# Study on Ecological Risk Evaluation and Optimum Selection of Desert Expressway Schemes Based on the Two-Dimensional Cloud Model

Authors: Feng Han; Zhibo Liu; Liangying Li; Wenhua Yin; Jiyin Wu
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Aimed at the fragile ecological environment in desert, once the resources along routes are destroyed, it will be difficult to restore the original ecological equilibrium in a short time. This paper studies the ecological-equilibrium-oriented risk evaluation of desert motorway schemes in order to choose route schemes reasonably and prevent the sandstorm aggravation caused by ecological damage. Having insight into the special geographical environment and road construction characteristics of Tengger Desert, the research establishes an index system for the ecological risk evaluation in desert areas from five aspects: the interference of living environment of animals and plants, the destruction of natural ecological landscapes, the pollution of water and soil resources, the development and utilization of natural resources, and the sand fixation of plants and the subsequent maintenance; then it confirms each evaluation index’s weight by using the set-valued statistics method to transform the description of the evaluation indexes to an interval value and furthermore determines the comprehensive ecological risk evaluation level of the route scheme in virtue of the two-dimensional cloud image MATLAB outputs which takes the ecological damage and remediation cost as the basic variables. By constructing the model under the method above, the ecological risk evaluations of two route schemes in Zhongwei sand crossing section of Wuhai-Maqin Expressway have been made. The result shows that the western route scheme’s evaluation grade is “good,” is better than the southern route scheme, is within the scope of acceptable risk, agrees with the practical project condition, and verifies the applicability and effectiveness of the model for ecological risk evaluation in desert areas.


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## Body

## 1. Introduction

Ecological risk evaluation is an important issue considered in the comparison and selection of route schemes, especially in the areas where the ecological environment is fragile. Constructing a long strip of large-scale belt infrastructure like expressways in desert areas will damage the fragile ecological factors along the route such as vegetation, soil, and water sources. Due to the weak self-repairing ability of the ecosystem in the windy sand area, it is difficult to recover the original ecological balance in a short time. The windy sand will aggravate over time, causing sand to react upon the road adversely. Therefore, how to resolve the conflicts among expressway construction, ecological environment, and the rational exploitation natural resources and how to build a standard framework for the ecological environment risk evaluation of road schemes have become the point issue for experts and scholars [1–3]. In the past ten years, there have been a lot of work carried out on the ecological risk evaluation of expressway schemes: based on the principle of ecology, many scholars have established the evaluation index system of green expressway from many perspectives such as human environment [4], sustainable development [5], road safety [6, 7], use of AHP [8], fuzzy comprehensive evaluation [9], grey correlation analysis [10], cluster analysis [11], and other evaluation methods included in fuzzy mathematics theory to evaluate the impact of road construction on ecological environment. With the development of modern surveying and mapping technology, GIS technology has been also used in the evaluation of the ecological environment of expressways, which has further improved the scientific and standardized level of environmental protection work [12, 13]. However, these existing researches only take one fact, the degree of environmental damage, into consideration when evaluating the expressway scheme and lacks the multidimensional consideration of ecological risk. At the same time, the evaluation index is short of the pertinence to the specific environment and ignores the differences of ecological factors in different regions. The accuracy of the evaluation results needs to be further improved.Cloud model, proposed by Professor D. Li et al., is a transformation concept based on fuzzy mathematics and probability theory [14], which is used to solve the transformation between fuzzy description and quantitative value [15]. The cloud model combines the characteristics of fuzziness and probability theory and can evaluate from many aspects. It has been widely used in many fields such as ecological remediation [16], quality evaluation [17, 18], image processing [19], and data mining [20]. Based on the research status, this paper takes the Zhongwei sand-crossing section of the Wu-Ma Expressway as the research object and the Tengger Desert as the research background and makes an evaluation of the ecological environment along different road schemes from the damage degree and the remediation costs. Given the special natural environment and geographical characteristics in desert hinterland, the authors establish the ecological risk index evaluation system of desert expressway after referring to the data, consulting the experts in the desert expressway feasibility study, and investigating on-site. The set-valued statistics method is used to consider the relative contribution of different factors to the desert ecological environment and then the comprehensive evaluation is made combined with two-dimensional cloud theory from the ecological damage situation and remediation cost. With the help of MATLAB positive cloud generator to output two-dimensional cloud images, the ecological risk evaluation of different desert expressway schemes can be reflected intuitively. Through the application of the research methods above, this paper provides a theoretical basis for the ecological risk evaluation of desert expressway construction and also provides a reference for similar projects.


## 2. Establishment of the Evaluation Index System

### 2.1. Hierarchical Model of the Evaluation Index

Ecological risk refers to the possibility that the original ecosystem is threatened by the external interference factors in a certain area [21]. This effect can cause damage to the ecosystem’s structure and function, thus endangering the safety and health of the ecosystem.On account of the fact that harsh climate and barren land are the characteristics of desert area, its ecosystem is very fragile. Based on the meaning and standard of ecological risk, this paper establishes a comprehensive evaluation index system from five aspects: the interference of wildlife living environment, the destruction of natural ecological landscape, the pollution of water and soil resources, the development and utilization of natural resources, and the sand fixation of plants and the subsequent maintenance. During expressways’ construction period, not only will vegetation be destroyed [22], but also various equipment and vehicles used for construction or transport on the site will generate noise and vibration, affecting animal habitats and plant growth areas [23]. In addition, the waste generated by road construction will also pollute the water environment and soil environment [24] and can even cause geological disasters such as sandstorms and soil erosion in severe cases. There would be difference of the ways to exploit natural resources rationally according to the different engineering schemes. Therefore, reasonable exploitation should be achieved to avoid exacerbating environmental deterioration. After the completion of the project, it is necessary to maintain and clean up the accumulated sand regularly to stabilize the ability of the protection system to prevent sand. Consequently, in desert areas, the importance of environmental protection should be recognized, and the idea of ecological environment-oriented route selection should be upheld to reduce the damage of route layout to the ecological environment as much as possible.Throughout the analysis above, this paper is on the basis of five first-level indexes, further selects 18 second-level indexes, and then establishes a comprehensive evaluation index system for the ecological risk of the sand-crossing expressway scheme, as shown in Figure1.Figure 1
Comprehensive evaluation index system of ecological risk in desert expressway construction.


### 2.2. Ecological Risk Indexes’ Grade

According to the unique characteristics of the natural geographic environment and the project in the desert area, the detailed classification of the index factors is listed in Table1.Table 1
Classification of index factors.
IndexesIIIIIIIVDisturbance of living environment of wild animals and plants (U1)Destruction of the original vegetation along the expressway,U11Minor impactShort-term damageLong-term damageTotal lossSelf-recovery ability of natural vegetation,U12ExcellentGoodGeneralPoorWildlife corridor partition,U13Almost noA few partsMany partsCompletelyDisturbance of wild animal living environment,U14Very weakWeakGeneralSevereDestruction of natural ecological landscape (U2)Loss of integrity of natural landscape,U21SlightSmallLargeSevereDamaged land occupied by construction,U22Very weakWeakGeneralSevereRestoration methods of landscape ecology,U23No repairNatural repairArtificial repairIrreparablePollution of water and soil resources (U3)Number of surface water crossings along the line,U31012>2Pollution degree of water source,U32Very weakWeakMediumStrongCause the severity of soil erosion,U33Very fewSmall areaMultiareaWhole line areaDegree of soil structure change,U34Very weakWeakMediumStrongDevelopment and utilization of natural resources (U4)Development of solar energy resources,U41Abundant natural resources, no impact on the ecological environmentAdequate natural resources, with little impact on the ecological environmentAdequate natural resources, with greater impact on the ecological environmentInsufficient natural resources, with greater impact on the ecological environmentDevelopment of wind power resources,U42Development of characteristic tourism resources,U43Sand fixation of plants and subsequent maintenance (U5)Effect of sand fixation on original ecology,U51Very beneficialBeneficialGeneralHarmfulAnnual loss rate of ecological protection effect,U52<2%2∼3%3∼5%>5%Available water source for plant irrigation,U53Very sufficientSufficientAverageInsufficientMaintenance cycle,U54>10a8–10a5-8a<5a


