CN108647842B - Method for detecting sudden change of industrial gathering spatial pattern - Google Patents

Method for detecting sudden change of industrial gathering spatial pattern Download PDF

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CN108647842B
CN108647842B CN201810171593.6A CN201810171593A CN108647842B CN 108647842 B CN108647842 B CN 108647842B CN 201810171593 A CN201810171593 A CN 201810171593A CN 108647842 B CN108647842 B CN 108647842B
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葛莹
刘磊
鲍倩
李均凯
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Hohai University HHU
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Abstract

The invention relates to a method for detecting sudden change of an industrial gathering spatial mode, which comprises the steps of firstly generating an industrial geographic spatial element field, and establishing an industrial geographic and related social and economic database; secondly, introducing a Ripley's K function of a spatial point pattern analysis method to quantitatively estimate a Ripley's K function value of the industrial gathering spatial pattern; then, normalizing Ripley's K function values by using an L function, and further acquiring a multi-scale spatial mode boundary L function value sequence of industrial geography or industrial economic layout; and finally, determining the spatial mode mutation point and the mutation position of the industrial geography or economic layout by applying a Mann-Kendall mutation point analysis method in mathematical statistics and performing mutation inspection on the spatial mode marginal L function value sequence of the industrial geography or economic layout. The invention can effectively reveal the space overflow effect range of the industrial aggregation while acquiring the change characteristics of the industrial aggregation space mode.

Description

Method for detecting sudden change of industrial gathering spatial pattern
Technical Field
The invention relates to a method for detecting sudden change of an industrial aggregation spatial mode, and belongs to the technical field of regional industry planning.
Background
The gathering of the industry as the most prominent geographical feature of economic activities is always the research hotspot of scholars in relevant fields of urban geography, regional economics and the like. According to new economic theory of geography, the concentration in the industrial space will result in economies of scale that exhibit different spatial patterns of industrial clustering, but economies of scale have distance decay characteristics that when they reach a critical range, the industrial clustering in a region will effect a sudden change from one spatial pattern to another. The method has the advantages that the mutation points and mutation positions of the industrial economic layout space mode are detected and obtained, the space overflow effect range of industrial aggregation can be expressed quantitatively, the change characteristics of the industrial aggregation space mode in China can be analyzed, the specific current situation of regional economic development can be known, and a certain degree of decision basis is provided for regional industrial layout optimization in China. However, at present, there are few methods for examining and researching mutation phenomena in the continuous change process of industrial spatial structures at home and abroad.
Disclosure of Invention
The invention aims to provide a method for detecting sudden change of an industrial gathering space mode, which can accurately detect the change trend of the industrial gathering space mode and accurately determine the initial position of the change trend.
The invention adopts the following technical scheme for solving the technical problems: the invention designs an industrial aggregation spatial mode mutation detection method, which is used for realizing spatial mode mutation detection aiming at the layout of a target industrial zone bit in a target research region, initializing a circumscribed rectangular region with the minimum area of the target research region as a target calculation region, and presetting a group of spatial scales r ═ r (r ═ r)1,...,rs,...,rS) S is more than or equal to 10, wherein at least 3 adjacent target industrial areas are arranged in an area with the geographic position of any target industrial area in the target calculation area as the center of a circle and the minimum spatial dimension as the radius, and the maximum spatial dimension does not exceed 1/2 of the short side of the target calculation area; the spatial mode mutation detection method comprises an industrial gathering spatial mode mutation detection method based on a target industrial zone bit, and comprises the following steps of:
step A1: obtaining all target industrial zone bits in the target calculation region and respectively corresponding to each space scale rsThe Ripley's K function value and form a target industry location space mode K function value sequence
Figure GDA0003108004550000011
Then step A2 is entered;
step A2: target industry zone bit space mode K function value sequence by adopting L function
Figure GDA0003108004550000012
Correcting, updating and obtaining the L function value sequence of the target industrial zone bit space mode
Figure GDA0003108004550000013
Then step A3 is entered;
step A3: constructing a boundary L function value sequence of a target industrial zone spatial mode
Figure GDA0003108004550000014
Then step A4 is entered;
step A4: adopting a Mann-Kendall method to inspect and determine a marginal L function value sequence of a target industrial zone bit spatial mode
Figure GDA0003108004550000021
The mutation point position interval of (1).
As a preferred technical solution of the present invention, the method for detecting spatial pattern mutation in industry clustering based on target industry location further comprises step a5, after step a4 is executed, step a5 is performed;
step A5: according to the boundary L function value sequence of the target industry zone bit space mode
Figure GDA0003108004550000022
Determining the boundary L function value sequence of the space mode of the target industrial zone
Figure GDA0003108004550000023
The specific location of the mutation point.
