Fully automated operational modal identification based on scale-space peak picking algorithm and power spectral density estimation

A coprime sensor array (CSA) is a sparse array geometry that interleaves two spatially undersampled uniform linear arrays (ULAs) with coprime undersampling factors. The CSA spans the same aperture and has equivalent resolution as a fully populated ULA, but uses fewer sensors. Previous works have introduced three CSA processors as spatial power spectral density (PSD) estimators: the Product, Min, and Blend processors. However, two of these processors display increased PSD esti-mate variance over the ULA PSD estimate. This dissertation focuses on reducing the variance of the CSA PSD estimators. PSD estimation traditionally relies on averag-ing uncorrelated coherent measurements (snapshots) to reduce variance. However,non-stationary underwater sonar environments often preclude increasing the num-ber of snapshots required to achieve a desirable PSD variance. In the traditional signal processing literature, there are two alternative methods to reduce variance without additional snapshot cost. The multitaper (MT) method and Welch's over-lapping segment averaging (WOSA) method improve PSD variance by O(K) at the expense of an O(K) resolution decrease by averaging K uncorrelated PSD estimates. Multitaper obtains these uncorrelated estimates by windowing the array with K or-thogonal tapers that span the entire array aperture. In contrast, WOSA obtains the uncorrelated estimates by subdividing the array into K possibly overlapping segments.This dissertation extends these two existing ULA variance reduction techniques to the CSA processors, making four main contributions. The first proposes the multitapered Product processor (MT-Product) that estimates the spatial PSD with reduced variance with respect to the traditional CSA Product processor but still uses fewer sensors than a fully populated ULA. The second proposes the multita-pered Min processor (MT-Min) that reduces the PSD estimate variance further than either MT-Product or Product. The MT-Min estimator has variance comparable to a multitapered ULA. The third proposes the multitapered Blend processor (MT-Blend) that blends MT-Product's attenuation of multiple source cross-terms with MT-Min's low variance while still achieving an O(K) variance reduction over the traditional Blend processor. The final contribution proposes the Welch overlapping segment averaging Product processor (WOSA-Product) that estimates the spatial PSD with reduced variance with respect to the traditional CSA Product processor but still uses fewer sensors than a fully populated ULA. WOSA-Product is gener-ally able to form a larger number of uncorrelated PSD estimates than MT-Product. Closed-form statistics for spatially white Gaussian processes are derived for MT-Product, MT-Min, and WOSA-Product. Simulations verify the variance reduction predicted by the analytical derivations each processor, and the effects of WOSA-Product segment length on resolution, variance reduction, and peak sidelobe levels are discussed.

Modal parameter identification is an important content for the research on dynamic behavior of civil engineering structures. For the conventional modal parameter identification techniques, excitation signal and response signal are necessary. But excitations can not be measured for structures under natural loading conditions, or excited by random forces. So, the operational modal parameter identification approaches are developing to identify structural modal parameters by using vibration response signal directly. In this paper, a new method for modal parameter identification depending on ambient excitation response signal is proposed based on independent component analysis (ICA). For modal coordinates independent of each other, ICA can extract modal coordinates of structure and estimate mode shape matrix using vibration response signal directly. The free vibration responses can be obtained by random decrement technique (RDT) from modal coordinates which are random processes, and then the natural frequencies and damping ratios are calculated by Hilbert transform. Numerical simulation results indicate that this method is effective and suitable for output-only structural modal parameter identification.

This paper analyzes algorithms which are suitable for spectral estimates of noisy signals in the frequency domain based on the use of the fast Fourier transform (FFT). Several causes of inaccuracy are analyzed and characterized so that the expressions of different components of error on the power spectral density (psd) estimate are given, in terms both of spectral properties of noise and typical parameters of the used filter. These simple expressions point out how an appropriate choice of some window parameters may increase considerably the accuracy of the estimate. The effects of choice on the accuracy are examined. In any case, the performance of the psd estimator can be improved by adopting linear or nonlinear averaging techniques; in the paper the statistical properties of geometric mean of periodograms are particularly examined and compared with those of the more traditional Welch's method. It is proved that, under appropriate conditions, the geometric mean produces a reduction both of bias and variance of psd. Numerical simulations confirm these theoretical results.

