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It is well known that high-level noise exposure can lead to hearing loss. Noise-induced hearing loss (NIHL) continues to be one of the major occupational health hazards. An underlying assumption in current noise standards, e.g., ISO 1999:2013 (1), is that hearing loss is related to the total energy of the exposure. Thus, the risk of NIHL can be predicted according to the ISO 1999 prediction model. Unfortunately, the validity of the prediction model to correctly predict the NIHL for all types of noise exposure is still under question, especially for complex noise of impulsive character. The basis of current noise guidelines is the equal-energy hypothesis (EEH) approach, i.e., equivalent effects on hearing for a 3-dB increase or decrease in exposure intensity with a halving or doubling of the exposure duration, respectively. This approach is generally considered appropriate for steady-state noise but not for complex noise.
Steady-state continuous noise exposure has a Gaussian amplitude distribution. Therefore, the temporal characteristics of steady-state noise do not change over time. However, noise exposures often vary in the temporal pattern in many work environments. A complex noise is a non-Gaussian noise consisting of a Gaussian background noise punctuated by a temporally complex series of randomly occurring high-level noise transients. These transients can be brief high-level noise bursts or impacts. Industrial workers are often exposed to complex noise environments. Noises of the same or similar acoustic energies and spectra can have very different effects on hearing because of their different temporal structures.
The fundamental problem with current noise standards, e.g., ISO 1999 (1), is their reliance on an acoustic energy metric to quantify noise exposure. An acoustic energy metric completely ignores the effects of the temporal characteristics of noise exposure known to be important in affecting complex noise-induced hearing loss. Many published papers have shown that exposure to complex noise produces more hearing loss and sensory cell loss than an equivalent energy exposure to steady-state noise does in both animal and human models (2-5). It is reasonable that a metric that would incorporate and reflect the temporal structure of exposure might be a useful adjunct to the equivalent sound pressure level (Leq) metric. One such metric is the kurtosis of a noise exposure (3,5). Kurtosis (β) is a statistical measure of extreme values or outliers of a distribution. Kurtosis can be used to describe the amplitude “peakedness” of noise waveforms. It is worth mentioning that the Gaussian distribution has a kurtosis of 3. A complex non-Gaussian noise, β>3, can be effectively modeled as a combination of Gaussian noise, β=3, with various high-level transients superimposed.
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If, based on existing data, one accepts the proposition that kurtosis should be routinely measured in all industrial noise exposures, then the question of how best to measure the kurtosis metric should be considered. The kurtosis of the noise sample is dependent upon not just the probability of a high amplitude event to occur within the sample window, but also the length of the sample window. Recently, two algorithms were designed by Tian and colleagues (8) to investigate the correlation between window duration for kurtosis computation and the accuracy of NIHL prediction using a Chinese industrial database. They found that 60 seconds is the optimal window length for kurtosis calculation. Therefore, the kurtosis of noise exposure should be computed over consecutive 60-second time windows without overlap over the shift-long noise record using a sampling rate of 48 kHz. The mean of the measured kurtosis values is calculated and used as the kurtosis metric.
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So far, two kurtosis adjustment models have been proposed as follows:
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This model was used in Zhao et al. (4) and Xie et al. (9). The adjustment formula is listed below:
$$ {CNE}_{kurtosis-adjusted}={L}_{Aeq.8h}+\frac{\mathrm{ln}\left(\beta \right)+1.9}{\mathrm{l}\mathrm{o}\mathrm{g}\left(2\right)}\mathrm{l}\mathrm{o}\mathrm{g}\left(T\right) $$ (1) This form was chosen for calculating the kurtosis-adjusted cumulative noise exposure (CNE) because Gaussian noise has a kurtosis of β=3, and the term [(ln(β)+1.9)/log(2)] is close to 10. Thus, for Gaussian noise, the kurtosis-adjusted CNE equals the unadjusted CNE. According to Equation (1), for a fixed LAeq,8h, the kurtosis adjusted CNE of the non-Gaussian noise (β>3) is larger than that of the Gaussian noise (β=3), which is equivalent to prolonging the noise exposure duration.
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Goley et al. (10) presented another way to use kurtosis in NIHL evaluation. Goley and colleagues proposed a scheme that uses kurtosis to adjust the A-weighted equivalent sound pressure level (LAeq) directly. The basic form of the kurtosis-adjusted L'Aeq was determined as follows:
$$ {L}_{Aeq}^{'}={L}_{Aeq}+\lambda {log}_{10}\frac{{\beta }_{N}}{{\beta }_{G}} $$ (2) where λ is a positive constant to be determined from the dose-response correlation study, βN is the kurtosis of the noise, and βG=3 is the kurtosis of the Gaussian noise. Taking noise-induced permanent threshold shift as the dependent variable and LAeq and log(βN/3) as independent variables, the coefficient λ was calculated by multiple linear regression model. Based on the animal (chinchilla) model, Goley obtained λ=4.02. If the model is applied to humans, the value needs to be re-estimated using human data. Using Goley’s model is equivalent to adding an increment determined by the second term of the formula to the resulting total sound pressure level.
Calculating the Kurtosis of Noise Exposure
The Kurtosis Adjustment Models
Model 1 — kurtosis adjustment through exposure time:
Model 2 — kurtosis adjustment through LAeq
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