1 Introduction

Cities can be defined as products of the agglomeration of human beings, their life and production. Nowadays, the process of urban agglomeration in China is still far from climax, nor does it even slow down (Wu Z et al., 2016). Cities will be pushed towards a more compact and efficient direction regardless of the influence of the driving force of the agglomeration effect or the new problems of energy shortage and environmental degradation that the world is facing today (Ye Z, 2008). In the meantime, high density of the urban conurbation poses great challenges for the flow within the city. In a general sense, urban mobility includes the mobility status of all people, vehicles, goods, information, wealth, etc. in a city. The smoothness and convenience of the urban transportation network play a core role in reflecting urban mobility, acting as the main standards to measure urban mobility (Yang J et al., 2009). In China, traffic congestion has become a problem that confuses almost all big cities and most medium-sized cities, leading to many secondary urban problems. How to keep good mobility with high-density agglomeration and reach the status of “the problem is relieved with improved transportation circulation” is an important topic of modern urban planning research (Luo M et al., 2008).

2 Urban mobility diagnosis

Diagnostics originated from medical concepts and is a discipline that makes use of basic medical theory, basic knowledge and basic skills of disease diagnosis. Apart from the application in clinical medicine, diagnostic thinking has been widely used in many other professional fields and has even formed complete disciplinary systems.. For example, the basic logical thinking and methods in medical diagnosis were applied to engineering technology to further form engineering diagnostics. Besides, they were applied to the identification and judgment of enterprise operation status to further form enterprise diagnostics and so on.

For cities, accurate urban diagnosis is a scientific means that can analyze urban diseases and urban problems while it is an important prerequisite for preparing an effective planning strategy. In virtue of the characteristics of the urban system, urban diagnosis can be divided into the coordinated control force diagnosis, mobility diagnosis, environmental diagnosis, supply diagnosis, public service diagnosis, spatial culture diagnosis, social consciousness diagnosis and community relationship diagnosis. The main object of urban mobility diagnosis is the health status of urban material exchange and metabolism. The broad sense of urban mobility covers the flow status of all people, vehicles, goods, information and wealth in the city. In most urban diagnosis practices, the mobility of cities is generally measured by the smoothness and convenience of the urban transportation network.

The quantitative description of the physical condition of the diagnostic object is an important development trend from the perspective of the development of modern diagnostics. The accuracy of diagnosis was greatly enhanced by the establishment of a large number of health indicator systems and the application of corresponding measuring instruments and quantitative means. For cities, quantitative research on urban health status is also the key technology of modern urban diagnosis. In terms of the various systems involved in urban diagnosis, the urban mobility diagnosis that takes urban transportation as the main object has been provided with the most abundant quantitative research results and the most extensive application in urban systems in recent decades due to its obvious quantitative characteristics and convenient data acquisition. As the big data age approaches, the birth of new data types and processing technology provides a new perspective and method for the research of urban mobility while creating significant improvement space for the urban mobility diagnosis in integrity and dynamic real-time aspects.

3 Diagnostic indicator and its quantification

The establishment and quantification of the indicator system is the basis of modern diagnostics. There are a large number of indicators describing urban transportation in a modern urban research system. On this basis, the Paper proposed diagnosis indicators of traffic source, performance and subsystems for the overall mobility of the city in collection with the information backgrounds of today’s big data and mobile Internet era.

Among them, the diagnosis indicators of transportation sources mainly refer to the generation and attraction of urban transportation, including the balance of work and residence, the distribution of facilities, etc. The performance indicators mainly diagnose the service effect of the urban transportation system from the perspective of users, including three categories: time cost, economic cost and comfort cost. The subsystem indicators mainly focus on the components of the urban transportation system and diagnose the software and hardware components of the transportation system, including slow transportation indicators, public transportation indicators, rail transportation indicators, taxi indicators and car indicators, etc. The performance indicators mainly show the “flow” data, that is, the actual operation of the urban transportation system. The subsystem indicators mainly show the “shape” state, including the total supply and spatial distribution of various factors that can affect the performance indicators, such as road network, means of transport, transportation facilities, etc. In terms of planning and design of the urban transportation system, performance indicators describe goals while supporting indicators describe means. The process of urban transportation system diagnosis is to diagnose whether the operation of urban transportation is healthy through performance indicators and to optimize performance indicators through diagnosis and adjustment of supporting indicators to achieve good mobility of urban transportation.

