An Integrated Approach for Displacement Prediction of Landslides Based on the Data Mining and VMD-FOA-BPNN Model

: Landslide prediction is important for mitigating geohazards but is very challenging. The fluctuation of 32 reservoir water level and rainfall are the main external triggering factors controlling the deformation of riverine 33 landslides. In this paper, the Baishuihe landslide in the Three Gorges Reservoir area, which has a typical “step-like” 34 behavior, is taken as the study case, and an integrated approach for landslide displacement prediction combining data 35 mining and Variational Mode Decomposition, Fruit Fly Optimization Algorithm, Back Propagation Neural Network 36 (VMD-FOA-BPNN) is proposed. Nine triggering factors including the reservoir level and rainfall are extracted. First, 37 triggering factors and monthly velocity of the landslide are clustered into several categories by Two-step Clustering 38 (TSC). Then, Apriori algorithm is used to mine the association rules between triggering factors and monthly velocity, and 39 comprehensive contribution of each factor is calculated based on the data mining results. Next, the displacement of 40 monitoring point ZG93 and triggering factors are decomposed by VMD based on the time series analysis of the landslide. 41 Last, the trend term displacement is trained and predicted by the subsection functions, and FOA-BPNN models are used 42 to train and predict the periodic and random term. The prediction results show that, compared with the current popular 43 prediction models, the proposed model can effectively improve the prediction accuracy, which has high practicability and 44 application value in the study of landslide displacement prediction.


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Landslide prediction is important for mitigating geohazards but is very challenging, especially for the 49 mountain and reservoir area. Landslides are one of the worst types of natural disasters, which occur frequently 50 around the world (Hong et al. 2016;Juang et al. 2019). The Three Gorges Reservoir area is in the middle and upper 51 reaches of the Yangtze River. Since the impoundment of water began in 2003, the reservoir bank has experienced 52 periodic fluctuation of reservoir water level, which causes the rock and soil of the slope at the reservoir bank to 53 undergo a change of dynamic osmotic pressure repeatedly. This process has a great impact on the surrounding 54 regional geological environment, resulting in the deformation and destruction of the original stable reservoir bank, 55 and leading to the reactivation and deformation of many ancient landslides (Tang et al., 2019). The political, 56 economic, and social impact of a large hydropower hub is significant (Wu et al., 2017;Li et al., 2019). Therefore, it 57 is important to carry out the research on the riverbank landslides in the Three Gorges Reservoir area (Miao et al., 58 2018a). 59 The study of landslide displacement prediction is a hot topic at the cutting edge in engineering geology to select the appropriate inducing factor as the input layer to establish the model. In order to optimize the triggering 92 factors to find the most suitable factors for displacement prediction, data mining technology could be used. 93 In this paper, the Baishuihe landslide in the Three Gorges Reservoir area was taken as an example, and an 94 integrated approach for landslide displacement prediction combining data mining and VMD-FOA-BPNN was 95 proposed. A total of ten triggering factors were extracted. Two-step Clustering (TSC) and Apriori algorithm were 96 used to mine the association rules and comprehensive contribution of each factor. Based on the time series analysis 97 of landslides, the displacement of monitoring point ZG93 and triggering factors are decomposed by VMD. The 98 trend term displacement was trained and predicted by one-dimensional cubic subsection functions, and FOA-BPNN 99 models were used to train and predict the periodic and random terms. A flow chart is shown in Fig. 1. Apriori algorithm was first proposed by Agrawal and Srikant and has become the core algorithm of association 107 rule mining (Agrawal et al., 1994). This algorithm can deal only with categorical variables rather than numeric 108 variables. The algorithm mainly includes two steps: (1) generate frequent item sets that meet the minimum support; 109 (2) association rules that satisfy the minimum credibility are generated in the frequent item set generated in the first 110 step (Perego et al., 2001).

