Data-Driven Deformation Prediction of Accumulation Landslides in the Middle Qinling-Bashan Mountains Area

By inergency On Feb 3, 2024

2.1. Classification of Landslides Method

Landslides are formed in different geological environments, and manifested in different forms and features; all types of landslides have their own development and evolution process and law, and there are significant differences in the sliding law presented by different influencing factors. There are many existing classification standards for landslides and many scholars have studied the classification of landslides over the years. Classification of landslides according to material composition is one of the most commonly used means of classification at home and abroad, classifying landslides into rocky and soil landslides, of which soil landslides include stockpiled soil landslides, loess landslides, clayey soil landslides, and landfill landslides, etc. Varnes (1978) [20] categorized slope movements based on rock and soil movement characteristics into falls, topples, slides, lateral spreads, flows, and complex movements. Liu Guangrun (1992) [21], in his study on major geological and seismic issues in the Three Gorges of the Yangtze River, classified slope structures based on the relationship between structural planes and the slope surface into dip-slope normal, dip-slope reverse, and inverse slope types. Liu Guangrun and Xu Kaixiang (1993) divided slope deformations into natural and anthropogenic dynamics based on different causative factors. Wang Lansheng, Zhang Zhuoyuan, et al. (1994) [22] proposed five basic combination models for the deformation mechanism of slopes composed of layered or layer-containing rock bodies: creep-shear, slip-induced tension cracking, bending-tension cracking, plastic flow-tension cracking, and slip-bending. Yan Tongzhen et al. (1994, 2000) [23] summarized nine types of sliding mechanisms based on the initial conditions, fundamental causes, and apparent sliding modes of landslides: rheological overturning landslide, stress release translational landslide, vibration collapse or liquefaction landslide, subsidence landslide due to erosion, geochemical suspension-sinking landslide, high potential energy leapfrog landslide, pore water pressure floatation landslide, erosion-loading landslide, and giant high-speed long-runout landslide. Liu Guangrun et al. (2002) [24,25] proposed a comprehensive and systematic landslide classification system for the first time, based on the characteristics of the landslide body, deformation dynamics, and activity features, offering a detailed classification of landslides.

In recent years, the landslide classification system has continually evolved and developed, gradually forming a comprehensive classification system based on “category, size, type, mode, and stage”. The type of landslide mass (material structural composition) is classified by “category”, which includes rock landslides, soil landslides, and accumulation layer landslides, further subdivided based on material composition and the relationship between structural planes and slope surfaces. Rock landslides include rock layer-conformable, rock layer-nonconformable, and rock cross-layer landslides. Soil landslides include loess, clayey soil, and man-made fill landslides. Accumulation layer landslides include colluvium and talus landslides. The scale of the landslide is categorized by “size”, dividing landslides into nine types based on landslide volume and landslide mass thickness, ranging from small to gigantic, and shallow to super-deep. The causative forces are classified by “type”, with nine types of causative forces divided into natural and anthropogenic. The deformation movement characteristics and failure modes are sorted by “mode”, classifying landslides based on kinematic features, dynamic characteristics, and deformation failure modes. The development stage of the landslide is classified by “stage”, distinguishing between new and reactivated landslides in terms of their evolutionary stages. The research group based on the aforementioned geological model carries out a refined classification of accumulation layer landslides in the middle Qinling–Bashan Mountains (Figure 1).

2.2. Model Construction Method

For on-site landslide monitoring data, processing such as data partitioning is performed. According to the characteristics of time variables, data can be divided into time-series and non-time-series data, and preprocessing is conducted based on the unique attributes of the two datasets. The landslide basic survey table records non-time-series data, including landslide scale, thickness, volume, quantity, and basic information on deformation movement characteristics. On the other hand, landslide monitoring data, such as surface displacement, rainfall, and tilt, constitute time-series data. The model needs to be capable of processing time-series data while also possessing good interpretability to assist professional technical personnel in monitoring and early warning of geological disasters, and understanding the influencing factors in landslide deformation [26]. Deep learning models have difficulty interpreting the relationship between prediction results and input features.

Predictive methods based on individual slopes are closely related to historical data and struggle to reveal the characteristics of landslide movement over the complete lifecycle. Similar-type landslide prediction models consider the interpretability of the model, the landslide’s primary influencing factors, and the characteristics of landslide movement throughout the lifecycle of similar landslides to construct a predictive model based on the concept of similar-type landslides. This predictive model mainly consists of two steps: the first step uses the XGBoost machine learning model for feature importance analysis, with the analyzed results serving as feature input for subsequent deformation prediction. The second step employs the LSTM deep learning model to output predictions.

