CN110020409B - Ground air temperature observation data analysis method based on self-adaptive kernel density estimation algorithm - Google Patents

Ground air temperature observation data analysis method based on self-adaptive kernel density estimation algorithm Download PDF

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CN110020409B
CN110020409B CN201910256176.6A CN201910256176A CN110020409B CN 110020409 B CN110020409 B CN 110020409B CN 201910256176 A CN201910256176 A CN 201910256176A CN 110020409 B CN110020409 B CN 110020409B
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叶小岭
阚亚进
熊雄
陈昕
王佐鹏
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Nanjing University of Information Science and Technology
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Abstract

The invention relates to a ground air temperature observation data analysis method based on a self-adaptive kernel density estimation algorithm, which belongs to the field of ground air temperature observation data analysis.

Description

Ground air temperature observation data analysis method based on self-adaptive kernel density estimation algorithm
Technical Field
The invention relates to the field of analysis of ground air temperature observation data, in particular to an improved nuclear density estimation algorithm for analyzing ground air temperature elements.
Background
In recent years, the trend of global warming is more obvious, and the air temperature change has serious influence on society, so that the wide attention of various nationists is paid, and a plurality of meaningful conclusions are drawn for research. In China, many researches on areas with special geographic positions such as plateaus, basins and the like are more studied, a plurality of achievements are obtained, and the southeast area with stable air temperature is not researched enough. Most of the traditional air temperature analysis methods are based on time series to predict and analyze future change trend, and expert students in various countries also conduct a series of researches on space angle, but factors influencing air temperature change are very complex, and obvious regional and seasonal differences exist. The existing studies have failed to analyze the cause of the air temperature change.
Disclosure of Invention
The invention provides a method for analyzing ground air temperature observation data in order to solve the problems in the prior art.
In order to achieve the above purpose, the technical scheme provided by the invention is as follows: a ground air temperature observation data analysis method based on a self-adaptive kernel density estimation algorithm comprises the following steps:
step 1, selecting site data samples in a time sequence of ground air temperature observation data of a target area, wherein the ith site data is X i ＝(x i1 ,x i2 ,…x ij ,…,x in ) T ；
Step 2, estimating a formula according to the nuclear density
Figure GDA0004124627160000011
Calculating a nuclear density estimated value; wherein K (x) is a kernel function, h is window width, h i The window width corresponding to the ith station is set, and n is the sample capacity;
step 3, designing window width coefficient
Figure GDA0004124627160000012
The self-adaptive window width is h i * ＝λ i h i Replacing the window width in the kernel density estimation formula with the free adaptive window width to obtain a self-adaptive kernel density estimation formula
Figure GDA0004124627160000013
Wherein g is
Figure GDA0004124627160000014
An arithmetic mean of (a); alpha is a sensitive parameter, and satisfies 0-1;
step 4, designing the optimal window width
Figure GDA0004124627160000015
Replacing the window width in the self-adaptive kernel density estimation formula with the optimal window width to obtain
Figure GDA0004124627160000016
Wherein, c is a parameter,
Figure GDA0004124627160000017
for standingStandard deviation of point data samples.
The technical scheme is further designed as follows: the kernel function employs a Gaussian function.
And (3) respectively selecting parameters c and alpha by adopting an adjusted particle swarm algorithm, and adjusting the optimal window width formula in the step (4) to be:
Figure GDA0004124627160000021
the improved adaptive kernel density estimation formula:
Figure GDA0004124627160000022
wherein ω and μ are parameters, and the range of values is between [ -0.5,0.5] and [ -0.1,0.5], respectively.
The initial values of parameters c and alpha are set to 1.06 and 0.2.
Compared with the prior art, the invention has the following beneficial effects:
the self-adaptive kernel density estimation algorithm is better than the traditional fixed window width algorithm in both precision and fitting degree, and the algorithm provided by the invention has good prediction precision and fitting degree under multiple scales, and the traditional algorithm can only be applied under small scales.
From the principle aspect, the change characteristics of the air temperature and the change characteristics of each region under multiple time scales are known, which is helpful for the deep understanding of the air temperature change trend and the influence factors thereof, so that the frequency, the numerical value, the trend and other attributes of the ground air temperature observation data and the influence of the climate and the position on the air temperature under multiple time scales are required to be analyzed, and further the analysis and the research can be conducted in depth. The algorithm provided by the invention can well analyze the statistical characteristics of the ground air temperature observation data in China, and provides a theoretical basis for further researching the ground air temperature observation data.
The method provided by the invention can effectively analyze the statistical characteristics of the ground air temperature observation data and can further analyze the influence reasons of the statistical characteristics, so that the method can be effectively applied to the analysis and application of the ground air temperature observation data.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2a is a graph showing MAE effect versus histogram for a method of the present invention and a conventional fixed window width kernel density estimation algorithm;
FIG. 2b is a graph showing the RMSE effect versus histogram of the method of the invention versus a conventional fixed window width kernel density estimation algorithm;
FIG. 2c is a bar graph comparing NSC effects of the method of the present invention with a conventional fixed window width kernel density estimation algorithm;
FIG. 2d is a graph comparing IOA effects of the method of the present invention with a conventional fixed window width kernel density estimation algorithm;
