Chirplet Parameters Research Articles

Synchro-reassigning generalized Chirplet basis transform for analyzing signals with crossover frequencies

Analysis of signals with crossover frequencies, existing in rotating machinery, is one of the challenges in time–frequency analysis (TFA). The classical TFA methods can only provide a single base in the step window, whereas the signal with crossover frequencies has at least two nonproportional fundamental frequencies. Therefore, classical methods are not suitable for addressing non-proportional multi-component signals such as those with crossover frequencies. This paper presents a novel TFA method, referred to as the synchro-reassigning generalized Chirplet basis transform (SRGCBT), which is designed for processing the signal with crossover frequencies. In the proposed SRGCBT, the peak ridges search method is utilized to find out all of the Chirplet parameters that match with multiple non-proportional fundamental frequencies in the signal. The precision and computational efficiency are enhanced by eliminating the interference of redundant parameters in the enumeration. Then, the synchro-reassigning operator is formulated and applied to extract the time–frequency (TF) coefficients at the instantaneous frequency (IF) ridges. Subsequently, the TF coefficients are reassembled to obtain a new time–frequency representation (TFR). The advantages of SRGCBT are validated by the simulation signal and the vibration signals gathered in the laboratory. The validation results indicate that the proposed SRGCBT delivers improvements in noise robustness, energy concentration, computational efficiency and accuracy in rendering the final TFR for the signal with crossover frequencies.

Ultrasonic Flaw Detection in Composite Materials Using SSP-MPSD Algorithm

Due to the inherent inhomogeneous and anisotropy nature of the composite materials, the detection of internal defects in these materials with non-destructive techniques is an important requirement both for quality checks during the production phase and in service inspection during maintenance operations. The estimation of the time-of-arrival (TOA) and/or time-of-flight (TOF) of the ultrasonic echoes is essential in ultrasonic non-destructive testing (NDT). In this paper, we used split-spectrum processing (SSP) combined with matching pursuit signal decomposition (MPSD) to develop a dedicated ultrasonic detection system. SSP algorithm is used for Signal-to-Noise Ratio (SNR) enhancement, and the MPSD algorithm is used to decompose backscattered signals into a linear expansion of chirplet echoes and estimate the chirplet parameters. Therefore, the combination of SSP and MPSD (SSP-MPSD) presents a powerful technique for ultrasonic NDT. The SSP algorithm is achieved by using Gaussian band pass filters. Then, MPSD algorithm uses the Maximum Likelihood Estimation. The good performance of the proposed method is experimentally verified using ultrasonic traces acquired from three specimens of carbon fibre reinforced polymer multi-layered composite materials (CFRP).

Multi component signal decomposition based on chirplet pursuit and genetic algorithms

In this paper, we will propose a method based on genetic algorithms, chirplet atoms and the matching pursuit algorithm that by using prior knowledge about the chirplet parameters can do higher quality decomposition of multi component signals. The Matching pursuit is an iterative greedy algorithm that can be used for decomposing of the biological signals into basis functions in time and frequency domain. Decomposition of a non-stationary multi component biological signal by using chirplet basis functions in the matching pursuit algorithm is an optimization problem. We will use a genetic algorithm for solving this optimization problem. We will compare the mean and variance of estimated parameters of chirplets with Cramér–Rao Lower Bounds (CRLB) and the actual values. As we will see, the algorithm is robust against noise, and can do efficient decompositions. In addition, the results show that the algorithm can improve the SNR of the multi component signals. The traditional Adaptive Chirplet Decomposition (ACD) method is commonly used to decompose the multi-component signals to the chirplets. The ACD method uses the Quasi–Newton optimization method and expectation maximization refinement. The comparison between the results of the proposed method with the ACD method for real experimental data shows the improvement in “Signal to Reconstructed Error Ratio (SRER)” using the proposed method.

Chirplet Signal and Empirical Mode Decompositions of Ultrasonic Signals for Echo Detection and Estimation

In this study, the performance of chirplet signal decomposition (CSD) and empirical mode decomposition (EMD) coupled with Hilbert spectrum have been evaluated and compared for ultrasonic imaging applications. Numerical and experimental results indicate that both the EMD and CSD are able to decompose sparsely distributed chirplets from noise. In case of signals consisting of multiple interfering chirplets, the CSD algorithm, based on successive search for estimating optimal chirplet parameters, outperforms the EMD algorithm which estimates a series of intrinsic mode functions (IMFs). In particular, we have utilized the EMD as a signal conditioning method for Hilbert time-frequency representation in order to estimate the arrival time and center frequency of chirplets in order to quantify the ultrasonic signals. Experimental results clearly exhibit that the combined EMD and CSD is an effective processing tools to analyze ultrasonic signals for target detection and pattern recognition.

Characterisation of anomalies embedded in graphite fibre reinforced aluminium composite by chirplet parameters

To characterise anomalies embedded in graphite fibre reinforced aluminium matrix composite, chirplet parameters of ultrasonic signals were obtained by chirplet signal decomposition method. It was confirmed that the parameters of decomposed chirplets can represent the characteristic of ultrasonic signals in time and frequency domains compared with conventional time and frequency analysis method. Chirplet parameters were used to identify three types of anomalies embedded in graphite fibre reinforced aluminium matrix composite. The variations of centre frequency and phase of three anomalies were interpreted by frequency dependent attenuation coefficient of composite and frequency dependent reflection coefficient of thin anomalies embedded in composite.

Fast Chirplet Transform With FPGA-Based Implementation

This letter presents a fast chirplet transform (FCT) algorithm, a computationally efficient method, for decomposing highly convoluted signals into a linear expansion of chirplets. The FCT algorithm successively estimates the chirplet parameters in order to represent a broad range of chirplet shapes, including the broadband, narrowband, symmetric, skewed, nondispersive, or dispersive. These parameters have significant physical interpretations for radar, sonar, seismic, and ultrasonic applications. For the real-time application and embedded implementation of the FCT algorithm, an FPGA-based hardware/software co-design is developed on Xilinx Virtex-II Pro FPGA development platform. Based on the balance among the system constraints, cost, and the efficiency of estimations, the performance of different algorithm implementation schemes have been explored. The developed system-on-chip successfully exhibits robustness in the chirplet transform of experimental signals. The FCT algorithm addresses a broad range of applications including velocity measurement, target detection, deconvolution, object classification, data compression, and pattern recognition.

New Approaches for Chirplet Approximation

This correspondence proposes efficient algorithms for approximating complex-valued and real-valued signals as a weighted sum of multiple chirplet atoms, which are characterized by four parameters, namely the scale, time, frequency, and chirp rate. Direct sequential estimation of the parameters of multiple chirplets causes error propagations, i.e., the estimated parameters of the initial chirplets significantly affect the parameter estimation of the subsequent chirplets and may result in large chirplet approximation errors. To deal with this problem, we further exploit a relaxation (RELAX) method for recursive chirplet parameter estimation. RELAX can be used in conjunction with time-domain or frequency-domain algorithms to improve the parameter estimation accuracy for multiple chirplets. Unlike previous methods, our chirplet approximations require neither any a priori complete dictionary of chirplets nor complicated multidimensional searches to obtain suitable choices of chirplet parameters. The effectiveness of the proposed approaches is demonstrated via a number of simulated examples