The Chi-Chi earthquake in 1999 caused tremendous landslides which triggered many debris flows and resulted in significant loss of public lives and property. To prevent the disaster of debris flow, setting a critical rainfall line for each debris-flow stream is necessary. Firstly, 8 predisposing factors of debris flow were used to cluster 377 streams which have similar rainfall lines into 7 groups via the genetic algorithm. Then, support vector machines (SVM) were applied to setup the critical rainfall line for debris flows. SVM is a machine learning approach proposed based on statistical learning theory and has been widely used on pattern recognition and regression. This theory raises the generalized ability of learning mechanisms according to the minimum structural risk. Therefore, the advantage of using SVM can obtain results of minimized error rates without many training samples. Finally, the experimental results confirm that SVM method performs well in setting a critical rainfall line for each group of debris-flow streams.
Taiwan is a mountainous island with very steep terrain and fragile geology. The extremely heavy rainfall caused by typhoon and Mei-Yu yearly often lead to large-scale debris flow disasters in mountains of Taiwan. Especially after the Chi-Chi earthquake in 1999, a lot of landslides have occurred in the center of Taiwan. These tremendous landslides often lead to the amount of sediment material on the streambed in the initiation area of debris flow. These sediment material will mobilize by the rainfall and cause numerous debris flow disasters which result in significant loss of public lives and property in the following rainy or typhoon seasons. Furthermore, the landslides triggered by the Chi-Chi Earthquake will have a significantly upward trend in scale and frequency. It means that the debris flow disasters have been more unpredictable and destructive with the amount of sediment material. As if the literature of Shieh et al. (2009), it showed that the numerous landslides triggered by Chi-Chi Earthquake caused a lot of debris-flows and lowered the rainfall threshold of these debris-flows in subsequent years. Nakamura et al. (2000) also indicated that there was a huge number of landslides for about 42 years after the Kanto earthquake in Japan, and almost every landslides during that time induced server debris-flow disasters, presented in Fig. 1.
Thus, in order to prevent the disaster of debris flow, setting a critical rainfall line for each debris-flow stream is necessary. In this research, we aims to setting a critical rainfall line for each debris-flow stream via a series of statistical method. Firstly, 377 debris-flow streams in the center of Taiwan affected by Chi-Chi earthquake was considered. Then, 8 predisposing factors of debris flow were used to cluster streams into 7 groups via the genetic algorithm. After streams with similar characteristics were clustered together, support vector machines (SVMs) were applied to setup the critical rainfall line for each debris-flow clusters. Finally, the experimental result shows that SVM method performs well in setting a critical rainfall line for each group of debris-flow streams.
The Chi-Chi earthquake occurred in 1999 in Taiwan caused numerous landslides, the blocks of these landslides were up to 2365 units and the area were approximate 14 347 ha, represented in Fig. 2a. These landslides mostly located in the mountains of central Taiwan. The debris flow streams triggered by the landslides which affected seriously by the Chi-Chi earthquake were studied in the experiments. 377 debris flow streams were chosen from 7 counties included Nan-Tou county, Maio-Li county, Taichung City, Taichung county, Chun-Chua county, Yun-Lin county and Chia-Yi county, represented in Fig. 2b.
According to Shieh and Tsai (2001), 8 important characteristics of the
377 debris-flow streams including rock type (
In order to cluster the 377 debris flow streams into different groups, the
statistical data including geographical information, hydrological
information, historical data of disaster and statistical tables of eight
predisposing factors have to preprocessed. The preprocessing involved
presentation of the data, normalization of the data and the measurement of
the distance between two debris-flow streams. Equation (1) represents the
normalization of the data (
After the data were normalized, the distance between two debris-flows could
be calculated. The centered Person correlation was used to define the
distance
This section aims to cluster 377 debris-flow streams into seven groups via clustering analysis such that streams in each group have similar characteristics. An efficient clustering algorithm was considered for describing debris flows in order to illustrate the relationships by constructing a binary hierarchical tree. This approach was employed to group 377 debris flow streams into seven groups such that the critical rainfall line in the same group could be set. Many approaches to constructing binary hierarchical trees have been proposed. For example, Ward's method (Ward, 1963), the single-linkage method (Sibson, 1973), the average-linkage method (Defays, 1977), and the average-linkage (Voorhees, 1986) hierarchical clustering approach have been extensively applied in various fields to approximate such trees, including the fields of document clustering (Willet, 1988) and bioinformatics (Eisen et al., 1998; Alizadeh et al., 2000).