FIG. 2e is a graph of MAE effect versus line for the method of the present invention versus a conventional fixed window width kernel density estimation algorithm;
FIG. 2f is a graph of the RMSE effect versus line for the method of the present invention versus a conventional fixed window width kernel density estimation algorithm;
FIG. 2g is a plot of NSC effect versus conventional fixed window width kernel density estimation algorithm for the method of the present invention;
FIG. 2h is a graph of the IOA effect versus line for the method of the present invention versus a conventional fixed window width kernel density estimation algorithm;
FIG. 3a is a graph of the results of a test of the kernel density estimation algorithm of the method of the present invention at a Xuzhou site;
FIG. 3b is a graph of the experimental results of the nuclear density estimation algorithm of the method of the present invention at the hangover site;
FIG. 3c is a graph showing the test results of the nuclear density estimation algorithm of the method of the present invention at the Lianghong Kong site;
FIG. 3d is a graph of the test results of the kernel density estimation algorithm of the method of the present invention at the Huaian site;
FIG. 3e is a graph of the results of a test of the kernel density estimation algorithm of the method of the present invention at the Yangzhou site;
FIG. 3f is a graph of the experimental results of the kernel density estimation algorithm of the method of the present invention at the Nanjing site;
FIG. 3g is a graph showing the test results of the kernel density estimation algorithm of the method of the present invention at the Zhenjiang station;
FIG. 3h is a graph of the experimental results of the kernel density estimation algorithm of the method of the present invention at the Changzhou site;
FIG. 3i is a graph of the experimental results of the nuclear density estimation algorithm of the method of the present invention at a salt city site;
FIG. 3j is a graph of the experimental results of the kernel density estimation algorithm of the method of the present invention at a tin-free station;
FIG. 3k is a graph of the experimental results of the kernel density estimation algorithm of the method of the present invention at the Suzhou site;
FIG. 3l is a graph showing the test results of the kernel density estimation algorithm of the method of the present invention at the Nantong site;
FIG. 4 shows a 12 site distribution diagram in Jiangsu province.
Detailed Description
The invention will now be described in detail with reference to the accompanying drawings and specific examples.
According to the flow chart of the method of the embodiment of the invention, as shown in fig. 1, firstly, the air temperature data of the required site in a certain time sequence is acquired, then the data are subjected to basic pretreatment, then different nuclear density estimation tests are respectively carried out, different evaluation indexes are adopted for evaluation, and finally the test of the Jiangsu province 12 site is carried out and analyzed by utilizing the algorithm provided by the invention.
The following examples were conducted for analysis of the average air temperature values of Xuzhou (station number: 58027), suzhou (station number: 58131), liyun harbor (station number: 58044), huaian (station number: 58141), yangzhou (station number: 58245), nanjing (station number: 58238), zhenjiang (station number: 58248), changzhou (station number: 58343), yancheng (station number: 58154), wuxi (station number: 58354), suzhou (station number: 58349), nantong (station number: 58259) for 12 stations in total, day, night, quarter from 1988 to 2007, and further explaining the present invention:
comparative example one
The data of the ground air temperature observation data of 12 stations in Jiangsu province, namely six hours of air temperature data from 1988 to 2007 and average month data are selected as the observation data, and preprocessing is carried out on the obtained data, wherein the preprocessing data are as follows: taking the average value of the air temperatures at 08 and 14 as the average daily temperature, and taking the average value of the air temperatures at 20 and 02 as the average night temperatureTaking 1-3 months as first quarter, 4-6 months as second quarter, 7-9 months as third quarter, and 10-12 months as fourth quarter to obtain corresponding time sequence X= (X) 1 ,X 2 ,…,X 12 ) Wherein the ith site data is X i ＝(x i1 ,x i2 ,…x ij ,…,x in ) T 。
The test is carried out by adopting a traditional nuclear density estimation algorithm with fixed window width, and the formula of nuclear density estimation is adopted
Figure GDA0004124627160000031
And (3) performing calculation, wherein K (x) is a kernel function, h is more than 0, the window width parameter is a fixed value, 1.8-2 is generally selected, and n is the sample capacity.
Selecting a Gaussian kernel function with good mathematical properties:
Figure GDA0004124627160000032
as a kernel function.
Based on the idea of least squares variation (LSCV), the optimal fixed window width is obtained according to the minimum integral mean square error (MISE), and the specific reasoning process is as follows: according to integral mean square error formula
Figure GDA0004124627160000041
Wherein the deviation formula is
Figure GDA0004124627160000042
Variance->
Figure GDA0004124627160000043
Further reduction of the deviation formula can be obtained:
Figure GDA0004124627160000044
and +.>
Figure GDA0004124627160000045
Substituting its deviation and variance into the integral mean square error formula +.>
Figure GDA0004124627160000046
Wherein k is 2 ＝∫x 2 K (x) dx, let->
Figure GDA0004124627160000047
If MISE is minimum, AMISE is minimum, so the first derivative of AMIS is calculated to be equal to 0, and the optimal window width h is calculated. The deduced optimal window width h is:
Figure GDA0004124627160000048
after the kernel function is determined to be a gaussian kernel, it can be deduced that: />
Figure GDA0004124627160000049
Wherein the method comprises the steps of
Figure GDA00041246271600000410
Is the standard deviation of the samples.
Comparative example two
The window widths adopted in the first comparative example are fixed window widths, and cannot effectively reflect the influence caused by the sparseness degree of the observed value of the sample, and the self-adaptive algorithm is added to the first comparative example.
Core density estimation value obtained according to comparative example one
Figure GDA00041246271600000411
At h i And->
Figure GDA00041246271600000412
On a proportional basis by designing the window width factor +.>
Figure GDA00041246271600000413
Is improved, wherein g is->
Figure GDA00041246271600000414
Is the arithmetic average of (a): i.e. < ->
Figure GDA00041246271600000415
