Comprehensive Evaluation of Urban Integrated Transportation Network with Multivariate Statistical Analysis: a case study of Haimen

This paper proposed a comprehensive evaluation (CE) framework concerning multivariate statistical analysis to provide a systematic assessment and a hierarchical analysis for the urban integrated transportation network (UITN). Specifically, this research contributed the following technical approaches: Firstly, 4 criteria (scale, structure, level of service (LOS), layout) was adopted and indexes were screened from heterogeneous aspects to establish the hierarchical model using correlation coefficient method (CCM). Built upon that, fuzzy comprehensive evaluation method (FCEM) and linear dimensionless (LD) were applied to quantify and nondimensionalize the qualitative and quantitative indexes. In order to improve accuracy and guarantee rationality, this paper then integrated analytic hierarchy process (AHP) with entropy weight method (EWM) to get the index weight. At last, the combination of value analysis (VA) and grey relational analysis (GRA) was used to calculate the CE value. The experimental study shows that our introduced CE framework can offer a thorough evaluation of the UITN, the CE value of UITN in Haimen city is 0.740 and its grade level is "Medium". Pros and cons of the structural layout of each transport mode can also be judged through the hierarchical analysis of different indexes. In view of this, corresponding suggestions were given for future improved transportation planning.


I. INTRODUCTION
As the significant branch of the urban transportation system, the development of UITN greatly prompts the social progress. However, with the growth of urbanization, the contradiction between the UITN planning and the increasing demand has become distinctive, negatively interfering the socioeconomic growth. Related studies suggest that in order to address the urban transport problems while coordinate the relationship between UITN construction and social progress, it is obligatory to investigate the impacts of related influence factors, with which to reasonably plan the UITN and pilot the limpid development direction [1]- [3].
In recent years, the growing diversification and complexity of transport demand urge a comprehensive and effective transportation planning [4]. As far as it is concerned, as its solid basis, a comprehensive transportation evaluation incorporating multiple layers (highway, railway, waterway, airway et al.) is essential [5]. In fact, researchers and engineers have addressed this issue both theoretically and empirically. However, in related studies, the investigation of land transport accounts for the vast majority [6]- [8] and that of the other transport modes was quite roughly mentioned and assessed.
During the planning process, the notion of UITN was raised and studied [9]. The fully development of UITN can provide powerful support for building nation's strength in transport [10] and is considered to be the pioneer of economic growth [11] since it can improve regional accessibility. In studies of assessing transportation network, accessibility was assumed as the indicator [12]- [13] and it is found that its influence degree is varied for regions of different sizes (national and continental), with which the regional economic growth can also be predicted. However, the previous studies are mainly confined in one transport mode (especially in highway or railway network) [14]- [15]. The characteristics of different transport modes should be notified and highlighted and the spatiotemporal effects should be assessed in a more integrated network [16]. Meanwhile, with the rapid growth of social economy, residents' travel pattern becomes more diversified, which imposes great pressure on the transportation system operation. The complex population structure and their accordingly varied travel behavior require the transformation of UITN [17]- [18]. Therefore, in order to clarify how its development can provide satisfactory transport service, it is necessary to incorporate the influence of population in the CE framework [19].
Scholars have designed the quality ranking methodology to analyze the variables and criteria adopted in transportation network evaluation [20]- [22]. In their studies, they pointed that the homogeneity and suitability of the selected variables are rather important for building the evaluation system and environmental and aesthetic impacts were presumed as the significant indexes for assessing transport projects [23]. Though the formulated plans were specifically evaluated and the results were reasonable, it is notable that the environmental and landscape factors they laid great importance on are not the only considerations. The aim of their studies is either achieving sustainability or emphasizing economic benefits [24], which is far from enough to meet the needs of the society. The transportation network system needs the CE, which should incorporate heterogeneous evaluation aspects [25]. In addition, it should also be emphasized that little attention has hitherto been paid to the operation mechanism inside the UITN and a unified and standardized measure that can quantitively and systematically assess the UITN is not built yet.
Varying from single index evaluation, CE provides a systematic and standardized method integrating qualitative and quantitative indexes for evaluating multiple units at the same time. It can comprehensively judge the overall state of the research object and its complex mechanism can be investigated by hierarchical analysis. For cities with multiple transport modes, the CE system of UITN should reflect the real situation and the coordination degree among social, transport and geographical conditions. Scale and structure [26] are major influence factors of CE system because they are the objective reflection of the components of UITN. In addition to that, the social contentment of the quality of transport operation can be judged from the LOS [27], so it should as well be considered. Besides, the network layout was defined as the coupling and coordination degree of capacity and demand [28], as the core of regional UITN planning, it is also an indispensable part of the CE system.
Enormous studies on the methodology of establishing the UITN evaluation framework have emerged in recent years. Data Envelopment Analysis (DEA) as an evaluation method based on convex analysis and linear programming is widely adopted in the mathematical evaluation model. Although it can calculate the output value accurately, the concept of infinitesimal that is extremely computational intensive [29]- [30] needs to be introduced in the process of programming. In contrast, FCEM is easier to implement and suitable to multi-factor and multi-level problems [31], so in this paper, FCEM and LD are adopted to quantify and nondimensionalize the qualitative and quantitative indexes respectively. AHP can integrate relevant elements to establish a hierarchical model and use less quantitative information to program the thinking process of decisionmaking. For its concise concept and procedures, it is usually combined with other methods to deal with evaluation problems and verified practical [32]- [34]. In this paper, AHP is integrated with EWM [35] to calculate the CE index weight, with which the accuracy can be improved. GRA can determine the development trend of the system affected by the coordinated action of multiple factors, which is also able to determine each factor's influence degree. The spotlight of this method is that the results obtained fit that of the qualitative analysis [36]- [38]. Therefore, after obtaining the index weights, GRA and VA [39] are combined to establish the CE model.
It can be drawn that enormous researches about the transportation network evaluation focus on the unimodal (land transport), instead few can evaluate from an integrated perspective (as shown in FIGURE 1). Comprehensive and detailed evaluation should not ignore multi-layer nature of UITN and the result of evaluation is affected by the synergism of various factors.
CE has been applied in various fields [40]- [42], for transportation planning, it can form a holistic evaluation of the UITN and carry out hierarchical analysis of each index. Besides, in previous studies, the fitness between the qualitative and quantitative indexes is not yet been discussed and few introduce a standardized measure for realizing CE.  Evaluating unimodal transport unilaterally [45]- [47] Impacts of different transport modes on the overall transportation network The major contributions of this paper are summarized as follows: (1) The indexes were screened to build the evaluation index system and put forward specific methods of determining the CE index value; (2) AHP and EWM are integrated to determine the index weight, with which the accuracy is improved; (3) The combination of VA and GRA is used to establish the CE model and calculate the CE value to avoid subjectivity; (4) The case analysis proves the practicability and feasibility of the proposed model and the effectiveness of the adopted methods. Some reasonable suggestions on the improved planning of UITN in Haimen city were raised for reference.
The rest of the paper is organized as follows. Section 2 introduces the established CE index system and its components. Section 3 formulates the methodology of establishing the CE model. Section 4 presents the case analysis, which was carried out to validate our proposed evaluation framework. Finally, conclusions of this paper and some future research directions are discussed in Section 5.

