Sponge City Drainage System Prediction Based on Artificial Neural Networks: Taking SCRC System as Example

Abstract

The concept of sponge cities is widely recognized, but there is still no research on what a new drainage system for sponge cities should look like. This study proposes a new drainage system for sponge cities, a sponge-type comprehensive pipe corridor rainwater chamber (SCRC) system, which combines a comprehensive pipe corridor with low-impact development measures (LIDs) into one system. The SCRC system is predicted by using a long- and short-term neural network to verify whether the neural network can be applied to the prediction of flooding in sponge cities. The results show that the SCRC system can effectively control sponge city flooding, where the surface runoff coefficient under different rainfall intensities (P = 1–10 yr) is between 0.273 and 0.44, the pipe overload time is between 0.11 and 3.929 h, and the node overflow volume is between 0 and 23.89 Mltr. The neural network has a high reliability in sponge city flood prediction, and the coefficients of determination R² of the test set of PSO–LSTM prediction models are all above 0.95. This study may provide an idea for predicting flooding in sponge cities.

1. Introduction

Urban flooding has become more frequent due to the rapid pace of urbanization, the proliferation of impermeable pavements, and the effects of global warming [1,2,3,4]. Traditional urban drainage systems rely on a network of drainage ditches and stormwater pipelines to remove rainwater from urban areas [5]. With increasing urbanization, these traditional drainage systems are unable able to meet cities’ flooding needs. This can cause damage to buildings, transport, and other public facilities, resulting in economic losses and posing a serious threat to the lives and properties of citizens [6,7]. Therefore, there is a need for more efficient and sustainable drainage systems [8].

Therefore, sustainable urban drainage systems such as sponge cities and low-impact development have been proposed [9,10,11,12]. Similarly, some scholars have discussed the problem of urban flooding in terms of political approaches and scientific advances [13]. The sponge city concept is now widely recognized as a new drainage concept. It aims to enable cities to absorb, permeate, and store water like a sponge through a series of measures. The sponge city concept not only reduces urban flooding, but also improves environmental quality. At present, the sponge city concept is in a rapid development stage. Although research results on sponge city flooding have gradually increased [14,15,16], there is still a lack of research on what a new drainage system for sponge cities should look like, and there are very few scholars who have explored flood prediction in sponge cities. This makes it necessary to propose a new sponge city drainage system and find a new method to study sponge city flood prediction.

Regarding sponge city drainage systems, most scholars’ research currently focuses on surface low-impact development (LID) measures. Most of them do not consider surface and underground drainage systems together as one system, which is not conducive to the overall planning of sponge cities. For sponge city flood prediction, artificial neural network techniques have been successfully applied to assist with decision making in weather forecasting and identifying extreme weather events [17,18]. Some scholars’ studies have shown the good applicability of AI in predicting stormwater network overflows based on rainfall forecasts [19,20,21,22]. The current research in the urban flooding field still suffers from the problem of having fewer training samples, whereas more samples can better ensure the performance of prediction models [23]. However, it is difficult for actual rainfall to meet the requirements of high-quality training samples in terms of number, rainfall intensity, and measured flood data, both quantitatively and qualitatively, which limits the performance of neural networks. The problem of the insufficient number and quality of training samples can be effectively solved by designing rainfall events of different intensities and durations based on local storm intensity formulas in different regions and combining them with local historical rainfall data. Moreover, there are many kinds of artificial neural network models, and how to choose a suitable neural network to predict sponge city flooding is a key issue.

Although there are a wide variety of neural network models available, the LSTM neural network model is considered to be the most suitable for application in predicting time series [24]. The Long Short-Term Memory (LSTM) neural network model is a widely used and technically mature artificial neural network model in the field of information prediction [25]. Traditional recurrent neural networks (RNNs) often encounter problems such as gradient vanishing or explosion when dealing with lengthy sequences, and LSTM solves this problem by efficiently capturing the temporal information and long-term dependencies in sequences through cell states [26,27,28]. LSTM has a stronger long-term memory capability and flexibility compared to traditional RNNs, which can better cope with the processing needs of long sequence data. Therefore, we built a prediction model and optimized the hyperparameters in LSTM using the Particle Swarm Algorithm (PSO). We verified the accuracy and validity of the prediction model and predicted the SCRC system.

