CN114372625A - Urban waterlogging rapid forecasting method based on multi-output machine learning algorithm - Google Patents
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Abstract
The invention discloses a method for quickly forecasting urban waterlogging based on a multi-output machine learning algorithm. The method comprises the following steps: according to the data of the existing research area, an urban waterlogging model is constructed; extracting historical rainstorm rainfall time interval distribution information, generating rainstorms with different characteristics, and simulating and constructing a rainstorm waterlogging database through the constructed urban waterlogging model; constructing a multi-output random forest model, training and testing the multi-output random forest model by using a rainstorm waterlogging database with a rainfall factor as an independent variable and a submerging depth as a dependent variable; based on rainfall forecast input conditions, the rapid and real-time forecast of two-dimensional waterlogging submergence is realized through the constructed multi-output random forest model. The method has important significance for early warning and prevention of urban waterlogging disasters, prevention of waterlogging, reduction of disasters and the like, can effectively improve the real-time waterlogging situation forecasting efficiency and precision of high-incidence areas of the waterlogging disasters, and can provide certain guidance for quickly forecasting the waterlogging situations.
Description
Technical Field
The invention relates to the technical field of urban waterlogging disaster prevention and control, in particular to the technical field of waterlogging simulation, and particularly relates to a method for quickly forecasting urban waterlogging based on a multi-output machine learning algorithm.
Background
In the background of global climate change and rapid urbanization, rainstorm and waterlogging disasters become increasingly frequent, resulting in continuous increase of casualties and economic losses. The rainstorm waterlogging causes huge personal casualties and property losses to countries and society, seriously influences the social and economic development and the happiness of people, for example, Guangzhou suffers from the attack of '5.22' extra heavy rainstorm in 2020, rainfall breaks through the historical extreme value in 42 sites per hour, and causes serious waterlogging in a plurality of regions in the whole city, so that 443-place region is flooded, wherein the 13 th line of the subway causes 4 deaths due to the full-line stoppage of the reverse irrigation, and the economic loss is huge. The waterlogging forecast is used as an important component of non-engineering measures for flood control and drainage, so that the exposure and the vulnerability of a disaster bearing body can be effectively reduced, and the disaster prevention and reduction capability of a drainage basin and an area is improved. Therefore, the development of the research work for rapidly forecasting the waterlogging has important practical significance.
The urban waterlogging model based on the hydrokinetic principle provides important technical support for urban waterlogging simulation forecast, can realize refined simulation of waterlogging, but can solve the problems of complex iterative solution equation, overlarge simulation time efficiency and the like, and can be limited to a certain extent in the application of rapid and large-scale urban waterlogging forecast. Due to the data-driven characteristics of machine learning, the relationship between elements such as rainfall input and water depth output can be quickly learned in the results of the traditional numerical model. At present, most of the previous machine learning models are based on water depth prediction of a single or few accumulated water points (Xuwei red, Wang fir, high build mark, Zhangniang, Shu Rubia, Lina, Korean pine, Wang Jing, Wang Yan, Ding Shi Xiong, urban inland accumulated water point water accumulation process prediction method and system based on machine learning), water depth on urban inland water accumulation surfaces is difficult to predict at the same time, and submerging range information cannot be provided; at present, some researches realize prediction of all grids by constructing a corresponding number of machine learning models for grid points one by one, however, the method does not consider spatial correlation among various water depth points, and the precision is limited to a certain extent. With the development of the technology, the rapid prediction problem of waterlogging can be better solved by introducing a multi-output algorithm, but how to combine the advantages of the machine learning algorithm and the hydrohydrodynamic model and construct a scientific waterlogging prediction model by using the algorithms to realize the rapid and accurate prediction of early waterlogging inundation becomes a key problem to be solved urgently in urban flood control and disaster reduction work.
Disclosure of Invention
The invention aims to overcome the defects and shortcomings in the prior art and provides a rapid urban waterlogging forecasting method based on a multi-output machine learning algorithm.
The purpose of the invention is realized by at least one of the following technical solutions.
A city waterlogging rapid forecasting method based on a multi-output machine learning algorithm comprises the following steps:
s1, constructing an urban waterlogging model according to the data of the existing research area;
s2, extracting historical rainstorm rainfall time interval distribution information, generating rainstorms with different characteristics, and simulating and constructing a rainstorm waterlogging database through the constructed urban waterlogging model;
s3, constructing a multi-output random forest model, and training and testing the multi-output random forest model by using a rainstorm waterlogging database with a rainfall factor as an independent variable and a submerging depth as a dependent variable;
and S4, based on rainfall forecast input conditions, realizing rapid and real-time forecast of two-dimensional waterlogging inundation through the constructed multi-output random forest model.
Further, in step S1, the elevation, pipe network and land utilization data of the existing research area are collected, the elevation and land utilization data are cut and extracted by using the ArcGIS software, and the pipe network is corrected and topology is checked.
Further, in step S1, the constructed urban inland inundation model is a two-dimensional hydrohydrodynamic coupling model based on SWMM and WCA 2D;
in the constructed urban inland inundation model, a rainstorm runoff management model (SWMM) is constructed according to elevation, pipe network and land utilization data; inputting rainfall data into a storm runoff management model (SWMM), deriving the spatial position of an overflow point and an overflow process by the storm runoff management model (SWMM), inputting a cellular automaton model (WCA2D) to carry out ponding two-dimensional simulation, and finally outputting submerging range and submerging water depth information by the cellular automaton model (WCA 2D);
and (4) carrying out calibration and verification on the constructed urban waterlogging model, namely adjusting the model parameters until the urban waterlogging model meets the requirement of simulation precision.
