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KURTOSIS METRIC IN NOISE ANALYSIS
Figure 6. The estimated marginal means of the actual measured noise-induced permanent threshold shift (NIPTS) at each kurtosis value across test frequencies for four noise- level bins in two different exposure durations: A: less than or equal to 10 years. B: greater than 10 years. Error bars, standard error of the means. Adapted from Zhang et al., 2020.
which the calculation is made, its calculation is limited by the computer’s processing capabilities. All previously cited human studies chose to use a 40-second time window based on the work of Hamernik et al. (2003). The mean of the measured kurtosis values was calculated and used as the kurtosis metric for a full-shift noise exposure.
Kurtosis as an Adjunct to Energy in the Evaluation of Noise-Induced Hearing Loss Because noise-induced hearing loss is directly related to both noise level and exposure duration, increases in
each parameter can be expected to increase the extent of hearing loss. As mentioned in the Introduction, a complex non-Gaussian noise is more harmful to hearing than a Gaussian noise with the same noise level and exposure duration. Additional hearing loss caused by complex noise is positively correlated with the kurtosis of noise. Thus, a proper kurtosis correction through an equivalent exposure level (LAeq,8h) or exposure duration may serve as a good noise metric for assessing the risk of noise with different temporal characteristics. So far, two kurtosis adjustment methods have been considered.
Method 1: Kurtosis Adjustment Through Exposure Time
This method was used in Zhao et al. (2010) and Xie et al. (2016) and was discussed in Kurtosis Calculations. The adjustment formula is shown below
CNE(β) = LAeq,8h+ log(T) (2)
where T is exposure duration in years. It can be seen from Eq. 2 that for a fixed 8-hour exposure (LAeq,8h), the kurtosis adjusted CNE will be larger for non-Gaussian noise (β > 3) than for Gaussian noise (β = 3), which is equivalent to extending the duration of noise exposure, provided that the exposure time is greater than one year. The application of Zhao’s method was introduced above and the results are shown in Figure 5.
Method 2: Kurtosis Adjustment Through Energy
Goley et al. (2011) presented another way to use kurtosis in the evaluation of hearing loss, which differed from the method proposed by Zhao et al. (2010). Instead of making the kurtosis correction through the exposure time, Goley et al. proposed a method that uses kurtosis to directly adjust the A-weighted equivalent sound pressure level (LAeq). The following kurtosis-correction formula was proposed
L'Aeq = LAeq+λlog10 (3)
where λ is a positive constant determined from the dose- response correlation study, β is the kurtosis of the noise, and βG =3 is the kurtosis of the Gaussian noise. Using Goley et al. (2011) method is equivalent to adding a penalty, determined by the second term in the formula, to the overall sound pressure level. Goley and colleagues applied this model to Zhao et al.’s data (2010) and found similar results, as shown in Figure 5B.
44 Acoustics Today • Winter 2020
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