Kurtosis Statistic Research Articles

THE GROWTH OF NIGERIA'S ECONOMY FROM 1981 TO 2019 IN RELATION TO THE FINANCING OF AGRICULTURE

The analysis of various economic variables in Nigeria from 1981 to 2019 shows that the country’s economy has been heavily reliant on oil exports, which has left it vulnerable to external shocks and hindered economic growth. This over-reliance on oil exports has led to neglect of the agricultural sector, which was once the main source of foreign currency earnings for Nigeria. As a result, there has been a decline in food production and an increase in imports. However, a study investigating the impact of government spending on agriculture on Nigeria’s economic growth using secondary data covering the same period shows that investing in agriculture is essential for Nigeria to achieve a diversified economy and sustainable economic growth. The study uses the Ordinary Least Square (OLS) approach and the Augmented Dickey-Fuller (ADF) unit root test to analyze the data and concludes that diversifying the economy into non-oil industries, such as agriculture, is likely to have a significant impact on economic growth. The regression analysis showed that government agricultural spending has a positive impact on economic growth. The findings suggest that RGDP, AO, AL, AE, and IFR had an up-down tendency, while INT had an up-down-up trend. The skewness statistic indicates that the variables’ frequency distributions were positively skewed, while the Kurtosis statistic indicates that they were normally distributed. The unit root tests indicate that all variables were stationary at 5%. The regression analysis showed that AO had a positive association with RGDP, while AL had a negative association with it. The study also provides additional information, such as the contribution of agriculture to Nigeria’s GDP and the statistical reliability of the variables.

Advancing support for cause-and-effect models by estimating the kurtosis statistic using fractional-octave-band filters

This paper presents a preliminary method for estimating signal processing parameters that optimally satisfies accuracy and resolution requirements for the sound pressure level and kurtosis level. The kurtosis statistic has long been studied and more recently used for applications in acoustics and vibrations such as architectural acoustics, hearing loss, noise exposure, and accelerated material and structural life testing. The temporal and spectral characteristics of many quantities are evident by time-frequency analysis including hearing, finger sensation, sound diffusion, and reverberation. Some research has conditioned on frequency content while other research has not. Simpson's reversal may potentially adversely affect the models if frequency content is not considered. Modeling techniques which relate cause-and-effect are more likely to result in successful models. Models of human hearing are particularly sensitive to the frequency content because the tonotopic organization of the cochlea induces a cause-and-effect relationship from sound incident on the ear to the basilar membrane. The fractional-octave-band filters specified in ANSI S1.11 and IEC 61260-1 are well developed for conditioning on frequency bands. This paper provides details of the process for optimizing the filter parameters. Additional optimization and testing is described for developing a faster and more accurate method with better support for causal inference.

Evaluating worker noise exposure levels in the presence of complex noise

Recent research into the assessment of worker noise exposure has demonstrated that the combination of impulsive noise and continuous noise creates an additional risk of developing noise-induced hearing loss (NIHL). Zhang et al (2021) demonstrated that workers exposed to non-Gaussian noise accumulated NIHL at a faster rate over their careers than worker exposed to Gaussian noise. The kurtosis statistic of the sound pressure distribution provides a means to adjust the estimated risk of hearing loss between exposure groups exposed to different types of noise. This paper will review the results from our recent studies of kurtosis and exposure level. Some unanswered questions involve the selection of a suitable sample length to estimate kurtosis, the selection of a compensation factor to apply, and understanding the differences exhibited in short (less than 10 years) and long-term exposures and kurtosis.

