| Summary: | Abstract Background Previous studies have indicated that oxygen uptake ($$VO_2$$ VO2 ) is one of the most accurate indices for assessing the cardiorespiratory response to exercise. In most existing studies, the response of $$VO_2$$ VO2 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 $$VO_2$$ VO2 response to provide a more robust estimation. Methods Twenty healthy non-athlete participants conducted treadmill exercises with monotonous stimulation (e.g., single step function as input). During the exercise, $$VO_2$$ VO2 was measured and recorded by a popular portable gas analyser ($$K4b^2$$ K4b2 , COSMED). Based on the recorded data, a kernel-based estimation method was proposed to perform the nonparametric modelling of $$VO_2$$ VO2 . 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 $$\mathcal {L}_1$$ L1 norm and kernelised $$\mathcal {L}_2$$ L2 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. Results Several kernels were introduced for the kernel-based $$VO_2$$ VO2 modelling method. The results clearly indicated that the stable spline (SS) kernel has the best performance for $$VO_2$$ VO2 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)] ($$76.0\pm 5.72$$ 76.0±5.72 vs $$71.4\pm 7.24\%$$ 71.4±7.24% ). Conclusions The proposed nonparametric modelling method is an effective method for the estimation of the impulse response of VO 2—Speed system. Furthermore, the identified average nonparametric model method can dynamically predict $$VO_2$$ VO2 response with acceptable accuracy during treadmill exercise.
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