Power Spectral Density Estimation Research Articles

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

Modal analysis is a fundamental and essential research direction in the field of structural engineering. The ultimate goal is to determine the modal parameters of the structures. However, the existing modal analysis algorithms often require a large number of parameter adjustments and manual intervention during operation, which cannot be fully automated. In order to realize the automatic identification of modal parameters, the automatic operational modal identification method (AOMI) is proposed based on the interpolated power spectral density estimation (IPSE). To achieve more precise spectrum analysis in the low-frequency band, IPSE is employed to perform Fourier transform on the original frequency domain segment with optimized frequency resolution. This enhances the sharpness of the obtained spectrum in the low-frequency range, making peak frequencies more discernible. Subsequently, the scale-space peak picking algorithm is used to automatically obtain the peak of the power spectral density (PSD), thus enabling the automatic identification of the natural frequency. Finally, the frequency domain decomposition method (FDD) is used to identify modal parameters based on the natural frequencies. The effectiveness of AOMI is verified through the modal identification of the old steel truss bridge and the three layer framework. Under the environmental excitation, the frequencies identified by the IPSE method is close to that of FDD, Bayesian fast fourier transform (FFT) and covariance driven stochastic subspace identification (SSI-COV). Furthermore, the PSD obtained through IPSE has sharper peak than that of FDD and the Welch’s method. The damping ratio identification accuracy and modal assurance criterion (MAC) are satisfactory in AOMI, which can improve the automatic performance.

Large-Area Thickness Measurement of Transparent Films Based on a Multichannel Spectral Interference Sensor

Thickness measurement of thin films is essential for quality control in the manufacturing process of the semiconductor and display industries. Real-time monitoring of film thickness during production is an urgent technical problem to be solved. In this study, a method for large-area thickness measurement of transparent films based on a multichannel spectral interference sensor is proposed. The sensor simultaneously acquires multichannel spectral interference signals through a combination of fan-out fiber optic bundles, detection probes, and an imaging spectrometer. The spectral data are calibrated and transformed into the wavenumber dimension, and then the power spectral density estimation method is used to demodulate the data frequency to swiftly derive the film thickness. The thickness measurement capacity of the proposed system is successfully validated on two standard film samples with a relative deviation of less than 0.38% and a relative standard deviation of less than 0.044%. The total spectral acquisition and calculation time for a single multichannel measurement was approximately 7.5 ms. The experimental results on polyimide films show that the measurement efficiency of the system is at least 4 times higher than that of the traditional system, indicating the potential of the multichannel spectral interference sensor for online monitoring in film production.

Structural EEG signal analysis for sleep apnea classification.

Diagnosing the sleep apnea can be critical in preventing the person having sleep disorder from unhealthy results. The aim of this study is to obtain a sleep apnea scoring approach by comparing parametric and non-parametric power spectral density (PSD) estimation methods from EEGsignals recorded from different brain regions (C4-M1 and O2-M1) for transient signal analysis of sleep apnea patients. Power Spectral Density (PSD) methods (Burg, Yule-Walker, periodogram, Welch and multi-taper) are examined for the detection of apnea transition states including pre-apnea, intra-apnea and post-apnea together with statistical methods. In the experimental studies, EEG recordings available in the database were analyzed with PSD methods. Results showed that there are statistically significant differences between parametric and non-parametric methods applied for PSD analysis of apnea transition states in delta, theta, alpha and beta bands. Moreover, it was also revealed that PSD of EEG signals obtained from C4-M1 and O2-M1 channels were also found statistically different as proved by classification using the K-nearest neighbour (KNN) method. It was concluded that not only applying different PSD methods, but also EEG signals from different brain regions provided different statistical results in terms of apnea transition states as obtained from KNN classification.

Background Seismic Noise Levels among the Caribbean Network and the Role of Station Proximity to Coastline

Abstract The amplitude and frequency content of background seismic noise is highly variable with geographic location. Understanding the characteristics and behavior of background seismic noise as a function of location can inform approaches to improve network performance and in turn increase earthquake detection capabilities. Here, we calculate power spectral density estimates in one-hour windows for over 15 yr of vertical-component data from the nine-station Caribbean network (CU) and look at background noise within the 0.05–300 s period range. We describe the most visually apparent features observed at the CU stations. One of the most prominent features occurs in the 0.75–3 s band for which power levels are systematically elevated and decay as a function of proximity to the coastline. Further examination of this band on 1679 contiguous USArray Transportable Array stations reveals the same relationship. Such a relationship with coastal distance is not observed in the 4–8 s range more typical of globally observed secondary microseisms. A simple surface-wave amplitude decay model fits the observed decay well with geometric spreading as the most important factor for stations near the coast (<∼50 km). The model indicates that power levels are strongly influenced by proximity to coastline at 0.75–3 s. This may be because power from nearshore wave action at 0.75–3 s overwhelms more distant and spatially distributed secondary microseism generation. Application of this basic model indicates that a power reduction of ∼25 dB can be achieved by simply installing the seismometer 25 km away from the coastline. This finding may help to inform future site locations and array design thereby improving network performance and data quality, and subsequently earthquake detection capabilities.

