Prediction of floodwater impacts on vehicle blockages at bridges using artificial neural network

Abstract. During extreme flood events, various debris like floating vehicles can block the bridges in urban rivers and floodplains. Blockage of vehicles can influence the floodwater hydrodynamics and potentially on the flood risk implications. Such obstructions often raise upstream water levels with back water effects, causing more water to be redirected into nearby metropolitan areas. This study attempts at evaluating artificial neural network (ANN) model in predicting the variations in floodwater depths and velocities along the channel centreline based on the changes in flowrate and distances from the inlet. The floodwater depth and velocity variations were obtained for three different types of bridges at specified sites along the channel centreline with three incoming discharges. A multilayer feedforward neural network (FFNN) model was used to investigate the effects of discharge (Q) and distance, on depth variation rate (D) or velocity (V). Additionally, a comparison study was done between 2 input 1 output and 2 input 2 output i.e. single output (depth variation rate (D) or velocity (V) versus multi-output depth variation rate (D) and velocity (V) for all the three models of bridges that are blocked by vehicles. The study has applied 12 training algorithms (TA) in the ANN modelling to optimize the TA that is most suitable for the dataset of three different bridges. The optimization is based on the performance criterion namely regression (R), mean squared error (MSE), mean absolute error (MAE), mean absolute percentage (MAPE), accuracy and coefficient of determinant (R2). Bayesian regularization backpropagation (BR) training algorithm gives a highest accuracy when compared in all three bridges. The scenario 2 input 2 output gave greatest accuracy results compared to 2 input 1 output. The findings showed a reliable estimation of significant impacts on the flow propagations and the hydrodynamic processes along rivers and floodplains. This study can help the decision makers in effective river and floodplain management practices.


Introduction
Floodwaters in urban rivers caused by bridges being blocked by different floating debris may cause significant damage to local property, infrastructure, and citizens, and such obstructions have grown increasingly common in recent years [1][2][3][4]. Various types of vegetation, such as bushes and trees, as well as urban detritus, such as shopping carts, swept vehicles, and floating containers, might obstruct local bridges over urban waterways in the floodplains [1,5,6].
To name a few instances, a severe flooding in a village during Storm Dennis was mainly caused by "woody debris" which was blocking a culvert and has affected 159 homes and 10 businesses [7]. The flood water level at the Ba-Tu Railway Bridge was determined to be 2.4 m higher than the right embankment height due to a significant overbank flow caused by the obstruction [2]. Due to severe rainfall of up to 200 mm in 5 hours, the tiny town of Boscastle in the United Kingdom was hit by a disastrous flash flood in 2004 [8]. Despite the fact that no one was killed, the incident caused millions of pounds in damage, with about 116 automobiles being carried away into the sea [8][9][10][11]. Several automobiles and big tree debris were stuck under a local bridge during this flood event, obstructing the flow path and diverting much of the floodwater out of the channel and into the flooded urban area, resulting in significant flood damage. Flooding is certainly exacerbated by massive debris obstructing bridges, which resulted in substantially higher flood levels and, as a result, a greater danger of flooding in surrounding metropolitan areas. ____________________ *Corresponding authors: Anurita.Selvarajoo@nottingham.edu.my; Senthil.Arumugasamy@nottingham.edu.my Enhanced flood levels, flow diversions out of urban rivers or channels, creation of unanticipated overland flood passageways, and increased flood damage and possible flood risk effect are all common results of bridge obstructions during urban flood events [1,12]. Various studies, including observed data analysis [1,4] and physical and numerical modelling [13][14], have been conducted to investigate the issues related to debris blockage at bridges crossing urban rivers.
The interaction of structures and flood flows in urban settings has been studied extensively using scaled physical models and two-dimensional hydrodynamic models [13][14][15]. These research led to laboratory experiments to study the hydrodynamic properties and flood risk consequences of debris blockage at bridges in urban floods [3,9]. In their study, the authors built a small-scale physical replica of an urban river in a laboratory flume, complete with a partially obstructed bridge. The hydrodynamic effects of vehicle obstructions on three model bridges were then assessed through a series of tests. The experimental data was then utilised to look at the hydrodynamic effects of flood flows caused by cars obstructing bridges. Even though these researchers focused on the development of physical models which can aid to study a large bridge but at a small scale, these models do not have the ability to predict or forecast the future impacts of flood conditions on these debris.
Artificial neural network (ANN) is an emerging technology and is a part of an Artificial Intelligence (AI) technique that has been gaining significant attraction in various fields of study. AI models can decipher the intricate and extremely non-linear relationships between variables. As a result, AI models just require the inputoutput dataset to be incorporated into the model, rather than all the process's characteristics. Due to its versatility, it has been used in various applications. To name a few ANN has been applied to various hydrological problems and help predict the flow for catchments in semi-arid and Mediterranean regions [16]. In addition, ANN has been used also to predict the flow in Tomebamba river, at a real time and at a particular time of the year by collecting information of rainfall [17]. It was found that ANN can solve river-flow forecasting problems better than a conceptual rainfall-runoff model when it was used to study the downstream flow forecasting in the Apure River basin, Venezuela [18]. In this study ANN model was developed for the hydrodynamic impacts of these vehicles blocking bridges. To the best of the authors' knowledge, there is no published research work where ANN model was developed to compare 12 training algorithms (TA) in this field of study. Also no study was done to compare one output (Velocity or depth variation rate) with two outputs (Velocity and depth variation rate) for hydrodynamics experiments of vehicle blockages at bridges. Therefore, the aim of this study was to develop models that can help to assess different types of scenarios of vehicle blockages at bridges using ANN modelling techniques. Flood events would take into account many variables and this study wants to establish a model to access this ever-changing variable [3,9]. A total of 12 different training algorithms were used in the ANN model, and 10 hidden layers were compared and statistically evaluated in terms of estimation errors, which are mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) and accuracy with the experimental results.