## 2.1. Hierarchical Model of the Evaluation Index

Ecological risk refers to the possibility that the original ecosystem is threatened by the external interference factors in a certain area [21]. This effect can cause damage to the ecosystem’s structure and function, thus endangering the safety and health of the ecosystem.On account of the fact that harsh climate and barren land are the characteristics of desert area, its ecosystem is very fragile. Based on the meaning and standard of ecological risk, this paper establishes a comprehensive evaluation index system from five aspects: the interference of wildlife living environment, the destruction of natural ecological landscape, the pollution of water and soil resources, the development and utilization of natural resources, and the sand fixation of plants and the subsequent maintenance. During expressways’ construction period, not only will vegetation be destroyed [22], but also various equipment and vehicles used for construction or transport on the site will generate noise and vibration, affecting animal habitats and plant growth areas [23]. In addition, the waste generated by road construction will also pollute the water environment and soil environment [24] and can even cause geological disasters such as sandstorms and soil erosion in severe cases. There would be difference of the ways to exploit natural resources rationally according to the different engineering schemes. Therefore, reasonable exploitation should be achieved to avoid exacerbating environmental deterioration. After the completion of the project, it is necessary to maintain and clean up the accumulated sand regularly to stabilize the ability of the protection system to prevent sand. Consequently, in desert areas, the importance of environmental protection should be recognized, and the idea of ecological environment-oriented route selection should be upheld to reduce the damage of route layout to the ecological environment as much as possible.Throughout the analysis above, this paper is on the basis of five first-level indexes, further selects 18 second-level indexes, and then establishes a comprehensive evaluation index system for the ecological risk of the sand-crossing expressway scheme, as shown in Figure1.Figure 1
Comprehensive evaluation index system of ecological risk in desert expressway construction.


## 2.2. Ecological Risk Indexes’ Grade

According to the unique characteristics of the natural geographic environment and the project in the desert area, the detailed classification of the index factors is listed in Table1.Table 1
Classification of index factors.
IndexesIIIIIIIVDisturbance of living environment of wild animals and plants (U1)Destruction of the original vegetation along the expressway,U11Minor impactShort-term damageLong-term damageTotal lossSelf-recovery ability of natural vegetation,U12ExcellentGoodGeneralPoorWildlife corridor partition,U13Almost noA few partsMany partsCompletelyDisturbance of wild animal living environment,U14Very weakWeakGeneralSevereDestruction of natural ecological landscape (U2)Loss of integrity of natural landscape,U21SlightSmallLargeSevereDamaged land occupied by construction,U22Very weakWeakGeneralSevereRestoration methods of landscape ecology,U23No repairNatural repairArtificial repairIrreparablePollution of water and soil resources (U3)Number of surface water crossings along the line,U31012>2Pollution degree of water source,U32Very weakWeakMediumStrongCause the severity of soil erosion,U33Very fewSmall areaMultiareaWhole line areaDegree of soil structure change,U34Very weakWeakMediumStrongDevelopment and utilization of natural resources (U4)Development of solar energy resources,U41Abundant natural resources, no impact on the ecological environmentAdequate natural resources, with little impact on the ecological environmentAdequate natural resources, with greater impact on the ecological environmentInsufficient natural resources, with greater impact on the ecological environmentDevelopment of wind power resources,U42Development of characteristic tourism resources,U43Sand fixation of plants and subsequent maintenance (U5)Effect of sand fixation on original ecology,U51Very beneficialBeneficialGeneralHarmfulAnnual loss rate of ecological protection effect,U52<2%2∼3%3∼5%>5%Available water source for plant irrigation,U53Very sufficientSufficientAverageInsufficientMaintenance cycle,U54>10a8–10a5-8a<5a


## 3. Determination of the Weight of the Evaluation Indexes

### 3.1. Set-Valued Statistics Theory

Owing to the fuzziness and randomness of the ecological environment evaluation indexes of sand crossing road, it is difficult to get a definite value for quantitative description and comparison in the actual evaluation. However, if a relative interval is used for description, it can be more consistent with the actual evaluation situation, that is, the set-valued statistical theory. The boundary range of set-valued statistical interval depends on the experts’ cognition of the evaluation index and the fuzziness of the index itself. The interval range is calculated by classical statistical methods, and this kind of risk evaluation process is closer to the actual situation.


### 3.2. Evaluation Indexes’ Weight Calculation

According to the index system of the evaluation model, the index factor setU=u1,u2,⋯,um is established, which refers to the set of factors affecting ecological environment along the scheme route. There are n members of the expert group participating in the evaluation, and their overall comment set for the index system is X, and the comment set X is the set of evaluation estimates of the relative importance of each index by the evaluator. If an expert adjusts the weight of the i-th index and stabilizes it within an interval yik1,yik2, then n experts evaluate it, and a new positive bound closed interval distribution is formed after the superposition of evaluation values (Figure 2).Figure 2
Weight superposition interval distribution.The derivation equation of the relative weight of the evaluation indexui is(1)y¯i=12∑k=1nyik22−yik12∑k=1nyik2−yik1i=1,2,⋯,m;k=1,2,⋯,n.Considering the differences of academic achievement, work experience, and professional title among the members in the expert groups, the contribution degreeqk of each expert in the total weight is given, and ∑k=1nqk=1k=1,2,⋯,n; then the relative weight of the improved evaluation index ui is(2)y¯i=12∑k=1nqkyik22−yik12∑k=1nqkyik2−yik1,i=1,2,⋯,m;k=1,2,⋯,n.According to (2), the relative weight of each index ui in the factor set U can be calculated and then normalized, as shown in (3)w¯i=y¯i∑i=1myi.The weight vector of the overall evaluation system can be obtained:(4)W=w1,w2,⋯,wn.


### 3.3. Weight Reliability Inspection

For the indexes weight results obtained by the set-valued statistics method, this paper uses the interval variance method to determine its reliability [25]. For any index ui, its weight interval variance Si is defined as(5)Si=∑k=1nyik2−w¯i3−yik1−w¯i33∑k=1nyik2−yik1.i=1,2,⋯,m;k=1,2,⋯,n.where Si indicates the experts’ divergence of index ui. The larger Si is, the more divergent the experts' evaluation of index ui is, and the lower the reliability is. On the contrary, the smaller Si is, the smaller the experts' evaluation divergence on index ui is, and the higher the reliability is.


## 3.1. Set-Valued Statistics Theory

Owing to the fuzziness and randomness of the ecological environment evaluation indexes of sand crossing road, it is difficult to get a definite value for quantitative description and comparison in the actual evaluation. However, if a relative interval is used for description, it can be more consistent with the actual evaluation situation, that is, the set-valued statistical theory. The boundary range of set-valued statistical interval depends on the experts’ cognition of the evaluation index and the fuzziness of the index itself. The interval range is calculated by classical statistical methods, and this kind of risk evaluation process is closer to the actual situation.


## 3.2. Evaluation Indexes’ Weight Calculation

According to the index system of the evaluation model, the index factor setU=u1,u2,⋯,um is established, which refers to the set of factors affecting ecological environment along the scheme route. There are n members of the expert group participating in the evaluation, and their overall comment set for the index system is X, and the comment set X is the set of evaluation estimates of the relative importance of each index by the evaluator. If an expert adjusts the weight of the i-th index and stabilizes it within an interval yik1,yik2, then n experts evaluate it, and a new positive bound closed interval distribution is formed after the superposition of evaluation values (Figure 2).Figure 2
Weight superposition interval distribution.The derivation equation of the relative weight of the evaluation indexui is(1)y¯i=12∑k=1nyik22−yik12∑k=1nyik2−yik1i=1,2,⋯,m;k=1,2,⋯,n.Considering the differences of academic achievement, work experience, and professional title among the members in the expert groups, the contribution degreeqk of each expert in the total weight is given, and ∑k=1nqk=1k=1,2,⋯,n; then the relative weight of the improved evaluation index ui is(2)y¯i=12∑k=1nqkyik22−yik12∑k=1nqkyik2−yik1,i=1,2,⋯,m;k=1,2,⋯,n.According to (2), the relative weight of each index ui in the factor set U can be calculated and then normalized, as shown in (3)w¯i=y¯i∑i=1myi.The weight vector of the overall evaluation system can be obtained:(4)W=w1,w2,⋯,wn.