Random vibration-based progressive fatigue damage monitoring in thermoplastic coupons: a preliminary investigation

In recent years there has been an increasing trend towards the utilization of composites, particularly thermoplastics, in various components of aerostructures. The prelusion of such materials has underscored the significance of investigating their fatigue behavior and developing reliable methods for detecting fatigue damage. In this context, vibration-based techniques hold significant potential as they leverage the inherent excitation provided by in-flight noise and turbulence. This study aims at assessing the progressively accumulated fatigue damage in thermoplastic coupons via random vibration signals while accounting for operational and inter-structural uncertainties. The experimental process consists of preliminary tension and fatigue tests, interrupted fatigue tests, C-Scan inspection tests, and non-contact random vibration tests. Consecutive fatigue states are obtained by performing fatigue tests at intervals of 10 000 cycles for a population of 7 coupons. At each interruption, ultrasonic C-Scan and vibration inspection tests are performed, allowing for the visualization of fatigue damage and random vibration signal analysis. Welch Power Spectral Density estimates are employed and are shown to have good potential for distinguishing among different fatigue states despite the inevitable population and experimental uncertainty. Furthermore, fatigue damage is found to progress symmetrically and laterally along the free edges of the test coupons, which is explained by the free edge effect.

Development of software for information-measuring Systems for frequency analysis of binary-quantized Signals

The article discusses the methodology and design template for a complex of structurally, functionally, informationally and metrologically compatible software modules that implement algorithms for calculating estimates of the PSD power spectral density based on binary-signed analog-stochastic quantization with reduced multiplicative complexity. Algorithmic support makes it possible to calculate PSD estimates by the method of averaged modified periodograms and by the correlogram method using time correlation windows based on a discrete-event representation of the results of binary-sign analog-stochastic quantization. This approach made it possible to perform integration operations analytically, which eliminates the methodological error caused by performing these operations in digital form. In addition, the multiplication operations degenerate into procedures that basically require the execution of logical operations and simple arithmetic operations of summing and subtracting the values of the correlation windows, which significantly reduces the complexity of estimating the PSD.

Uncovering acoustic signatures of pore formation in laser powder bed fusion

We present a machine learning workflow to discover signatures in acoustic measurements that can be utilized to create a low-dimensional model to accurately predict the location of keyhole pores formed during additive manufacturing processes. Acoustic measurements were sampled at 100 kHz during single-layer laser powder bed fusion (LPBF) experiments, and spatio-temporal registration of pore locations was obtained from post-build radiography. Power spectral density (PSD) estimates of the acoustic data were then decomposed using non-negative matrix factorization with custom varvec{k}-means clustering (NMFvarvec{k}) to learn the underlying spectral patterns associated with pore formation. NMFvarvec{k} returned a library of basis signals and matching coefficients to blindly construct a feature space based on the PSD estimates in an optimized fashion. Moreover, the NMFvarvec{k} decomposition led to the development of computationally inexpensive machine learning models which are capable of quickly and accurately identifying pore formation with classification accuracy of supervised and unsupervised label learning greater than 95% and 90%, respectively. The intrinsic data compression of NMFk, the relatively light computational cost of the machine learning workflow, and the high classification accuracy makes the proposed workflow an attractive candidate for edge computing toward in-situ keyhole pore prediction in LPBF.

A multiscale feature fusion network based on attention mechanism for motor imagery EEG decoding

The decoding of motor imagery (MI) electroencephalogram (EEG) is an essential component of the brain–computer interface (BCI), which can help patients with motor impairment communicate directly with the outside world through assistive devices. The key to motor imagery electroencephalogram (MI-EEG) classification is to extract multiple temporal, spatial, and spectral features, to obtain more comprehensive and representative information. However, current deep learning methods must fully consider the depth of temporal features and multi-spectral knowledge in EEG and often ignore the temporal or spectrum dependence in MI-EEG. In addition, the lack of effective feature fusion methods can lead to information redundancy, which affects decoding performance. To solve the above problems, this paper proposes a novel MI-EEG decoding method, named multi-scale feature fusion network based on attention mechanism (MSFF-SENet). Firstly, the multi-scale spatio-temporal module (MS-STM) and the multi-scale temporal module (MSTM) extract spatial and high-dimensional temporal features from the original signal. Then, the power spectral density estimation (PSD) convolution module (PSD-Conv module) acquires the multi-spectral features of the MI-EEG signal. Secondly, the feature fusion module fuses spatio-temporal and multi-spectral features to generate integrated feature mappings and establish the dependencies between different features. Finally, we conducted a visual analysis of the results, explaining the neural activity patterns of various motor imagery tasks in different frequency ranges and revealing the potential relationship between body movement and changes related to brain activity. The experimental results show that the classification accuracy of this model in BCI Competition IV 2a (BCI IV 2a) and High Gamma (HGD) datasets is 85.37% and 96.60%, respectively, which is superior to the most advanced methods.

