CN111047136A - Sponge city pipe network facility deployment assessment method - Google Patents

Sponge city pipe network facility deployment assessment method Download PDF

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CN111047136A
CN111047136A CN201911070466.8A CN201911070466A CN111047136A CN 111047136 A CN111047136 A CN 111047136A CN 201911070466 A CN201911070466 A CN 201911070466A CN 111047136 A CN111047136 A CN 111047136A
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pipe network
waterlogging
point
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vertex
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CN111047136B (en
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王怀军
侯精明
马越
李军怀
邓朝显
曹霆
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Xian University of Technology
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Abstract

The invention discloses a sponge urban pipe network facility deployment assessment method, which comprises the steps of setting urban waterlogging ponding in a relatively static state, selecting an urban local area, and establishing an urban waterlogging prediction area model; collecting pipe network facility basic data and rainfall data of a city to be evaluated, and establishing an actual facility deployment abstract model by combining with a city waterlogging prediction region model; completing the preliminary evaluation of a pipe network in an waterlogging coverage area through an waterlogging point; and (3) calculating the coverage rate of the sponge city pipe network facility nodes by using a node coverage algorithm of sign (x) to finish evaluation. The evaluation method combines a sponge urban waterlogging prediction region model and an actual facility deployment abstract model, adopts a parallelization node coverage algorithm to calculate the distribution of waterlogging points, the waterlogging grade and the node coverage rate of pipe network facilities in a corresponding region, and analyzes whether the pipe network facility deployment in the region is reasonable; the problem of current municipal drainage pipe network facility distribute unreasonablely, easily cause urban waterlogging is solved.

Description

Sponge city pipe network facility deployment assessment method
Technical Field
The invention belongs to the technical field of urban rainwater treatment methods, and particularly relates to a sponge urban pipe network facility deployment evaluation method.
Background
With the factors of increasing urbanization rate year by year, gathering of a large number of rural population to cities and the like, a serious urban problem, namely urban waterlogging, occurs, and the main reasons are as follows:
1) original vegetation and soil on the ground are replaced by high-rise buildings and hard pavements which are developed at a high speed, and hardened 'steel cities' are formed gradually, so that the infiltration of rainwater is covered, and the rainwater can be only discharged from rainwater pipe network facilities;
2) the urban waterlogging is caused by factors such as low design standard of most urban rainwater pipe network facilities, incomplete arrangement of pipe network facilities, concept of 'quick discharge' of waterlogging water and 'tail end centralized' control.
In order to deal with the increasingly enlarged urban scale and solve the increasingly worsened urban problem, the construction mode of the traditional urban is changed, and the construction of the sponge city is gradually increased. A large amount of practical experiences have been accumulated in the aspects of prevention, control, utilization and the like of sponge urban rainstorm water abroad, and meanwhile, a new water ecological city is being vigorously promoted, wherein the new water ecological city comprises intelligent construction, later-stage operation and maintenance, waterlogging prevention construction of the sponge urban infrastructure and the like.
In the existing urban rainwater management system, rainwater is discharged into a municipal pipe network by staggering peaks through automatically opening an overflow valve, and a spongization comprehensive treatment mode is adopted for hard ground, so that the circulation process of urban surface water is enhanced, the rainfall infiltration capacity is increased, the peak amount of rainfall runoff is reduced, and the urban inland inundation points are reduced.
With the development of sponge cities, infrastructure evaluation, operation and maintenance and rational utilization thereof have become urgent current needs. For example, some test point cities only focus on engineering construction, but do not focus on the overall planning and contact of the cities; most of test point cities are rarely combined with new-generation information technology concepts in sponge city construction, so that the problems of repeated construction, poor effect of newly-built green facilities, urban waterlogging and the like are caused. Therefore, how to accelerate the construction of sponge cities and the operation and maintenance of later-period infrastructure, exert the social, ecological, environmental, resource, disaster prevention and other benefits of the sponge cities, and enhance the urban waterlogging prevention capability is a current critical problem. The drainage pipe network facility is used as an important infrastructure of the sponge city, and plays a basic role in the waterlogging prevention and drainage process. The area of the hardened pavement is gradually enlarged, and urban inland inundation is caused because the urban laid pipe network facilities are old and cannot drain water in real time; solid substances such as household garbage, pollutants and the like enter surface water along with runoff of rainwater to cause ecological damage, wherein the most important is whether drainage pipe network facilities are reasonably distributed.
Disclosure of Invention
The invention aims to provide a sponge urban pipe network facility deployment evaluation method which can evaluate whether urban drainage pipe network facilities are reasonably distributed or not so as to reduce the urban waterlogging problem caused by the drainage problem.
