Comparison of Fourier and wavelet analysis for fatigue assessment during repetitive dynamic exertion

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Abstract

The comparative ability of the Fourier transform (FFT) and discrete wavelet transform (DWT) algorithms in assessing muscle fatigue during sub-maximal repetitive dynamic exertion was investigated in this study. Surface electromyography data recorded from the upper trapezius muscle during forty minutes of repetitive upper extremity exertion performed by 10 male participants were used in the analysis. Multi-model regression analysis was performed to study the trend in the power values of the different frequency bands estimated using the FFT and DWT algorithms. Less variability and higher statistical significance was observed for the power value trend computed using the DWT algorithm compared to the FFT algorithm. The regression models provided a better fit for the power values estimated under more fatigued condition compared to the less fatigued condition. The lower frequency bands of 23–46 Hz and 46–93 Hz exhibited the expected and consistent power trend independent of the algorithm (DWT or FFT) used. For the exertions tested in this study, a cubic or curvilinear model explained the fatigue development process with a higher precision than the linear models.

Introduction

Repetitive arm and neck movements constitute a major facet of workplace tasks in several industries. A causal relationship between such exertions and neck/shoulder musculoskeletal disorders has been proposed in the literature (Côté et al., 2008). Repetitive exertions performed over a sustained period of time lead to fatigue, which is believed to be the precursor of musculoskeletal disorders (MSDs). Therefore, in order to eliminate the risk of MSDs due to repetitive exertions, it is essential that accurate fatigue assessment methods are available.

Among the methods that are used to estimate muscle fatigue, surface electromyography (SEMG) is a preferred method due to its high precision, non-invasiveness, and unobtrusiveness. Previous studies have used SEMG based measures to investigate the muscle fatigue associated with various occupational tasks (Bosch et al., 2007, Chowdhury et al., 2013). Three measures – mean frequency, median frequency, and the power of the spectrum estimated using the fast Fourier transform (FFT), have been commonly used to report neuromuscular fatigue. A shift in the mean or median frequencies toward lower values or an increase in the power of the low frequency components and a decrease in the power of high frequency components of the SEMG signal have been identified as indicators of muscle fatigue (Eberstein and Beattie, 1985, Georgakis et al., 2003).

The FFT algorithm is based upon the hypothesis that any signal can be represented by a sum of appropriately weighted sine and cosine functions (Bracewell and Bracewell, 1986). The algorithm assumes that the signal under investigation is stationary (Bilodeau et al., 1997). A signal is said to be stationary if the joint distribution of any set of samples within the signal are time independent and randomly distributed, i.e., the average, variance, and frequency contents of the signal do not alter over time. In case of non-stationary signals, the set of samples are statistically dependent and the mean, variance, and frequency content of the signals change over time (Bendat and Piersol, 2000). The SEMG signals are stationary during isometric exertion due to a stable and constant force exertion and body posture (Basmajian and De Luca, 1985). However, during dynamic exertion, the magnitude and direction of force application as well as body posture changes continuously. The SEMG signal recorded under such a condition may not satisfy the stationarity assumption (Merletti et al., 2004). Alternatively, short time Fourier transforms (STFT) are used to analyze nonstationary dynamic signals (MacIsaac et al., 2001). In STFT, the window sizes are altered (mostly reduced) to satisfy the stationarity assumption of the Fourier transform. However, the window size approximation used in STFT may introduce time and frequency resolution issues; i.e., a short window size may provide better time resolution but poor frequency resolution while a relatively longer window provides better frequency resolution but poor time resolution (Bonato et al., 1996).

Another viable choice to FFT based spectral analysis for fatigue estimation is the use of discrete wavelet transform (DWT) analysis. Unlike FFT, which is restricted to one feature morphology, the sinusoid, DWT provides a range of orthogonal wavelet functions for conducting spectral analysis (Polikar, 2006). There is no assumption of signal stationarity under this analysis and the SEMG signal can be evaluated to elucidate spectral and temporal information simultaneously. However, the computation method for DWT analysis is more tedious than FFT. The signal decomposition takes place at several levels based on the duration and/or selection of the window size. The DWT has been used in analyzing non-stationary SEMG signals for studying the muscle fatigue in a variety of exertion tasks (Beck et al., 2005, Hostens et al., 2004, Kumar et al., 2003, Nimbarte et al., 2013). The root mean square (RMS), the power, and the center frequency of the wavelet coefficients at different levels (frequency bands) have been used in previous DWT studies to report the onset and development of fatigue. A drop in the center frequency (Beck et al., 2005, Kumar et al., 2003) and an increase in the power (Chowdhury et al., 2013, Kumar et al., 2003) and the RMS values (Sparto et al., 2000) of the wavelet coefficients in the lower frequency bands were associated with the development of muscle fatigue.