As a preferred embodiment of the present invention, the step a1 includes the following steps:
step A1-1: initializing s ═ 1, and proceeding to step a 1-2;
step A1-2: respectively aiming at each target industrial zone in the target calculation area, taking the geographic position of the target industrial zone as the center of a circle and rsFor the radius, construct the corresponding space dimension r of the target industrial zonesThe circular area of (a) is obtained, namely, the space scale r corresponding to each target industrial zone is obtainedsThen to step a 1-3;
step A1-3: according to the following formula:
Figure GDA0003108004550000024
obtaining a target calculation regionAll target industrial zone integral corresponding space scale rsThe function value of Ripley's K, then go to step A1-4, where A is the area of the calculation region, N is the number of target industrial locations in the target calculation region, dijIndicating the distance between the target industrial location i and the target industrial location j,
Figure GDA0003108004550000025
as an indicator, if the target industrial location j falls into the circular area corresponding to the target industrial location i, then
Figure GDA0003108004550000026
Otherwise
Figure GDA0003108004550000027
Step A1-4: judging whether S is equal to S, if so, entering the step A1-5; otherwise, updating by adding 1 according to the value of s, and returning to the step A1-2;
step A1-5: aiming at the Ripley's K function values of all the target industry zone bits in the target calculation region, which respectively correspond to all scales, a target industry zone bit space mode K function value sequence is formed
Figure GDA0003108004550000028
As a preferred embodiment of the present invention, the step a4 includes the following steps:
step A4-1: setting a threshold t for the location of a spatial mode break point of a target industrial zoneLoc；
Step A4-2: for a sample sequence containing p target industry location spatial mode boundary L function values
Figure GDA0003108004550000029
Construct order statistic opThe following;
Figure GDA0003108004550000031
in the formula，opRepresenting the jth sample as a sequential statistic
Figure GDA0003108004550000032
Greater than the ith sample
Figure GDA0003108004550000033
I is more than or equal to 1 and less than or equal to j, IijIs an indicator;
step A4-3: defining and calculating S-1 statistics U obeying N (0,1) distribution under the assumption that the boundary L function value sequence of the target industrial zone spatial mode is independent randomlyLoc(op) The following were used:
Figure GDA0003108004550000034
in the formula, ELoc(op)、VarLoc(op) Respectively, the order statistic opMean and variance of (1), target industry zone bit spatial mode margin L function value sequence
Figure GDA0003108004550000035
Independently and randomly distributed, and calculating E according to the following expressionLoc(op) And VarLoc(op)：
ELoc(op)＝p(p-1)/4
VarLoc(op)＝p(p-1)(2p+5)/72
Step A4-4: sample sequence of boundary L function value of spatial mode of p target industrial zone bits
Figure GDA0003108004550000036
In reverse order
Figure GDA0003108004550000037
Repeating step A4-2 and step A4-3 to obtain a new statistical U'Loc(op)(p＝1,2,…,S-1)；
Step A4-5: selecting a significant confidence level alpha according to a standard normalDistribution table acquisition critical value Uα；
Step A4-6: with rpThe value is horizontal axis, the value of U is vertical axis, let U* Loc(op)＝-U′Loc(op′) Where p' is S-p, the statistic ULoc(op) And U* Loc(op) Calculating the intersection of two lines in the same graph
Figure GDA0003108004550000038
Is provided with a ULocValue, and its corresponding spatial scale
Figure GDA0003108004550000039
If U isLocThe value satisfies the inequality | ULoc|<UαThen the spatial scale is considered to be at the confidence level α
Figure GDA00031080045500000310
Interval (r) ofa,ra+1) (a ∈ (1,2, …, S-2)) there is an industry locational spatial pattern mutation point.
As a preferred embodiment of the present invention, the step a5 includes the following steps:
step A5-1: computing
Figure GDA00031080045500000311
To ra、ra+1Is a minimum difference value ar ofLocAnd the corresponding spatial scale
Figure GDA00031080045500000312
The expression is as follows:
Figure GDA00031080045500000313
step A5-2: according to the threshold value tLocJudgment of
Figure GDA00031080045500000314
Whether the position is a specific position of a mutation point or not is judgedThe rules are as follows:
if Δ rLoc≤tLocThen space scale
Figure GDA00031080045500000315
The position of the mutation of the spatial mode of the industrial zone, namely the spatial overflow effect range of the industrial zone;
if Δ rLoc＞tLocThen r is respectively changeda、ra+1Setting a set of new space dimensions r 'as the space dimension limit range'LocReturn to step A1 until Δ r 'is satisfied'Loc≤tLocUp to this time, the space scale
Figure GDA0003108004550000041
Is the specific location of the spatial pattern mutation point of the target industrial zone.
As a preferred embodiment of the present invention, the mutation detection method further comprises an industry aggregation spatial pattern mutation detection method based on socioeconomic data related to target industry designation, and comprises the steps of:
step B1: obtaining all target industry zone bits in the target calculation area, respectively corresponding to all scales r based on the target industry specified relevant social and economic datasThe Ripley's K function value and forms a target industry related social economic data space mode K function value sequence
Figure GDA0003108004550000042
Then step B2 is entered;
step B2: k function value sequence aiming at target industry related social and economic data spatial mode by adopting L function
Figure GDA0003108004550000043
Correcting, updating and obtaining the L function value sequence of the space mode of the social and economic data related to the target industry
Figure GDA0003108004550000044
Then step B3 is entered;
step B3: constructing a boundary L function value sequence of a target industry related social and economic data spatial mode
Figure GDA0003108004550000045
Then step B4 is entered;
step B4: adopting a Mann-Kendall method to inspect and determine a marginal L function value sequence of the target industry related social and economic data space mode
Figure GDA0003108004550000046
The mutation point position interval of (1).
As a preferred embodiment of the present invention, the method for detecting mutations in the spatial pattern of industry aggregation based on socioeconomic data related to target industry designation further includes step B5, and after step B4 is executed, the method proceeds to step B5;
step B5: according to the marginal L function value sequence of the target industry related social and economic data space mode
Figure GDA0003108004550000047
Determining the marginal L function value sequence of the space mode of the social and economic data related to the target industry
Figure GDA0003108004550000048
The specific location of the mutation point.