In our study, we propose a new research program which upgrades the traditional urban drainage system to a sponge-type comprehensive pipe corridor rainwater chamber system. This system combines an urban underground comprehensive corridor system with low-impact development measures to form a new drainage system which is sustainable and conducive to the harmonious coexistence of human and nature [29]. We use LSTM neural networks to predict the SCRC system. In summary, based on the shortcomings of existing research, we propose a new sponge city drainage system and explore the application of neural networks in the field of sponge city flood prediction. This study provides valuable information for flood control in sponge cities.

2. Materials and Methods

2.1. Research Process

In this study, we propose a new sponge city drainage system and validate the effectiveness of neural networks applied to predict flooding in sponge cities. An economic development zone in southeast Asia is also used as a case study to validate this research. The study flowchart is shown in Figure 1.

2.2. Study Area

We propose a new sponge city drainage system, taking an economic development zone in southeast Asia as an example. The total area of the study area is 1150 hectares, with a varied topography and higher elevations in the northeast and lower elevations in the northwest. The average elevation ranges from 167 to 180 m above sea level, accompanied by a temperate climate with temperatures averaging between 24.5 and 27.3 °C. The region experiences an average annual rainfall of approximately 1700 mm. Various sizes and types of drainage pipes are laid in the study area, with a total pipe length of 73 km. The study area is shown in Figure 2.

This economic development zone was chosen as the study area because we could obtain relevant data from the project department to help us to complete this study. This area was chosen as an example, but the predictive model constructed in this study is applicable to any area with similar stormwater network systems and topographic features.

2.3. Storm Water Management Model

In this study, we used the Stormwater Management Model (SWMM) to build a stormwater model for the study area. The SWMM is a dynamic runoff model developed by the U.S. Environmental Protection Agency (EPA) in the 1970s [30].

2.3.1. Design Rainfall

Based on the local short duration and high concentration of rainfall in the study area, 228 short-duration (2 h) mixed rainfall events with different rainfall return periods (from 1.00 to 10.00 years) were designed based on the local Chicago Storm Intensity Equation (Equation (1)) and combined with the historical rainfall data in the study area over the past 10 years (rainfall data were obtained from the project department of the study area). These rainfalls were mainly manifested as single-peak rainfalls with a peak rainfall crest factor (r) = 0.5, 0.4. Figure 3 and

Table 1. Rainfall under recurrence periods 2, 3, and 5 yrs (r = 0.5).

Rains Return Period (yr)	2	3	5
Rainfall depth (mm)	57.48	60.51	68.10

show the rainfall processes and rainfall amounts for the excerpted rainfall return periods of 2, 3, and 5 years.

Figure 4 shows the historical rainfall data in the study area over the last 10 years. These data are collected on an hourly basis, with the peak rainfall occurring around August each year, up to and even exceeding 500 mm per month. We firstly designed the rainfall events under different rainfall return periods based on the storm formulae, and then modified the designed rainfall events based on the actual rainfall peaks, amounts, and processes to ensure that the designed rainfall events were closer to the actual conditions in the study area.

$$q={\displaystyle \frac{700\times \left(1+0.775\mathit{lg}P\right)}{{\left(15+t\right)}^{0.496}}}$$

(1)

where q is the design rainstorm intensity L/(s·hm²); t is the rainfall duration (120 min); and P is the designed rainfall return periods (1.00 to 10.00 yr).

2.3.2. Sub-Catchment Delineation

The study area was manually divided into sub-watersheds based on the land use type and stormwater network design map. Each sub-catchment contained information on precipitation, imperviousness, slope, the surface runoff coefficient, Manning’s roughness coefficient, the density of pipes, and pipe length and width [31]. The entire study area was divided into 186 sub-catchments. The sub-catchments of the study area are shown in Figure 5.

2.4. The SCRC System Design

The SCRC system is a new sponge city drainage system built by combining above-ground low-impact development (LID) measures with an underground comprehensive pipe corridor rainwater chamber. We designed these two parts separately and then combined them together.

2.4.1. Comprehensive Pipe Corridor Rainwater Chamber

Firstly, we designed the comprehensive pipe corridor rainwater chamber according to the actual situation of the study area and relevant design codes, then replaced the original traditional stormwater network system with the comprehensive pipe corridor rainwater chamber. We added separate rainwater chambers to the traditional comprehensive corridors, providing a greater drainage capacity. The rest of the chambers were comprehensive chambers allowing for the laying of cables, water supply pipes, and other facilities. Considering the subsequent optimization of the design, and after discussion with the designers of the project department based on the actual situation of the study area, the height of the rainwater chamber was kept unchanged at 2.4 m and the width was designed to range from 0.6 m to 2.4 m. The design of the comprehensive pipe corridor rainwater chamber is shown in Figure 6.

