Prediction of Three‑Dimensional Fractal Dimension of Hematite Flocs Based on Particle Swarm Optimization Optimized Back Propagation Neural Network

The three-dimensional (3D) fractal dimension is an important parameter to analyze the 3D structure and flocculation effect of the hematite flocs. In this work, the 3D fractal dimension of hematite flocs was predicted by establishing the particle swarm optimization (PSO) algorithm optimized with the back propagation (BP) neural network (PSO-BP). The proposed model considers four factors, namely, the flocculant quantity, flocculation time, stirring speed, and temperature, as the input parameters. We normalize the input data during the preprocessing stage. The BP neural network was optimized by using the PSO algorithm for realizing the 3D fractal dimension. The prediction accuracy and effectiveness of the model were evaluated. The experimental results showed that the predictions performed by the proposed PSO-BP neural network were better than that of BP neural network. In addition, the root mean square error (RMSE), mean squared relative error (MSRE), mean absolute error (MAE), and mean absolute relative error (MARE) of the proposed model are lower, compared with the errors of the BP network. Similarly, the measurement coefficient R2 of the proposed model is higher, compared with the BP network. The maximum absolute error of the model is 0.0772, the maximum relative error is 0.02405, and the regression coefficient r is 0.98592. These results showed that the proposed model has a good performance and high prediction accuracy. When verifying the practicability and the effectiveness of the proposed PSO-BP model, the prediction results of 10 groups of hematite flocculation experimental data under different conditions showed that the prediction value of the proposed PSO-BP model was closer to the ground truth as compared to the BP model. Therefore, the proposed model is suitable for predicting the 3D fractal dimension of hematite flocculation.