CN112084672B - Method for judging groundwater pollution based on fractal dimension - Google Patents

Method for judging groundwater pollution based on fractal dimension Download PDF

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CN112084672B
CN112084672B CN202010978252.7A CN202010978252A CN112084672B CN 112084672 B CN112084672 B CN 112084672B CN 202010978252 A CN202010978252 A CN 202010978252A CN 112084672 B CN112084672 B CN 112084672B
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fractal dimension
data
curved surface
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groundwater
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陈歌
孙亚军
徐智敏
张莉
赵先鸣
李鑫
冯琳
袁慧卿
张玉卓
周丽洁
卢伟宁
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China University of Mining and Technology CUMT
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Abstract

The invention discloses a method for judging groundwater pollution based on fractal dimension, which comprises the following steps of (1) selecting a certain sequence of groundwater pollution plume data of a polluted site, (2)) The nth section of groundwater pollution feather is subjected to gridding treatment and is regarded as a curved surface Sn(3) bending the curved surface SnDividing the curved surface into cuboid boxes with equal length and width, (4) calculating the total number Nr of boxes required for covering the whole curved surface, (5) calculating the total number of boxes when the boxes with different volumes cover the curved surface, (6) obtaining a Hurst index by adopting least square fitting, and (7) calculating the curved surface SnThe fractal dimension of the Hausdorff box counting, (8) the fractal dimension of the Hausdorff box counting of long-sequence groundwater pollution plume data is calculated, and (9) whether new pollution exists in the groundwater is judged. The method improves the calculation precision of the fractal dimension, provides a method for investigation, monitoring and restoration of underground water in a polluted site, and lays the foundation for research on migration and diffusion of pollutants in a heterogeneous aquifer.