Asymptotic Variance of Test Statistics in the ML and QML Frameworks

In this study, we consider the test statistics that can be written as the sample average of data and derive their limiting distributions under the maximum likelihood (ML) and the quasi-maximum likelihood (QML) frameworks. We first generalize the asymptotic variance formula suggested in Pierce (Ann Stat 10(2):475–478, 1982) in the ML framework and illustrate its applications through some well-known test statistics: (1) the skewness statistic, (2) the kurtosis statistic, (3) the Cox statistic, (4) the information matrix test statistic, and (5) the Durbin’s h-statistic. We next provide a similar result in the QML setting and illustrate its applications by providing two examples. Illustrations show the simplicity and the effectiveness of our results for the asymptotic variance of test statistics, and therefore, they are recommended for practical applications.

DETECTING BID-RIGGING CARTELS WITH DESCRIPTIVE STATISTICS

Abstract The paper shows that descriptive statistics, used as screens, capture the effect of bid rigging in the distribution of the bids. The bid-rigging cartel studied in this paper negatively affected the variance of the bids as illustrated by the coefficient of variance and the kurtosis statistic. Furthermore, it cleverly manipulated the differences between bids to secure that the designated bidder from the cartel won the contract. Such cover-bidding mechanism produced asymmetry in the distribution of the bids illustrated by the relative distance, the skewness statistic, and the percentage difference between the first and second lowest bids. The descriptive statistics capture the change in the statistical pattern of the distribution of the bids between periods of collusion and competition. Moreover, the bid rotation screen shows that the behavior of firms changed radically between the cartel and post-cartel periods. Finally, the paper discusses policy implications for competition agencies wishing to set up a detection method for screening procurement markets.

Asymptotic Variance of Test Statistics in ML and QML Frameworks

In this study, we consider the test statistics that can be written as the sample average of data and derive their limiting distribution under the maximum likelihood (ML) and the quasi-maximum likelihood (QML) frameworks. We first generalize the asymptotic variance formula suggested in Pierce (1982) in the ML framework and illustrate its applications through some well-known test statistics: (i) the skewness statistic, (ii) the kurtosis statistic, (iii) the Cox statistic, (iv) the information matrix test statistic, and (v) the Durbin's h-statistic. We next provide a similar result in the QML setting and illustrate its applications by providing two examples. Illustrations show the simplicity and the effectiveness of our results for the asymptotic variance of test statistics, and therefore, they are recommended for practical applications.

Use of the kurtosis statistic in an evaluation of the effects of noise and solvent exposures on the hearing thresholds of workers: An exploratory study.

The aim of this exploratory study was to examine whether the kurtosis metric can contribute to investigations of the effects of combined exposure to noise and solvents on human hearing thresholds. Twenty factory workers exposed to noise and solvents along with 20 workers of similar age exposed only to noise in eastern China were investigated using pure-tone audiometry (1000-8000 Hz). Exposure histories and shift-long noise recording files were obtained for each participant. The data were used in the calculation of the cumulative noise exposure (CNE) and CNE adjusted by the kurtosis metric for each participant. Passive samplers were used to measure solvent concentrations for each worker exposed to solvents over the full work shift. Results showed an interaction between noise exposure and solvents for the hearing threshold at 6000 Hz. This effect was observed only when the CNE level was adjusted by the kurtosis metric.

Quantifying the non-normality of shear strength of geomaterials

Geotechnical shear strength variables generally include the cohesion and angle of internal friction based upon the Mohr-Coulomb failure criterion. In this study, the non-normality of a univariate probability density function (PDF) and the bivariate probability density contour (PDC) of observed shear strength pairs is examined for 33 geomaterial types, comprising of soils (24 types), rocks (7 types), and geosynthetic clay liners (2 types), with sample sizes ranging from 14 to 97. After a detailed analysis on the graphic features of probability density and box-whisker plots of shear strength parameters, normality testing is further quantified by skewness, kurtosis, and energy statistic tests. In most cases (23/31), distributions of cohesion are positively skewed, as are distributions of friction angle (17/29), while the distribution of these parameters is mostly platykurtic (characterised by negative excess kurtosis). Bivariate energy statistic analyses of shear strength pairs indicate that, in ten cases, p-values are below .05, demonstrating that the joint distribution differs from the bivariate normal distribution, and these results are largely consistent with those achieved by the Shapiro-Wilk test. Moreover, a slope stability analysis with different joint distributions is used to assess the impact of marginal PDFs on the failure probability.

