Author ' s personal copy Short communication Comparison of different state space definitions for local dynamic stability analyses
Author ' s personal copy Short communication Comparison of different state space definitions for local dynamic stability analyses
复制标题
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
D. Gates;J. Dingwell
中科院分区：
文献类型：
--
作者：
D. Gates;J. Dingwell
局部动态稳定性的度量，如局部散度指数（l s）量化了小扰动偏离定义运动的吸引子的速度。当运动控制方程未知时，可以通过定义适当的状态空间来重构吸引子。然而，状态空间的定义并不是唯一的，生物力学研究中尚未建立公认的定义状态空间的方法。这项研究首先确定了不同的状态空间定义如何影响洛伦兹吸引子的s，因为精确的理论值是先验已知的。在测试的9个状态空间中，有7个状态空间的ls值显示出10%的误差。包含冗余信息的状态空间性能最差。为了在生物力学背景下检验这些影响，20名健康受试者在疲劳前后分别进行了5分钟的重复性锯样任务。比较了6种不同状态空间定义下疲劳前后肩关节运动的局部稳定性。在这里，所有6个状态空间的后疲劳都减少了。其中3个状态空间的差异具有统计学意义。对于使用延迟嵌入定义的状态空间，增加嵌入维数会降低洛伦兹数据和实验数据的l s。总的来说，我们的研究结果表明，使用不同状态空间定义的研究之间的直接数值比较应该谨慎进行。然而，跨实验比较的趋势似乎持续存在。使用位置和速度构建的生物力学状态空间，或单个状态的延迟重建，可能会提供一致的结果。& 2009 Elsevier Ltd版权所有。
Measures of local dynamic stability, such as the local divergence exponent (l s ) quantify how quickly small perturbations deviate from an attractor that defines the motion. When the governing equations of motion are unknown, an attractor can be reconstructed by defining an appropriate state space. However, state space definitions are not unique and accepted methods for defining state spaces have not been established for biomechanical studies. This study first determined how different state space definitions affected l s for the Lorenz attractor, since exact theoretical values were known a priori. Values of l s exhibited errors o10% for 7 of the 9 state spaces tested. State spaces containing redundant information performed the poorest. To examine these effects in a biomechanical context, 20 healthy subjects performed a repetitive sawing-like task for 5 min before and after fatigue. Local stability of preand post-fatigue shoulder movements was compared for 6 different state space definitions. Here, l s decreased post-fatigue for all 6 state spaces. Differences were statistically significant for 3 of these state spaces. For state spaces defined using delay embedding, increasing the embedding dimension decreased l s in both the Lorenz and experimental data. Overall, our findings suggest that direct numerical comparisons between studies that use different state space definitions should be made with caution. However, trends across experimental comparisons appear to persist. Biomechanical state spaces constructed using positions and velocities, or delay reconstruction of individual states, are likely to provide consistent results. & 2009 Elsevier Ltd. All rights reserved.