2.4.2. Combination LID Measures

Next, we designed the combined LID measures in the study area. We chose four LID measures (green roofs, permeable paving, bioretention basins, and grassed swales) and combined them according to the land use types in the study area. These land use types and LID combinations are shown in

Table 2. Land use type.

Land Use Type	Area (hm2)	Percentage (%)
Residential land	299.00	26.0
Public administration and public service land	113.85	9.9
Business services facilities land	136.85	11.9
Industrial land	162.15	14.1
Logistics and warehousing land	148.35	12.9
Roads and transportation facility land	164.45	14.3
Serviced land	21.85	1.9
Green space and plaza land	103.50	9.0
Total	1150.00	100

and

Table 3. LID measure combination approach [29].

No.	Land Use Type	Combination
1	Residential land, public administration and public service land, and business services facilities land	50% green roof + 30% permeable pavement +10% vegetative swale + 10% bioretention pond
2	Industrial land	40% green roof + 40% permeable pavement +10% vegetative swale + 10% bioretention pond
3	Logistics and warehousing land	30% green roof + 50% permeable pavement +10% vegetative swale + 10% bioretention pond
4	Roads and transportation facility land	80% permeable pavement +10% vegetative swale + 10% bioretention pond
5	Green space and plaza land	40% permeable pavement +30% vegetative swale + 30% bioretention pond

. Depending on the land use type, we set different combination LID measures within each sub-catchment. The percentage of LID measures in each sub-catchment was the same, and the way the LID measures were combined remained the same for each land use type. When the area of LID measures in the study area needed to be adjusted, only the percentage of LID measures in the sub-catchment was adjusted, which could improve efficiency.

2.4.3. The SCRC System

As previously stated, the SCRC system was combined by a comprehensive pipe corridor rainwater chamber and combination LID measures. Specifically, first, all of the main rainwater pipes in the study area were replaced with the comprehensive pipe corridor rainwater chamber, and based on this, the combination LID measures were placed in each sub-catchment. Then for the entire study area, the SCRC system was laid down.

Finally, we optimized the design information (rainwater chamber section width and percentage of combination LID measures) of the SCRC system. Based on the actual situation of the study area, we determined the most suitable SCRC system solution for the study area. The rainwater chamber width was 0.8 m, its height was 2.4 m, and the combination LID measures represented 20% in the study area.

2.4.4. SWMM Model Building and Running

We installed 244 conduits, 38 outfalls, and 236 nodes throughout the area based on the stormwater network plan. Figure 7 shows a rough map of the study area. Based on the design of the SCRC system, we constructed an SWMM model and obtained simulation results for three key urban flooding indicators, as follows: surface runoff coefficient, node overflow volume, and pipe overload time. These indicators provide a more intuitive understanding of the extent of urban flooding. The simulation results of the model were used to train and test the predictive model.

In order to highlight the effectiveness of the SCRC system, we built an SWMM model of the original drainage system in the study area. By comparing the simulation results of the two systems, we can determine the effectiveness of the SCRC system in mitigating urban flooding.

2.5. Prediction Model

2.5.1. Predictive Model Training Sample

In order to ensure that the training samples could meet the requirement of high quality, we designed 228 rainfall events with different intensities based on the storm formulas in the study area and combined these with the actual rainfall data. After inputting the designed rainfall events into the SWMM model, we obtained flooding data for the entire study area under different rainfall intensity conditions. Then, we obtained a high-quality training sample library, consisting of three data sets, with each set containing 228 simulated data results. Three urban flood indicators were involved, as follows: surface runoff coefficient, pipe overload time, and node overflow volume. Considering the stochastic nature of the occurrence of rainfall events, we randomly disrupted the obtained SWMM simulation data separately. Then, 70% of the samples were selected as training samples and the other 30% were used as test samples when training the prediction model. The trained prediction model could predict the effectiveness of sponge-type comprehensive pipe corridor rainwater chambers in alleviating urban flooding.

