Research on Urban Contraction of Liaoning Province Based on Population Influencing Factors

: In the process of urbanization in China, the problem of urban contraction in Liaoning Province has become increasingly prominent. In this paper, through the preprocessing of the data of 30 cities in Liaoning Province from 2009 to 2020, an one-dimensional classification model is established by using population factors, and 23 shrinking cities are identified, accounting for 76.7%. Furthermore, considering the changes of total population and GDP, combined with comprehensive influencing factors, a multi-dimensional classification model is established, and 30 cities are divided into absolute growth type, population aggregation type, intelligent contraction type and absolute contraction type. The results show that the cities of Liaoning Province generally show a shrinking trend from 2009 to 2020, among which the population contraction trend of Lighthouse City and Linghai City is particularly obvious. In addition, the economic development of shrinking cities in Liaoning Province tends to slow down, or even decline. Combining the analysis results of the two identification methods, it is found that Anshan City, Donggang City, Fengcheng City, Dashiqiao City, Tiefa City and Kaiyuan City are six cities with a large degree of contraction.


Introduction
At a time when China's economy has entered the "new normal" and the demographic structural pressure has gradually become prominent, the localized urban contraction is gradually coming into people's view [1].Population decline and economic weakness are the concrete manifestations of urban shrinkage.
Urban shrinkage exists widely at home and abroad, and is also an economic and social phenomenon with significant regional characteristics.It has been noted that under the influence of globalization, deindustrialization and resource depletion, many cities have experienced population loss and economic decline.This phenomenon is also common in Europe and the United States, the transition countries of Eastern Europe, Central and South America and Asian countries.
Nowadays, China's economy is advancing by leaps and bounds, urbanization is developing rapidly, industry and regional development is unbalanced, and the problem of urban shrinkage has aroused people's attention in recent years.Through the study of the old industrial zone in northeast China, the traditional heavy industry city in central China, the developed urban circle in eastern China and the remote areas in western China, there are local and different degrees of urban shrinkage, and the urban shrinkage in the three eastern provinces is the most significant.
Liaoning, as the national traditional heavy industry base, is also the first province to start industrialization and urbanization.At present, Liaoning has 2 sub-provincial cities such as Shenyang and Dalian, 12 prefecture-level cities such as Anshan, and 16 county-level cities such as Xinmin, a total of 30 cities, which are also facing the problem of urban shrinkage.
The definition of shrinking cities can be roughly divided into two categories: the definition based on the change of single population number index and the definition with comprehensive multi-index change.A single population indicator, such as: a shrinking city is defined as having a population decline for three consecutive years; A city that has lost population for more than two years and experienced a structural economic crisis can be defined as a shrinking city; A city with a population loss of at least 10% of the total population or an average annual population loss rate greater than 1% can be defined as a shrinking city.The categories of urban shrinkage are mild, moderate and severe.Based on multiple indicators such as simultaneous population and urban GDP changes, cities are classified into four types: absolute growth (both growth), population agglomeration (population increase, urban GDP decrease), smart contraction (population decrease, urban GDP increase) and absolute contraction (both contraction).
This paper classifies 30 cities in Liaoning Province, uses the definition method to identify shrinking cities, and establishes the classification model.

Research Method
First of all, we judge according to the data given in the title, which can be divided into one-dimensional population urban shrinkage type and joint comprehensive index urban shrinkage type according to the definition.This is a shrinking city with a shrinking population for three consecutive years.
Cities with a population loss of more than two years and experiencing a structural economic crisis; cities whose population loss accounts for at least 10% of the total population or with an average annual population wastage rate of more than 1%; combined with population and urban GDP changes, cities are divided into four types: absolute growth (double growth), population agglomeration (population increase, urban GDP decrease), smart contraction (population decline, urban GDP increase) and absolute contraction (both contraction).
After analyzing the two types, first fill in the missing data to ensure the integrity of the data.
Then, according to the definition and data, the shrinking type of the city with one-dimensional population is calculated, and the city in the shrinking state is obtained.
After the shrinking cities are obtained, the shrinking cities are further classified by the joint comprehensive index (GDP, demographics).

