Numerical Optimization and Cyber-Physical- Social Computing for Vibrations of the Elliptical Treadmill Based on GSO-BPNN Model.

The finite element method was used to compute the vibration characteristics of the elliptical treadmill, and the computational results were then compared with those of the experimental test to verify its correctness. The vibrations of the elliptical treadmill were optimized by glowworm swarm optimization back propagation neural network (GSO-BPNN) model to obtain an elliptical treadmill with the minimum mass and vibration. The experimental test was completed using the intelligent sensor device, and the collected signal will be processed by people. Therefore, in this paper, the numerical computation involved the cyber-physical-social system. The computational results proved that: Tri-axial excitation forces presented an obvious periodicity. Power spectral density was mainly distributed within 10–20 Hz. Power spectral densities of the elliptical treadmill with different materials were also mainly distributed within 10–20 Hz. In addition, the maximum peak value of power spectral densities of the elliptical treadmill with aluminum alloy was 2.1 g 2 /Hz, while the maximum peak value of power spectral densities of the elliptical treadmill with magnesium alloy was 1.7 g 2 /Hz. Compared with a steel elliptical treadmill, the maximum power spectral density of an aluminum elliptical treadmill was decreased by 19.2%, and the maximum power spectral density of a magnesium elliptical treadmill was decreased by 34.6%. Therefore, using magnesium alloy to make the elliptical treadmill can obtain a comparatively better structure. Vibration displacement, velocity and acceleration in Z direction were obviously more than those in X and Y directions and presented certain periodicity because excitation forces in Z direction were also the largest. GSO-BPNN model was compared with BP neural network model and genetic algorithm-BP neural network model. They adopted the same neural network topology structure to conduct a multi-objective optimization for the power spectral density and acceleration of the elliptical treadmill. GSO-BPNN not only improved the optimized accuracy, but also reduced the computational time.