Power Spectrum Density Estimation Research Articles

PSD estimation and modal parameter identification for random vibrations with blade tip timing measurement

Abstract Blade tip timing (BTT) is a vibration measurement technique for blade health monitoring. Most of the existing BTT analysis methods are suitable for deterministic vibration signals but are ineffective for random vibration signals that often occur in practice. Statistical analysis of BTT data is significant for random vibration analysis and improving blade monitoring efficiency. This study proposes a compressive model for power spectral density (PSD) estimation and modal parameter identification. The efficiencies of three compressive sensing algorithms, including the least absolute shrinkage and selection operator (Lasso), nonnegative least squares (NLS), and nonnegative orthogonal matching pursuit, are compared. The effects of the duration of the signal and the frequency resolution on the quality of the estimated PSD and the identified parameters are discussed. According to the analysis, to obtain accurate damping ratios, it is recommended that the duration of the signal be greater than 3000 revolutions. A Q criterion based on the half-power bandwidth is proposed to determine the set of frequency resolutions. Numerical and field tests were conducted to verify the proposed method. The results indicate that the NLS algorithm is recommended to use. The root-mean-square errors of the identified natural frequencies and damping ratios obtained by the proposed method were 0.065 Hz and 0.023%, respectively. The proposed method was verified at different rotational speeds in a field test, demonstrating the capability of the method over a wide rotational speed range and providing more opportunities to detect blade damage.

Interfacial debonding detection of steel beams reinforced by CFRP plates based on percussion method

Steel structure reinforced engineering makes extensive use of carbon fiber reinforced plastic (CFRP) plates. Although it happens frequently, the interfacial debonding of CFRP plate-reinforced steel beams has been the main cause of failure in flexural strengthened steel beams, which results in the brittle failure of steel structures. This paper proposes a novel percussion method to locate and quantify the debonding area based on the Welch power spectrum density (PSD) estimate, mel frequency cepstral coefficient (MFCC), and convolutional neural network (CNN). According to our knowledge, this is the first attempt to use the percussion method to identify and measure the debonding defects of steel beams strengthened by CFRP plates. Additionally, this experiment takes into account how percussion instruments affect localization and quantification. To begin with, the debonding location is qualitatively detected using the Welch PSD estimate method. The presented percussion method can successfully and accurately detect the interfacial debonding of CFRP plate-reinforced steel beams, according to repeated results. Subsequently, a novel CNN model is constructed to classify the various debonding areas based on the MFCC feature. In the end, the experimental findings show that the localization and quantification of the hammer types vary only slightly. Overall, the percussion-based approach can offer a fresh line of inquiry into the debonding problem on steel beams reinforced with CFRP plates.

Pulsed and Continuous Signal Enhancement Based on Improved Noise Power Spectrum Density Estimation in the Passive Underwater Acoustic Data

The pulsed and continuous narrow-band signal enhancement is quite important for the target detection and recognition in a passive sonar system. In this paper, a novel signal enhancement approach is proposed for both pulsed and continuous narrow-band components in the passive underwater acoustic data. The short time Fourier transform (STFT) method is firstly used in the time-domain radiated noise data, and then an improved noise power spectrum density (PSD) estimation is proposed to obtain the accurate noise power by using a two-dimension (2-D) sliding window. Finally, the improved PSD is utilized to enhance both pulsed and continuous narrow-band components. The proposed method has the capability of enhancing pulsed and continuous narrow-band components with avoiding the annoying tuning of the window length. Both simulation and experimental results verify the effectiveness and robustness of the proposed method.

