A fractal interpolation algorithm based on adaptive mutation Particle Swarm Optimization (PSO) was proposed aiming at the interpolation problem of a large number of continuous missing data in wind speed data of wind farms. First, the mutation factor was introduced into the particle swarm optimization algorithm to enhance the diversity of particles and the search accuracy of the algorithm. Second, the optimal value of the vertical scaling factor in the fractal interpolation algorithm was obtained by the adaptive mutation particle swarm optimization algorithm. Finally, two datasets with different trends and change characteristics were analyzed by fractal interpolation, and the proposed algorithm was compared with Lagrange interpolation and cubic spline interpolation. The results show that fractal interpolation is not only able to maintain the overall fluctuation characteristics and local characteristics of wind speed curve, but also is more accurate than the traditional interpolation methods. In the experiment based on Dataset A, the Root Mean Square Error (RMSE) of fractal interpolation was reduced by 66.52% and 58.57% respectively compared with those of Lagrange interpolation and cubic spline interpolation. In the experiment based on Dataset B, the RMSE of fractal interpolation was decreased by 76.72% and 67.33% respectively compared with those of Lagrange interpolation and cubic spline interpolation. It is verified that fractal interpolation is more suitable for the interpolation of wind speed time series with strong fluctuation and continuous missing data.

Focused on the issue that Elman neural network has slow convergence speed and low prediction accuracy in the closing price prediction based on the network public opinion of the stock market, a prediction model combining Improved Whale Optimization Algorithm (IWOA) and Elman neural network was proposed, which is based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN)algorithm. Firstly, text mining technology was used to mine and quantify the network public opinions of Shanghai Stock Exchange (SSE) 180 shares, and in order to reduce the complexity of attribute set, Boruta algorithm was used to select the important attributes. Then, CEEMDAN algorithm was used to add a certain number of white noises with specific variances in order to realize the decomposition and noise reduction of the attribute sequence. At the same time, in order to enhance the global search and local mining capabilities, adaptive weight was used to improve Whale Optimization Algorithm (WOA). Finally, the initial weights and thresholds of Elman neural network were optimized by WOA in the iterative process. The results show that, compared to Elman neural network, the proposed model has the Mean Absolute Error (MAE) reduced from 358.812 0 to 113.055 3； compared to the original dataset without CEEMDAN algorithm, the proposed model has the Mean Absolute Percentage Error (MAPE) reduced from 4.942 3% to 1.445 31%, demonstrating that the model effectively improves the prediction accuracy and provides an effective experimental method for predicting the network public opinion of stock market.