4 Design of the diagnosis model

4.1 General settings

The three kinds of performance indicators are direct reflections of the city’s mobility, whose impact on mobility is decided by the travelers, travel destination, travel environment, etc. In today’s social and economic environment of cities, especially big cities, the response of time cost to urban mobility efficiency is more intuitive (Gutierrez, 2001). Considering this point, the Study took time cost as the main factor to establish a quantitative model.

The time cost of the flow between a specific node and another node in the city is determined by the layout of the transportation network and the selectivity of means of transport. The set of the time cost of the flow between the specific node and all other nodes in the city constitutes the accessibility of the node while the set of accessibility of all nodes in the city constitutes the overall mobility of the city (Ozbay K et al., 2006). As a result, the sum or average value of the accessibility of each node in the city can be adopted for measuring the overall mobility of the city.

4.2 Traditional model analysis

The problem of urban internal accessibility is an early systematic study of urban mobility. As early as the nineteenth century, the classical location theory has pushed the study of urban internal accessibility to the height of system theory. Domestic and foreign researchers have adopted a lot of methods to quantitatively analyze and study the accessibility of urban internal space. From the quantitative method of accessibility, the commonly-used models include distance model, opportunity model, potential model, utility model and space–time prism model (Chen J et al., 2007; Li P et al., 2005; Wu B, 2010; Lu H, 2009). These models have their own advantages in the attenuation of distance impact, land use types, individual choice intention and facility competitiveness.

With the development of urbanization level and city scale, the mobility of the city presents the following trends: 1) the internal transportation mode is becoming more and more diversified. 2) The traffic network is becoming complex. 3) The dispersion of accessibility distribution of each node increases in the city. 4) The overall mobility of the city changes more significantly with time. Consequently, the difficulty of quantitative research on urban internal accessibility is gradually increasing. Influenced by the limitations of data sources and operation conditions, the original model stresses static analysis and is limited to the flow analysis of a point (or some points) in the city and the whole city. Meanwhile, it lacks a quantitative description of the overall urban mobility.

4.3 Standard model and reference system model

4.3.1 Standard model

To establish a more overall, dynamic and systematic understanding of urban mobility, it was planned to establish a calculation model of the overall urban mobility (Formula 1) in the Study based on the traditional potential model through using Internet big data and algorithm program. The advantage of the model is that it covers the flow relationship between all nodes and is provided with strong integrity and accuracy (Song Z et al., 2010). But it involves a lot of parameter setting and calculation work and has a high dependence on data acquisition, generation and calculation tools. So, it is suitable for the research object with mature data and a small area.

$$\mathrm{F}=\sum {\mathrm{A}}_{\mathrm{i}},{\mathrm{A}}_{\mathrm{i}}=\sum_{j=\mathrm{l}}^{n}\frac{{\mathrm{R}}_{\mathrm{ij}}}{{\mathrm{C}}_{\mathrm{ij}}^{\mathrm{b}}}$$
(1)

where, F is the overall urban mobility and Ai is the accessibility of the target node i. Rij is the attraction between node j and target point i. Cij is the traffic cost between target node i and node j. b is the distance friction coefficient. j = 1, 2, 3…, n and n is the number of nodes.