As a preferred embodiment of the present invention, the step B1 includes the following steps:
step B1-1: initializing s ═ 1, and proceeding to step B1-2;
step B1-2: aiming at each target industrial zone in the target calculation region, respectively, taking the geographic position of the target industrial zone as the center of a circle and taking the spatial scale rsFor the radius, construct the corresponding space dimension r of the target industrial zonesThe circular area of (a) is obtained, namely, the space scale r corresponding to each target industrial zone is obtainedsThen to step B1-3;
step B1-3: according to the following formula:
Figure GDA0003108004550000051
obtaining all target industry zone bits in the target calculation area, and appointing related social and economic data and corresponding spatial scale r based on the target industrysThen to step B1-4, where A is the area of the calculation region, N is the number of target industrial locations in the target calculation region, and xiAssigning relevant socioeconomic data, x, to the target industry of the target industry location iij(rs) To fall into the corresponding space scale r of the target industrial zone isThe target industry of a target industry zone j in the circular area specifies related social and economic data;
step B1-4: judging whether S is equal to S, if so, entering step B1-5; otherwise, updating by adding 1 according to the value of s, and returning to the step B1-2;
step B1-5: aiming at all target industry zone bits in a target calculation area, a target industry specified related social and economic data is designated based on the target industry, Ripley' sK function values corresponding to all spatial scales are respectively formed, and a target industry zone bit spatial mode K function value sequence is formed
Figure GDA0003108004550000052
As a preferred embodiment of the present invention, the step B4 includes the following steps:
step B4-1: setting target industry related social and economic data space mode margin L function value sequence
Figure GDA0003108004550000053
Threshold t of abrupt change point positionSoc；
Step B4-2: for a sample sequence containing p target industry related social economic data space mode boundary L function values
Figure GDA0003108004550000054
Construct order statistic opThe following were used:
Figure GDA0003108004550000055
in the formula opRepresenting the jth sample as a sequential statistic
Figure GDA0003108004550000056
Greater than the ith sample
Figure GDA0003108004550000057
Cumulative number of (I)ijIs an indicator;
step B4-3: defining and calculating S-1 statistics U obeying N (0,1) distribution under the assumption that target industry related socioeconomic data space pattern sequences are independent randomlySoc(op) The following were used:
Figure GDA0003108004550000058
in the formula, ESoc(op)、VarSoc(op) Respectively, the order statistic opMean and variance of (1), margin L function value sequence of industry-related social and economic data space mode
Figure GDA0003108004550000061
Independently and randomly distributed, and calculating E according to the following expressionSoc(op) And VarSoc(op)：
ESoc(op)＝p(p-1)/4
VarSoc(op)＝p(p-1)(2p+5)/72
Step B4-4: will contain p target industry related socioeconomic data space pattern sequences
Figure GDA0003108004550000062
In reverse order
Figure GDA0003108004550000063
Figure GDA0003108004550000064
Steps B4-2 and B4-3 were repeated to give a new statistical U'Soc(op)(p＝1,2,…,S-1)；
Step B4-5: selecting significant confidence level alpha, and obtaining critical value U according to standard normal distribution tableα；
Step B4-6: with rpThe value is horizontal axis, the value of U is vertical axis, let U* Soc(op)＝-U′Soc(op′) Where p' is S-p, the statistic USoc(op) And U* Soc(op) Calculating the intersection of two lines in the same graph
Figure GDA0003108004550000065
Is provided with a USocValue and its corresponding spatial scale
Figure GDA0003108004550000066
If U isSocThe value satisfies the inequality | USoc|<UαThen the spatial scale is considered to be at the confidence level α
Figure GDA0003108004550000067
Interval (r) ofb,rb+1) (b ∈ (1,2, …, S-2)) has an industry-related socioeconomic data spatial pattern mutation point.
As a preferred embodiment of the present invention, the step B5 includes the following steps:
step B5-1: computing
Figure GDA0003108004550000068
To rb、rb+1Is a minimum difference value ar ofSocAnd the corresponding spatial scale
Figure GDA0003108004550000069
The expression is as follows:
Figure GDA00031080045500000610
step B5-2: according to the threshold value tSocJudgment of
Figure GDA00031080045500000611
Whether the position is a specific position of a mutation point or not is judged according to the following rule:
if Δ rSoc≤tSocThen space scale
Figure GDA00031080045500000612
The mutation position of the spatial pattern of the target industry-related social and economic data is also the spatial overflow effect range of the industry-related social and economic data;
if Δ rSoc＞tSocThen r is respectively changedb、rb+1Setting a new set of spatial scales as the spatial scale limit range, and returning to the step B1 until delta r 'is met'Soc≤tSocUp to this time, the space scale
Figure GDA00031080045500000613
The specific position of the mutation point of the target industrial zone bit space pattern sequence.
Compared with the prior art, the industrial gathering space mode mutation detection method adopting the technical scheme has the following technical effects: the invention relates to a method for detecting sudden change of an industrial gathering spatial mode, which comprises the steps of firstly generating an industrial geographic spatial element field and establishing an industrial geographic and related social and economic database; secondly, introducing a Ripley's K function of a spatial point pattern analysis method to estimate a Ripley's K function value of an industrial gathering spatial pattern; then, normalizing Ripley's K function values by using an L function, and further acquiring a multi-scale spatial mode boundary L function value sequence of industrial geography or industrial economic layout; and finally, determining the spatial mode mutation point and the mutation position of the industrial geography or economic layout by applying a Mann-Kendall mutation point analysis method in mathematical statistics and performing mutation inspection on the spatial mode marginal L function value sequence of the industrial geography or economic layout. The method has the characteristics of high quantification degree and wide detection range, effectively reveals the space overflow effect range of the industrial aggregation while acquiring the change characteristics of the industrial aggregation space mode, and reflects the detailed condition of regional economic development, thereby providing a certain decision basis for regional industrial optimization layout in China.
Drawings
FIG. 1 is a schematic diagram of the method for detecting mutations in spatial patterns of industrial aggregation according to the present invention;
FIG. 2 is a schematic diagram of spatial patterns of urban areas in the Long triangular region of China;
FIG. 3 is a Mann-Kendall statistical curve of urban zone bit space mode in Long triangular region;
FIG. 4 is a schematic diagram of a large-scale spatial model of a manufacturing population of a city in the Yangtze river region of China;
FIG. 5 is a drawing showingSocA man-Kendall statistic curve of a population scale space mode of urban manufacturing in inner-long triangular regions;
FIG. 6 is r'SocAnd (3) a man-Kendall statistic curve of a population scale space mode of urban manufacturing in inner-long triangular region.
Detailed Description
The following description will explain embodiments of the present invention in further detail with reference to the accompanying drawings.
Ripley's K function was first used for ecological spatial pattern analysis, and then gradually applied to economic geography to study the continuous variation process of the position relationship of industrial elements, feature clustering or other heterogeneous spatial patterns. Therefore, for obtaining the industrial clustering spatial pattern sequence, the Ripley's K function is different from other spatial point pattern analysis methods mainly in that the Ripley's K function can reflect the spatial pattern of the industrial clustering under each set spatial scale, realize the quantitative research of the spatial heterogeneity and reveal the change rule of the industrial clustering spatial pattern along with the spatial scale.
Since the actual Ripley's K function value is usually larger and the Ripley's K function curve graph has limited expression capability, in order to obtain more implicit data information in the Ripley's K function value, an L function with zero as a comparison standard is often adopted. The L function is a further modification and normalization of the Ripley's K function.
