Correlation between the IMF component and the original signal.

Correlation between the IMF component and the original signal.</p

Data decomposition error under different parameters.

Data decomposition error under different parameters.</p

The 13 IMF components obtained by SSA-VMD decomposition of the original signal.

The 13 IMF components obtained by SSA-VMD decomposition of the original signal.</p

Data fluctuations under different denoising methods.

Data fluctuations under different denoising methods.</p

Network structure of BiLSTM.

In view of the strong randomness and non-stationarity of complex system, this study suggests a hybrid multi-strategy prediction technique based on optimized hybrid denoising and deep learning. Firstly, the Sparrow search algorithm (SSA) is used to optimize Variational mode decomposition (VMD) which can decompose the original signal into several Intrinsic mode functions (IMF). Secondly, calculating the Pearson correlation coefficient (PCC) between each IMF component and the original signal, the subsequences with low correlation are eliminated, and the remaining subsequence are denoised by Wavelet soft threshold (WST) method to obtain effective signals. Thirdly, on the basis of the above data noise reduction and reconstruction, our proposal combines Convolutional neural network (CNN) and Bidirectional short-term memory (BiLSTM) model, which is used to analyze the evolution trend of real time sequence data. Finally, we applied the CNN-BiLSTM-SSA-VMD-WST to predict the real time sequence data together with the other methods in order to prove it’s effectiveness. The results show that SNR and CC of the SSA-VMD-WST are the largest (the values are 20.2383 and 0.9342). The performance of the CNN-BiLSTM-SSA-VMD-WST are the best, MAE and RMSE are the smallest (which are 0.150 and 0.188), the goodness of fit R2 is the highest(its value is 0.9364). In contrast with other methods, CNN-BiLSTM-SSA-VMD-WST method is more suitable for denoising and prediction of real time series data than the traditional and singular deep learning methods. The proposed method may provide a reliable way for related prediction in various industries.</div

Flow of wavelet threshold denoising.

In view of the strong randomness and non-stationarity of complex system, this study suggests a hybrid multi-strategy prediction technique based on optimized hybrid denoising and deep learning. Firstly, the Sparrow search algorithm (SSA) is used to optimize Variational mode decomposition (VMD) which can decompose the original signal into several Intrinsic mode functions (IMF). Secondly, calculating the Pearson correlation coefficient (PCC) between each IMF component and the original signal, the subsequences with low correlation are eliminated, and the remaining subsequence are denoised by Wavelet soft threshold (WST) method to obtain effective signals. Thirdly, on the basis of the above data noise reduction and reconstruction, our proposal combines Convolutional neural network (CNN) and Bidirectional short-term memory (BiLSTM) model, which is used to analyze the evolution trend of real time sequence data. Finally, we applied the CNN-BiLSTM-SSA-VMD-WST to predict the real time sequence data together with the other methods in order to prove it’s effectiveness. The results show that SNR and CC of the SSA-VMD-WST are the largest (the values are 20.2383 and 0.9342). The performance of the CNN-BiLSTM-SSA-VMD-WST are the best, MAE and RMSE are the smallest (which are 0.150 and 0.188), the goodness of fit R2 is the highest(its value is 0.9364). In contrast with other methods, CNN-BiLSTM-SSA-VMD-WST method is more suitable for denoising and prediction of real time series data than the traditional and singular deep learning methods. The proposed method may provide a reliable way for related prediction in various industries.</div

Flow of SSA-VMD-WST model.

In view of the strong randomness and non-stationarity of complex system, this study suggests a hybrid multi-strategy prediction technique based on optimized hybrid denoising and deep learning. Firstly, the Sparrow search algorithm (SSA) is used to optimize Variational mode decomposition (VMD) which can decompose the original signal into several Intrinsic mode functions (IMF). Secondly, calculating the Pearson correlation coefficient (PCC) between each IMF component and the original signal, the subsequences with low correlation are eliminated, and the remaining subsequence are denoised by Wavelet soft threshold (WST) method to obtain effective signals. Thirdly, on the basis of the above data noise reduction and reconstruction, our proposal combines Convolutional neural network (CNN) and Bidirectional short-term memory (BiLSTM) model, which is used to analyze the evolution trend of real time sequence data. Finally, we applied the CNN-BiLSTM-SSA-VMD-WST to predict the real time sequence data together with the other methods in order to prove it’s effectiveness. The results show that SNR and CC of the SSA-VMD-WST are the largest (the values are 20.2383 and 0.9342). The performance of the CNN-BiLSTM-SSA-VMD-WST are the best, MAE and RMSE are the smallest (which are 0.150 and 0.188), the goodness of fit R2 is the highest(its value is 0.9364). In contrast with other methods, CNN-BiLSTM-SSA-VMD-WST method is more suitable for denoising and prediction of real time series data than the traditional and singular deep learning methods. The proposed method may provide a reliable way for related prediction in various industries.</div

Sufficient dimension reduction and prediction through cumulative slicing PFC

<p>In this article, a new method named cumulative slicing principle fitted component (CUPFC) model is proposed to conduct sufficient dimension reduction and prediction in regression. Based on the classical PFC methods, the CUPFC avoids selecting some parameters such as the specific basis function form or the number of slices in slicing estimation. We develop the estimator of the central subspace in the CUPFC method under three error-term structures and establish its consistency. The simulations investigate the effectiveness of the new method in prediction and reduction estimation with other competitors. The results indicate that the new proposed method generally outperforms the existing PFC methods no matter how the predictors are truly related to the response. The application to real data also verifies the validity of the proposed method.</p

Flowchart of VMD optimization in SSA.

In view of the strong randomness and non-stationarity of complex system, this study suggests a hybrid multi-strategy prediction technique based on optimized hybrid denoising and deep learning. Firstly, the Sparrow search algorithm (SSA) is used to optimize Variational mode decomposition (VMD) which can decompose the original signal into several Intrinsic mode functions (IMF). Secondly, calculating the Pearson correlation coefficient (PCC) between each IMF component and the original signal, the subsequences with low correlation are eliminated, and the remaining subsequence are denoised by Wavelet soft threshold (WST) method to obtain effective signals. Thirdly, on the basis of the above data noise reduction and reconstruction, our proposal combines Convolutional neural network (CNN) and Bidirectional short-term memory (BiLSTM) model, which is used to analyze the evolution trend of real time sequence data. Finally, we applied the CNN-BiLSTM-SSA-VMD-WST to predict the real time sequence data together with the other methods in order to prove it’s effectiveness. The results show that SNR and CC of the SSA-VMD-WST are the largest (the values are 20.2383 and 0.9342). The performance of the CNN-BiLSTM-SSA-VMD-WST are the best, MAE and RMSE are the smallest (which are 0.150 and 0.188), the goodness of fit R2 is the highest(its value is 0.9364). In contrast with other methods, CNN-BiLSTM-SSA-VMD-WST method is more suitable for denoising and prediction of real time series data than the traditional and singular deep learning methods. The proposed method may provide a reliable way for related prediction in various industries.</div

SNR under different wavelet bases, wavelet thresholds and decomposition layers.

SNR under different wavelet bases, wavelet thresholds and decomposition layers.</p