4.3.2 Reference system model

For a certain specific node in the city, the number of nodes with a high connection degree is very limited compared with the number of nodes in the whole city. Compared with these nodes with a high connection degree, most other nodes have little attraction to them and the corresponding willingness to flow is also small. As a result, it was planned to use only the most attractive part of the nodes in the city to establish a reference system for calculating the accessibility of the target nodes. Then, a reference system model of urban mobility was established (Formula 2). The advantage of the model covered the great simplification of the parameter setting and the amount of calculation and the strengthening of the feasibility of application in practical cases. At the same time, it is needed to pay attention to the great impact of the selection of the reference system on the diagnosis results of the model. The daily flow needs of most nodes and people in the city were considered in the Study and the reference system was mainly established by using the city center, the nearest commercial center, the nearest park and various external traffic facilities (Fig. 1). Meanwhile, when calculating the time cost, the time consumption of cars and public transportation was taken into consideration.

$$\mathrm{F}=\sum {\mathrm{A}}_{\mathrm{i}}, {\mathrm{A}}_{\mathrm{i}}=\sum_{j=\mathrm{l}}^{n}\frac{\left({w}_{1}{\mathrm{R}}_{1}+{W}_{2}{\mathrm{R}}_{2}+{w}_{3}{\mathrm{R}}_{3}+{w}_{4}{\mathrm{R}}_{4}\right)}{\left(\alpha {\mathrm{S}}_{\mathrm{ij}}^{\mathrm{b}}+\beta {t}_{\mathrm{ij}}^{c}\right)/\left(\alpha +\beta \right)}$$
(2)

where, F is the overall urban mobility and Ai is the accessibility of target point i. w1, w2, w3 and w4 refer to the judgment coefficient of point type. w1 corresponds to whether it is a municipal center or not. If yes, w1 = 1, otherwise, w1 = 0. w2, w3 and w4 correspond to the nearest commercial center, the nearest park facility and external transportation hub respectively. R1, R2, R3 and R4 are the attraction (reference weight) of different types of reference points. sij is the time cost of public transportation from the target point to the reference point j. tij is the time cost of car traffic from the target point to the reference point j. b and c are the distance friction coefficients and α is the weight coefficient of public transport time. β is the weight coefficient of car traffic time.

Fig. 1
figure 1

Calculation method of standard model and reference system model

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5 Mobility diagnosis of the downtown area of Shanghai based on the network map data

5.1 Establishment of the research object and reference system

The downtown area of Shanghai is within the outer-ring road, covering an area of 660 square kilometers. It is the political, economic and cultural center of Shanghai. Within this range, based on the corresponding planning at all levels and official network data, a mobile reference system of the downtown area of Shanghai was established, which was composed of a city center, business center, external transport facilities and park facilities.

5.1.1 City center

According to the Shanghai Master Plan (1999–2020), the structure of the downtown area of Shanghai is “multi-centric and open”. The city center is centered on People’s Square and the central business district is composed of Pudong small Lujiazui and the Bund. The sub-centers of the city are Xujiahui, Huamu, Jiangwan Wujiaochang and Zhenru.

5.1.2 Commercial center

According to the Layout Plan of Shanghai Commercial Service Facilities (2013–2020), there are 14 municipal commercial centers within the outer-ring road, such as East Nanjing Road Commercial Center, West Nanjing Road Commercial Center and North Sichuan Road Commercial Center, and 22 regional commercial centers, such as Kongjiang Road Commercial Center, Dapu Bridge Commercial Center, Gongkang Commercial Center and Changshou Commercial Center.

5.1.3 External traffic facilities

At present, Shanghai’s external traffic facilities mainly for passenger transport include two airports, that is, the “three-main and two-auxiliary” railway passenger station system and the international shipping port. From the perspective of accuracy and calculation amount of the balance model, Hongqiao Comprehensive Transportation Hub, Pudong International Airport, Shanghai Railway Station and Shanghai South Railway Station are selected as reference points for external traffic facilities.

5.1.4 Park facilities

One hundred twenty-nine open urban parks in the downtown area of Shanghai (as of 2011) are taken as reference objects, excluding small community parks and street green spaces.

