Precipitation is an important parameter of water resource management, flood warning and hydrological analysis, so it is important to predict rainfall accurately. However, many previous studies did not extract the information of error series and only used a single model to predict rainfall data, ignoring the importance of model stability. Therefore, based on the idea of combination prediction and error correction strategy, this paper proposes a novel combined prediction model for monthly mean precipitation. It combines the variational mode decomposition (VMD), the improved butterfly optimization algorithm (IBOA), the least squares support vector machine model (LSSVM), the adaptive Volterra and autoregressive moving average (ARMA) model. Firstly, in order to find the best parameters of LSSVM, an improved butterfly optimization algorithm is proposed. The simulation results show the performance of IBOA is better than that of other algorithms, such as PSO, DE and BOA. Then the IBOA-LSSVM model and Volterra model are established for the mode components of the VMD, named VMD-IBOA-LSSVM and VMD-Volterra. Secondly, to solve the problem that the uncertainty of the hydrological prediction model, a combined precipitation prediction method based on the induced ordered weighted average (IOWA) operator of VMD-IBOA-LSSVM and VMD-Volterra is proposed. Finally, the ARMA model is established to correct the error sequence of the combined forecasting model. The precipitation data of two stations in Shaanxi Province are predicted. Experiment 1 is taken as an example, the maximum error of the proposed prediction model for rainfall is less than 9 mm, and the performance of the proposed model is improved by at least 43%. It shows that the proposed model can effectively reduce the prediction error of precipitation, and provide a new idea for precipitation prediction.

The prediction of underwater acoustic signal is the basis of underwater acoustic signal processing, which can be applied to underwater target signal noise reduction, detection, and feature extraction. Therefore, it is of great significance to improve the prediction accuracy of underwater acoustic signal. Aiming at the difficulty in underwater acoustic signal sequence prediction, a new hybrid prediction model for underwater acoustic signal is proposed in this paper, which combines the advantages of variational mode decomposition (VMD), artificial intelligence method, and optimization algorithm. In order to reduce the complexity of underwater acoustic signal sequence and improve operation efficiency, the original signal is decomposed by VMD into intrinsic mode components (IMFs) according to the characteristics of the signal, and dispersion entropy (DE) is used to analyze the complexity of IMF. The subsequences (VMD-DE) are obtained by adding the IMF with similar complexity. Then, extreme learning machine (ELM) is used to predict the low-frequency subsequence obtained by VMD-DE. Support vector regression (SVR) is used to predict the high-frequency subsequence. In addition, an artificial bee colony (ABC) algorithm is used to optimize model performance by adjusting the parameters of SVR. The experimental results show that the proposed new hybrid model can provide enhanced accuracy with the reduction of prediction error compared with other existing prediction methods.

Climate is a complex and chaotic system, and temperature prediction is a challenging problem. Accurate temperature prediction is also concerned in the fields of energy, environment, industry, and agriculture. In order to improve the accuracy of monthly mean temperature prediction and reduce the calculation scale of hybrid prediction process, a combined prediction model based on variational mode decomposition-differential symbolic entropy (VMD-DSE) and Volterra is proposed. Firstly, the original monthly mean meteorological temperature sequence is decomposed into finite mode components by VMD. The DSE is used to analyze the complexity and reconstruct the sequences. Then, the new sequence is reconstructed in phase space. The delay time and embedding dimension are determined by the mutual information method and G-P method, respectively. On this basis, the Volterra adaptive prediction model is established to modeling and predicting each component. Finally, the final predicted values are obtained by superimposing the predicted results. The monthly mean temperature data of Xianyang and Yan’an are used to verify the prediction performance of the proposed model. The experimental results show that the VMD-DSE-Volterra model shows better performance in the prediction of monthly mean temperature compared with other benchmark models in this paper. In addition, the combined forecasting model proposed in this paper can reduce the modeling time and improve the forecasting accuracy, so it is an effective forecasting model.

Empirical results illustrate the pitfalls of applying an artificial neural network (ANN) to classifying underwater active sonar returns. During training, a back propagation ANN classifier ‘‘learns’’ to recognize two classes of reflected active sonar waveforms. Waveforms in class 1 have two major sonar echoes or peaks. Waveforms in class 2 have one major echo or peak. Our results show how the classifier ‘‘learns’’ to distinguish between the two classes. Testing the ANN classifier with different waveforms having one major peak, and waveforms having two major peaks generated unexpected results: The number of echo peaks was not the feature used to separate classes.