For mutation tests of a certain sequence, a mean value change point analysis method in mathematical statistics is mostly adopted, and the mean value change point analysis method is more applied to climate mutation tests to search for the rapid change of the climate from one statistical characteristic to another statistical characteristic in time series. In the industrial aggregation spatial pattern sequence mutation test, compared with other variable point analysis methods, the Mann-Kendall method has wide applicability and obvious effectiveness, can better reveal the trend characteristics of the industrial aggregation spatial pattern in a certain spatial sequence, can also divide a spatial pattern mutation region and determine the mutation starting position, and does not need a sample to follow certain distribution and is not interfered by a few abnormal values.
As shown in fig. 1, the present invention designs an industrial aggregation spatial pattern mutation detection method, which is used for layout of a target industrial location in a target research area, and in practical applications, mutation detection is designed to be implemented from two directions, one is an industrial aggregation spatial pattern mutation detection method based on the target industrial location, and the other is an industrial aggregation spatial pattern mutation detection method based on target industry-specified related socioeconomic data, and then mutation detection implemented from the two directions is explained by combining with specific embodiments.
Aiming at an industrial aggregation space mode mutation detection method based on a target industrial zone in the first direction, a first embodiment is introduced, aiming at an urban zone position aggregation space mode of a Yangtze river delta region in China, mutation detection is realized, in application, county-level and above 232 urban zone data of the Yangtze river delta region (Shanghai city, Jiangsu province and Zhejiang province) in 2010 and Yangtze river region research area data are collected, data are integrated based on ArcGIS software and a file geographic database is recorded, and the method specifically comprises the following steps.
Initializing a circumscribed rectangular region with the minimum area of a target research region as a target calculation region, and presetting a set of spatial scales r ═ r (r1,...,rs,...,rS) S is more than or equal to 10, wherein at least 3 adjacent target industrial areas are arranged in an area with the geographic position of any target industrial area in the target calculation area as the center of a circle and the minimum spatial dimension as the radiusAnd 1/2 where the maximum spatial dimension does not exceed the target calculation region short edge; in practical application, for the spatial scale r, r is specifically increased by 22 times from a minimum value of 30km in a scale increment of 10km, and the maximum value is 250km, that is, r ═ 30,40, …,250}, that is, S ═ 23, the method for detecting the spatial mode mutation of the industry aggregation based on the target industry location comprises the following steps:
step A1: obtaining all urban zone bits of the 2010-old triangular region integrally corresponding to each spatial scale rsThe Ripley's K function value and form a target industry location space mode K function value sequence
Figure GDA0003108004550000081
Then proceed to step a 2.
In the specific implementation process of the step a1, the method includes the following steps:
step A1-1: the initialization s is 1 and the process proceeds to step a 1-2.
Step A1-2: respectively aiming at each target industrial zone in the target calculation area, taking the geographic position of the target industrial zone as the center of a circle and rsFor the radius, construct the corresponding space dimension r of the target industrial zonesThe circular area of (a) is obtained, namely, the space scale r corresponding to each target industrial zone is obtainedsThen step a 1-3.
Step A1-3: according to the following formula:
Figure GDA0003108004550000082
obtaining the integral corresponding space scale r of all target industrial zone bits in the target calculation regionsThe function value of Ripley's K, then enter step A1-4, where A is the area of the calculation region, 232 is the number of target industrial locations in the target calculation region, dijIndicating the distance between the target industrial location i and the target industrial location j,
Figure GDA0003108004550000091
as an indicator, if the target industrial location j falls into the target industrial location i pairWithin the corresponding circular area, then
Figure GDA0003108004550000092
Otherwise
Figure GDA0003108004550000093
Step A1-4: judging whether s is equal to 23, if so, entering the step A1-5; otherwise, the value of s is updated by adding 1, and the step A1-2 is returned.
Step A1-5: aiming at the Ripley's K function values of all the target industry zone bits in the target calculation region, which respectively correspond to all scales, a target industry zone bit space mode K function value sequence is formed
Figure GDA0003108004550000094
As shown in table 1 below.
Figure GDA0003108004550000095
TABLE 1
Step A2: according to the following formula:
Figure GDA0003108004550000096
target industry zone bit space mode K function value sequence by adopting L function
Figure GDA0003108004550000097
Correcting, updating and obtaining the L function value sequence of the target industrial zone bit space mode
Figure GDA0003108004550000098
Then proceed to step a 3.
Selecting a confidence level alpha which is 0.001, simulating and storing 999 times of Space Complete Random (SCR) processes of the urban area of the Long triangular region in the calculation region by adopting a Monte Carlo dynamic simulation method under a space scale r, and estimating a space mode margin for each simulated SCR processSequence of values of L function
Figure GDA0003108004550000099
Calculating the maximum analog value HiLoc(r) and a minimum analog value LwLoc(r) forming spatial pattern confidence interval [ Lw ] of long triangular region urban zone SCR processLoc(r),HiLoc(r)]。
From estimated spatial pattern sequences
Figure GDA0003108004550000101
Whether it falls within a confidence interval [ LwLoc(r),HiLoc(r)]And judging the specific distribution mode of the urban areas in the rectangular region within the space scale r. The result shows that the L function values of the urban areas in the Long triangular region are all larger than zero and are all arranged above the upper limit of the confidence interval, which shows that the urban areas in the Long triangular region always show significant centralized distribution in all set spatial scale ranges, as shown in FIG. 2.
Step A3: according to the following formula (3):
Figure GDA0003108004550000102
constructing a target industry location space mode boundary L function value sequence as follows:
Figure GDA0003108004550000103
as shown in table 2 below, then proceed to step a 4.
Figure GDA0003108004550000104
TABLE 2
Step A4: adopting a Mann-Kendall method to inspect and determine a marginal L function value sequence of a target industrial zone bit spatial mode
Figure GDA0003108004550000105
In the break point position interval of (2), i.e. inLong triangular region city zone bit space mode sequence
Figure GDA0003108004550000106
For the sample, it was examined whether it had a mutation on the spatial sequence r {30,40, …,240} and its mutation position was determined, and then it proceeded to step a 5.
