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.