2.5.2. PSO–LSTM Neural Network Prediction Model Building

(1)

LSTM neural network

In this study, we used the LSTM neural network model optimized by the PSO algorithm to build the prediction model. The LSTM neural network was first proposed by Hochreiter et al. [25] in 1997, and has been improved by Alex Graves in the recent past [32]. The LSTM neural network model is an enhancement of the recurrent neural network (RNN). It incorporates a self-looping mechanism in the RNN architecture to facilitate the handling of long-range dependencies and non-linear information. The gating structure in LSTM enables it to effectively mitigate gradient vanishing and gradient explosion problems, which makes LSTM better able to maintain the stability of the gradient, thus improving training efficiency and performance. Compared with other recurrent neural network models, LSTM has a stronger learning ability [24], which was also an important factor in our choice of LSTM. The structure of the LSTM neural network is shown in Figure 8.

The structural unit of the LSTM neural network consists of three main parts, as follows: the forget gate (red), the input gate (blue), and the output gate (green). First, the input gate$i_t$ is used to update the cell state $x_t$ and determine what kind of new information can be stored in the cell state. The formulae are shown in Equations (2)–(4).

$$i_t=\sigma \left(W_i·h_{t-1}+W_i·x_t+b_i\right)$$

(2)

$${\tilde{c}}_t=\tan h\left(W_c·h_{t-1}+W_c·x_t+b_c\right)$$

(3)

$$c_t=f_t·c_{t-1}+i_t·{\tilde{c}}_t$$

(4)

where $i_t$ represents the input gate, $W_i$ is the input gate weight, $b_i$ is the input gate bias, ${\tilde{c}}_t$ represents the current state, and $c_t$ is the current t-moment memory cell output.

The forget gate is used to decide which part of $c_{t-1}$ outputted from the previous cell is to be kept and forgotten. The calculation formula is shown by Equation (5), and the incorporation of the forget gate effectively addresses the issue of gradient vanishing present in RNN networks [33,34].

$$f_t=\sigma \left(W_f·h_{t-1}+W_f·x_t+b_f\right)$$

(5)

The output gate is based on the state of the cell and determines the output value. The calculation formula is shown by Equations (6) and (7).

$$o_t=\sigma \left(W_o·h_{t-1}+W_o·x_t+b_o\right)$$

(6)

$$h_t=o_t·\tan h\left(c_t\right)$$

(7)

where $o_t$ represents the output gate, $W_o$ is the output gate weight, $b_o$ is the output gate bias, and $\sigma$ and $\tan h$ are the activation functions.

(2)

Particle Swarm Optimization

Particle Swarm Optimization (PSO) was proposed by Eberhart and Kennedy in 1995 [35]. We used the PSO algorithm to optimize three key parameters of the LSTM model, as follows: the learning rate, the number of hidden layer nodes, and the regularization factor. Particle swarm algorithms were inspired by two-dimensional spatial simulations of foraging biology and group behavior in populations of avian animals. Firstly, numerous search particles with random positions and velocities are established in a two-dimensional space. These particles are then guided towards an optimal point in the space by iteratively updating their positions based on their velocities. This process facilitates both local and global optimization [36,37]. The PSO optimization algorithm is theoretically simple and easy to implement, making it widely used in various applications for the self-adaptive optimization search of optimal parameters.

We optimized three hyperparameters by using the PSO algorithm—the learning rate, the number of hidden nodes, and the regularization coefficients—in the LSTM neural network. Once the maximum number of iterations was reached, we obtained the global optimal values for these hyperparameters. These optimized values were then substituted into the prediction model.

Firstly, we took the error function as the objective function of the optimization algorithm. Secondly, we identified three hyperparameters (learning rate, number of hidden nodes, and regularization factor) in LSTM as optimization objectives and computed the particle fitness. Then, we updated the positions and speeds of the examples according to the global optimal solution and individual optimal solution, and repeated the execution until reaching the maximum number of iterations, in which the upper and lower bounds of the optimization search for the three hyperparameters were the learning rate (10⁻⁴, 10⁻³), number of hidden nodes (10, 30), and regularization factor (10⁻⁴, 10⁻¹). The maximum number of model iterations was 200 and the maximum number of training sessions was 3000. The process of using the PSO algorithm to optimize the LSTM hyperparameters is shown in Figure 9.

We built two prediction models for both cases of the SCRC system and original pipe network. After building the prediction model, we used rainfall as a single input variable, and the output variable was a single quantity, the flooding indicator. The predictive model was run for one indicator for each running.