In practical application, the step a4 specifically includes the following steps:
step A4-1: setting a position threshold t of a sudden change point of a spatial mode of a long-triangle area urban zone bitLoc＝1000m。
Step A4-2: sample sequence of boundary L function value of spatial mode of urban area comprising p Long triangular regions
Figure GDA0003108004550000107
According to the following formula:
Figure GDA0003108004550000111
construct order statistic opAnd further using the following formula:
ELoc(op)＝p(p-1)/4，VarLoc(op)＝p(p-1)(2p+5)/72
Figure GDA0003108004550000112
step A4-3: under the assumption that the boundary L function value sequence of the target industry zone position space mode is independent randomly, 21 statistics U (o) are defined and calculatedp) (p ═ 1,2, …,22), as shown in table 3 below.
Figure GDA0003108004550000113
TABLE 3
Step A4-4: sequencing the samples
Figure GDA0003108004550000114
In reverse order
Figure GDA0003108004550000115
Repeating the steps A4-2 and A4-3, reconstructing and calculating 22 statistics U' (o)p) Further obtain a new statistic U*(op) (p ═ 1,2, …,22), as shown in table 4 below.
Figure GDA0003108004550000116
Figure GDA0003108004550000121
TABLE 4
Step A4-5: taking the significance confidence level alpha as 0.05, and obtaining a critical value Uα＝1.96。
Step A4-6: with rpThe value is horizontal axis, the value of U is vertical axis, let U* Loc(op)＝-U′Loc(op′) Where p' ═ S-p, two sets of statistics U (o)p)、U*(op) In the same graph, as shown in FIG. 3, the intersection point of two lines at this time is calculated
Figure GDA0003108004550000122
Corresponding spatial scale
Figure GDA0003108004550000123
ULoc≈-1.317，ULocSatisfy inequality | ULoc|<UαIt shows that the urban area of the long triangular region has a variable point in a space scale interval (180km,190km) under the confidence level alpha being 0.05.
Step A5: according to the boundary L function value sequence of the target industry zone bit space mode
Figure GDA0003108004550000124
The position interval of the mutation point, and the space mode edge of the target industrial zone bitSequence of functions of the boundary L
Figure GDA0003108004550000125
And determining the position of the mutation point of the spatial mode of the urban area location in the Long triangular region.
In practical application, the step a5 specifically includes the following steps:
step A5-1: according to the following formula:
Figure GDA0003108004550000126
calculating rLocMinimum difference value delta r between 180km and 190kmLocAnd the corresponding spatial scale
Figure GDA0003108004550000127
Namely deltarLoc＝27m，
Figure GDA0003108004550000128
Step A5-2: according to Δ rLocWhether or not it is less than or equal to threshold tLocJudgment of
Figure GDA0003108004550000129
Whether the position is a spatial mode mutation position gathered by urban areas in the Long triangular region or not is determined by 27<1000, then consider that
Figure GDA00031080045500001210
The boundary L function value sequence mutation point is a mutation point, so that the mutation starting position of the urban area spatial mode in the Yangtze river delta region is 190km, and the spatial scale also reflects the spatial overflow effect range of the industrial aggregation.
Aiming at the second direction, the industrial aggregation space mode mutation detection method based on the target industry specified relevant social and economic data is introduced into the second embodiment, aiming at the urban manufacturing population scale aggregation space mode of the Yangtze river delta region in China, mutation detection is realized, in application, county-level and above 232 urban district data, urban manufacturing population scale data and Yangtze river region research area data of the Yangtze river delta region (Shanghai city, Jiangsu province and Zhejiang province) in 2010 are collected, and data are integrated and recorded into a file geographic database based on ArcGIS software.
Initializing a circumscribed rectangular region with the minimum area of a target research region as a target calculation region, and presetting a set of spatial scales r ═ r (r1,...,rs,...,rS) S is more than or equal to 10, wherein at least 3 adjacent target industrial areas are arranged in an area with the geographic position of any target industrial area in the target calculation area as the center of a circle and the minimum spatial dimension as the radius, and the maximum spatial dimension does not exceed 1/2 of the short side of the target calculation area; in practical application, for the spatial scale r, r is specifically increased by 22 times from a minimum value of 30km in a scale increment of 10km, and the maximum value is 250km, that is, r ═ 30,40, …,250}, that is, S ═ 23, the method for detecting the spatial mode mutation of the industry aggregation based on the target industry location comprises the following steps:
step B1: acquiring the scales of urban manufacturing population in the triangular region of 2010 year and respectively corresponding to the scales rsThe Ripley's K function value and forms a target industry related social economic data space mode K function value sequence
Figure GDA0003108004550000131
Step B2 is then entered.
In practical application, the step B1 specifically includes the following steps:
step B1-1: the initialization s is 1 and the process proceeds to step B1-2.
Step B1-2: aiming at each target industrial zone in the target calculation region, respectively, taking the geographic position of the target industrial zone as the center of a circle and taking the spatial scale rsFor the radius, construct the corresponding space dimension r of the target industrial zonesThe circular area of (a) is obtained, namely, the space scale r corresponding to each target industrial zone is obtainedsThen step B1-3.
Step B1-3: according to the following formula:
Figure GDA0003108004550000132
obtaining all target industry zone bits in the target calculation area, and appointing related social and economic data and corresponding spatial scale r based on the target industrysThen to step B1-4, where A is the area of the calculation region, N is the number of target industrial locations in the target calculation region, and xiAssigning relevant socioeconomic data, x, to the target industry of the target industry location iij(rs) To fall into the corresponding space scale r of the target industrial zone isAnd the target industry of the target industry position j in the circular area specifies the related social and economic data.
Step B1-4: judging whether s is equal to 23, if so, entering the step B1-5; otherwise, the value of s is updated by adding 1, and the step B1-2 is returned.
Step B1-5: aiming at all target industry zone bits in a target calculation area, a target industry specified related social and economic data is designated based on the target industry, Ripley' sK function values corresponding to all spatial scales are respectively formed, and a target industry zone bit spatial mode K function value sequence is formed
Figure GDA0003108004550000133
As shown in table 5 below.
Figure GDA0003108004550000134
Figure GDA0003108004550000141
TABLE 5
Step B2: according to the following formula:
Figure GDA0003108004550000142
k function value sequence aiming at target industry related social and economic data spatial mode by adopting L function
Figure GDA0003108004550000143
Correcting, updating and obtaining the L function value sequence of the space mode of the social and economic data related to the target industry
Figure GDA0003108004550000144
Step B3 is then entered.