The technical scheme adopted by the invention is that the sponge city pipe network facility deployment assessment method comprises the following steps:
step 1, setting urban waterlogging to be in a relatively static state, selecting an urban local area, and establishing an urban waterlogging prediction area model;
step 2, collecting pipe network facility basic data and rainfall data of a city to be evaluated, and establishing an actual facility deployment abstract model by combining the urban waterlogging prediction region model in the step 1;
step 3, deploying an abstract model aiming at the actual facilities in the step 2, and finishing preliminary evaluation of a pipe network in an inland inundation coverage area through inland inundation points;
and 4, based on the preliminary evaluation method of the pipe network in the step 3, calculating the coverage rate of the sponge city pipe network facility nodes by a node coverage algorithm of sign (x) to finish evaluation.
The present invention is also characterized in that,
the specific operation of the step 1 is as follows: dividing a local city area into a plurality of coarse units, wherein the timed accumulated water amount in each coarse unit consists of duration rainfall total amount, smooth combination among the coarse units, infiltration reduction quantity parameters and accumulated water depth of the coarse units;
calculating total rainfall Q of any coarse unit in any period of timet_rAs in the formula (1),
Figure BDA0002260792460000031
in the formula (1), the parameter RijThe amount of rainfall over time for the grid cell, parameter XijAs accumulated weight of divided grid cells, parameter CijThe cell is a grid cell, the parameter A is a coarse cell, the parameter n is the number of rows of the coarse cell in the region, and the parameter m is the number of columns of the coarse cell in the region;
calculating the soil infiltration Q of each coarse uniti_rAs in the formula (2),
Figure BDA0002260792460000032
in the formula (2), the parameter XkFor the soil accumulated weight, parameter SkThe cumulative total infiltration amount of k type soil per unit area over t, parameter YijAdding the weight for the coarse unit, parameter AijThe area of the grid unit is shown, and a parameter c represents that a corresponding city has c soil types;
calculating the water accumulation depth of each coarse unit as shown in formula (3),
Qc_r＝Qt_r-Qi_r(3)。
the actual facility deployment abstract model in the step 2 is specifically as follows:
step 2.1, setting parameters based on graph theory:
let G ═ (Q, E) be a directed weighted graph,<qi,qj>representing a directed edge, wherein the parameter qiA parameter q representing the starting point of the directed edgejRepresenting an end point of the directed edge;
the number of entries to any vertex q in the weighted graph G is q, and the entry is expressed as
Figure BDA0002260792460000041
The number of edge strips at any vertex q is called the out-degree of q, and is recorded as
Figure BDA0002260792460000042
The sum of the number of the incoming strips and the number of the outgoing strips of any vertex q, namely the degree of which the sum of the incoming degree and the outgoing degree is q, is recorded as deg (q);
let the degree of penetration of any vertex q be 0, i.e.
Figure BDA0002260792460000043
When the current time goes, the vertex q is recorded as a source; let the out-degree of any one vertex q be 0, i.e.
Figure BDA0002260792460000044
When the vertex q is a sink, the vertex q is recorded as a sink; let the in degree and out degree of any vertex q not equal to 0, i.e.
Figure BDA0002260792460000045
And is
Figure BDA0002260792460000046
Then, the vertex q is called as a turning point;
2.2, simulating the parameters in the step 2.1 into an abstract model of a drainage pipe network, namely, the following parameters are provided:
pipe network source point: only the pipe section is connected out, and no node for connecting the pipe section is connected in, and the node is also a drainage inlet of the whole drainage pipe network; in step 2.1, the node with the in-degree of 0 and the out-degree of not equal to 0 is selected;
pipe network collection: only the pipe section is connected, and no node for connecting the pipe section is connected, and the node is also a drainage outlet of the whole drainage pipe network; in step 2.1, the node with the in-degree not equal to 0 and the out-degree of 0 is selected;
pipe network transfer point: namely, the node except the source point and the sink point, and the node has the pipe section access and also has the pipe section access; in step 2.1, nodes with the in degree not equal to 0 and the out degree not equal to 0 are selected;
step 2.3, establishing a facility deployment abstract model through the parameters in the step 2.2:
setting the rainwater pipe network as a directed weighted graph G (Q, E), wherein the parameter E is an edge set of the graph G and mainly comprises a main pipe and a branch pipe, and the parameter Q is a vertex set of the graph G and mainly comprises a rainwater grate, an inspection well and a water outlet;
let X be a subset of Q, if each vertex X in XiAll are the starting points of the edges in the graph G, then X is the source set of G, let Z be a subset of the set of vertices Q, and X ∩ Z be φ, if each vertex Z in ZiAll end points of the edges in the graph G, then Z is the collection of G, let Y also be a subset of the set of vertices Q, and X ∩ Y is phi and Y ∩ Z is phi, and if each vertex Y in Y is YiThat is, the starting point of the edge G of the graph is also called the end point of the edge G of the graph, Y is called a transition point set of G, and the vertex set of the rainwater pipe network G is expressed by the following formula (4):
V＝{X；Y；Z}＝{x1,x2,...,xp；y1,y2,...,ym；z1,z2,...,zq} (4)。
the step 3 specifically comprises the following steps:
step 3.1, setting any waterlogging point as VnThe overflow range of the waterlogging points is circular, the coverage area formed by a single node of the sponge urban pipe network facility, namely a single waterlogging point, is circular, and the coverage area formed by double nodes of the sponge urban pipe network facility, namely two waterlogging points, is tangent to two circles;
step 3.2, setting three nodes of the sponge urban pipe network facility, namely the coverage area formed by the three waterlogging points, as follows; the circle centers of the three waterlogging points are respectively set as V1、V2、V3The overlapping area is the area S enclosed by arcs ab, ac and bc1When the intersection points a, b and c of the three circles coincide with the point P, S is present1The area is minimized, thereby obtaining PV1＝PV2＝PV3R, R is the radius of the circle.
