CN114936505B - Method for rapidly forecasting multi-point water depth of urban rainwater well - Google Patents
Method for rapidly forecasting multi-point water depth of urban rainwater well Download PDFInfo
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Abstract
The invention discloses a method for rapidly forecasting multi-point water depths of an urban rainwater well, which comprises the following steps: constructing a street-rainwater sewer double-drainage system coupling model, and obtaining a water depth data set by using the coupling model; a pearson correlation coefficient method based on cross-correlation analysis is adopted for the water depth data set, and a time correlation analysis result is obtained; normalizing the water depth data set by using a Min-Max method; analyzing the spatial correlation in the water depth data set by adopting a soft attention maximum weight method to obtain a spatial correlation analysis result; constructing a multi-point water depth rapid forecasting model of the urban rainwater well according to the time-space correlation analysis result; training a water depth rapid forecasting model by using the mean square error as a loss function and optimizing to obtain an optimized model; evaluating the optimized model; and applying the model subjected to evaluation to actual water depth forecast to obtain a forecast result. The invention has the beneficial effects that: the speed and the precision of multi-point-position water depth forecasting of the rainwater well are improved.
Description
Technical Field
The invention relates to the field of urban flood forecasting, in particular to a method for rapidly forecasting multi-point water depths of urban catch basins.
Background
Rapid urban ization causes rapid increase of the waterproof area of the urban under-laying surface, which inevitably has some influence on the natural ecosystem, including: increased water-impermeable area, reduced water and green vegetation, reduced rain water infiltration, and increased confluence of water flow in the area. The changes cause the hydrologic phenomenon of the urban area to be obviously changed, influence each link of the water circulation process such as evaporation, runoff, infiltration and the like, and cause various hydrologic effects such as acceleration of water circulation rate, reduction of regional evaporation, increase of surface runoff, acceleration of flow rate, improvement of flood peak, advance of peak time and the like, and the changes lead to an increase of urban flood disaster risks to a certain extent.
The root cause of urban flood disasters is that the supply and demand of the drainage system are unbalanced, i.e. the water quantity entering the drainage system exceeds the self-contained quantity. At present, urban drainage system management is mainly performed through two ways: and (3) a physical capacity-expansion drainage system and a quick prediction model of the water depth of the urban rainwater well are established.
For cities in which the infrastructure is formed, further strengthening the infrastructure construction to increase the capacity of the drain pipe network requires not only a significant capital investment but also a significant amount of manpower support. Therefore, from the management of urban flood forecast, the runoff which falls under the rain in short time is predicted in advance, and protective measures are taken in time, so that the disaster loss is effectively reduced, and the method is an important non-engineering measure.
Urban flood forecast management effectively and comprehensively applies geographical information technology, computer technology and the like to the field of flood forecast, can provide real-time information of road ponding for a leader of a decision-making mechanism, can provide scheduling support for municipal drainage management mechanisms, can provide travel guidance for vast people through mass media, and is important and urgent in research of urban flood quick forecast from the aspects of actual demands of urban flood disaster prevention and control in China and development demands of smart city construction.
Physical-based numerical models of urban floods have achieved great success in the field of urban flood prediction, but have the disadvantage of requiring considerable simulation time, so that it is difficult to guarantee advanced prediction. The neural network model does not consider the underlying physical relationship, and focuses on the nonlinear correlation relationship between the independent variable and the dependent variable, so that the neural network model has great advantages in calculation speed compared with the physical model. At present, a plurality of urban flood prediction neural network models exist, but the urban flood prediction neural network models are concentrated on the research of single-point prediction models, the consideration of spatial correlation among multiple points of a rainwater well is lacking, and the relation between the correlation among the points and the model topological structure is split, so that the problems that the model variable is improperly selected, the transfer function among layers, the number of hidden neurons, the training iteration epoch and other related parameters fall into a local optimal solution are very easy to occur.
