Research on the Application of Artificial Neural Network to the Flood Risk Assessment

Research on the Application of Artificial Neural Network to the Flood Risk Assessment

Qiong Li a Donghan Liu b

a School of Mathematics and Physics, Hubei Polytechnic University, Huangshi, Hubei,

China

b Mechanical and electrical school, Hubei Polytechnic University, Huangshi, Hubei, China

Abstract: Flood is a most serious hazard to life and property. The traditional probability statistical method is acceptable in analyzing the flood risk but requires a large sample size of hydrological data. This paper puts forward a method based on artificial neural network (ANN) for flood analysis. An artificial neural network model-BP neural network is used to map multi-dimensional space of disaster situation to one-dimensional disaster situation and to raise the grade resolution of flood disaster loss. This technique contributes to a reasonable prediction of natural disasters risk. As an example, its application is verified in the flood risk analysis in China, and the risks of different flood grades are obtained. Our model yield very good results and suggests that the methodology is effective and practical so that it has the potentiality to be used to forecast the flood risk in flood risk management.

Keywords: artificial neural network·flood·risk analysis·assessment

1. Introduction

   Natural disasters are increasing alarmingly worldwide. Flooding is a common natural disaster which very often causes property and human losses. Recent flooding disasters have shown the vulnerability of the so called developed and developing countries to such events. In China, flood disasters occur frequently, and about two-thirds of its area are facing the threat of different types and degrees of floods which is the result of natural and unnatural reasons such as social, economic factors. Given this, natural disasters present a great challenge to society today. And flood risk

   assessment of an area is important for flood disaster managers so they could implement a compensation and disaster-reduction plan. As severe floods occurring frequently, flood risk assessment and management play an important role in guiding the government take timely and correct decision for disaster rescue and relief.

   Risk management for the operation of an existing flood protection system is the sum of actions for a rational approach to flood disaster mitigation. Its purpose is the control of flood disasters, in the sense of being prepared for a flood, and to minimize its impact. It includes the process of risk analysis, which forms the basis for decisions on maintaining and improving the system.

   Risk analysis, one of the main subjects of flood management is a challenging task at the present. However, assessing flood risk is difficult because of the lack of objective measures of acceptable risk, scarcity of data, and abundance of unknown probability distributions. The flood risk analysis methods have shown a progress from direct integral method, Monte Carlo method, and mean first-order-second-moment method, to advanced first-order-second-moment method, second-order-method and JC method. The theories and methods of flood risk analysis were established according to the studied by the authors (Ang and Tang, 1984, Ashkar and Rousselle, 1981, Diaz-Granados et al. , 1984, Kuczera, 1982, Stedinger and Taylor, 1982, Todorovic and Rousselle, 1971, Todorovic and Zelenhasic, 1970, Wood and Rodríguez-Iturbe, 1975). Recently, many risk analysis approaches have been based on using linguistic assessments instead of numerical values. Using fuzzy sets theory (Zadeh 1965), data may be defined on vague, linguistic terms such as low probability, serious impact, or high risk.

   In traditional flood risk assessment, probability statistics method is usually used to estimate hydrological variables exceedance probability because of its mature basic theory and easy application. But in the case of practical issues, problems exist in the feasibility and reliability. Especially in small sample issues, results based on the classical statistical methods are usually unreliable. In fact, it is rather difficult to collect long sequence flood data and the sample is usually small.

   Till now, scholars have made a deep research on the floods random characteristics

   in risk analysis, but the study on some aspects such as its fuzziness (Chen 1998), gray characteristic (Xia 2000), unascertained characteristic (Liu et al. 1994), fractal dimension characteristic and chaos characteristic of the flood is relatively weak, so the researches of the risk analysis on such aspects need to be developed further. And neural network is data driven, and it can be described as mapping an input space to an output space. Many problems exist for which there is no underlying knowledge of the process that converts the measured inputs into the observed outputs. Artificial neural networks are well suited to this class of problem because they are excellent data mappers in that they map inputs to outputs. Its suggested that some neural net algorithm might provide a solution. Therefore, an artificial neural network model-BP neural network is used in this paper for evaluating the degree of flood disaster, where the disaster loss degree is a more reasonable continuous real number.

2. Basis of Artificial Neural Network

   The essential of the risk analysis is to estimate the probability density of an index. Because of the incompleteness of the data, the application of traditional statistical methods can not guarantee a high precision. So we use the neural network with the observed sample and get their degree values, and then get the risk estimations by risk analysis. This paper uses artificial neural network and gets continuous degree index values of the samples, then it turns the degree values of observed sample into the continuous real degree number and then gets the risk values. It is tested by a case showing that the method is superior to traditional statistic model , so as to improve the result of traditional estimation.

