={x1−,…,xn−} is the ideal worst sequence; it is adopted as ξ = 0.5, the comprehensive gray correlation coefficient is

Substituting r_ij into formula (17), the uncertainty reliability D(I_j) of each index can be obtained, the corresponding certainty reliability is 1-D(I_j).

The q-order uncertainty reliability of indicator j is

Where, q = 2.

The basic reliability distribution function for different targets of each index is

Where, m_j(i) is the basic reliability distribution function of target i under the action of index j, and ∑𝐢=1𝐦mj(i)<1, that is to say, there is certainty and uncertainty of the whole cognition. Then this part of the basic reliability assignment function is assigned to the recognition framework Θ, that is the degree of certainty about all the goals. Therefore, the certainty and uncertainty reliability of indicator j can be obtained respectively as follows:

The Construction of Assessment Model

(1) The construction of the evaluation frame

To evaluate the water quality in Lhasa River, a new suggested model is constructed; its schematic diagram is plotted in Fig. 2. At first, the different evidence body of classification standard is collected, then according to the above evidence body, the essential reliability can be determined by using the Entropy-Weight gray theory; secondly, according to the relevant essential reliability, the synthetic rule of evidence theory is performed, their results are regarded as the identification framework; thirdly, the actual monitoring data is analyzed, and the decision making is performed in the identification framework; finally, the model of water quality assessment is constructed, and evaluation results are obtained.

(2) Determining the certainty reliability

It can found that the risk grade increases with the increase of magnitudes of the indicator X₁, so it is an inverse index; the rest of indicators in the Table 2 are positive indicators, based on Eq. (3) and (4), and in combination with the Table 2, the classification matrix of water quality assessment can be shown as:

Fig. 2.

Schematic diagram of water quality assessment based on the suggested model.

Based on Table 1, and in combination with the Eqs (10)-(12), the weight coefficients of different indicators can be obtained as:

According to Eq. (13), the weighted membership degree matrix can be expressed as

The ideal optimal sequence is

The ideal worst sequence is

The maximum difference and minimum difference respectively are:

Based on Eq. (16), the gray correlation coefficient matrix can be obtained as follows:

According to Eq. (17), the uncertainty reliability of different indices is obtained as

According to Eq. (18), the Mass function of different indicators can be expressed as:

Based on Eqs (19)-(20), the total certainty and uncertainty reliability can be shown in Table 3.

(3) The calculation of identify frame

Substituting the data in Table 1 and the index value in the classification boundary into Eq. (5), the distribution function of essential basic reliability is constructed, and then the synthesis between different confidence intervals is performed. Their results are shown in Table 4.

(4) Determining the assessment level of the water quality

The data of A₁ is adopted as an example, substituting these data into Eqs (1) and (2), the primary reliability distribution of A₁ can be shown in Table 5.

Similarly, the synthetic reliability of A₂-A₅ can be calculated in Table 6, respectively.

The Evidence-Entropy weight gray incidence theory is applied to evaluate the water quality assessment. The assessment results are respectively shown in Table 6. It can be found from Table 6 that the assessment levels of the water quality from A₁ to A₅ cross sections are different. The assessment level of water quality at A₂ and A₅ cross sections is III; one at the rest cross sections is II, which means that the assessment level of water quality at A₂ and A₅ cross sections is good. One at the rest cross sections are common, the qualified rate of water quality level in all cross sections arrive at 100%. However, for A₁ to A₅ cross sections, the necessary prevention measurement should be taken to avoid the deterioration of water quality; for example, the clean-up operation of river channel should be performed, et al.

According to the comparative results of the assessment model in Table 6, conclusions can be drawn that the results obtained by the suggested method are consistent with the investigation for five different cross-sections. Its accuracy reaches 100% for the proposed method, which is higher than the results from the statistical probability and comprehensive fuzzy approach (60%) [21]. So the conclusion demonstrates that it is feasible to estimate water quality levels using the Evidence-Entropy weight gray incidence theory model. And the method can provide more details for assessing water quality level; for example, the COD of water quality at the A₃ cross section is 16, which should belong to level III based on Table 2. In addition, the primary reliability distribution of the other indicators obtained by using the suggested model belongs to level II, so the quality level probability of the A₃ cross-section at level II is higher than that of groups I, III, and IV. So the water quality level at the A₃ cross-section only belongs to level II and almost impossibly belongs to levels I, III, and IV. Furthermore, the risk level of the A₃ cross-section is more likely to be level III than that of the A₁ cross-section because the synthetic reliability(0.947) of the A₃ cross-section for group III is higher than that of the A₁ cross-section (0.8272). The results obtained using the suggested model accurately demonstrate the assessment level of water quality and further determine the quality grade ranking for different cross sections at the same level.

Discussions

The evidence theory is applied to fuse the evidence body of various information resources; the assessment results demonstrate the interaction of different factors; relatively to the statistical probability and comprehensive fuzzy method, it can improve the predictive accuracy and determine the certainty reliability of other evidence bodies, the difference of importance between various evidence bodies can be reflected. So the suggested model enhances the predictive efficiency of water quality levels.

In comparison with the traditional method, its assessment result has higher reliability and efficiency, and an interval scale can be taken into consideration in the evaluation process,so the suggested theory can well predict the grade criterion which are interval form.