Alpha is a sensitive parameter, satisfies that alpha is more than or equal to 0 and less than or equal to 1, and in practical application, alpha is 0.The 5 th effect is best, so the self-adaptive window width is h i * ＝λ i h i Replace h in comparative example one i Obtaining adaptive kernel density estimation +.>
Figure GDA00041246271600000416
However, the method is not suitable for directly applying to the analysis of ground air temperature observation data, wherein the initial window width h lacks a selection standard, and different initial window widths h are selected for different sites by substituting the selection method of the optimal window width i And (3) obtaining an adaptive nuclear density estimation formula applicable to ground air temperature observation data by combining the adaptive parameters:
Figure GDA00041246271600000417
examples
The result obtained by the algorithm of the second comparative example under the ground air temperature observation data cannot meet that all mean square errors are minimum, which shows that the method is not completely suitable for the ground air temperature observation data, so that the selection method of the optimal window width needs to be determined again, and the embodiment provides the optimization method as follows: giving a new window width formula based on the optimal window width formula:
Figure GDA0004124627160000051
in order to make the obtained nuclear density estimation curve graph close to the real situation of data, an intelligent optimizing algorithm is adopted to determine parameters c and a, so that the smaller the RMSE value is, the better the RMSE value is, and the improved formula is as follows:
Figure GDA0004124627160000052
where n is the sample size, K (x) is the Gaussian kernel,
Figure GDA0004124627160000053
parameters c and α are undetermined for the adaptive window width coefficient. The embodiment adopts adjustmentThe particle swarm algorithm of (1) selects parameters c and alpha respectively: taking a kernel density estimation function as an objective function, assuming an N-dimensional space, a particle population X= (X) consisting of air temperature data of a plurality of sites 1 ,X 2 ,…,X d ) Wherein the ith particle data X i ＝(x i1 ,x i2 ,…x ij ,…,x in ) T By objective function->
Figure GDA0004124627160000054
A set of potential solutions from which the kernel density estimate can be derived is calculated: />
Figure GDA0004124627160000055
And then taking the root mean square error RMSE as a fitness function, wherein parameters c and alpha in the initial solution refer to the optimal window width in the fixed window width algorithm
Figure GDA0004124627160000056
Is set to be 1.06 and 0.2, the speed V of the traditional PSO is adjusted to double change factors omega and mu, and the position X is adjusted to be the window width +.>
Figure GDA0004124627160000057
The formula adjusts to: />
Figure GDA0004124627160000058
At the same time, the range of the parameters omega and mu is limited to be [ -0.5,0.5]-0.1,0.5]In between, the improved adaptive kernel density estimation formula is obtained by the above method:
Figure GDA0004124627160000059
the embodiment has better fitting degree on real data and can show the trend of the data.
As shown in fig. 2, four general evaluation parameters were selected: mean Absolute Error (MAE), root Mean Square Error (RMSE), nash coefficient (NSC) and uniformity Index (IOA) to describe the experimental effect at fixed window width, optimal fixed window width and improved adaptive window width:
Figure GDA00041246271600000510
Figure GDA00041246271600000511
Figure GDA0004124627160000061
wherein n is the number of sample points,
Figure GDA0004124627160000062
for the ij-th kernel density estimate, y (x ij ) For the mean value of each bin of the ijth raw data frequency histogram,/for each bin>
Figure GDA0004124627160000063
Is the mean value of the frequency histogram.
As shown in fig. 3, the improved nuclear density estimation algorithm was applied to 12-station ground air temperature observations in Jiangsu province for testing, and the test results thereof were analyzed and summarized in combination with the location (shown in fig. 4) and the climate characteristics.
The test effects of the three algorithms are compared with the index MAE, RMSE, NSC and the IOA, and the fact that the traditional fixed window width algorithm is not suitable for application in the aspect of the quarter air temperature of the ground air temperature observation data in Jiangsu province in terms of precision and fitting degree is explained, and the improved self-adaptive kernel density estimation algorithm is good in precision and fitting degree. It is further found that the accuracy and the fitting effect of the algorithm provided by the embodiment of the invention are optimal under the multi-scale condition, and the conventional fixed window width algorithm in the first comparative example can only be applied to a test of small-scale data, so that the method provided by the invention has enough excellent effects on the aspects of accuracy and fitting under the multi-site condition and the multi-scale condition compared with the conventional method.
The influence factors of the climate characteristics are larger than those of the position characteristics, under the quarter scale, the position is more toward the south, the overall uniform temperature is higher, the temperature change is more stable, the spring Qiu Jijun temperature represented by 15 ℃ is prolonged, and the influence caused by the position south is offset to a certain extent by the ocean regulation effect; in summer represented by 20-30 ℃ at day and night, the change trend of the temperature uniformity is influenced by the climate, the duration of the temperature uniformity is influenced by the position, the influence difference between marine climate and monsoon climate in the climate is small, and the size and duration of the temperature uniformity can be improved by ocean regulation; for spring and autumn represented by 10-20 ℃, the closer to the southeast coastal area, the larger the difference between the day and night temperature uniformity curves is; for winter represented by 0-10 ℃, the position is more northwest, the night temperature is longer in duration and is always higher than the day temperature, so that the influence mode and influence capability of climate and position on temperature change are different under different time scales, and the analysis of the influence of different characteristics on the temperature is helpful for the deep research of follow-up.
The method of the present invention is not limited to the above embodiments, and all technical solutions obtained by adopting equivalent substitution modes fall within the scope of the present invention.

