The narrowing deformation of reservoir valley during the initial operation period threatens the long-term safety of the dam, and an accurate prediction of valley deformation (VD) remains a challenging part of risk mitigation. In order to enhance the accuracy of VD prediction, a novel hybrid model combining Ensemble empirical mode decomposition based interval threshold denoising (EEMD-ITD), Differential evolutions—Shuffled frog leaping algorithm (DE-SFLA) and Least squares support vector machine (LSSVM) is proposed. The non-stationary VD series is firstly decomposed into several stationary sub-series by EEMD; then, ITD is applied for redundant information denoising on special sub-series, and the denoised deformation is divided into the trend and periodic deformation components. Meanwhile, several relevant triggering factors affecting the VD are considered, from which the input features are extracted by Grey relational analysis (GRA). After that, DE-SFLA-LSSVM is separately performed to predict the trend and periodic deformation with the optimal inputs. Ultimately, the two individual forecast components are reconstructed to obtain the final predicted values. Two VD series monitored in Xiluodu reservoir region are utilized to verify the proposed model. The results demonstrate that: (1) Compared with Discrete wavelet transform (DWT), better denoising performance can be achieved by EEMD-ITD; (2) Using GRA to screen the optimal input features can effectively quantify the deformation response relationship to the triggering factors, and reduce the model complexity; (3) The proposed hybrid model in this study displays superior performance on some compared models (e.g., LSSVM, Backward Propagation neural network (BPNN), and DE-SFLA-BPNN) in terms of forecast accuracy.
With a number of high arch dams that have been constructed for the development of hydropower resources in Southwest China [
The evolution of slope deformation is a nonlinear dynamic process triggered by various factors (e.g., geological conditions, external hydraulic environment, and earthquakes) [
Besides the model parameters optimization, suitable preprocessing of the non-stationary time series with many noises is the other main foci. The commonly used Wavelet transform (WT) and Empirical mode decomposition (EMD) methods have achieved good prediction performance in many research cases combined with ML [
In this study, we proposed a novel hybrid model that combines EEMD-ITD, Grey relational analysis (GRA), and DE-SFLA-LSSVM for VD forecasting by considering triggering factors, including reservoir level fluctuation, precipitation and temperature. EEMD is firstly exploited to decompose the raw sequence into multiple Intrinsic mode functions (IMFs) and a residue. The special IMFs are denoised by ITD, and the denoised series is divided into the trend and periodic components, which makes the periodic characteristics distinct. Then, GRA is employed to extract the optimal features from potential triggering factors, which can reduce the dimension of the inputs and accelerate the training rate. Finally, DE-SFLA-LSSVM is applied to predict the trend and periodic deformation with optimal inputs separately, and the individual forecast results are reconstructed to obtain the final deformation prediction. Two VD series monitored in Xiluodu reservoir region are utilized to take experiments. Furthermore, the forecasting performance of the proposed approach is verified and evaluated by comparing with conventional methods, including LSSVM, ABC-LSSVM, Backward propagation neural network (BPNN), and DE-SFLA-BPNN.
EEMD is a noise-assisted enhancement of EMD [
Given the amplitude of added white noise and the ensemble number of trials, add a group of white noise series
where
2. Decompose the series
3. Repeat steps 1–2 with the different scales of white noise, and the root mean square of white noise in each trial is equal.
Finally, ensemble means of the corresponding IMFs gives the decomposing result, the original time series
where
Inspired by the wavelet threshold denoising principle, an alternative thresholding denoising procedure termed EMD direct thresholding (EMD-DT) was applied to the decomposed IMFs to enhance the denoising performance. However, EMD-DT can result in discontinuity consequence of the denoised signal [
where
Followed by the above procedures, the denoised signal
where
where low MSE value indicates the denoised signal
LSSVM is a nonlinear regression-forecasting algorithm proposed by Suykens et al. [
In an LSSVM model, considering the given training dataset of
subjected to the equality constraints:
where
where
where
where
SFLA is a meta-heuristic optimization algorithm with excellent global search capability, which can be integrated with LSSVM to improve computational efficiency and accuracy. SFLA starts from a randomly generated initial population consisting of
In this study, DE-SFLA is used to optimize the regularization parameter
Set parameters of the DE and SFLA algorithms. Then the initial population of
All frogs are sorted in descending order according to the fitness values calculated using LSSVM and partitioned into
In the memetic evolution, frog with the worst fitness value in a memeplex is updated with the new frog, which is produced by DE with mutation, crossover, and selection operators, while the optimal global solution is updated by SFLA.
The local evaluation and global shuffling continue until convergence criteria are satisfied, and the best frog in the whole population is identified as the optimal solution.
Export the optimal solution to the LSSVM model for deformation forecasting.
To improve model performance in the VD forecasting, we proposed a novel hybrid model based on the idea of decomposition and integration.