Disclosure of Invention
In order to solve the problems, the method for rapidly forecasting the multi-point water depth of the urban rainwater well is characterized by firstly constructing a coupling model of a double drainage system of an urban street and a rainwater sewer to supplement water depth data of the rainwater well without a water level gauge in the city; and then, analyzing the time correlation of rainfall-water depth by adopting a Pearson correlation coefficient method based on cross-correlation analysis, so that the forecasting time cost is reduced, meanwhile, the problem of forecasting precision is considered, and the space correlation among all the points of the rainwater well is analyzed.
The method specifically comprises the following steps:
S101: constructing a street-rainwater sewer double-drainage system coupling model, and obtaining a water depth data set by using the coupling model;
S102: analyzing the time correlation of rainfall and water depth by adopting a Pearson correlation coefficient method based on cross-correlation analysis on the water depth data set to obtain a time correlation analysis result;
S103: normalizing the water depth data set by using a Min-Max method to obtain a normalized data set;
S104: analyzing the spatial correlation among all the points of the catch basin in the water depth data set by adopting a soft attention maximum weight method to obtain a spatial correlation analysis result;
S105: constructing a rapid urban catch basin multi-point water depth forecasting model based on space-time correlation analysis according to A, B;
s106: according to the normalized data set, training a water depth rapid forecasting model by using a mean square error as a loss function, and optimizing the water depth rapid forecasting model to obtain an optimized model;
S107: evaluating the optimized model by adopting Root Mean Square Error (RMSE) and Nash efficiency coefficient (NSE) to obtain a model passing the evaluation;
s108: and applying the model subjected to evaluation to actual water depth forecast to obtain a forecast result.
Further, the street-rainwater sewer double-drainage system coupling model is built by using a rain and flood management model SWMM.
Further, the specific formula of the time correlation analysis in step S102 is as follows:
in the formulas (1) and (2), When the sliding window is i, the average value of rainfall-water depth correlation coefficients of n rainwater wells; i is the number of sliding windows; PCC i(R,Dj) is the correlation coefficient value of the jth catch basin when the sliding window is i; n is the number of rainwater wells; r t-i is the t-i th rainfall data in the rainfall data sequence; /(I)Is average rainfall; /(I)Is the i+1th water depth value of the jth catch water in the catch water well water depth data sequence; /(I)Is the average value of the water depth of the j-th catch basin in the catch basin water depth data sequence; t is the total length of the rainfall data sequence; s R is the standard deviation of the rainfall data sequence; /(I)Is the standard deviation of the j-th catch-basin data sequence.
Further, the normalization in step S103 is specifically expressed as follows:
In formula (3), X i * is the normalized data sequence; x i is the original data sequence; x min is the minimum in the data sequence; x max is the maximum value in the data sequence.
Further, the spatial correlation analysis in step S104 is specifically as follows:
In the formulas (4) - (7), alpha i is the space weight coefficient of the ith rainwater well; Is the j-th water depth value of the i-th catch basin in the catch basin water depth data sequence; t is the total length of the rainfall data sequence; ratio PCC>N is the Ratio when the pearson correlation coefficient is greater than N; a N＜PCC＜1.0 is the area of the Pelson correlation coefficient in each catch basin cross-correlation confusion matrix when N is 1.0; a total is the total area of cross-correlation confusion matrix of each catch basin; /(I) Is the number that the i-th catch basin pearson correlation coefficient is larger than N; n is more than 0 and less than 1.
Further, in step S105, the water depth rapid prediction model is specifically as follows:
in the formulae (8) to (10), The predicted water depth taking the space-time correlation into account; /(I)The predicted water depth taking into account the time dependence; /(I)Is the kth neuron in the output layer; f (·) is an activation function; the result is a Hadamard product, a matrix operation; alpha is the space weight coefficient of the catch basin; /(I)The method is characterized in that the method is a weight coefficient between a q-th neuron of a hidden layer and a k-th rainwater well of an output layer in a second layer of a multi-rainwater well water depth rapid prediction model structure; h q is the q-th neuron in the hidden layer; m is the total number of hidden layer neurons; n is the total number of rainwater wells; /(I)The method is characterized in that in a first layer of a multi-catch basin water depth rapid forecasting model structure, a weight coefficient between a jth rainfall of an input layer and a q-th neuron of a hidden layer is input; r' j is the j-th data of the rainfall input considering the time dependence; l is the optimal sliding window length; wherein ω is continuously updated by back propagation until the model accuracy meets the requirement, and the update formula of ω is adopted/> Omega * is the updated weight; omega is the weight before updating; η is an iteration step length for adjusting the convergence speed and the accuracy; e total is a model loss function for evaluating model accuracy.