Previous studies comparing the fatigue prediction ability of DWT with FFT have reported contradictory findings. Canal (2010) reported better resolution and visualization performance for DWT compared to STFT during fatiguing isokinetic exertions. Karlsson et al. (1999) estimated the SEMG power spectrum and the mean frequency using both wavelet and the Fourier transform methods. The wavelet based methods (DWT and wavelet packet transform) were more accurate than the Fourier transform for the nonstationary dynamic signal. In another study, Camata et al. (2010) compared STFT and continuous wavelet transform (CWT) in assessing muscle fatigue during a constant load dynamic task. The results indicated higher variability in the median frequency estimated by the STFT compared to the CWT method. In contrast to the aforementioned studies, Beck et al. (2005) reported a similar pattern of center frequency when comparing FFT and DWT in analyzing fatiguing isokinetic exertions. In another study, Hostens et al. (2004) compared Fourier and wavelet transform methods when examining the spectral pattern of the SEMG signal during fatiguing submaximal isometric and dynamic exertions. Similarities in the wavelet and Fourier based center frequency patterns were also observed in this study.

In summary, spectral analysis performed using FFT and DWT based algorithms were used in the previous studies to perform fatigue estimation. Each algorithm has its strengths and weaknesses and previous comparison studies have reported conflicting findings. Moreover, the dynamic exertions investigated in previous studies were mostly isokinetic in nature whereas most occupational dynamic exertions are rarely isokinetic. The comparative ability of the FFT and DWT algorithms in estimating spectral changes during fatiguing real world dynamic exertions has never been studied. The present study attempted to compare the spectral trends computed by the FFT algorithm with the time–frequency approaches of the DWT algorithm in assessing muscle fatigue during sub-maximal repetitive dynamic exertions. The sub-maximal repetitive exertions were defined as the exertions that a worker/ human participant is capable of performing for a longer period of time.

Section snippets

Approach

A lab-based study was performed in order to compare the abilities of the FFT and DWT algorithms in assessing fatigue generated by dynamic exertions. Human participants completed a task consisting of 40 min of repetitive upper extremity exertions. Activity of the muscle responsible for these exertions was recorded using SEMG. Spectral analysis was performed using FFT and DWT algorithms to estimate the power of different frequency bands.

Participants

Ten healthy male participants (age = 27 ± 4.8 years; weight = 71.1 ± 

Results

The mean duration of loading and unloading exertions ranged from 2.02 s to 1.57 s. The mean duration of exertion decreased from 2.02 s to 1.67 s and from 1.87 s to 1.57 s during sessions 1 and 2, respectively.

The mean discomfort scores recorded using Borg’s CR-10 scale showed an increasing discomfort trend towards the end of sessions 1 and 2. A baseline discomfort of 1 (= nothing at all) was recorded at the beginning of the first session. After twenty minutes of loading and unloading exertions, a

Discussion

In this study the power trend of different frequency bands was used to evaluate the fatigue prediction ability of the FFT and DWT algorithms. The muscle fatigue was also assessed using a standardized and widely used subjective tool (Borg’s CR-10 scale). A significant correlation between CR-10 ratings and the muscle fatigue was reported in the past studies (Dedering et al., 1999, Dedering et al., 2002). A 30% reduction in the median and mean frequencies, and endurance time were observed at a

Conclusions

The comparative ability of the FFT and DWT algorithms to predict fatigue generated during repetitive dynamic exertions was evaluated in the current study. The results showed less variability in the power values computed by the DWT algorithm compared to the FFT algorithm. Frequency band (lower vs higher) and amount of fatigue (less vs more) were found to influence the trend in the power values.

Conflict of interest

The authors declare that they have no conflict of interest

Suman Kanti Chowdhury is a PhD student at the faculty of Industrial and Management System Engineering of West Virginia University. He received his M.S. degree in Industrial Engineering from West Virginia University in 2012, and received his B.Sc. degree in Industrial and Production Engineering from Bangladesh University of Engineering and Technology, Bangladesh in 2006. His research interest is in the general areas of industrial ergonomics and human factors engineering. His recent research

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    Suman Kanti Chowdhury is a PhD student at the faculty of Industrial and Management System Engineering of West Virginia University. He received his M.S. degree in Industrial Engineering from West Virginia University in 2012, and received his B.Sc. degree in Industrial and Production Engineering from Bangladesh University of Engineering and Technology, Bangladesh in 2006. His research interest is in the general areas of industrial ergonomics and human factors engineering. His recent research focuses on the estimation of muscle fatigue using advanced digital signal processing techniques.

    Dr. Ashish D. Nimbarte is an Assistant Professor and the Director of Occupational Safety and Health Engineering program in the Industrial and Management Systems Engineering Department at West Virginia University. His training and expertise is in the general areas of ergonomics and occupational biomechanics. Dr. Nimbarte’s research interest is motivated by the need to better characterize occupational risk factors so that effective control strategies can be implemented in the workplace. Specifically, he focuses on improving the understanding of the pathogenesis of work-related musculoskeletal disorders of the upper extremities and cervical spine.

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