## 3.3. Weight Reliability Inspection

For the indexes weight results obtained by the set-valued statistics method, this paper uses the interval variance method to determine its reliability [25]. For any index ui, its weight interval variance Si is defined as(5)Si=∑k=1nyik2−w¯i3−yik1−w¯i33∑k=1nyik2−yik1.i=1,2,⋯,m;k=1,2,⋯,n.where Si indicates the experts’ divergence of index ui. The larger Si is, the more divergent the experts' evaluation of index ui is, and the lower the reliability is. On the contrary, the smaller Si is, the smaller the experts' evaluation divergence on index ui is, and the higher the reliability is.


## 4. Cloud Model Theory

### 4.1. The Concept of the Cloud Model

#### 4.1.1. One-Dimensional Cloud Model

LetU be a quantitative domain represented by exact numerical value, and C is a qualitative concept on U. If the quantitative value x∈U and x is a random realization of the qualitative concept C and μx∈0,1, the certainty of x with respect to C will be a random number with stable tendency, the distribution of x on domain U is called a cloud, and each x is called a cloud droplet [26]. One-dimensional cloud models usually use numerical features Ex,En,He to express qualitative concepts quantitatively, in which the central value of domain is reflected by expectance Ex and the range of domain is reflected by entropy En and the uncertainty of entropy En is reflected by the hyperentropy He. The expected curve determined by the digital characteristics of the cloud model is(6)μi=exp−xi−Ex22Eni′2−,where μi is membership degree and Eni′ obeys normal distribution, which is Eni′∼NEn,He.


#### 4.1.2. Two-Dimensional Cloud Model

LetU be a two-dimensional domain and C is a qualitative concept on U. X can be considered as a random realization of the qualitative concept C in the domain. If xx1,x2∼NExEx1,Ex2En′En1′,En2′2 in which En′ obeys the normal distribution, the certainty of xx1,x2 with respect to C will be satisfied with(7)μi=exp−x1−Ex122En1i′2+x2−Ex222En2i′2.The distribution ofxx1,x2 in domain U is called two-dimensional normal cloud [27]. In the equation, the expectation Ex is the position of the centroid on the projection plane and the fuzziness, the boundary curve of projection, is reflected by entropy En1,En2 and the randomness and discreteness [28], thickness of the two-dimensional cloud model, are reflected by hyperentropy He1,He2.


### 4.2. Two-Dimensional Risk Cloud

Based on the one-dimensional cloud model, the concept of multidimensional cloud model is introduced to describe the complex concepts under the synergistic action of multidimensional factors. The ecological security in the desert area is reflected by both the degree of natural damage during the sand-crossing expressway construction and the later remediation cost, so that the evaluation indexes are used as the measurement, and the ecological damage and remediation cost are selected as the two-dimensional basic variables of ecological risk evaluation. By inviting experts who have made ecological evaluation during project construction period to score and analyze the underlying indexes, a cloud drop will be formed for the natural damage degree and later remediation cost measured by each evaluation index, forming two-dimensional comprehensive risk cloud including each index’s damage situation cloud and remediation cost. The respective digital characteristics of ecological damage cloud and remediation cost cloud can be calculated by programing in MATLAB according to (7).(8)Ex=1q∑k=1qxk,En=π2×1q∑k=1qxk−Ex,He=1q−1∑i=1qxk−Ex2−En2,where Ex is the sample expectation; En is the entropy, which reflects the randomness of the sample information; He, the entropy of En, is called hyperentropy, which reflects the level of cloud droplets’ tightness in the cloud diagram; q is the number of samples; x is the expert's score on the sample.The comprehensive risk evaluation cloud is synthesized by both the digital feature matrix which belongs to the damage cloud and the remediation cost cloud of the first level ecological and the corresponding set-valued statistical weight matrix. Similarly, the first-level risk cloud is also synthesized by the second-risk cloud and its corresponding weight. The equation of synthesis is as follows:(9)C=w1,w2,⋯,wnEx1En1He1⋮⋮⋮ExnEnnHen=Ex′,En′,He′,where Ex′,En′,He′ is the digital characteristic of the previous level of risk cloud.


### 4.3. Standard Cloud Model

The standard cloud model refers to a reference cloud diagram that contrasts with the risk cloud under standard conditions. This paper divides the evaluation scores into 4 subintervalsLjmin,Ljmax according to the interval [1, 10] and then uses (9) to calculate the numerical characteristics of each subinterval.(10)Ex¯=Ljmax+Ljmin2,En¯=Ljmax−Ljmin6,He=k,where k is a constant and the value range is between 0.01 and 1. In this paper, according to the fuzzy threshold of the variable, the value of k is 0.01 according to experience [29].


#### 4.3.1. Ecological Damage Standard

The ecological damage has been classified after consulting the data and referring to the previous research results, and the specific situation is shown in Table1. The interval score and numerical characteristics of the grade are the same as those in Table 2.Table 2
Description of economic cost levels.
Evaluation criterionClassSpecific descriptionSubinterval scoreStandard digital featuresExcellentIVery economical, the cost is negligible[7.5, 10](8.75, 0.42, 0.01)GoodIIMore economical, moderate cost[5.0, 7.5](6.25, 0.42, 0.01)GeneralIIINot economical, the cost is close to rebuilding[2.5, 5.0](3.75, 0.42, 0.01)PoorIVRepair costs more than rebuilding[0.0, 2.5](1.25, 0.42, 0.01)


#### 4.3.2. Remediation Cost Standard

Ecoenvironment remediation costs are economic descriptions, and the interval scores and numerical characteristics of their cost levels are shown in Table2.


### 4.4. Two-Dimensional Cloud Generator

Cloud model generator is a concrete representation method of cloud. The two-dimensional cloud model is constructed by two sets of digital characteristicEx,EnandHe representing two qualitative concepts and describes complex concepts under the synergy of multidimensional factors [30]. The two-dimensional evaluation cloud images are produced by the positive cloud generator in MATLAB, and the key process is shown in Figure 3.Figure 3
Two-dimensional positive cloud generator.The specific algorithm of two-dimensional cloud generator is as follows:Input: parameters of the two-dimensional cloud model, expectationEx1,Ex2, entropy En1,En2, hyperentropy HeHe1,He2, and the number of cloud droplets N.Output:N three-dimensional points dropxi,yi,μi, i=1,2,⋯,N.(1)
Generate the two-dimensional normal random numberEn′En1′,En2′ in which the mathematical expectation is En1,En2 and the standard deviation is HeHe1,He2.(2)
Generate the two-dimensional normal random numberxx1,x2 in which the mathematical expectation is Ex1,Ex2 and the standard deviation is En′En1′,En2′ which is calculated in the last step.(3)
Calculateμi=exp−x1−Ex12/2En1i′2+x2−Ex22/2En2i′2, and get a cloud droplet x1,x2,μi.(4)
Set the numberN of cloud droplets generated in the algorithm, and repeat Steps 1–3. The algorithm stops until generating N cloud droplets.


### 4.5. Similarity of the Cloud Model

The similarity between the evaluation result cloud image and the standard cloud image affects distinguishing the risk level directly. According to the similarity measurement method of cloud model introduced in literature [31–33] and considering the risk factors and structural characteristics of the evaluation object in this paper, the similarity calculation equation in literature [34] is adopted.(11)SD=1Ex¯−Ex2+Ex′¯−Ex′2,where SD is the nearness degree between clouds; Ex and Ey are the expected values of the ecological damage level and remediation cost level of the comprehensive risk cloud; Ex¯ and Ey¯ are the expected values of the ecological damage level and remediation cost level of the standard cloud, respectively.


## 4.1. The Concept of the Cloud Model

### 4.1.1. One-Dimensional Cloud Model

LetU be a quantitative domain represented by exact numerical value, and C is a qualitative concept on U. If the quantitative value x∈U and x is a random realization of the qualitative concept C and μx∈0,1, the certainty of x with respect to C will be a random number with stable tendency, the distribution of x on domain U is called a cloud, and each x is called a cloud droplet [26]. One-dimensional cloud models usually use numerical features Ex,En,He to express qualitative concepts quantitatively, in which the central value of domain is reflected by expectance Ex and the range of domain is reflected by entropy En and the uncertainty of entropy En is reflected by the hyperentropy He. The expected curve determined by the digital characteristics of the cloud model is(6)μi=exp−xi−Ex22Eni′2−,where μi is membership degree and Eni′ obeys normal distribution, which is Eni′∼NEn,He.