Further, the specific process of optimizing the model in step S106 is as follows: firstly, carrying out inverse normalization processing on the data by using a formula (11), and then calculating a loss function by using a formula (12);
X＝Xnorm*(Xmax-Xmin)+Xmin (11)
In equations (11) - (12), E total is the predictive model loss function; Is the forecast water depth value of the j-th catch basin; d j is the target water depth value of the jth catch basin; n is the total number of rainwater wells in the research area; x is the inverse normalized value; x norm is the normalized value; x max is the maximum in the original data sequence; x min is the minimum in the original data sequence; after the loss function value of the prediction model is calculated, judging whether to circulate or not according to inequality E total < E or E poch > M, and updating the weight again; if the loss function is smaller than E or E poch is larger than M, stopping circulation, and completing model training optimization.
Compared with the prior art, the invention has the beneficial effects that: the speed and the precision of multi-point-position water depth forecasting of the rainwater well are improved.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention;
FIG. 2 is training data of a urban catch basin multi-point water depth rapid prediction model;
FIG. 3 is a graph of a rainfall-water depth time dependence analysis;
FIG. 4 is a diagram of analysis of spatial correlation between rain wells;
FIG. 5 is a diagram of the prediction results of a rapid prediction model of urban catch basin multi-point water depth in a catch basin based on space-time correlation analysis;
FIG. 6 is a graph of evaluation of forecast results for 358 dewatering wells in an area;
Fig. 7 is a frame diagram of a training of a urban catch basin multi-point water depth rapid prediction model.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Referring to fig. 1, the invention provides a method for rapidly forecasting multi-point water depths of an urban rainwater well, which comprises the following steps:
S101: constructing a street-rainwater sewer double-drainage system coupling model, and obtaining a water depth data set by using the coupling model;
It should be noted that, the coupling model supplements the water depth data of the rain water well without the water level gauge in the city to obtain the training data set;
As an example, the urban street-rainwater sewer double drainage system coupling Model of the present invention is constructed by a Storm flood management Model (SWMM), and the construction process can be summarized as follows.
The double drainage system is divided into a rainwater sewer system and a surface street diffuse ground flow system.
The drainage of the rainwater sewer pipeline system is simulated by a water delivery trunk (EXTRAN) module in a SWMM model, the module adopts the concept of pipeline-Node (Link-Node), namely, a momentum equation is met in the pipeline (Link), a continuity equation is met at the Node (Node), and the hydraulic information of each section position in the rainwater sewer pipeline and the overflow quantity of each overflow Node are calculated by using a one-dimensional Saint-VENANT SYSTEM of equations.
The surface street diffuse ground flow system is simulated by a surface Runoff (RUNOFF) module in the SWMM model, the module regards the city as a small-medium-sized river basin, the city is divided into a plurality of sub-river basins, namely sub-water areas, and the surface runoff generated by rainfall in each sub-water collecting area is simulated by a nonlinear reservoir model.
SWMM assumes that the diffuse ground flow formed by the rainfall falling to the ground flows directly into the rain water channel system through the nearest catch basin, and the runoff calendar generated by RUNOFF module is transmitted to EXTRAN module for calculation.
The input parameters required by EXTRAN modules are hydraulic parameters such as rainwater sewer pipe connection relation, section shape, length, manning roughness coefficient, upstream and downstream offset, rainwater bottom hole elevation and maximum depth, downstream boundary conditions and the like; the input parameters required by RUNOFF modules are hydrologic parameters such as secondary water collection area, characteristic width, surface roughness, average gradient, impermeable area percentage and the like. Wherein, the buried depth of the pipeline = the rainwater well depth-the outlet offset-the pipeline height, the gradient of the pipeline = [ (upstream rainwater bottom hole elevation + inlet offset) - (downstream rainwater bottom hole elevation + outlet offset) ]/length.
