The multi-fractal de-trended fluctuation analysis was used to estimate the mental stress in the present study. In order to obtain the optimal fractal order of the multi-fractal de-trended fluctuation analysis, we analyzed the relationship between singular index and Hurst index with order. We recorded the electroencephalogram (EEG) of 14 students, compared the relationship between singular index, Hurst index and quality index, ensured the optimal order being [-5, 5] and achieved the estimation of mental stress with the β wave in the EEGs. The result indicated that Hurst index and quality index of the EEGs under mental stress were greater than those of EEGs in the relaxing state. The Hurst index was gradually decreasing with the order increasing and was finally approaching a constant, while the quality index was amplified and variation of amplitude of the singular index was more obvious. We also compared the amplitude and the width of singular spectrum of the EEGs under the two conditions, and results indicated that the characteristics of multi-fractal spectrum of the EEGs under different conditions were different, namely the width of singular spectrum of the EEGs under mental stress was greater than that under relax condition.
本文基于多重分形去趋势波动分析方法（MFDFA）实现了对受试者心理压力状态的评估。研究针对不同心理压力状态下，脑电信号多重分形去趋势波动分析中最优分形阶数确定问题，重点分析了多重分形去趋势波动分析方法中的奇异指数、Hurst 指数等参数与阶数的关系，进而确定最优分形阶数，实现了基于脑电信号多重分形去趋势波动分析的心理压力状态评估。试验采集了 14 名在校学生有/无心理压力状态下的脑电信号，分别比较了奇异指数、奇异维数、Hurst 指数、质量指数与阶数关系，确定了最优分形阶数范围为 [—5, 5]，实现了基于脑电信号 β 波多重分形去趋势波动分析方法的心理压力状态评估。研究结果表明，心理压力状态下，脑电信号的 Hurst 指数和质量指数大于无压力状态下，脑电信号的相应参数，随着阶数的变大，Hurst 指数减小，趋近于定值，而质量指数增大，奇异值随阶数的变化幅度较明显。本文还比较了有/无心理压力状态下，脑电信号的峰值和奇异谱宽度，结果表明，不同心理压力状态下脑电信号多重分形谱特性不同，心理压力状态下，脑电信号的奇异谱宽度明显大于无压力状态下脑电信号的奇异谱宽度。本文研究结果说明，该方法可以有效地评估心理压力状态，为实现心理压力状态干预，提高心理健康等提供支持与帮助。.
Keywords: electroencephalogram; multi-fractal de-trended fluctuation analysis; singular index; singular spectrum width.