Xingjian Dong

General Parameterized Time-Frequency Transform

Interest in parameterized time-frequency analysis for non-stationary signal processing is increasing steadily. An important advantage of such analysis is to provide highly concentrated time-frequency representation with signal-dependent resolution. In this paper, a general scheme, named as general parameterized time-frequency transform (GPTF transform), is proposed for carrying out parameterized time-frequency analysis. The GPTF transform is defined by applying generalized kernel based rotation operator and shift operator. It provides the availability of a single generalized time-frequency transform for applications on signals of different natures. Furthermore, by replacing kernel function, it facilitates the implementation of various parameterized time - frequency transforms from the same standpoint. The desirable properties and the dual definition in the frequency domain of GPTF transform are also described in this paper. One of the advantages of the GPTF transform is that the generalized kernel can be customized to characterize the time - frequency signature of non-stationary signal. As different kernel formulation has bias toward the signal to be analyzed, a proper kernel is vital to the GPTF. Thus, several potential kernels are provided and discussed in this paper to develop the desired parameterized time - frequency transforms. In real applications, it is desired to identify proper kernel with respect to the considered signal. This motivates us to propose an effective method to identify the kernel for the GPTF.

Closed Loop Finite Element Modeling of Piezoelectric Smart Structures

The objective of this paper is to develop a general design and analysis scheme for actively controlled piezoelectric smart structures. The scheme involves dynamic modeling of a smart structure, designing control laws and closed-loop simulation in a finite element environment. Based on the structure responses determined by finite element method, a modern system identification technique known as Observer/Kalman filter Identification (OKID) technique is used to determine the system Markov parameters. The Eigensystem Realization Algorithm (ERA) is then employed to develop an explicit state space model of the equivalent linear system for control law design. The Linear Quadratic Gaussian (LQG) control law design technique is employed to design a control law. By using ANSYS parametric design language (APDL), the control law is incorporated into the ANSYS finite element model to perform closed loop simulations. Therefore, the control law performance can be evaluated in the context of a finite element environment. Finally, numerical examples have demonstrated the validity and efficiency of the proposed design scheme. Without any further modifications, the design scheme can be readily applied to other complex smart structures.

Component Extraction for Non-Stationary Multi-Component Signal Using Parameterized De-chirping and Band-Pass Filter

In most applications, component extraction is important when components of non-stationary multi-component signal are key features to be monitored and analyzed. Existing methods are either sensitive to noise or forced to select a proper time-frequency representation for the considered signal. In this paper, we present a novel component extraction method for non-stationary multi-component signal. The proposed method combines parameterized de-chirping and band-pass filter to obtain components of multi-component signal, which avoids dealing with time-frequency representation of the signal and works well under heavy noise. In addition, it is able to analyze the multi-component signal whose components have intersected instantaneous frequency trajectories. Simulation results show that the proposed method is promising in analyzing complicated multi-component signals. Moreover, it works effective in a high noise environment in terms of improving the output signal-to-noise rate for the interested component.

Application of Parameterized Time-Frequency Analysis on Multicomponent Frequency Modulated Signals

Parameterized time-frequency (TF) transforms, with signal-dependent kernel parameters, have been proposed to analyze multicomponent frequency modulated (FM) signals. Usually, the kernel parameters are estimated through recursive approximation of TF representation (TFR) ridge when instantaneous frequency models of the components have the same parameter settings. However, it will be inapplicable if the components have the different FM sources. In this paper, we introduce a novel method that enables the parameterized TF transform to generate the well-concentrated TFR for both the monocomponent signal and a wide class of multicomponent FM signals, whose components are modulated by either the same or the different sources. The proposed method contains two aspects: 1) estimating kernel parameters based on spectrum concentration index and 2) separating components and assembling the parameterized TFRs of the separated components. An advantage of the proposed method is that it avoids the dependence of the TFR while estimating the parameters. Moreover, it is effective at low signal-to-noise rate. The validity and practical utility of the proposed method are demonstrated by both the simulated and real signals. The results show that it outperforms the traditional TF methods in providing the TFR of the improved concentration for various multicomponent FM signals.

Time-Varying Frequency-Modulated Component Extraction Based on Parameterized Demodulation and Singular Value Decomposition

To analyze the valuable frequency component for time-varying frequency-modulated (FM) signals, component extraction is necessary in most applications. Considering the advantage of parameterized demodulation (PD) in transforming FM signals to be stationary, a novel component extraction method based on PD and singular value decomposition (PD-SVD) for both monocomponent and multicomponent signals is proposed. By extending the idea of PD, the time-varying term of the continuous phase function for the interested FM component can be removed, thus resulting in a highly self-correlated component with constant phase. Then, the extraction of the target component from noise or other components can be realized by SVD. Compared with the existing methods, the proposed algorithm is able to analyze the multicomponent signal with crossed instantaneous frequency trajectories and effectively improve the signal-to-noise ratio of the extracted component. The effectiveness of the proposed method is demonstrated by applying it on several numerical signals and the radial vibration signal of a hydroturbine rotor, indicating the potential of analyzing many practical FM signals.

