Prediction accuracy improvement of pressure pulsation signals of reversible pump‐turbine: A LSTM and VMD‐based optimization approach

The reversible pump‐turbine plays an important role in hydropower stations, but pressure pulsation during their operation affects their performance and lifespan. Accurate prediction of pressure pulsation signals can provide an important basis for energy planning and stable operation of pumped storage units, thereby promoting sustainable development of the environment. This study introduces an optimization method that combines long short‐term memory (LSTM) and variable mode decomposition (VMD) to enhance the prediction accuracy of pressure pulsation signals. First, by decomposing the pressure pulsation signal into multiple relatively stable subsequence components using VMD, the characteristics of the original signal become more distinct. Subsequently, individual LSTM‐based time series prediction models were constructed for each modal function, and the hyperparameters related to subsequence were optimized using the sparrow search algorithm. To validate the efficacy of the proposed approach, this paper conducted experiments using pressure pulsation signals of a pump‐turbine obtained through numerical simulation. The experimental data was divided into training and testing sets, with the former used to train the LSTM model and the latter used for validation. The experimental results show that the optimized VMD with an optimized LSTM method can effectively improve the prediction accuracy of pressure pulsation signals in reversible pump‐turbine.

2][3] With the continuous growth of global energy demand and the increasingly prominent environmental issues, the pollution, greenhouse effect and climate change caused by fossil energy utilization have become more serious. 4The issue of carbon emissions in the process of energy utilization is receiving increasing attention from people. 5,6Therefore, seeking renewable energy and efficient energy storage technologies has gained significant attention as a current research focus.In the field of energy storage, battery energy storage technology has made significant progress as an important way of storing energy. 7,8Battery energy storage is extensively utilized in various domains, including mobile devices, emergency backup power, and distributed energy systems, owing to its numerous advantages such as high energy density, rapid response, and emission-free operation. 9,10However, there are also some limitations to battery energy storage technology, such as limited energy density, short lifespan and high cost.These factors have constrained the further development and widespread application of battery energy storage technology.][13] The reversible pump-turbine can convert water energy and electrical energy through the utilization of the terrain difference.During peak electricity demand, it generates electricity by releasing water from the reservoir to drive the turbine.5][16] Therefore, pumped storage power generation units have the advantages of quick start-up, high energy density, and flexible and reliable operation. 17They can both reduce peak load and fill in valleys during power regulation processes.This makes pumped storage power generation units an important means to achieve large-scale energy storage for renewable energy sources and balance the power system. 18umped storage technology is an important energy storage and dispatching technology with broad application prospects in the field of energy.However, pressure pulsation problems are commonly found in the operation of pumped storage units. 19This not only has adverse effects on the safe and reliable operation of equipment, but may also have a certain impact on power grid stability and supply quality. 20,21Fu et al. 22 believe that cavitation in the pump-turbine of a hydraulic turbine can be induced by significant pressure pulsation.Liu et al. 23 conducted particle image velocimetry.experiments to examine the formation of internal vortices within a pump-turbine.They concluded that the characteristics of pressure pulsation within the pump-turbine are intricately linked to the vortices present in the internal flow field.Therefore, accurately predicting the pressure pulsation properties at various locations during the operation of pumped storage units is of great research value and practical significance for optimizing operations, improving efficiency, and ensuring stable operation of the power system. 24,25raditional prediction methods often fail to fully capture the nonlinear and temporal characteristics in pressure pulsation signals of pump-turbine units.7][28] One popular type of recurrent neural network (RNN) model that has gained prominence in time series prediction is the long short-term memory (LSTM) network.LSTM networks exhibit exceptional memory and temporal modeling capabilities. 29By adaptively learning and capturing long-term dependencies in time series data, the LSTM network effectively utilizes the features of pressure pulsation signals over time.This enables the model to learn and predict the future distribution of pressure pulsation signals while utilizing their temporal characteristics.To enhance the accuracy of ultra-short-term wind power prediction, Zhang et al. 30 introduced a modified LSTM model specifically designed for predicting ultra-short-term wind power.Hua et al. 31 presented a power generation forecasting method that combines LSTM with backpropagation.The research results demonstrated that the LSTM-back-propagation neural network, using an enhanced data set, outperformed traditional methods with a reduced prediction error.Due to the highly nonlinear and time-varying characteristics of pressure pulsation signals, it is necessary to introduce the method of variable mode decomposition (VMD) for signal decomposition. 32,33This method can decompose pressure pulsation signals into multiple intrinsic mode functions (IMFs), thereby capturing different frequency components and temporal features in the pressure pulsation signals.Zhao et al. 34 employed the VMD-LSTM/GRU model to forecast nonstationary and irregular waves along the east coast of China.The findings highlighted the proficiency of this model in forecasting nonlinear and nonstationary wave patterns.The integration of the VMD-LSTM prediction model allows for effective utilization of VMD-extracted features in training LSTM models, thereby improving the accuracy and stability of pressure pulsation signal prediction.However, the selection of parameters in VMD and LSTM is often an empirical and experimental process. 35,36Inappropriate selection can have an impact on VMD decomposition results and LSTM prediction accuracy.sparrow search algorithm (SSA) is a global optimization technique that mimics the foraging behavior and cooperative nature of sparrows in searching for optimal solutions. 37It can be used to optimize the parameters and weights of LSTM and VMD through searching.
Based on this, this article proposes a dual-optimized SSA-VMD-SSA-LSTM model for predicting pumpturbine pressure pulsation signals.By setting pressure pulsation monitoring points on various components of a certain model of pump-turbine, the pressure pulsation data obtained from calculations were predicted using the SSA-VMD-SSA-LSTM forecasting model suggested in this study.The comparative analysis involved evaluating the predicted outcomes of the proposed dualoptimization model against those of LSTM, VMD-LSTM, and VMD-SSA-LSTM models.This comparison serves to highlight the superior performance of the proposed model in forecasting pressure pulsation signals.
This study offers valuable insights for the prediction of pressure pulsation signals in pump-turbine units.The findings can significantly contribute to the safe operation of pumped storage power stations and the provision of reliable power supply within the power system.