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Frequent item set T contains item a. If its support is equal to or greater than the support threshold specified by 112 the user, that is: 113 Then a is called frequent item set. The set including 1 item (length 1) is called frequent 1 item set, which is 115 recorded as L1. As shown in Fig. 2, a, b, c, d at the bottom layer can be called frequent 1-term set when the 116 minimum support degree is met. The frequent item set with k items is called frequent k item set, which is recorded 117 as Lk. The upper-level project sets ab, abc and abcd are frequent k-item sets when they meet the minimum support. 118 Apriori algorithm uses the iterative method of layer-by-layer search to generate frequent item sets. Frequent k-item 119 sets are used to explore and generate (k +1) item sets. The algorithm implementation process is shown in Fig. 2 Simple association rules are generated from frequent item sets, and association rules with confidence greater 125 than the threshold value are selected to form an effective rule set. For each frequent item set L, calculate the 126 confidence of all non-empty subsets L'. If is greater than the confidence threshold specified by the user, 127 that is: 128 Then, the association rule can be generated. 130

VMD 131
VMD (Variational Mode Decomposition) was proposed by Dragomiretskiy and Zosso based on the EMD 132 model (Dragomiretskiy and Zosso, 2013). VMD is an adaptive, completely non recursive method of modal 133 variation and signal processing. This technology has the advantage of determining the number of modal 134 decompositions. Its self-adaptability lies in determining the number of modal decompositions of the given sequence 135 according to the actual situation. In the subsequent search and solution process, it can adaptively match the optimal 136 center frequency and limited bandwidth of each mode, and can realize the effective separation of the intrinsic mode 137 function (IMF) and the division of the signal frequency domain, and then get the effective decomposition 138 components of the signal. Finally, optimal solutions of the variational problem can be obtained. The core idea of 139 VMD is to construct and solve the variational problem. 140 For the construction of variation, assuming that the original signal f(t) is decomposed into K components, the 141 corresponding constraint variation expression is: 142 where is the component obtained after decomposition; is the actual center frequency of each IMF 144 component; is the Dirac function; * is the Convolution operator; is the analytical signal of 145 each component; is the estimated center frequency of each analytical signal. 146 The Lagrange multiplication operator λ is introduced to solve Eq. (8), and the constrained variational problem 147 is transformed into the unconstrained variational problem, as following: 148 where λ is the Lagrange multiplier. 150 By using the alternative direction method of multipliers (ADMM), the saddle point of the above-unconstrained 151 model can be obtained, which is the optimal solution of the constrained variational model, so that the original 152 signal can be decomposed into IMF components.

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VMD overcomes the problems of end-point effect and modal component overlapping associated with the 154 EMD method, which has a more solid mathematical theoretical basis. It can reduce the non-stationary of time series 155 with high complexity and strong nonlinearity, and decompose multiple subsequences with different frequency 156 scales and relatively stationary, which are suitable for non-stationary sequences. The steps of the FOA process are as follows:

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(2) Give individuals random distance and direction to search for food by olfaction.

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(3) Since the position of food cannot be known, the distance from the origin (Dist) should be estimated first, 168 and then the taste concentration judgment value (S) is calculated, which is the reciprocal of the distance.

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(4) S was substituted into the taste function (or Fitness function) to get the taste concentration of the individual 170 position.

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(5) Identify the fruit fly with the highest taste concentration in these populations.

