In order to develop safe training intensity and training methods for the passive balance rehabilitation training system, we propose in this paper a mathematical model for human standing balance adjustment based on T-S fuzzy identification method. This model takes the acceleration of a multidimensional motion platform as its inputs, and human joint angles as its outputs. We used the artificial bee colony optimization algorithm to improve fuzzy C-means clustering algorithm, which enhanced the efficiency of the identification for antecedent parameters. Through some experiments, the data of 9 testees were collected, which were used for model training and model results validation. With the mean square error and cross-correlation between the simulation data and measured data, we concluded that the model was accurate and reasonable.
The present study was aimed at the optimal solution of the main muscular force distribution in the lower extremity during standing balance of human. The movement musculoskeletal system of lower extremity was simplified to a physical model with 3 joints and 9 muscles. Then on the basis of this model, an optimum mathematical model was built up to solve the problem of redundant muscle forces. Particle swarm optimization (PSO) algorithm is used to calculate the single objective and multi-objective problem respectively. The numerical results indicated that the multi-objective optimization could be more reasonable to obtain the distribution and variation of the 9 muscular forces. Finally, the coordination of each muscle group during maintaining standing balance under the passive movement was qualitatively analyzed using the simulation results obtained.
In order to evaluate the ability of human standing balance scientifically, we in this study proposed a new evaluation method based on the chaos nonlinear analysis theory. In this method, a sinusoidal acceleration stimulus in forward/backward direction was forced under the subjects' feet, which was supplied by a motion platform. In addition, three acceleration sensors, which were fixed to the shoulder, hip and knee of each subject, were applied to capture the balance adjustment dynamic data. Through reconstructing the system phase space, we calculated the largest Lyapunov exponent (LLE) of the dynamic data of subjects' different segments, then used the sum of the squares of the difference between each LLE (SSDLLE) as the balance capabilities evaluation index. Finally, 20 subjects' indexes were calculated, and compared with evaluation results of existing methods. The results showed that the SSDLLE were more in line with the subjects' performance during the experiment, and it could measure the body's balance ability to some extent. Moreover, the results also illustrated that balance level was determined by the coordinate ability of various joints, and there might be more balance control strategy in the process of maintaining balance.