The Thermal Structure of Central Te Riu a Māui/Zealandia Continent as Determined From the Depth to Base of Magnetic Sources

AbstractTo investigate the thermal structure of central Te Riu a Māui/Zealandia continent we estimate the depth to base of magnetic sources (DBMS), using an updated compilation of magnetic data. We calculate thousands of power spectral density estimates and solve an analytic solution for the fractal distribution of magnetization using a Bayesian method constrained by a sediment thickness model. Our DBMS results are broadly similar to a global model yet show complex relationships with independent models of crust and elastic thicknesses, and depth to base of seismicity (D90). Across central Zealandia, DBMS occurs above, coincident with, and below the Moho reflecting that factors additional to temperature influence DBMS. Away from subduction zones crustal thickness likely modulates DBMS while plate margins show varying influence dependent on margin characteristics. In the Taupō Volcanic Zone we interpret DBMS to reflect Curie point temperature at an average depth of 9–11 km. Error analysis shows that the choice of prior influences the posterior standard deviation and can result in counter intuitive error versus DBMS relationships. We use the DBMS as a basal temperature isotherm in heat flow models to compare with heat flow derived from borehole temperature measurements. Using the standard Curie point temperature of 580°C we find that DBMS derived heat flow models over estimate heat flow in areas underlain by plutonic rocks. We propose this reflects a higher titanomagnetite content in these rocks, although detailed studies of the magnetic mineralogy of Zealandia's plutonic rocks are required.

Performance evaluation of sound source localisation and tracking methods using multiple drones

This study evaluates methods to improve sound source localisation and tracking performance using microphone arrays from multiple drones. Previous studies have demonstrated the feasibility of multi-drone sound source tracking by triangulating their respective direction estimations using the MUltiple SIgnal Classification (MUSIC) algorithm. In addition, we evaluate techniques to reduce the influence of rotor noise. Namely, this includes a Wiener filter that utilises rotor noises' power spectral density (PSD) estimations and a noise correlation matrix (NCM) estimation scheme exploiting the geometries of the drone and the microphone array. This is to reduce the rotor noise's influence on the microphone array input correlation matrix prior to localising with MUSIC. Results show that applying the rotor noise reduction method improves localisation and tracking accuracy under a wider range of signal-to-noise ratios, regardless of the sound source tracking method.

A fine-tuning deep residual convolutional neural network for emotion recognition based on frequency-channel matrices representation of one-dimensional electroencephalography

Emotion recognition (ER) plays a crucial role in enabling machines to perceive human emotional and psychological states, thus enhancing human-machine interaction. Recently, there has been a growing interest in ER based on electroencephalogram (EEG) signals. However, due to the noisy, nonlinear, and nonstationary properties of electroencephalography signals, developing an automatic and high-accuracy ER system is still a challenging task. In this study, a pretrained deep residual convolutional neural network model, including 17 convolutional layers and one fully connected layer with transfer learning technique in combination frequency-channel matrices (FCM) of two-dimensional data based on Welch power spectral density estimate from the one-dimensional EEG data has been proposed for improving the ER by automatically learning the underlying intrinsic features of multi-channel EEG data. The experiment result shows a mean accuracy of 93.61 ± 0.84%, a mean precision of 94.70 ± 0.60%, a mean sensitivity of 95.13 ± 1.02%, a mean specificity of 91.04 ± 1.02%, and a mean F1-score of 94.91 ± 0.68%, respectively using 5-fold cross-validation on the DEAP dataset. Meanwhile, to better explore and understand how the proposed model works, we noted that the ranking of clustering effect of FCM for the same category by employing the t-distributed stochastic neighbor embedding strategy is: softmax layer activation is the best, the middle convolutional layer activation is the second, and the early max pooling layer activation is the worst. These findings confirm the promising potential of combining deep learning approaches with transfer learning techniques and FCM for effective ER tasks.