Intrinsic chirp component decomposition by using Fourier Series representation

We introduce a general model to characterize multi-component chirp signals.The model represents instantaneous frequencies and instantaneous amplitudes of the intrinsic chirp components as Fourier series.We propose a novel chirp component decomposition method based on the model.The method is able to decompose multi-component chirp signals with intersecting IFs. In this paper, we consider the decomposition problem for multi-component chirp signals (MCCSs). We develop a general model to characterize MCCSs, where instantaneous frequencies (IFs) and instantaneous amplitudes (IAs) of the intrinsic chirp components (ICCs) are modeled as Fourier series. The decomposition problem thus boils down to identifying the developed model. The IF estimation is addressed using the framework of the general parameterized time-frequency transform and then the signal can be easily reconstructed by solving a linear system. For the practical implementation of our method, we present a two-step algorithm, which is initiated by an iterative scheme to achieve preliminary separation of the ICCs, followed by a joint-refinement step to get high-resolution ICC reconstructions. Our method acts as a time-varying band-pass filter and can even separate ICCs that cross in the time-frequency domain. The method is applied to analyze several simulated and real signals, which indicates its usefulness in various applications.

Separation of Overlapped Non-Stationary Signals by Ridge Path Regrouping and Intrinsic Chirp Component Decomposition

In some applications, it is necessary to analyze multi-component non-stationary signals whose components severely overlap in the time-frequency (T-F) domain. Separating those signal components is desired but very challenging for existing methods. To address this issue, we propose a novel non-parametric algorithm called ridge path regrouping (RPRG) to extract the instantaneous frequencies (IFs) of the overlapped components from a T-F representation (TFR). The RPRG first detects the ridges of a multi-component signal from a TFR and then extracts the desired IFs by regrouping the ridge curves according to their variation rates at the intersections. After the IFs are obtained, component separation is achieved by using the intrinsic chirp component decomposition (ICCD) method. Different from traditional T-F filter-based methods, the ICCD can accurately reconstruct overlapped components by using a joint-estimation scheme. Finally, applications of separating some simulated and experimental micro-Doppler signals are presented to show the effectiveness of the method.

Nonlinear Chirp Mode Decomposition: A Variational Method

Variational mode decomposition (VMD), a recently introduced method for adaptive data analysis, has aroused much attention in various fields. However, the VMD is formulated based on the assumption of narrow-band property of the signal model. To analyze wide-band nonlinear chirp signals (NCSs), we present an alternative method called variational nonlinear chirp mode decomposition (VNCMD). The VNCMD is developed from the fact that a wideband NCS can be transformed to a narrow-band signal by using demodulation techniques. Our decomposition problem is, thus, formulated as an optimal demodulation problem, which is efficiently solved by the alternating direction method of multipliers. Our method can be viewed as a time–frequency filter bank, which concurrently extracts all the signal modes. Some simulated and real data examples are provided showing the effectiveness of the VNCMD in analyzing NCSs containing close or even crossed modes.

Research on Spillover Effects for Vibration Control of Piezoelectric Smart Structures by ANSYS

To control vibration of a piezoelectric smart structure, a controller is usually designed based on a reduced order model (ROM) of the system. When such a ROM based controller operates in closed loop with the actual structure, spillover phenomenon occurs because the unmodeled dynamics, which are not included in ROM, will be excited. In this paper, a new approach aiming at investigating spillover effects in ANSYS software is presented. By using the ANSYS parametric design language (APDL), the ROM based controller is integrated into finite element model to provide an accurate representation of what will happen when the controller is connected to the real plant. Therefore, the issues of spillover effects can be addressed in the closed loop simulation. Numerical examples are presented for investigating spillover effects of a cantilever piezoelectric plate subjected to various types of loading. The importance of considering spillover effects in closed loop simulation of piezoelectric smart structures is demonstrated. Moreover, the present study may provide an efficient method especially beneficial for preliminary design of piezoelectric smart structure to evaluate the performance of candidate control laws in finite element environment considering spillover effects.

Chirplet Path Fusion for the Analysis of Time-Varying Frequency-Modulated Signals

We propose a novel method, called chirplet path fusion, to analyze nonstationary signals with time-varying frequencies. As opposed to many existing methods that assume the signal persists throughout the whole time, the proposed method can be applied in cases where the signals are only present in short time frames. A demodulation-operator-based method is introduced to estimate the locally matched chirplet atoms which can form a chirplet path in the time-frequency domain. According to the density of the multiple chirplet paths obtained under different scales, the effective time support and the instantaneous frequency (IF) of the target signal can be estimated. Our method is effective in analyzing the nonstationary signal with discontinuous IF curve and works well under heavy noise. Several simulated signals and the vibration signal of a rotor test rig are considered to verify the effectiveness of the proposed method.