Claims (4)

1. The ground air temperature observation data analysis method based on the self-adaptive kernel density estimation algorithm is characterized by comprising the following steps of:
step 1, selecting site data samples in a time sequence of ground air temperature observation data of a target area, wherein the ith site data is X i ＝(x i1 ,x i2 ,…x ij ,…,x in ) T ；
Step 2, estimating a formula according to the nuclear density
Figure FDA0004124627150000011
Calculating a nuclear density estimated value; wherein K (x) is a kernel function, h is window width, h i The window width corresponding to the ith station is set, and n is the sample capacity;
step 3, designing window width coefficient
Figure FDA0004124627150000012
The self-adaptive window width is h i * ＝λ i h i Replacing the window width in the kernel density estimation formula with the free adaptive window width to obtain a self-adaptive kernel density estimation formula
Figure FDA0004124627150000013
Wherein g is
Figure FDA0004124627150000014
An arithmetic mean of (a); alpha is a sensitive parameter, and satisfies 0-1;
step 4, designing the optimal window width
Figure FDA0004124627150000015
Replacing the window width in the self-adaptive kernel density estimation formula with the optimal window width to obtain
Figure FDA0004124627150000016
Wherein, c is a parameter,
Figure FDA0004124627150000017
is the standard deviation of the site data samples.
2. The method for analyzing the ground air temperature observation data based on the adaptive kernel density estimation algorithm according to claim 1, wherein the method comprises the following steps of: the kernel function employs a Gaussian function,
Figure FDA0004124627150000018
3. the method for analyzing the ground air temperature observation data based on the adaptive kernel density estimation algorithm according to claim 2, wherein the method comprises the following steps of: the parameters c and alpha are respectively entered by adopting an adjusted particle swarm algorithmAnd (3) selecting a row, and adjusting the optimal window width formula in the step (4) to be:
Figure FDA0004124627150000019
the improved adaptive kernel density estimation formula:
Figure FDA00041246271500000110
wherein ω and μ are parameters, and the range of values is between [ -0.5,0.5] and [ -0.1,0.5], respectively.
4. The method for analyzing ground air temperature observation data based on an adaptive kernel density estimation algorithm according to claim 3, wherein: the initial values of parameters c and alpha are set to 1.06 and 0.2.
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