The XGBoost decision tree algorithm [27] can calculate the importance of each input feature to the final prediction result. The greater the weight of feature importance, the more significant its impact on the prediction outcome. Thus, this model is selected for feature importance analysis. Additionally, XGBoost is known for its efficiency, flexibility, and robustness: it employs parallel processing to rapidly train large datasets, it can handle both numerical and categorical features, and it is capable of managing missing values.

The XGBoost objective function is shown in Equation (1):

$L (ϕ) = \sum_{i} l (y_{i}, {\hat{y}}_{i}) + \sum_{k} Ω (f_{k})$

(1)

where $Ω$ (f_k) as shown in Equation (2):

$Ω (f_{k}) = γ T + \frac{1}{2} λ {‖ω‖}^{2}$

(2)

contains the regularization term, ${\hat{y}}_{i}$ is the output of the model, y_i is the true label, f_k denotes the kth base classifier, T is the number of leaves in the tree, ω denotes the score in the corresponding leaves, and γ is the penalty term.

Expanding Equation (1) using Taylor’s formula yields Equation (3):

$L^{(t)} = \sum_{i = 1}^{n} [g_{i} f_{t} (x_{i}) + \frac{1}{2} h_{t} {f_{t}}^{2} (x_{i})] + Ω (f_{t})$

(3)

The formula g_i is the same as h_t and

Ω

(f_t). The expression equations are Equations (4)–(6), respectively, as follows:

$g_{i} = \partial_{{\hat{y}}_{i} (t - 1)} l (y_{i}, {\hat{y}}_{i}^{(t - 1)})$

(4)

$h_{i} = {\partial^{2}}_{{\hat{y}}_{i}^{(t - 1)}} l (y_{i}, {\hat{y}}_{i}^{(t - 1)})$

(5)

$Ω (f_{t}) = γ T + \frac{1}{2} λ \sum_{j = 1}^{T} ω_{j}^{2}$

(6)

Substituting Equations (4)–(6) into Equation (3) yields the leaf node weight formula shown in Equation (7):

$ω_{j}^{*} = - \frac{G_{j}}{H_{j} + λ}$

(7)

G_j and H_j denote the values of first-order gradient and second-order gradient at the leaf nodes, respectively; the optimal solution of the objective function is obtained by bringing Equation (7) into Equation (3) as shown in Equation (8):

${\hat{L}}^{*} = - \frac{1}{2} \sum_{j = 1}^{T} \frac{G_{j}^{2}}{H_{j} + λ} + γ T$

(8)

Landslide deformation prediction primarily focuses on forecasting time-series data for surface displacement [28]. The Long Short-Term Memory (LSTM) network algorithm, compared to traditional Recurrent Neural Networks (RNNs), is more adept at addressing gradient vanishing problems in long sequences. It can handle longer sequence data and better capture long-term dependencies within sequential data. Its time sensitivity enables more effective learning of the features in time-series data [29]. The plan is to apply a hybrid XGBoost and LSTM model to landslide deformation prediction to enhance the accuracy of predictions while also achieving model interpretability [30,31,32].

LSTM [33] introduces a memory cell that stores and accesses information and controls the flow of information through a gating mechanism. The key parts of LSTM include input gate, forget gate, and output gate (Figure 2).

The first step in LSTM is to decide what information we need to throw away from the cell state. This decision is made by a sigmoid layer called the forget gate. With the inputs $h_{t - 1}$ and $x_{t}$ it outputs a number between 0 and 1. An output of 1 means “keep this value completely” and 0 means “throw this value away completely”.

The forgetting gate is calculated as in Equation (9).

$f_{t} = σ (W_{f} \cdot [h_{t - 1}, x_{t}]) + b_{f}$

(9)

The second step is to decide what kind of information we need to store in the cell state. There are two parts to this problem. First, the sigmoid layer calls an “input gate” to decide what data needs to be updated. Then, a tan h layer creates a vector ${\tilde{C}}_{t}$ as new candidate value that can be added to the state. In the next step, we want to merge these two parts to create an update to the state.

The input gate is calculated as in Equations (10) and (11):

$i_{t} = σ (W_{i} \cdot [h_{t - 1}, x_{t}]) + b_{i}$

(10)

${\tilde{C}}_{t} = \tan h (W_{c} \cdot [h_{t - 1}, x_{t}]) + b_{c}$

(11)

The forgetting gate and input gate are combined as in Equation (12):

$C_{t} = f_{t} * C_{t - 1} + i_{t} * {\tilde{C}}_{t}$

(12)

Finally, we need to decide what we want to output. This output is based on our cell state but will be a filtered value.

The output gate is calculated as in Equations (13) and (14):

$o_{t} = σ (W_{o} \cdot [h_{t - 1}, x_{t}]) + b_{o}$

(13)

$h_{t} = o_{t} * \tan h (C_{t})$

(14)