2.5.3. Predictive Model Performance Evaluation Indicators

We chose three assessment metrics, the Mean Absolute Percentage Error (MAPE), Root Mean Squared Error (RMSE), and Coefficient of Determination R², to evaluate the performance of the prediction model.

MAPE ranges between 0 and positive infinity. The smaller the value of MAPE, the better the model performance. The MAPE calculation is shown in Equation (8).

$$MAPE={\displaystyle \frac{100\%}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{{\widehat{y}}_i-y_i}{y_i}}\right|$$

(8)

where ${\widehat{y}}_i$ is the predicted value of the model, $y_i$ is the simulated value of the SWMM model, and $n$ is the number of samples.

RMSE is generally used to describe the deviation of a predicted value from the true value of a sample. The smaller value of RMSE, the better prediction model performs. The RMSE calculation is shown in Equation (9).

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n\left({\widehat{y}}_i-y_i\right)}$$

(9)

The last indicator is the coefficient of determination R², which effectively measures the correlation between true and predicted values. Its specific calculation formula is shown in Equation (10).

$$R^2=1-\left(\sum _{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2/\sum _{i=1}^n{\left(y_i-{\overline{y}}_i\right)}^2\right)$$

(10)

2.5.4. Projected Targets

After completing the above steps, we used the prediction model to predict three indicators of urban flooding under different rainfall intensities for the two drainage systems (original drainage system and SCRC system). The specific formulas for the three indicators are provided below.

The first indicator is the surface runoff coefficient. This indicator is the ratio of the total surface runoff to the total rainfall in the study area.

$$\phi ={\displaystyle \frac{V_1}{V_2}}$$

(11)

where $\phi$ is the integrated surface runoff coefficient, $V_1$ is the total surface runoff (mm), and $V_2$ is the total rainfall (mm).

The second indicator is the pipe overload time of the drainage system. This indicator is the sum of the overload times of all pipes in the study area.

$$t_c=\sum _{t_i=1}^{Num.C}{t}_i$$

(12)

where $t_c$ is the total pipe overload time (h), $Num.C$ is the total number of overloaded pipes, and $t_i$ is the pipe overload time (h). SWMM simulates a rainfall duration of 120 min, and it is normal that the sum of all pipe overload times may exceed this.

The third indicator is the node overflow volume of the drainage system. This indicator is the sum of all nodal overflows in the study area.

$$V_c=\sum _{V_i=1}^{Num.C}{V}_i$$

(13)

where $V_c$ is the total node overflow volume (Mltr, 1 Mltr = 10⁶ L), $Num.C$ is the number of nodes where overflow occurs, and $V_i$ is the node overflow volume (Mltr).

The prediction results of these three indicators can reflect the effectiveness of the SCRC system in alleviating urban flooding under different intensity rainfall conditions.

3. Results

3.1. Predictive Model Performance Analysis

In this study, we chose three evaluation indicators (MAPE, RMSE, and R²) to evaluate the performance of the prediction model. The model was trained by using the training set data during the PSO–LSTM prediction model training phase, and then the performance of the prediction model was evaluated by using the test data.

We first conducted a prediction analysis for the entire study area, and three urban flooding indicators were selected for prediction. Figure 10 and Figure 11 show the results of the training and test sets of the PSO–LSTM prediction model, and the accuracy indicators of the training and test sets are listed in

Table 4. Training set accuracy table.

Drainage System	Flooding Indicators	MAPE (%)	RMSE	R2
Original drainage system	Surface runoff coefficient	0.3290	0.0034	0.9823
	Pipe overload time	0.6903	0.0409	0.9957
	Node overflow volume	1.2980	0.0823	0.9965
SCRC	Surface runoff coefficient	0.2173	0.0010	0.9963
	Pipe overload time	0.8276	0.0151	0.9998
	Node overflow volume	1.3056	0.0751	0.9994

and

Table 5. Test set accuracy table.

