Chaotic Signal Denoising Based on Adaptive Smoothing Multiscale Morphological Filtering

A method based on compound multiscale permutation entropy, support vector machine, and particle swarm optimization for roller bearings fault diagnosis was presented in this study. Firstly, the roller bearings vibration signals under different conditions were decomposed into permutation entropy values by the multiscale permutation entropy and compound multiscale permutation entropy methods. The compound multiscale permutation entropy model combined the different graining sequence information under each scale factor. The average value of each scale factor was regarded as the final entropy value in the compound multiscale permutation entropy model. The compound multiscale permutation entropy model suppressed the shortcomings of poor stability caused by the length of the original signals in the multiscale permutation entropy model. Validity and accuracy are considered in the numerical experiments, and then compared with the computational efficiency of the multiscale permutation entropy method. Secondly, the entropy values of the multiscale permutation entropy/compound multiscale permutation entropy under different scales are regarded as the input of the particle swarm optimization–support vector machine models for fulfilling the fault identification, the classification accuracy is used to verify the effectiveness of the multiscale permutation entropy/compound multiscale permutation entropy with particle swarm optimization–support vector machine. Finally, the experimental results show that the classification accuracy of the compound multiscale permutation entropy model is higher than that of the multiscale permutation entropy.

According to the different features between chaotic signals and noise, a new noise reduction method is proposed based on wavelet modulus maximum. First, the discrete wavelet transform of chaotic signals is given in this method, then the approximate parts are handled by the singular spectrum analysis in order to lower the containing noise; For the detail parts after the wavelet modulus maximum treatment, the spatial scales correlation is used for the analysis of the wavelet coefficients in different scales in order to reserve the useful signals mixed in noise. The chaotic signals generated by Duffing model and sunspots are respectively applied for simulation analysis, the numerical experiment results confirm the effectiveness of noise reduction for chaotic signals observed.

Publication in the conference proceedings of EUSIPCO, Tampere, Finland, 2000

It is an important practical problem to accurately recognize whether biological tissue is denatured during high intensity focused ultrasound (HIFU) treatment. Ultrasonic scattering echo signals are related to some physical properties of biological tissues. According to the characteristics of ultrasonic scattering echo signals, the recognition of denatured biological tissues is studied based on the variational mode decomposition (VMD) and multi-scale permutation entropy (MPE) in this paper. The ultrasonic echo signals are decomposed into various modal components by the VMD. The noise components and the useful components are separated according to the power spectrum information entropy of various modal components. The separated useful signals are reconstructed and the MPE are extracted. Furthermore, Gustafson-Kessel (GK) fuzzy clustering analysis is employed to obtain the standard clustering center, and the recognition of denatured biological tissues is carried out by Euclid approach degree and principle of proximity. The proposed method is applied to ultrasonic scattering echo signal during HIFU treatment. In order to determine the parameters of MPE algorithm for ultrasonic scattering echo signals, the embedding dimension of the MPE is discussed, and the scale factor of the MPE algorithm is optimized by genetic algorithm. When the delay time and the embedding dimension are 2 and 7 respectively, the MPE values decrease with scale factor increasing. Assuming that the scale factor is 12 from optimization results, the 293 ultrasonic scattering echo signals from normal tissues and denatured tissues are analyzed by the MPE. It is found that the MPE values of the denatured tissues are higher than those of the normal tissues. The MPE can be used to distinguish normal tissues and denatured tissues. Comparing with the recognition methods of the EMD-MPE-GK fuzzy clustering method and the VMD-WE-GK fuzzy clustering, the proposed method has good clustering performance and separability. Its partition coefficient (PC) is close to 1 and the Xie-Beni (XB) index is smaller. There are fewer feature points in the overlap region between MPE features of denatured tissues and normal tissues. The recognition results of denatured biological tissues in this experimental environment show that the recognition rate based on this method is higher, reaching up to 93.81%.

Financial time series analysis using the relation between MPE and MWPE

The purpose of this paper is to analyse the statistical characteristics of a Direct Chaotic Differentially Coherent communication scheme based on chaotic radio pulses in a communication channel with additive white Gaussian noise, where the chaotic signal is given by different instantaneous distributions. Methods. To achieve this goal, numerical modelling of the noise immunity of Direct Chaotic Differentially Coherent communication is conducted and compared with the results of analytical research. Results. The regularities associated with the use of chaotic signals with various statistical distributions of instantaneous values were studied. The minimum values of energy per bit to white Gaussian noise power spectral density ratio were obtained, providing the required error probabilities. Conclusion. It is shown that the proposed system works efficiently at high values of processing gain, and as the processing gain increases, the dependence of noise immunity on the specific statistical distribution of the chaotic signal is levelled out.