Further, in step S2, the rainstorms with different characteristics refer to rainstorms with different reappearance periods and different rain types;
the different rain types include 8 types: type I is before a unimodal peak, type II is after a unimodal peak, type III is in a unimodal peak, type IV is a uniform rain type, type V is before and after a bimodal, type VI is near the front bimodal, type VII is near the back bimodal, and Chicago rain type.
Further, the building of the rainstorm waterlogging database refers to inputting rainstorms with different characteristics into the built urban waterlogging model to simulate the submerging range and the waterlogging depth under different scenes.
Further, in step S3, the multi-output random forest algorithm is an algorithm based on a combination of the multi-output algorithm and the random forest algorithm; the multi-output algorithm, also called a multi-target algorithm, is a generalization of multi-target regression and multi-target classification;
constructing a single-output regression tree, wherein in the single-output regression tree, y is a single-output vector, and impurities i (t) related to a node t are defined as:
wherein, ykIs an observed value of a single output vector y,
is the mean value of the single output vector y at node t, NtIs the number of data points on node t;
setting a single output predictor variable XpSplitting a node t as a father node into t at a splitting point cLAnd tRTwo child nodes, where tLIncluding all single-output predictor variables XpData points ≦ c, tRIncluding all single-output predictor variables XpData points > c; since the variable X is predicted by a single outputpReduction of impurity associated with node t caused by splitting at splitting point c
The calculation formula of (a) is as follows:
wherein N ist,NtLAnd NtRRespectively being a node t, a first child node tLAnd a second child node tRThe number of data points at.
Further, for the multi-output random forest algorithm, the construction process of the multi-output random forest model is based on a multi-output regression tree model; a multi-output regression tree, also known as a multi-objective regression tree, is a tree that can predict multiple successive objectives simultaneously; when constructing a multi-output regression tree, assume a training set D with N instances, the training set D includes multi-output predictor variable assignments X with m features1,…,XmAnd a multiple output response variable assignment Y with d targets1,…,YdI.e. D { (x)(1),y(1)),…,(x(N),y(N)) }; fruit of Chinese wolfberryExample l Multi-output input vector comprising m features describing arguments
And a multi-output vector of d targets
Wherein i belongs to {1, …, m }, j belongs to {1, …, d }, and l belongs to {1, …, N }; wherein x is(l)And y(l)The multiple-output-input vector and the multiple-output vector of instance i are represented separately,
and
respectively an input vector value under the mth characteristic in the example l and an output vector value under the d target;
the construction steps of the multi-output regression tree are similar to those of the single-output regression tree, the single-output regression tree is expanded to the multi-output regression tree by replacing the univariate response with the multivariate response, namely the multi-output regression tree redefines the impurity of the node by summing the univariate impurity measurement on the multivariate response, and the specific steps are as follows:
in the formula:
denotes y under the jth target(l)The value of (a) is,
indicating y under jth target in node(l)Is selected to minimize the square error
The sum of the two is used as a dividing point; each leaf of the multiple output regression tree is openCharacterizing the multivariate average value of each instance on the leaf, the number of instances and the characteristic value defined by the leaf;
and finally, constructing a multi-output random forest model through a multi-output decision tree based on the randomly selected feature set.
Further, dividing N instances in the rainstorm waterlogging database into a training set D and a test set T according to the ratio of 8: 2;
the training set D includes predictor variable assignments X with m features1,…,XmAnd a response variable assignment Y with d targets1,…,Yd；
Rainfall factor corresponds to X of training set D1,…,XmThe depth of flooding corresponds to Y1,…,Yd。
Further, the test set T also includes predictor variable assignments X with m features1,…,XmAnd a response variable assignment Y with d targets1,…,YdTest set T and training set D differ from different instances;
and constructing a multi-output random forest model by using a training set D comprising rainfall factors and submerging depth, and checking the effect of the multi-output random forest model through a test set T.
Further, in step S4, inputting the time-series data of the real-time rainfall forecast into the constructed multi-output random forest model, outputting the water depth of each spatial grid point, and realizing the forecast of the two-dimensional inland inundation scope and the water depth; because the time required by the multi-output random forest model for predicting the water depth is extremely short, and the accuracy meets the requirement, the rapid and real-time prediction of the waterlogging submerging condition can be realized.
Compared with the prior art, the invention has the following advantages and beneficial effects:
(1) the method applies the multi-output random forest model to the waterlogging submerging water depth prediction, and can realize the rapid and accurate prediction of the two-dimensional waterlogging submerging water depth. Compared with the traditional machine learning model (such as an artificial neural network) with single variable output, the method has the advantages that the defects that a large number of models need to be built, the time consumption is high and the spatial correlation is not considered in the prediction of a plurality of spatial points, the multi-output random forest model can complete simultaneous prediction of the water depth of a large number of spatial points by only building one model, the spatial correlation of a plurality of grid points can be considered, and the prediction precision and the timeliness are greatly improved.