In this study, a means of family competition genetic algorithm (FCGA) was presented to construct a hierarchical tree of streams. The FCGA combines family competition, neighbor-join mutation (NJ) and edge assembly crossover (EAX) (Nagata and Kobayashi, 1997). The concepts of family competition have been successfully applied to solve numerous continuous parameter optimization problems, including protein docking (Yang and Kao, 2000). In the authors' earlier work (Tsai et al., 2001), family competition and EAX were successfully integrated to solve traveling salesman problems (TCPs). Neighbor-join mutation (Tsai et al., 2002) was developed to coordinate with the EAX and thus balance exploration and exploitation. The primary difference between the method in this study and that in our previous work is in the integration of these three mechanisms.
The experimental results revealed that the FCGA is a promising method for
constructing the optimal tree of streams. Figure 3 presents the seven groups
of 377 debris-flow streams. In Fig. 3a–g, the
When the streams with similar characteristics have clustered together, the critical rainfall line of debris flow could be set via SVM. SVM is a new machine learning approach proposed by Vapnic (1998) based on statistical learning theory. The advantage of SVM is that this theory raises the generalized ability of learning mechanisms according to minimize the structural risk. Therefore, we can obtain the results with minimum error rates and without many training samples. Otherwise, SVM is an optimized algorithm which can rapidly performed by a standard programming algorithm and obtained the global optima. The SVM has been widely applied in many disciplines to solve the problems of classification and regression in the field of hydrological engineering (Yu et al., 2011; Lin and Chen, 2011; Shen et al., 2011). This study tried to establish the critical rainfall line of debris flow via SVM.
In this study, each data of debris flow stream were consider as a vector or a point in a multidimensional space. The destination of this research is to find a hyper-plane which can separate the vectors into two parts, according to the occurrence of debris flow, represented in Fig. 4.
However, two problems have encountered frequently in most cases during the process of classification. Figure 5 shows the two problems, it is likely that there are many hyper-planes existed in the multidimensional space, or it does not have any hyper-plane could separate the training data into two parts exactly.
Therefore, we switched these training data to a higher dimensional space
called feature space via a non-linear function
This section describes the result of the proposed method SVM to establish the critical rainfall line for each group of debris flows. When the debris flow streams with similar characteristics have clustered together into seven group, the critical rainfall line of each debris-flow group could be set via SVM. Figure 7a–g shows the critical rainfall line of group A, group B, group C, group D, group E, group F and group G, respectively. In Fig. 7, the blue dots represent the rainfall data with debris flow events and the purple dots symbolize the rainfall data without debris-flow event. The green zone represents a range of hazardous area with debris flow. In contrast, the black zone represents a range without debris flow. The boundary between the green area and black region stands for a critical rainfall line of each debris flow groups.
Compared with the critical rainfall lines of each groups respectively, it
could find that the critical rainfall lines of group D and group F were
lower than others, showed in Table 2. It is likely that the group F have a
higher landslides ratio (
This study aims to set up the critical rainfall line of debris flows via a series of statistical methods. 377 debris-flow streams in the center of Taiwan affected by Chi-Chi earthquake and 8 predisposing factors of debris flow were considered. Firstly, 377 debris flow streams were clustered into 7 groups with similar characteristic via family competition genetic algorithm, then support vector machine was used to set up the critical rainfall line of each debris flow groups. The results reveal that SVM can establish the critical rainfall lines of debris flow successfully and the critical rainfall lines were set according to the characteristic of each debris flow groups. Hence, the method proposed in this study can be an effective instrument for establishing critical rainfall lines. In the future, the weights and the interactions of the predisposing characteristics would be the focus of research.
This work was supported by the National Science Council of Taiwan (Grant No.: NSC-94-2211-E-152-001 and NSC 93-2211-E-152-001).
The statistical table of 8 characteristics with 377 streams.
The value of critical rainfall line of each debris flow groups.
The statistical information of the landslides after the Kanto earthquake in Japan (Nakamura et al., 2000).
The results of clustering analysis on 377 debris-flow streams.
The multidimensional space with vector of debris-flow.
The examples of problems encountered in most cases.
An example of maximum margin hyper-plane and support vector.
The result of our research tested on 7 groups.