   Artificial Neural Network (ANN) are massively parallel interconnected networks of simple (usually adaptive) nodes which are intended to interact with objects of the real world in the same way as biological nervous systems do(Simon Haykin, 2009). It was proposed based on modern biology research concerning human brain tissue, and can be used to simulate neural activity in the human brain (Markopoulos1, Manolakos, & Vaxevanidis, 2008). ANN has the topological structures of information processing, distributing parallel. The mappings of input and output estimation responses are

   obtained via combinations of nonlinear functions.

   In terms of their structures, neural networks can be divided into two types: feedforward networks and recurrent networks. In a feedforward network, the neurons are generally grouped into layers. Signals flow from the input layer through to the output layer via unidirectional connections, the neurons being connected from one layer to the next, but not within the same layer. The multi-layer perceptron (MLP) is perhaps the best known type of feedforward networks. For the typical multi-layer perceptron of the feed-forward mode neural network, it consists of the input layer, output layer, and hidden layer. Neurons in the input layer only act as buffers for

   distributing the input signals x j

   to neurons in the hidden layer. Each neuron j in the

   hidden layer sums up its input signals

   x j after weighting them with the strengths of

   the respective connections

   w ji

   from the input layer and computes its output

   y j as a

   function f of the sum,viz.

   y j

   f (wji xi )

   (1)

   In which f can be a simple threshold function or sigmoidal, hyperbolic tangent or radial basis function. The output of neurons in the output layer is computed similarly.

   The backpropagation (BP) algorithm, a gradient descent algorithm, is the most

   commonly adopted MLP training algorithm. It gives the change

   w ji the weight of a

   connection between neurons i and j as follows:

   wji j xi

   Where is a parameter called the learning rate and j

   (2)

   is a factor depending on

   whether neuron j is an output neuron or a hidden neuron. For output neurons,

   j

   And for hidden neurons,

   j (

   f

   j

   net j

   )( y

   (t ) y )

   (3)

   ( f )w

   (4)

   j

   q

   j net qj q

   In Equation (3), net j is the total weighted sum of input signals to neuron j and

   is the target output for neuron j.

   (t )

   y

   j

   The neural cell of each layer only affects the status of the next neural cell. If the expected output signals cannot be obtained in the output layer, the weight values of each layer of the neural cells must be modified. Erroneous output signals will be backward from the source. Finally, the signal error will arrive in certain areas with repeated propagation. After the neural networks training procedure is complete we can start to analyze the forecast information with weight values and thresholds.

3. Flood Disaster Risk Assessment

   According to the above theory, we can calculated the probabilities of each degree of flood disasters in China based on the historical data from 1950 to 2009 collected by the Ministry of Water Resources of the Peoples Republic of China(see Table 1). We select the set of 60 records as the large sample, and then 30 records are randomly chosen to form a small sample in order to compare the results of them by the method. Damage area, inundated area, dead population, and collapsed houses have been chosen as the disaster indicator in flood risk analysis. And by frequency analysis we classify it into four levels: small, medium, large and extreme (see Table 2).

   Table 1 Values of flood indexes during 60 years

   Table 2 Flood disaster rating standard

   1. Artificial Neural Network Procession

      In order to map multi-dimentional space of disaster situation to one-dimensional disaster situation, a relationship between the disaster degree and the degree indexes is needed. But it is impossible to describe the relationship using a related function. Therefore, we adopt the simulation and memory of the neural networks in flood degree evaluation. This is because the advantages of neural networks can be used to simulate and record the relationship of the input variables and output variables in the

      complex function through training and learning without any mathematical models.

      We take damage area, inundated area, dead population, and collapsed houses as input variables and disaster grading value as an output variable, and then we set the nodes of the input as 4 and of the output layers as 1. It follows on from Kolmogorovs theorem(Hecht-Nielsen, 1987) that the number of nodes in the hidden layer is at least 2n + 1, where n is the number of nodes in the input layer. Since n = 4, the number of nodes in the hidden layer is at least 9. Considering the accuracy, we determine that the number of nodes in the hidden layer is 10. Thus, we can obtain the topology structure (4, 10, and 1) of the neural networks for flood degree forecasting.

      The four flood grades are small, medium, large and extreme flood, whose degree value are in the interval [0,1][1,2][2,3][3,4]; We use the disaster grading standard boundary values (table 1) as 5 two-dimensional training samples for training and learning in the BP neural network. Meanwhile initial parameters of BP model weights and biases are randomly assigned before the commencement of training. With

      100,000 cycles of training and learning in the training samples, the global error of the networks was set E=10-6. Learning rate and impulse parameter of the network are changed adaptive, and function trainlm is used for fast training.