The step 4 specifically comprises the following steps:
step 4.1, parameter setting
Polygonal: with a series of coplanar points V on the plane1,V2,...,VnConnecting the points by line segments in sequence to obtain a closed graph;
three-dimensional spatial coordinates of points: the position of a set point in the xoy plane of the two-dimensional space is (x, y); the position of a point in the three-dimensional space o 'x' y 'z' stereo space is (x, y, z); therefore, an arbitrary point Q on the two-dimensional plane is a point Q 'on the x' o 'y' plane of the three-dimensional space o 'x' y 'z', and the coordinates (x, y) of the point Q on the two-dimensional plane are expanded to the spatial coordinates to become (x, y, 0);
sign (x) function is defined as formula (8):
Figure BDA0002260792460000051
step 4.2, point Q on the xoy planej(xj,yj) Vertex V of the polygoni(xi,yi) And Vi+1(xi+1,yi+1) Viewed as points Q ', V of the three-dimensional space o' x 'y' z 'on the x' o 'y' planei' and Vi+1', extended to spatial coordinates, denoted as (x)j,yj,0)、(xi,yi0) and (x)i+1,yj+1,0)；
Step 4.3, calculate Q by equations (9) and (10)j'Vi' and Qj'Vi+1'；
Qj'Vi'＝((xi-xj),(yi-yj),0) (9)
Qj'Vi+1'＝((xi+1-xj),(yi+1-yj),0) (10)
Step 4.4, calculating the product of the two vectors by the formula (11);
Figure BDA0002260792460000061
step 4.5, according to the different positions of the points, corresponding crThere are three cases, as in equation (12);
and the corresponding sign (x) is calculated according to the formula (13):
cr＞0,cr＜0,cr＝0 (12)
Figure BDA0002260792460000062
step 4.6, by varying crCalculating a sign (x) value, and judging the position relation between the nodes of the pipe network facilities to be detected and the waterlogging polygon through the sign (x) value;
if sign (x) is 0, then sponge city pipe network facility node QjWaterlogging point ViAnd Vi+1The three points are positioned on the same line, but when the sponge city pipe network facility node corresponds to the condition of the coordinate formula (14), the sponge city pipe network facility node is positioned on the waterlogging polygonal boundary or the vertex;
Figure BDA0002260792460000063
if sign (x) is not equal to 0, then sponge city pipe network facility node QjWaterlogging point ViAnd Vi+1Three points are not on the same line, and the coordinates of the sponge city pipe network facility nodes and the coordinates of the waterlogging polygon vertexes have yi＜yj＜yi+1Or yi＜yj＜yi+1Two cases, calculated according to equations (15) and (16):
kr＝sign(x)＝sign(cr) (15)
Figure BDA0002260792460000071
if K is not equal to 0, sponge city pipe network facility node Q is located inside waterlogging polygon S, if K is not equal to 0, sponge city pipe network facility node Q is located outside waterlogging polygon S.
The invention has the beneficial effects that: the invention relates to a sponge city pipe network facility deployment evaluation method, which combines a sponge city waterlogging prediction region model and an actual facility deployment abstract model, adopts a parallelization node coverage algorithm to calculate the distribution of waterlogging points, waterlogging grades and pipe network facility node coverage of corresponding regions, and analyzes whether the pipe network facility deployment of the region is reasonable; the problem of current municipal drainage pipe network facility distribute unreasonablely, easily cause urban waterlogging is solved.
