Research Article Uncertainty Analysis for Natural Gas Transport Pipeline Network Layout: a New Methodology Based on Monte Carlo Method

Hindawi Journal of Advanced Transportation Volume 2018, Article ID 9213648, 10 pages https://doi.org/10.1155/2018/9213648

Research Article Uncertainty Analysis for Natural Gas Transport Pipeline Network Layout: A New Methodology Based on Monte Carlo Method

Jun Zeng ,1,2 Chaoxu Sun ,3 Zhenjun Zhu ,1,4 Jiangling Wu,5 and Hongsheng Chen6

1 School of Transportation, Southeast University, Nanjing 211189, China 2DepartmentofCivil,ArchitecturalandEnvironmentalEngineering,TeUniversityofTexasatAustin,Austin,TX78712,USA 3Zhejiang Provincial Natural Gas Development Co. Ltd., Hangzhou 310052, China 4Department of City and Regional Planning, University of California, Berkeley, Berkeley, CA 94720, USA 5School of Civil Engineering and Architecture, Henan University, Kaifeng 475004, China 6School of Architecture, Southeast University, Nanjing 210096, China

Correspondence should be addressed to Zhenjun Zhu; [email protected]

Received 2 November 2017; Revised 6 April 2018; Accepted 10 April 2018; Published 23 May 2018

Academic Editor: Zhi-Chun Li

Copyright © 2018 Jun Zeng et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Natural gas plays an increasing important role in the China’s energy revolution. Te rapid market development and refned government regulation demand improvements in the natural gas transport pipeline network. Terefore, it is of great theoretical and practical signifcance to conduct a study regarding the layout of pipeline networks. To refect the comprehensive benefts of pipeline projects and obtain global optimal solution, this study introduces the dominance degree model (DDM). Aiming at optimizing the layout of natural gas transport pipeline networks, this paper studies the uncertainty of the DDM and the corresponding method for network layout. Tis study proposes an uncertainty analysis based on the Monte Carlo method to quantify the uncertainty of the DDM and its infuential factors. Finally, the methodology is appliedtotherealcaseofanaturalgastransportpipelineproject in Zhejiang Province, China. Te calculation results suggest that the methodology appropriately addresses the problem of pipeline network layout for natural gas transport. Tis has important implications for other potential pipeline networks not only in the Zhejiang Province but also throughout China and beyond.

1. Introduction the overall regional socioeconomic conditions. Although pipeline projects require a large investment and have a long Natural gas is an efcient and clean energy source that can be payback period, the gas market is exhibiting a dynamic utilised in the production of low-carbon energy consumption development trend [2]. Terefore, when planning the pipeline [1]. According to China’s energy development strategic plan network, the benefts from investments on pipeline projects, and natural gas transport pipeline network plan, the share of construction costs, other infuential factors, and the impact natural gas in the primary energy consumption will continue of uncertainty should be considered to determine the optimal to increase up to 10% by 2020, while the total length of layout scheme. natural gas pipelines is planned to reach 104,000 km. Driven Previous studies on the layout of natural gas transport by the continued growth of consumption and infrastructure pipeline networks have proposed several methods based on strengthening, the trunk pipeline coverage will be further pipeline network topology, such as graph theory, dynamic expanded and the regional gas transport pipeline network programming, neural networks, genetic algorithms, and will be improved. complex methods [3, 4]. Tese methods essentially solve the Te natural gas transport pipeline network is tasked with network structure to satisfy a given criterion and focus on gas distribution, which plays a signifcant role in improving mathematical optimization [5, 6]. Te minimum spanning 2 Journal of Advanced Transportation

Table 1: Advantages and limitations of existing methods.