Fault Diagnosis of Diesel Engine Valve Clearance Based on Wavelet Packet Decomposition and Neural Networks

In order to improve the accuracy of engine valve clearance fault diagnosis, in this study, a fault identification algorithm based on wavelet packet decomposition and an artificial neural network is proposed. Firstly, the vibration signals of the engine cylinder head were collected, and different levels of noise were superimposed on the extended data sets. Then, the test data were decomposed into wavelet packets, and the power spectrum of the sub-band signal was analyzed using the autoregressive power spectrum density estimation method. A group of values were obtained from the power spectrum integration to form the fault eigenvalue. Finally, a neural network model was designed to classify the fault eigenvalues. In the training process, the test data set was divided into three parts, the training set, the verification set, and the test set, and the dropout layer was added to avoid the overfitting phenomenon of the neural network. The experimental results show that the wavelet packet neural network model in this paper has a good diagnostic accuracy for data with different levels of noise.

Singular Spectrum Analysis and Circulant Maximum Variance Frames

Singular spectrum analysis (SSA) is a powerful method that is frequently used in dynamical systems theory and time series analysis. However, the algorithm itself is only partially understood. In this paper, we tackle the problem of a thorough interpretation of the complete basic SSA algorithm. We point out the relationship between SSA and Fourier analysis (FA), linear filtering (LF), principal component analysis (PCA), and power spectrum density estimation (PSDE). The main contribution is a reformulation and comprehensive interpretation of SSA by means of a novel class of data-adaptive circulant frames. Based on this class of frames, we introduce a formalism for time series decomposition and reconstruction. This mathematical framework generalizes principle component analysis and SSA. We show that SSA, PCA, FA, LF, and PSDE can be found from special cases of the proposed frame structures. This way we are able to provide a formal description of SSA and its relationship to the aforementioned methods. Whilst previous approaches to the interpretation of SSA relied on approximations, we provide exact mathematical descriptions of the relation between the above-mentioned techniques.

Adaptive Youla–Kučera parametric control of unknown tip-tilt disturbance rejection in image stabilization systems

We propose a new, to the best of our knowledge, adaptive control method to attenuate beam jitter in image stabilization systems, which breaks the restrictions of existing adaptive control methods in terms of time consumption and control stability, and then provides an innovative way for tip-tilt disturbance rejection. In this approach, disturbance rejection could be converted to optimize error attenuation through the parameters design of the Youla-Kučera (YK) parametric controller, which are determined by a new on-line power spectrum density (PSD) estimation of tip-tilt errors to identify the frequency and amplitude of unknown disturbances. Experimental results demonstrate that the proposed method working in an adaptive correction process can attenuate the beam jitter to approximately 1/3 less than the original control error.

On finding possible frequencies for recognizing microearthquakes at Cotopaxi volcano: A machine learning based approach

Adequate detection and classification of seismic events are crucial for understanding the internal status of a Volcano. Machine learning-based classifiers use different features from the time, frequency, and scale domains related to seismic events. Regarding power spectrum-based features, several methods can be used to compute such features. However, the more suitable method for analyzing volcanic activity is undetermined. This paper presents a study about the main frequency bands, which allows maximizing the performance metrics of an automated classifier for long-period (LP) and volcano-tectonic (VT) events based on parametric (Yule-Walker and Burg) and non-parametric (Welch and Multitaper) power spectrum density estimation methods. Feature selection using embedded (pruning) and wrapper (recursive feature elimination) methods was applied to select the main frequencies that maximize the balanced error rate of suitable classification algorithms, such as decision trees (DT) and support vector machines (SVM). Bootstrapping was used to estimate a confidence interval for the frequencies of the microearthquakes. An amplitude threshold difference of at least 3 dB was used to guarantee that possible frequency features that characterize each type of event do not overlap between classes. The method who achieved the worst overall performance was not considered by the voting strategy. A Dataset from Cotopaxi volcano was used to test the proposed classification schema. The best results show for DT classifier a total of 10 key frequencies, while for SVM classifier 39 key frequencies grouped in three main frequency bands, as main features to distinguish LP events from VT earthquakes. The best classification results were achieved by the Welch method with the DT and by the Multitaper method with the SVM classifiers. Furthermore, the study confirms that there is a frequency band above 40 Hz, which seems like a critical feature for the detection and classification of stages.