### 4.1.2. Two-Dimensional Cloud Model

LetU be a two-dimensional domain and C is a qualitative concept on U. X can be considered as a random realization of the qualitative concept C in the domain. If xx1,x2∼NExEx1,Ex2En′En1′,En2′2 in which En′ obeys the normal distribution, the certainty of xx1,x2 with respect to C will be satisfied with(7)μi=exp−x1−Ex122En1i′2+x2−Ex222En2i′2.The distribution ofxx1,x2 in domain U is called two-dimensional normal cloud [27]. In the equation, the expectation Ex is the position of the centroid on the projection plane and the fuzziness, the boundary curve of projection, is reflected by entropy En1,En2 and the randomness and discreteness [28], thickness of the two-dimensional cloud model, are reflected by hyperentropy He1,He2.


## 4.1.1. One-Dimensional Cloud Model

LetU be a quantitative domain represented by exact numerical value, and C is a qualitative concept on U. If the quantitative value x∈U and x is a random realization of the qualitative concept C and μx∈0,1, the certainty of x with respect to C will be a random number with stable tendency, the distribution of x on domain U is called a cloud, and each x is called a cloud droplet [26]. One-dimensional cloud models usually use numerical features Ex,En,He to express qualitative concepts quantitatively, in which the central value of domain is reflected by expectance Ex and the range of domain is reflected by entropy En and the uncertainty of entropy En is reflected by the hyperentropy He. The expected curve determined by the digital characteristics of the cloud model is(6)μi=exp−xi−Ex22Eni′2−,where μi is membership degree and Eni′ obeys normal distribution, which is Eni′∼NEn,He.


## 4.1.2. Two-Dimensional Cloud Model

LetU be a two-dimensional domain and C is a qualitative concept on U. X can be considered as a random realization of the qualitative concept C in the domain. If xx1,x2∼NExEx1,Ex2En′En1′,En2′2 in which En′ obeys the normal distribution, the certainty of xx1,x2 with respect to C will be satisfied with(7)μi=exp−x1−Ex122En1i′2+x2−Ex222En2i′2.The distribution ofxx1,x2 in domain U is called two-dimensional normal cloud [27]. In the equation, the expectation Ex is the position of the centroid on the projection plane and the fuzziness, the boundary curve of projection, is reflected by entropy En1,En2 and the randomness and discreteness [28], thickness of the two-dimensional cloud model, are reflected by hyperentropy He1,He2.


## 4.2. Two-Dimensional Risk Cloud

Based on the one-dimensional cloud model, the concept of multidimensional cloud model is introduced to describe the complex concepts under the synergistic action of multidimensional factors. The ecological security in the desert area is reflected by both the degree of natural damage during the sand-crossing expressway construction and the later remediation cost, so that the evaluation indexes are used as the measurement, and the ecological damage and remediation cost are selected as the two-dimensional basic variables of ecological risk evaluation. By inviting experts who have made ecological evaluation during project construction period to score and analyze the underlying indexes, a cloud drop will be formed for the natural damage degree and later remediation cost measured by each evaluation index, forming two-dimensional comprehensive risk cloud including each index’s damage situation cloud and remediation cost. The respective digital characteristics of ecological damage cloud and remediation cost cloud can be calculated by programing in MATLAB according to (7).(8)Ex=1q∑k=1qxk,En=π2×1q∑k=1qxk−Ex,He=1q−1∑i=1qxk−Ex2−En2,where Ex is the sample expectation; En is the entropy, which reflects the randomness of the sample information; He, the entropy of En, is called hyperentropy, which reflects the level of cloud droplets’ tightness in the cloud diagram; q is the number of samples; x is the expert's score on the sample.The comprehensive risk evaluation cloud is synthesized by both the digital feature matrix which belongs to the damage cloud and the remediation cost cloud of the first level ecological and the corresponding set-valued statistical weight matrix. Similarly, the first-level risk cloud is also synthesized by the second-risk cloud and its corresponding weight. The equation of synthesis is as follows:(9)C=w1,w2,⋯,wnEx1En1He1⋮⋮⋮ExnEnnHen=Ex′,En′,He′,where Ex′,En′,He′ is the digital characteristic of the previous level of risk cloud.


## 4.3. Standard Cloud Model

The standard cloud model refers to a reference cloud diagram that contrasts with the risk cloud under standard conditions. This paper divides the evaluation scores into 4 subintervalsLjmin,Ljmax according to the interval [1, 10] and then uses (9) to calculate the numerical characteristics of each subinterval.(10)Ex¯=Ljmax+Ljmin2,En¯=Ljmax−Ljmin6,He=k,where k is a constant and the value range is between 0.01 and 1. In this paper, according to the fuzzy threshold of the variable, the value of k is 0.01 according to experience [29].


### 4.3.1. Ecological Damage Standard

The ecological damage has been classified after consulting the data and referring to the previous research results, and the specific situation is shown in Table1. The interval score and numerical characteristics of the grade are the same as those in Table 2.Table 2
Description of economic cost levels.
Evaluation criterionClassSpecific descriptionSubinterval scoreStandard digital featuresExcellentIVery economical, the cost is negligible[7.5, 10](8.75, 0.42, 0.01)GoodIIMore economical, moderate cost[5.0, 7.5](6.25, 0.42, 0.01)GeneralIIINot economical, the cost is close to rebuilding[2.5, 5.0](3.75, 0.42, 0.01)PoorIVRepair costs more than rebuilding[0.0, 2.5](1.25, 0.42, 0.01)


### 4.3.2. Remediation Cost Standard

Ecoenvironment remediation costs are economic descriptions, and the interval scores and numerical characteristics of their cost levels are shown in Table2.


## 4.3.1. Ecological Damage Standard

The ecological damage has been classified after consulting the data and referring to the previous research results, and the specific situation is shown in Table1. The interval score and numerical characteristics of the grade are the same as those in Table 2.Table 2
Description of economic cost levels.
Evaluation criterionClassSpecific descriptionSubinterval scoreStandard digital featuresExcellentIVery economical, the cost is negligible[7.5, 10](8.75, 0.42, 0.01)GoodIIMore economical, moderate cost[5.0, 7.5](6.25, 0.42, 0.01)GeneralIIINot economical, the cost is close to rebuilding[2.5, 5.0](3.75, 0.42, 0.01)PoorIVRepair costs more than rebuilding[0.0, 2.5](1.25, 0.42, 0.01)


## 4.3.2. Remediation Cost Standard

Ecoenvironment remediation costs are economic descriptions, and the interval scores and numerical characteristics of their cost levels are shown in Table2.


## 4.4. Two-Dimensional Cloud Generator

Cloud model generator is a concrete representation method of cloud. The two-dimensional cloud model is constructed by two sets of digital characteristicEx,EnandHe representing two qualitative concepts and describes complex concepts under the synergy of multidimensional factors [30]. The two-dimensional evaluation cloud images are produced by the positive cloud generator in MATLAB, and the key process is shown in Figure 3.Figure 3
Two-dimensional positive cloud generator.The specific algorithm of two-dimensional cloud generator is as follows:Input: parameters of the two-dimensional cloud model, expectationEx1,Ex2, entropy En1,En2, hyperentropy HeHe1,He2, and the number of cloud droplets N.Output:N three-dimensional points dropxi,yi,μi, i=1,2,⋯,N.(1)
Generate the two-dimensional normal random numberEn′En1′,En2′ in which the mathematical expectation is En1,En2 and the standard deviation is HeHe1,He2.(2)
Generate the two-dimensional normal random numberxx1,x2 in which the mathematical expectation is Ex1,Ex2 and the standard deviation is En′En1′,En2′ which is calculated in the last step.(3)
Calculateμi=exp−x1−Ex12/2En1i′2+x2−Ex22/2En2i′2, and get a cloud droplet x1,x2,μi.(4)
Set the numberN of cloud droplets generated in the algorithm, and repeat Steps 1–3. The algorithm stops until generating N cloud droplets.