II. ESTABLISHMENT OF CE INDEX SYSTEM
Based on the previous theoretical and empirical studies, it is determined to divide the preliminary CE indexes into four criteria: scale, structure, LOS and layout, which is shown in TABLE I.
The objectivity and reliability of the CE results depend on whether the selected indexes are accurate and representative. Because of the multi-layer nature of UITN, there existing various transport modes so the indexes come in great varieties. However, it can be found that some of the indexes can be deduced from the others and some of the contents different indexes reflect overlap. Therefore, this paper adopted the Correlation Coefficient Method (CCM) to analyze and screen the indexes. 1) All the indexes have been clustered into 4 criteria, the next step is to choose one as the typical index of each transport mode in each criteria.   TABLE I. For  example, when  , represents the index "Double-track mileage" of "Railway" mode in "Structure" criteria.
(2) Let denote the sample value of the index of the mode in the criteria, denotes the number of samples, the correlation coefficient can be calculated as Eq. (1). (1) (3) Coefficient of determination can be calculated as Eq. (2). (2) (4) Choose as the typical index of each transport mode in each criteria.
2) Calculate the correlation coefficient between the indexes and typical indexes. In this paper, the critical value M is 0.6. If , the index will be considered being retained; otherwise it will be deleted.
After analyzing and screening the indexes, the CE index system of UITN is shown in FIGURE 2.
Several explanations of CE indexes are as follows: A. SCALE

1) Total mileage of highway network A1
The total mileage of the highway network can reflect the development of the highway network scale and the coordination degree between the urban economy and the overall transportation system. In this paper, the Connectivity Method (CM) and the Territory Coefficient Method (TCM) are used to calculate the total mileage of highway network, and then the average value is taken as the standard value.
The basic formula of the CM can be expressed as Eq. (3), where is the total mileage of the highway network (km); is the connectivity; is the total area of the city (km 2 ); is the number of connected nodes in this region; is the deformation coefficient of the highway network.
The basic formula of the TCM can be expressed as Eq. (4), where is the total mileage of the highway network (km); is the coefficient of the urban highway network; is the total population of the city (10,000 people).
2) Total mileage of railway network A2 (5) In Eq. (5), is the scale of the railway network (km); is the number of important towns; is the connection coefficient.

