The selection of an appropriate wavelet is an essential issue that should be addressed in the wavelet-based filtering of electrocardiogram (ECG) signals. Since entropy can measure the features of uncertainty associated with the ECG signal, a novel comprehensive entropy criterion E_com based on multiple criteria related to entropy and energy is proposed in this paper to search for an optimal base wavelet for a specific ECG signal. Taking account of the decomposition capability of wavelets and the similarity in information between the decomposed coefficients and the analyzed signal, the proposed E_com criterion integrates eight criteria, i.e., energy, entropy, energy-to-entropy ratio, joint entropy, conditional entropy, mutual information, relative entropy, as well as comparison information entropy for optimal wavelet selection. The experimental validation is conducted on the basis of ECG signals of sixteen subjects selected from the MIT-BIH Arrhythmia Database. The E_com is compared with each of these eight criteria through four filtering performance indexes, i.e., output signal to noise ratio (SNR_o), root mean square error (RMSE), percent root mean-square difference (PRD) and correlation coefficients. The filtering results of ninety-six ECG signals contaminated by noise have verified that E_com has outperformed the other eight criteria in the selection of best base wavelets for ECG signal filtering. The wavelet identified by the E_com has achieved the best filtering performance than the other comparative criteria. A hypothesis test also validates that SNR_o, RMSE, PRD and correlation coefficients of E_com are significantly different from those of the shape-matched approach (α = 0.05 , two-sided t- test).

Due to high dimensionality and multiple variables, unsupervised classification of multivariate time series (MTS) involves more challenging problems than those of univariate ones. Unlike the vectorization of a feature matrix in traditional clustering algorithms, an unsupervised pattern recognition scheme based on matrix data is proposed for MTS samples in this paper. To reduce the computational load and time consumption, a novel variable-based principal component analysis (VPCA) is first devised for the dimensionality reduction of MTS samples. Afterward, a spatial weighted matrix distance-based fuzzy clustering (SWMDFC) algorithm is proposed to directly group MTS samples into clusters as well as preserve the structure of the data matrix. The spatial weighted matrix distance (SWMD) integrates the spatial dimensionality difference of elements of data into the distance of MST pairs. In terms of the SWMD, the MTS samples are clustered without vectorization in the dimensionality-reduced feature matrix space. Finally, three open-access datasets are utilized for the validation of the proposed unsupervised classification scheme. The results show that the VPCA can capture more features of MTS data than principal component analysis (PCA) and 2-D PCA. Furthermore, the clustering performance of SWMDFC is superior to that of fuzzy c-means clustering algorithms based on the Euclidean distance or image Euclidean distance.

In this paper, a data-driven modeling method for electromagnetically actuated micromirror in random noisy environment is proposed. In this method, the electromagnetic micromirror is considered as a dynamic system with preceded hysteresis. Then, a linear dynamic submodel is used to describe the angular deflection mechanism, while a preceded rate-dependent hysteresis submodel is used to depict the hysteresis phenomenon inherent in the electromagnetic driver. By considering the influence of random noise on the micromirror, an on-line modeling scheme with varying weighting factors is studied to handle the data contaminated by random noises. Subsequently, the convergence of proposed modeling method is analyzed. Finally, the experimental results of the proposed modeling scheme for an electromagnetically actuated micromirror are presented.

Underdamped feature and hysteresis existing in electromagnetic scanning micro-mirrors (EMSMs) often lead to oscillation and undesired positioning error of deflection angle. In this paper, a model-based robust scheme is proposed for the angle tuning of mirror plate of the EMSM. To build a proper model for describing the behavior of EMSM, which is also convenient for the design of tuning strategy, a data-driven model composed of linear dynamic submodel as well as hysteresis submodel is developed. In the data-driven model, the deflection mechanism is described by a linear dynamic submodel while the hysteresis in EMSM is depicted by a nonsmooth hysteresis basis function submodel. Then, in order to compensate for the internal oscillation caused by both underdamping factor and hysteresis, a pseudo-feedforward oscillation compensator (PFOC) not relying on the inverse model is proposed. Then, the design procedure of the angle tuning strategy with the PFOC is presented. Afterward, the robust design of the angle tuning scheme is also studied to overcome the effect of compensation residual. Subsequently, the proposed scheme is applied to the angle tuning of EMSM.

Many actuators and sensors made by smart materials have hysteresis feature which is a complex nonlinear phenomenon with multivalued mapping. Accurate identification of hysteresis pattern in those sensors and actuators is helpful for improving the modeling and control strategies of the systems. In this paper, a general framework of the pattern clustering of hysteretic time series is developed on the basis of tensor decomposition. First, high-dimensional multivariate data of hysteresis objects are transformed into three-order hysteresis tensors. Then the multilinear principal component analysis (MPCA) is utilized to reduce the dimensionality of hysteresis tensors. Afterward, a novel tensor k-means clustering (CTKmeans) based on tensor distance and cycle variation feature initialization is developed for the clustering of tensor objects. In order to evaluate the performance of the proposed approach, the experiment of hysteresis feature test using polyvinylidene fluoride (PVDF)-based pressure sensors is implemented. The measured high-dimensional hysteresis time series of PVDF successively undergoes the procedures of filtering, segmentation, MPCA dimensionality reduction and CTKmeans clustering. The experimental results show that the MPCA can capture more significant inherent features of hysteresis objects than the principal component analysis (PCA) or the kernel PCA in the dimensionality reduction. In terms of tensor distance and cycle variation feature initialization, the CTKmeans outperforms the random-initialization-based tensor k-means and standard k-means in the clustering of hysteresis tensors. With the tensor decomposition approach of multivariate time series, the hysteresis objects with nonlinear multivalued mapping features can be effectively identified by the combination of MPCA and CTKmeans.

On the basis of wavelet theory, a novel Adaptive wavelet thresholding method (AWT) is proposed for the ECG signal enhancement. The best base wavelet for ECG signal filtering can be automatically obtained through the cross correlation coefficient and the energy to entropy ratio. The variable universal threshold (VarUniversal) is applied to different decomposition level so as to suppress diverse noise. To achieve a smooth cut-off transition, an identical correlation shrinkage function (IcoShrinkage) is also adopted in the AWT according to its correlation coefficients with the hard thresholding and the soft thresholding. The performance of AWT is compared with four threshold approaches and six shrinkage functions, respectively, on the basis of 150 practical ECG signals of 30 subjects. The filtering results reveal that the AWT can adaptively choose an optimal base wavelet for a specific ECG signal. With the VarUniversal threshold and IcoShrinkage, the AWT obtains the better filtering results than the other compared methods.