Through verification of measured data, the constructed street-rainwater sewer double-drainage system coupling model can be used for supplementing water depth data of a rainwater well without a water level gauge in a city.
S102: analyzing the time correlation of rainfall and water depth by adopting a Pearson correlation coefficient method based on cross-correlation analysis on the water depth data set to obtain a time correlation analysis result;
in order to reduce the time cost of model prediction, based on the data of a double-drainage system coupling model, a pearson correlation coefficient method based on cross-correlation analysis is adopted to analyze the time correlation of rainfall-water depth; the specific formula of the time correlation analysis in step S102 is as follows:
in the formulas (1) and (2), When the sliding window is i, the average value of rainfall-water depth correlation coefficients of n rainwater wells; i is the number of sliding windows; PCC i(R,Dj) is the correlation coefficient value of the jth catch basin when the sliding window is i; n is the number of rainwater wells; r t-i is the t-i th rainfall data in the rainfall data sequence; /(I)Is average rainfall; /(I)Is the i+1th water depth value of the jth catch water in the catch water well water depth data sequence; /(I)Is the average value of the water depth of the j-th catch basin in the catch basin water depth data sequence; t is the total length of the rainfall data sequence; s R is the standard deviation of the rainfall data sequence; /(I)Is the standard deviation of the j-th catch-basin data sequence.
S103: normalizing the water depth data set by using a Min-Max method to obtain a normalized data set;
The data set is normalized by using a Min-Max method, so that the problem that a model cannot be trained due to numerical gradient explosion is avoided. Normalization in step S103 is specifically expressed as follows:
In formula (3), X i * is the normalized data sequence; x i is the original data sequence; x min is the minimum in the data sequence; x max is the maximum value in the data sequence.
S104: analyzing the spatial correlation among all the points of the catch basin in the water depth data set by adopting a soft attention maximum weight method to obtain a spatial correlation analysis result;
In order to improve model prediction accuracy, a soft attention maximum weight method is adopted to analyze the spatial correlation among all the points of the rainwater well in the water depth data set; firstly, the spatial correlation among the rainwater wells in the research area is analyzed by adopting a formula (4), and the analysis result is shown in fig. 4. As can be seen from fig. 4 (a), the spatial correlation coefficient of most of the rainwater wells in the case of the present invention is 0.6 to 1.0. Further, as can be intuitively seen from fig. 4 (b), the area ratios of the spatial correlation coefficients between the respective catch basins greater than 0.8, 0.6, and 0.4 are 0.742, 0.894, and 0.939, respectively. This shows that more than 74% of the rain wells have a strong cross-correlation (spatial correlation coefficient=0.8-1.0), that nearly 90% of the rain wells have a strong cross-correlation (spatial correlation coefficient=0.6-1.0), and that more than 93% of the rain wells have a strong cross-correlation (spatial correlation coefficient=0.4-1.0). Therefore, in the case of the invention, the rainwater wells have stronger cross correlation, and all the rainwater wells can be used as a whole for constructing a multi-output topological structure.
In the formulas (4) - (7), alpha i is the space weight coefficient of the ith rainwater well; Is the j-th water depth value of the i-th catch basin in the catch basin water depth data sequence; t is the total length of the rainfall data sequence; ratio PCC>N is the Ratio when the pearson correlation coefficient is greater than N; a N＜PCC<1.0 is the area of the Pelson correlation coefficient in each catch basin cross-correlation confusion matrix when N is 1.0; a total is the total area of cross-correlation confusion matrix of each catch basin; /(I) Is the number that the i-th catch basin pearson correlation coefficient is larger than N; n is more than 0 and less than 1.