1) Proportion of expressway B1
The standard value of the expressway proportion is obtained by the analogy analysis (AA).
2) Electrification proportion B4 The proportion of electrification in the railway network is directly proportional to the socioeconomic development of the city.

1) Saturation of artery network C1
The saturation of artery network can reflect the demand adaptability of the highway network and the degree of congestion. The evaluation standard adopted in this paper is shown in TABLE II.

2) Waterway network congestion degree C4
The congestion degree of waterway network can reflect the operation condition of waterway network. (6) In Eq. (6), is the congestion degree of waterway network; is the mileage per waterway (km); is the planned traffic volume per waterway; is the capacity per waterway.

1) Administrative village rate connected by highway D1
With implementation of rural revitalization strategy, there should be roads connecting cities and villages. Roads connecting administrative villages can drive the economic development of regions along the route and facilitate the development of urban-rural integration.
2) Railway network density D3 This paper uses the proportion of operating railway mileage per 100 m 2 as an indicator to evaluate the rationality of the railway network layout. In this paper, the standard value of the railway network density is determined by AA.
3) Railway station coverage rate D4 Rail travel has the advantages of punctuality, high-speed, comfort and safety, so more and more tourists prefer to travel by rail. High accessibility can bring about the boom of economy [50], thus the coverage of railway station is particularly prominent. 4) Graded waterway network connectivity D5 Graded waterway network connectivity can reflect the characteristics of the layout of the waterway network by examining the connectivity of the node ports and urban transport hubs. 5) Congestion degree of commuting in peak hours C5 Congestion degree of commuting in peak hours can reflect the urban traffic congestion situation. The evaluation standard adopted in this paper is shown in TABLE III [51]- [52].

III. ESTABLISHMENT OF CE MODEL
After obtaining the screened indexes, they are nondimensionalized through dimensionless treatment, after which the evaluation value of each index is obtained. Afterwards, the integration of AHP and EWM is explored to calculate and tune the index weight. Finally, VA and GRA are combined to obtain the CE value and assess the grade level of UITN. The established CE framework is shown in FIGURE 3.

A. DIMENSIONLESS TREATMENT OF CE INDEXES
The ultimate purpose of CE is to integrate the information of multiple indexes describing the studied object to obtain a CE value and then conduct analysis to assess this object as a whole. During the process, the integration should be based on the homogeneity of each CE index. However, specific indexes of the CE index system are often non-homogeneous. On the one hand, the dimension of each index value is varied; on the other hand, because each CE index reflects different criteria of the studied object, so the representation forms of these indexes are different. In this way, these CE indexes values will be different in terms of magnitude. The homogeneity transformation of the indexes can be solved by dimensionless treatment to convert the actual value of the index into a CE value, the integration of different CE indexes can then be proceeded. The specific methods are as follows: 1) Dimensionless treatment of qualitative indexes. This paper uses FCEM to quantify and nondimensionalize the qualitative indexes, the results are obtained through Expert Scoring Method (ESM) and the evaluation standard is shown in TABLE IV. 2) Dimensionless treatment of quantitative indexes. This paper uses LD to nondimensionalize the quantitative indexes. Suppose the calculated value of index is ，the upper bound and lower bound of are and respectively, is the nondimensionalized standard function of the index value of . The dimensionless process is formulated as Eqs. (7)- (10).
(4) Moderate index (the value closer to the median is better):