A novel time-varying modeling and signal processing approach for epileptic seizure detection and classification

Electroencephalogram (EEG) signal analysis plays an essential role in detecting and understanding epileptic seizures. It is known that seizure processes are nonlinear and non-stationary, discriminating between rhythmic discharges and dynamic change is a challenging task in EEG-based seizure detection. In this paper, a new time-varying (TV) modeling framework, based on an autoregressive (AR) model structure, is proposed to characterize and analyze EEG signals. The TV parameters of the AR model are approximated through a multi-wavelet basis function expansion (MWBF) approach. An effective ultra-regularized orthogonal forward regression (UROFR) algorithm is employed to significantly reduce and refine the resulting expanded model. Given a time-varying process, the proposed TVAR–MWBF–UROFR method can generate a parsimonious TVAR model, based on which a high-resolution power spectrum density (PSD) estimation can be obtained. Informative features are then defined and extracted from the PSD estimation. The TVAR–MWBF–UROFR method is applied to a number of real EEG datasets; features obtained from these datasets are then used for seizure detection and classification. To make the results more accurate and reliable, a PCA algorithm is adopted to select the optimal feature subset, and a Bayesian optimization technique based on the Gaussian process is performed to determine the coefficients associated with each of the classifiers. The performance of the proposed method is tested on two benchmark datasets, and the experimental results indicate that TVAR–MWBF–UROFR outperforms the compared state-of-the-art classifiers in terms of accuracy, specificity, sensitivity and robustness.

Dynamic modeling of ultra-precision fly cutting machine tool and the effect of ambient vibration on its tool tip response

The dynamic performances of an ultra-precision fly cutting machine tool (UFCMT) has a dramatic impact on the quality of ultra-precision machining. In this study, the dynamic model of an UFCMT was established based on the transfer matrix method for multibody systems. In particular, the large-span scale flow field mesh model was created; and the variation in linear and angular stiffness of journal and thrust bearings with respect to film thickness was investigated by adopting the dynamic mesh technique. The dynamic model was proven to be valid by comparing the dynamic characteristics of the machine tool obtained by numerical simulation with the experimental results. In addition, the power spectrum density estimation method was adopted to simulate the statistical ambient vibration excitation by processing the ambient vibration signal measured over a long period of time. Applying it to the dynamic model, the dynamic response of the tool tip under ambient vibration was investigated. The results elucidated that the tool tip response was significantly affected by ambient vibration, and the isolation foundation had a good effect on vibration isolation.

Lecture Notes on Time Transposed Conjugated Signal with Applications to Power Spectrum Density Estimation

Power spectrum density (PSD) is a quite important tool in signal processing, since you can get the frequency components of the random signal by power spectrum analysis. Here we discuss the application of backward conjugate signal/sequence in power spectrum estimation. During the research, we noted that the backward conjugate signal/sequence can improve the performance of PSD estimation with low SNR and even small sample size. We hope that the results of this paper can give some inspiration to students who are studying digital signal processing.

Understanding Several Power Spectrum Density Estimation Algorithms Based on the Problems Solved

Starting from the estimation criterion and the essential problem of algorithmic computing, this paper introduces four kinds of spectral estimation methods commonly used in teaching: Periodogram to fit frequency vector under least square criterion，AR model estimation converts spectrum estimation into parameter estimation, MVDR converts spectrum estimation into filter weight coefficient estimation, and MUSIC converts spectral estimation into subspace estimation. Then we analyze and solve the equation, derive the assumption of signal and the defects caused by this assumption.