S105: constructing a rapid urban catch basin multi-point water depth forecasting model based on space-time correlation analysis according to A, B;
In step S105, the water depth rapid forecasting model is specifically as follows:
in the formulae (8) to (10), The predicted water depth taking the space-time correlation into account; /(I)The predicted water depth taking into account the time dependence; /(I)Is the kth neuron in the output layer; f (·) is an activation function; the result is a Hadamard product, a matrix operation; alpha is the space weight coefficient of the catch basin; /(I)The method is characterized in that the method is a weight coefficient between a q-th neuron of a hidden layer and a k-th rainwater well of an output layer in a second layer of a multi-rainwater well water depth rapid prediction model structure; h q is the q-th neuron in the hidden layer; m is the total number of hidden layer neurons; n is the total number of rainwater wells; /(I)The method is characterized in that in a first layer of a multi-catch basin water depth rapid forecasting model structure, a weight coefficient between a jth rainfall of an input layer and a q-th neuron of a hidden layer is input; r' j is the j-th data of the rainfall input considering the time dependence; l is the optimal sliding window length; wherein ω is continuously updated by back propagation until the model accuracy meets the requirement, and the update formula of ω is adopted/> Omega * is the updated weight; omega is the weight before updating; η is an iteration step length for adjusting the convergence speed and the accuracy; e total is a model loss function for evaluating model accuracy.
S106: according to the normalized data set, training a water depth rapid forecasting model by using a mean square error as a loss function, and optimizing the water depth rapid forecasting model to obtain an optimized model;
It should be noted that, since the normalization processing is already performed on the data when the model is trained, the inverse normalization processing is performed on the data by using the formula (11) before the loss function is calculated, and then the loss function is calculated by using the formula (12).
X＝Xnorm*(Xmax-Xmin)+Xmin (11)
In equations (11) - (12), E total is the predictive model loss function; Is the forecast water depth value of the j-th catch basin; d j is the target water depth value of the jth catch basin; n is the total number of rainwater wells in the research area; x is the inverse normalized value; x norm is the normalized value; x max is the maximum in the original data sequence; x min is the minimum in the original data sequence; after the loss function value of the prediction model is calculated, judging whether to circulate or not according to the inequality E total < E or E poch > M, and updating the weight again; if the loss function is smaller than E or E poch is larger than M, stopping circulation, and completing model training optimization.
S107: evaluating the optimized model by adopting Root Mean Square Error (RMSE) and Nash efficiency coefficient (NSE) to obtain a model passing the evaluation;
In step S107, the evaluation index of the model is as follows:
in the formulas (13) - (14), m is the total number of the rainwater wells; The method is a forecast water depth value of a multi-point water depth rapid forecast model of the rainwater well; d i is the target water depth value; /(I) Is the target water depth average.
S108: and applying the model subjected to evaluation to actual water depth forecast to obtain a forecast result.
The beneficial effects of the method of the invention are verified by the following example, which is as follows:
The data adopted in the embodiment of the invention is a 24-field rainfall-water depth mixed data set of 358 rainwater wells in a certain urban area, the mixed data set comprises actual measurement data of a water level gauge and supplementary data of a street-rainwater sewer double-drainage system coupling model to a position without the water level gauge, a process line of a certain point of data in the area is shown in fig. 2, and the time resolution is 10min. The hybrid dataset is divided into a training set and a testing set. The training set included 20 rainfall-water depth data, of which 80% is training data and 20% is validation data, and the test set included 4 rainfall-water depth data.