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(6) The coordinates of the best taste concentration value are reserved, and then the fruit fly population flies to 173 this position by vision. 174 (7) Enter the iterative optimization process. Repeat steps (2)-(5) and judge whether the taste concentration is 175 better than that of the previous iteration. If so, carry out the step 6. pattern classification and excellent multi-dimensional function mapping. It solves "exclusive or" (XOR) and some 181 other problems that simple perceptron can't solve. In terms of structure, BPNN has an input layer, a hidden layer, 182 and an output layer. BP algorithm takes the square of network error as the objective function and uses gradient 183 descent method to calculate the minimum value of the objective function. 184 The basic BPNN includes two processes: the forward propagation of signal and the back propagation of error. 185 That is to say, the error output is calculated according to the direction from input to output, while the adjustment of 186 weight and threshold is carried out from output to input. In the forward propagation, the input signal acts on the 187 output node through the hidden layer and generates the output signal through a nonlinear transformation. If the 188 actual output does not match the expected output, the error is transferred into the back-propagation process. Error 189 retransmission occurs when the output error is retransmitted to the input layer by layer through the hidden layer, 190 and the error is allocated to all cells of each layer, and the error signal obtained from each layer is used as the basis 191 for adjusting the weight of each cell. By adjusting the connection strength between the input node and the hidden 192 layer node, the connection strength between the hidden layer node and the threshold value, the error is reduced Baishuihe Landslide is shown in Fig. 3 and 4. 209  3

.2 Deformation of the landslide 217
The Baishuihe Landslide has been monitored since the reservoir water level reached 135 m in June 2003, and 218 the monitoring surface layout is shown in Fig. 3(b). According to the characteristics of surface monitoring 219 displacement and surface macro deformation, Baishuihe Landslide was divided into two areas: (1) the active area 220 (area A) is the middle and front part of the landslide with strong deformation. After the completion of the Three 221 Gorges Dam, the landslide has produced obvious displacement due to the impoundment of the reservoir. Several was synchronous. The monitoring period of ZG93, ZG118 and XD01 was long, which was representative and can 239 reflect the whole movement process of the landslide. Therefore, in this paper, these three points were taken for 240 detailed analysis (Fig. 6). According to the filling scheduling of the reservoir, the monitoring data can be divided 241 into 3 stages for analysis: 242 ( and 30.6 mm respectively during the three impoundment periods. The reservoir basically maintains the highest 245 water level from November to January of the next year, and the maximum monthly displacement rates of these 246 three points were under 13 mm/month respectively, which was relatively slow. The water level began to drop in 247 February every year and reached the lowest level (135 m) in July. During this period, the minimum increase of 248 these three points was over 80 mm, and the maximum increase was over 150 mm. Especially in May and June, the 249 increase rate of landslide displacement was the largest. From the end of July to the beginning of September, the 250 reservoir water level maintained the lowest level, but the landslide displacement first continued to grow rapidly and 251 then basically remained the same. It can be observed that a heavy rainfall in July 2005 did not increase 252 The fluctuation of reservoir level and rainfall are usually the main triggering factors affecting the deformation 275 of the reservoir bank landslide. In this paper, ZG93 monitoring data was selected for the following reasons: (1) 276 ZG93 was the earliest deformation monitoring point with complete monitoring period; (2) ZG93 monitoring point 277 was in the middle of the landslide, which can basically reflect the deformation trend of the landslide. Monitoring 278 points ZG93, ZG118 and XD01 have similar deformation characteristics. Therefore, monitoring data of points 279 ZG118 and XD01 were added to increase the sample size and overcome model overfitting error, as well as to 280 provide a better representative prediction of the overall landslide displacement. In this research, a total of ten 281 triggering factors were selected to carry out displacement prediction research, including five reservoir level related 282 factors, four rainfall related factors, and one deformation factor, as shown in Table 1. Among them, nine factors 283 related to reservoir water level and rainfall were external triggering factors, while the deformation rate of the last 284 month (F10) was an internal factor, which could reflect the deformation and failure of the landslide itself.    Tables 2 and 3. 293 Monthly velocity (v) was clustered into three categories (Low V1; Medium V2; High V3), as shown in Table 4. 294 295