5.2 Data source

The appearance of the network map traffic query function provides a convenient way to obtain data for the traffic time consumption of different traffic modes between any two points in the city over the years. Some network maps also consider the real-time congestion of the road network when calculating the traffic time cost, so the accuracy of the data is greatly improved. Based on the traffic query provided by Baidu Map, the Study carried out the batch acquisition of traffic time consumption between points, weight assignment and mobility evaluation of nodes in the city by using the self-developed data acquisition program (Fig. 2) and then synthesized the overall mobility distribution data of the downtown area of Shanghai.

Fig. 2
figure 2

Self-programming Interface of traffic time consumption acquisition based on the reference system

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5.3 Mobility distribution

To obtain the overall urban mobility distribution in the downtown area of Shanghai, 18000 target POI points were randomly selected in the downtown area in the Study by using R language. After de-weighting the coordinate, the accessibility of these points relative to the reference system established in the previous paper was calculated and evaluated. Finally, the diagnosis of overall urban mobility distribution was completed by the GIS interpolation (Fig. 3). In the process of accessibility evaluation of each target point, the accessibility of public transportation mode and car mode were calculated respectively. On this basis, the comprehensive score of accessibility was calculated. Considering the dominant trend and demand of urban public transportation, the accessibility of public transportation was given a higher weight.

Fig. 3
figure 3

Overall situation of mobility in the Downtown Area of Shanghai

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It could be seen from Fig. 3 that the urban mobility of the downtown area of Shanghai showed a trend of high inside and low outside. From the center of the city to the outside, with the increase of the overall distance away from the reference system and the decrease of the supply of road network and traffic facilities, the flow cost gradually increases and the mobility decreases. At the same time, the overall mobility also presents the characteristics of finger radiation and form several “high mobility corridors” from the inside to the outside along the subway line, indicating that rail transportation has a significant role in improving the mobility of the surrounding areas in large cities. Besides, the overall mobility of Puxi was obviously higher than that of Pudong. Apart from Lujiazui, Century Avenue and Binjiang Area, there is still much room for improvement of the mobility of Pudong, reflecting that the overall location and transportation resources of Puxi are still better than Pudong despite the rapid development of Pudong in recent two decades.

In terms of the important nodes in the downtown area of Shanghai, the main nodes with less mobility than those in the same area include:

  1. 1))

    Within the inner ring: Tangqiao Area, Shanghai New International Expo Centre Area and Pingliang Road Area.

  2. 2)

    Between the inner and middle rings: Jinjiang Park Area, Dongjiao State Guest Hotel Area, Beicai Area and South Zhangjiang Area.

  3. 3)

    Between the middle and outer rings: Large Park Area, Tiecheng Road Area, Binjiang Forest Park Area, Gaodong Ecological Park Area and Sunqiao Area.

6 Conclusion

Based on traditional urban transportation evaluation and accessibility model and the idea of quantitative diagnosis, a city mobility diagnosis model based on big data and accessibility model was established in this study through exploring the network map data. Compared with the previous urban transportation evaluation methods, this model calculated the mobility of each node based on the network dynamic data and it was real-time and dynamic. The traffic congestion, road maintenance and other factors were taken into account so that the accuracy was greatly improved. In terms of transportation mode, the influence of car and public transportation on node accessibility and urban mobility was considered in this model at the same time and the corresponding weights were set according to the structure of urban transportation mode. Compared with the ideal model, this model was closer to the actual usage scenario of transportation resources regarding the urban population.

Based on the above algorithm and data optimization, the quantification and diagnosis of the overall mobility distribution of the city were carried out in this study. The study results reflected the combination effect of various types of urban traffic and road resources and their spatial allocation, which was not only conducive to finding the weak links of supply of urban transportation resources conveniently and intuitively but also provided a rational basis for the planning and layout of urban land use and development control by the comparison and matching analysis of the overall spatial structure, land value, land use type and development intensity of the city.