The Use of the Kurtosis-Adjusted Cumulative Noise Exposure Metric in Evaluating the Hearing Loss Risk for Complex Noise.

To test a kurtosis-adjusted cumulative noise exposure (CNE) metric for use in evaluating the risk of hearing loss among workers exposed to industrial noises. Specifically, to evaluate whether the kurtosis-adjusted CNE (1) provides a better association with observed industrial noise-induced hearing loss, and (2) provides a single metric applicable to both complex (non-Gaussian [non-G]) and continuous or steady state (Gaussian [G]) noise exposures for predicting noise-induced hearing loss (dose-response curves). Audiometric and noise exposure data were acquired on a population of screened workers (N = 341) from two steel manufacturing plants located in Zhejiang province and a textile manufacturing plant located in Henan province, China. All the subjects from the two steel manufacturing plants (N = 178) were exposed to complex noise, whereas the subjects from textile manufacturing plant (N = 163) were exposed to a G continuous noise. Each subject was given an otologic examination to determine their pure-tone HTL and had their personal 8-hr equivalent A-weighted noise exposure (LAeq) and full-shift noise kurtosis statistic (which is sensitive to the peaks and temporal characteristics of noise exposures) measured. For each subject, an unadjusted and kurtosis-adjusted CNE index for the years worked was created. Multiple linear regression analysis controlling for age was used to determine the relationship between CNE (unadjusted and kurtosis adjusted) and the mean HTL at 3, 4, and 6 kHz (HTL346) among the complex noise-exposed group. In addition, each subject's HTLs from 0.5 to 8.0 kHz were age and sex adjusted using Annex A (ISO-1999) to determine whether they had adjusted high-frequency noise-induced hearing loss (AHFNIHL), defined as an adjusted HTL shift of 30 dB or greater at 3.0, 4.0, or 6.0 kHz in either ear. Dose-response curves for AHFNIHL were developed separately for workers exposed to G and non-G noise using both unadjusted and adjusted CNE as the exposure matric. Multiple linear regression analysis among complex exposed workers demonstrated that the correlation between HTL3,4,6 and CNE controlling for age was improved when using the kurtosis-adjusted CNE compared with the unadjusted CNE (R = 0.386 versus 0.350) and that noise accounted for a greater proportion of hearing loss. In addition, although dose-response curves for AHFNIHL were distinctly different when using unadjusted CNE, they overlapped when using the kurtosis-adjusted CNE. For the same exposure level, the prevalence of NIHL is greater in workers exposed to complex noise environments than in workers exposed to a continuous noise. Kurtosis adjustment of CNE improved the correlation with NIHL and provided a single metric for dose-response effects across different types of noise. The kurtosis-adjusted CNE may be a reasonable candidate for use in NIHL risk assessment across a wide variety of noise environments.

Curvelet domain denoising based on kurtosis characteristics

Curvelet transform can be effective in eliminating seismic noise by properly setting a threshold to the curvelet coefficients. However, when the signal-to-noise ratio (SNR) of data is low, it is difficult to select a suitable threshold to remove data noise, because the curvelet coefficients are similar between signals and noise. In this paper, we propose to incorporate the kurtosis statistic representing non-Gaussian characteristics of signals into an adaptive threshold-setting scheme. Curvelet transform decomposes noisy seismic data into curvelets with different scales and directions. The kurtosis estimated from the coefficient matrix at each scale and direction is then used to weight the threshold. Therefore, the threshold difference between signals and noise is enlarged and signals will be better preserved in seismic reconstruction. Synthetic and real data examples demonstrate that curvelet selection based on the kurtosis statistic removes data noise effectively, and thus is a credible method for denoising and signal preserving of seismic data with low SNR.