## 4.5. Similarity of the Cloud Model

The similarity between the evaluation result cloud image and the standard cloud image affects distinguishing the risk level directly. According to the similarity measurement method of cloud model introduced in literature [31–33] and considering the risk factors and structural characteristics of the evaluation object in this paper, the similarity calculation equation in literature [34] is adopted.(11)SD=1Ex¯−Ex2+Ex′¯−Ex′2,where SD is the nearness degree between clouds; Ex and Ey are the expected values of the ecological damage level and remediation cost level of the comprehensive risk cloud; Ex¯ and Ey¯ are the expected values of the ecological damage level and remediation cost level of the standard cloud, respectively.


## 5. Case Study and Result Analysis

### 5.1. Project Overview

The Qingtongxia-Zhongwei section of the Uma Expressway is China’s first high-grade expressway crossing the desert hinterland. The project is initiated by Ningxia Department of transportation “research on key technologies of expressway construction in desert hinterland based on green ecological principle.” In the way of monitoring and analyzing the ecological environment and the current situation of wind and sand in the desert areas, the ecological balance and high-level construction quality along the expressway can be ensured.At present, from the ecological environment investigation, wind sand movement monitoring, and geological survey in the project layout area [35] mastering its environmental characteristics, two route schemes, A and B, are proposed to cross the hinterland of Tengger Desert in Zhongwei section (Figure 4). Therefore, according to the actual situation of the project and the requirements of the subject, the two-dimensional cloud model established is used to evaluate the ecological environment risk of different schemes in this paper.Figure 4
Geographical location of the Uma Expressway. (a) Line route. (b) Geomorphic environment of aeolian sand.Scheme A. The starting point of the route is connected with Qingtongxia section. Pass through Tengger Desert from west to southwest, successively go by mobile dunes, flat sand land, and proluvial-alluvial plain in front of mountains, and finally end at Dingbian-Wuwei Expressway (about 1.5 km away from Hongwei station). A viewing platform covering an area of 25 mu is set on the way, which is 5 km away from Shapotou tourist area in the east and 9 km away from Tonghu Grassland scenic area in Inner Mongolia in the west.Scheme B. An interchange is set up at the end of the Qingtongxia section, and the route is built along the Yingyan Expressway to the south. After a short distance through the exposed desert area, it crosses the Baotou-Lanzhou Railway and connects to the Dingbian-Wuwei Expressway. On the way, it crosses the Shapotou scenic Area and the Yellow River and is adjacent to the Shapotou Water Source Protection Area at the end point.


### 5.2. Determining Indexes’ Weight

According to the ecological risk assessment index system established in this paper, there are 5 indexes in the first layer and 18 indexes in the second layer. Set-valued statistics method is used to determine the weights of evaluation index system. For the convenience of each evaluation index weight range of evaluation experts giving, the sum of all the index weights is set to 10. With a total of six experts participating in the evaluation, it is concluded that the weight of each expert itself forK = (0.115, 0.225, 0.155, 0.245, 0.135, 0.125) through comprehensive assessment of each expert to the site ability and their education level. The interval estimates of evaluation indicators are shown in Table 3.Table 3
The weight range of assessment indexes.
Evaluation expertsWeight of evaluation expertsEvaluation indexes’ weight intervalU1U2U3U4U5P10.115[1.4, 1.9][2.0, 2.2][1.8, 2.0][0.8, 1.2][1.5, 1.8]P20.225[1.2, 1.7][1.5, 1.7][1.1, 1.6][1.2, 1.5][1.4, 1.6]P30.155[1.3, 1.6][1.3, 1.8][1.3, 1.7][1.1, 1.5][1.5, 1.9]P40.245[1.7, 2.1][1.5, 2.1][1.7, 2.0][1.3, 1.8][1.2, 1.5]P50.135[1.3, 1.7][1.2, 1.6][1.2, 1.5][1.1, 1.6][1.0, 1.2]P60.125[1.4, 1.8][1.3, 1.7][1.7, 2.1][1.7, 2.1][1.3, 1.6]According to equation (2), the relative weight of each evaluation index Uii=1,2,⋯,5 is ω=1.607,1.654,1.589,1.429,1.478. Equation (3) is used to normalize it, and the weight of each level evaluation index Uii=1,2,⋯,5 is W = (0.207, 0.213, 0.205, 0.184, 0.191).Similarly, the weights of the secondary index are calculated. The calculated results are as follows:W1 = (0.271, 0.241, 0.239, 0.249)W2 = (0.374, 0.312, 0.314)W3 = (0.202, 0.336, 0.243, 0.219)W4 = (0.341, 0.311, 0.348)W5 = (0.241, 0.293, 0.226, 0.240)According to equation (5), the variance of each index Uii=1,2,⋯,5 can be calculated, which is d = (0.039, 0.058, 0.073, 0.088, 0.044). According to the calculation results, the value of S4 is relatively large, indicating that the reliability of evaluation index U4 is relatively low, but on the whole each index’s variances of all indexes are less than 0.1, indicating that experts have relatively consistent opinions on weight evaluation.