Data Preprocessing
In order to ensure the integrity of the data, we preprocessed the data and processed the missing values of the missing data by Lagrange interpolation and Newton interpolation.

Lagrange interpolation method
(1) Set to the corresponding year, for the corresponding number of people in the corresponding year.    Find the basis function of the point pair.( 1 ,  1 ), ( 2 ,  2 ) … (  ,   ).
(3) Substitute the points corresponding to the missing function value into the interpolation polynomial to get the missing value approximation().

Newton interpolation method
(1) Formula for finding all order difference quotients of known n point pairs (2) Combine the above difference quotient formula to establish the following interpolation polynomial().
(3) The point corresponding to the missing function value is substituted into the interpolation polynomial to get the approximate value of the missing value ().

Data Processing Result
Two methods 3.1.1and 3.1.2were used to calculate the missing data and outliers with MATLAB, and the results were shown in Table 1.

Single population factor shrinks city identification
One of the most important characteristics of urban shrinkage is population shrinkage, so population shrinkage is regarded as the core and key index to define urban shrinkage [2].The definition of the change of a single population number index is diverse.This paper divides it into two stages according to the time series, from 2009 to 2018 and from 2019 to 2020, and analyzes the shrinking cities of Liaoning Province in the two stages.According to the criteria of mild shrinkage (-5% < SSD < 0), moderate shrinkage (-10% < SSD≤ -5%) and severe shrinkage (SSD≤ -10%), the shrinking trends of different cities were analyzed.

Research methods
(1) Standardized data: (2) Calculate the weight of the desired index: (3) Calculate the development index of the JTH city: The formula (6) -( 9) represents the difference between the original value   and the standardized value   ′ prime of evaluation index j for evaluation unit i.Here,   and   denote the maximum and minimum values of evaluation index j, respectively.  refers to the urban development index of evaluation unit i, while   represents the weight assigned to evaluation index j.Additionally,  denotes the number of samples,  signifies the number of evaluation indicators, SSD stands for city shrinkage, and t indicates the time year [3].

Analysis of results of shrinking cities by single population factor
The population dimension changes of 30 cities in Liaoning Province during 2009-2018, 2019-2020 and 2009-2020 are obtained, and according to SSD evaluation, when the value is negative, they are judged as shrinking cities.The collective judgment results are shown in Figure 1.

Combined comprehensive factors shrink city identification factors
Through the classification and judgment of a single factor on urban shrinkage, we further study and classify shrinking cities by combining comprehensive factors.Because there are too many factors affecting GDP, it is impossible to make a judgment by direct prediction.Therefore, the shrinking cities of Liaoning Province are also divided into two stages according to the time series: 2009-2018 and 2019-2020.The development status of the research unit was evaluated by using the changes of urban GDP and population size.The formula is as follows: Where,   and   represent the respective change values of GDP and population size for city i;  , and  ,0 denote the total GDP of city i in year t and base year, respectively.Similarly,  , and  ,0 refer to the urban population size of city i in year t and base year, respectively [4,5].In cases where both population and GDP increase   > 1,   > 1 ), the shrinking city is referred to as experiencing absolute growth.If the urban population increases while GDP decreases (  < 1,   > 1), it is termed as a case of population agglomeration.Conversely, if the urban population decreases while GDP increases (  > 1,   < 1), it is classified as smart shrinking type.Finally, when both city's population and GDP decrease (  < 1,   < 1), it falls under the category of absolute shrinking type.

Analysis of identification results of shrinking cities by combining comprehensive factors
As for shrinking cities caused by joint factors, it is necessary to conduct multidimensional comprehensive analysis from GDP and population.According to the formula and method 5.

Figure 1 :
Figure 1: Results of urban shrinkage with population dimension change 3.1, the attached urban population statistics table of Liaoning Province is used to divide the 30 cities in Liaoning Province into two stages from 2009 to 2018 and from 2019 to 2020 according to the time series.The cities are classified, and the specific identification results are shown in Figure 2.

Figure 2 :
Figure 2: Results of multi-dimensional joint indication of urban shrinkage According to Figure 2, we further classify the 30 cities into four types and two stages.From the data in Table, it can be seen that among the 30 cities in the time series from 2009 to 2018, 8 are

Table 1 :
Urban population of Liaoning