A Dam Safety State Prediction and Analysis Method Based on EMD-SSA-LSTM
Abstract
:1. Introduction
2. The Selection of Factors Affecting the Service State of the Dam Is Diverse
2.1. Empirical Mode Decomposition of Aging Factors
- (1)
- The number of zero crossings and extrema is the same throughout the entire data set, or the two differ by at most one.
- (2)
- The sum of the mean of the upper and lower envelopes composed of local maxima and local minima at any point is zero.
2.2. Multivariate Time Series Analysis and Modeling
3. Prediction Model Construction
3.1. Long Short-Term Memory Network
- (1)
- Initially, using the external state from the previous time step and the current input , calculate the forget gate , input gate , and output gate ; then, compute the candidate value .
- (2)
- Combine and to determine whether to update the memory cell .
- (3)
- Combine to output the updated internal state information from the gate mechanism to the external state .
3.2. Sparrow Search Algorithm
3.3. EMD-SSA-LSTM Prediction Model Calculation Process
- (1)
- Data preprocessing: For the collected seepage flow monitoring data of the dam, the preprocessing method in Section 2.1 is used to handle outliers without compromising the integrity and trend of the original data.
- (2)
- Parameter selection: Taking dam seepage pressure as an example, along with the collected environmental factors, 15 influencing factors, including water pressure, temperature, and aging, are selected for factor parameter configuration. The mathematical model is shown in Equation (7).
- (3)
- Data set partitioning and transformation: The preprocessed data are transformed into supervised learning data using the series_to_supervised function to construct a 3-to-1 supervised learning data type, predicting the current day’s data using the data from the previous three days. A total of 16 years of monitoring data from 2004 to 2020 was collected, with the first 90% used as training data and the last 10% (approximately 2 years) used as prediction data, with normalization applied to the data using the MinMaxScaler function.
- (4)
- Model construction: For the prediction of dam seepage data, an LSTM neural network is built based on Tensorflow. To improve computational efficiency, GPU support is utilized, and a double-layer LSTM neural network is constructed.
- (5)
- Model initialization: The iteration count, the number of nodes in two hidden layers, and the training sample size in the LSTM neural network model are selected as optimization objectives. The SSA algorithm is initialized with the iteration count, population size, producer ratio, and initial parameter threshold, followed by the initialization calculation. See as Table 1.
- (6)
- Fitness calculation: The validation set mean squared error is used as the fitness function to find a set of hyperparameters that minimize the network’s error. Equations (8)–(10) are employed to update the positions of the sparrows in SSA, obtaining new fitness values for the sparrow population and saving the optimal individual and global optimal positions in the population.
- (7)
- Output optimization results: The particle values calculated by SSA optimization are used as the iteration count, the number of nodes in two hidden layers, and the training sample size for the LSTM neural network model.
- (8)
- Calculation and comparative analysis: For the predicted data, metrics such as Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and R-squared (R2) are used to evaluate the model accuracy. A comparative analysis is conducted with the prediction effects of GPU, Recurrent Neural Network (RNN), Backpropagation Neural Network (BPNN), and the commonly used multiple linear regression.
4. Study Area Introduction
5. Results and Discussion
5.1. EMD-SSA-LSTM Prediction Model Calculation Process
5.2. Parameter Optimization of Multivariate Time Prediction Model
- Optimizer
- 2.
- Loss Function
- 3.