Data mining and association rules 302
In the data mining process, nine triggering factors of the landslide (h, , , , 303 , , , , ) were set as the former item of association rules, and the deformation rate 304 (Monthly velocity v) was set as the consequent item. In the Apriori algorithm, the minimum conditional support 305 was set to 0.01, and the minimum rule confidence was set to 100% (ensure that the mining association criteria were 306 absolutely correct). A total of 5447 association rules were generated, most of which were V1 and V2 stages of the 307 landslide (4247 and 1008 respectively). The main factors controlling V1 deformation of the landslide were smooth 308 fluctuation of reservoir level and weak rainfall. The main factors controlling the V2 deformation of the landslide 309 were the sharp fluctuation of reservoir water level and medium~heavy rainfall. And the main factor controlling the 310 V3 deformation of the landslide was heavy rainfall. According to the Baishuihe landslide monitoring data, rainfall 311 was generally concentrated in June to September every year, and the reservoir was controlled from high water level 312 to low water level before this period. In other words, there was a certain negative correlation between monthly 313 rainfall and monthly average water level elevation. This period was also the time when the landslide deformation 314 was severe. 315 Statistics results of the data mining and association rules are shown in Table 5. Total support, average support, 316 and contribution without support of each triggering factor were counted, and the comprehensive contribution was 317 the mean value of these three contributions. Comprehensive contribution of each factor according to the association 318 rules is shown in Fig. 7. Factors with contribution degree less than 0.3 were eliminated and were not used as input 319 layer in the prediction model. Therefore, eight triggering factors were taken as the input layer in the V1 and V3 320 prediction models (F1, F3, F5, F6, F7, F8, F9, F10), and eight triggering factors were taken as the input layer in the 321 V2 prediction model (F1, F2, F5, F6, F7, F8, F9, F10). 322 323

VMD decomposition 329
Before using VMD to decompose the displacement of ZG93, it is necessary to know the modal number K in 330 the object to be decomposed in advance. In order to ensure that each component obtained by decomposition has 331 practical physical significance and reduce the possibility of false components, according to the time series theory of 332 landslide deformation, landslide displacement can be divided into three parts: 333 Where is the observed value of landslide displacement, is the trend displacement, is the periodic 335 displacement and is the random displacement. 336 Therefore, K = 3 was determined when the landslide displacement was decomposed. At the same time, in 337 order to ensure the fidelity of the displacement time series after decomposition, aiming at the decomposition effect 338 (residual term) of displacement decomposition, the penalty parameter a and the rising step τ (a = 1.5 and τ = 0.1) 339 were finally determined through multiple trials. Using the above parameter settings to decompose the displacement 340 data, the decomposed high-frequency component corresponds to the random displacement, the low-frequency 341 component corresponds to the periodic displacement, and the residual component corresponds to the trend 342 displacement. Composition of training and prediction samples are shown in Table 6. 343 When decomposing the triggering factors, K was set to 2. In order to ensure the time sequence of these factors 344 after decomposing, in this paper, decomposition effect of low-frequency factors was set as the object, and the 345 penalty parameter a and the rising step τ were finally determined through multiple trials (a = 700, τ = 0.5), as 346 shown in Fig. 8. 347 348

Displacement prediction 354
Trend term prediction 355 The displacement of the trend term showed a distinct piecewise function. Therefore, the trend term of ZG93 The fitting and prediction curves of the trend term are shown in Fig. 9, and the parameters of the fitting 361 functions are shown in Table 7. It can be known that the prediction accuracy R 2 of the trend term was over 99%,  368

Periodic and random term prediction 369
The FOA-BPNN was used to train and predict the periodic and random terms of the ZG93 displacement. In 370 the FOA algorithm, the population size (p) was set as 10, and the iterations of FOA (k) was set to 1000. In the 371 BPNN model, the hidden layer of the neural network was set to 12 based on multiple attempts. A total of six 372 FOA-BPNN models were built, including individual periodic prediction models for V1, V2, and V3, and individual 373 random prediction models for V1, V2, and V3. Training and prediction results for the periodic and random terms 374 are shown in Fig. 10. 375 It can be known that the FOA-BPNN models established in this paper have achieved good accuracy in the 376 prediction of periodic and random displacement of the Baishuihe landslide. From the results of residual error 377 analysis, in the training process of the model, the residual error of displacement was relatively stable, which also 378 verified the robustness and reliability of the model. For the prediction samples, there were some fluctuations in the 379 residual error. The prediction accuracy of the model is analyzed in Discussion section. 380