The experimental approach
A small-scale physical river model was created by Teo (2010) to replicate a straight reach seen in many urban river basins, and it consists of a simplified replication of a compound cross-sectional profile (i.e. for a main channel with relatively shallow floodplain zones on each side) [3,9]. These features are primarily used as a foundation for investigating flows caused by partially obstructed bridges.
The small-scale physical river model was built in a laboratory flume with glass, using a rectangular flume with a cross-sectional geometry of 1.2 m wide by 1.5 m deep and an overall length of 17.0 m. Figure 1 depicts the laboratory flume as well as the built physical river model. The hydraulic flume was equipped with a recirculation system, and the flow was regulated by valves on the input pipe and an adjustable weir at the flume's downstream end. The flow meter linked to the input pipe provided the discharge of the flow. For the various experiments in this investigation, the flume's bed slope was modified to be horizontal.
Three distinct types of model bridges were examined to simulate a real urban river set-up. (a). A single opening arch bridge (scenario 1), (b) a straight deck bridge (scenario 2), and (c) a three opening straight deck bridge (scenario 3) were among the model bridge layouts chosen, as shown in Figure 2. Experiments for the three configurations were carried out in the same laboratory flume to limit the number of mistakes that may occur. Three experiments were done for each bridge layout, with a blockage effect for four small-scaled model cars, and for various incoming discharges.
The discharges in the flume were monitored using a calibrated flow meter, and water depths were recorded with a basic pointer depth gauge device in the current investigation. Three distinct steady discharges were executed at the upstream boundary site for each model bridge configuration, with corresponding values of 6.0, 10.5 and 13.0 L/s for scenario 1 or 2, and 45.0, 90.0, and 150.0 L/s for scenario 3. However, because the downstream water depth was set to a constant amount for each example, these discharge levels did not represent a specific flood frequency. A propeller-type velocity metre was used to measure the velocity at a specific spot, which has the benefit of being durable, capable of recording lower velocities, and entirely portable with a digital indication. It cannot, however, measure velocity at the water's surface or near the bed. As a result, the velocity near to the sea surface was considered to be about equal to the velocity at the relative depth of 0.8 in the following study, while the velocity on the bed was assumed to be zero. Three scenarios which indicates the type of bridge have classified in this study and in each scenario has its determined inputs and outputs which further breakdown into (a), (b) and (c). The input and output considered for each scenario is shown in Table 1.

Artificial Neural Network (ANN) structure
Artificial neural network structure is made up of three layers, similar to biological neurons: input, hidden, and output. Coefficients (weights), which are made up of neural structures, link the neurons. The ANN is greatly influenced by the connections between neurons. In general, there are two sorts of connections : feedback (recurrent) and feedforward. The output of either the previous or the same layer returns to the input layer in a feedback link. The output of a feedforward system does not return to the input neurons. Feedforward Neural Network (FFNN) is a widely used and effective neural network design that has been shown to be a universal approximator in a wide range of applications [19]. This study took into account two inputs : discharge and distance from intake, as well as two outputs: depth variation rate and velocity. FFNN with one hidden layer and one to ten hidden neurons was utilised in this study.

Hidden layer selection
The hidden layer is an intermediate layer among the enter and output layers. Neurons within the hidden layer are activated via the means of a function. In this case, only 1 hidden layer is used. During the majority of the procedure, one concealed layer is chosen. Since one hidden layer is adequate in this task, an FFNN with one hidden layer is utilised.

Hidden neuron selection
An important feature of an FFNN or perceptron network is determining the number of neurons in a hidden layer. The overall neural network architect is determined by neuron collection, which has a significant impact on the ultimate output. If there aren't enough neurons in the network, it won't be able to simulate complicated data, resulting in underfitting. If the network has an excessive number of superfluous neurons, the training period may become too long, resulting in overfitting. When a network overfits, it begins to simulate random noise in the data. As a result, a model may match the training data exceptionally well yet perform badly when applied to fresh data. The goal of this project is to gather data for one to 10 hidden nodes in order to determine the optimal number of hidden nodes.

Training algorithms
A training algorithm is a method for extracting patterns from data and optimising network parameters to adapt a system to a specific input output transformation task [20,21]. Depending on the type of data, complexity, and amount of data available, no single algorithm is best for every problem.