The value of a kurtosis metric in estimating the hazard to hearing of complex industrial noise exposures

A series of Gaussian and non-Gaussian equal energy noise exposures were designed with the objective of establishing the extent to which the kurtosis statistic could be used to grade the severity of noise trauma produced by the exposures. Here, 225 chinchillas distributed in 29 groups, with 6 to 8 animals per group, were exposed at 97 dB SPL. The equal energy exposures were presented either continuously for 5 d or on an interrupted schedule for 19 d. The non-Gaussian noises all differed in the level of the kurtosis statistic or in the temporal structure of the noise, where the latter was defined by different peak, interval, and duration histograms of the impact noise transients embedded in the noise signal. Noise-induced trauma was estimated from auditory evoked potential hearing thresholds and surface preparation histology that quantified sensory cell loss. Results indicated that the equal energy hypothesis is a valid unifying principle for estimating the consequences of an exposure if and only if the equivalent energy exposures had the same kurtosis. Furthermore, for the same level of kurtosis the detailed temporal structure of an exposure does not have a strong effect on trauma.

Focal Peak Activities in Spread of Interictal-Ictal Discharges in Epilepsy with Beamformer MEG: Evidence for an Epileptic Network?

Non-invasive studies to predict regions of seizure onset are important for planning intracranial grid locations for invasive cortical recordings prior to resective surgery for patients with medically intractable epilepsy. The neurosurgeon needs to know both the seizure onset zone (SOZ) and the region of immediate cortical spread to determine the epileptogenic zone to be resected. The immediate zone of spread may be immediately adjacent, on a nearby gyrus, in a different lobe, and sometimes even in the contralateral cerebral hemisphere. We reviewed consecutive simultaneous EEG/MEG recordings on 162 children with medically intractable epilepsy. We analyzed the MEG signals in the bandwidth 20–70 Hz with a beamformer algorithm, synthetic aperture magnetometry, at a 2.5 mm voxel spacing throughout the brain (virtual sensor locations, VSLs) with the kurtosis statistic (g2) to determine presence of excess kurtosis (γ2) consistent with intermittent increased high frequency spikiness of the background. The MEG time series was reconstructed (virtual sensor signals) at each of these VSLs. The VS signals were further examined with a relative peak amplitude spike detection algorithm. The time of VS spike detection was compared to the simultaneous EEG and MEG sensor signals for presence of conventional epileptiform spike morphology in the latter signals. The time of VS spike detection was compared across VSLs to determine earliest and last VSL to show a VS spike. Seven subjects showed delay in activation across VS locations detectable on visual examination. We compared the VS locations that showed earliest and later VS spikes with the locations on intracranial grid locations by electrocorticography (ECoG) that showed spikes and both onset and spread of seizures. We compared completeness of resection of VS locations to postoperative outcome. The VS locations for spike onset and spread were similar to locations for ictal onset and spread by ECoG.

A Comparison of Chronic Manual and Automated Red Blood Cell Exchange Transfusion in Sickle Cell Disease Patients From Two Comprehensive Care Centres in the United Kingdom