Methods Advantages Limitations Easy access to computer program Only solves the network layout among known fxed processing; higher computing efciency; points; project investment costs are not considered; Graph Teory efectively solving the shortest tree problem solutions can only be used as the initial network within a large scale network layout Not suitable for dealing with large-scale network Solving optimization problems with Dynamic Programming systems, dimension obstacles exist in solution multiple decision-making variables process Solving optimization problems with Neural Network Method Only obtaining the local optimal solution multiple decision-making variables Lower computing efciency; no efective quantitative Higher adaptability that can overcome the Genetic Algorithm analysis concerning algorithm precision, feasibility difculties of solving nonlinear optimization and computational complexity Te algorithm is simple and suitable for Unable to deal with multi-variable, multi-constraint Complex Method dealing with constrained optimization optimization problems problems tree method (MSTM) and dynamic programming (DP) are layout of the natural gas transport pipeline network have not themostcommonlyusedsolutions.MSTMabstractsthe been reported. pipeline network into an undirected network, including the Terefore, this study uses the dominance degree model classic solutions of the Dijkstra, Kruskal, and Steiner algo- (DDM) of pipeline projects and the corresponding layout rithms [7, 8]. Compared to traditional graph theory solutions, method, which considers socioeconomic benefts and con- these algorithms are implemented by computer programs for struction costs. Te layout method based on the DDM is processing and have a relatively higher operational efciency. simple: it provides a global optimal solution to obtain the Te Steiner algorithms are efective in solving the shortest comprehensive benefts of the pipeline network. Terefore, path problem of a large-scale network [9–11]. However, the by analyzing the uncertain infuential factors of the DDM, three algorithms mentioned above do not consider the invest- this study proposes an innovative uncertainty analysis of ment costs of pipeline projects, and their results can only be the natural gas transport pipeline network layout based on regarded as the initial pipeline network layout. DP can deal the Monte Carlo method. Tis proposed method uses the with the optimization problem of multiple decision-making Monte Carlo method and sensitivity analysis to determine the variables. However, dimension obstacles exist during the impact of uncertainty factors on the model results. Tis can solution process. Specifcally, the computation will increase quantify the uncertainty and its infuence and thus strengthen exponentially as the number of variables grows. When the the practicability of the DDM and function as a future dimension of this problem increases to a certain extent, the referencefortheoptimallayoutofthepipelinenetwork. problem cannot be solved [12]. Tus, the current commonly Finally, to verify the validity of the methodology, natural gas used methods have certain advantages and limitations, as transport pipeline projects in Zhejiang Province, China, are presented in Table 1. In summary, the optimization of the taken as a case study. natural gas transport pipeline network is a multiobjective nonlinear programming problem, which should consider the 2. Dominance Degree Model and uncertainty caused by the gas market and costs. However, this problem cannot be solved easily and efectively by using the Its Layout Method abovementioned methods. Te dominance degree model (DDM) of pipeline projects is With regard to uncertainty and network layout, pre- a new method that was developed to optimize the pipeline vious studies have mainly focused on transportation and network layout [20]. Tis method used the dominance degree logistics [13–15]. For example, regarding uncertainty and to refect the comprehensive benefts of transport pipeline trafc network layout, Partriksson used a stochastic bilevel projects by combining the potential model (PM) and eco- programming model to solve the optimal transportation nomic potential theory (EPT) to build the dominance degree network layout scheme based on the uncertainty of demand model (DDM) for pipeline projects. [16]. Yin et al. [17, 18] studied the urban road network Te DDM of pipeline projects embodies the comprehen- layout methods under the impact of demand uncertainty sive socioeconomic benefts of the projects. By comparing andproposedsensitivity-based,scenario-based,andmin- the dominance degree of pipeline projects when applying the max optimization models. Zhang et al. [19] investigated the DDM to the layout of natural gas transport pipeline network, joint optimization problem of the green vehicle scheduling the optimal layout scheme and construction sequences are and routing problem in time-varying trafc networks and determined, which will leverage the advantages of pipeline developed a corresponding joint optimization model. How- projects to obtain the maximum socioeconomic benefts of ever, extensive studies on uncertainty associated with and the the pipeline network. Journal of Advanced Transportation 3