(2) Compared with the traditional waterlogging model based on a physical mechanism, the multi-output random forest model constructed for predicting the spatial inundation water depth is similar to the simulation precision of the waterlogging model, but the calculation and prediction efficiency of the model is far higher than that of the model. Therefore, the multi-output random forest model can replace part of functions of the traditional physical model in waterlogging forecasting, and therefore real-time and rapid forecasting of the waterlogging submerging range and the waterlogging depth based on rainfall forecasting is achieved.
Drawings
FIG. 1 is a flow chart of a technique for rapidly forecasting urban waterlogging based on a multi-output machine learning algorithm according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a one-dimensional hydrokinetic model of a waterlogging-prone area in guangzhou city constructed in embodiment 1 of the present invention;
FIG. 3 is a schematic diagram of a rainfall process with different recurrence periods and rain-type characteristics;
FIG. 4 is a schematic diagram of a multiple output algorithm;
FIG. 5 is a schematic diagram showing correlation between the multiple output random forest model (RF) prediction and the simulated submerging depth of a hydrohydrodynamic model (SWMM + CA) in a waterlogging-prone area in example 1;
fig. 6 is a schematic diagram of a one-dimensional hydrographic hydrodynamic model of a watershed in guangzhou city constructed in embodiment 2 of the present invention;
FIG. 7a and FIG. 7b are schematic diagrams of the 2-field measured rainfall process in a certain drainage basin in example 2;
fig. 8 is a schematic diagram of correlation between the multiple output random forest model (RF) prediction and the simulated submerging water depth of the hydrohydrodynamic model (SWMM + CA) in a certain watershed in example 2.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention.
Example 1:
a method for rapidly forecasting urban waterlogging based on a multi-output machine learning algorithm is shown in figure 1 and comprises the following steps:
s1, constructing an urban waterlogging model according to the data of the existing research area;
the elevation, pipe network and land utilization data of the existing research area are collected, the elevation and land utilization data are cut and extracted by ArcGIS software, and the pipe network is corrected and topology inspection is carried out.
The constructed urban inland inundation model is a two-dimensional hydrohydrodynamic coupling model based on SWMM and WCA 2D; in this embodiment, as shown in fig. 2, a certain waterlogging-prone area in Guangzhou city is taken as an example (the area is 1.6 km)2) Constructing an inland inundation coupling model of the city one-dimensional pipe network SWMM and the two-dimensional hydrodynamic force WCA 2D;
in the constructed urban inland inundation model, a rainstorm runoff management model (SWMM) is constructed according to elevation, pipe network and land utilization data; inputting rainfall data into a storm runoff management model (SWMM), deriving the spatial position of an overflow point and an overflow process by the storm runoff management model (SWMM), inputting a cellular automaton model (WCA2D) to carry out ponding two-dimensional simulation, and finally outputting submerging range and submerging water depth information by the cellular automaton model (WCA 2D);
and (4) carrying out calibration and verification on the constructed urban waterlogging model, namely adjusting the model parameters until the urban waterlogging model meets the requirement of simulation precision.
S2, extracting historical rainstorm rainfall time interval distribution information, generating rainstorms with different characteristics, and simulating and constructing a rainstorm waterlogging database through the constructed urban waterlogging model;
the rainstorms with different characteristics refer to rainstorms with different reappearance periods and different rain types; in this example, different recurring periods were employed for 1 year, 5 years, 10 years, 20 years, 50 years, and 100 years (total 6);
as shown in fig. 3, a, b, c, d, e, f, g, and h, the different rain patterns include 8 types: type I is before the unimodal peak, type II is after the unimodal peak, type III is in the unimodal peak, type IV is the uniform rainfall type, type V is after the bimodal front, type VI is before the bimodal front, type VII is after the bimodal back, and Chicago rainfall type, in this example, 48 rainfall scenarios are total.
The method for constructing the rainstorm waterlogging database comprises the steps of inputting rainstorms with different characteristics into the constructed urban waterlogging model, and simulating the submerging range and the waterlogging depth under different scenes.
S3, constructing a multi-output random forest model, and training and testing the multi-output random forest model by using a rainstorm waterlogging database with a rainfall factor as an independent variable and a submerging depth as a dependent variable;
the multi-output random forest algorithm is an algorithm based on the combination of the multi-output algorithm and the random forest algorithm; the multi-output algorithm, also called a multi-target algorithm, is a generalization of multi-target regression and multi-target classification;
constructing a single-output regression tree, wherein in the single-output regression tree, y is a single-output vector, and impurities i (t) related to a node t are defined as:
wherein, ykIs an observed value of a single output vector y,
is the mean value of the single output vector y at node t, NtIs the number of data points on node t;
setting a single output predictor variable XpSplitting a node t as a father node into t at a splitting point cLAnd tRTwo child nodes, where tLIncluding all single-output predictor variables XpData points ≦ c, tRIncluding all single-output predictor variables XpData points > c; since the variable X is predicted by a single outputpReduction of impurity associated with node t caused by splitting at splitting point c
The calculation formula of (a) is as follows:
wherein N ist,NtLAnd NtRRespectively being a node t, a first child node tLAnd a second child node tRThe number of data points at.
