*4.2. Evaluation Results of Coupling Coordination Model*

Since the indexes selected in this paper are inter-related and the information covered is overlapped, this paper adopted the principal component analysis method to extract the information contributed by each index to each subsystem, determine the corresponding weight coefficient of each index according to the component matrix and corresponding variance (see Table 6), and then calculate the comprehensive index of the atmospheric environment system and the industrial system according to Formula (3). The comprehensive index of atmospheric environmental and industrial systems, coupling degree, coupling coordination degree, comprehensive coordination index, and corresponding coupling coordination stages of the two systems are shown in Table 7 and Figure 5.


**Table 6.** Corresponding weight of each index.

**Table 7.** Coupling and coordination of the atmospheric environment system and the industrial system in Taiyuan.


**Figure 5.** Coupling and coordination trends of the atmospheric environment system and the industrial system in Taiyuan from 2003 to 2017.

It can be seen from the chart that the atmospheric environment of Taiyuan is systematically rising. From 2003 to 2010, it maintained a rapid upward trend, and the comprehensive index increased from 0.036 to 0.679, indicating the continuous improvement of atmospheric quality. However, the composite index fell in shock, and fell to 0.342 in 2014. This is mainly because China revised the ambient air quality standard (GB 3095-2012) in 2012 and adopted more stringent standards. After four years of adjustment and adaptation to the new standard, the development of the atmospheric environment system in Taiyuan showed an upward trend again, and the comprehensive index reached 0.797.

In terms of the industrial system, the comprehensive index of the industrial system basically maintained an upward trend from 2003 to 2015, rising from 0.048 to 1.011. Taiyuan's industrial structure has experienced the transformation from "secondary, tertiary, and primary" to "tertiary, secondary, and primary". The advanced index of the industrial structure continued to rise. However, the rationalisation index fluctuated, which reflects that the matching degree of elements in Taiyuan's industrial system and the internal optimisation of the three industries are important factors affecting the development of the system. After 2015, the decline of the comprehensive index of the industrial system also reflects this situation to a certain extent. After 2017, Taiyuan also began to publish relevant statistical data of strategic emerging industries and high-tech industries to refine and analyse the development quality within the industry.

The coupling degree, *C*, of the two systems fluctuated greatly before 2009 and became stable and close to 1 after 2009, indicating that the interaction between the atmospheric environment system and the industrial system is obvious. The coupling and coordination dispatching, *D*, maintained an upward trend, indicating that the two systems were developing in the direction of benign coupling. The coordination of the two systems has experienced the process of "uncoordinated—primary coordination—moderately coordinated—well-coordinated—quality coordination", indicating that the development between the systems tends to be gradually synchronised. However, it is also noted that the coupling coordination degree of the two systems slightly fluctuated, which reflects that the two systems in Taiyuan are currently in the transitional stage of "mutual running in and tend to coordination—high-level coupling coordination" in the above theoretical analysis framework.
