Study on the comprehensive evaluation of low carbon city based on PSR model and normalized index transformation

Referring the “stress-state-response” (PSR) model, the index system of low-carbon city was constructed. The Immune Evolution Chaos Weed Algorithm was used to optimize the Weber Fechner index formula and the universal Carson index formula. A low-carbon city evaluation method was established and applied to evaluate the low-carbon development level of Beijing, Tianjin, Shanghai, and Chongqing in 2015. The results showed that the evaluation results of the Weber Fechner index formula and the universal Carson index formula for the four cities were basically the same. The low-carbon development level (Weber Fechner Composite Index XI) of the four cities in 2015 was ranked as follows: Beijing (0.590), Shanghai (0.499), Tianjin (0.467), Chongqing (0.461).

With the continuous acceleration of urbanization, the continuous growth of economic scale, and the massive consumption of energy, the global catastrophic climate change caused by the increase in the concentration of carbon dioxide in the atmosphere has repeatedly appeared, which has seriously threatened the survival and development of human beings. As an important measure to deal with global climate change, low-carbon city construction is booming.
This article adopts the "pressure-state-response" (PSR) model to establish a low-carbon city evaluation index system. Based on the setting of the reference value of the low-carbon city evaluation index and the standard transformation formula, the immune evolution chaos weed algorithm is used to optimize the parameters of the Weber Fechner index formula and the universal Carson index formula. The equal weight method is adopted to determine the comprehensive index classification standard, and empirical analysis is carried out in four cities of Beijing, Shanghai, Tianjin and Chongqing.
1 Low-carbon city index system construction and evaluation methods

Construction of PSR model
In the pressure-state-response (PSR) model, pressure refers to the effects of human economic and social activities on the environment, state refers to the environmental state and changes in a specific time period, and response refers to actions taken by humans to reduce, prevent and restore the negative impact of human activities on the environment.
From the perspective of carbon source-carbon flowcarbon sink, this article focused on the availability of data, the cohesion between indicator systems, and the ease of assessment [1][2] . The pressure layer selects indicators such as energy consumption per unit of GDP and the level of urbanization, the state layer selects indicators such as urban air quality and forest coverage, and the response layer selects indicators such as the proportion of clean energy in energy consumption and the proportion of energy-saving buildings to establish a PSR model.

Data standardization
Since the evaluation index system has two types of indicators, forward and reverse, the standard values of different indicators often differ greatly between the same level. Therefore, the data needs to be standardized before evaluation. This article adopts formula (1) and formula (2) to carry out the specification transformation.
Among them, � and � ′ are the transformed value and the standard value of index ; �� is the reference value of index ; � is the grading standard value or actual value of index ; � is the threshold value of index ; The power exponent of the set index , and � � �. Through a lot of practice, the selection method of nj is summarized as follows. Estimate the most probable value of � according to the variation range of the ratio of the maximum value �� � �� � to the minimum value �� � �� � or the ratio of �� � � � �� � to �� � � � �� � in the various standards of index , as shown in Table 1. Secondly, the standard is divided into 5 levels, and �� is set based on the preliminary determination of � , so that the standard normative value of index calculated by formula (1) and formula (2) can be within the range.
shown in Table 2.

Formula selection and parameter optimization
Based on the normative transformation of indicators, a universal W-F (Weber-Fechner) index formula and universal Carson index formula expressed by index norm values are established [3][4][5] . Among them, � , � , and � are the parameters to be optimized in formula (3) and formula (4) respectively, which are applicable to all indexes and have nothing to do with the specific index value. � , � are the index values of the two universal index formulas corresponding to index . The parameters of the above formula are optimized by the immune evolution chaos weed algorithm, and the optimized formulas are shown in formula 5 and formula 6. After verification, the formula is reliable [6] .
Weber Fechner(W-F)index formula: Universal Carson Index formula: The index specification value �� or the corresponding index transformation value �� ( � 1,2,…,100� � � 1,2,3,4,5) is taken into formula 5 and formula 6 for calculation. Regarding the value of each index with equal weight, the comprehensive index grading standard value �� applicable to any index is calculated by formula (7).
In formula (7), is the comprehensive index value of indicators. � is the index value of a single index calculated by formula (5) and formula (6) respectively. � is the normalized weight of index , . If there is little difference in the norm value of each indicator after norm transformation, the form of equal weight is generally adopted.
Otherwise, the index needs to be weighted calculation. If the index needs to be weighted and calculated, the linear weighting method such as formula (8) is generally used to linearly weight the conversion value � of each index.
Weber Fechner(W-F)index formula: Universal Carson Index formula:

