Overview of methodology

Figure 1 shows the framework and process of the whole study. In the first step, the article selects nine historical and cultural districts in Beijing, China according to three types: cultural, commercial and residential, and the selection standard is the proportion of different types of functions. The vitality of these districts is analyzed from three aspects: historical value, use value and sustainable value. These three values correspond to the past, present and future of value respectively. It provides a framework for dealing with time and change. For example, if the value of a historical area is determined today, and some differences appear 20 years later, what do these changes mean to the value of this place? Therefore, the value type must solve the problem of time. Each value corresponds to three sub factors.

Fig. 1
figure 1

The second step is to list the hierarchical model diagram of the three target values after collecting the data from on-site investigation and expert interview. And ranking and analyzing the importance degree according to the score of experts. Analytic hierarchy process refers to a systematic method that takes a complex multi-objective decision-making problem as a system, decomposes the goal into multiple goals or criteria, and then decomposes it into several levels of multiple indicators, and calculates the hierarchical single ranking and total ranking through the fuzzy quantitative method of qualitative indicators, so as to be used as the objective and multi scheme optimization decision-making. This method is often used to evaluate the value and attractiveness of heritage [58]. Ma h et al. used this method to evaluate the value of heritage buildings [59]. Turskis Z et al. used this method to carry out multi criteria side ranking of heritage value [60]. Jiang P et al. used this method to analyze the value advantages of Railway Heritage [61].And Xu Y et al. used this method in the social value evaluation related to the heritage value [62]. In short, the method takes the research object as a system and makes decisions according to the thinking mode of decomposition, comparative judgment and synthesis. This study takes vitality as the goal, decomposes it from the perspective of value, and sorts and analyzes it in the way of expert consensus.

Finally, three aspects are analyzed: (1) comprehensive ranking of three values of 9 districts; (2) Rank the three values for each type of district; (3) Rank each target value in different types of districts. This study provides a direction for the improvement and development of historical and cultural districts.

Evaluation index

The assessment system consists of three hierarchies: A-target, B-criterion and C-indicator. A1, A2 and A3 correspond to the historic value assessment, the use value assessment and the sustainable value assessment respectively (Figs. 2, 3, 4). The evaluation criteria and their indicators were determined by expert consensus to evaluate vitality of nine historical and cultural districts. For the historic value assessment, three type criterions were adopted: historic environment, cultural environment and space environment. In the use value assessment, communication environment, business environment and living environment were selected as criteria. In the sustainable value assessment, education environment, attraction, and creativity were included in the criteria. The following is the explanation of each indicator:

Fig. 2
figure 2

Structure of historic value assessment

Fig. 3
figure 3

Structure of Use Value Assessment

Fig. 4
figure 4

Structure of Sustainable Value Assessment

C111 Through building type, roof form and material, facade style, building height, building density, greening, open space and other elements, it is specifically reflected in the two-dimensional space.C112 Buildings that can reflect historical features and local characteristics.C113 It refers to the overall appearance of the natural and human environment of the street, which reflects the historical and cultural characteristics.C121 The unchanged part of the historical characteristics of the street. C122 Unique culture. C123 Artistic characteristics. C131 It refers to the proportion between the total base area of buildings and the occupied land area within a certain range. Other parts are used for roads, greening, squares, parking lots, etc. C132 Ratio of the total building area of various buildings above the ground to the base area. C133 Ratio of height of street buildings to street width.

C211 Layout of public spaces such as squares on both sides of the street. C212 Greening degree of public space. C213 Number and style of recreational facilities in public space. C221 Number of commercial buildings and facilities. C222 Density of commercial buildings and facilities. C223 Types of commercial buildings and facilities. C231 Communication environment between neighbors. C232 Living service sharing facilities. Outdoor seats, etc. C233 Toilets, garbage cans and other sanitation facilities.

C311 Square for public activities. C312 Activities of primary and secondary school students, tourists, photographers and other groups in the block. C313 Important activities in the region, such as praying for blessings in Yonghegong district. C321 Public activity space, such as skiing in Shichahai area every winter. C322 Style and features, facilities, activities and other factors of the block remain in a state. C323 Level of heritage. C331 Literature about each blocks. C332 New activities about historical and cultural districts, such as the logo design of block. C333 The ages of historical sites and buildings in historical blocks.

The targets, the criteria and the indicators were ordered by the consensus of twenty experts, and the weights of the targets, the criteria and the indicators were determined by the order relation analysis method. Authority and representativeness are the basic principles for selecting consensus experts. To guarantee that experts are familiar with Beijing’s urban history and changes, the twenty experts were selected from Beijing think tank related to the Beijing central axis application for world heritage, and their majors were in Beijing history, architectural history, landscape, urban planning, and the other eight from Beijing cultural tourism department. The standard for selecting experts is to have senior professional titles, a certain popularity, and more than 10 years of working experiences. Finally, the values were computed through the following formula:

$${text{Vitality value of each district }} = , left( {text{value of target A1}} right) times {text{weight A1}} + left( {text{value of target A2}} right) times {text{weight A2}} + left( {text{value of target A3}} right) times {text{weight A3}}$$


Through the order relation analysis method, the values of the weights were calculated by using an rk scale from 1.0 to 1.8 to judge the relative importance of each target, each criterion and each indicator. The rk is the ratio of the weight wk-1 of factor xk-1 to the weight wk of factor xk as follows:

$$r_{k} = {{w_{k – 1} } mathord{left/ {vphantom {{w_{k – 1} } {w_{k} }}} right. kern-nulldelimiterspace} {w_{k} }},,,k = 2,3, cdots n$$