Drainage System	Flooding Indicators	MAPE (%)	RMSE	R2
Original drainage system	Surface runoff coefficient	0.9635	0.0045	0.9637
	Pipe overload time	1.2242	0.0473	0.9926
	Node overflow volume	1.4977	0.0865	0.9907
SCRC	Surface runoff coefficient	0.5402	0.0039	0.9922
	Pipe overload time	1.1326	0.0529	0.9978
	Node overflow volume	1.4267	0.0823	0.9968

. The R² of both the training and test sets was above 0.95. For the training set of the PSO–LSTM prediction model, the highest MAPE indicator was 1.3056% with an average of 0.7780%, the highest RMSE was 0.0823 with an average of 0.0363, and the lowest R² was 0.9823 with an average of 0.9950. For the test set, the highest MAPE indicator was 1.4977% with an average of 1.4977%, the highest RMSE was 0.0865 with an average of 0.0462, and the lowest R² was 0.9637 with an average of 0.9890. These results show that the deviation between the simulation results of the SWMM model and the PSO–LSTM prediction model was extremely small. Overall, the PSO–LSTM prediction model was satisfactory.

3.2. Comparison of Prediction Models

In addition, we conducted new research on recent rainfall events in the study area. We used sensors to record the amount of rainfall at different moments and the depth of water accumulation at each node throughout the region. Subsequently, we input these measured data into the SWMM model for simulation. By simulation, we could obtain the maximum water depth data for all nodes in the study area and use them as a library of training samples for the prediction model. In order to highlight the performance of the PSO–LSTM prediction model, we also built an LSTM prediction model for comparison. In the prediction process, we used the rainfall data of the three moments before the maximum water depth occurred and the corresponding node water depths at these moments as input variables for the prediction models. The output variable was the maximum water depth reached by the node at a single moment. Figure 12 shows the actual local rainfall process on 22 August 2023 in the study area. Figure 13 shows a comparison of the maximum water depths at the nodes modeled by the two drainage systems.

Table 6. Error table for prediction results.

Node	Measured Value	SWMM Analogue Value	PSO–LSTM Predicted Value	LSTM Predicted Value
26	0.179	0.182	0.188	0.175
27	0.217	0.213	0.228	0.244
28	0.278	0.276	0.292	0.273
29	0.243	0.239	0.255	0.241
30	0.239	0.235	0.242	0.232
31	0.209	0.211	0.218	0.203
……	……	……	……	……
236	0.854	0.865	0.835	0.895
Average error		1.76%	4.24%	8.05%

shows the errors between the measured, simulated, and predicted maximum water depths within the 236 major nodes. The average error between the SWMM simulated and PSO–LSTM predicted values was 1.76%, the average error between the PSO–LSTM predicted and actual values was 4.24%, and the average error between the LSTM predicted and actual values was significantly higher at 8.05%. Since the PSO–LSTM prediction model in this work used measurements as training samples, the error between the predicted and measured values accumulated with the increase in iterations, and the error between the predicted and measured values in PSO–LSTM was 2.48% more than that between the simulated and actual values in SWMM. The error between the predicted and measured values of PSO–LSTM was 3.81% lower than that of LSTM. The PSO–LSTM prediction model outperformed the unoptimized LSTM model, highlighting its superior prediction effect and higher accuracy.

Figure 14 shows a comparison of the performances of the PSO–LSTM prediction model, the LSTM prediction model, and the SWMM model on three evaluation metrics, as follows: MAPE, RMSE, and R². For all three indicators, the PSO–LSTM prediction model consistently outperformed the LSTM prediction model, with a better match to the actual values. The PSO–LSTM model provided more accurate predictions, which could improve the reliability of sponge city drainage predictions.

3.3. Predictive Modeling Results

After we verified the performance of the predictive model, we made predictions for twenty subsequent rainfall events, inputting the same rainfall amount, rainfall duration, and rainfall crest factor (r = 0.5) into both the prediction model and the SWMM model. We obtained two sets of data, one from the prediction model and the other from the SWMM model simulation. The average error for both sets of data was very small.

Table 7. Comparison of predicted and simulated results.

	Flooding Indicators	Surface Runoff Coefficient		Node Overflow Volume (Mltr)		Pipe Overload Time (h)
Recurrence Period (yr)		SWMM	PSO–LSTM	SWMM	PSO–LSTM	SWMM	PSO–LSTM
1.5		0.301	0.298	0.671	0.677	0.11	0.108
2.4		0.34	0.338	2.994	2.899	1.898	1.891
2.6		0.349	0.351	3.149	3.151	1.923	1.913
4.5		0.39	0.387	9.833	9.828	2.945	2.932
4.8		0.392	0.39	10.677	10.674	2.979	2.968
5.5		0.405	0.403	24.265	24.263	3.127	3.11
Average error		0.66%		0.70%		0.68%

shows the data comparing the simulation results with the prediction results for five of the rainfall events. It can be seen that the average value of the data error for the three flood indicators was around 0.7%, and all of them were within 1%, indicating that the prediction results and the accuracy of the prediction are valid.