The rapid prediction process of the multi-point water depth of the rainwater well based on space-time correlation analysis comprises the following steps:
1) Determining the input and output topological structure of the forecasting model: in order to determine the input and output topological structures of the forecasting model, the time correlation of rainfall and water depth and the spatial correlation among the points of the rainwater well are respectively analyzed. Firstly, the effective rainfall spans affecting the water depths of different rain wells are considered, namely the time stagnation of rainfall-water depths is considered, and the input topological structure of the forecasting model is determined through the analysis of the time correlation of the rainfall-water depths (see figure 3). The correlation analysis results of 358 rain well points in the researched area of the embodiment of the invention under different rainfall-water depth time differences are shown in fig. 3 (a), and each broken line represents one rain well point. As can be seen from the figure, the time correlation coefficient of all the catch basins is less than 0.4 by 300 minutes, indicating that the time correlation of the rainfall-water depth exceeds a certain period of time to show weak correlation. Thus, determining an effective rainfall input value is determining the point in time at which the rainfall-water depth time correlation changes from strong to weak. Because rainfall with strong time correlation has a large influence on water depth, the point position duty ratio of the rainwater well with the time correlation coefficient larger than 0.4 and larger than 0.6 under different time differences is calculated. As can be seen from fig. 3 (b), when the time correlation coefficient is greater than 0.6, the precipitation well point position ratio is greatly reduced by less than 50% at 8×10min, and approaches zero at 13×10 min; when the time correlation coefficient is larger than 0.4, the rainwater well proportion is greatly reduced by less than 50% at 19×10min, and the rainwater well proportion is zero at 28×10 min. Therefore, we hypothesize that the better input dimension of the rainfall time series is between 13 and 28. After the rainfall-water depth time correlation analysis result is obtained, a trial algorithm is adopted to further determine the input topology structure of the forecasting model (fig. 3 (c)). In the case of the invention, an LSTM (Long Short-Term Memory Network) operation network is adopted to illustrate the feasibility of the invention. In order to eliminate the influence of random errors, the input topology structure of the model is further determined by adopting 4-field typhoon rainfall data in the embodiment of the invention, and as can be seen from fig. 3 (c), as the sliding window increases, the Nash efficiency coefficients of 4 simulation results are continuously increased. And the stability is achieved after the sliding window is 15, the optimal input topology of the rainwater well multi-point water depth rapid forecasting model is determined to be 15.
Secondly, the difference of the water depth change among different rain well points and the mutual influence of the water depths among different rain well points are considered. The spatial correlation among the various points of the rainwater well is analyzed by adopting a soft attention maximum weight method (see figure 4) to determine the output topological structure of the forecasting model, and the spatial correlation coefficient among the various points of the rainwater well in the most studied area of the embodiment of the invention is 0.6-1.0. In addition, the space correlation intensity interval ratio among the various points of the rainwater well in the research area can be more intuitively seen in fig. 4 (a), and the area ratios with the space correlation coefficients larger than 0.8, 0.6 and 0.4 are respectively 0.742, 0.894 and 0.939 obtained by the formula (4). This shows that more than 74% of the dewatering wells in the investigation region have a strong cross-correlation (spatial correlation coefficient=0.8-1.0), nearly 90% of the dewatering wells have a strong cross-correlation (spatial correlation coefficient=0.6-1.0), and more than 93% of the dewatering wells have a strong cross-correlation (spatial correlation coefficient=0.4-1.0). Therefore, the rainwater wells in the research area have stronger cross correlation, and all the rainwater wells can be used as a whole for constructing a multi-output topological structure.
2) Model construction: constructing a multi-point water depth rapid forecasting model of the rainwater well according to the time correlation of rainfall and water depth and the space correlation among the points of the rainwater well, wherein the formula of the model is already cross-bred and is not specifically described herein; referring to fig. 7, fig. 7 is a frame diagram of training a multi-point water depth rapid forecasting model of an urban rainwater well.
In the case of the invention, an Adam optimization algorithm is adopted, and eta is 0.01; omega * is the updated weight; r' j is the j-th data of the rainfall input considering the time dependence; l is the optimal sliding window length; The method is characterized in that in a first layer of a multi-catch basin water depth rapid forecasting model structure, a weight coefficient between a jth rainfall of an input layer and a q-th neuron of a hidden layer is input; f (·) represents an activation function of the output layer, and in the present invention, a Sigmoid function is adopted; h q is the q-th neuron in the hidden layer; m is the total number of hidden layer neurons; /(I) The method is characterized in that the method is a weight coefficient between a q-th neuron of a hidden layer and a k-th rainwater well of an output layer in a second layer of a multi-rainwater well water depth rapid prediction model structure; /(I)The k-th rainwater well water depth value considering the time correlation; the result is a Hadamard product, a matrix operation; alpha is the spatial weight coefficient of the catch basin.
In order to ensure model accuracy, the data sets can be divided into training data sets and test data sets and normalized, and characteristic values of the data sets are shown in table 1, so that the data characteristics of the training sets cover the test sets.
Table 1 dataset characteristics table
Secondly, training the model is started on the basis of determining the topological structure and the data set of the multi-point water depth forecasting model of the rainwater well, and the training flow is shown in figure 1.