      The calculated output values are compared with the expected values where the mean square error is 5.49809*exp(-8), indicating a good fitting. Thus the BP neural network has completed the training procedure. So we can use the BP network to forecast disaster degrees of all the samples with the weighting coefficients and the thresholds modified. The flood degree estimations of the 60 samples can be calculated out in Table 3 with BP neural network.

      Table3 Disaster degree estimations based on the BP network evaluation

   2. Flood risk assessment

In this way, the disaster degree values of all the 60 samples are obtained as shown in

Table 3. The relationship between the recurrence interval N and probability p can

be expressed as

N 1 p , and then the exceedance probability curve of flood to

disaster degree value is shown as Figure 1 using piecewise cubic hermite interpolating polynomial.

Figure 1: The exceedance probability curves of flood to disaster degree value based on neural network and piecewise cubic hermite interpolating polynomial

Due to the standard of four grades, so we have:

1. If

2. If

3. If

4. If

1. xi 1, then flood degree belongs to small.

2. xi 2 , then it belongs to medium.

3. xi 3, then it belongs to large.

4. xi 4 , then it belongs to extreme.

   The result in Figure 1 illustrates the risk estimation i.e. the probability of exceeding

   the disaster degree value. From Figure 1 we know the risk estimation is 0.1180 when the disaster index is 3, in other words, in China, floods exceeding 3 degree value (extreme floods) occur every 8.4757 years. Similarly, the probability of floods exceeding 2 degree (large floods) is 0.3246, namely China suffers the floods exceeding that intensity every 3.0807 years. This indicates the serious situation of floods in China whether on the aspect of frequency or intensity. It also means that BP neural network is useful to analyze probability risk of flood disaster. The frequency and the recurrence interval of the floods of the four grades are shown in Table 4 . These indicate the serious situation of floods in China. The frequency and the recurrence interval of the floods of the four grades are shown in Table 4.

   Table 4 Flood disaster risk assessment values in China

   Then we calculate the mean error between the results with large sample and small sample by neural network method and traditional statistics. From Table 5, it can be seen that errors given by neural network method are much smaller than that by statistical method, so neural network method is more efficient in solving this problem

   Compared with traditional probabilistic method, the risk values obtained by this

   neural network method can provide more characteristics of risk system when we analyze the risk of system. The result could help in strategic decision making to manage flood disasters.

   Table 5 Comparison of two methods

5. Conclusion

   Floods occur frequently in China and cause significant property losses and casualties. In order to implement a compensation and disaster reduction plan, the losses caused by flood disasters are among critically important information to flood disaster managers. This study develops a method of flood risk assessment disasters based on artificial neural network, and some preliminary findings of the analysis of

   the disaster flood of the state of china have been presented. The approach has been the application of the technique and it has been tested that the method is reliable and that the results are reasonableand stable.

   Moreover, the analysis has shown that the method has the potentiality to be used to identify the risks of natural disasters in some area. In view of the facts that the theoretic system of flood risk assessment has been developed enough so far, and the observed series of disasters are quite short or even unavailable, the method based on BP neural network adopted in the paper is indisputably an effective and practical method. This is a new attempt that the model is applied to the case of flood disaster, and more work is needed in order to draw some final lessons from the flood disaster.

6. Acknowledgments

This work is supported by a grant from the National Basic Research Program of China (Project No.2007CB714107), a grant from the Key Projects in the National Science and Technology Pillar Program (Project No. 2008BAB29B08), and a grant from the Special Research Foundation for the Public Welfare Industry of the Ministry of Science and Technology and the Ministry of Water Resources (Project No. 201001080).

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Tables and Figures:

Table 1: Values of flood indexes during 60 years

year

disaster area (thousand hectares)

inundated area (thousand hectares)

Dead Population

collapsed houses (ten thousand)

year

disaster area (thousand hectares)

inundated area (thousand hectares)

Dead Population

collapsed houses (ten thousand)

year

disaster area (thousand hectares)

inundated area (thousand hectares)

Dead Population

collapsed houses (ten thousand)

Table 3disaster degree estimations based on the BP network evaluation during the 60 years in China

Table 4Flood disaster risk evaluation values

Disasters level

Small flood

Medium flood

Large flood Extreme flood

Exceedance probability risk

1.0000 0.7269 0.3246 0.1180

Recurrence interval(years)

1.0000 1.3757 3.0807 8.4757

Table 5 Comparison of two methods