Total displacement 381
Prediction results of the total displacement of landslide can be obtained by summation the trend term, periodic 382 term, and random term of displacement, as shown in Fig. 11. It can be known that the prediction model established 383 in this paper has achieved good accuracy in the total displacement of monitoring point ZG93. Residual error results 384 showed that in June 2007, there was a big difference between the total displacement training value and the actual 385 value, resulting in the obvious mutation of the residual error. This was because in the three parts of landslide 386 displacement (trend, periodic, random), the trend displacement accounts for more than 85%. In June 2007, it was 387 the boundary between Phase 1 and Phase 2, where there were some differences in the training results of the two 388 polynomial fitting functions, resulting in a large residual error in the total displacement. For the prediction samples, 389 the residual error was relatively stable.

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When the time series analysis method is used to predict the landslide displacement, the trend displacement is 399 relatively easy to be predicted. Therefore, choosing the appropriate periodic displacement prediction model is the 400 key to improve the effect of landslide displacement prediction. The landslide prediction model has experienced 401 rapid development in the past 50 years, and various machine learning models have been widely used in landslide 402 displacement prediction. However, each algorithm has its limitations. For instance, SVM has low computational 403 complexity, but it is sensitive to the choice of parameters and kernel function. Decision Tree model does not need 404 any prior assumptions on the data, but the demand for sample size is relatively large, and the function of dealing 405 with missing values is quite limited. ELM uses the principle of least square and pseudo inverse matrix to solve the 406 problem, which is only suitable for single hidden layer neural network. BPNN has strong self-learning, 407 self-adaptive ability, and good generalization ability, but it is prone to slow convergence. Therefore, it is of 408 profound significance to select the appropriate optimization algorithm to optimize the machine model for the 409 accuracy of displacement prediction of landslides. In this paper, based on the VMD and data mining results, the 410 FOA-BPNN was used to predict the periodic and random term of monitoring point ZG93 displacement. BPNN, 411 SVM, and ELM algorithms were chosen as the comparison models (Model 2~4). Performance of various 412 displacement prediction models of the Baishuihe landslide are shown in Table 8 and Fig. 12. The prediction 413 accuracy of the FOA-BPNN model was the highest. The R 2 reached 0.977, and its RMSE was only 10.041. In 414 contrast, the proposed model can improve the accuracy of landslide displacement prediction.. In this paper, ZG93 monitoring data was selected for displacement prediction, and the monitoring data of 422 points ZG118 and XD01 were added to increase the sample size and overcome model overfitting error, as well as to 423 provide a better representative prediction of the overall landslide displacement. The accuracy of various models for 424 ZG93 displacement prediction has been discussed. The monitoring points of ZG118 and XD01 in 2016 were used 425 for the model validation. Measured and prediction displacements of ZG93, ZG118, XD01 are shown in Fig. 13. R 2 426 between the measured and prediction displacements of ZG118 and XD01 were 0.977 and 0.978. RMSE of these 427 two monitoring points were 12.40 and 16.04 respectively. It can be seen that the model proposed in this paper has 428 achieved ideal results for the displacement prediction of different monitoring points of landslide, which has high 429 practicability and application value in the study of landslide displacement prediction. However, it's worth noting 430 that due to the small amount of displacement data in V3 state of monitoring point (Table 6), the prediction results of 431 XD01 have obvious errors in July 2016. Therefore, in order to obtain more ideal prediction results, the monitoring 432 data of various states should be supplemented as much as possible. In this paper, the Baishuihe landslide, which has a typical "step-like" behavior, was taken as an example, and 438