3) Model verification: in the case, 4 fields of mixed data sets are adopted to verify the forecasting result, the verification result is shown in fig. 5, the evaluation index of the forecasting model is shown in fig. 6, and the model is evaluated in a box-type diagram and frequency distribution histogram mode because of excessive quantity of the rainwater wells, so that the RMSE and NSE median of the rainwater well multi-point water depth forecasting model based on space-time correlation analysis are distributed between 0.02 and 0.03 and between 0.975 and 0.985 respectively, the average value of the RMSE and NSE is distributed between 0.02 and 0.03 and between 0.9 and 1.0 respectively, the RMSE of most of the rainwater wells is lower than 0.05 and the NSE is higher than 0.9, which means that the water depth forecasting error of most of the rainwater wells is smaller than 0.05m, and the forecasting accuracy of the rainwater well multi-point water depth quick forecasting model is high.
In a comprehensive view, the invention is based on consideration of correlation between outputs, and the interaction between different outputs is coupled, so that a rapid urban rainwater well multi-point water depth forecasting model based on space-time correlation analysis is constructed, and the model is shown in fig. 1.
The street-rainwater sewer double-drainage coupling system is adopted to replace the traditional rainwater sewer drainage system to construct a hydrodynamic model, meanwhile, the rainfall runoff coupling process of the rainwater sewer system and the street system is considered, and water flow exchange is carried out between the two systems through a rainwater well.
Considering the influence of time lag in the rainfall-runoff process on the water depth of a rainwater well, the time correlation of the rainfall-water depth is analyzed by adopting a pearson correlation coefficient method based on cross-correlation analysis, and the analysis is shown in fig. 3.
The influence of the spatial correlation among the rainwater wells on the water depth of the rainwater wells is considered, and the spatial correlation among the rainwater wells is analyzed by adopting a soft attention maximum weight method, which is shown in fig. 4.
The beneficial effects of the invention are as follows: the speed and the precision of multi-point-position water depth forecasting of the rainwater well are improved.
The above-described embodiments of the present invention do not limit the scope of the present invention. Any other corresponding changes and modifications made in accordance with the technical idea of the present invention shall be included in the scope of the claims of the present invention.
Claims (7)
1. A method for rapidly forecasting the multi-point water depth of an urban rainwater well is characterized by comprising the following steps: the method comprises the following steps:
S101: constructing a street-rainwater sewer double-drainage system coupling model, and obtaining a water depth data set by using the coupling model;
S102: analyzing the time correlation of rainfall and water depth by adopting a Pearson correlation coefficient method based on cross-correlation analysis on the water depth data set to obtain a time correlation analysis result;
S103: normalizing the water depth data set by using a Min-Max method to obtain a normalized data set;
S104: analyzing the spatial correlation among all the points of the catch basin in the water depth data set by adopting a soft attention maximum weight method to obtain a spatial correlation analysis result;
s105: constructing a rapid urban rainwater well multi-point water depth forecasting model based on space-time correlation analysis according to the time correlation analysis result and the space correlation analysis result;
In step S105, the water depth rapid forecasting model is specifically as follows:
in the formulae (8) to (10), The predicted water depth taking the space-time correlation into account; /(I)The predicted water depth taking into account the time dependence; /(I)Is the kth neuron in the output layer; f (·) is an activation function; the result is a Hadamard product, a matrix operation; alpha is the space weight coefficient of the catch basin; /(I)The method is characterized in that the method is a weight coefficient between a q-th neuron of a hidden layer and a k-th rainwater well of an output layer in a second layer of a multi-rainwater well water depth rapid prediction model structure; h q is the q-th neuron in the hidden layer; m is the total number of hidden layer neurons; n is the total number of rainwater wells; /(I)The method is characterized in that in a first layer of a multi-catch basin water depth rapid forecasting model structure, a weight coefficient between a jth rainfall of an input layer and a q-th neuron of a hidden layer is input; r' j is the j-th data of the rainfall input considering the time dependence; l is the optimal sliding window length; wherein ω is continuously updated by back propagation until the model accuracy meets the requirement, and the update formula of ω is adopted/> Omega * is the updated weight; omega is the weight before updating; v is an iteration step length for adjusting convergence speed and accuracy; e total is a model loss function for judging model accuracy;
s106: according to the normalized data set, training a water depth rapid forecasting model by using a mean square error as a loss function, and optimizing the water depth rapid forecasting model to obtain an optimized model;
s107: evaluating the optimized model by adopting a Root Mean Square Error (RMSE) and a Nash efficiency coefficient (NSE) to obtain an evaluated model;
s108: and applying the model subjected to evaluation to actual water depth forecast to obtain a forecast result.