For the multi-output random forest algorithm, the construction process of the multi-output random forest model is based on a multi-output regression tree model; a multi-output regression tree, also known as a multi-objective regression tree, is a tree that can predict multiple successive objectives simultaneously; when constructing a multi-output regression tree, assume a training set D with N instances, the training set D includes multi-output predictor variable assignments X with m features1,…,XmAnd a multiple output response variable assignment Y with d targets1,…,YdI.e. D { (x)(1),y(1)),…,(x(N),y(N)) }; example l Multi-output input vector comprising m features describing arguments
And a multi-output vector of d targets
Wherein i belongs to {1, …, m }, j belongs to {1, …, d }, and l belongs to {1, …, N }; wherein x is(l)And y(l)The multiple-output-input vector and the multiple-output vector of instance i are represented separately,
and
respectively an input vector value under the mth characteristic in the example l and an output vector value under the d target;
the construction steps of the multi-output regression tree are similar to those of the single-output regression tree, the single-output regression tree is expanded to the multi-output regression tree by replacing the univariate response with the multivariate response, namely the multi-output regression tree redefines the impurity of the node by summing the univariate impurity measurement on the multivariate response, and the specific steps are as follows:
in the formula:
denotes y under the jth target(l)The value of (a) is,
indicating y under jth target in node(l)Is selected to minimize the square error
The sum of the two is used as a dividing point; each leaf of the multi-output regression tree is characterized by a multivariate average value of each instance on the leaf, the number of instances and a characteristic value defined by the leaf;
and finally, constructing a multi-output random forest model through a multi-output decision tree based on the randomly selected feature set.
Dividing N instances in the rainstorm waterlogging database into a training set D and a test set T according to the ratio of 8: 2;
the training set D includes predictor variable assignments X with m features1,…,XmAnd a response variable assignment Y with d targets1,…,Yd；
Rainfall factor corresponds to X of training set D1,…,XmThe depth of flooding corresponds to Y1,…,Yd。
The test set T likewise comprises predictor variable assignments X with m features1,…,XmAnd a response variable assignment Y with d targets1,…,YdTest set T and training set D differ from different instances;
and constructing a multi-output random forest model by using a training set D comprising rainfall factors and submerging depth, and checking the effect of the multi-output random forest model through a test set T.
In this embodiment, a multi-output random forest model is constructed to learn a large amount of rainfall-waterlogging data. As shown in fig. 4, the input of the multi-output random forest model is the rainfall process, and the output of the multi-output random forest model is the water depth at different spatial points. In this embodiment, the independent variable of the multi-output random forest model is the rainfall process (the rainfall duration is 120min, and there are 120 input variables in total), and the dependent variable is the water depth of different spatial points (there are 5749 grid points in total, and the grid resolution is 5m × 5 m). And dividing 48 simulated rainstorm waterlogging databases into training sets and test sets (38 training sets and 10 test sets) according to the ratio of 8:2, and training the constructed multi-output random forest model.
When the multi-output random forest model is constructed, two important parameters are respectively the number ntree of the regression tree and the number mtry of independent variables for specifying each node of the regression tree to divide the data into two. Considering the calculation accuracy and the calculation time together, in this embodiment, mtry is 40, ntree is 100, and the other parameters are default parameters.
S4, based on rainfall forecast input conditions, realizing rapid and real-time forecast of two-dimensional waterlogging submergence through the constructed multi-output random forest model;
inputting the time sequence data of the real-time rainfall forecast into the constructed multi-output random forest model, and outputting the water depth of each spatial grid point to realize the forecast of the two-dimensional waterlogging submerging range and the water depth; because the time required by the multi-output random forest model for predicting the water depth is extremely short, and the accuracy meets the requirement, the rapid and real-time prediction of the waterlogging submerging condition can be realized.
In this embodiment, the prediction effect of the urban waterlogging model is tested by using 10-field design rainstorms. The 10 designed rainstorms respectively refer to 50-year-first type I rainstorms, 50-year-first type IV rainstorms, 50-year-first type II rainstorms, 20-year-first type V rainstorms, 10-year-first type III rainstorms, 10-year-first type VI rainstorms, and 5-year-first type I rainstorms and 5-year-first type IV rainstorms.
And evaluating the space water depth prediction effect of the multi-output random forest model. Under 10 test scenarios, the relationship between the water depth results of the multi-output random forest model and the urban waterlogging model based on hydrodynamics is shown in a diagram, b diagram, c diagram, d diagram, e diagram, f diagram, g diagram, h diagram, i diagram and j diagram in fig. 5, which respectively refer to 50-year-first type I rainstorm, IV-type rainstorm, VII-type rainstorm, 20-year-first type II rainstorm, V-type rainstorm, Chicago-type rainstorm, 10-year-first type III rainstorm, VI-type rainstorm and 5-year-first type I rainstorm and IV-type rainstorm. The result shows that the multi-output random forest model constructed in the embodiment 1 has a good prediction effect. The spatial water depth predicted by the multi-output random forest model is closer to the result of the urban waterlogging model, the waterlogging-prone positions are matched, and the spatial maximum water depth difference between the spatial water depth and the waterlogging-prone positions is smaller (basically smaller than 7 cm); the correlation between the water depth predicted by the multi-output random forest model and the simulated water depth of the hydrokinetic model is high, and a remarkable linear correlation (P <0.001) is presented. The average error ME of the prediction performance of the multi-output random forest model is between-4.5 cm and 6.5cm, and the correlation coefficients PCC are all above 0.840.