The performance of the maximum likelihood estimator for a 1-D chaotic signal in white Gaussian noise is derived. It is found that the estimator is inconsistent and therefore the usual asymptotic distribution (large data record length) is invalid. However, for high signal-to-noise ratios (SNR's), the maximum likelihood estimator is asymptotically unbiased and attains the Cramér-Rao lower bound (CRLB). © 1995 IEEE

This paper presents a method to detect weak harmonic signal embedded in chaotic noise. Using different correlation characteristic of harmonic and chaotic signal ,we can transform the sample signal to a new data sequence which has new harmonic . The new harmonic frequency is m times of the original harmonic and beyond the center bandwidth of noise. Then use wavelet packet decomposition to analysis the energy distribution of harmonic and chaotic signals and extract the component which the harmonic energy concentrated on, In the end, a multiple signal classification (MUSIC) algorithm is employed to estimate harmonic frequencies . The method suit for the complex background noise (strong chaotic noise and gaussian noise).

Multiscale Permutation Entropy (MPE) analysis is a powerful ordinal tool in the measurement of information content of time series. MPE refinements, such as Composite MPE (cMPE) and Refined Composite MPE (rcMPE), greatly increase the precision of the entropy estimation by modifying the original method. Nonetheless, these techniques have only been proposed as algorithms, and are yet to be described from the theoretical perspective. Therefore, the purpose of this article is two-fold. First, we develop the statistical theory behind cMPE and rcMPE. Second, we propose an alternative method, Refined Composite Downsampling Permutation Entropy (rcDPE) to further increase the entropy estimation’s precision. Although cMPE and rcMPE outperform MPE when applied on uncorrelated noise, the results are higher than our predictions due to inherent redundancies found in the composite algorithms. The rcDPE method, on the other hand, not only conforms to our theoretical predictions, but also greatly improves over the other methods, showing the smallest bias and variance. By using MPE, rcMPE and rcDPE to classify faults in bearing vibration signals, rcDPE outperforms the multiscaling methods, enhancing the difference between faulty and non-faulty signals, provided we apply a proper anti-aliasing low-pass filter at each time scale.

Optical chaotic communication using correlation demodulation between two synchronized chaos lasers

Modelling of long-wave chaotic radar system for anti-stealth applications

A comparative study of four multi-scale entropies combined with grey relational degree in classification of ship-radiated noise

The active noise control is the best approach to limit the low-frequency noise present in any applications and also to estimate the signals, which are corrupted by interference or additive noise. In this paper, the design of an active noise control system is proposed with the hybrid combination of functional link artificial neural network and finite impulse response filter. The filter coefficients of both functional link artificial neural network and finite impulse response filters are optimized by firefly algorithm, and the ensemble mean square error value is computed through the filtered-s least mean square algorithm, in which the convergence of the filter is improved through the proposed approach. The signals like Chaotic noise signal and Gaussian noise signal are considered to assess the proposed method. Then, the noise reduction capability of the proposed active noise control with firefly algorithm is compared with that achieved by the same active noise control with another optimization algorithm known as BAT algorithm in place of firefly algorithm. The performance analysis is carried out under the MATLAB environment.

Considering the diversity, complexity and uncertainty existing in bearing vibrations, an extended intelligent identification paradigm for bearing faults was proposed based on multiscale permutation entropy (MPE) and extension theory. MPE can reflect the random degree and detect the dynamic mutation of time series over subsequent scales, while extension theory provides an approach to address the extensibility and regularity of complicated problems. In the present paradigm, MPE was employed to compute the entropies over multiple scales as an original feature vector to represent bearing vibrations, which were then graded using Fisher ratio to choose the most informative features. The chosen features were exploited to determine the classical domain and joint domain of matter elements associated with various bearing health conditions. Bearing fault pattern was assigned to the one with maximum dependence degree among the afore-constructed matter elements. An experiment was conducted on an electrical motor involving four bearing conditions including normal, inner race, outer race and rolling element faults. The test was repeated 100 times with an averaged rate of 92.2% by the proposed method which outperforms the method using multiscale sample entropy and extension theory.

Dynamic characteristics of absence EEG recordings with multiscale permutation entropy analysis