Xiluodu hydropower station is located at the Xiluodu canyon of Jinsha river, which is between Yongshan County of the Yunnan Province and Leibo County of the Sichuan Province. The Xiluodu dam is a concrete double curvature arch dam with a maximum height of 285.5 m and a dam crest elevation of 610.0 m. The normal impoundment water level and dead water level of Xiluodu reservoir are 600.0 m and 540.0 m, respectively. As presented in
For simplicity and better understanding, the reservoir storage depth (RSD) is defined as the elevation difference between the reservoir level and the riverbed foundation (at an elevation of 324.50 m) to represent the reservoir level fluctuation. According to the field monitoring, the survey line VD03 at the upstream contracted a maximal deformation of 89.54 mm, besides the arch dam structure is particularly sensitive to shrinkage deformation at the abutment. Moreover, the survey line VD05, which is installed downstream and located far away from the dam, can be less affected by the hydraulic structures. Therefore, in this study, the recorded VD time series of VD03 and VD05, RSD, precipitation, and atmospheric temperature from December 2012 to October 2018 are selected for model training and testing.
As shown in
Since a lack of measured deformation values from December 2012 to May 2013, the dataset from May 2013 to October 2018 was used in this study. EEMD was first performed in MATLAB to decompose the original deformation series of VD03 and VD05 into several IMFs and a residue, respectively. In EEMD, an ensemble member of 100 was used, and the added Gaussian white noise in each ensemble member had a standard deviation of 0.2.
According to the ITD procedure,
The denoised deformation series and the recorded external triggering factors datasets (precipitation, temperature, and RSD) of 65-month were used for the prediction model establishing and validating. The first 55-month dataset was adopted for model training, while the remaining 10-month dataset was employed for model validation. The two denoised IMFs and the remaining three IMFs were reconstituted as the periodic deformation component, and the residue is considered as the trend deformation. Therefore, DE-SFLA-LSSVM models are separately applied to predict the two components with different optimal inputs. It is noted that the validation data is not considered in establishing the forecasting model, and thus the performance of the validation period can represent the real application effect. Therefore, we pay more attention to the forecast performance of the validation period, and just the forecast results of the validation period are shown in the following sections.
As shown in
Three indicators to evaluate model accuracy and prediction ability in this study consist of the root mean square error (RMSE), mean absolute percentage error (MAPE), and correlation coefficient (R). These indicators are defined as follows:
For VD03, the value of RMSE, MAPE and R is 0.104, 0.106, and 0.999, respectively. The optimal parameters
In order to effectively reconstruct the evolution characters of VD, the mechanics and triggering factors can be considered carefully. According to the analysis of the relationship between the deformation and the external influencing factors in Section 3.2, a total of 13 initial triggering factors were considered [
The fluctuation of RSD: in consideration of the lag period of the seepage field adjustment corresponding to reservoir operation, the current RSD (J_{1}) and the average fluctuation rate of RSD over the past 15 days (J_{2}), 30 days (J_{3}), and 60 days (J_{4}) were adopted as the RSD factors.
Precipitation: the cumulative antecedent precipitation during the last 15 days (J_{5}), 30 days (J_{6}), and 60 days (J_{7}) were selected as the precipitation factors due to the slow process of precipitation infiltration.
Water temperature: the atmospheric temperature in the reservoir region was used to represent the effect of water temperature due to a lack of monitored temperature of river bedrock. The average atmospheric temperature of anterior 15 days (J_{8}), 30 days (J_{9}), and 60 days (J_{10}) were used as the temperature factors.
Evolution state: the deformation over the past 15 days (J_{11}), 30 days (J_{12}), and 60 days (J_{13}) are considered.
GRA was employed to quantized the relation degree between the periodic deformation and triggering factors. Datasets of factors were used as the input for GRA, and the optimal inputs were selected from potential factors. The results of GRA are listed in
Survey Line | Triggering factors | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
J_{1} | J_{2} | J_{3} | J_{4} | J_{5} | J_{6} | J_{7} | J_{8} | J_{9} | J_{10} | J_{11} | J_{12} | J_{13} | |
VD03 | 0.638 | 0.701 | 0.621 | 0.605 | 0.718 | ||||||||
VD05 | 0.627 | 0.712 | 0.609 | 0.602 | 0.731 |
The result indicates that the periodic deformation is significantly influenced by the rate of fluctuation of RSD (J_{2}, J_{3,} and J_{4}), whereas the current RSD (J_{1}) and water temperature factors (J_{8}, J_{9,} and J_{10}) have relatively less influence. As a result, the eight optimal triggering factors were selected as the input features of prediction models, which are highlighted in
The optimal inputs and periodic deformation series were used as the input and output variables, respectively. Datasets were divided into a training set and validation set as same as the modeling of trend componence. To stabilize the learning process of ML models, all input data were normalized in the interval [0,1] using the Minmax normalization.