Spectrum analysis is one of the momentous fields in signal processing. It has a large variety of applications in radar, sonar, speech and image processing. Parametric methods have been proposed and employed for spectrum analysis including power spectral density (PSD) estimation. These methods estimate the parameters of a statistical model and compute the PSD, afterwards. In some circumstances one is obliged to deal with observations of numerous geographically dispersed sensors, to either increase the precision or based on application demands. Having a set of sensors linked together to take the advantages of cooperation and network topology, one obtains a more comprehensive estimation. In this chapter, the authors propose and study four different algorithms capable of facing spatio-temporal variations for parametric modeling and PSD estimation using wireless sensor networks (WSNs). For this purpose, the authors first validate the proposed algorithms using theoretical and mathematical formulations. Thereafter, performing simulation tasks demonstrates and supports the theoretical achievements. The next section of the chapter illustrates the concepts to a greater degree, the authors analyze and compare the performance of these algorithms with each other, as well as with the simple PSD estimation using individual sensors, wherein there is no cooperation among the nodes.

The aim of this study was to assess whether power spectrum estimates of electroencephalogram (EEG) can be used as a biomarker for autism spectrum disorder (ASD). EEG collected from ASD and control participants performing a short-memory task was preprocessed to remove noise and artefacts, power spectral density (PSD) estimates were obtained by the modified covariance method and used as the study features that were subjected next to the Kruskal-Wallis analysis of differences. After verifying that the features (PSD estimates) were statistically different between the autistic and control subjects, these PSD estimates were classified using the 'k nearest neighbour' (KNN) classification algorithm with the average accuracy of 89.29%. This result indicates that EEG of autistic and control individuals may contain statistically different features; therefore, EEG power spectrum may be used as a biomarker for autism.

Three power spectral density estimation problems are considered in this presentation. These are the estimation of power spectral density for a single scalar time series (or equivalently a line array), estimation of power spectral density matrices for vector valued time series, and the estimation of wavenumber or frequency-wavenumber spectra for random fields. The paper is primarily a tutorial coverage of autoregressive (also called maximum entropy) and maximum likelihood methods of spectral analysis. In addition to standard material on these subjects a recent generalization of the Burg algorithm from scalar to vector time series is included.

Modal parameter identification via ambient vibration is popular but faces challenges from uncertainties due to unknown inputs and low signal‐to‐noise ratio. Bayesian methods are gaining increasing attention for operational modal identification due to their ability to quantify uncertainties. However, improvements in computational efficiency are needed, particularly when addressing numerous modes and degrees of freedom. To address this challenge, this study proposes an innovative approach, termed the “Bayesian spectral decomposition” method (BSD), employing the decompose‐and‐conquer strategy. This novel method, operating within the frequency domain, identifies each mode individually by exploiting their inherent separated modal characteristics. For each mode, the response spectrum matrix undergoes an eigenvalue decomposition, yielding crucial eigenvalues (incorporating frequency and damping information) and eigenvectors (containing mode shape information). Subsequently, statistical properties of the eigenvalues and eigenvectors are utilized to establish likelihood functions for Bayesian parameter identification. By combining prior information, the posterior probability distribution functions of modal parameters are derived. The optimal solution is then obtained by resolving the maximum posterior probability distribution function problem. To further quantify the uncertainty of modal parameters, Gaussian distributions are employed to approximate the posterior probability distribution functions. The adoption of the decomposition approach circumvents the joint identification of all modal parameters, substantially reducing the parameter dimensions for optimization. Consequently, this strategy leads to decreased computational complexity and significantly improved computational stability. The effectiveness of the BSD is confirmed through simulated data generated from an 8‐story shear building as well as measured data collected from both an experimental shear frame and the Canton Tower. The results demonstrate that the proposed method achieves high accuracy in identifying modal parameters, greatly improves computational efficiency, and effectively quantifies the uncertainties in modal parameters.

Many well-known and frequently employed Bayesian clean speech estimators have been derived under the assumption that the true power spectral densities (PSDs) of speech and noise are exactly known. In practice, however, only power spectral density (PSD) estimates are available. Simply neglecting PSD estimation errors and handling the estimates as true values leads to speech estimation errors causing musical noise and undesired suppression of speech. In this paper, the uncertainty of the available speech PSD estimates is addressed. The main contributions are the following. First, we summarize and examine ways to model and incorporate the uncertainty of PSD estimates for a more robust speech enhancement performance. Second, a novel nonlinear clean speech estimator is derived that takes into account prior knowledge about the absolute value of typical speech PSDs. Third, we show that the derived statistical framework provides uncertainty-aware counterparts to a number of well-known conventional clean speech estimators such as the Wiener filter and Ephraim and Malah's amplitude estimators. Fourth, we show how modern PSD estimators can be incorporated into the theoretical framework and propose to employ frequency dependent priors. Finally, the effects and benefits of considering the uncertainty of speech PSD estimates are analyzed, discussed, and evaluated via instrumental measures and a listening experiment.

