Constructing the prediction model of maximal oxygen uptake by back-propagation neural network based on the cardiorespiratory optimal point

doi:10.12307/2023.054

Abstract

Abstract: BACKGROUND: Maximal oxygen uptake is considered as the “gold standard” for evaluating aerobic exercise capacity and cardiopulmonary health. However, the measurement of maximal oxygen uptake requires a strong exercise load, and there are some limitations such as low reproducibility of the index and subjective effect of the test participants.
OBJECTIVE: To construct the prediction model of maximal oxygen uptake using the new sub-maximal exercise evaluation index - cardiorespiratory optimal point - through the back-propagation neural network.
METHODS: The trial protocol was approved by the Ethics Committee of the China Institute of Sports Science. Eighty healthy college students (40 males and 40 females) were randomly recruited. They were fully informed of the trial process and purpose and voluntarily signed informed consent to cooperate with the whole trial process. The participants underwent an incremental load cardiopulmonary exercise test to identify the maximal oxygen uptake, cardiorespiratory optimal point, and other related indicators for correlation analysis to obtain statistically significant indicators. Then, the prediction model of maximal oxygen uptake was built.
RESULTS AND CONCLUSION: There were significant correlations between maximal oxygen uptake and cardiorespiratory optimal point, body mass index, sex, oxygen uptake and power corresponding to the cardiorespiratory optimal point (P < 0.01). The prediction model of maximal oxygen uptake with classical three-layer topology was established using the back-propagation neural network, including 5 input layers, 10 hidden layers and 1 output layer. The mean absolute and relative errors between the predicted and measured values of the model were 0.227 L/min and 12%, respectively. This indicated that the back propagation neural network model built based on the cardiorespiratory optimal point could accurately and effectively predict the maximal oxygen uptake. There was no significant difference between the maximal oxygen uptake predicted value of the back propagation neural network model and that of the multiple linear regression model (P > 0.05). However, the prediction accuracy of the back propagation neural network model constructed according to the cardiorespiratory optimal point was better than that of the multiple linear regression model.

Key words: cardiorespiratory optimal point, maximal oxygen uptake, back-propagation neural network, cardiopulmonary exercise test

CLC Number:

Wu Dongzhe, Gao Xiaolin, Li Chuangtao, Wang Hao. Constructing the prediction model of maximal oxygen uptake by back-propagation neural network based on the cardiorespiratory optimal point[J]. Chinese Journal of Tissue Engineering Research, 2023, 27(8): 1224-1231.

Figures/Tables 12

2.6 反向传播神经网络模型 2.6.1 反向传播神经网络的选择由上文可知，反向传播神经网络具备良好的非线性映射能力、精确泛化能力与高度的容错性，基于该网络对数据预测所具有的独特优势，选择反向传播神经网络作为最大摄氧量预测的数学模型。根据以往研究证明多隐藏层神经网络虽依据数据特性具有一定的优势，但其预测效果并未优异于单层隐藏层的神经网络[25]。此次研究选择采用经典3层拓扑结构以构建最大摄氧量预测模型。 2.6.2 输入输出变量的选取由相关分析结果可知，受试者性别、体质量指数、心肺最佳点、VO2COP和WRCOP均与最大摄氧量呈高度相关(P < 0.01)，故选取该5个指标引入反向传播神经网络输入层(Input)，输入层节点数为5。将最大摄氧量引入反向传播神经网络输出层(Output)作为该神经网络的唯一输出变量，输出层节点数为1。 2.6.3 数据归一化处理反向传播神经网络输入层输出层数据及节点数确定后，为减小因数据范围差距较大导致的预测误差，所以对试验数据进行归一化处理。因性别取值范围采用[1，2]，故将输入层5项指标均按公式Y=(X-Zmin)/(Zmax-Zmin)进行归一化处理，数据归一化后Y取值在[-1，1]。 2.6.4 隐藏层节点数量的选择由上文可知，该反向传播神经网络预测模型输入层选取具有统计学意义的性别、体质量指数、心肺最佳点、VO2COP和WRCOP，节点数为5；输出层选择最大摄氧量作为模型唯一输出变量，节点数为1。隐藏层节点数的选择对于反向传播神经网络模型成功构建至关重要，节点数过多将会增加模型计算量和复杂性且可能导致数据产生过度拟合，而隐藏层节点数过小将导致模型未达到最优预测效果便结束，影响模型预测准确性。根据以往研究，隐藏层数量的选择是据经验公式 nl为隐藏层节点数；n为输入层节点数；m为输出层节点数；a∈[1，10]。因该网络输入层节点数为5、输出层为1[26]，将其引入经验公式进行推导，并根据神经网络预测结果进行调整，最终确定当隐藏层数量为10的时候预测效果较好，故该神经网络隐藏层数量选择10，构建结构为5-10-1的反向传播神经网络预测模型。 2.6.5 反向传播神经网络模型建立与训练此次试验中顺利完成整个试验流程视为有效数据，80名志愿者均完成整个试验流程。从受试者人数中随机选取80%(64名)作为训练集、20%(16名)作为测试集。该反向传播神经网络输入层到隐藏层的传递函数及输出层的传递函数均采用S型正切函数tansig作为隐藏层神经元的激励函数，隐藏层到输出层的传递函数选择Pruelin线性函数。基于均方根误差(Mean squared error，MSE)网络性能函数设定该网络最大迭代次数为1 000次；反向传播神经网络运算过程中学习率的选择尤为重要，学习率取值越大网络处理及收敛速度也就越快，但数值过大会引起网络模型不稳定状况；相反，学习率取值越低网络模型稳定性便越强，但网络模型相应的运算速度及收敛速度会受到一定程度的影响。因此，基于以往研究该神经网络模型学习率设定为0.01。选择准确性较强、收敛速度较快的Levenberg-Marquardt算法进行计算并完成建模，见图2。反向传播神经网络模型构建完成后开始进行反复迭代训练，经8次迭代后神经网络模型收敛完成，训练集R=0.957 28，验证集R=0.965 12，训练集R=0.966 95，整体R=0.940 76，各数据点均匀分布在拟合曲线附近，提示该模型拟合度尚可且具有良好的预测效果，见图3，4。 "

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