B. CALCULATION METHODS OF CE INDEX WEIGHT
Different indexes have varied impacts on the studied object and the determination of their weights reflects their priority and directly affects the CE results. Therefore, weighing treatment is required. In this paper, AHP is utilized to calculate the weights of the indexes and EWM is explored to modify the results. The specific procedures are introduced as follows: 1) Calculate the weight using AHP.
Step1: Establish the judgment matrix according to the relative importance of each index in each criteria.
Suppose that element in criterion layer is the upper level of element in index layer , the judgment matrix is constructed as Eq. (11). (11) where is the relative importance of relative to , .
When proceeding the relative importance comparation among the indexes, this paper uses the scale of 1-9 to calibrate the relative importance of each index (as shown in TABLE V). Index is slightly more important than index 3 Index is more important than index 5 Index is quite important compared to index 7 Index is extremely important compared to index 9 The relative importance between index and is set between any two hierarchies 2，4，6，8 Step2: Perform hierarchical single sorting and concordance test (CT).
Calculate the index weight and determine the maximum eigenvalue of the judgment matrix, then conduct the CT. Eq. (12) indicates the formulation of concordance ratio (CR), if CR<0.1, the judgement matrix will pass the CT; otherwise the judgement matrix should be modified to reconduct CT until it is passed. The formulation of the concordance index (CI) is given in Eq. (13), where denotes the order of the judge matrix. The correspondence between RI and is shown in TABLE VI.
Step3: Perform hierarchical total sorting and CT. Calculate all the index weights from the top to the bottom layer and conduct the CT for total ranking results.
2) Modify the calculated weight using EWM.
Step1: Suppose the weight obtained by AHP is , then transform the matrix into a standardized matrix.  Eqs. (15) and (16) denote the formulations of entropy of the index ( ) and the deviation degree ( ).
The correction coefficient obtained by Eq. (17) is used to revise the index weight got from AHP. In Eq. (18), is the revised weight of index . 3) Calculate the final weight of each index. (19) Eq. (19) represents that the initial weight obtained by AHP and the modified weight obtained by EWM are weighed to get the final weight of each index, where is usually 0.5.
The results of the index weights are shown in   The initial weight obtained by AHP and the modified weight obtained by EWM are weighed and calculated by Eq. (19) to obtain the final weight, the result of each index weight in each criteria is shown in FIGURE 4.

C. CALCULATION METHODS OF CE VALUE
In this paper, in order to eliminate the subjectivity of employing only one method, the combination of VA and GRA is utilized to obtain the CE value. The specific procedures are as follows: 1) Calculate the preliminary CE value using VA.
(20) (21) Eqs. (20) and (21) indicate the formulations of VA, where is the preliminary CE value; is the CE value of index ; is the evaluation value after dimensionless treatment.
2) Calculate the preliminary CE value using the GRA.
(23) (24) Eq. (22) represents the basic formulation of GRA. The correlation coefficient matrix is given in Eq. (23), where is the correlation coefficient of the index in the criteria. Eq.
Step1: Determine the optimal index set. Suppose there are indexes, select the optimal indexes (Eq. (25)). (25) (26) In Eq. (26), matrix D is built according to the original data, here the dimensionless treatment is explored to standardize the indexes in matrix D to that in matrix C.
Step2: Calculate the gray correlation coefficient. Split matrix C, suppose the reference series: and the comparison series: , then calculate the correlation coefficient (Eq. (27)). (27) where is the identification coefficient, . Step3: Calculate the preliminary CE value. (28) In Eq. (28) 3) Calculate the final CE value. (29) Eq. (29) denotes the formulation of getting the final CE value and the grade of the evaluated UITN can be referred in TABLE X [53].