From the analysis of the simulation duration, the multi-output random forest model can complete the maximum submerging range and water depth calculation of the waterlogging-prone area within 1s, the simulation time of the urban waterlogging model based on hydrodynamics reaches 26-74 s, and the simulation efficiency of the multi-output random forest model is greatly improved compared with that of the urban waterlogging model based on hydrodynamics. The research area of the embodiment 1 is small, and the prediction efficiency of the multi-output random forest model relative to the urban waterlogging model is greatly improved. For other research areas, when the research range is expanded or the grid precision requirement is higher (the number of grids is increased), the computational efficiency advantage of the multi-output random forest model is more prominent, and will be further explained in combination with embodiment 2.
Comparative example 1:
comparative example 1 a conventional water depth prediction method was used, and a comparison was made with example 1. Comparative example 1 the study area, training set, test set data from example 1 were used, but the water depth prediction method utilized the traditional K-nearest neighbor method. The K-nearest neighbor method is an example learning-based nonparametric regression prediction method in the field of data mining, and carries out classification and prediction by searching K samples which are most similar to prediction variables in a training set. In comparative example 1, a K neighbor model of the research area is constructed based on training set data, the spatial water depth prediction effects of the K neighbor model and the urban waterlogging model are compared, and the prediction effects of the multi-output random forest are compared. The K-nearest neighbor model was tested and evaluated using 10-field design storms of the test set. Under 10 test scenes, the K neighbor model prediction is closer to the submergence depth of each grid point simulated by the urban waterlogging model. The evaluation result of the prediction performance index of the K neighbor model shows that the average error ME is between-8.1 cm and 7.5cm, the correlation between the prediction of the K neighbor model and the water depth simulated by the urban waterlogging model is higher, the PCC is above 0.797, and the obvious linear correlation (P <0.001) is presented.
The comparison result of the K neighbor model and the multi-output random forest model shows that the space water depth prediction effect of the K neighbor model and the multi-output random forest model is good, but the prediction accuracy of the multi-output random forest model is obviously better. The two methods are similar in aging. Therefore, the comparison between the comparative example 1 and the example 1 shows that the multi-output random forest model has better prediction performance than the K neighbor model.
Example 2:
a method for rapidly forecasting urban waterlogging based on a multi-output machine learning algorithm is shown in figure 1 and comprises the following steps:
s1, constructing an urban waterlogging model according to the data of the existing research area;
collecting elevation, pipe network and land utilization data of the existing research area, and processing by utilizing ArcGIS software; the constructed urban inland inundation model is a two-dimensional hydrohydrodynamic coupling model based on SWMM and WCA 2D; in this embodiment, as shown in fig. 6, a certain drainage basin in Guangzhou city is taken as an example (the area is 74 km)2) Constructing an inland inundation coupling model of the city one-dimensional pipe network SWMM and the two-dimensional hydrodynamic force WCA 2D; in the constructed urban inland inundation model, a rainstorm runoff management model (SWMM) is constructed according to elevation, pipe network and land utilization data; inputting rainfall data into a storm runoff management model (SWMM), deriving the spatial position of an overflow point and the overflow process by the storm runoff management model (SWMM), inputting a cellular automaton model (WCA2D) to perform ponding two-dimensional simulation, and finally outputting a submerging range by the cellular automaton model (WCA2D)Enclosing and submerging water depth information;
and (4) carrying out calibration and verification on the constructed urban waterlogging model, namely adjusting the model parameters until the urban waterlogging model meets the requirement of simulation precision.
S2, extracting historical rainstorm rainfall time interval distribution information, generating rainstorms with different characteristics, and simulating and constructing a rainstorm waterlogging database through the constructed urban waterlogging model;
the rainstorms with different characteristics refer to rainstorms with different reappearance periods and different rain types; in this example, different recurring periods were employed for 1 year, 5 years, 10 years, 20 years, 50 years, and 100 years (total 6); as shown in fig. 3, a, b, c, d, e, f, g, and h, the different rain patterns include 8 types: type i before unimodal, type ii after unimodal, type iii in unimodal, type iv in homogeneous rain, type v in tandem with bimodal, type vi in front of bimodal, type vii in back of bimodal, and type chicago (total of 8), for a total of 48 rainfall scenarios, identical to the different characteristic rainstorms employed in example 1.
The rainstorm waterlogging database with different characteristics is that rainstorms with different characteristics are input into a constructed urban waterlogging model to simulate the submerging range and the waterlogging depth under different scenes.
S3, constructing a multi-output random forest model, and training and testing the multi-output random forest model by using a rainstorm waterlogging database with a rainfall factor as an independent variable and a submerging depth as a dependent variable;
the multi-output random forest algorithm is an algorithm based on the combination of a multi-output algorithm and a random forest algorithm; the multi-output algorithm, also called a multi-target algorithm, is a generalization of multi-target regression and multi-target classification; the construction of the multi-output random forest algorithm is as follows:
constructing a single-output regression tree, wherein in the single-output regression tree, y is a single-output vector, and impurities i (t) related to a node t are defined as:
wherein, ykIs the observed value of y and is,
is the mean value of y at node t, NtIs the number of data points on node t;
setting a single output predictor variable XpSplitting a node t as a father node into t at a splitting point cLAnd tRTwo child nodes, where tLIncluding all single-output predictor variables XpData points ≦ c, tRIncluding all single-output predictor variables XpData points > c; since the variable X is predicted by a single outputpReduction of impurity associated with node t caused by splitting at splitting point c
The calculation formula of (a) is as follows:
wherein N ist,NtLAnd NtRRespectively being a node t, a first child node tLAnd a second child node tRThe number of data points at.