Selecting a confidence level alpha which is 0.001, simulating and storing a Space Complete Random (SCR) process of the urban manufacturing population scale in the calculation area of the 999 th-order Long triangular region by adopting a Monte Carlo simulation dynamic method under the space scale r, and estimating a space mode marginal L function value sequence for each simulated SCR process
Figure GDA0003108004550000145
Calculating the maximum analog value HiSoc(r) and a minimum analog value LwSoc(r) forming spatial pattern confidence intervals [ Lw ] for the Long triangular region City manufacturing population size SCR processSoc(r),HiSoc(r)]。
From estimated spatial pattern sequences
Figure GDA0003108004550000146
Whether it falls within a confidence interval [ LwSoc(r),HiSoc(r)]And (3) judging the specific distribution mode of the population scale of the urban manufacturing industry in the Yangtze river delta region under the spatial scale r, wherein the result shows that: although when r is<When the number of the L function values of the population scale of the urban manufacturing industry in the Yangtze river delta region in China is 45km, the L function values can not pass significance test, but are still larger than zero, and in other set space scales, the L function values are all arranged above confidence limits, so that the space mode of the population scale of the urban manufacturing industry in the Yangtze river delta region has a centralized trend, and when the number of the L function values is 40km<r<At 250km, there is a significant concentration of spatial modes, as shown in fig. 4.
Step B3: according to the following equation (10):
Figure GDA0003108004550000151
structural objectIndustry-related social and economic data spatial mode boundary L function value sequence
Figure GDA0003108004550000152
As shown in table 6 below, then proceed to step B4.
Figure GDA0003108004550000153
TABLE 6
Step B4: adopting a Mann-Kendall method to inspect and determine a marginal L function value sequence of the target industry related social and economic data space mode
Figure GDA0003108004550000154
The position interval of the break point, i.e. the spatial pattern sequence of the population scale of urban manufacturing in the Long triangular region
Figure GDA0003108004550000155
For a sample, examine its mutation point position interval on the spatial sequence r ═ {30,40, …,240}, and then proceed to step B5.
In practical application, the step B4 specifically includes the following steps:
step B4-1: setting a position threshold t of a sudden change point of a spatial mode of a long-triangle area urban zone bitSoc＝1000m。
Step B4-2: sample sequence of boundary L function values of population scale spatial mode of urban manufacturing industry in P Long triangular regions
Figure GDA0003108004550000156
According to the following formula (11):
Figure GDA0003108004550000157
construct order statistic opAnd further using the following formulas (12), (13):
ESoc(op)＝p(p-1)/4，VarSoc(op)＝p(p-1)(2p+5)/72
Figure GDA0003108004550000158
step B4-3: under the assumption that the target industry related socioeconomic data space pattern sequence is independent randomly, 21 statistics U (o) are defined and calculatedp) (p ═ 1,2, …,22), as shown in table 7 below.
Figure GDA0003108004550000161
TABLE 7
Step B4-4: sequencing the samples
Figure GDA0003108004550000162
In reverse order
Figure GDA0003108004550000163
Repeating the steps B4-2 and B4-3, reconstructing the order statistics and calculating 22 statistics U' (o)p) Further obtain a new statistic U*(op) (p ═ 1,2, …,22), as shown in table 8 below.
Figure GDA0003108004550000164
TABLE 8
Step B4-5: taking the significance confidence level alpha as 0.05, and obtaining a critical value Uα＝1.96。
Step B4-6: with rpThe value is horizontal axis, the value of U is vertical axis, let U* Soc(op)＝-U′Soc(op′) Where p' ═ S-p, two sets of statistics U (o)p)、U*(op) In the same graph, as shown in FIG. 5, the intersection of two lines at that time is calculated
Figure GDA0003108004550000165
Corresponding spatial scale
Figure GDA0003108004550000166
Figure GDA0003108004550000167
USoc＝-1.339，USocSatisfy inequality | USoc|<UαIt shows that at the confidence level α of 0.05, the urban area in the long triangle has a variable point within the spatial scale interval (200km,210 km).
Step B5: according to the marginal L function value sequence of the target industry related social and economic data space mode
Figure GDA0003108004550000171
Determining the marginal L function value sequence of the space mode of the social and economic data related to the target industry
Figure GDA0003108004550000172
And (3) determining the position of the mutation point of the population-scale spatial mode of the urban manufacturing industry in the Yangtze river delta area.
In practical application, the step B5 specifically includes the following steps:
step B5-1: according to the following formula:
Figure GDA0003108004550000173
respectively calculate rLocMinimum difference value delta r between 200km and 210kmSocAnd the corresponding spatial scale
Figure GDA0003108004550000174
Namely deltarSoc＝1659m，
Figure GDA0003108004550000175
Step B5-2: according to Δ rSocWhether or not it is less than or equal to threshold tSocJudgment of
Figure GDA0003108004550000176
Whether the urban area is a clustered space mode mutation position in the Yangtze river delta region or not is determined by 1659>1000, therefore
Figure GDA0003108004550000177
Since the urban zone bit aggregation space mode mutation position in the Long triangular region is not, a set of new space dimensions r 'are set by respectively using 200km and 210km as space dimension limiting ranges'SocAnd returning to the step B1 according to the newly set space scale until delta r 'is met'Soc≤tSocWhen the second iteration is performed, the man-Kendall statistic curve for the majors in the long delta area is shown in fig. 6 below. Calculating a change point satisfying a condition
Figure GDA0003108004550000178
Corresponding to 200.442km, 201.344km, 203.089km, 205.425km and 208.558km, corresponding to the space scale
Figure GDA0003108004550000179
200km, 201km, 203km, 205km and 209km respectively, and the U value is less than zero, which indicates that the population scale aggregation degree of the urban manufacturing industry in the Long triangular region shows a plurality of descending mutation points from 200km, namely, the spatial scale also reflects the aggregation overflow effect range.
The embodiments of the present invention have been described in detail with reference to the drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the gist of the present invention.