All these models were developed in MATLAB environment. For the DE-SFLA-LSSVM model, DE-SFLA was applied to optimize the hyper-parameters (
For LSSVM, RBF was chosen as the kernel function, and the hyper-parameters were determined using the grid-search with 5
The forecast results of the periodic deformation in the validation period for VD03 and VD05 are shown in
Survey Line | Models | RMSE | MAPE | R | ||
---|---|---|---|---|---|---|
VD03 | LSSVM | 0.415 | 0.530 | 0.939 | 132.481 | 10.228 |
ABC-LSSVM | 0.350 | 0.418 | 0.954 | 455.679 | 633.652 | |
BPNN | 0.385 | 0.598 | 0.935 | |||
DE-SFLA-BPNN | 0.223 | 0.258 | 0.988 | |||
DE-SFLA-LSSVM | 0.198 | 0.230 | 0.986 | 148.876 | 98.592 | |
VD05 | LSSVM | 0.422 | 0.485 | 0.921 | 158.015 | 22.840 |
ABC-LSSVM | 0.312 | 0.390 | 0.959 | 665.435 | 305.387 | |
BPNN | 0.451 | 0.411 | 0.936 | |||
DE-SFLA-BPNN | 0.294 | 0.406 | 0.964 | |||
DE-SFLA-LSSVM | 0.222 | 0.297 | 0.978 | 168.041 | 53.492 |
Performance comparison between the original models (i.e., LSSVM and BPNN) and hybrid models (i.e., DE-SFLA-LSSVM, ABC-LSSVM, and DE-SFLA-BPNN). It is depicted further from
Performance comparison between DE-SFLA-LSSVM and the LSSVM based models (i.e., LSSVM and ABC-LSSVM). As illustrated in
Performance comparison between DE-SFLA-LSSVM and the ANN based models (i.e., BPNN and DE-SFLA-BPNN).
For VD05, according to the forecast result shown in
Finally, the forecast results of the cumulative VD were calculated by reconstructing the predicted trend and periodic deformation results. The comparison between the predicted values and the denoised cumulative deformation in the validation period is shown in
Survey Line | Models | RMSE | MAPE (%) | R |
---|---|---|---|---|
VD03 | LSSVM | 0.429 | 0.385 | 0.873 |
ABC-LSSVM | 0.349 | 0.272 | 0.924 | |
BPNN | 0.397 | 0.348 | 0.895 | |
DE-SFLA-BPNN | 0.266 | 0.254 | 0.945 | |
DE-SFLA-LSSVM | 0.217 | 0.168 | 0.973 | |
VD05 | LSSVM | 0.415 | 0.449 | 0.708 |
ABC-LSSVM | 0.307 | 0.312 | 0.863 | |
BPNN | 0.428 | 0.441 | 0.770 | |
DE-SFLA-BPNN | 0.300 | 0.323 | 0.884 | |
DE-SFLA-LSSVM | 0.222 | 0.238 | 0.929 |
As can be clearly seen in
As illustrated in
By comparison, it is indicated that using the proposed DE-SFLA-LSSVM model for trend and periodic deformation prediction by considering the relevant triggering factors can provide better predictive performance for cumulative VD prediction. Generally, the prediction performance of the DE-SFLA-LSSVM model outperforms that of all the BPNN-based models and LSSVM-based models. The deformation series cannot be perfectly predicted by LSSVM and BPNN due to the improperly searched ability of the grid search method and the random generated internal weights and the simple structure of BPNN. Nevertheless, the DE-SFLA-LSSVM model and DE-SFLA-BPNN model exhibit better performance in terms of accuracy and percentage error in the validation period for VD prediction.
This paper studies the VD prediction by using a novel hybrid forecasting model that is made up of EEMD-ITD and DE-SFLA-LSSVM. The performance of LSSVM has much to do with the preprocessing of non-stationary and noisy series and optimizing the hyper-parameters. Two actual VD series monitored in Xiluodu reservoir region are used for model testing, and the forecast performance of the proposed model is validated and outperforms other common methods.
According to the corresponding comprehensive analysis, the EEMD-ITD denoising procedure can adequately maintain the major evolution features of the original series, while the redundant noise is eliminated. By comparing with WTD, EEMD-ITD achieved better performance with higher SNR and lower MSE of 0.486, 86.821 for VD03, and 0.320, 86.048 forVD05, respectively. It reveals that the introduced EEMD-ITD is an effective denoising method for signal preprocessing. The result of GRA indicates that the periodic deformation is significantly influenced by the rate of fluctuation of RSD, whereas the current RSD and temperature have less influence on VD. Moreover, GRA removes redundant information and extracts the relevant factors, which can reduce the model complexity and improves prediction performance. The performance of DE-SFLA-LSSVM and other conventional methods including LSSVM, ABC-LSSVM, BPNN, and DE-SFLA-BPNN is validated and compared for the periodic deformation forecasting. The result shows that the proposed hybrid model outperforms the other methods with high precision. Therefore, the proposed hybrid model has the potential to be applied for the early-warning in Xiluodu project.
Special thanks are given to the journal editors and anonymous reviewers for their valuable comments and suggested revisions.