For the multi-output random forest algorithm, the construction process of the submodel is based on a multi-output regression tree model; a multi-output regression tree, also known as a multi-objective regression tree, is a tree that can predict multiple successive objectives simultaneously; when constructing a multi-output regression tree, assume a training set D with N instances, the training set D includes multi-output predictor variable assignments X with m features1,…,XmAnd a multiple output response variable assignment Y with d targets1,…,YdI.e. D { (x)(1),y(1)),…,(x(N),y(N)) }; example l Multi-output input vector comprising m features describing arguments
And a multi-output vector of d targets
Wherein i belongs to {1, …, m }, j belongs to {1, …, d }, and l belongs to {1, …, N }; wherein x is(l)And y(l)The multiple-output-input vector and the multiple-output vector of instance i are represented separately,
and
respectively an input vector value under the mth characteristic in the example l and an output vector value under the d target;
the construction steps of the multi-output regression tree are similar to those of the single-output regression tree, the single-output regression tree is expanded to the multi-output regression tree by replacing the univariate response with the multivariate response, namely the multi-output regression tree redefines the impurity of the node by summing the univariate impurity measurement on the multivariate response, and the specific steps are as follows:
in the formula:
denotes y under the jth target(l)The value of (a) is,
indicating y under jth target in node(l)Is selected to minimize the square error
The sum of the two is used as a dividing point; each leaf of the multi-output regression tree is characterized by a multivariate average value of each instance on the leaf, the number of instances and a characteristic value defined by the leaf; and finally, constructing a multi-output random forest model through a multi-output decision tree based on the randomly selected feature set.
Dividing N instances in the rainstorm waterlogging database into a training set D and a test set T according to the ratio of 8: 2;
the training set D includes predictor variable assignments X with m features1,…,XmAnd a response variable assignment Y with d targets1,…,Yd；
Rainfall factor corresponds to X of training set D1,…,XmThe depth of flooding corresponds to Y1,…,Yd；
The test set T likewise comprises predictor variable assignments X with m features1,…,XmAnd a response variable assignment Y with d targets1,…,YdTest set T and training set D differ from different instances;
and constructing a multi-output random forest model by using a training set D comprising rainfall factors and submerging depth, and checking the effect of the multi-output random forest model through a test set T.
In this embodiment, a multi-output random forest model is constructed to learn a large amount of rainfall-waterlogging data. As shown in fig. 4, the input of the multi-output random forest model is the rainfall process, and the output of the multi-output random forest model is the water depth at different spatial points. In this embodiment, the independent variable of the multi-output random forest model is the rainfall process (the rainfall duration is 120min, and there are 120 input variables), and the dependent variable is the water depth of different spatial points (there are 114812 grid points, and the grid resolution is 8m × 8 m). And dividing 48 simulated rainstorm waterlogging databases into training sets and test sets (38 training sets and 10 test sets) according to the ratio of 8:2, and training the constructed multi-output random forest model.
When the multi-output random forest model is constructed, two important parameters are respectively the number ntree of the regression tree and the number mtry of independent variables for specifying each node of the regression tree to divide the data into two. Considering the calculation accuracy and the calculation time together, in this embodiment, mtry is 40, ntree is 100, and the other parameters are default parameters.
S4, based on rainfall forecast input conditions, realizing rapid and real-time forecast of two-dimensional waterlogging submergence through the constructed multi-output random forest model;
the rapid and real-time forecasting means that the time sequence data of the real-time rainfall forecasting is input into the constructed multi-output random forest model to realize the forecasting of the waterlogging submerging range and water depth; because the time required by the multi-output random forest model for predicting the water depth is extremely short, and the accuracy meets the requirement, the rapid and real-time prediction of the two-dimensional waterlogging submerging condition can be realized.
In the embodiment, the prediction effect of the urban waterlogging model is tested and verified by using 10 designed rainstorms and 2 actually measured rainstorms and waterlogging scenes. The 10 designed rainstorms respectively refer to 50-year-first type I rainstorms, 50-year-first type IV rainstorms, 50-year-first type II rainstorms, 20-year-first type V rainstorms, 10-year-first type III rainstorms, 10-year-first type VI rainstorms, and 5-year-first type I rainstorms and 5-year-first type IV rainstorms. Meanwhile, in order to evaluate the performance of predicting the submergence depth under actual rainfall by a multi-output random forest prediction model, as shown in fig. 7a and 7b, 2 actual measurement rainstorms are selected to perform prediction effect tests, wherein the time is 06, 23 and 07, 28 days 2021, respectively, and the rainfall is 72mm and 103mm respectively, which respectively exceed the 1-year-one-meeting and 5-year-one-meeting standards.