AbstractAbstract 3430Chronic transfusion is indicated in the treatment and prevention of sickle cell disease (SCD) related-complications. Red blood cell exchange (RBCX) is preferred over top-up transfusion as it enables iron balance and rapid reduction of sickle hemoglobin (HbS) without increasing blood viscosity. RBCX can be done manually by sequential phlebotomy and transfusion or by automated apheresis, but the two methods have not been formally compared. Bart’s Health NHS Trust (BHT) performs manual RBCX and Guy’s and St. Thomas NHS Trust (GSTT) automated RBCX. Manual RBCX consists of isovolumetric exchange 15 to 20 mL/kg of venesected blood for normal saline and packed RBC, generally at a 1:1 ratio. Automated RBCX utilizes the Spectra Optia Apheresis System with a fractional cell remaining between 24 and 44, end Hct within 0.02 of pre-RBCX Hct, and a fluid replacement balance of 100%. The indications for RBCX and pre-RBCX HbS or hemoglobin SC (HbSC) target (30% or 50%, depending on indication) are the same in both units. All packed RBC were leukodepleted, HbS negative, ≤ 7 days old, and phenotypically matched for C, D, E, and Kell.A retrospective observational cohort study as part of a quality assurance audit was conducted examining all SCD patients attending regular RBCX at BHT and GSTT between 1 May 2011 and 30 April 2012. Fifty-one patients (21 manual, 30 automated), totaling 401 RBCX sessions were included. Ten patients in the manual group and 7 patients in the automated group targeted an HbS of < 30%, while the rest were targeted to < 50%. There was no significant difference in baseline characteristics between the two groups. Peripheral vein was the most common method of cannulation in manual RBCX while temporary central venous catheterization was most common in automated RBCX (P < 0.0001). Time interval differed between manual and automated RBCX (median 4.4 vs. 7.1 weeks, P < 0.0001). Both groups consistently achieved a post-RBCX Hct < 0.350. More patients on automated RBCX were able to consistently achieve their prescribed HbS or HbSC target (defined as > 2/3 of RBCX sessions) than on manual RBCX (37% vs. 10%, unadjusted OR 5.5, 95% CI 1.07 – 28.22, P = 0.048). When adjusted for the prescribed pre-RBCX HbS or HbSC target, the Mantel-Haenszel OR estimate was 4.72 (95% CI 0.885 – 25.17). Older age was also associated with consistently achieving the prescribed HbS or HbSC target (P = 0.010 on multivariable logistric regression). Although the yearly volume of RBC and donor units used were significantly higher in the automated group (241.1 mL/kg/year and 55 units/year) compared to the manual group (127 mL/kg/year and 32 units/year), there was no difference in the rate of allo-antibody formation. There was no difference in the mean ferritin trend between manual and automated RBCX in non-chelated patients (−0.068 ± 1.439 vs. −0.297 ± 2.027 ug/L/day, P = 0.439). Automated RBCX was better at maintaining a near zero iron balance than manual RBCX due to considerable individual variability in the manual group (kurtosis statistic 13.221 ± 0.935 SE vs. 0.398 ± 1.121 SE). It took a significantly longer time to perform a manual RBCX session than an automated one (257 min. vs. 115 min.). There was no significant difference in the number of adverse events. The number of RBCX sessions that had to be converted to top-up transfusions in the manual group because of low pre-RBCX haematocrit far exceeded that of the automated group (11 vs. 0 sessions). None of the patients in either group had new or progressive neurological events.Manual RBCX, despite an optimized protocol and strict adherence to treatement, is inferior to automated RBCX in being able to consistently achieve the prescribed HbS target, although consistent adherence with automated RBCX can also be challenging. Automated RBCX requires less time to perform than manual RBCX, but involves higher RBC use and more donor exposure. Adverse events and antibody formation are the same for both methods. Automated RBCX can maintain a near zero iron balance in most patients without the use of iron chelation and with less individual variability than manual RBCX. The results suggest that automated RBCX is the preferred RBC exchange method in controlling HbS in SCD patients. Further longitudinal study is required to determine whether a better control of HbS translates into differences in patient-related outcomes. Disclosures:No relevant conflicts of interest to declare.

