Shuen De Wu

Time Series Analysis Using Composite Multiscale Entropy

Multiscale entropy (MSE) was recently developed to evaluate the complexity of time series over different time scales. Although the MSE algorithm has been successfully applied in a number of different fields, it encounters a problem in that the statistical reliability of the sample entropy (SampEn) of a coarse-grained series is reduced as a time scale factor is increased. Therefore, in this paper, the concept of a composite multiscale entropy (CMSE) is introduced to overcome this difficulty. Simulation results on both white noise and 1/f noise show that the CMSE provides higher entropy reliablity than the MSE approach for large time scale factors. On real data analysis, both the MSE and CMSE are applied to extract features from fault bearing vibration signals. Experimental results demonstrate that the proposed CMSE-based feature extractor provides higher separability than the MSE-based feature extractor.

Bearing fault diagnosis based on multiscale permutation entropy and support vector machine

Bearing fault diagnosis has attracted significant attention over the past few decades. It consists of two major parts: vibration signal feature extraction and condition classification for the extracted features. In this paper, multiscale permutation entropy (MPE) was introduced for feature extraction from faulty bearing vibration signals. After extracting feature vectors by MPE, the support vector machine (SVM) was applied to automate the fault diagnosis procedure. Simulation results demonstrated that the proposed method is a very powerful algorithm for bearing fault diagnosis and has much better performance than the methods based on single scale permutation entropy (PE) and multiscale entropy (MSE).

Multi-Scale Analysis Based Ball Bearing Defect Diagnostics Using Mahalanobis Distance and Support Vector Machine

The objective of this research is to investigate the feasibility of utilizing the multi-scale analysis and support vector machine (SVM) classification scheme to diagnose the bearing faults in rotating machinery. For complicated signals, the characteristics of dynamic systems may not be apparently observed in a scale, particularly for the fault-related features of rotating machinery. In this research, the multi-scale analysis is employed to extract the possible fault-related features in different scales, such as the multi-scale entropy (MSE), multi-scale permutation entropy (MPE), multi-scale root-mean-square (MSRMS) and multi-band spectrum entropy (MBSE). Some of the features are then selected as the inputs of the support vector machine (SVM) classifier through the Fisher score (FS) as well as the Mahalanobis distance (MD) evaluations. The vibration signals of bearing test data at Case Western Reserve University (CWRU) are utilized as the illustrated examples. The analysis results demonstrate that an accurate bearing defect diagnosis can be achieved by using the extracted machine features in different scales. It can be also noted that the diagnostic results of bearing faults can be further enhanced through the feature selection procedures of FS and MD evaluations.

Constraint Violation Stabilization Using Input-Output Feedback Linearization in Multibody Dynamic Analysis

A constraint violation stabilization technique for solving differential algebraic equations (DAE) of multibody dynamic systems is presented. The technique, based on the input ‐output feedback linearization, is employed to transform the nonlinear DAE into a set of linear equations. On reaching the input ‐output linear relationship with proven stable zero dynamics, a robust control design is adopted to construct constraint forces that can be used to effectively correct the errors accumulated in the constraint equations during the process of time integration. In the present development, if the pole placement method is used in control design of the resulting linear differential equations, constraint forces based on Baumgarte’ s constraint violation stabilization technique are recovered. On the other hand, if variable structure control design is adopted, a new method in calculating constraint forces is obtained. Two numerical examples are used to demonstrate the effectiveness of stabilizing the constraint violation by using the proposed technique.

Open Newton-Cotes differential methods as multilayer symplectic integrators

Open Newton–Cotes differential methods that possess the characteristics of multilayer symplectic structures are shown in this paper. In numerical simulation, volume-preservation plays an important role in solving the Hamiltonian system. In this regard, developing a numerical integrator that preserves the volume in the phase space of a Hamiltonian system is a great challenge to the researchers in this field. Symplectic integrators were proven to be good candidates for volume-preserving integrators (VPIs) in the past ten years. Several one-step (single-stage or multistages) symplectic integrators have been developed based on the symplectic geometric theory. However, multistep VPIs have seldom been investigated by other researchers for the lack of an advanced theory. Recently, Zhu et al. converted open Newton–Cotes differential methods into a multilayer symplectic structure so that multistep VPIs of a Hamiltonian system are obtained. Mainly, their work has concentrated on the issue of achieving both the accu...