### 5.3. The Process of Two-Dimensional Cloud Evaluation

Six experts from Ningxia Highway Survey and Design Institute and universities are invited to participate in the evaluation of the route scheme. In accordance with the importance of each index, the ecological damage consequence and remediation cost of each index in the ecological risk evaluation system of expressway construction are scored in the four grades in Tables1 and 2. Taking scheme A as an example, score X is shown in Table 4.Table 4
Grading values of ecological damage consequence and remediation cost.
Risk indexesX1/X1′X2/X2′X3/X3′X4/X4′X5/X5′X6/X6′U115.1/6.25.8/5.55.7/6.95.2/6.16.1/5.75.0/6.5U124.5/5.53.5/4.54.2/3.45.0/3.93.9/3.64.1/3.7U135.4/5.76.0/6.25.3/6.75.8/6.54.9/6.55.1/6.4U144.1/6.54.7/6.74.2/7.04.5/6.44.1/6.53.8/6.4U218.1/8.38.2/8.07.9/7.98.0/7.76.9/8.18.1/8.0U227.7/7.47.4/7.76.9/7.57.6/7.67.0/7.47.1/7.1U237.9/8.15.9/8.07.1/7.66.5/7.46.7/8.17.3/7.9U317.5/8.07.9/7.87.7/7.77.7/8.07.5/7.97.5/7.1U327.5/8.17.6/7.58.1/8.07.9/7.98.0/7.47.7/7.6U336.6/5.97.0/4.97.1/5.16.9/4.77.4/5.07.2/5.5U347.1/6.96.4/6.56.1/6.76.3/6.16.1/6.46.6/6.5U418.0/7.78.8/7.18.5/7.58.4/7.48.9/7.68.4/8.1U426.5/6.85.8/7.15.7/6.95.9/6.56.1/6.35.5/7.3U437.4/5.37.6/6.77.5/6.58.1/7.17.2/6.97.5/5.9U444.5/5.15.2/4.64.1/5.14.7/4.14.5/4.94.4/5.0U517.2/6.57.6/6.18.1/7.07.7/6.57.5/6.17.7/6.6U525.1/5.14.9/5.55.0/4.94.5/4.24.3/5.14.6/4.4U535.5/6.25.1/5.46.1/5.95.2/5.55.4/5.15.1/5.4Note. Xi and Xi′ are ecological damage consequences and remediation cost values, respectively.The description of the evaluation indexes is transformed into an interval value by the set-valued statistics method. Then the weight of each evaluation index is determined according to equations (2) and (5) and the reliability is tested. The digital characteristics of the ecological damage cloud and remediation cost cloud of the secondary evaluation indexes can be obtained by applying (7). The digital characteristics of the primary risk cloud can be obtained through the way which applies equation (8) to the digital characteristics of the secondary evaluation cloud and its corresponding weight matrix. Furthermore, the digital characteristics of the comprehensive risk cloud could be obtained. Finally, the weight results and digital characteristics of the primary and secondary indexes are shown in Table 5.Table 5
Digital characteristics of environmental damage and remediation cost evaluation cloud.
Comprehensive risk cloudFirst-level risk cloudSecond-level risk cloudSchemeEcological damageRemediation costFirst-level indexesWeightEcological damageRemediation costSecond-level indexesWeightEcological damageRemediation costU(6.513, 0.350, 0.309)(6.589, 0.357, 0.308)U10.207(4.847, 0.414, 0.368)(5.808, 0.443, 0.339)U110.056(5.483, 0.480, 0.438)(6.150, 0.480, 0.402)U120.050(4.200, 0.460, 0.376)(4.101, 0.752, 0.437)U130.049(5.417, 0.404, 0.365)(6.333, 0.320, 0.296)U140.052(4.233, 0.306, 0.289)(6.583, 0.223, 0.216)U20.213(7.381, 0.472, 0.374)(7.781, 0.213, 0.206)U210.080(7.867, 0.404, 0.329)(8.001, 0.167, 0.162)U220.066(7.283, 0.355, 0.338)(7.450, 0.188, 0.183)U230.067(6.901, 0.668, 0.465)(7.851, 0.292, 0.280)U30.205(7.281, 0.255, 0.243)(6.856, 0.321, 0.299)U310.041(7.633, 0.167, 0.165)(7.750, 0.292, 0.269)U320.069(7.801, 0.251, 0.244)(7.750, 0.313, 0.302)U330.050(7.033, 0.251, 0.239)(5.183, 0.432, 0.386)U340.045(6.433, 0.348, 0.318)(6.517, 0.237, 0.225)U40.184(7.366, 0.287, 0.267)(6.927, 0.443, 0.363)U410.063(8.501, 0.292, 0.273)(7.567, 0.292, 0.271)U420.057(5.917, 0.320, 0.296)(6.817, 0.355, 0.327)U430.064(7.550, 0.251, 0.234)(6.401, 0.668, 0.485)U50.191(5.703, 0.306, 0.284)(5.491, 0.381, 0.345)U510.046(4.567, 0.320, 0.291)(4.801, 0.376, 0.344)U520.056(7.633, 0.251, 0.235)(6.467, 0.306, 0.284)U530.043(4.733, 0.334, 0.319)(4.867, 0.473, 0.411)U540.046(5.401, 0.334, 0.302)(5.583, 0.390, 0.357)In order to determine the detailed indexes evaluation nephogram of the two schemes, there are four first-level evaluation indexes selected to illustrate: interference of living environment of wild animals and plantsU1, destruction of natural ecological landscape U2, pollution of water and soil resources U3, and exploitation of natural resources U4. The comparison diagram of the first level risk cloud and the standard risk cloud with the same index of different schemes, as shown in Figure 5, is generated by inputting the digital characteristics of the risk cloud of schemes A and B, respectively, into the MATLAB positive cloud generator.Figure 5
First-level indexes’ risk cloud. (a) Disturbance of the living environment of wild animals and plants. (b) Destruction of natural ecological landscape. (c) Pollution of water and soil resources. (d) Development and utilization of natural resources.
(a)(b)(c)(d)In terms of the interference of wild animals’ and plants’ living environment, the total length of plan B is 15.6 km, and the sand-crossing length accounts for 60% of the total expressway mileage. Most of the expressway is within the range of human activities, and there are few wild animals and plants. Plan A’s total length is 28.58 km, of which the sand-crossing length accounts for more than 85%. Long sand-crossing mileage of the expressway impedes the normal growth and prevailing of wild animals and plants in the desert. When the route was being designed, there would be several small culverts for wildlife’s normal traffic back to habitat and there would be protective fences among the plants along the wild, thus contributing to an increase in the cost of ecological remediation in Plan A. However, in fact, there are few wild animals and plants in the desert and the remediation scope is only a small part, which explains why, compared with Plan B, Plan A in the figure has greater interference in the wild animals and plants environment, but Plan A is still acceptable in terms of remediation cost.In terms of the natural landscape, a wide gulf about ecological damage and repair costs exists between the two schemes. Plan B crosses the river directly to reach the south Dingbian-Wuwei Expressway. Although the regular expressway length is short, ecologically sensitive areas are dense along the road. The road across the sand area enters the buffer zone of Zhongwei Shapotou National Reserve, only 5 km away from the core area, and the road was heading south close to the water reserve. The construction of roads has greatly damaged the closure of Zhongwei Shapotou National Reserve and the safety of water source protection area and later ecological remediation costs are huge nearly to the cost of reconstruction. In order to avoid passing through the core area and buffer zone of ecologically sensitive areas, Plan A detoured southwest, thus passing through more areas where wild plants and animals live and costing less to restore ecology and protecting the ecological equilibrium and the safety of Zhongwei Shapotou National Reserve and the water reserve effectively.In terms of soil and water pollution, the study area belongs to arid region and semiarid region with less groundwater where the strata substance is mainly sand and breccia soil. In particular, there is 85% road of Plan A in desert areas where flat sand and mobile dunes are the majority and groundwater resources are scarce and deeply buried, thus contributing to the situation that the road has less pollution to water and soil resources in general. The first half of the road in Plan B is in the flat sand area. Although the second half of the road does not pass through the reservoir water source area directly, the road is nearly to the reservoir water source area and crosses the Yellow River at the end point. Therefore, external factors such as road construction can destroy the original ecological environment of the water source easily and can cause a certain degree of pollution to water and soil resources.In the terms of development and utilization of natural resources, constructing Plan A can have an advantage in the development of new energy and tourism resources. The road in Plan A across the desert hinterland where the light source is adequate is an optimal location of light energy resources utilization. Due to the road alignment, if the same scale light source base is developed in Plan B, it will be unavoidable to destroy the planted forest leading to the destruction of the ecological environment, which is reflected in theU4 risk cloud. In addition, in view of the impact of sand erosion, the utilization of wind power energy should be reduced.


### 5.4. Evaluation Results

A comparison chart of the comprehensive risk cloud of the route scheme and the standard cloud can be obtained by using the MATLAB positive cloud generator to input the digital characteristics of the risk cloud in Table5. It can be seen from Figure 6 that the advantages and disadvantages of the two schemes are very clear . But reduction in the speed of desertification is guaranteed to a great extent by the balance of the ecological environment in the desert area. Despite the short length of scheme B’s regular line and the short sand-crossing length, it passes through dense ecological sensitive areas in the region, and the road construction greatly damages both the closure of Shapotou scene spot and the safety of water source protection area. In order to avoid crossing the core area and buffer zone of ecologically sensitive areas, scheme A makes a detour to the southwest. With a large sand-crossing length of regular line and the increased number of wild animals and plants, there will be an inevitable increase of the sand prevention’s cost in the later period. However, the ecological balance and safety of Shapotou scenic area and water source protection area are protected effectively. What is mentioned above explains the reason for the difference of risk clouds in the aspects of direct damage to ecological environment caused by road construction in the two schemes.Figure 6
Comparison of the comprehensive risk cloud of schemes A and B.It can be illustrated from Figures6 and 7 that scheme A is between good and excellent, closer to good, while scheme B is between general and good, closer to general. In order to further determine the nearness degree between the comprehensive risk cloud and the standard cloud, (10) is applied for calculation. The results show that the ecological risk comprehensive evaluations of schemes A and B are “good” and “general,” respectively. Therefore, in accordance with the comparative analysis based on the calculation results, scheme A is more recommended as the implementation scheme for road construction, which is consistent with the choice of the actual engineering route scheme.Figure 7
Top view of the comprehensive risk cloud of schemes A and B.