| Long short-term memory
LSTM is a neural network architecture widely employed in deep learning, known for its ability to handle longterm dependencies in data sequences, originally proposed by Hochreiter and Schmidhuber in 1997. 38raditional RNN suffers from the problem of exponentially increasing or decreasing gradients over time when processing long sequence data.However, LSTM networks are designed with gate mechanisms and memory cells that better control gradient flow, avoiding issues such as vanishing or exploding gradients.
Within each LSTM unit, there are three distinct gate units, namely the forget gate, input gate, and output gate, in addition to a memory cell.The internal structure and working principle are shown in Figure 1 as follows.
The central component of LSTM is the storage unit, referred to as C t .At each time step, both input data and output data from the previous time step are fed into the LSTM model to calculate the values of gate units and memory units.Therefore, the specific workflow of LSTM is as follows: In the initial stage of LSTM operation, a key step involves discarding certain data information.This yields the switch value of forget gate.This value determines how much information from the previous state needs to be forgotten for this time step's input.
The switch values of the input gate and forget gate are utilized to update the information stored within the memory cell: The cell state is updated by incorporating the input gate and forget gate information: Lastly, the output gate is responsible for updating the data that will be outputted: The formulas mentioned above involve the weight matrix (W f ), the weight matrix for the previous time step (U f ), and the bias vector (b f ).These parameters are specifically utilized in the calculation of the forget gate's switch value at the current time step.W i , U i , and b i represent the weight matrix and bias vector of the input gate used to calculate the switch value of the input gate at the current time step.W c , U c , and b c are used to calculate candidate memory for the current time step.W o , U o , and b o are, respectively, output gate's weight matrix and bias vector used to calculate the output gate's switch value at the current time step.The variables f t , i t , and o t represent the computed results of the forget gate, input gate, and output gate at time step t, respectively.The sigmoid activation function is between 0 and 1 with its formula as Among them, the tanh function maps input values to between −1 and 1, which can normalize the input values and perform nonlinear transformations on them.This increases the expression ability of memory units and enables models to better learn complex patterns and relationships.Its specific expression is: However, LSTM also has some drawbacks.For example, it requires processing a large number of parameters and complex gate control mechanisms, which leads to longer training time and overfitting when dealing with complex data.Therefore, it is necessary to optimize LSTM through optimization algorithms with the aim of enhancing the predictive accuracy of the model.