Improved MB Cognitive Radio Spectrum Sensing Using Wavelet Spectrum Filtering

In cognitive radio (CR), the sensed aggregate bandwidth could be as large as several GHz. This is especially challenging if the bandwidths and central frequencies of the sensed signals are unknown and need to be estimated. This work discusses a new improved method for MB spectrum sensing (iMB-SS) based on edge detection and using Wavelet Spectrum Filtering. The proposed iMB-SS method uses a Welch power spectrum density (PSD) estimate and a multi-scale Wavelet approach to reveal the spectrum transition (edges), which is deployed to characterize the spectrum occupancy in CR scenarios where the operation frequencies of the primary users (PUs) are unknown. The focus of this work lies in improving the performance of the MB spectrum sensor, particularly by refining the spectral edge location and reducing misleading detection. A comprehensive analytical description and numerical analysis have been carried out by focusing on orthogonal-frequency-division-multiplexing (OFDM) signal applications in CR networks. Numerical results corroborate the effectiveness of the proposed iMB-SS approach. The simulated results for the multiple-PU’s OFDM-based transmission CR system demonstrate that the proposed iMB-SS method can achieve high performance even under low signal-to-noise ratio (SNR) regime, turning it out as an attractive choice for SS in the MB CR systems.

Cognitive Design of Radar Waveform and the Receive Filter for Multitarget Parameter Estimation

This research work considers waveform design for an adaptive radar system. The aim is to achieve enhanced feature extraction performance for multiple extended targets. There are two scenarios to consider: multiple extended targets separated in range and multiple extended targets close in range. We propose a waveform optimization scheme based on Kalman filtering by minimizing the mean square error of separated target scattering coefficient estimation and a waveform optimization approach by minimizing the mean square error of closed power spectrum density estimation. A convex cost function is established, and the optimal solution can be obtained using the existing convex programming algorithm. With subsequent iterations of the algorithm, the simulation results demonstrate an improvement in the estimation of target parameters from the dynamic scene, such as target scattering coefficient and power spectrum density, while maintaining relatively lower computational complexity.

Orbital-Angular-Momentum-Based ISAR Imaging at Terahertz Frequencies

The electromagnetic (EM) wave carrying orbital angular momentum (OAM) is usually named vortex EM wave, which has been found great potential to improve the target imaging performance. For conventional ISAR imaging, only 2-D target image can be obtained. In this paper, the OAM-based ISAR technique is developed to achieve 3-D target image with high resolution at terahertz frequencies. First, the imaging model is derived, and the point spread function is analyzed. Subsequently, two imaging algorithms, namely the FFT-based imaging method and the imaging method based on convolution backprojection and power spectrum density estimation, are proposed. Simulation results validate the effectiveness of the proposed methods and indicate that the high-resolution cross-range profile can still be obtained at terahertz frequencies with small rotational angle. This paper can provide a novel manner to realize 3-D imaging of universal targets with high resolution.

Denoising different types of acoustic partial discharge signals using power spectral subtraction

Measuring acoustic emission (AE) of partial discharge (PD) phenomena can be adopted to estimate the condition of power transformers. However, the environmental noise encountered with AE of PD measurements negatively affects the accuracy of PD localisation and classification. Thus, efficient signal denoising techniques are required for noise suppression and hence, better detection accuracy. This study deals with white noise and it is a continuation of a previously published work that deals with random noise. The published work addresses the random noise suppression using a method named, power spectral subtraction denoising (PSSD). This study applies PSSD to the PD signals contaminated with white noise and uses a novel scheme of noise power spectrum density estimation. Multiple types of AE signals are examined including signals produced by corona, surface, parallel, and void PDs. Synthetic and real data demonstrate the superiority of the proposed method over the wavelet shrinkage denoising method as it can more effectively eliminate white noise and preserve signals of low signal-to-noise ratio.

Optimization Acceleration Integral Method Based on Power Spectrum Estimation

Due to the excellent performance of the frequency domain integration method, it is widely used for acceleration integral calculations. However, the frequency-domain integration needs to select the effective integration frequency band to achieve its optimal integration performance. This paper proposes the method with power spectrum density (PSD) estimation to realize the optimization integral of the acceleration signal. By analysing the power spectrum density of the acceleration signal, the optimal low frequency cut-off frequency is obtained. Combined with frequency domain integration algorithm, it can effectively remove low-frequency noise and improve integral accuracy. Then, the novel algorithm tested by an experiment platform with a vibration bench. Experiment results show that this algorithm can adaptively select the low-frequency cut-off frequency and realize frequency domain integration optimization and the integration error is controlled within ±0.2mm.

