CHARACTERIZATION OF NOISE WITH FRACTIONAL-OCTAVE-BAND FILTERS AND THE VARIANCE AND KURTOSIS OF THE SOUND PRESSURE
Open Access
- Author:
- Zechmann, Edward Louis
- Graduate Program:
- Acoustics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- October 25, 2018
- Committee Members:
- Daniel Allen Russell, Dissertation Advisor/Co-Advisor
Daniel Allen Russell, Committee Chair/Co-Chair
Michelle Celine Vigeant, Committee Member
Victor Ward Sparrow, Committee Member
Aleksandra B Slavkovic, Outside Member
William Murphy, Special Member
Ingrid Blood, Committee Member - Keywords:
- highest density interval
fractional octave band
impulsive noise
moment
region of practical equivalence
kurtosis
kurtosis
highest density interval
fractional octave band
impulsive noise
moment
region of practical equivalence - Abstract:
- Approximately 22 million workers in the United States have been exposed to hazardous occupational noise within the previous year. Current noise exposure metrics are not adequate for characterizing noise exposure to impulsive noise. For the same A-weighted sound pressure level, noise with a higher marginalized time frequency kurtosis value has been found to have a greater risk of causing hearing impairment. The marginalized time-frequency kurtosis has certain limitations. Optimizing the resolution in time and frequency for the calculation of kurtosis may help to get past those limitations. A signal processing methodology which completely characterizes the sound pressure time waveform at a worker’s ear is needed. The signal processing methodology needs to produce a set of predictors which can be used to model hearing loss. This dissertation describes the effects which substantially influence hearing loss caused by hair cell death resulting from metabolic damage to the hair cells. One method of modeling the effects influencing hearing loss uses probability models with a theoretical foundation in stochastic process theory. This dissertation describes the theoretical foundations for a stochastic process model of hearing loss due to hair cell death with the aim of satisfying all of the underlying assumptions. This dissertation proposes a new signal processing methodology which simultaneously considers both time and frequency dependency. In the proposed time frequency analysis, Butterworth fractional-octave-band filters with resampling are implemented such that all of the time-frequency frames have an equal area, the same number of wave periods, and the same number of samples. The sound pressure distribution in each frame is characterized by the method of moments. In each frame, the time window size is chosen to be as small as reasonably possible. The time step size is chosen so that estimates of the moments are at least piecewise linear continuous. The frequency window size and frequency step size of one-third-octave-bands were found to have a reasonable compromise of resolution in time and frequency. A new way to determine a reasonable sample size is proposed for estimating the sample moments. The reasonable sample size was determined using a statistical methodology for inference appropriate for empirical distributions that are not normally distributed and have outliers. The statistical methodology needed to distinguish between different distributions of sound pressure commonly encountered in acoustics and control for both false negatives and false positives. The methodology uses practical equivalence of moments based on an interval equal to the typical uncertainty of a sound level measurement of 2 dB. To control for false negatives and false positives in a practical way two goals were established. Goal 1 tests whether a sample statistic is practically equivalent to a known population parameter. Goal 2 tests whether a sample statistic is not practically equivalent to a specified population parameter. The sample size was chosen so that the probabilities that the 95% Highest Density Interval (HDI) was entirely included within the Goal 1 Region of Practical Equivalence (ROPE) and the 95% HDI was entirely excluded outside the Goal 2 ROPE were approximately equal to 1. The proposed signal processing method with fifth order one-third-octave-band Butterworth filters was tested on simulations, and noise exposure recordings from data sets of chinchillas, and from data sets of workers in China. When using the proposed signal processing methodology, the time and frequency conditioned mean, variance, skewness, and kurtosis are shown to be sufficient to describe the first ten moments. The log-scaled variance is similar to the sound pressure level. The kurtosis level is the log-scaled kurtosis. The sound pressure level and kurtosis level are generally adequate to describe sound pressure distributions for peak sound pressure levels less than 130 dB. When using the proposed signal processing methodology, log-scaled variance and the kurtosis level provide different information. The log-scaled variance is a measure of the spread of the sound pressure distribution about the mean in a frame. The log-scaled variance is can be interpreted as a continuous scale of the log-scaled amplitude of the sound pressure distribution in a frame. The kurtosis level is a measure of the tendency of a sound pressure distribution to produce a single extreme outlier in a frame. The kurtosis level can be interpreted as a continuous scale for the relative amplitude contribution of pure tones, white noise, and impulse noise in a frame. Kurtosis levels near -3 dB indicate a dominant pure tone. Kurtosis levels near 0 dB indicate white noise. Kurtosis levels of 5 dB and greater indicate an impulse. When using the proposed signal processing methodology, the kurtosis level is useful for indicating the relative contributions of pure tones, white noise, and impulsive noise in a frame for many different sound pressure time waveforms. By using the proposed signal processing methodology the kurtosis level has a consistent interpretation across all frequency bands. The log-scaled variance and kurtosis level should both be considered for development of a new metric for characterizing noise exposure to impulsive noise using the proposed signal processing methodology.