| Variational mode decomposition
Variational modal decomposition is an adaptive signal processing technique introduced by Dragomiretskiy in 2014. 39It can effectively separate different components in a signal by decomposing it into multiple intrinsic mode functions with certain bandwidths.This section will introduce the basic principles and algorithmic process of the VMD method.
First, obtain the one-sided spectrum of each subsignal corresponding analytic signal of u k through Hilbert transform: Then, by multiplying each subsignal with a complex exponential function estimated at its respective center frequency according to Equation ( 9), the frequencies of all subsignals are adjusted to baseband, resulting in Then, the bandwidth of each subsignal u k is estimated through square regularization and Gaussian smoothing, with the constraint that the sum of all subsignal bandwidths is minimized.The variational model for the bandwidth of each subsignal can be expressed as Among these variables, δ(t) represents the Dirichlet function, * denotes the convolution symbol, K signifies the number of intrinsic mode functions (IMFs), {u k } represents the IMFs, and ω k represents the center frequency of u k .
In addition, the sum of all subsignals should be equal to the original input signal.Based on Equation (11), the augmented Lagrangian function is derived by incorporating the Lagrange multiplier λ and penalty factor α: The minimization problem in Equation (11), this transformation results in the conversion of the problem into a saddle point problem in Equation (12).The alternating direction method of multipliers is introduced into Equation ( 12), and the initialization formulas for {u k }, {ω k }, and λ of each subsignal are respectively: In the formula, τ is the updating factor of Lagrange multiplier and n represents the iteration number n = {1, …, N}.The convergence condition for cyclic iteration is: The pressure pulsation signal of the pump-turbine has high nonlinearity and non-stationarity.Traditional signal processing methods are not effective in dealing with this type of signal.In contrast, the VMD method has good adaptability and localization ability, which can efficiently process such signals.Simultaneously, the VMD method can extract frequency domain data from signals, thereby better analyzing and diagnosing faults in pump-turbine systems.

| Sparrow search algorithm
In the field of computer science, search algorithms are a class of fundamental algorithms used to solve search problems.SSA is a relatively new optimization model in the field of algorithms, known for its robustness and ability to handle highly nonlinear and multimodal problems. 40,41It simulates the interactive behavior of sparrows and regards the process of searching for solutions as the process of sparrows foraging in the search space.SSA combines the characteristics of swarm intelligence algorithms and search algorithms, showing excellent performance in solving optimization problems.This section mainly introduces the principles and processes of SSA.
To begin with, the population size n, search space dimension d, and fitness function f are initialized.The position update formula for discoverers during iteration is as follows: In the formula, α is a random number between 0 and 1, N is the maximum number of iterations, R 2 is the warning value ranging from 0 to 1, T is the alert threshold ranging from 0.5 to 1, and Q is a standard normal distribution random number.
It can be seen that when R 2 ≥ T, it means that a sparrow has detected a predator and issued an alarm.During this phase, all sparrows are required to migrate to a secure location.When R 2 < T, it means it is safe to search for food.
Followers will constantly monitor the discoverer.Upon observing the discovery of superior food resources of explorers, other sparrows will engage in a competitive pursuit for the available nourishment.The formula for updating their position is as follows: In the equation, X p denotes the optimal position held by the explorer, X worst represents the poorest position occupied by the explorer, A represents a matrix, and L is a matrix of 1 row and D columns with elements all equal to 1.
During the process of searching for food, a certain population of sparrows will engage in warning behavior.This group of sparrows is called the "warning group."The position update formula for the warning group is given as follows In the formula, X best represents the global optimal position, f best and f worst represent the global best fitness and worst fitness, respectively, f i represents sparrow's fitness, β is a random number from standard normal distribution, K is the direction of sparrow movement with a range of random numbers from −1 to 1, ε is a small nonzero number.
After completing the above steps, record the current optimal solution for the search and repeat the above steps until reaching the maximum iteration limit or meeting the precision requirements of the objective function, then end the loop.

| Acquisition position
This article examines the properties of pressure pulsation signals produced during the operation of a pump-turbine.The flow components mainly include volute, guide vane, stay vane, impeller and draft tube.Their structural distribution is shown in Figure 2.During the actual operation of a pump-turbine, strong pressure pulsation signals with highly nonlinear and nonstationary characteristics are generated due to the two rotor-stator interactions between the guide vane and impeller, as well as between the impeller and draft tube.Furthermore, the pressure pulsation variations differ for each overcurrent component.Therefore, it is necessary to add pressure pulsation monitoring points for data collection on each flow component.The specific layout of pressure pulsation monitoring points is displayed in Figure 3: a pressure pulsation monitoring point named P VT is set at the outlet of the volute, and monitoring points named P RN-GV is set at the impeller and guide vane.Monitoring points named P DT1 and P DT2 are respectively set near the inlet of the impeller in the draft tube and at the elbow of the draft tube.