Robust attitude control of spacecraft using sliding mode control and productive networks

A new robust attitude control design of spacecraft is proposed by combining sliding mode control (SMC) and productive networks (PN). Essentially, the sliding mode control uses discontinuous control action to drive state trajectories toward a specific hyperplane in the state space, and to maintain the state trajectories sliding on the specific hyperplane. This principle provides a guideline to design a robust controller. Productive networks, which are a special type of artificial neural network, are then used to implement reaching and sliding conditions, and tackle the drawbacks of SMC such as chattering and high control gains. Attractive features of the proposed method include a systematic procedure of controller design, a reduction in chattering, robustness against model uncertainties and external disturbances. An inverted pendulum and a spacecraft attitude control problem are given to deomonstrate the effectiveness of the proposed method.

Refined Composite Multiscale Permutation Entropy to Overcome Multiscale Permutation Entropy Length Dependence

Multiscale permutation entropy (MPE) has recently been proposed to evaluate complexity of time series. MPE has numerous advantages over other multiscale complexity measures, such as its simplicity, robustness to noise and its low computational cost. However, MPE may loose statistical reliability as the scale factor increases, because the coarse-graining procedure used in the MPE algorithm reduces the length of the time series as the scale factor grows. To overcome this drawback, we introduce the refined composite MPE (RCMPE). Through applications on both synthetic and real data, we show that RCMPE is much less dependent on the signal length than MPE. In this sense, RCMPE is more reliable than MPE. RCMPE could therefore replace MPE for short times series or at large scale factors.

Solution for mode mixing phenomenon of the empirical mode decomposition

Empirical mode decomposition (EMD) is a signal analysis method which has received much attention lately due to its application in a number of fields. However, EMD method has some limitations in decomposing signals which amplitude-frequency ranges are too close to each other. The aim of present paper is to show existing knowledge base for mode mix problem of two harmonics decomposition and introduce the differential operator as a possible solution of EMD algorithm for this topic. In this paper, the new methods are compared with the conventional EMD by numerical examples.

The design and assembly of surface-micromachined optical switch for optical add/drop multiplexer application

An assembly process including: flip-chip bonding, microelectromechanical (MEMS) structure release, and atomic layer deposition (ALD) is proposed to integrate a surface micromachined optical switch for optical add/drop multiplexer (OADM) applications. In the current optical switch designs, pre-stressed beams were used to pop up the micromirror and an electrode (substrate) under the beams was designed to perform ON/OFF function of the optical switch. In order to achieve desired popped-up angle for precise optical switching, a flip-chip bonding technique is applied to a mechanical stopper with an accurate joint height that can be used to constrain the movement of the micromirror. A conformal thin layer of dielectric material (Al/sub 2/O/sub 3/) coated on the surfaces of device through an ALD coating process is used to improve vertical actuation force, as well as electrical isolation. Experiments indicate that the micromirrors fabricated by the present assembly process can achieve desired angle that meet the requirements of the proposed OADM configuration.

Refined Multiscale Hilbert–Huang Spectral Entropy and Its Application to Central and Peripheral Cardiovascular Data

Objective: Spectral entropy has been applied in variety of fields. Multiscale spectral entropy (MSSE) has also recently been proposed to take into account structures on several scales. However, MSSE has some drawbacks, such as the coarse-graining procedure performed in the time domain. In this study, we propose a new framework to compute MSSE. This framework is also adapted for nonstationary data. Methods: Our work relies on processing steps performed directly in the frequency domain. For nonstationary signals, the evolution of entropy values with scales is observed along time. Our algorithm is herein evaluated both on synthetic time series (stationary and non-stationary signals) and on data from the cardiovascular system (CVS). For this purpose, heart rate variability (from the central CVS), laser Doppler flowmetry, and laser speckle contrast data (both from the peripheral CVS) are analyzed. Results: The results show that our framework has better performances than the existing algorithms to compute MSSE, both in terms of reliability and computational cost. Moreover, it is able to reveal repetitive patterns on central and peripheral CVS signals. These patterns may be linked to physiological activities. Furthermore, from the processing of microvascular data, it is able to distinguish young from elderly subjects. Conclusion: Our framework outperforms other algorithms to compute MSSE. It also has the advantage of revealing physiological information. Significance: By showing better performances than existing algorithms to compute MSSE, our work is a new and promising way to compute an entropy measure from the spectral domain. It also has the advantage of stressing physiologically linked phenomena.