Hong-Bo Xie

Various time-series decomposition techniques, including wavelet transform, singular spectrum analysis, empirical mode decomposition and independent component analysis, have been developed for non-linear dynamic system analysis. In this paper, we describe a symplectic geometry spectrum analysis (SGSA) method to decompose a time series into a set of independent additive components. SGSA is performed in four steps: embedding, symplectic QR decomposition, grouping and diagonal averaging. The obtained components can be used for de-noising, prediction, control and synchronization. We demonstrate the effectiveness of SGSA in reconstructing and predicting two noisy benchmark nonlinear dynamic systems: the Lorenz and Mackey-Glass attractors. Examples of prediction of a decadal average sunspot number time series and a mechanomyographic signal recorded from human skeletal muscle further demonstrate the applicability of the SGSA method in real-life applications.

Electromyographic (EMG) is a bio-signal collected on human skeletal muscle. Analysis of EMG signals has been widely used to detect human movement intent, control various human-machine interfaces, diagnose neuromuscular diseases, and model neuromusculoskeletal system. With the advances of artificial intelligence and soft computing, many sophisticated techniques have been proposed for such purpose. Hybrid soft computing system (HSCS), the integration of these different techniques, aims to further improve the effectiveness, efficiency, and accuracy of EMG analysis. This paper reviews and compares key combinations of neural network, support vector machine, fuzzy logic, evolutionary computing, and swarm intelligence for EMG analysis. Our suggestions on the possible future development of HSCS in EMG analysis are also given in terms of basic soft computing techniques, further combination of these techniques, and their other applications in EMG analysis.

We present a hybrid symplectic geometry and central tendency measure (CTM) method for detection of determinism in noisy time series. CTM is effective for detecting determinism in short time series and has been applied in many areas of nonlinear analysis. However, its performance significantly degrades in the presence of strong noise. In order to circumvent this difficulty, we propose to use symplectic principal component analysis (SPCA), a new chaotic signal de-noising method, as the first step to recover the system dynamics. CTM is then applied to determine whether the time series arises from a stochastic process or has a deterministic component. Results from numerical experiments, ranging from six benchmark deterministic models to 1/f noise, suggest that the hybrid method can significantly improve detection of determinism in noisy time series by about 20 dB when the data are contaminated by Gaussian noise. Furthermore, we apply our algorithm to study the mechanomyographic (MMG) signals arising from contraction of human skeletal muscle. Results obtained from the hybrid symplectic principal component analysis and central tendency measure demonstrate that the skeletal muscle motor unit dynamics can indeed be deterministic, in agreement with previous studies. However, the conventional CTM method was not able to definitely detect the underlying deterministic dynamics. This result on MMG signal analysis is helpful in understanding neuromuscular control mechanisms and developing MMG-based engineering control applications.

In the present contribution, a complexity measure is proposed to assess surface electromyography (EMG) in the study of muscle fatigue during sustained, isometric muscle contractions. Approximate entropy (ApEn) is believed to provide quantitative information about the complexity of experimental data that is often corrupted with noise, short data length, and in many cases, has inherent dynamics that exhibit both deterministic and stochastic behaviors. We developed an improved ApEn measure, i.e., fuzzy approximate entropy (fApEn), which utilizes the fuzzy membership function to define the vectors’ similarity. Tests were conducted on independent, identically distributed (i.i.d.) Gaussian and uniform noises, a chirp signal, MIX processes, Rossler equation, and Henon map. Compared with the standard ApEn, the fApEn showed better monotonicity, relative consistency, and more robustness to noise when characterizing signals with different complexities. Performance analysis on experimental EMG signals demonstrated that the fApEn significantly decreased during the development of muscle fatigue, which is a similar trend to that of the mean frequency (MNF) of the EMG signal, while the standard ApEn failed to detect this change. Moreover, fApEn of EMG demonstrated a better robustness to the length of the analysis window in comparison with the MNF of EMG. The results suggest that the fApEn of an EMG signal may potentially become a new reliable method for muscle fatigue assessment and be applicable to other short noisy physiological signal analysis.

Cross-approximate entropy (X-ApEn) and cross-sample entropy (X-SampEn) have been employed as bivariate pattern synchronization measures for characterizing interdependencies between neural signals. In this study, we proposed a new measure, cross-fuzzy entropy (X-FuzzyEn), to describe the synchronicity of patterns. The performances of three statistics were first quantitatively tested using five different coupled systems including both deterministic and stochastic models, i.e., coupled broadband noises, Lorenz–Lorenz, Rossler–Rossler, Rossler–Lorenz, and neural mass model. All the measures were compared with each other with respect to their ability to distinguish between different levels of coupling and their robustness against noise. The three measures were then applied to a real-life problem, pattern synchronization analysis of left and right hemisphere rat electroencephalographic (EEG) signals. Both simulated and real EEG data analysis results showed that the X-FuzzyEn provided an improved evaluation of bivariate series pattern synchronization and could be more conveniently and powerfully applied to different neural dynamical systems contaminated by noise.

A new method, namely Cross fuzzy entropy (C-FuzzyEn) analysis, that could enable the measurement of the synchrony or similarity of patterns between two distinct signals, was presented in this study. Tests on simulated data sets showed that C-FuzzyEn was superior to the conventional cross sample entropy (C-SampEn) in several aspects, including giving entropy definition in case of small parameters, better relative consistency, and less dependence on record length. The proposed C-FuzzyEn was then applied for the analysis of simultaneously recorded electromyography (EMG) and mechanomyography (MMG) signals during sustained isometric contraction for monitoring local muscle fatigue. The results showed that the C-FuzzyEn of EMG-MMG decreased significantly during the development of muscle fatigue. The time-decrease trend of C-FuzzyEn is similar to the mean frequency (MNF) of EMG, the commonly used muscle fatigue indicator.

Previous works have resulted in some practical achievements for mechanomyogram (MMG) to control powered prostheses. This work presents the investigation of classifying the hand motion using MMG signals for multifunctional prosthetic control. MMG is thought to reflect the intrinsic mechanical activity of muscle from the lateral oscillations of fibers during contraction. However, external mechanical noise sources such as a movement artifact are known to cause considerable interference to MMG, compromising the classification accuracy. To solve this noise problem, we proposed a new scheme to extract robust MMG features by the integration of the wavelet packet transform (WPT), singular value decomposition (SVD) and a feature selection technique based on distance evaluation criteria for the classification of hand motions. The WPT was first adopted to provide an effective time-frequency representation of non-stationary MMG signals. Then, the SVD and the distance evaluation technique were utilized to extract and select the optimal feature representing the hand motion patterns from the MMG time-frequency representation matrix. Experimental results of 12 subjects showed that four different motions of the forearm and hand could be reliably differentiated using the proposed method when two channels of MMG signals were used. Compared with three previously reported time-frequency decomposition methods, i.e. short-time Fourier transform, stationary wavelet transform and S-transform, the proposed classification system gave the highest average classification accuracy up to 89.7%. The results indicated that MMG could potentially serve as an alternative source of electromyogram for multifunctional prosthetic control using the proposed classification method.