| CFD setup
The training and prediction data used in this article are pressure fluctuation data simulated using the computational fluid dynamics (CFD) method.Although CFD simulation data has certain model assumptions and biases, which may differ from the actual pressure fluctuation data generated during the operation of pump-turbine, experimental measurements require high costs, and errors between simulation values and experimental values do not affect model comparison, meeting the requirements of this article.Overall, it is feasible to use CFD simulation data for prediction model training and prediction.
In the numerical simulation process, the choice of turbulence model has a significant impact on computational accuracy.In this paper, we have selected the SST k-ω model, 42 which provides good inclusivity and convergence characteristics, for the simulation.The mass flow type was chosen for the inlet boundary, while the outlet boundary was set to the pressure type.Additionally, all the walls were configured as no-slip walls.The interface type is designated as the dynamic-static interface in interfaces between guide vane and runner, as well as between the runner and draft tube.When both sides of the interface consist of stationary components, it is termed the static-static interface.To ensure accurate data transmission, the connection method for the interface is selected as general grid interface (GGI).Throughout the entire solving process, the convergence criteria for both the continuity equation and momentum equation are set at 10 −5 .
Equation (20) shows the continuity equation and Equation (21) shows the momentum equation in the following: where ρ represents density of the fluid medium; t represents time; v x , v y , and v z are the components of the velocity vector in the X, Y, and Z directions respectively.
F I G U R E 2 Flow domain of the objective pump-turbine.To evaluate the predictive accuracy of diverse composite models for pressure pulsation signals across distinct positions within the pump-turbine unit, mean absolute error (MAE) is selected to measure the differences between the predicted results of different models and the observed values.

| Time-domain characteristics
To begin, an analysis is performed to examine the timedomain characteristics of each monitoring point.As depicted in Figure 4, it is evident that the pressure pulsation signals at various measurement positions demonstrate significant periodicity over time.Within a complete impeller revolution cycle, the pressure pulsation signals show multiple peaks and valleys.Due to the influence of rotor-stator interaction, the pressure pulsation amplitude at P RN-GV is relatively large.Comparatively, the pressure pulsation amplitude at the P VT monitoring point positioned at the volute outlet is slightly smaller than that observed at the preceding two points.Additionally, the pressure pulsation amplitudes at the monitoring points within the draft tube are relatively small.The variation of pressure pulsation over time is not the same for each monitoring point.Therefore, it is crucial to use optimized VMD and LSTM methods to predict the pressure pulsation signal over a period of time, with the aim of assessing the operating status and performance of pump-turbine.

| DATA PREDICTION STRATEGIES 4.1 | LSTM based prediction
First, a separate LSTM model is employed for predicting the pressure fluctuation signal.The model training process uses a backpropagation algorithm combined with Adam's optimization algorithm.The initial learning rate (I r ) of the model is set to 0.01 and adjusted after 60 iterations with a factor of 0.2.The regularization coefficient (R c ) is set to 0.001, and the maximum number of trained timesteps is 100.The specific workflow diagram is shown in Figure 5: The first step is to normalize the pressure pulsation signal data to ensure the quality and usability of the signal.Subsequently, the feature sequence is extracted and fed into an LSTM network for modeling purposes.The first 900 pieces of data are utilized for training the LSTM model.During training, the parameters of the model are optimized through a backpropagation algorithm so that the model can predict target variables more accurately.After meeting accuracy requirements or reaching maximum iteration times, a well-trained LSTM model is obtained for predicting the remaining 380 pressure pulsation data.
Due to the multiscale characteristics of pressure pulsation signals in pump-turbine, which usually contain multiple low-frequency and high-frequency components, employing only LSTM for prediction may ignore these scale information, resulting in limitations of the model in capturing signal features.