Drawings
FIG. 1 is a flow chart of a sponge city pipe network facility deployment evaluation method of the present invention;
FIG. 2 is a schematic diagram of the number of waterlogging points and the coverage area in the sponge urban pipe network facility deployment evaluation method;
wherein FIG. 2(a) shows waterlogging; FIG. 2(b) shows a double waterlogging spot; FIG. 2(c) shows triple waterlogging points; FIG. 2(d) shows a triple waterlogging optimization;
FIG. 3 is a model diagram of a triple waterlogging point verification process in the sponge city pipe network facility deployment evaluation method of the present invention;
FIG. 4 is a coordinate diagram of waterlogging points in the sponge urban pipe network facility deployment evaluation method of the present invention;
fig. 4(a) is a two-dimensional spatial coordinate diagram, and fig. 4(b) is a three-dimensional spatial coordinate diagram.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention discloses a sponge city pipe network facility deployment evaluation method, which comprises the following steps of:
step 1, because the urban terrain is relatively flat, the urban 'ironized' building limits the flow of surface water, the urban waterlogging water is set to be in a relatively static state, and an urban local area is selected to establish an urban waterlogging prediction area model;
dividing a local urban area into a plurality of coarse units, wherein the timed accumulated water in each coarse unit consists of the total rainfall amount after time, smooth combination and infiltration reduction quantity parameters among the coarse units and the accumulated water depth of the coarse units;
calculating total rainfall Q of any coarse unit in any period of timet_rAs in the formula (1),
Figure BDA0002260792460000081
smooth merging between coarse units: in the process of calculating the water accumulation duration in the research area in a certain time period, merging all divided coarse units in the research area, wherein in the merging process, because the water accumulation depth between two adjacent coarse units is deviated, merging is carried out in a smoothing treatment mode, and the adjacent coarse units are merged by utilizing an iterative idea to generate a new coarse unit;
in the formula (1), the parameter RijThe amount of rainfall over time for the grid cell, parameter XijAs accumulated weight of divided grid cells, parameter CijThe cell is a grid cell, the parameter A is a coarse cell, the parameter n is the number of rows of the coarse cell in the region, and the parameter m is the number of columns of the coarse cell in the region;
calculating the soil infiltration Q of each coarse uniti_rAs in the formula (2),
Figure BDA0002260792460000082
in the formula (2), the parameter XkFor the soil accumulated weight, parameter SkThe cumulative total infiltration amount of k type soil per unit area over t, parameter YijAdding the weight for the coarse unit, parameter AijThe area of the grid unit is shown, and a parameter c represents that a corresponding city has c soil types;
calculating the water accumulation depth of each coarse unit as shown in formula (3),
Qc_r＝Qt_r-Qi_r(3)。
and 2, collecting pipe network facility basic data and rainfall data of the city to be evaluated, and establishing an actual facility deployment abstract model by combining the urban waterlogging prediction region model in the step 1.
The Fengxi New city of the city of Xian is taken as a research area, and the floor area of the research area is 3.67hm2And a flow and liquid level monitor is installed at a southwest discharge port of a certain cell, so that a catchment subarea model of a pipe network and a pipe network service connected with the southwest discharge port is established. The facility deployment abstract model is to divide the region into a plurality of sub-regions and correspond to the sub-regionsThe method comprises the steps of generalizing the pipe network facilities, then selecting actual terrains to judge proper flow direction, and finally performing simulation monitoring at an outlet through a production convergence process and a pipe network convergence process.
Step 2.1, according to the relevant definition of the graph theory, the branch model of the drainage pipe network can be formalized, and parameters are set on the basis of the graph theory:
let G ═ (Q, E) be a directed weighted graph,<qi,qjrepresents a directed edge, wherein the parameter qiA parameter q representing the starting point of the directed edgejRepresenting an end point of the directed edge;
the number of entries to any vertex q in the weighted graph G is q, and the entry is expressed as
Figure BDA0002260792460000091
The number of edge strips at any vertex q is called the out-degree of q, and is recorded as
Figure BDA0002260792460000092
The sum of the number of the incoming strips and the number of the outgoing strips of any vertex q, namely the degree of which the sum of the incoming degree and the outgoing degree is q, is recorded as deg (q);
let the degree of penetration of any vertex q be 0, i.e.
Figure BDA0002260792460000093
When the current time goes, the vertex q is recorded as a source; let the out-degree of any one vertex q be 0, i.e.
Figure BDA0002260792460000094
When the vertex q is a sink, the vertex q is recorded as a sink; let the in degree and out degree of any vertex q not equal to 0, i.e.