And evaluating the space water depth prediction effect of the multi-output random forest model. Under 12 test scenes, the relationship between the water depth results of the multi-output random forest model and the urban waterlogging model based on hydrodynamics is shown in a graph a, a graph b, a graph c, a graph d, a graph e, a graph f, a graph g, a graph h, a graph i, a graph j, a graph k and a graph l in fig. 8, which respectively refer to 50-year-first type I rainstorm, IV-type rainstorm, VII-type rainstorm, 20-year-first type II rainstorm, V-type rainstorm, Chicago-type rainstorm, 10-year-first type III rainstorm, VI-type rainstorm, 5-year-first type I rainstorm, IV-type rainstorm, 2021-year 06-month 23-day actually measured rainstorm, 2021-year 07-month 28-day actually measured rainstorm. The result shows that the space inundation water depth predicted by the multi-output random forest model is closer to the result of the urban inland inundation model, the waterlogging positions are easy to coincide, and the space maximum water depth difference between the space inundation water depth and the waterlogging position is smaller (basically smaller than 10 cm); the correlation between the water depth predicted by the multi-output random forest model and the simulated water depth of the hydrokinetic model is high, and a remarkable linear correlation (P <0.001) is presented. The average error ME of the prediction performance of the multi-output random forest model is between-0.07 cm and 10.05cm, and the correlation coefficients PCC are all above 0.904. It should be noted that the constructed multi-output random forest model also shows higher water depth prediction accuracy for actual rainfall, ME for predicting the waterlogging submergence water depth of two actually measured rainstorms (time 20210623 and time 20210728 respectively) is respectively as low as 5.75cm and 0.27cm, PCC is respectively 0.936 and 0.956, and the prediction effect is better.
From the analysis of the simulation duration, the multi-output random forest model can complete the calculation of the maximum submerging range and the water depth of the basin within 2s, the simulation time of the urban waterlogging model based on hydrodynamics reaches 468-1614 s, and the simulation efficiency of the multi-output random forest model is improved by more than 200 times compared with that of the urban waterlogging model based on hydrodynamics. The result shows that when the area of the research area is large, the efficiency of predicting the submerging depth of the multi-output random forest model is further improved compared with that of an urban waterlogging model.
Comparative example 2:
comparative example 2 a conventional water depth prediction method was used, and a comparison was made with example 2. Comparative example 2 the study area, training set, test set data from example 2 were used, but the water depth prediction method used the traditional K-nearest neighbor method. The K-nearest neighbor method performs classification and prediction by searching K samples in the training set that are most similar to the predictor variables. In comparative example 2, a K neighbor model of the research area is constructed based on the training set data, the spatial water depth prediction effect of the K neighbor model and the urban waterlogging model is compared, and the prediction effect of the multi-output random forest is compared. The K-nearest neighbor model was tested and evaluated using 12 rainstorms of the test set. Under 12 test scenes, the K neighbor model prediction is closer to the submergence depth of each grid point simulated by the urban waterlogging model. The evaluation result of the prediction performance index of the K neighbor model shows that the average error ME is between-9.8 cm and 10.3cm, the correlation between the prediction of the K neighbor model and the water depth simulated by the urban waterlogging model is higher, the PCC is above 0.897, and the obvious linear correlation (P <0.001) is presented.
The comparison result of the K neighbor model and the multi-output random forest model shows that the space water depth prediction effect of the K neighbor model and the multi-output random forest model is good, but the prediction accuracy of the multi-output random forest model is obviously better. The two methods are similar in aging. Therefore, the comparison between the comparative example 2 and the example 2 shows that the multi-output random forest model has better prediction performance than the K neighbor model.
Example 3:
in this embodiment, the difference from embodiment 1 is that, in step S2, 56 kinds of rainfall situations are adopted for different recurring periods, i.e., 1 year, 2 years, 5 years, 10 years, 20 years, 50 years, and 100 years (7 in total).
In conclusion, the simulation results of the multi-output random forest model and the urban waterlogging model are small in difference and strong in correlation. Under the condition of fully considering the realistic scene, the simulation precision of the multi-output random forest model for predicting the spatial inundation water depth is close to that of the urban inland inundation model based on hydrodynamics, but the calculation efficiency of the multi-output random forest model is far higher than that of the urban inland inundation model based on hydrodynamics, and the prediction performance is better than that of the traditional method. Because the time required by the multi-output random forest model to simulate and predict the water depth is extremely short, and the accuracy also meets the requirement, the method can be used for quickly and timely forecasting the waterlogging submerging condition.
Claims (10)
1. A city waterlogging rapid forecasting method based on a multi-output machine learning algorithm is characterized by comprising the following steps:
s1, constructing an urban waterlogging model according to the data of the existing research area;
s2, extracting historical rainstorm rainfall time interval distribution information, generating rainstorms with different characteristics, and simulating and constructing a rainstorm waterlogging database through the constructed urban waterlogging model;
s3, constructing a multi-output random forest model, and training and testing the multi-output random forest model by using a rainstorm waterlogging database with a rainfall factor as an independent variable and a submerging depth as a dependent variable;
and S4, based on rainfall forecast input conditions, realizing rapid and real-time forecast of two-dimensional waterlogging inundation through the constructed multi-output random forest model.
2. The method for rapidly forecasting the urban waterlogging based on the multi-output machine learning algorithm as claimed in claim 1, wherein in step S1, elevation, land utilization and pipe network data of the existing research area are collected, the elevation and land utilization data are cut and extracted by using ArcGIS software, and the pipe network data are corrected and topology checked.