Table 2: Calibration for the value of ��. determined by referring to engineering data within the study � � � � � area. � is the number of crossings of the th type, and � is (10,000 People) � the corresponding construction cost. � = 1, 2, 3, 4 represent < 20 1 a river, grade highway, substandard highway, and railway, 20∼50 1.25 respectively. 50∼100 1.5 ∼ 100 300 2.0 2.2. Layout Methods Based on DDM. By analyzing and com- 300∼500 2.5 paringthedominancedegreeofpipelineprojectswithinthe 500∼1000 3.0 natural gas transport pipeline network, the layout methods based on DDM can not only determine the optimal layout scheme, but also obtain construction sequences of pipeline 2.1. Dominance Degree Model. Tis study combined the projects. Tus, the socioeconomic benefts of the pipeline potential model (PM) and economic potential theory (EPT) network will be maximized. Te basic application process is to establish the dominance degree model (DDM) of the showninFigure1. pipeline projects. Te following assumptions and methods According to the layout process, the layout method for a were used when developing the model: natural gas transport network based on DDM consists of four (1) Pipeline projects will generate economic potential, steps, as follows. which can be regarded as an index refecting the city scale. (2) Construction costs of pipeline projects will directly Step 1 (abstract pipeline network in the regional area). First, afect their economic benefts; therefore, construction costs abstract gas transport stations and valve chests into spatial were taken as a parameter refecting the impedance in the nodes and record a set of nodes � = {1,2,...,�}. Determine PM. their locations on the map by using a geographic information (3)Teinfuenceofpipelineprojectsoneconomicpoten- system (GIS). Ten, connect these nodes based on pipeline tialofthecityiscloselyrelatedtoitsdevelopmentlevel. alignments and obtain a spatial structure diagram of the Pipeline projects will directly afect the transformation of regional pipeline network. economic potential. Terefore, some specifc indicators can be selected to Step 2 (calculate the dominance degree of pipeline projects). refect these infuential factors. Above all, the DDM of gas Similarly, abstract the cities and towns uncovered by the gas transport pipeline projects is established as follows: transport pipeline network into a set of nodes �={1,2,...,�}. CalibratemodelparametersandusetheDDMtocalculatethe � � � =� � � , dominance degree between node � and node � sequentially. �� 2 4 (1) �� +�� ∑�=1 �� Ten, sort the calculation results in descending order. where �� is the dominance degree of pipeline projects Step 3 (update the pipeline network in the regional area). between city � and gas transport station �. �� is the dielectric According to the calculation results, take the pipeline project constant, which is closely related to the urban functional of maximum dominance degree and connect its nodes at both orientation of cities and towns. For the DDM of natural gas ends to form a new pipeline route. Ten, the corresponding transport pipeline projects, the city scale � is selected to nodes � are incorporated into a set of node �:thatis,�= refect this parameter. Considering the adjustment in 2014 of {1,2,...,�+1}. For example, assume that �={1,2,3,4}and �={1,2} � the classifcation criteria for city scales, �� canbecalibrated , the calculated maximum dominance degree 21, as shown in Table 2. which means �=2is removed from a set of node �,subsumed � �=3 �={1,3,4} �� isrelatedtotherichnessofurbanresources,market into a set of node and denoted as ;then, and development level, living standards of residents, and existing �={1,2,3}. Finally, the updated spatial structure diagram of state of the industry. In this study, the macroeconomic indi- the regional pipeline network is obtained. catorofGDPpercapitaisusedtorepresentthisparameter. �� is the gas demand of city �, which is related to the local Step 4 (calculate cyclically and output the results). Repeat �={1,2,...,�} energy consumption structure and policies. To facilitate the Steps 2 and 3 until the set of nodes is an empty � = {1,2,...,�+�} analysis of this question, the energy consumption per unit set, while the set of nodes .Atthistime, GDP is selected to refect the status of energy consumption allcitiesandtownshavebeencoveredbythepipelinenetwork and saving. To some extent, it also refects the current gas and the layout scheme of pipeline network is obtained. demand and development potential of natural gas. � � �� is the distance between city and gas transport station 3. Uncertainty of Dominance Degree Model �, which can be expressed by a straight-line distance. � is the pipeline price per unit weight. � is the pipeline 3.1. Source of Model Uncertainty. Te uncertainty of the DDM weight per unit length. Te values of � and � can be arises from a series of factors, including wrong settings of obtained from pipelines of the same diameter, material, and the model, imperfect input information, and the inherent thickness, as a standard. � is the terrain correction coefcient, randomness of events and behaviors [21]. Te PM and EPT whichisusedtomodifythepipelineroutelength.Diferent arecombinedtoestablishtheDDM,whichfullyembodiesthe topography conditions have diferent values, which can be comprehensive socioeconomic benefts of pipeline projects. 4 Journal of Advanced Transportation

Determine study area

Spatial structure diagram of Abstract pipeline network regional pipeline network

Calculate dominance degree of pipeline projects

Project of maximum dominance degree

Update pipeline network

No Whether pipeline network cover all cities and towns or not

Yes

layout scheme of regional pipeline network

Figure 1: Natural gas transport pipeline network layout process.