A FOREGROUND-CLEANED COSMIC MICROWAVE BACKGROUND MAP FROM NON-GAUSSIANITY MEASUREMENT

In this paper we present a new method to estimate a foreground cleaned Cosmic Microwave Background (CMB) map at a resolution of $1^\circ$ by minimizing the non-Gaussian properties of the cleaned map which arise dominantly due to diffuse foreground emission components from the Milky Way. We employ simple kurtosis statistic as the measure of non-Gaussian properties and perform a linear combination of 5 frequency maps provided by Wilkinson Microwave Anisotropy Probe (WMAP) in its 7 year data release in such a way that the cleaned map has a minimum kurtosis which leads to a non-Gaussianity minimized, foreground cleaned CMB map. We validate the method by performing Monte-Carlo simulations. To minimize any residual foreground contamination from the cleaned map we flag out region near the galactic plane based upon results from simulations. Outside the masked region our new estimate of CMB map matches well with the WMAP's ILC map. A simple pseudo-$C_l$ based CMB TT power spectrum derived from the non-gaussianity minimized map reproduces the earlier results of WMAP's power spectrum. {\it An important advantage of the method is that it does not introduce any negative bias in angular power spectrum in low multipole regime, unlike usual ILC method.} Comparing our results with the previously published results we argue that CMB results are robust with respect to specific foreground removal algorithms employed.

Test for dispersion constancy in stochastic differential equation models

In this paper, we propose a constancy test for volatility in It processes based on discretely sampled data. The test statistic constitutes an integration of the Ljung–Box test statistic and the kurtosis statistic in the Jarque–Bera test. It is shown that under regularity conditions, the proposed test asymptotically follows a chi‐square distribution under the null hypothesis of constant volatility. To evaluate the test, empirical sizes and powers were examined through a simulation study. Analysis of real data including ultra‐high frequency transaction data and interest rates was also conducted for illustration. Copyright © 2011 John Wiley &amp; Sons, Ltd.

Application of the Kurtosis Statistic to the Evaluation of the Risk of Hearing Loss in Workers Exposed to High-Level Complex Noise

Develop dose-response relations for two groups of industrial workers exposed to Gaussian or non-Gaussian (complex) types of continuous noises and to investigate what role, if any, the kurtosis statistic can play in the evaluation of industrial noise-induced hearing loss (NIHL). Audiometric and noise exposure data were acquired on a population (N = 195) of screened workers from a textile manufacturing plant and a metal fabrication facility located in Henan province of China. Thirty-two of the subjects were exposed to non-Gaussian (non-G) noise and 163 were exposed to a Gaussian (G) continuous noise. Each subject was given a general physical and an otologic examination. Hearing threshold levels (0.5-8.0 kHz) were age adjusted (ISI-1999) and the prevalence of NIHL at 3, 4, or 6 kHz was determined. The kurtosis metric, which is sensitive to the peak and temporal characteristics of a noise, was introduced into the calculation of the cumulative noise exposure metric. Using the prevalence of hearing loss and the cumulative noise exposure metric, a dose-response relation for the G and non-G noise-exposed groups was constructed. An analysis of the noise environments in the two plants showed that the noise exposures in the textile plant were of a Gaussian type with an Leq(A)8hr that varied from 96 to 105 dB whereas the exposures in the metal fabrication facility with an Leq(A)8hr = 95 dB were of a non-G type containing high levels (up to 125 dB peak SPL) of impact noise. The kurtosis statistic was used to quantify the deviation of the non-G noise environment from the Gaussian. The dose-response relation for the non-G noise-exposed subjects showed a higher prevalence of hearing loss for a comparable cumulative noise exposure than did the G noise-exposed subjects. By introducing the kurtosis variable into the temporal component of the cumulative noise exposure calculation, the two dose-response curves could be made to overlap, essentially yielding an equivalent noise-induced effect for the two study groups. For the same exposure level, the prevalence of NIHL is greater in workers exposed to non-G noise environments than for workers exposed to G noise. The kurtosis metric may be a reasonable candidate for use in modifying exposure level calculations that are used to estimate the risk of NIHL from any type of noise exposure environment. However, studies involving a large number of workers with well-documented exposures are needed before a relation between a metric such as the kurtosis and the risk of hearing loss can be refined.