Recursive Frequency Domain Decomposition for Multidimensional Ambient Modal Estimation

This paper proposes a multidimensional recursive ambient modal analysis algorithm called recursive frequency domain decomposition (recursive FDD or RFDD). The method enables simultaneous processing of a large number of synchrophasor measurements for real-time ambient modal estimation. The method combines a previously proposed multidimensional block processing algorithm FDD with a single input recursive least square (RLS) algorithm into developing a new frequency domain multidimensional recursive algorithm. First, an auto-regressive model is fitted onto the sampled data of each signal using the time-domain RLS approach. Subsequent modal analysis is carried out in frequency domain in the spirit of FDD. The conventional FDD method uses non-parametric methods for power spectrum density (PSD) estimation. The proposed method in this paper by estimating PSD with a parametric method provides smoother PSD estimation which results in less standard deviation in RFDD estimates compared to FDD. The algorithm is tested on archived synchrophasor data from a real power system.

Intelligent Bandwidth-Estimation Technique for Orthogonal Frequency Division Multiplexing-Based Elastic Optical Networking

In orthogonal frequency division multiplexing (OFDM)-based elastic optical networking (EON), it is imperative to identify the parameters of the unknown OFDM signal intelligently, quickly, and robustly. Among these parameters, the bandwidth should be the first to be identified for the reason that other useful parameters such as number of subcarriers, baud rate, and frequency spacing can be obtained subsequently. In this paper we propose, for the first time to our knowledge, an intelligent bandwidth-identification technique for OFDM-based EON. The proposed technique can be divided into three sub-stages: estimation of power spectrum density, noise filtering based on empirical mode decomposition, and bandwidth identification based on a sliding window. When the number of samples is fixed at 215 and the optical signal-to-noise rate varies from 15 to 25 dB, the simulation results demonstrate that a bandwidth range from 2 to 40 GHz can all be successfully recognized with a minimum resolution of 39.1 MHz, and the average estimation absolute accuracies (EAAs) exceed 95%. Moreover, the technique has a good tolerance to chromatic dispersion and is independent of the number of subcarriers and frequency offsets. Finally, we verify the effectiveness of this technique by an experiment involving a 7.04 Gbps OFDM-based EON with minimum EAA of 94.12%, in which its bandwidth can be successfully recognized.

Frequency‐domain wideband compressive spectrum sensing

The authors study the power spectrum density (PSD) estimation of wideband wide-sense stationary (WSS) signals with sub-Nyquist sampling rate. Owing to the large bandwidth, Nyquist rate sampling of such signals needs very high rate analogue-to-digital converters. It is important to note that PSD estimation does not necessarily require reconstruction of the original signal. Indeed, the power spectrum can be directly obtained from sub-Nyquist samples. In this study, a new method for reconstructing the power spectrum in the frequency domain for WSS signals is presented. The main idea is to divide the whole spectrum into N equal-length segments and calculate the average PSD in each segment using a frequency-domain representation of sub-Nyquist samples. In addition, the capability of the proposed method, as a detector of spectrum holes, is studied using receiver operating characteristic (ROC) curves. Then, the analysis of false alarm probability is provided. Simulation results for the additive white Gaussian noise channel and the slowly fading frequency selective channel show that the proposed method considerably outperforms available techniques.

Spoken Digits Recognition Using Wavelet Transform and Power Spectrum Density Estimation

This work aims to develop an automatic recognition system for isolated spoken words based on power spectrum density estimation and similarity measurements. The pre-processing step prepares the signal for the ulterior phases. For features extraction, we apply the discrete wavelet transform to the speech signal and then the algorithm of Welch is used to estimate the power spectrum density. At the stage of matching, we determine the similarity between power spectra using discrete to continuous algorithm. The experiments give considerable recognition rates with the parameters used.