However,thenaturalgasmarketissubjecttoeconomic costs, will have a signifcant impact on model uncertainty. development, gas pricing, policy adjustments, and other If, owing to conditional constraints, the survey of geograph- factors, whose development trend shows a certain irregular- ical environment conditions along the pipeline project is ity. In addition, the construction costs of pipeline projects not detailed, the data will be more subjective. Tere are vary when the market prices and construction costs of steel inevitable diferences in geographical and environmental pipelineschange.WhenapplyingtheDDMtoobtainthe conditions along diferent natural gas transport pipeline layout scheme of a pipeline network, the inputs that refect projects,andthus,analogousdatafromsimilarprojectsmay the market scale and construction costs should be determined difer from the actual project. Terefore, the uncertainty of based on statistical data or similar empirical engineering data. the model is likely to be dominated by the uncertainty of these Terefore, there is a certain degree of uncertainty in the inputs. DDM, which is mainly derived from the inputs. 4. Uncertainty Analysis of Model 3.2. Uncertainty of Inputs. Model inputs mainly refer to data that describes the basic situation and related events 4.1. Quantitative Analysis of Uncertainty. Te method of and factors that afect the model performance [22]. Te moments and Monte Carlo method are two main methods inputs of the DDM are obtained through related statistical used to evaluate the model outputs [23]. Te method of survey data and by reference to similar empirical engineering momentsrequiresthattheoutputsarespecifedasanexplicit, data, which have a certain uncertainty. Te survey data are single function of the inputs, where higher order derivatives the basic data, which are mainly used to characterize the areusedtoensurecomputationalaccuracy[24].Fromthe urban socioeconomic conditions, energy consumption, and perspective of model setting, owing to the computational related policies along the pipeline project. Generally, there complexityinherenttotheDDManditslayoutmethod,itis are errors in the surveys, although such data errors are difculttocalculatetheoutputsbythemethodofmoments. somewhat limited to a certain extent and do not expand Terefore, this study uses the Monte Carlo method, since it in the layout loop computation thanks to modern statistical can obtain more accurate results to quantify the uncertainty methods. Terefore, the impact of the survey data error of the DDM. According to the general process of Monte Carlo on the model uncertainty is relatively small. However, the method [25], based on the characteristics of the DDM, the inputs determined by similar empirical engineering data, quantitative analysis of uncertainty includes the following such as the terrain correction coefcient and construction three aspects. Journal of Advanced Transportation 5

4.1.1. Determine the Probability Distribution of Inputs. Te 4.2.1. Multiple Linear Regression Analysis. Te multiple linear appropriate probability distribution is selected based on the regression analysis is a statistical method to investigate the characteristicsofinputsoftheDDM.IntheDDM,many relationship between a dependent variable and multiple variables vary within the nonnegative range. To avoid the independent variables [30]. Assume that there is a number of occurrence of negative numbers in the process of generat- independent variables �1,�2,...,�� and a dependent variable ing random numbers, the logarithmic normal distribution �. Te model between them can be expressed as follows: (LND) is used to represent the probability distribution of the DDM. Te probability density function of the LND can be �=�0 +�1�1 +�2�2 +⋅⋅⋅+�� +�, (6) calculated as follows: where �0,�1,...,�� represents the regression coefcient. � 1 1 −� 2 � (�) = [− (Int Int ) ], represents the error term that obeys normal distribution √ exp 2 � (2) 2 2��Int Int �(0, � ). By observing the variables �1,�2,...,��,� for � times, � where Int is the location parameter, which represents the the observations of (��1,��2,...,��,��) of � groups are logarithmic mean of the probability distribution. �Int is the obtained.Teleastsquaresmethodisusedtocalculate ̂ ̂ ̂ shape parameter, which represents the logarithmic standard �0,�1,...,��,andthen,theestimatedvalue�0, �1,...,�� can deviation. be obtained. � Te mean and variance of random variable can be When carrying out the model uncertainty analysis, the represented as follows: outputs are set as dependent variables and the inputs are set 1 as independent variables. Combined with the Monte Carlo � (�) = (� + �2 ) simulation results, the regression coefcients were obtained exp Int 2 Int (3) by regression analysis. 2 �Int 2 � (�) = (� −1) exp (2�Int +�Int) . (4) 4.2.2. Signifcance Tests of Regression Coefcients. To test if a regression coefcient �� (1≤�≤�)is zero, it is equivalent From (3) and (4), the coefcient of variation (CoV) can � be obtained as follows: to test whether its corresponding value � has an impact on �. Based on the linear regression model, we assume that �0 : ̂ �2 2 �� =0,1≤�≤�,anduse�� as a test to obtain the statistics √� (�) √(� Int −1)exp (2�Int +� ) = = Int � of Student’s distribution. CoV 2 � (�) exp (�Int + (1/2) �Int) (5) ̂ �� 2 �= = √� Int −1. √��√�/ (� − � − 1) (7) 4.1.2. Determine the CoV of Inputs. Te CoV can be used to � ̂ 2 compare the degree of variation among two or more units �=∑ (�� − ��) , [26]. Terefore, the CoV can be regarded as the expression of �=1 parameters of uncertainty. Considering that the CoV of some where �� represents the �th element on the main diagonal of inputs is difcult to be determined directly, the CoV of inputs −1 can be assumed based on the relevant research results to matrix �=� and matrix � is expressed as follows: analyze its impact on the outputs of the DDM [27]. Moreover, thestandarddeviationcanbecalculatedbymultiplyingthe � ∑ ��1 ∑ ��2 ⋅⋅⋅ ∑ �� [ � ] CoV and mean value of the inputs. [ � � � ] [∑ � ∑ �2 ∑ � � ⋅⋅⋅ ∑ � � ] [ �1 �1 �1 �2 �1 ��] [ ] �=[ � � � � ] . 4.1.3. Simulation Analysis of Dominance Degree Model. Te [ . . . . ] (8) [ . . . . ] MATLAB sofware was used to program and solve the [ ] Monte Carlo simulation analysis of the DDM. According to [ 2 ] ∑ �� ∑ ��1 ∑ ��2 ⋅⋅⋅ ∑ �� the probability distribution of inputs, random samples are [ � � � � ] generated. Ten, the results of outputs of DDM and their distributioncanbecalculated. Given a signifcant level �,if|�| ≥ ��/2(�−�−1), �0 is rejected, and �� is signifcantly not equal to zero. If 4.2. Te Analysis Method of Uncertainty. Tis study uses |�| < ��/2(�−�−1), �0 is accepted, and �� is signifcantly a multivariate sensitivity analysis method to quantify the equal to zero. When making a signifcant test of regression uncertainty of the DDM. Based on the linear regression coefcients, the value of � and � of �� can be obtained. If of inputs and outputs, the impact of inputs on output �<�, it can also be determined that it is not equal to uncertainty is analyzed. Tis method provides assistance in zero; namely, �� has a signifcant impact on model outputs. determining this impact and uses the normalized regression If �>�, �� hasnoimpactonmodeloutputs,andthus,the coefcient to represent the infuence degree [28, 29]. variablecanbeexcluded. 6 Journal of Advanced Transportation