Figure BDA0002260792460000095
And is
Figure BDA0002260792460000096
Then, the vertex q is called as a turning point;
step 2.2, simulating the parameters in the step 2.1 into an abstract model of a drainage pipe network, namely, the parameters are as follows:
pipe network source point: only the pipe section is connected out, and no node for connecting the pipe section is connected in, and the node is also a drainage inlet of the whole drainage pipe network; in step 2.1, the node with the in-degree of 0 and the out-degree of not equal to 0 is selected;
pipe network collection: only the pipe section is connected, and no node for connecting the pipe section is connected, and the node is also a drainage outlet of the whole drainage pipe network; in step 2.1, the node with the in-degree not equal to 0 and the out-degree of 0 is selected;
pipe network transfer point: namely, the node except the source point and the sink point, and the node has the pipe section access and also has the pipe section access; in step 2.1, nodes with the in degree not equal to 0 and the out degree not equal to 0 are selected;
step 2.3, establishing a facility deployment abstract model through the parameters in the step 2.2:
setting the rainwater pipe network as a directed weighted graph G (Q, E), wherein the parameter E is an edge set of the graph G and mainly comprises a main pipe and a branch pipe, and the parameter Q is a vertex set of the graph G and mainly comprises a rainwater grate, an inspection well and a water outlet;
let X be a subset of Q, if each vertex X in XiAll are the starting points of the edges in the graph G, then X is the source set of G, let Z be a subset of the set of vertices Q, and X ∩ Z be φ, if each vertex Z in ZiAll end points of the edges in the graph G, then Z is the collection of G, let Y also be a subset of the set of vertices Q, and X ∩ Y is phi and Y ∩ Z is phi, and if each vertex Y in Y is YiThat is, the starting point of the edge G of the graph is also called the end point of the edge G of the graph, Y is called a transition point set of G, and the vertex set of the rainwater pipe network G is expressed by the following formula (4):
V＝{X；Y；Z}＝{x1,x2,...,xp；y1,y2,...,ym；z1,z2,...,zq} (4)。
and 3, the deployment environments of the sponge urban pipe network facilities are relatively dispersed, the pipe network facility nodes corresponding to the waterlogging points are easy to determine, the mobility requirements of the pipe network facility nodes are not high, and the positions of the pipe network facilities are basically kept unchanged once the pipe network facilities are deployed. In the sponge city pipe network facility deployment evaluation, a node coverage algorithm is adopted. The point coverage problem is a traditional classical NP completeness problem, and the finite vertex undirected graph minimum coverage problem is one of the earliest famous NPC problems proposed, which, despite its relatively large complexity, is widely used in various fields. The invention explains the node coverage algorithm in turn from three aspects of the radius of the waterlogging point, the drawing of the polygon of the waterlogging point and the judgment of the node on the polygon by using the advantages of the node coverage algorithm.
Deploying an abstract model aiming at the actual facilities in the step 2, and finishing the preliminary evaluation of the pipe network of the waterlogging coverage area through waterlogging points;
and 3.1, acquiring waterlogging points of different levels according to the urban waterlogging prediction area model in the step 1, and assuming that the waterlogging overflow range of each node in a certain level is a circle and the overflow range of each node in the certain level has the same property, so that the coverage problem of the pipe network facility nodes in a certain research area of the sponge city is equal to the circular coverage problem with the same radius.
Setting any waterlogging point as VnThe overflow range of the waterlogging points is circular, as shown in fig. 2(a), the coverage area formed by a single node of the sponge urban pipe network facility, namely a single waterlogging point, is circular, and as shown in fig. 2(b), the coverage area formed by two nodes of the sponge urban pipe network facility, namely two waterlogging points, is tangent to two circles;
step 3.2, as shown in fig. 2(c), setting the coverage area formed by three nodes, namely three waterlogging points, of the sponge urban pipe network facility as follows; the circle centers of the three waterlogging points are respectively set as V1、V2、V3The overlapping area is the area S enclosed by arcs ab, ac and bc1The seamless maximum coverage area formed by the three nodes, namely three centers of circles are separated as far as possible, namely the distance between the centers of circles V1V2、V2V3、V1V3As long as possible, Δ V must be set to obtain the maximum seamless coverage area1V2V3Has the largest area, and as shown in FIG. 2(d), when the intersection points a, b, c of the three circles coincide with the point P, S is present1The area is minimized, thereby obtaining PV1＝PV2＝PV3R, R is a circle radius. The verification process is as follows:
step 3.2.1, inscribing triangles andthe overlapped circles are equivalent to a two-dimensional coordinate system, and corresponding coordinate points of the overlapped circles are assumed; v inscribing triangle, as shown in FIG. 32V3The side is parallel to the X axis, and the radius of the circle is assumed to be 1, and the V can be obtained by combining the knowledge of mathematical theory2V3Is a bottom edge, V1The triangle area is largest possible on the Y-axis because the height of the triangle is largest, and thus V1、V2、V3Has a coordinate of V1(0,-1)、 V2(-cosθ,sinθ)、V3(cos θ, sin θ), wherein
Figure BDA0002260792460000111
Step 3.2.2, calculating the inscribed polygon V1V2V3As in equation (5):
Figure BDA0002260792460000112
Figure BDA0002260792460000113
and t is sin θ, then:
Figure BDA0002260792460000114
step 3.2.3, solving the maximum radius value according to a scaling method;
Figure BDA0002260792460000121
Figure BDA0002260792460000122
Figure BDA0002260792460000123
get
Figure BDA0002260792460000124
At this time
Figure BDA0002260792460000125
Namely, it is
Figure BDA0002260792460000126
Thus: Δ V1V2V3Is side length of
Figure BDA0002260792460000127
An equilateral triangle.