A. STUDY SITE SELECTION AND DESCRIPTION
The UITN of Haimen is selected as the study scenario to validate the proposed CE model, then corresponding discussions are given through hierarchical analysis. Haimen city is located at the Yangtze River estuary and close to Shanghai. Benefited from its geographic location, it has rich transport compositions (involve all the 4 modes [54]), as shown in FIGURE 5.   (29)). By referring TABLE X, the grade level of UITN in Haimen city is "Medium". The rapid development of UITN in Haimen has strongly promoted the socioeconomic growth. However, from the perspective of CE and its obtained results, there are still deficiencies. Highway network can strive for further progress and improvement, while the development of railway, waterway and airway is still in a shallow level. The overall transport status of Haimen still lags behind the national average level and there is little possibility for the landing of a comprehensive transport hub in the short run. It can also be drawn that the scale and structure of UITN play a significant role in the CE process (FIGURE 4), so it is particularly important to improve the scale and optimize the structure of the UITN. In addition, the indexes concerning population indicate that with the population growth, the current traffic condition of Haimen is unable to satisfy the surging travel demand and requires evolution. The current status and suggestions for the improved planning of each transport mode can be expounded as follows: 1) Highway As shown in FIGURE 6 (a), the total mileage of the highway network is insufficient, which is slightly lower than the lower bound of the national level. Though the highway network connectivity reaches the average level, the proportion of expressway is rather lower (FIGURE 6 (b)). Besides, there are few high-grade highways (mainly 3rd-grade and 4th-grade highways) and the saturation of its artery network is high, these weaknesses result in the low overall accessibility both inside and outside the city. The proportion of different grade highways is unbalanced and not coordinated, which leads to the unreasonable overall layout. Considering the current situation that 1) most of the national and provincial arteries are concentrated in the main city and areas along the Yangtze River; 2) some highway channels overlap seriously; 3) insufficient highway coverage in the northern area of the city, as exhibited in FIGURE 7, it is advised that 4 national and provincial roads be routed and 4 provincial roads be newly upgraded (http://www.jshmzc.com/hmzc/zwzx/content/7bbe7b9f-0a66-45b4-8984-e7d0d9fdd13b.html).
2) Railway The railway scale of Haimen City is so small. It possesses only one Ningqi Railway and its length is just 38km, no wonder it provides poor railway LOS for its low railway line capacity (FIGURE 6 (c)). The layout is also not perfect, the railway network density is low (FIGURE 6 (d)) so its impact on supporting the development of the overall urban transportation system is quite limited. The function of the railway station should be strengthened as well. At present, for the high-speed rail travel can provide comfortable and reliable service, more and more people tend to choose travelling by rail. However, Haimen Station of Ningqi Railway is of low service level and its functions are imperfect, the freight function of the railway hub has also not been fully utilized, so its layout needs to be further optimized to improve its transport efficiency. As shown in FIGURE 8, it is suggested that a high-speed railway be newly built and Haimen North Railway Station be newly set (https://www.yangtse.com/content/1236900.html) to realize high-speed railway travel and improve the railway network density and railway station coverage, which further optimize the transport structural layout and improve LOS.
3) Waterway Although the scale of the port reaches the national average level, the cognition of port is vague and its functions are not fully exploited. The proportion of high-grade waterway is quite low (FIGURE 6 (e), FIGURE 9) so its interflow with high-grade ports is rather limited. The waterway network congestion degree goes beyond the upper bound of the standard value (FIGURE 6 (f)), thus low LOS and poor transport efficiency are provided and the advantages of waterway transport can't be given into full play, which strongly restrict its development. In view of this, it is suggested to build a high-quality inland waterway network with the artery of Yangtze River as the core and the 3rd-grade waterways as the framework (as shown in FIGURE 10). The purpose is to connect the sea port and Haimen port with the 3rd-grade waterway channels to strengthen the River-Ocean combined transport (http://jtysj.nantong.gov.cn/ntjy/upload/27d6130b-22f5-4337-b2ce-23ee9d52b523.pdf). 4) Airway Haimen residents mainly used Nantong Xingdong International Airport for travelling while its airway development is lagged behind. As shown in FIGURE 6 (g), the airport has few airlines and flights and small air service coverage. To meet the rapid growth of Haimen economy, in the long run, it is suggested to learn from the construction experience, scale and positioning of Chengdu Tianfu Airport and build a 4F airport in Haimen. Haimen Airport Economic Zone should be recognized as the Regional Aviation Hub and Advanced Aviation Industrial Agglomeration Zone, which takes airway transportation, air logistics and international business as the main development industries (https://www.ettoday.net/news/20190215/1378443.htm).

V. CONCLUSIONS AND DIRECTIONS FOR FUTURE WORKS
This paper proposed a CE framework to comprehensively evaluate UITN with multivariate statistical analysis. Due to the diversity of the evaluation indexes, 4 criteria was adopted and indexes were screened through CCM. In the next, FCEM and LD were used to quantify and nondimensionalize the qualitative and quantitative indexes. Then the weights of the selected CE indexes are calculated through the integration of AHP and EWM. After obtaining the weights, the CE value was given by the combination of VA and GRA. At last, the case of UITN in Haimen was chosen to apply our established CE model, the results were analyzed and suggestions for the improved UITN planning were raised for reference.
The advancements and innovations are as follows: 1) Our CE model can provide a systematic view of UITN, the CE value can be referred to assess the studied object's general development trend and comprehensive level, based on which the improved decisions can be made.
2) The integration of AHP and EWM can improve the accuracy of the index weight and the subjectivity of employing one approach is avoided through averaging the value of VA and GRA.
3) The established CE framework exhibits adequate practicability and feasibility, it provides a theoretical foundation for partial-global planning and structural layout optimization of UITN.
There are several promising future research directions stemmed from this study. During the process of dimensionless treatment of qualitative indexes, ESM is applied and kind of subjective, so it is the same with the process of determining the weight by applying AHP (ESM). Methods shunning subjectivity in the analysis are few and therefore worth studying. Besides, with the rapid development of the transportation system, pipeline transport has gradually come into practice and is also a significant component of the UITN, the index selection of pipeline transport and its evaluation criteria is also an interesting direction for digging into. Such extensions will make our study more scientific and functional and be addressed in our future works.