- Comparative analysis of prediction accuracy
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Name of Parameter | Value | |
---|---|---|
Iterations | 10 | |
Sparrow population | 20 | |
Optimization dimension | 4 | |
Finder alert threshold | 0.8 | |
Finder ratio | 20% | |
Scout ratio | 20% | |
Data range | Iterations | [10–100] |
Number of nodes in the first hidden layer | [1–100] | |
Number of nodes in the second hidden layer | [1–100] | |
Number of samples selected for training | [10–100] |
Hole Number | Dam Axis Distance (m) | Station Number |
---|---|---|
Under the geomembrane | −18.50 | SW3-1 |
U-3 | +33.00 | JC4-2 |
U-4 | +100.00 | JC1-2, SC2-6 |
Optimizer Type | MAPE | RMSE | MAE | MSE | R2 |
---|---|---|---|---|---|
Adagrad | 0.0087 | 0.0569 | 0.0448 | 0.0032 | 0.6380 |
Adadelta | 0.0233 | 0.1405 | 0.1195 | 0.0197 | −1.2067 |
Adam | 0.0393 | 0.2228 | 0.2018 | 0.0496 | −4.5486 |
Adamax | 0.0100 | 0.0650 | 0.0510 | 0.0042 | 0.5270 |
Ftrl | 0.0542 | 0.2935 | 0.2779 | 0.0862 | −8.6334 |
Nadam | 0.0182 | 0.1082 | 0.0936 | 0.0117 | −0.3097 |
RMSprop | 0.0182 | 0.1124 | 0.0938 | 0.0126 | −0.4125 |
SGD | 0.0094 | 0.0599 | 0.0482 | 0.0035 | 0.5976 |
Optimizer Type | MAPE | RMSE | MAE | MSE | R2 |
---|---|---|---|---|---|
MSE | 0.0087 | 0.0569 | 0.0448 | 0.0032 | 0.6380 |
MAE | 0.0083 | 0.0528 | 0.0426 | 0.0027 | 0.6884 |
MAPE | 0.1244 | 0.6545 | 0.6360 | 0.4284 | −46.9011 |
MSLE | 0.0094 | 0.0611 | 0.0484 | 0.0037 | 0.5815 |
squared_hinge | 1.0873 | 5.5581 | 5.5437 | 30.8931 | −3452.79 |
categorical_hinge | 0.5152 | 2.6577 | 2.6308 | 7.0637 | −788.71 |
LogCosh | 0.0116 | 0.0731 | 0.0597 | 0.4024 | 0.0053 |
Evaluation Index | EMD-SSA-LSTM | RNN | GRU | BP Neural Network | Multiple Linear Regression |
---|---|---|---|---|---|
MSE | 0.0026 | 0.0107 | 0.0106 | 0.0086 | 0.0038 |
RMSE | 0.0519 | 0.1035 | 0.1030 | 0.1052 | 0.0616 |
MAE | 0.0407 | 0.0884 | 0.0893 | 0.0854 | 0.0485 |
R2 | 0.6759 | −0.2892 | −0.2775 | −0.0356 | 0.6068 |
Evaluation Index | EMD-SSA-LSTM | RNN | GRU | BP Neural Network | Multiple Linear Regression |
---|---|---|---|---|---|
MSE | 0.0016 | 0.0027 | 0.0026 | 0.0066 | 0.0071 |
RMSE | 0.0401 | 0.0516 | 0.0513 | 0.1352 | 0.0842 |
MAE | 0.0314 | 0.0410 | 0.0405 | 0.1129 | 0.0711 |
R2 | 0.8674 | 0.7803 | 0.7833 | 0.4504 | 0.8067 |
Evaluation Index | EMD-SSA-LSTM | RNN | GRU | BP Neural Network | Multiple Linear Regression |
---|---|---|---|---|---|
MSE | 0.0156 | 0.0070 | 0.0070 | 0.0366 | 0.0113 |
RMSE | 0.0395 | 0.0838 | 0.0836 | 0.2584 | 0.1061 |
MAE | 0.0340 | 0.0626 | 0.0629 | 0.2120 | 0.0819 |
R2 | 0.9199 | 0.6404 | 0.6417 | −0.8765 | 0.7878 |
Evaluation Index | EMD-SSA-LSTM | RNN | GRU | BP Neural Network | Multiple Linear Regression |
---|---|---|---|---|---|
MSE | 0.0026 | 0.0085 | 0.0083 | 0.0117 | 0.0038 |
RMSE | 0.0512 | 0.0924 | 0.0911 | 0.1267 | 0.0616 |
MAE | 0.0386 | 0.0796 | 0.0776 | 0.1040 | 0.0486 |
R2 | 0.7710 | 0.2562 | 0.2768 | −0.0179 | 0.7333 |
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Yang, X.; Xiang, Y.; Wang, Y.; Shen, G. A Dam Safety State Prediction and Analysis Method Based on EMD-SSA-LSTM. Water 2024, 16, 395. https://doi.org/10.3390/w16030395
Yang X, Xiang Y, Wang Y, Shen G. A Dam Safety State Prediction and Analysis Method Based on EMD-SSA-LSTM. Water. 2024; 16(3):395. https://doi.org/10.3390/w16030395
Chicago/Turabian StyleYang, Xin, Yan Xiang, Yakun Wang, and Guangze Shen. 2024. "A Dam Safety State Prediction and Analysis Method Based on EMD-SSA-LSTM" Water 16, no. 3: 395. https://doi.org/10.3390/w16030395