Grading standard determination
Based on the comprehensive indicators of low-carbon cities and reference standards, the development level of low-carbon cities is divided into 5 levels. The median value of each grading range in Table 2 is taken as the standard value of low-carbon city grading standard, and they are respectively brought into equation (5) and equation (6). The difference between the indexes after the standard transformation is very small. The W-F index formula and the universal Carson index formula are calculated using the equal weight method to obtain the comprehensive index classification standard values � and � as shown in Table 3. In the evaluation process, the pros and cons of all levels of indicators are judged according to the positive and negative indicators.
Summarize the collected data and judge the pros and cons of the 18 indicators. According to the threshold value of index j set by relevant data, the standard transformation formula of 18 indexes is designed.
Calculate the relevant range value of � �� �� � � �� �� �� � or � �� � � � �� � � �� �� � � � �� � from the data of each year. It is determined that except for the index 18 to be 0.5, the other indexes � are all 2, and the reference value �� of each index is calculated, and the standard value of each level (k=1~5) is calculated inversely. The results are shown in the table below.

Data sources
The

Result analysis
From Table 5 and Table 6, it can be seen that the index values � , the standardized conversion values �� of the indicators and the comprehensive index value of the two formulas in the four cities of Beijing, Shanghai, Tianjin and Chongqing.The evaluation results of the Weber Fechner index formula and the universal Carson index formula for the four cities of Beijing, Shanghai, Chongqing and Tianjin are basically the same.  Status indicators: the low-carbon development level (Weber Fischner Composite Index XI) of the four cities is ranked: Chongqing (0.541), Shanghai (0.475), Beijing (0.467), Tianjin (0.420). Beijing, Chongqing, and Chengdu had higher forest coverage rates. Chongqing's forest coverage rate in 2015 was 45.4%, and the per capita public green area was relatively high; Tianjin's forest coverage rate and per capita public green area were relatively low. In addition, the air quality indicators of 4 cities, especially Beijing, account for a low proportion of the 4 status indicators, indicating that the air quality of the cities has declined and urgently needs improvement.
Responsive indicators: the low-carbon development level (Weber Fischner Composite Index XI) of the four cities is ranked: Beijing (0.602), Shanghai (0.522), Tianjin (0.498), Chongqing (0.459). Beijing's tertiary industry accounted for the highest proportion of GDP and energy processing and conversion efficiency; Tianjin was relatively dependent on the development of heavy industry, and clean energy accounted for a low proportion of energy consumption; Chongqing's industrial solid waste disposal utilization rate was low.

Conclusion
This article established a low-carbon city evaluation index system and evaluation model on the basis of grasping the connotation of low-carbon city development. The optimized universal Carson index formula and Weber Fechner index formula were used in the comprehensive evaluation of low-carbon development in four cities of Beijing, Shanghai, Tianjin and Chongqing. a) Different types of index data were standardized to make the comprehensive evaluation results comparable; b) To ensure the objectivity of the evaluation results, the basic evaluation method adopted the equal weight method; c) To ensure the effectiveness of the combined evaluation results, reliability analysis was carried out during the evaluation process, so as to finally obtained the evaluation result that can comprehensively measure the level of urban low-carbon development. Based on the actual data of the four cities, and the use of optimized evaluation methods for empirical analysis, the results showed that the Weber Fechner index formula and the universal Carson index formula had basically the same evaluation results for the four cities of Beijing, Shanghai, Tianjin and Chongqing.