Claims (4)

1. A method for detecting spatial mode mutation of industry aggregation is used for realizing the detection of spatial mode mutation aiming at the layout of a target industry zone bit in a target research area, and is characterized in that: initializing a circumscribed rectangular region with the minimum area of a target research region as a target calculation region, and presetting a group of nullsM-scale of r ═ r1,...,rs,...,rS) S is more than or equal to 10, wherein at least 3 adjacent target industrial areas are arranged in an area with the geographic position of any target industrial area in the target calculation area as the center of a circle and the minimum spatial dimension as the radius, and the maximum spatial dimension does not exceed 1/2 of the short side of the target calculation area; the spatial mode mutation detection method comprises an industrial gathering spatial mode mutation detection method based on a target industrial zone bit, and comprises the following steps of:
step A1: obtaining all target industrial zone bits in the target calculation region and respectively corresponding to each space scale rsThe Ripley's K function value and form a target industry location space mode K function value sequence
Figure FDA0003108004540000011
Then step A2 is entered;
the step a1 includes the following steps:
step A1-1: initializing s ═ 1, and proceeding to step a 1-2;
step A1-2: respectively aiming at each target industrial zone in the target calculation area, taking the geographic position of the target industrial zone as the center of a circle and rsFor the radius, construct the corresponding space dimension r of the target industrial zonesThe circular area of (a) is obtained, namely, the space scale r corresponding to each target industrial zone is obtainedsThen to step a 1-3;
step A1-3: according to the following formula:
Figure FDA0003108004540000012
obtaining the integral corresponding space scale r of all target industrial zone bits in the target calculation regionsThe function value of Ripley's K, then enter step A1-4, where A is the area of the calculation region, N is the number of target industrial locations in the target calculation region, dijIndicating the distance between the target industrial location i and the target industrial location j,
Figure FDA0003108004540000013
as an indicator, if the target industrial location j falls into the circular area corresponding to the target industrial location i, then
Figure FDA0003108004540000014
Otherwise
Figure FDA0003108004540000015
Step A1-4: judging whether S is equal to S, if so, entering the step A1-5; otherwise, updating by adding 1 according to the value of s, and returning to the step A1-2;
step A1-5: aiming at the Ripley's K function values of all the target industry zone bits in the target calculation region, which respectively correspond to all scales, a target industry zone bit space mode K function value sequence is formed
Figure FDA0003108004540000016
Step A2: target industry zone bit space mode K function value sequence by adopting L function
Figure FDA0003108004540000017
Correcting, updating and obtaining the L function value sequence of the target industrial zone bit space mode
Figure FDA0003108004540000018
Then step A3 is entered;
step A3: constructing a boundary L function value sequence of a target industrial zone spatial mode
Figure FDA0003108004540000021
Then step A4 is entered;
step A4: adopting a Mann-Kendall method to inspect and determine a marginal L function value sequence of a target industrial zone bit spatial mode
Figure FDA0003108004540000022
The mutation point position interval of (2);
the step a4 includes the following steps:
step A4-1: setting a threshold t for the location of a spatial mode break point of a target industrial zoneLoc；
Step A4-2: for a sample sequence containing p target industry location spatial mode boundary L function values
Figure FDA0003108004540000023
Construct order statistic opThe following;
Figure FDA0003108004540000024
in the formula opRepresenting the jth sample as a sequential statistic
Figure FDA0003108004540000025
Greater than the ith sample
Figure FDA0003108004540000026
I is more than or equal to 1 and less than or equal to j, IijIs an indicator;
step A4-3: defining and calculating S-1 statistics U obeying N (0,1) distribution under the assumption that the boundary L function value sequence of the target industrial zone spatial mode is independent randomlyLoc(op) The following were used:
Figure FDA0003108004540000027
in the formula, ELoc(op)、VarLoc(op) Respectively, the order statistic opMean and variance of (1), target industry zone bit spatial mode margin L function value sequence
Figure FDA0003108004540000028
Independently and randomly distributed, and calculating E according to the following expressionLoc(op) And VarLoc(op)：
ELoc(op)＝p(p-1)/4
VarLoc(op)＝p(p-1)(2p+5)/72
Step A4-4: sample sequence of boundary L function value of spatial mode of p target industrial zone bits
Figure FDA0003108004540000029
In reverse order
Figure FDA00031080045400000210
Repeating step A4-2 and step A4-3 to obtain a new statistical U'Loc(op)(p＝1,2,…,S-1)；
Step A4-5: selecting a significant confidence level alpha, and obtaining a critical value U according to a standard normal distribution tableα；
Step A4-6: with rpThe value is horizontal axis, the value of U is vertical axis, let U* Loc(op)＝-U′Loc(op′) Where p' is S-p, the statistic ULoc(op) And U* Loc(op) Calculating the intersection of two lines in the same graph
Figure FDA00031080045400000211
Is provided with a ULocValue, and its corresponding spatial scale
Figure FDA00031080045400000212
If U isLocThe value satisfies the inequality | ULoc|<UαThen the spatial scale is considered to be at the confidence level α
Figure FDA00031080045400000213
Interval (r) ofa,ra+1) (a ∈ (1,2, …, S-2)) there is an industry locational spatial pattern mutation point.
2. The method as claimed in claim 1, further comprising step A5, after step A4, entering step A5;
step A5: according to the boundary L function value sequence of the target industry zone bit space mode
Figure FDA0003108004540000031
Determining the boundary L function value sequence of the space mode of the target industrial zone
Figure FDA0003108004540000032
The specific location of the mutation point;
the step a5 includes the following steps:
step A5-1: computing
Figure FDA0003108004540000033
To ra、ra+1Is a minimum difference value ar ofLocAnd the corresponding spatial scale
Figure FDA0003108004540000034
The expression is as follows:
Figure FDA0003108004540000035
step A5-2: according to the threshold value tLocJudgment of
Figure FDA0003108004540000036
Whether the position is a specific position of a mutation point or not is judged according to the following rule:
if Δ rLoc≤tLocThen space scale
Figure FDA0003108004540000037
The position of the mutation of the spatial mode of the industrial zone, namely the spatial overflow effect range of the industrial zone;
if Δ rLoc＞tLocThen r is respectively changeda、ra+1Setting a set of new space dimensions r 'as the space dimension limit range'LocReturn to step A1 until Δ r 'is satisfied'Loc≤tLocUp to this time, the space scale
Figure FDA0003108004540000038
Is the specific location of the spatial pattern mutation point of the target industrial zone.