ABSTRACTA radio frequency interference (RFI) excision algorithm based on spectral kurtosis, a spectral variant of time‐domain kurtosis, is proposed and implemented in software. The algorithm works by providing a robust estimator for Gaussian noise that, when violated, indicates the presence of non‐Gaussian RFI. A theoretical formalism is used that unifies the well‐known time‐domain kurtosis estimator with past work related to spectral kurtosis, and leads naturally to a single expression encompassing both. The algorithm accumulates the first two powers of M power spectral density (PSD) estimates, obtained via Fourier transform, to form a spectral kurtosis (SK) estimator whose expected statistical variance is used to define an RFI detection threshold. The performance of the algorithm is theoretically evaluated for different time‐domain RFI characteristics and signal‐to‐noise ratios η. The theoretical performance of the algorithm for intermittent RFI (RFI present in R out of M PSD estimates) is evaluated and shown to depend greatly on the duty cycle, d = R/M. The algorithm is most effective for d = 1/(4 + η), but cannot distinguish RFI from Gaussian noise at any η when d = 0.5. The expected efficiency and robustness of the algorithm are tested using data from the newly designed FASR Subsystem Testbed radio interferometer operating at the Owens Valley Solar Array. The ability of the algorithm to discriminate RFI against the temporally and spectrally complex radio emission produced during solar radio bursts is demonstrated.

Broken rotor bars in an induction motor create asymmetries and result in abnormal amplitude of the sidebands around the fundamental supply frequency and its harmonics. Applying a spectrum analysis technique on motor current and inspecting the spectrum amplitudes at the broken rotor bar specific frequencies for abnormality is a well-known procedure for broken rotor bar fault detection and diagnosis. Among the spectrum analysis techniques for broken rotor bar fault detection, the fast Fourier transform (FFT) is the most widely used technique. There are other spectrum techniques, which are based on the power spectral density estimates. In this paper we compare the three well-known spectrum analysis methods: FFT, periodogram and Welch's periodogram methods according to their performance on the broken rotor bar fault detection problem. The results indicate that Welch's periodogram method has better fault discrimination capability and is more robust compared to the other two methods. A statistical hypothesis test applied to the results of the three methods depicts the comparison results quantitatively.

Tensor-based approach for underdetermined operational modal identification

Traditional fast Fourier transform (FFT) has gained enormous recognition for broken rotor bar (BRB) fault detection in induction motors using the sideband features as fault indices, however, the false alarm from inaccurate diagnosis remains a major setback associated with the technique. This paper presents two reliable spectral analysis approaches for BRB fault detection and analysis for induction motors: Thompson Multitaper (MTM) power spectral density (PSD) estimate, and Welch PSD estimate. The two methods are implemented using the simulated stator current signal of an induction motor obtained by the finite element method. The Finite Element analysis software, ANSYS, is used to design and simulate different motor conditions: a healthy motor, a motor with one, two and three BRBs. It is verified that the proposed methods provide robust and reliable BRB fault detection for induction motors.

Frequency Domain Decomposition (FDD) is an operational modal analysis method by which the dynamic parameters of structures are obtained using response signals recorded on several locations of structures. In recent years, many researchers have employed the method to estimate the modal parameters of several Multi-Degree-of-Freedom (MDOF) mechanical and civil systems. The accuracy of the results depends on recording and signal processing parameters such as sampling frequency, windowing, filtering etc. As a result, investigation on the influence of these parameters on the accuracy of the estimates is a good practice. In this research, the uncertainty of modal frequencies obtained from FDD method is analyzed. In order to achieve this goal, the exact values of modal parameters must be available to be compared with the results from FDD method. For this purpose, synthetic signals with random characteristics the same as the ambient vibrations’ are produced and structures with known dynamic parameters are simulated and loaded. The effect of several parameters are investigated in the accuracy of results and proper values and settings are proposed to minimize the errors.

On the application of blind source separation for damping estimation of bridges under traffic loading

Modified frequency and spatial domain decomposition method based on maximum likelihood estimation