2. The method for rapidly forecasting the multi-point water depth of the urban rainwater well according to claim 1, wherein the method comprises the following steps: the street-rainwater sewer double-drainage system coupling model is built by using a rain flood management model SWMM.
3. The method for rapidly forecasting the multi-point water depth of the urban rainwater well according to claim 1, wherein the method comprises the following steps: the specific formula of the time correlation analysis in step S102 is as follows:
in the formulas (1) and (2), When the sliding window is i, the average value of rainfall-water depth correlation coefficients of n rainwater wells; i is the number of sliding windows; PCC i(R,Dj) is the correlation coefficient value of the jth catch basin when the sliding window is i; n is the number of rainwater wells; r t-i is the t-i th rainfall data in the rainfall data sequence; /(I)Is average rainfall; /(I)Is the i+1th water depth value of the jth catch water in the catch water well water depth data sequence; /(I)Is the average value of the water depth of the j-th catch basin in the catch basin water depth data sequence; t is the total length of the rainfall data sequence; s R is the standard deviation of the rainfall data sequence; /(I)Is the standard deviation of the j-th catch-basin data sequence.
4. The method for rapidly forecasting the multi-point water depth of the urban rainwater well according to claim 1, wherein the method comprises the following steps: normalization in step S103 is specifically expressed as follows:
In formula (3), X i * is the normalized data sequence; x i is the original data sequence; x min is the minimum in the data sequence; x max is the maximum value in the data sequence.
5. The method for rapidly forecasting the multi-point water depth of the urban rainwater well according to claim 1, wherein the method comprises the following steps: in step S104, the spatial correlation analysis is specifically as follows:
In the formulas (4) - (7), alpha i is the space weight coefficient of the ith rainwater well; Is the j-th water depth value of the i-th catch basin in the catch basin water depth data sequence; t is the total length of the rainfall data sequence; ratio PCC＞N is the Ratio when the pearson correlation coefficient is greater than N; a N＜PCC＜1.0 is the area of the Pelson correlation coefficient in each catch basin cross-correlation confusion matrix when N is 1.0; a total is the total area of cross-correlation confusion matrix of each catch basin; /(I) Is the number that the i-th catch basin pearson correlation coefficient is larger than N; 0< N <1.
6. The method for rapidly forecasting the multi-point water depth of the urban rainwater well according to claim 1, wherein the method comprises the following steps: the specific process of optimizing the model in step S106 is: firstly, carrying out inverse normalization processing on the data by using a formula (11), and then calculating a loss function by using a formula (12);
X＝Xnorm*(Xmax-Xmin)+Xmin (11)
In equations (11) - (12), E total is the predictive model loss function; Is the forecast water depth value of the j-th catch basin; d j is the target water depth value of the jth catch basin; n is the total number of rainwater wells in the research area; x is the inverse normalized value; x norm is the normalized value; x max is the maximum in the original data sequence; x min is the minimum in the original data sequence; after the loss function value of the prediction model is calculated, judging whether to circulate or not according to inequality E total < E or E poch > M, and updating the weight again; if the loss function is smaller than E or E poch is larger than M, stopping circulation, and completing model training optimization; e poch represents the current iteration number, and M represents the preset total iteration number; e denotes a preset loss function threshold.
7. The method for rapidly forecasting the multi-point water depth of the urban rainwater well according to claim 1, wherein the method comprises the following steps: in step S107, the evaluation index of the model is as follows:
in the formulas (13) - (14), m is the total number of the rainwater wells; The method is a forecast water depth value of a multi-point water depth rapid forecast model of the rainwater well; d i is the target water depth value; /(I) Is the target water depth average.
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