Jinyun gas transport station j=1

Suichang County i=1

Songyang County Terminal station in Lishui City i=2 j=2 Zijin valve chest j=3

Qintian gas transport station Yunhe County j=4 Youzhu valve chest Longquan City i=3 j=5 i=5

Jingning County i=4

Qinyuan City i=6

Built pipeline projects New pipeline projects Cities or towns

Figure 2: Natural gas transport pipeline network.

4.2.3. Sensitivity Analysis. A nonparametric statistics method stations and two valve chests. Ten, the pipeline network in is proposed to examine sensitivity [31]. Afer the linear the regional area is schematized as shown in Figure 2. regression analysis and signifcance test of model outputs According to the Statistical Yearbook of Lishui City of and inputs, the standardized regression coefcient SRC�, 2015, and energy consumption statistics of each county of which can be used to determine the impact of inputs on the Lishui City (Maty´ as´ 1998), input parameters are as listed in uncertainty of outputs, can be calculated as follows: Table 3. By reference to related data of the Lishui section of � ×� � � the Jinhua-Lishui-Wenzhou pipeline engineering project, the SRC� = , (9) �� L450Msteelisusedforstandardpipelines.Tevalueof� is 1.032. V is 0.77 ten thousand yuan/tons. G is 222.3 tons/km. � � where � represents the regression coefcient. � represents �1,�2,�3,�4 are, respectively, 250, 15, 4, and 25 thousand � the standard deviation of independent variables. � repre- yuan/crossing. sents the standard deviation of dependent variables. 5.2. Model Calculation Results. By assuming that the model 5. Case Study inputsobeytheLND,theCoVisassignedavalueof0.3based on related studies [32, 33]. Using the proposed methodology, Te Lishui region along the Jinhua-Lishui-Wenzhou gas the two layout schemes and project construction sequence of transport trunk pipeline engineering in Zhejiang Province, thegaspipelinenetworkintheLishuiareaareobtained,as China, is taken as a case study. DDM and uncertainty analysis showninFigures3and4. areusedtodeterminetheoptimallayoutscheme. Te results present in Table 4 are obtained by setting the signifcant level � = 0.05 andusingthemultivariate 5.1. Pipeline Network and Model Inputs. GIS is used to sensitivity analysis method to quantify uncertainty of the determine the locations of the three natural gas transport DDM. Journal of Advanced Transportation 7

Jinyun gas transport station

Suichang County

1 Songyang County Terminal station in Lishui City

Zijin valve chest

5 Qintian gas transport station Longquan City Yunhe County Youzhu valve chest 4

Jingning County

Qinyuan City

Built pipeline projects Cities or towns New pipeline projects 1~6 Construction sequences of pipeline projects Gas transport stations or valve chests

Figure 3: Layout scheme of natural gas transport pipeline network (Scheme 1).