3. The method for rapidly forecasting the urban waterlogging based on the multi-output machine learning algorithm as claimed in claim 2, wherein in step S1, the constructed urban waterlogging model is a two-dimensional hydrohydrodynamic coupling model based on a rainstorm runoff management model (SWMM) and a cellular automata model (WCA 2D);
in the constructed urban inland inundation model, a rainstorm runoff management model (SWMM) is constructed according to elevation, pipe network and land utilization data; inputting rainfall data into a storm runoff management model (SWMM), deriving the spatial position of an overflow point and an overflow process by the storm runoff management model (SWMM), inputting a cellular automaton model (WCA2D) to carry out ponding two-dimensional simulation, and finally outputting submerging range and submerging water depth information by the cellular automaton model (WCA 2D);
and (4) carrying out calibration and verification on the constructed urban waterlogging model, namely adjusting the model parameters until the urban waterlogging model meets the requirement of simulation precision.
4. The method for rapid urban waterlogging forecasting based on multi-output machine learning algorithm as claimed in claim 1, wherein in step S2, the rainstorms with different characteristics refer to rainstorms with different recurrence periods and different rain types;
the different rain types include 8 types: type I is before a unimodal peak, type II is after a unimodal peak, type III is in a unimodal peak, type IV is a uniform rain type, type V is before and after a bimodal, type VI is near the front bimodal, type VII is near the back bimodal, and Chicago rain type.
5. The method for rapidly forecasting the urban waterlogging based on the multi-output machine learning algorithm as claimed in claim 4, wherein the step of constructing the rainstorm waterlogging database is to input rainstorms with different characteristics into the constructed urban waterlogging model to simulate the submerging range and the waterlogging depth under different situations.
6. The method for rapidly forecasting the urban waterlogging based on the multi-output machine learning algorithm as claimed in claim 1, wherein in step S3, a single-output regression tree is constructed, wherein in the single-output regression tree, y is a single-output vector, and the impurity i (t) associated with the node t is defined as:
wherein, ykIs an observed value of a single output vector y,
is the mean value of the single output vector y at node t, NtIs the number of data points on node t;
setting a single output predictor variable XpSplitting a node t as a father node into t at a splitting point cLAnd tRTwo child nodes, where tLIncluding all single-output predictor variables XpData points ≦ c, tRIncluding all single-output predictor variables XpData points > c; since the variable X is predicted by a single outputpReduction of impurity associated with node t caused by splitting at splitting point c
The calculation formula of (a) is as follows:
wherein N ist,NtLAnd NtRRespectively being a node t, a first child node tLAnd a second child node tRThe number of data points at.
7. A multiple output based machine as claimed in claim 6The method for rapidly forecasting urban waterlogging of the learning algorithm is characterized in that for the multi-output random forest algorithm, the construction process of a multi-output random forest model is based on a multi-output regression tree model; when constructing a multi-output regression tree, assume a training set D with N instances, the training set D includes multi-output predictor variable assignments X with m features1,…,XmAnd a multiple output response variable assignment Y with d targets1,…,YdI.e. D { (x)(1),y(1)),…,(x(N),y(N)) }; example l Multi-output input vector comprising m features describing arguments
And a multi-output vector of d targets
Wherein i belongs to {1, …, m }, j belongs to {1, …, d }, and l belongs to {1, …, N }; wherein x is(l)And y(l)The multiple-output-input vector and the multiple-output vector of instance i are represented separately,
and
respectively an input vector value under the mth characteristic in the example l and an output vector value under the d target;
the construction steps of the multi-output regression tree are similar to those of the single-output regression tree, the single-output regression tree is expanded to the multi-output regression tree by replacing the univariate response with the multivariate response, namely the multi-output regression tree redefines the impurity of the node by summing the univariate impurity measurement on the multivariate response, and the specific steps are as follows:
in the formula:
denotes y under the jth target(l)The value of (a) is,
indicating y under jth target in node(l)Is selected to minimize the square error
The sum of the two is used as a dividing point; each leaf of the multi-output regression tree is characterized by a multivariate average value of each instance on the leaf, the number of instances and a characteristic value defined by the leaf;
and finally, constructing a multi-output random forest model through a multi-output decision tree based on the randomly selected feature set.
8. The method for rapidly forecasting the urban waterlogging based on the multi-output machine learning algorithm as claimed in claim 7, characterized in that N instances in the rainstorm waterlogging database are divided into a training set D and a testing set T according to the ratio of 8: 2;
the training set D includes predictor variable assignments X with m features1,…,XmAnd a response variable assignment Y with d targets1,…,Yd；
Rainfall factor corresponds to X of training set D1,…,XmThe depth of flooding corresponds to Y1,…,Yd。
9. The method for rapid urban waterlogging prediction based on multi-output machine learning algorithm as claimed in claim 8,
the test set T likewise comprises predictor variable assignments X with m features1,…,XmAnd a response variable assignment Y with d targets1,…,YdTest set T and training set D differ from different instances;
and constructing a multi-output random forest model by using a training set D comprising rainfall factors and submerging depth, and checking the effect of the multi-output random forest model through a test set T.
10. The method for rapidly forecasting the urban waterlogging based on the multi-output machine learning algorithm according to any one of claims 1 to 9, wherein in step S4, the time series data of the real-time rainfall forecast is input into the constructed multi-output random forest model, and the water depth of each spatial grid point is output, so that the forecast of the two-dimensional waterlogging submerging range and the water depth is realized.
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