According to the above proof results, when the abstract circles of the adjacent three nodes of the pipe network facility mutually form an equilateral triangle, and the side length of the triangle is equal to that of the equilateral triangle
Figure BDA0002260792460000128
And then, the coverage area of the pipe network facility node to the sponge city research area is maximum, and the coverage redundancy is minimum.
According to the demonstration result selected by the radius of the waterlogging point, a certain waterlogging point under a certain grade can be obtained
Figure BDA0002260792460000129
When the side length is equal to the equilateral triangle, the coverage area of the research area by the sponge city pipe network facility node is the largest and the coverage redundancy is the least. Selecting a pipe network facility node under a certain waterlogging level in a research area so as to
Figure BDA00022607924600001210
Circles are drawn for the radii. After the corresponding circle drawing is finished, different waterlogging points falling in the circle at the same level can be obtained, and the waterlogging points are sequentially connected and numbered in sequence.
And 4, based on the preliminary evaluation method of the pipe network in the step 3, calculating the coverage rate of the sponge city pipe network facility nodes by a node coverage algorithm of sign (x) to finish evaluation.
Step 4.1, parameter setting
Polygonal: on the plane are arranged a series ofCoplanar point V1,V2,...,VnConnecting the points by line segments in sequence to obtain a closed graph; wherein, the connected points are the vertexes of the polygon; the line segments are the sides of a polygon. In addition, a polygon formed by connecting line segments divides the plane into two pieces: inner (bounded) and outer (unbounded). Thus, any point on a plane will have three relationships with a polygon: the point is inside the polygon, the point is outside the polygon, the point is on a polygon edge, or a vertex.
Three-dimensional spatial coordinates of points: the position of a set point in the xoy plane of the two-dimensional space is (x, y); the position of a point in the three-dimensional space o 'x' y 'z' stereo space is (x, y, z); therefore, an arbitrary point Q on the two-dimensional plane is a point Q 'on the x' o 'y' plane of the three-dimensional space o 'x' y 'z', and the coordinates (x, y) of the point Q on the two-dimensional plane are expanded to the spatial coordinates to become (x, y, 0);
sign (x) function is defined as formula (8):
Figure BDA0002260792460000131
step 4.2, numbering the vertexes of the waterlogging polygons on the xoy plane from a certain point in sequence along the same direction (such as the anticlockwise direction), and as shown in the figure 4(a), numbering the vertexes of the waterlogging polygons, wherein the point V is a point Vi、Vi+1Respectively representing two waterlogging points, namely a point Q of a certain edge on the waterlogging polygonjIs an image extraction point corresponding to a certain node of a pipe network facility in a sponge city research area to judge a node Q of the pipe network facilityjAnd the position relation with the waterlogging polygon.
As shown in FIG. 4(b), point Q on the xoy plane is shownj(xj,yj) Vertex V of the polygoni(xi,yi) And Vi+1(xi+1,yi+1) Viewed as points Q ', V of the three-dimensional space o' x 'y' z 'on the x' o 'y' planei' and Vi+1', extended to spatial coordinates, denoted as (x)j,yj,0)、(xi,yi0) and (x)i+1,yj+1,0)；
Step 4.3, by formulae (9) and (C)10) Calculating Qj'Vi' and Qj'Vi+1'；
Qj'Vi'＝((xi-xj),(yi-yj),0) (9)
Qj'Vi+1'＝((xi+1-xj),(yi+1-yj),0) (10)
Step 4.4, calculating the product of the two vectors by the formula (11);
Figure BDA0002260792460000132
step 4.5, according to the different positions of the points, corresponding crThere are three cases, as in equation (12); meanwhile, the corresponding sign (x) is calculated according to the formula (13):
cr＞0,cr＜0,cr＝0 (12)
Figure BDA0002260792460000141
step 4.6, by varying crCalculating a sign (x) value, and judging the position relation between the nodes of the pipe network facilities to be detected and the waterlogging polygon through the sign (x) value;
if sign (x) is 0, then sponge city pipe network facility node QjWaterlogging point ViAnd Vi+1The three points are positioned on the same line, but when the sponge city pipe network facility node corresponds to the condition of the coordinate formula (14), the sponge city pipe network facility node is positioned on the waterlogging polygonal boundary or the vertex;
Figure BDA0002260792460000142
if sign (x) is not equal to 0, then sponge city pipe network facility node QjWaterlogging point ViAnd Vi+1Three points are not on the same line, and the coordinates of the sponge city pipe network facility nodes and the coordinates of the waterlogging polygon vertexes have yi＜yj＜yi+1Or yi＜yj＜yi+1Two cases, calculated according to equations (15) and (16):
kr＝sign(x)＝sign(cr) (15)
Figure BDA0002260792460000143
if K is not equal to 0, sponge city pipe network facility node Q is located inside waterlogging polygon S, if K is not equal to 0, sponge city pipe network facility node Q is located outside waterlogging polygon S.
