School of Biomedical Engineering, University of Technology Sydney, 15 Broadway, Sydney, Australia.
School of Electrical Engineering, University of New South Wales, Sydney, Australia.
Biomed Eng Online. 2018 Apr 23;17(1):44. doi: 10.1186/s12938-018-0476-6.
Previous studies have indicated that oxygen uptake ([Formula: see text]) is one of the most accurate indices for assessing the cardiorespiratory response to exercise. In most existing studies, the response of [Formula: see text] is often roughly modelled as a first-order system due to the inadequate stimulation and low signal to noise ratio. To overcome this difficulty, this paper proposes a novel nonparametric kernel-based method for the dynamic modelling of [Formula: see text] response to provide a more robust estimation.
Twenty healthy non-athlete participants conducted treadmill exercises with monotonous stimulation (e.g., single step function as input). During the exercise, [Formula: see text] was measured and recorded by a popular portable gas analyser ([Formula: see text], COSMED). Based on the recorded data, a kernel-based estimation method was proposed to perform the nonparametric modelling of [Formula: see text]. For the proposed method, a properly selected kernel can represent the prior modelling information to reduce the dependence of comprehensive stimulations. Furthermore, due to the special elastic net formed by [Formula: see text] norm and kernelised [Formula: see text] norm, the estimations are smooth and concise. Additionally, the finite impulse response based nonparametric model which estimated by the proposed method can optimally select the order and fit better in terms of goodness-of-fit comparing to classical methods.
Several kernels were introduced for the kernel-based [Formula: see text] modelling method. The results clearly indicated that the stable spline (SS) kernel has the best performance for [Formula: see text] modelling. Particularly, based on the experimental data from 20 participants, the estimated response from the proposed method with SS kernel was significantly better than the results from the benchmark method [i.e., prediction error method (PEM)] ([Formula: see text] vs [Formula: see text]).
The proposed nonparametric modelling method is an effective method for the estimation of the impulse response of VO-Speed system. Furthermore, the identified average nonparametric model method can dynamically predict [Formula: see text] response with acceptable accuracy during treadmill exercise.
先前的研究表明,摄氧量([Formula: see text])是评估运动心肺反应最准确的指标之一。在大多数现有研究中,由于刺激不足和信噪比低,[Formula: see text]的反应通常被粗略地建模为一阶系统。为了克服这一困难,本文提出了一种新的基于核的非参数方法,用于动态建模[Formula: see text]对提供更稳健的估计。
20 名健康的非运动员参与者进行了单调刺激(例如,单步功能作为输入)的跑步机运动。在运动过程中,通过流行的便携式气体分析仪([Formula: see text],COSMED)测量和记录[Formula: see text]。基于记录的数据,提出了一种基于核的估计方法来对[Formula: see text]进行非参数建模。对于所提出的方法,适当选择的核可以表示先验建模信息,以减少对全面刺激的依赖。此外,由于[Formula: see text]范数和核化[Formula: see text]范数形成的特殊弹性网,估计值是平滑和简洁的。此外,与经典方法相比,所提出的方法基于有限脉冲响应的非参数模型可以最优地选择阶数并更好地拟合。
引入了几种核用于基于核的[Formula: see text]建模方法。结果清楚地表明,稳定样条(SS)核对于[Formula: see text]建模具有最佳性能。特别是,基于 20 名参与者的实验数据,与基准方法(即预测误差法(PEM))相比,所提出的方法具有 SS 核的估计响应明显更好[Formula: see text]([Formula: see text]与[Formula: see text])。
所提出的非参数建模方法是估计 VO-Speed 系统脉冲响应的有效方法。此外,所识别的平均非参数模型方法可以在跑步机运动期间以可接受的精度动态预测[Formula: see text]响应。