Description

Method for judging groundwater pollution based on fractal dimension
Technical Field
The invention belongs to the field of water pollution control.
Background
Fractal dimension is applied to polluted hydrology and geology very rarely, and especially the difficulty of determining the space-time distribution of the pollution plume of the underground water in a heterogeneous water-containing medium is large and the detection is extremely difficult, while the acquisition of quantitative parameters of the pollution plume by adopting a conventional or traditional geophysical prospecting method is not only expensive in cost, but also time-consuming and labor-consuming.
In recent years, few researchers relate to calculation of migration complexity of underground water pollution plumes along with time, and other methods mainly calculate the area or the pollution volume of the underground water pollution plumes in a certain time period and do not quantitatively research the evolution of the space-time complexity of the pollution plumes, so that quantitative parameters capable of reflecting the whole situation are lacked in actual underground water restoration and pollution monitoring, and difficulty is brought to actual engineering; the method for actually assisting the geophysical field to detect and monitor is high in cost, the geophysical problem has multiple solutions and uncertainty, and the change rule of the geophysical problem is difficult to study from the characteristics of the underground water pollution plume.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the problems in the background art, the invention provides a method for judging groundwater pollution based on fractal dimension.
The technical scheme is as follows: the invention provides a method for judging groundwater pollution based on fractal dimension, which specifically comprises the following steps:
step 1: collecting time sequence data of groundwater pollution plumes of a certain polluted site; dividing the time sequence data into N sections according to the time length;
step 2: converting the nth section of groundwater pollution plume data into a square data body on a plane, wherein N is 1,2 and … N, the number L of data points on the side of the square data body is taken as the side length of the data body, and L is 22kK is an integer of 0 or more; according to the coordinates of each data point in the nth section of underground water pollution plume data on the plane and the underground water pollution plume concentration value corresponding to the data point, taking the square data body as a curved surface S of a three-dimensional coordinate systemn；
And step 3: performing the t-th calculation to obtain the curved surface SnDivision into 2 in three-dimensional coordinate system2(t-1)A cuboid box, and the length and the width of each cuboid box are all
Figure BDA0002686622890000011
Has a height of
Figure BDA0002686622890000012
H is the height of the rectangular box during the first iterative computation; t is 1,2, 3.. T, T being the total number of calculations;
and 4, step 4: calculating the number of boxes to be accumulated on the ith cuboid box based on the value of the data point in the ith cuboid box, wherein the length and the width of each box to be accumulated are all
Figure BDA0002686622890000013
Has a height of
Figure BDA0002686622890000014
i＝1,2,...22(t-1)(ii) a Thereby obtaining the total number Nr (t) of boxes required by the iterative computation;
and 5: t +1, judging whether T is greater than T, if so, turning to the step 6, otherwise, turning to the step 3;
step 6: drawing the volume of each box calculated in each iteration and the corresponding number of boxes to be accumulated into a log-log coordinate system, fitting by adopting a least square method, and taking the linear slope obtained by fitting as a curved surface SnThe Hurst index of (a);
and 7: according to DF3-Hurst, wherein DFExpressing the fractal dimension to obtain the fractal dimension of the curved surface corresponding to the nth section of groundwater pollution plume data;
and 8: n +1, judging whether N is larger than N, if so, turning to the step 9, otherwise, turning to the step 2;
and step 9: and (3) judging whether a new pollution source exists in the underground water of the polluted site according to the fractal dimension of the time sequence data acquired in the step (1).
Further, in the step 2, the kriging interpolation gridding method is adopted to convert the nth section of groundwater pollution plume data into a square data body.
Further, in the step 4, the number of boxes to be accumulated on the ith cuboid box is calculated by adopting a Hausdorf; the expression for nr (t) is as follows:
Figure BDA0002686622890000021
wherein maxS'i(i, j) is the maximum value of the water pollution plume in the ith box, where min S'i(i, j) is the minimum value of the water pollution plume in the ith box, and int represents rounding down.
Further, if the fractal dimension is in an ascending trend, determining that the underground water of the polluted site has a new pollution source in the time period; and if the fractal dimension is a steady trend, determining that no new pollution source exists in the time period.
Has the advantages that: the method aims to judge the pollution of the underground water, and quantitatively researches the time-space change evolution rule of a pollution plume by using fractal dimension so as to judge whether the underground water has new pollution; when the fractal dimension is used for covering the curved surface, the complexity of the curved surface is fully considered, the sufficient number of boxes is ensured, the accuracy of box number calculation is ensured, and the calculation precision of the fractal dimension is improved; and provides a method for investigation, monitoring and restoration of underground water in a polluted site, and lays the foundation of research on migration and diffusion of pollutants in a heterogeneous aquifer.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a curved surface SnThe process map of (a) is a map of the division at the time of the second iteration calculation, (b) is a map of the division at the time of the third iteration calculation, (c) is a map of the division at the time of the fourth iteration calculation, (d) is a map of the division at the time of the fifth iteration calculation, (e) is a map of the division at the time of the sixth iteration calculation, and (f) is a map of the division at the time of the seventh iteration calculation.
FIG. 3 is a least squares fit of a surface S to a log-log coordinate systemnThe different box sizes of (a) and the total number of boxes covered.
Detailed Description
The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate an embodiment of the invention and, together with the description, serve to explain the invention and not to limit the invention.
The migration and diffusion process of underground water in a polluted site has fractal characteristics, quantitative characterization can be realized through the fractal dimension, the Hausdorff box-counting dimension is a classic fractal dimension, the natural fractal characteristics of characteristic pollutants in the underground water in the diffusion and migration process along with time can be fully reflected, the self-affine and self-similarity characteristics of the characteristic pollutants are highlighted, and the fractal complexity of the pollution plume of the underground water is represented in a nonlinear mathematical mode. In summary, as shown in fig. 1, the present embodiment provides a method for determining groundwater pollution based on fractal dimension;
step 1, selecting underground water pollution plume monitoring data of a real-time measurement long sequence of a certain area pollution site as a research object based on a typical case site, dividing a long sequence period into N different stages according to the monitoring data time, and taking the underground water pollution plume of each stage as a sub-object for calculation and research;