3.4. Effects of SCRC in Alleviating Urban Flooding

Table 8. Three indicators of waterlogging under different intensity rainfall conditions (O: Original drainage system, S: SCRC system, rainfall crest factor = 0.5).

	Flooding Indicators	Surface Runoff Coefficient		Node Overflow Volume (Mltr)		Pipe Overload Time (h)
Recurrence Period (yr)		O	S	O	S	O	S
1 yr		0.679	0.273	8.397	0	23.487	0.11
2 yr		0.707	0.329	24.313	1.343	30.45	1.632
3 yr		0.726	0.361	37.712	4.799	34.409	2.193
4 yr		0.739	0.382	49.004	8.311	37.021	2.869
5 yr		0.748	0.397	58.701	11.455	38.625	3.021
10 yr		0.776	0.437	92.12	23.828	44.081	3.847

and

Table 9. Three indicators of waterlogging under different intensity rainfall conditions (O: Original drainage system, S: SCRC system, rainfall crest factor = 0.4).

	Flooding Indicators	Surface Runoff Coefficient		Node Overflow Volume (Mltr)		Pipe Overload Time (h)
Recurrence Period (yr)		O	S	O	S	O	S
1 yr		0.683	0.276	7.052	0	24.907	0.11
2 yr		0.71	0.331	22.094	0.591	32.178	1.517
3 yr		0.729	0.364	35.051	3.916	36.265	2.384
4 yr		0.741	0.385	46.194	7.181	39.063	2.81
5 yr		0.751	0.399	55.828	10.205	41.006	3.398
10 yr		0.779	0.44	89.52	23.89	45.858	3.929

and Figure 15 show the values of the three flood indicators for the two systems, the Original Drainage System (O) and the SCRC System (S), for different rainfall intensities. Generally speaking, the SCRC system reduced the three flooding indicators to different degrees under different rainfall intensities, and the degree of reduction was large, reflecting that the SCRC system is more efficient in mitigating urban flooding compared to traditional drainage systems. Interestingly, changes in rainfall peaking coefficients had little effect on the values of the three indicators.

As the rainfall return period increased, the rate of reduction of the three flood indicators by the SCRC system was gradually reduced. This may have been due to the fact that the surface LID measures were saturated in terms of slowing down surface runoff and increasing stormwater infiltration when the rainfall intensity was high, and high-intensity rainfall was fully converted into surface runoff. On the contrary, during low rainfall intensities, surface storage may not have reached capacity before the rainfall peak, thereby partially reducing the intensity of surface runoff, keeping in agreement with the findings of Jemberie et al. [38]. Cheng et al. [39] similarly showed, in their study, that the effectiveness of LID facilities in controlling runoff, flooding, and ponding is better in low-return periods than in high-return periods, and better in the short term than in the long term.

Table 10. Reduction rates of the three flooding indicators by the SCRC system.

	Flooding Indicators	Surface Runoff Coefficient		Node Overflow Volume (Mltr)		Pipe Overload Time (h)
Recurrence Period (yr)		r = 0.5	r = 0.4	r = 0.5	r = 0.4	r = 0.5	r = 0.4
1 yr		59.79%	59.59%	100.00%	100.00%	99.53%	99.56%
2 yr		53.47%	53.38%	94.48%	97.33%	94.64%	95.29%
3 yr		50.28%	50.07%	87.27%	88.83%	93.63%	93.43%
4 yr		48.31%	48.04%	83.04%	84.45%	92.25%	92.81%
5 yr		46.93%	46.87%	80.49%	81.72%	92.18%	91.71%
10 yr		43.69%	43.52%	74.13%	73.31%	91.27%	91.43%

shows the reduction rates of the three urban flooding indicators by the SCRC system, while Figure 16 showcases the SWMM simulation results of the two systems for the three indicators under the conditions of a rainfall return period (p = 10 yr) and a rainfall crest factor (r = 0.5. Relative position of the moment of peak storm occurrence in the overall rainfall process).