The evaluation method of the invention combines a sponge urban waterlogging prediction region model and an actual facility deployment abstract model, adopts a parallelization node coverage algorithm to calculate the distribution of waterlogging points, the waterlogging grade and the node coverage rate of the pipe network facility in a corresponding region, and analyzes whether the pipe network facility deployment in the region is reasonable; the problem of current municipal drainage pipe network facility distribute unreasonablely, easily cause urban waterlogging is solved.

Claims (5)

1. A sponge city pipe network facility deployment assessment method is characterized by comprising the following steps:
step 1, setting urban waterlogging to be in a relatively static state, selecting an urban local area, and establishing an urban waterlogging prediction area model;
step 2, collecting pipe network facility basic data and rainfall data of a city to be evaluated, and establishing an actual facility deployment abstract model by combining the urban waterlogging prediction region model in the step 1;
step 3, deploying an abstract model aiming at the actual facilities in the step 2, and finishing preliminary evaluation of a pipe network of an inland inundation coverage area through inland inundation points;
and 4, based on the preliminary evaluation method of the pipe network in the step 3, calculating the coverage rate of the sponge city pipe network facility nodes through a node coverage algorithm of sign (x), and finishing evaluation.
2. The sponge city pipe network facility deployment evaluation method according to claim 1, wherein the step 1 specifically operates as follows: dividing a local city area into a plurality of coarse units, wherein the timed accumulated water amount in each coarse unit consists of the total rainfall amount after time, smooth combination among the coarse units, an infiltration reduction amount parameter and the accumulated water depth of the coarse units;
calculating total rainfall Q of any coarse unit in any period of timet_rAs in the formula (1),
Figure RE-FDA0002409242200000011
in the formula (1), the parameter RijThe amount of rainfall over time for the grid cell, parameter XijFor the accumulated weight of the divided grid cells, parameter CijThe cell is a grid cell, the parameter A is a coarse cell, the parameter n is the number of rows of the coarse cell in the region, and the parameter m is the number of columns of the coarse cell in the region;
calculating the soil infiltration Q of each coarse uniti_rAs in the formula (2),
Figure RE-FDA0002409242200000012
in the formula (2), the parameter XkFor the soil accumulated weight, parameter SkThe cumulative total infiltration amount of k type soil per unit area over t, parameter YijAdding the weight for the coarse unit, parameter AijThe area of the grid unit is shown, and a parameter c represents that a corresponding city has c soil types;
calculating the water accumulation depth of each coarse unit as shown in formula (3),
Qc_r＝Qt_r-Qi_r(3)。
3. the sponge city pipe network facility deployment evaluation method according to claim 1, wherein the actual facility deployment abstract model in the step 2 is specifically:
step 2.1, setting parameters based on graph theory:
let G ═ (Q, E) be a directed weighted graph,<qi,qj>a directed edge is represented that is,wherein the parameter qiA parameter q representing the starting point of the directed edgejRepresenting an end point of the directed edge;
the number of entries to any vertex q in the weighted graph G is q, and the entry is expressed as
Figure RE-FDA0002409242200000021
The number of edge strips at any vertex q is called the out-degree of q, and is recorded as
Figure RE-FDA0002409242200000022
The sum of the number of the incoming strips and the number of the outgoing strips of any vertex q, namely the degree of which the sum of the incoming degree and the outgoing degree is q, is recorded as deg (q);
let the degree of penetration of any vertex q be 0, i.e.
Figure RE-FDA0002409242200000023
When the current time goes, the vertex q is recorded as a source; let the out-degree of any one vertex q be 0, i.e.
Figure RE-FDA0002409242200000024
When the vertex q is a sink, the vertex q is recorded as a sink; let the in-degree and out-degree of any vertex q not equal to 0, i.e.