step 2, converting the nth section of groundwater pollution plume data into a square data body on an (x, y) plane, wherein N is 1,2, … N, the number L of data points on the side length of the square data body is taken as the side length of the data body, and L is 22kK is an integer of 0 or more; according to the coordinates of each data point in the nth section of underground water pollution plume data on the plane and the underground water pollution plume concentration value corresponding to the data point, taking the square data body as a curved surface S of a three-dimensional coordinate systemn；
And step 3: as shown in fig. 2, the t-th calculation is performed to obtain the curved surface SnDividing into 2 parts in three-dimensional space2(t-1)A cuboid box, and the length and the width of each cuboid box are all
Figure BDA0002686622890000031
Has a height of
Figure BDA0002686622890000032
H is the height of the rectangular box during the first iterative computation; t is 1,2, 3.. T, T being the total number of calculations;
and 4, step 4: adopting global row-by-column search to obtain the highest concentration value maxS (i, j) and the highest concentration value maxS (i, j) of the water pollution plume in each boxA low concentration value minS (i, j), calculating a curved cover surface S according to equation (1)nThe total number of boxes required is Nr (t), and Nr (t) is the total number of boxes to be accumulated on all the cuboid boxes
And 5: t +1, judging whether T is greater than T, if so, turning to the step 6, otherwise, turning to the step 3;
step 6: as shown in FIG. 3, the volume of each box and the corresponding curved coverage surface S are calculated for each iterationnThe total number of the required boxes is fitted by adopting a least square method, and the slope of the straight line obtained by fitting is used as a curved surface SnThe Hurst index (Hurst index, which means that the diffusion and migration of the pollution plume have positive long-time positive correlation effect, the closer the Hurst index is to 1, the stronger the correlation);
and 7: by using DF3-Hurst, wherein DFExpressing the fractal dimension of the Hausdorff box counting to obtain the fractal dimension of the curved surface corresponding to the nth section of groundwater pollution plume data;
and 8: n +1, judging whether N is larger than N, if so, turning to the step 9, otherwise, turning to the step 2;
and step 9: and (3) judging whether a new pollution source exists in the underground water of the polluted site according to the fractal dimension of the time sequence data acquired in the step (1).
Preferably, in the step 4, the number of boxes to be accumulated on the ith cuboid box is calculated by adopting a Hausdorf; the expression for nr (t) is as follows:
Figure BDA0002686622890000041
wherein maxS'i(i, j) is the maximum value of the water pollution plume in the ith box (several data points are covered in the ith box), where min S'i(i, j) minimum value of water pollution plume in ith, int represents rounding down.
Preferably, the step 8 is specifically to determine that a new pollution source exists in the groundwater of the polluted site in the time period if the fractal dimension is in an ascending trend; and if the fractal dimension is a steady trend, determining that no new pollution source exists in the time period.
It should be noted that although the present invention is described with respect to the time complexity of the groundwater pollution plume of the polluted site, the present invention is also applicable to defining the pollution level of the aquifer of the polluted site at a certain time and quantifying the other cases related to the abnormal spatial and temporal evolution of geological pollution.
It should be noted that the present specification is clear and logical, and the terms defined in the specification do not exclude the processes, methods, and the like of the described elements.
Those skilled in the art will appreciate that all or part of the above-described implementation steps may be implemented by hardware program instructions, and the program may also be stored in a computer-readable storage device, including a memory, a magnetic or optical disk, and so on.
Any simple modification, equivalent change and modification of the above implementation steps according to the technical essence of the present invention still fall within the scope of the technical solution of the present invention.
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 judging groundwater pollution based on fractal dimension is characterized by comprising the following steps:
step 1: collecting time sequence data of groundwater pollution plumes of a certain polluted site; dividing the time sequence data into N sections according to the time length;
step 2: converting the nth section of groundwater pollution plume data into a square data body on a plane, wherein N is 1,2, … N, the number L of data points on the side of the square data body is taken as the side length of the data body, and L is 22kK is an integer of 0 or more; according to the coordinates of each data point in the nth section of underground water pollution plume data on the plane and the underground corresponding to the data pointThe water pollution plume concentration value is taken as a curved surface S of a three-dimensional coordinate systemn；
And step 3: performing the t-th iterative computation to obtain the curved surface SnDivided into 2 on a three-dimensional coordinate system2(t-1)A cuboid box, and the length and the width of each cuboid box are all
Figure FDA0003097165910000011
Has a height of
Figure FDA0003097165910000012
Calculating the volume of the cuboid box according to the volume, wherein H is the height of the cuboid box during the first iterative calculation; t is 1,2,3 … T, and T is the total number of times;
and 4, step 4: calculating the number of boxes to be accumulated on the ith cuboid box based on the value of the data point in the ith cuboid box, wherein the length and the width of each box to be accumulated are all
Figure FDA0003097165910000013
Has a height of
Figure FDA0003097165910000014
i＝1,2,...22(t-1)(ii) a Thereby obtaining the total number Nr (t) of boxes required by the iterative computation;
and 5: if T is greater than T +1, judging whether T is greater than T, if so, turning to the step 6, otherwise, turning to the step 3;
step 6: drawing the volume of the box calculated in each iteration and the total number of boxes required in the iteration calculation into a log-log coordinate system, fitting by adopting a least square method, and taking the linear slope obtained by fitting as a curved surface SnThe Hurst index of (a);
and 7: according to DF3-Hurst, wherein DFExpressing the fractal dimension to obtain the fractal dimension of the curved surface corresponding to the nth section of groundwater pollution plume data;
and 8: n is N +1, judging whether N is larger than N, if so, turning to the step 9, otherwise, turning to the step 2;
and step 9: and (3) judging whether a new pollution source exists in the underground water of the polluted site according to the fractal dimension of the time sequence data acquired in the step (1).
2. The method for judging groundwater pollution based on fractal dimension as claimed in claim 1, wherein the nth groundwater pollution plume data is converted into a square data body in step 2 by using a kriging interpolation gridding method.
3. The method for judging groundwater pollution based on fractal dimension as claimed in claim 1, wherein in the step 4, the number of boxes to be accumulated on the ith cuboid box is calculated by adopting a Hausdorff method; the expression for nr (t) is as follows:
Figure FDA0003097165910000021
wherein maxS'i(i, j) is the maximum value of the water pollution plume in the ith box, where min S'i(i, j) minimum of water pollution plume in ith box, int denotes rounding down.
4. The method for judging groundwater pollution based on fractal dimension as claimed in claim 1, wherein the step 9 is specifically to determine that a new pollution source exists in groundwater of the polluted site in the time period if the fractal dimension is in an ascending trend; and if the fractal dimension is a steady trend, determining that no new pollution source exists in the time period.
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