A Moment Ratio RFI Detection Algorithm That Can Detect Pulsed Sinusoids of Any Duty Cycle

The kurtosis statistic is an effective detector of pulsed sinusoidal radio frequency interference (RFI) in a microwave radiometer, but it fails to detect RFI when the pulsed sinusoid is present for exactly half of the integration period. That is, the kurtosis is blind at an RFI duty cycle of 50%. In this letter, we explore the possibilities of using a higher order statistic to eliminate this detection blind spot in the kurtosis statistic and to improve RFI detection performance. The sixth-order statistic does have sensitivity at an RFI duty cycle of 50%, but sensitivity is relatively low. In addition, it has a sensitivity comparable with the kurtosis for short duty cycle RFI, under certain circumstances.

A Simplified Calculation of the Kurtosis for RFI Detection

Microwave radiometers detecting geophysical parameters are susceptible to radio-frequency interference (RFI) from anthropogenic sources. The kurtosis statistic can be a powerful means of identifying some types of low-power RFI, as thermal noise has a distinct kurtosis value of three, while thermal noise contaminated even with low-power nonthermal RFI often has other values of kurtosis. This paper presents a method for calculating the kurtosis and brightness that significantly reduces the radiometer data download requirements.

Role of the Kurtosis Statistic in Evaluating Complex Noise Exposures for the Protection of Hearing

To highlight a selection of data that illustrate the need for better descriptors of complex industrial noise environments for use in the protection of hearing. The data were derived using a chinchilla model. All noise exposures had the same total energy and the same spectrum; that is, they were equal energy exposures presented at an overall 100 dB(A) SPL that differed only in the scheduling of the exposure and the value of the kurtosis, beta(t), a statistical metric. Hearing thresholds were determined before and after noise exposure using the auditory-evoked potential measured from the inferior colliculus in the brain stem. Cochlear damage was estimated from sensory-cell counts (cochleograms). (1) For equivalent energy and spectra, exposure to a high-kurtosis, non-Gaussian noise produced substantially greater hearing and sensory-cell loss in the chinchilla model than a low-kurtosis, Gaussian noise. (2) beta(t) computed on the amplitude distribution of the noise could clearly differentiate between the effects of Gaussian and non-Gaussian noise environments. (3) beta(t) can order the extent of the trauma as determined by hearing thresholds and sensory-cell loss. The noise level in combination with the statistical properties of the noise quantified by beta(t) clearly differentiate the effects between both continuous and interrupted and intermittent Gaussian and non-Gaussian noise environments. For the same energy and spectrum, the non-Gaussian environments are clearly the more hazardous. The use of both an energy and kurtosis metric can better predict the hazard of a high-level complex noise than the use of an energy metric alone (as is the current practice). These results point out the need for a new approach to the analysis and quantification of industrial noise for the purpose of hearing conservation practice.

Gearbox Deterioration Detection under Steady State, Variable Load, and Variable Speed Conditions

Multiple dominant gear meshing frequencies are present in the vibration signals collected from gearboxes and the conventional spiky features that represent initial gear fault conditions are usually difficult to detect. In order to solve this problem, we propose a new gearbox deterioration detection technique based on autoregressive modeling and hypothesis testing in this paper. A stationary autoregressive model was built by using a normal vibration signal from each shaft. The established autoregressive model was then applied to process fault signals from each shaft of a two-stage gearbox. What this paper investigated is a combined technique which unites a time-varying autoregressive model and a two sample Kolmogorov-Smirnov goodness-of-fit test, to detect the deterioration of gearing system with simultaneously variable shaft speed and variable load. The time-varying autoregressive model residuals representing both healthy and faulty gear conditions were compared with the original healthy time-synchronous average signals. Compared with the traditional kurtosis statistic, this technique for gearbox deterioration detection has shown significant advantages in highlighting the presence of incipient gear fault in all different speed shafts involved in the meshing motion under variable conditions.