The significance of the rk scale is shown in Table 1. Firstly, the weight wn is calculated in terms of the rk evaluated with experts for each target, each criterion and each indicator.

$$w_{n} = left( {1 + sumlimits_{k = 2}^{n} {prodlimits_{i = k}^{n} {r_{i} } } } right)^{ – 1}$$


Table1 Significance of the rk scale

Then, the weights wn-1, wn-2,…, w1 were calculated using the Eq. (4). Through the order relation analysis method, the weights of each target, each criterion and each indicator were obtained as shown in Table 2.

$$w_{k – 1} = r_{k} w_{k} ,,k = 2,3, cdots n$$


Table 2 Weights of target A, criterion B and indicator C

Lastly, the comprehensive weight of each indicator was calculated using the Eq. (5).

$${text{Comprehensive}},{text{weight}},{text{of}},{text{indicator}},{text{C}}_{{{text{ijk}}}} = left( {weight,w_{ij} ,{text{of}},{text{criterion}},{text{C}}_{{{text{ij}}}} } right) times left( {{text{weight}},w_{ijk} ,{text{of}},{text{indicator}},{text{C}}_{{{text{ijk}}}} } right)$$


Case study of nine districts

The nine historical and cultural districts are selected according to the three types of districts (Table 3). These three types are divided based on the three main functions of historical and cultural blocks. The first type is cultural blocks, which are characterized by distinctive cultural characteristics. At the same time, the proportion of cultural buildings is also the highest.The three most representative blocks are Dongjiao Minxiang, Shichahai and Yonghegong district. Dongjiao Minxiang is a famous embassy district in modern times after the second Opium War in 1860, Britain, France, the United States, Russia, Japan, Germany, Belgium and other countries successively set up embassies in dongjiaomin lane, and renamed dongjiaominxiang as embassy street. It is a European style block integrating embassies, churches, banks, official residences and clubs. The existing buildings are preserved in the original state, maintaining the eclectic style popular in Europe and America at the beginning of the twentieth century. The moldings and pilasters are built with plain bricks, brick arches and verandas, wooden corner purlins, and iron roof slopes. It is the only western style architectural complex in Beijing in the early twentieth century. Shichahai is the largest and best preserved historical district in Beijing. It plays an important role in Beijing’s cultural history, mainly represented by Prince Gong’s mansion and garden, Song Qingling’s former residence and Lord Chun’s mansion, Guo Moruo memorial hall, bell and Drum Tower, Deshengmen arrow tower, Guanghua temple, Huitong temple and Huixian hall. There are many distinctive folk activities in Shichahai Area, such as releasing lotus lanterns, boating around the lake, feasting and enjoying the lotus, drinking around the ice bed, reading skates, etc. Some vigorous folk activities still exist in Shichahai Area. Such as fishing, swimming, boating, rowing, playing chess, singing, summer dance, etc. “Hutong Tour” is active in this unique natural and cultural environment. Yonghegong district is a block with a concentration of important temple buildings and important cultural relics in the old city of Beijing, including the Imperial College, Confucius Temple, Imperial College Street, Lama Temple, Berlin Temple, etc. The second type is the commercial historical districts, which is selected based on the large scale and rich types of business. The three blocks with large commercial scale and rich types are Liulichang, Dashilan and Nanluoguxiang. Liulichang has many famous old stores, as well as China Bookstore, the largest antique bookstore in China. Dashilan has been a business district since 1420. And Nanluoguxiang is the area with the most complete preservation and the most concentrated quadrangles in the old city of Beijing at present. The third type is residential historical districts, and the function of these areas is mainly residential. Typical residential districts are Jingshan, Fuchengmennei and Beiluoguxiang district. These three historical blocks with residential functions are characterized by the concentration of residential houses with Beijing characteristics. Based on field observation and measurement, this study collected the basic data of the field and the evaluation results of experts for analysis.

Table 3 General information of 9 historical and cultural districts

Twenty of the experts scored the indicator for nine districts as shown in Tables 4, 5. The nine districts are Dongjiao Minxiang Shichahai Yonghegong district Liulichang Dashilan Nanluoguxiang Jingshan Fuchengmennei Beiluoguxiang. In Tables 4, 5, the allocation scores were obtained by comprehensive weights multiplied by 100. According to the standards in Table 6, the experts scored the nine blocks, and each index was divided into five levels from high to low.

Table 4 Indicator score of nine districts for historic value assessment

To justify the reliability of each target separately (A1, A2 and A3), the Cronbach’s alpha of target Aj is used to clarify its reliability according to the Eq. (6) where K equals 9, (S_{{{text{A}}_{j} i}}^{2}) represents the variance of the value of indicator i of target Aj, (S_{{{text{A}}_{j} }}^{2}) represents the variance of sum of all index values of target Aj. Through the calculation the Cronbach’s alphas of targets A1, A2 and A3 are 0.732, 0.791, and 0.750 respectively and the research data have desirable reliability.

$$alpha_{{{text{A}}_{j} }} = left[ {K/left( {K – 1} right)} right]left( {1 – sum {S_{{{text{A}}_{j} i}}^{2} /S_{{{text{A}}_{j} }}^{2} } } right),,,j = 1,2,3,,,i = 1,2, cdots ,K$$


According to the indicator score of nine districts, the vitality value was calculated using the Eq. (1). The calculation results were 74.79 for Dongjiao Minxiang, 83.13 for Shichahai, 87.41 for Yonghegong district, 75.30 for Liulichang, 74.48 for Dashilan, 77.57 for Nanluoguxiang, 71.98 for Jingshan, 64.03 for Fuchengmennei, 62.36 for Beiluoguxiang.

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