## 5.1. Project Overview

The Qingtongxia-Zhongwei section of the Uma Expressway is China’s first high-grade expressway crossing the desert hinterland. The project is initiated by Ningxia Department of transportation “research on key technologies of expressway construction in desert hinterland based on green ecological principle.” In the way of monitoring and analyzing the ecological environment and the current situation of wind and sand in the desert areas, the ecological balance and high-level construction quality along the expressway can be ensured.At present, from the ecological environment investigation, wind sand movement monitoring, and geological survey in the project layout area [35] mastering its environmental characteristics, two route schemes, A and B, are proposed to cross the hinterland of Tengger Desert in Zhongwei section (Figure 4). Therefore, according to the actual situation of the project and the requirements of the subject, the two-dimensional cloud model established is used to evaluate the ecological environment risk of different schemes in this paper.Figure 4
Geographical location of the Uma Expressway. (a) Line route. (b) Geomorphic environment of aeolian sand.Scheme A. The starting point of the route is connected with Qingtongxia section. Pass through Tengger Desert from west to southwest, successively go by mobile dunes, flat sand land, and proluvial-alluvial plain in front of mountains, and finally end at Dingbian-Wuwei Expressway (about 1.5 km away from Hongwei station). A viewing platform covering an area of 25 mu is set on the way, which is 5 km away from Shapotou tourist area in the east and 9 km away from Tonghu Grassland scenic area in Inner Mongolia in the west.Scheme B. An interchange is set up at the end of the Qingtongxia section, and the route is built along the Yingyan Expressway to the south. After a short distance through the exposed desert area, it crosses the Baotou-Lanzhou Railway and connects to the Dingbian-Wuwei Expressway. On the way, it crosses the Shapotou scenic Area and the Yellow River and is adjacent to the Shapotou Water Source Protection Area at the end point.


## 5.2. Determining Indexes’ Weight

According to the ecological risk assessment index system established in this paper, there are 5 indexes in the first layer and 18 indexes in the second layer. Set-valued statistics method is used to determine the weights of evaluation index system. For the convenience of each evaluation index weight range of evaluation experts giving, the sum of all the index weights is set to 10. With a total of six experts participating in the evaluation, it is concluded that the weight of each expert itself forK = (0.115, 0.225, 0.155, 0.245, 0.135, 0.125) through comprehensive assessment of each expert to the site ability and their education level. The interval estimates of evaluation indicators are shown in Table 3.Table 3
The weight range of assessment indexes.
Evaluation expertsWeight of evaluation expertsEvaluation indexes’ weight intervalU1U2U3U4U5P10.115[1.4, 1.9][2.0, 2.2][1.8, 2.0][0.8, 1.2][1.5, 1.8]P20.225[1.2, 1.7][1.5, 1.7][1.1, 1.6][1.2, 1.5][1.4, 1.6]P30.155[1.3, 1.6][1.3, 1.8][1.3, 1.7][1.1, 1.5][1.5, 1.9]P40.245[1.7, 2.1][1.5, 2.1][1.7, 2.0][1.3, 1.8][1.2, 1.5]P50.135[1.3, 1.7][1.2, 1.6][1.2, 1.5][1.1, 1.6][1.0, 1.2]P60.125[1.4, 1.8][1.3, 1.7][1.7, 2.1][1.7, 2.1][1.3, 1.6]According to equation (2), the relative weight of each evaluation index Uii=1,2,⋯,5 is ω=1.607,1.654,1.589,1.429,1.478. Equation (3) is used to normalize it, and the weight of each level evaluation index Uii=1,2,⋯,5 is W = (0.207, 0.213, 0.205, 0.184, 0.191).Similarly, the weights of the secondary index are calculated. The calculated results are as follows:W1 = (0.271, 0.241, 0.239, 0.249)W2 = (0.374, 0.312, 0.314)W3 = (0.202, 0.336, 0.243, 0.219)W4 = (0.341, 0.311, 0.348)W5 = (0.241, 0.293, 0.226, 0.240)According to equation (5), the variance of each index Uii=1,2,⋯,5 can be calculated, which is d = (0.039, 0.058, 0.073, 0.088, 0.044). According to the calculation results, the value of S4 is relatively large, indicating that the reliability of evaluation index U4 is relatively low, but on the whole each index’s variances of all indexes are less than 0.1, indicating that experts have relatively consistent opinions on weight evaluation.


## 5.3. The Process of Two-Dimensional Cloud Evaluation

Six experts from Ningxia Highway Survey and Design Institute and universities are invited to participate in the evaluation of the route scheme. In accordance with the importance of each index, the ecological damage consequence and remediation cost of each index in the ecological risk evaluation system of expressway construction are scored in the four grades in Tables1 and 2. Taking scheme A as an example, score X is shown in Table 4.Table 4
Grading values of ecological damage consequence and remediation cost.
Risk indexesX1/X1′X2/X2′X3/X3′X4/X4′X5/X5′X6/X6′U115.1/6.25.8/5.55.7/6.95.2/6.16.1/5.75.0/6.5U124.5/5.53.5/4.54.2/3.45.0/3.93.9/3.64.1/3.7U135.4/5.76.0/6.25.3/6.75.8/6.54.9/6.55.1/6.4U144.1/6.54.7/6.74.2/7.04.5/6.44.1/6.53.8/6.4U218.1/8.38.2/8.07.9/7.98.0/7.76.9/8.18.1/8.0U227.7/7.47.4/7.76.9/7.57.6/7.67.0/7.47.1/7.1U237.9/8.15.9/8.07.1/7.66.5/7.46.7/8.17.3/7.9U317.5/8.07.9/7.87.7/7.77.7/8.07.5/7.97.5/7.1U327.5/8.17.6/7.58.1/8.07.9/7.98.0/7.47.7/7.6U336.6/5.97.0/4.97.1/5.16.9/4.77.4/5.07.2/5.5U347.1/6.96.4/6.56.1/6.76.3/6.16.1/6.46.6/6.5U418.0/7.78.8/7.18.5/7.58.4/7.48.9/7.68.4/8.1U426.5/6.85.8/7.15.7/6.95.9/6.56.1/6.35.5/7.3U437.4/5.37.6/6.77.5/6.58.1/7.17.2/6.97.5/5.9U444.5/5.15.2/4.64.1/5.14.7/4.14.5/4.94.4/5.0U517.2/6.57.6/6.18.1/7.07.7/6.57.5/6.17.7/6.6U525.1/5.14.9/5.55.0/4.94.5/4.24.3/5.14.6/4.4U535.5/6.25.1/5.46.1/5.95.2/5.55.4/5.15.1/5.4Note. Xi and Xi′ are ecological damage consequences and remediation cost values, respectively.The description of the evaluation indexes is transformed into an interval value by the set-valued statistics method. Then the weight of each evaluation index is determined according to equations (2) and (5) and the reliability is tested. The digital characteristics of the ecological damage cloud and remediation cost cloud of the secondary evaluation indexes can be obtained by applying (7). The digital characteristics of the primary risk cloud can be obtained through the way which applies equation (8) to the digital characteristics of the secondary evaluation cloud and its corresponding weight matrix. Furthermore, the digital characteristics of the comprehensive risk cloud could be obtained. Finally, the weight results and digital characteristics of the primary and secondary indexes are shown in Table 5.Table 5
Digital characteristics of environmental damage and remediation cost evaluation cloud.
Comprehensive risk cloudFirst-level risk cloudSecond-level risk cloudSchemeEcological damageRemediation costFirst-level indexesWeightEcological damageRemediation costSecond-level indexesWeightEcological damageRemediation costU(6.513, 0.350, 0.309)(6.589, 0.357, 0.308)U10.207(4.847, 0.414, 0.368)(5.808, 0.443, 0.339)U110.056(5.483, 0.480, 0.438)(6.150, 0.480, 0.402)U120.050(4.200, 0.460, 0.376)(4.101, 0.752, 0.437)U130.049(5.417, 0.404, 0.365)(6.333, 0.320, 0.296)U140.052(4.233, 0.306, 0.289)(6.583, 0.223, 0.216)U20.213(7.381, 0.472, 0.374)(7.781, 0.213, 0.206)U210.080(7.867, 0.404, 0.329)(8.001, 0.167, 0.162)U220.066(7.283, 0.355, 0.338)(7.450, 0.188, 0.183)U230.067(6.901, 0.668, 0.465)(7.851, 0.292, 0.280)U30.205(7.281, 0.255, 0.243)(6.856, 0.321, 0.299)U310.041(7.633, 0.167, 0.165)(7.750, 0.292, 0.269)U320.069(7.801, 0.251, 0.244)(7.750, 0.313, 0.302)U330.050(7.033, 0.251, 0.239)(5.183, 0.432, 0.386)U340.045(6.433, 0.348, 0.318)(6.517, 0.237, 0.225)U40.184(7.366, 0.287, 0.267)(6.927, 0.443, 0.363)U410.063(8.501, 0.292, 0.273)(7.567, 0.292, 0.271)U420.057(5.917, 0.320, 0.296)(6.817, 0.355, 0.327)U430.064(7.550, 0.251, 0.234)(6.401, 0.668, 0.485)U50.191(5.703, 0.306, 0.284)(5.491, 0.381, 0.345)U510.046(4.567, 0.320, 0.291)(4.801, 0.376, 0.344)U520.056(7.633, 0.251, 0.235)(6.467, 0.306, 0.284)U530.043(4.733, 0.334, 0.319)(4.867, 0.473, 0.411)U540.046(5.401, 0.334, 0.302)(5.583, 0.390, 0.357)In order to determine the detailed indexes evaluation nephogram of the two schemes, there are four first-level evaluation indexes selected to illustrate: interference of living environment of wild animals and plantsU1, destruction of natural ecological landscape U2, pollution of water and soil resources U3, and exploitation of natural resources U4. The comparison diagram of the first level risk cloud and the standard risk cloud with the same index of different schemes, as shown in Figure 5, is generated by inputting the digital characteristics of the risk cloud of schemes A and B, respectively, into the MATLAB positive cloud generator.Figure 5
First-level indexes’ risk cloud. (a) Disturbance of the living environment of wild animals and plants. (b) Destruction of natural ecological landscape. (c) Pollution of water and soil resources. (d) Development and utilization of natural resources.
(a)(b)(c)(d)In terms of the interference of wild animals’ and plants’ living environment, the total length of plan B is 15.6 km, and the sand-crossing length accounts for 60% of the total expressway mileage. Most of the expressway is within the range of human activities, and there are few wild animals and plants. Plan A’s total length is 28.58 km, of which the sand-crossing length accounts for more than 85%. Long sand-crossing mileage of the expressway impedes the normal growth and prevailing of wild animals and plants in the desert. When the route was being designed, there would be several small culverts for wildlife’s normal traffic back to habitat and there would be protective fences among the plants along the wild, thus contributing to an increase in the cost of ecological remediation in Plan A. However, in fact, there are few wild animals and plants in the desert and the remediation scope is only a small part, which explains why, compared with Plan B, Plan A in the figure has greater interference in the wild animals and plants environment, but Plan A is still acceptable in terms of remediation cost.In terms of the natural landscape, a wide gulf about ecological damage and repair costs exists between the two schemes. Plan B crosses the river directly to reach the south Dingbian-Wuwei Expressway. Although the regular expressway length is short, ecologically sensitive areas are dense along the road. The road across the sand area enters the buffer zone of Zhongwei Shapotou National Reserve, only 5 km away from the core area, and the road was heading south close to the water reserve. The construction of roads has greatly damaged the closure of Zhongwei Shapotou National Reserve and the safety of water source protection area and later ecological remediation costs are huge nearly to the cost of reconstruction. In order to avoid passing through the core area and buffer zone of ecologically sensitive areas, Plan A detoured southwest, thus passing through more areas where wild plants and animals live and costing less to restore ecology and protecting the ecological equilibrium and the safety of Zhongwei Shapotou National Reserve and the water reserve effectively.In terms of soil and water pollution, the study area belongs to arid region and semiarid region with less groundwater where the strata substance is mainly sand and breccia soil. In particular, there is 85% road of Plan A in desert areas where flat sand and mobile dunes are the majority and groundwater resources are scarce and deeply buried, thus contributing to the situation that the road has less pollution to water and soil resources in general. The first half of the road in Plan B is in the flat sand area. Although the second half of the road does not pass through the reservoir water source area directly, the road is nearly to the reservoir water source area and crosses the Yellow River at the end point. Therefore, external factors such as road construction can destroy the original ecological environment of the water source easily and can cause a certain degree of pollution to water and soil resources.In the terms of development and utilization of natural resources, constructing Plan A can have an advantage in the development of new energy and tourism resources. The road in Plan A across the desert hinterland where the light source is adequate is an optimal location of light energy resources utilization. Due to the road alignment, if the same scale light source base is developed in Plan B, it will be unavoidable to destroy the planted forest leading to the destruction of the ecological environment, which is reflected in theU4 risk cloud. In addition, in view of the impact of sand erosion, the utilization of wind power energy should be reduced.