| VMD with LSTM
VMD-LSTM is a data prediction method that combines VMD and LSTM.It can extract features of different time scales from the signal, and fuse and learn them in LSTM, which can better perform nonlinear modeling and prediction of the signal.This effectively avoids the limitations of a single LSTM model that may ignore certain scale information.The specific workflow diagram is shown in Figure 6: Before using the LSTM model for predicting pressure pulsation signals, it is necessary to apply the VMD method to decompose the signal and filter and reconstruct the IMF components.Then, the signal can be modeled and predicted using the LSTM model.
Although the VMD-LSTM model has advantages in some aspects, there are also some disadvantages.The selection and adjustment of hyperparameters such as the number of hidden units in the LSTM layer (N u ), Initial learning rate (I r ) and Regularization coefficient (R c ) in LSTM require certain experience and domain knowledge.Inappropriate selection of hyperparameters may lead to a decrease in model performance or overfitting issues.

| VMD with optimized LSTM
The VMD-SSA-LSTM model applies the sparrow optimization algorithm to the parameter optimization process of LSTM.The SSA has global exploration | 109 capabilities and simulates the behavior of sparrows searching for food to find globally optimal or nearoptimal solutions.The specific workflow diagram is shown in Figure 7. Before constructing the LSTM network, SSA is used to optimize relevant parameters, including the N u , I r , and R c .The N u determines the quantity of hidden units in the model.Increasing this number allows for more complex patterns to be captured but also increases computational complexity.The I r controls the step size for each parameter update and determines how quickly the model learns during each training iteration.The R c is used to prevent overfitting by penalizing model complexity and avoiding excessive reliance on training data.Based on past experience, the value range of N u is between 10 and 30, I r is between 0.01 and 0.05, and R c is between 0.0001 and 0.01.After obtaining the optimal parameter combination, LSTM modeling and prediction will be performed.

| Optimized VMD with optimized LSTM
Due to the importance of the decomposition number of modes K and penalty factor α in VMD, they have an impact on the decomposition results.K represents the number of modes in the decomposition result, while α is used to balance signal smoothness and decomposition accuracy.The selection of these parameters requires certain experience, as inappropriate parameter selection may lead to unsatisfactory decomposition results.Therefore, this paper proposes a dual-optimized training prediction model called SSA-VMD-SSA-LSTM, with a specific workflow diagram shown in Figure 8: Before using VMD to decompose the pressure pulsation signal, SSA is first used to optimize the decomposition mode number K and penalty factor α to obtain the optimal parameter combination.Then, this parameter combination is used for VMD decomposition of the signal, and the remaining steps are identical to those of the previous model.Based on past experience, K ranges from 2 to 10 and α ranges from 100 to 3000.

| Parameter selection
In this study, we employed the Matlab programming language to implement LSTM model predictions and the signal decomposition using VMD.After dual optimization of three parameters of LSTM and two parameters of VMD, the specific values of each parameter under the prediction situation for each monitoring point are finally obtained, as shown in Table 1:

| Comparison of predicted results
Figure 9 shows the comparison of different prediction models for the predicted results at monitoring point P DT1 of pressure pulsation.From the perspective of both predicted and error results, there is not much difference between LSTM and VMD-LSTM prediction results.However, after introducing SSA optimization algorithm to optimize VMD decomposition parameters and LSTM prediction model parameters, LSTM can solve local optimization problems and greatly improve prediction Figure 11 presents the comparison of prediction outcomes for pressure fluctuation monitoring point P VT by different prediction models.The LSTM model has a large fluctuation in prediction error, and its average error value is much higher compared to the remaining three prediction models.The other three prediction models have similar prediction errors for pressure fluctuation signals at this point.Due to the complexity of the internal flow in the volute, there is significant variation in the pressure pulsation results.This has led to the observation that the MAE of the SSA-VMD-SSA-LSTM prediction model proposed in this study does not exhibit a significant improvement when compared to the traditional VMD-LSTM and VMD-SSA-LSTM models.
Figure 12 shows the comparison of prediction results for pressure fluctuation monitoring point P RN-GV by different prediction models.Based on the results and error distribution of the prediction set, it can be seen that compared to a single LSTM model, the SSA-VMD-SSA-LSTM combined prediction model has a more stable predictive effect.It can be observed that there is strong periodicity in the pressure pulsations between the runner and the guide vanes, and the prediction model exhibits strong adaptability to pressure pulsation data.Therefore, the MAE of the SSA-VMD-SSA-LSTM prediction model proposed in this study is significantly smaller than the other models.

| CONCLUSIONS
This article studies the prediction method of pressure pulsation in pump-turbine by combining with the existing research approaches in the domain of deep learning.The SSA-VMD-SSA-LSTM pressure pulsation prediction model is established, and the following conclusions are drawn: (1) LSTM is designed to handle sequential data and performs well in capturing long-term dependencies within a sequence, making it suitable for predicting the trend of pressure pulsation signals.However, due to the reliance on experience for parameter selection, inappropriate choices may lead to a decrease in prediction accuracy.Therefore, solely using LSTM for predicting pressure fluctuations can result in significant errors.

