Four subsystems of urban resilience which include urban engineering subsystem, urban economic subsystem, urban society subsystem, and urban ecology subsystem (see Table 1).

Two indicators of urban engineering subsystem have been selected, such as communication index and livelihood protection index. Some indicators of urban economic subsystem have been observed out, including economic potential index, economic effectiveness index, and economic innovation index. Society development index and human development index have been picked for urban society subsystem. Meanwhile, environmental efficiency index and environmental governance index have formed for urban ecology subsystem.

The urban system is an organic whole of urban engineering subsystem, urban economic subsystem, urban society subsystem, and urban ecology subsystem. In urban synthetic system, those subsystems interacted each other. Therefore, the composite urban resilience system is expressed as: S = f ( x 1 , x 2 , x 3 , x 4 ) , where x 1 represents urban engineering subsystem, x 2 is on behalf of urban economic subsystem, x 3 is urban society subsystem, x 4 represents urban ecology subsystem, and f is a composite function.

The indicator of the four subsystems is x i j = ( x i j 1 , x i j 2 , ⋯ , x i j k ) , i ∈ [ 1 , l ] , j ∈ [ 1 , m ] , l ≥ 1 , m ≥ 1 . It can describe running state of four subsystems (ij) about urban engineering subsystem, urban economic subsystem, urban society subsystem, and urban ecology subsystem. Where α i j k is upper limit and β i j k is lower limit. There are β i j k ≤ x i j k ≤ α i j k , k ∈ [ 1 , n ] , and n ≥ 1 .

In addition, one indicator has two kinds: one is positive index. It is better when one index value is higher; conversely, it is the lower. The other is a negative index. It is better when one index value is lower. Data standardized about index ( x i j k ) can be defined.

Y i j ( x i j ) = { x i j k − β i j k α i j k − β i j k   ( i ∈ [ 1 , 4 ] , j ∈ [ 1 , 3 ] , k ∈ [ 1 , 4 ] ) ,     when   x i j k   is positive α i j k − x i j k α i j k − β i j k   ( i ∈ [ 1 , 4 ] , j ∈ [ 1 , 3 ] , k ∈ [ 1 , 4 ] ) ,     when   x i j k   is negative (1)

where y i j ( x i j ) ∈ [ 0 , 1 ] . Its value is greater, and the contribution is higher.

At present, index weight methods include subjective method, objective method, and mixed method. The former has expert scoring method and Delphi method; the middle include entropy value method, standard deviation method and CRITIC method (Suárez et al., 2016); the latter is a mixture method subjective method and objective method. This study selected CRITIC method to do with weight of the index.

Firstly, confirming the effect of indexes:

C k = δ k ∑ k = 1 n ( 1 − r j k )     , k ∈ [ 1 , 4 ] (2)

Among them, C k represents the impact of index (k) in the subsystem, δ k is half on the standard deviation of index (k), r j k represents the correlation coefficient between index (j) and index (k). The value of C k is greater, and it is more important to the subsystem.

Secondly, confirming the weight of index:

ω k = C k ∑ k = 1 n C k , k ∈ [ 1 , 4 ] (3)

where ω k is objective weight of index (k). Then, the matrix of weight coefficient R ω = { ω 1 , ω 2 , ⋯ , ω k } will be gained.

Firstly, the contribution of index ( y i ) can be shown by y i j ( x i j ) . For using of different forms of data, it is necessary to use the linear weighted sum method for data processing. The model of subsystem is followed.

Y i ( x i ) = ∑ q = 1 p ω k Y i j ( x i j ) , w ≥ 0 , ∑ q = 1 p ω k = 1 (4)

Secondly, urban resilience index for each city can be got from following forum.

S = 1 4 ∑ q = 1 4 Y i ( x i ) , i ∈ [ 1 , 4 ] (5)

Sichuan province locate in Western China, which includes 21 cities, such as Chengdu city, Panzhihua City, Deyang City, Neijiang City, Mianyang City, Zigong City, Yibin City, Yi Autonomous Prefecture of Liangshan, Tibetan Autonomous Prefecture of Aba, and so on. Urban natural ecosystems are fragile, in recent years, natural disasters brought a serious threat to the urban security and urban development.

Relative data were collected about Sichuan province, including 21 cities. Index data came from Sichuan province statistical yearbook (2004-2014) and Chinese city statistics yearbook (2004-2014).

Firstly, according to Formula (1), standardized original data of the index by statistical software (SPSS21). Secondly, confirmed index weight for each city according to the former Formula (2) and Formula (3). Moreover, get urban subsystem resilience using Formula (4). Finally, using the Formula (5), urban resilience index was calculated respectively. Specific data are shown in Table 2.

Table 3 shows urban resilience index of Sichuan province presented a rising trend from 0.188 in 2003 to 0.752 in 2013. The change of urban resilience consists of two stages. On the first phase from 2003 to 2008, urban resilience of Sichuan province was promoted from 0.188 to 0.448 gradually. On the second phase from 2008 to 2013, it was promoted from 0.448 to 0.752. Figure 2 shows that there was a inflect point in 2008. Because the Wenchuan earthquake happened at Tibetan Autonomous Prefecture of Aba in Sichuan province. Sichuan was mistaken as “unsafe” area. With the policy and resource support of nation, urban resilience index demonstrated an increasing tendency in 2009.

Specially, there were different from change of urban subsystem resilience. Urban engineering resilience presented a little change from 2003 to 2007, but it kept a rapid growth since 2008. Urban economic resilience had a growth trend from 2003 to 2013, but there was a drop point in 2008. Urban social resilience and urban ecology resilience kept increasing since 2003. Figure 3 shows that both urban engineering resilience and urban economic resilience were hit hard by the earthquake. After disaster, due to the attention of social public, urban four subsystem resilience had been rapidly promoted. Meanwhile, because of people’s concern about ecological environment and social progress, urban ecology resilience and urban social resilience were getting better.

LISA figure has been used for judging the temporal-spatial aggregation and differentiation of urban resilience of Sichuan province. Figure 4 shows that the urban resilience of Sichuan province had obvious spatial differentiation pattern in 2003 and 2008. High-low regional polarized city, Ya’an city, had appeared in 2003. This means that urban resilience of Ya’an city was relatively flexible, and its surrounding cities were low. High-high regional diffused city, Guang’an city, had appeared in 2008. This mean that urban resilience of Guang’an city was relatively flexible, and its surrounding cities were high too. In 2013, there were two regional diffused cities (Tibetan Autonomous Prefecture of Garzê and Tibetan Autonomous Prefecture of Aba), one low-high regional subsiding city (Ya’an city) and two low-low regional infectious cities (Guang’an city and Nanchong city), as showed in Table 4.