3. The method according to claim 1, further comprising a method for detecting a mutation in an industrial aggregation spatial pattern based on socioeconomic data related to target industry designation, comprising the steps of:
step B1: obtaining all target industry zone bits in the target calculation area, respectively corresponding to all scales r based on the target industry specified relevant social and economic datasThe Ripley's K function value and forms a target industry related social economic data space mode K function value sequence
Figure FDA0003108004540000039
Then step B2 is entered;
the step B1 includes the following steps:
step B1-1: initializing s ═ 1, and proceeding to step B1-2;
step B1-2: aiming at each target industrial zone in the target calculation region, respectively, taking the geographic position of the target industrial zone as the center of a circle and taking the spatial scale rsFor the radius, construct the corresponding space dimension r of the target industrial zonesThe circular area of (a) is obtained, namely, the space scale r corresponding to each target industrial zone is obtainedsThen to step B1-3;
step B1-3: according to the following formula:
Figure FDA0003108004540000041
obtaining all target industry zone bits in the target calculation area, and appointing related social and economic data and corresponding spatial scale r based on the target industrysThe function value of Ripley's K, then go to step B1-4, where A is the area of the calculation region, N is the number of target industrial locations in the target calculation region, xiAssigning relevant socioeconomic data, x, to the target industry of the target industry location iij(rs) To fall into the corresponding space scale r of the target industrial zone isThe target industry of a target industry zone j in the circular area specifies related social and economic data;
step B1-4: judging whether S is equal to S, if so, entering step B1-5; otherwise, updating by adding 1 according to the value of s, and returning to the step B1-2;
step B1-5: aiming at all target industry location areas in the target calculation area, a target industry location space mode K function value sequence is formed on the basis of target industry appointed related social and economic data and Ripley's K function values respectively corresponding to all spatial scales
Figure FDA0003108004540000042
Step B2: k function value sequence aiming at target industry related social and economic data spatial mode by adopting L function
Figure FDA0003108004540000043
Correcting, updating and obtaining the L function value sequence of the space mode of the social and economic data related to the target industry
Figure FDA0003108004540000044
Then step B3 is entered;
step B3: constructing a boundary L function value sequence of a target industry related social and economic data spatial mode
Figure FDA0003108004540000045
Then step B4 is entered;
step B4: adopting a Mann-Kendall method to inspect and determine a marginal L function value sequence of the target industry related social and economic data space mode
Figure FDA0003108004540000046
The mutation point position interval of (2);
the step B4 includes the following steps:
step B4-1: setting target industry related social and economic data space mode margin L function value sequence
Figure FDA0003108004540000047
Threshold t of abrupt change point positionSoc；
Step B4-2: for a sample sequence containing p target industry related social economic data space mode boundary L function values
Figure FDA0003108004540000048
Construct order statistic opThe following were used:
Figure FDA0003108004540000051
in the formula opRepresenting the jth sample as a sequential statistic
Figure FDA0003108004540000052
Greater than the ith sample
Figure FDA0003108004540000053
(1. ltoreq. I. ltoreq. j) of the cumulative number ofijIs an indicator;
step B4-3: defining and calculating S-1 statistics U obeying N (0,1) distribution under the assumption that target industry related socioeconomic data space pattern sequences are independent randomlySoc(op) The following were used:
Figure FDA0003108004540000054
in the formula, ESoc(op)、VarSoc(op) Respectively, the order statistic opMean and variance of (1), margin L function value sequence of industry-related social and economic data space mode
Figure FDA0003108004540000055
Independently and randomly distributed, and calculating E according to the following expressionSoc(op) And VarSoc(op)：
ESoc(op)＝p(p-1)/4
VarSoc(op)＝p(p-1)(2p+5)/72
Step B4-4: will contain p target industry related socioeconomic data space pattern sequences
Figure FDA0003108004540000056
In reverse order
Figure FDA0003108004540000057
Figure FDA0003108004540000058
Steps B4-2 and B4-3 were repeated to give a new statistical U'Soc(op)(p＝1,2,…,S-1)；
Step B4-5: selecting significant confidence level alpha, and obtaining critical value U according to standard normal distribution tableα；
Step B4-6: with rpThe value is horizontal axis, the value of U is vertical axis, let U* Soc(op)＝-U′Soc(op′) Where p' is S-p, the statistic USoc(op) And U* Soc(op) Calculating the intersection of two lines in the same graph
Figure FDA0003108004540000059
Is provided with a USocValue and its corresponding spatial scale
Figure FDA00031080045400000510
If U isSocThe value satisfies the inequality | USoc|<UαThen the spatial scale is considered to be at the confidence level α
Figure FDA00031080045400000511
Interval (r) ofb,rb+1) (b ∈ (1,2, …, S-2)) has an industry-related socioeconomic data spatial pattern mutation point.
4. The method according to claim 3, further comprising a step B5, after the step B4 is executed, entering a step B5;
step B5: according to the marginal L function value sequence of the target industry related social and economic data space mode
Figure FDA00031080045400000512
Determining the marginal L function value sequence of the space mode of the social and economic data related to the target industry
Figure FDA00031080045400000513
The specific location of the mutation point;
the step B5 includes the following steps:
step B5-1: computing
Figure FDA0003108004540000061
To rb、rb+1Is a minimum difference value ar ofSocAnd the corresponding spatial scale
Figure FDA0003108004540000062
The expression is as follows:
Figure FDA0003108004540000063
step B5-2: according to the threshold value tSocJudgment of
Figure FDA0003108004540000064
Whether the position is a specific position of a mutation point or not is judged according to the following rule:
if Δ rSoc≤tSocThen space scale
Figure FDA0003108004540000065
The mutation position of the spatial pattern of the target industry-related social and economic data is also the spatial overflow effect range of the industry-related social and economic data;
if Δ rSoc＞tSocThen r is respectively changedb、rb+1Setting a new set of spatial scales as the spatial scale limit range, and returning to the step B1 until delta r 'is met'Soc≤tSocUp to this time, the space scale
Figure FDA0003108004540000066
The specific position of the mutation point of the target industrial zone bit space pattern sequence.
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