Evaluation of the model
Three different performance functions were used for the evaluation of target and output accuracy. These functions, namely mean absolute percentage error (MAPE), mean absolute error (MAE), and mean square error (MSE), Equations (1) to (5) were used to evaluate the measure of accuracy. The hidden neurons that provide the lowest MSE, MAE and MAPE values are considered to be the optimal values. The more these values are closer to zero the better is the model. Another important performance criterion is the coefficient of determination (R 2 ). The closer the R 2 value to 1, the better is the model.

Results and discussion
Comparison between scenarios is made to understand whether a single output ANN functions better or a two outputs ANN. This result will allow us to make better decision in the future when studying the many characteristics of the unpredictable effect of the flow of the above scenarios. The number of hidden neurons as well as the kind of training procedure have a significant influence on the network's accuracy. Much research has been conducted to identify the optimal number of hidden neurons in the network [22]; nevertheless, the selection is case dependent to avoid over-or underfitting. As a result, the number of neurons in the hidden layer was changed throughout data processing, ranging from 1 to 10. All 12 training algorithms are compared to determine the most suitable training algorithm for each of the sub-scenarios: scenario 1, 2, 3 (a -c). The comparison is illustrated in Table 2, Table 3 and Table 4. In scenario 1a, although LM had the highest MSE of 0.119, it also has the lowest MAE (0.009), MAPE (0.008) and the second highest R 2 value (0.977). Its accuracy is the highest at 99.12. In scenario 1b, BR has the lowest MSE (0.199), MAE (0.315), MAPE (0.023) and the highest R 2 value (0.989) and accuracy (97.65). In scenario 1c, BR had the has consistently one of the best MSE (0.840), MAE (0.229), MAPE (0.018), R 2 value (0.959) and the highest accuracy (99.45). After repeating the comparison of MSE, MAE, MAPE, R-squared and accuracy, the best training algorithm is found to be LM for scenario 1a, scenario 2a, scenario 2b, scenario 3a and scenario 3b, and BR for scenario 1b, scenario 1c, scenario 2c, scenario 3c. Its accuracy is the highest at 99.12. Other training algorithms show satisfactory results except for GDX, GDM and GD, which consistently obtains negative coefficient of determination (R-Squared values) and occasionally produces noticeably lower accuracy. In scenario 3c, the MSE value for GDM and GD is 662.67 and 132.63.
Comparisons between sub-scenario 1a, 2a, 3a, 1b, 2b and 3b with sub-scenario 1c, 2c and 3c shows that an ANN model with two inputs and two outputs is better than an ANN model with two input and one output. Comparing the best training algorithm with the optimum number of hidden neurons for all three scenarios shows that sub-scenario c has the highest accuracy. In Scenario 1, the highest accuracy in sub-scenario 1a and 1b are 99.12 and 97.65 while the highest accuracy in sub-scenario 1c is 99.45. In Scenario 2, the highest accuracy in sub-scenario 2a and 2b are 82.29 and 93.50 while the highest accuracy in sub-scenario 2c is 96.91. In Scenario 3, the highest accuracy in sub-scenario 3a and 3b are 99.59 and 99.12 while the highest accuracy in sub-scenario 3c is 99.79. Furthermore, comparing MSE, MAE, MAPE and R-squared shows that Scenario 3 have the best values. Comparing the best algorithm for sub-scenarios 1a, 2a and 3a, the MSE values are lowest for subscenario 3c (0.069), same goes for MAE (0.004) and MAPE (0.004). Although it does not have the highest Rsquared value, it still performs the best overall. The same occur when comparing sub-scenario 1b, 2b and 3b, sub-scenario 3b had the best MSE (0.120), MAE (0.010), MAPE (0.009) and R-squared (0.977). Sub -scenario 3c is the only one that doesn't perform as well when comparing MSE, MAE and MAPE, however, its accuracy is still the highest. Zhang et al. (2019) made similar reports in their study to use ANN to evaluate the adsorption capacity of graphene oxide, where GDM is the least accurate algorithm with its largest RMSE, followed by GD [23]. Similar to this study, they also concluded that the training algorithm LM performs the best through RMSE, followed by BR. In this study, LM and BR outperform other algorithms in the training dataset in which they showed the maximum prediction accuracy, lowest MAE, MAPE and highest coefficient of determination. Although they did not consistently have the lowest MSE values, the two algorithms would always have one of the lowest MSE and still be of acceptable value.

Conclusion
In this paper, ANN was used to predict outcomes in hydrodynamics impacts of vehicles blocking bridges. The input variables that was used in all three scenarios were discharge, Q and distance from inlet, D, whereas the output variables were varied by using (i) single output system (depth variation rate, D or velocity, V); and (ii) double output system (both). Overall, this study consisted of nine scenarios, where there is a scenario of (two inputs with either one of the output) and a scenario of (two inputs with two outputs). In this study, it can be seen that the number of hidden neurons was determined by comparing the accuracy of each training algorithm in each scenario. Bayesian regularization backpropagation (BR) algorithm with ten hidden neurons is selected as