Figure RE-FDA0002409242200000025
And is
Figure RE-FDA0002409242200000026
Then, the vertex q is called as a turning point;
2.2, simulating the parameters in the step 2.1 into an abstract model of a drainage pipe network, namely, the following parameters are provided:
pipe network source point: only the pipe section is connected out, and no node for connecting the pipe section is connected in, and the node is also a drainage inlet of the whole drainage pipe network; in step 2.1, the node with the in-degree of 0 and the out-degree of not equal to 0 is selected;
pipe network collection: only the pipe section is connected, and no node for connecting the pipe section is connected, and the node is also a drainage outlet of the whole drainage pipe network; in step 2.1, the node with the in-degree not equal to 0 and the out-degree of 0 is selected;
pipe network transfer point: namely, the node except the source point and the sink point, and the node has both a pipe section access and a pipe section access; in step 2.1, nodes with the in degree not equal to 0 and the out degree not equal to 0 are selected;
step 2.3, establishing a facility deployment abstract model through the parameters in the step 2.2:
setting the rainwater pipe network as a directed weighted graph G (Q, E), wherein the parameter E is an edge set of the graph G and mainly comprises a main pipe and a branch pipe, and the parameter Q is a vertex set of the graph G and mainly comprises a rainwater grate, an inspection well and a water outlet;
let X be a subset of Q, if each vertex X in XiAll are the starting points of the edges in the graph G, then X is the source set of G, let Z be a subset of the set of vertices Q, and X ∩ Z be φ, if each vertex Z in ZiAll end points of the edges in the graph G, then Z is the collection of G, let Y also be a subset of the set of vertices Q, and X ∩ Y is phi and Y ∩ Z is phi, and if each vertex Y in Y is YiThat is, the starting point of the edge G of the graph is also called the end point of the edge G of the graph, Y is called a transition point set of G, and the vertex set of the rainwater pipe network G is expressed by the following formula (4):
V＝{X；Y；Z}＝{x1,x2,...,xp；y1,y2,...,ym；z1,z2,...,zq} (4)。
4. the sponge city pipe network facility deployment evaluation method according to claim 1, wherein the step 3 specifically comprises:
step 3.1, setting any waterlogging point as VnThe overflow range of the waterlogging points is circular, the coverage area formed by a single node of the sponge urban pipe network facility, namely a single waterlogging point, is circular, and the coverage area formed by two nodes of the sponge urban pipe network facility, namely two waterlogging points, is tangent to two circles;
step 3.2, setting three nodes of the sponge urban pipe network facility, namely the coverage area formed by the three waterlogging points, as follows; the circle centers of the three waterlogging points are respectively set as V1、V2、V3The overlapping area is the area S enclosed by arcs ab, ac and bc1When the intersection points a, b and c of the three circles coincide with the point P, S is present1The area is minimized, thereby obtaining PV1＝PV2＝PV3R, R is the radius of the circle.
5. The sponge city pipe network facility deployment evaluation method according to claim 4, wherein the step 4 specifically comprises:
step 4.1, parameter setting
Polygonal: with a series of coplanar points V on the plane1,V2,...,VnConnecting the points by line segments in sequence to obtain a closed graph;
three-dimensional spatial coordinates of points: the position of a set point in the xoy plane of the two-dimensional space is (x, y); the position of a point in the three-dimensional space o 'x' y 'z' stereo space is (x, y, z); therefore, an arbitrary point Q on the two-dimensional plane is a point Q 'on the x' o 'y' plane of the three-dimensional space o 'x' y 'z', and the coordinates (x, y) of the point Q on the two-dimensional plane are extended to the spatial coordinates to become (x, y, 0);
sign (x) function is defined as formula (8):
Figure RE-FDA0002409242200000041
step 4.2, point Q on the xoy planej(xj,yj) Vertex V of the polygoni(xi,yi) And Vi+1(xi+1,yi+1) Viewed as points Q ', V of the three-dimensional space o' x 'y' z 'on the x' o 'y' planei' and Vi+1', extended to spatial coordinates, denoted as (x)j,yj,0)、(xi,yi0) and (x)i+1,yj+1,0)；
Step 4.3, calculate Q by equations (9) and (10)j'Vi' and Qj'Vi+1'；
Qj'Vi'＝((xi-xj),(yi-yj),0) (9)
Qj'Vi+1'＝((xi+1-xj),(yi+1-yj),0) (10)
Step 4.4, calculating the product of the two vectors by the formula (11);
Figure RE-FDA0002409242200000042
step 4.5, according to the different positions of the points, corresponding crThere are three cases, as in equation (12);
and the corresponding sign (x) is calculated according to the formula (13):
cr＞0,cr＜0,cr＝0 (12)
Figure RE-FDA0002409242200000051
step 4.6, by varying crCalculating a sign (x) value, and judging the position relation between the nodes of the pipe network facilities to be detected and the waterlogging polygon through the sign (x) value;
if sign (x) is 0, then sponge city pipe network facility node QjWaterlogging point ViAnd Vi+1The three points are positioned on the same line, but when the sponge city pipe network facility node corresponds to the condition of the coordinate formula (14), the sponge city pipe network facility node is positioned on the waterlogging polygonal boundary or vertex;
Figure RE-FDA0002409242200000052
if sign (x) is not equal to 0, then sponge city pipe network facility node QjWaterlogging point ViAnd Vi+1Three points are not on the same line, and the coordinates of the sponge city pipe network facility nodes and the coordinates of the waterlogging polygon vertexes have yi＜yj＜yi+1Or yi＜yj＜yi+1Two cases, calculated according to equations (15) and (16):
kr＝sign(x)＝sign(cr) (15)
Figure RE-FDA0002409242200000053
if K is not equal to 0, sponge city pipe network facility node Q is located inside waterlogging polygon S, if K is not equal to 0, sponge city pipe network facility node Q is located outside waterlogging polygon S.
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