Table 3: Input parameters of cities and towns.

Name ��(10,000 yuan/person) � (Tons of standard coal/10,000 yuan) Suiyang County 1.25 46.596 0.470 Songyang County 1.25 44.037 0.456 Yunhe County 1 45.627 0.532 Jingning County 1 38.541 0.458 Longquan City 1.25 39.546 0.491 Qinyuan County 1.25 43.943 0.490

Table 4: Results of sensitivity analysis. Te results reveal that the uncertainty of model inputs directly afects the pipeline network layout schemes and opti- � Inputs mal construction sequences. Te inputs having a signifcant SRC � impact on the uncertainty of the DDM are the GDP per capita � 3.050 0.000 �,thedielectricconstantK, the distance between city and gas � � 1.739 0.001 transport station , and the corresponding construction costs of crossing a river and railway �1, �4. � 0.379 0.030 Natural gas consumption and city scale are closely related �− 3.326 0.000 to economic development level, which determine the market �1 −1.594 0.000 development potential and growth rate and become the main

�4 −0.750 0.001 infuential factors that afect the natural gas market. Tus, the uncertainty of � and � has a signifcant impact on model �2 −0.279 0.001 results. Te pipeline project construction cost is related to �−0.221 0.025 the length of pipelines � and the corresponding construction − V 0.167 0.046 costs of crossings, which have a direct impact on the project 8 Journal of Advanced Transportation

Jinyun gas transport station

Suichang County 4

Songyang County Terminal station in Lishui City Zijin valve chest

3 1

5 Qintian gas transport station Youzhu valve chest Longquan City Yunhe County 2

Jingning County

Qinyuan City

Built pipeline projects Cities or towns New pipeline projects 1~6 Construction sequences of pipeline projects Gas transport stations or valve chests

Figure 4: Layout scheme of natural gas transport pipeline network (Scheme 2).

investment and income. Te higher costs of �1 and �4 and the corresponding pipeline network layout scheme and directly afect construction costs. Tus, the uncertainty of the uncertainty analysis results were obtained. �, �1,and�4 has a signifcant impact on the results of the Uncertainty is one type of limitation that exists almost model. in every model. Te uncertainty analysis method that was In summary, when the DDM is applied to determine developed for the DDM is a method that can quantify the layout of a natural gas transport pipeline network, we the uncertainty of the model and examine the infuence shouldconsidertheimpactofinputuncertainty,soasto of diferent uncertainty factors on the layout of a regional try and reduce this impact and improve the accuracy of the pipeline network. It was observed from the case study results model results. Accordingly, this will support the best decision that the uncertainty of the model directly afected the layout regarding the layout of the natural gas transport pipeline optimization for the gas transport pipeline network and network. provided us with diferent results. Terefore, in practical applications of the DDM for regional network layouts, it is 6. Conclusions and Future Studies necessary to conduct an uncertainty analysis and quantify uncertainty efects of the model. Trough the uncertainty Te optimization of the layout of a natural gas transport analysis, we were able to determine the factors that sig- pipeline network is a scientifc and forward-looking topic nifcantly afect the model uncertainty and take measures with socioeconomic benefts. It is also a complex problem, to improve the accuracy of these factors by reducing the which is afected by multiple factors including uncertainty. infuence of uncertainty and obtaining the optimal layout of Tis study investigated the DDM and its layout method and gas transport pipeline network, which could be used as a analyzes the source and impact of model uncertainty and then reference and provide technical support to decision-making proposed a new methodology for uncertainty analysis based with regard to an optimal pipeline network layout. on the Monte Carlo method. Te Jinhua-Lishui-Wenzhou gas However, there are several limitations in the present transport trunk pipeline engineering project at the Lishui study. First, this study set the CoV to refect changes in model region in Zhejiang Province, China, was taken as a case study, inputs, while various diferences existed between the set Journal of Advanced Transportation 9

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