In summary, the SCRC system, as a new sponge city drainage system, provided good mitigation of sponge city flooding. The prediction performance of the neural network prediction model was also verified, showing that artificial neural networks can be effectively used in the prediction of flooding in sponge cities

4. Discussion

4.1. Effects of Datasets and Hyperparameters

At present, the basic LSTM neural network and various improved LSTM neural networks are widely used in various fields of hydrological prediction [40,41]. LSTM neural networks can circumvent the shortcomings of traditional RNNs [42,43,44], which makes them more reliable and user-friendly when dealing with rainfall sequence information, especially long time series. In existing research [45], it has been shown that predictive models of LSTM and its improved versions perform well under normal conditions, but suffer from crashes in rare and extreme cases. In order to ensure the performance of these prediction models, high-quality and long time series of training set data is necessary, which often requires a large amount of collected and analyzed data.

In addition, some hyperparameters in the LSTM neural network also affect the performance of the prediction model. In this study, we optimized the learning rate, regularization factor, and number of hidden nodes of LSTM species using PSO. The size of the learning rate affects the training process of the model, variation in the regularization coefficient affects the degree of model fitting, as it being too large or too small will lead to a decline in the performance of the model, and the number of hidden nodes affects the expressive ability of the model, since an appropriate increase can help the prediction model to better learn the complex features of the data, while too many hidden nodes may lead to over-fitting. In this study, the basic LSTM neural network was improved by optimizing its parameters, and made some progress in prediction performance. In future work, there is still a need for further research on multiple parameter optimization, and the joint construction of multiple models can also be considered.

4.2. Neural Networks in Sponge Cities

In this study, we validated the effective application of neural networks in sponge city flood prediction. The application of neural networks in the sponge city field is not limited to flood prediction. For example, neural networks can be utilized in stormwater discharge optimization, where, by analyzing real-time data from urban drainage systems, neural networks can optimize the path and rate of stormwater discharge. Neural networks can also be applied in green space water management. Neural networks can analyze the state of urban green spaces and water bodies, including soil moisture, vegetation health, and water quality. In conclusion, neural networks can be applied in all aspects of sponge cities and can provide effective help for the construction and management of sponge cities.

4.3. Sponge City

The sponge city concept is currently in its initial development stage, and most scholars’ research on flood prevention and control in sponge cities focuses on surface LID measures [46,47]. In contrast, sponge city flood prevention and control should be considered from a more comprehensive perspective, including its economic benefits, social benefits, and impacts on the environment. Moreover, the construction of sponge cities is closely related to the type of land use, construction cost, and natural conditions, with the degree of their mutual influence being different. This means that the planning and construction of sponge cities should not only consider the urban drainage problem, but also the subsequent development of such cities.

The SCRC system exhibited promising potential for mitigating urban flooding under varying rainfall intensities. Future research should also give more consideration to planning issues in sponge city construction. The future mitigation of urban flooding is not only to drain rainwater out of the city, but also to collect and rationally utilize rainwater resources and make achieving the harmonious coexistence of man and nature possible.

The SCRC system is not limited to the areas seen in this study. Each sponge city can design its own SCRC system based on rainfall, land use type, and other relevant data. We used neural networks to predict sponge city flooding, exploring the application of neural networks in sponge cities. Each city can also use neural networks to deal with different problems such as pipe network optimization, data collection, and rainwater deployment according to its own situation.

5. Conclusions

In this study, a new sponge city drainage system, the SCRC system, was proposed, and the effectiveness of neural network application in the field of sponge city flood prevention and control was also verified. We built a prediction model for the SCRC system using a PSO–LSTM neural network. The main conclusions were as follows:

(1)

The PSO–LSTM prediction model provided an excellent prediction performance. The errors between the predicted values and the SWMM simulated values were all very small. The average MAPE of the three flood indicators in the test set was 1.1308%, the average RMSE was 0.0462, and the average R² was 0.9890, showing that the prediction model displayed an excellent performance.

(2)

The SCRC system was effective in mitigating urban flooding. With the extension of the rainfall return period, the reduction effect of the SCRC system on the three urban flooding indicators gradually decreased, but it still showed a good mitigation effect on urban flooding when the rainfall return period was large.

(3)

The PSO–LSTM neural network can be effectively used in the field of sponge city flooding, which can provide useful information for the planning and design of future sponge cities.

Sponge cities involve multifaceted data, including meteorological data, geographic information, socio-economic data, etc., and neural networks can effectively integrate and process these data. Future research should pay more attention to using neural networks for data integration and providing full decision support. It will help city managers to implement reasonable planning and policies.