FANG ET AL. | 107
where μ represents the dynamic viscosity coefficient of fluid, v represents the velocity vector, ▽ represents the Hamiltonian operator, and f represents the stress vector.Numerical simulation is performed on the calculation model of the pump-turbine, and finally, 1280 time steps pressure pulsation data are obtained at each monitoring point.The initial 900-time steps of this data set are allocated for the training set, while the remaining 380time steps are designated for the prediction set.

F I G U R E 3
Location of monitor points.(A) Impeller and volute region.(B) Draft tube region.F I G U R E 4 Location of monitor points.(A) P DT1 pressure pulsation signal.(B) P DT2 pressure pulsation signal.(C) P VT pressure pulsation signal.(D) P RN-GV pressure pulsation signal.

F I G U R E 5
Flowchart of LSTM model.LSTM, long short-term memory.FANG ET AL.

F I G U R E 6
Flowchart of VMD-LSTM combined prediction model.IMF, intrinsic mode function; LSTM, long short-term memory; VMD, variable mode decomposition.F I G U R E 7 Flowchart of VMD-SSA-LSTM combined prediction model.IMF, intrinsic mode function; LSTM, long short-term memory; SSA, sparrow search algorithm; VMD, variable mode decomposition.

F I G U R E 8
Flowchart of SSA-VMD-SSA-LSTM combined prediction model.IMF, intrinsic mode function; LSTM, long short-term memory; SSA, sparrow search algorithm.T A B L E 1 Parameter values optimized for each monitoring point.SSA-VMD-SSA-LSTM model has the smallest prediction error.Figure 10 illustrates the comparison among various prediction models for the pressure fluctuation monitoring point P DT2 .It can be seen that different prediction models have relatively consistent predictions for the trend of pressure fluctuation changes, while the LSTM model has a larger range of error curve changes in its predictions.The VMD-LSTM model has the lowest error results, while the MAE of SSA-VMD-SSA-LSTM model result is close to the VMD-LSTM result.

F
I G U R E 9 Comparison of monitoring point P DT1 prediction results.(A) Comparison of training set results.(B) Comparison of prediction set results.(C) Error monitoring curve.(D) MAE of different models.LSTM, long short-term memory; SSA, sparrow search algorithm; VMD, variable mode decomposition.

( 2 )
By introducing VMD to decompose pressure pulsation signals, extracting features of different time scales from the signals, and fusing and learning them in LSTM, the ability of model to perform nonlinear modeling and prediction on the signals has been improved.From the perspective of predicting results from different pressure pulsation monitoring points, the VMD-LSTM model has significantly improved F I G U R E 10 Comparison of monitoring point P DT2 prediction results.(A) Comparison of training set results.(B) Comparison of prediction set results.(C) Error monitoring curve.(D) MAE of different models.LSTM, long short-term memory; SSA, sparrow search algorithm; VMD, variable mode decomposition.accuracy in pressure pulsation prediction.With the exception of the result at P DT1 , the MAE value of the predictions at the other three monitoring points have decreased by 94%, 61%, and 21% compared to the LSTM model.(3) By introducing SSA to optimize the relevant parameters of VMD and LSTM, the limitations of arbitrary selection on model prediction performance have been addressed, leading to an enhancement of the prediction accuracy of the model.According to the forecasting outcomes of various models for pressure pulsation signals, the SSA-VMD-SSA-LSTM dual-optimization model has significant advantages in predicting pressure pulsation signals.Compared to the traditional LSTM prediction model, the MAE of SSA-VMD-SSA-LSTM model has decreased by 98%, 92%, 66%, and 84%, respectively.ORCID Ran Tao http://orcid.org/0000-0002-9558-4728Ruofu Xiao http://orcid.org/0000-0003-4629-2873