## 5.4. Evaluation Results

A comparison chart of the comprehensive risk cloud of the route scheme and the standard cloud can be obtained by using the MATLAB positive cloud generator to input the digital characteristics of the risk cloud in Table5. It can be seen from Figure 6 that the advantages and disadvantages of the two schemes are very clear . But reduction in the speed of desertification is guaranteed to a great extent by the balance of the ecological environment in the desert area. Despite the short length of scheme B’s regular line and the short sand-crossing length, it passes through dense ecological sensitive areas in the region, and the road construction greatly damages both the closure of Shapotou scene spot and the safety of water source protection area. In order to avoid crossing the core area and buffer zone of ecologically sensitive areas, scheme A makes a detour to the southwest. With a large sand-crossing length of regular line and the increased number of wild animals and plants, there will be an inevitable increase of the sand prevention’s cost in the later period. However, the ecological balance and safety of Shapotou scenic area and water source protection area are protected effectively. What is mentioned above explains the reason for the difference of risk clouds in the aspects of direct damage to ecological environment caused by road construction in the two schemes.Figure 6
Comparison of the comprehensive risk cloud of schemes A and B.It can be illustrated from Figures6 and 7 that scheme A is between good and excellent, closer to good, while scheme B is between general and good, closer to general. In order to further determine the nearness degree between the comprehensive risk cloud and the standard cloud, (10) is applied for calculation. The results show that the ecological risk comprehensive evaluations of schemes A and B are “good” and “general,” respectively. Therefore, in accordance with the comparative analysis based on the calculation results, scheme A is more recommended as the implementation scheme for road construction, which is consistent with the choice of the actual engineering route scheme.Figure 7
Top view of the comprehensive risk cloud of schemes A and B.


## 6. Discussion

It is difficult to make an equivocal determination of the route direction for many causes involved in the selection of route schemes and there is no clear distinction between the advantages and disadvantages. There is a certain degree of fuzziness in the comparison between the schemes [36] because each route scheme has its own characteristics, and there are no uniform and standardized constraints to measure it. The reason why the fragile ecological environment in the desert area is selected as the key evaluation factor in the selection of the scheme is that the destruction of the ecological environment has a serious impact on that sand reacting upon the road adversely. Many countries have also carried out systematic ecological evaluation before or after the construction of sand-crossing traffic projects. Therefore, by virtue of having the insight of the special geographical environment and road construction characteristics, this paper evaluates the route schemes from two aspects, ecological damage and remediation cost.Taking the systematic nature of expressway engineering into consideration, only a complete index system has been established which can make the actual project be reflected scientifically and reasonably. After the research, this paper selects 18 secondary indexes which are the most representative. Generally, the more abundant the evaluation indexes selected are, the more truly the actual projects are presented, so that the more scientific evaluation results can be produced. However, too many indexes would lead to the loss of the mutual independence and reduce the scientificity of the evaluation easily and a more complete evaluation model needs to be further studied.


## 7. Conclusion

(1)
The aim of this paper is to research the risk evaluation of expressway schemes based on ecological balance in desert areas. Through having the insight of the unique geographical environment and engineering characteristics of the area, the ecological risk comprehensive evaluation index system of sand-crossing expressway is established based on the principle which puts the equal emphasis on engineering technology and ecological environment protection.(2)
The issue of the uncertainty and randomness of the quantitative evaluation indexes can be solved through combing the set-valued statistics method and the two-dimensional cloud evaluation theory. Using the positive cloud generator of MATLAB, the ecological situation along the sand-crossing road can be evaluated from two aspects, ecological damage and remediation cost, and the risk cloud map is able to be output to reflect the ecological risk level of the two schemes directly.(3)
The ecological risk evaluation results obtained from the two-dimensional cloud model are consistent with the actual project, which not only proves the operability and applicability of the evaluation model but also provides a theoretical basis for the Uma Expressway that is being built in the sand-crossing section of Zhongwei; this method can be applied in practical engineering.



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*Source: 1361861-2022-03-10.xml*