The m-dimensional spatial Nyquist limit using the wave telescope for larger numbers of spacecraft

Abstract. Spacecraft constellations consisting of multiple satellites are becoming more and more interesting not only for commercial use but also for space science missions. The proposed and accepted scientific multi-satellite missions that will operate within Earth's magnetospheric environment, like HelioSwarm, require researchers to extend established methods for the analysis of multi-spacecraft data to more than four spacecraft. The wave telescope is one of those methods. It is used to detect waves and characterize turbulence from multi-point magnetic field data, by providing spectra in reciprocal position space. The wave telescope can be applied to an arbitrary number of spacecraft already. However, the exact limits of the detection for such cases are not known if the spacecraft, acting as sampling points, are irregularly spaced. We extend the wave telescope technique to an arbitrary number of spatial dimensions and show how the characteristic upper detection limit in k space imposed by aliasing, the spatial Nyquist limit, behaves for irregularly spaced sampling points. This is done by analyzing wave telescope k-space spectra obtained from synthetic plane wave data in 1D up to 3D. As known from discrete Fourier transform methods, the spatial Nyquist limit can be expressed as the greatest common divisor in 1D. We extend this to arbitrary numbers of spatial dimensions and spacecraft. We show that the spatial Nyquist limit can be found by determining the shortest possible basis of the spacecraft distance vectors. This may be done using linear combination in position space and transforming the obtained shortest basis to k space. Alternatively, the shortest basis can be determined mathematically by applying the modified Lenstra–Lenstra–Lovász (MLLL) algorithm combined with a lattice enumeration algorithm. Thus, we give a generalized solution to the determination of the spatial Nyquist limit for arbitrary numbers of spacecraft and dimensions without any need of a priori knowledge of the measured data. Additionally, we give first insights into the application to real-world data incorporating spacecraft position errors and minimizing k-space aliasing. As the wave telescope is an estimator for a multi-dimensional power spectrum substituting spatial Fourier transform, the results of this analysis can be applied to power spectral density estimation via Fourier transform or other methods making use of irregular sampling points. Therefore, our findings are also of interest to other fields of signal processing.

Direction-of-arrival and power spectral density estimation using a single directional microphone and group-sparse optimization

In this paper, two approaches are proposed for estimating the direction of arrival (DOA) and power spectral density (PSD) of stationary point sources by using a single, rotating, directional microphone. These approaches are based on a method previously presented by the authors, in which point source DOAs were estimated by using a broadband signal model and solving a group-sparse optimization problem, where the number of observations made by the rotating directional microphone can be lower than the number of candidate DOAs in an angular grid. The DOA estimation is followed by the estimation of the sources’ PSDs through the solution of an overdetermined least squares problem. The first approach proposed in this paper includes the use of an additional nonnegativity constraint on the residual noise term when solving the group-sparse optimization problem and is referred to as the Group Lasso Least Squares (GL-LS) approach. The second proposed approach, in addition to the new nonnegativity constraint, employs a narrowband signal model when building the linear system of equations used for formulating the group-sparse optimization problem, where the DOAs and PSDs can be jointly estimated by iterative, group-wise reweighting. This is referred to as the Group-Lasso with l_1-reweighting (GL-L1) approach. Both proposed approaches are implemented using the alternating direction method of multipliers (ADMM), and their performance is evaluated through simulations in which different setup conditions are considered, ranging from different types of model mismatch to variations in the acoustic scene and microphone directivity pattern. The results obtained show that in a scenario involving a microphone response mismatch between observed data and the signal model used, having the additional nonnegativity constraint on the residual noise can improve the DOA estimation for the case of GL-LS and the PSD estimation for the case of GL-L1. Moreover, the GL-L1 approach can present an advantage over GL-LS in terms of DOA estimation performance in scenarios with low SNR or where multiple sources are closely located to each other. Finally, it is shown that having the least squares PSD re-estimation step is beneficial in most scenarios, such that GL-LS outperformed GL-L1 in terms of PSD estimation errors.

Effects of negative shear on loads for a 15 MW offshore wind turbine during low-level jet events

Wind turbines are more often interacting with the negative shear region of a low-level jet due to increasing turbine sizes. However, the effects of negative shear on wind turbines are not sufficiently studied, particularly for offshore wind applications. In this paper, we studied the effects of negative shear on wind turbine loading. This was done using user-defined wind profiles and a model chain. The model chain consisted of a turbulence generator and a wake modelling tool coupled to an aero-hydro-servo-elastic engineering tool. We observed significant variations in the structural loading in the case of low-level jets. We also observed changes in the power spectral density estimates. Additionally, we briefly examined the wake recovery distance.

Distinguishing between deterministic oscillations and noise

AbstractTime-dependent dynamics is ubiquitous in the natural world and beyond. Effectively analysing its presence in data is essential to our ability to understand the systems from which it is recorded. However, the traditional framework for dynamics analysis is in terms of time-independent dynamical systems and long-term statistics, as opposed to the explicit tracking over time of time-localised dynamical behaviour. We review commonly used analysis techniques based on this traditional statistical framework—such as the autocorrelation function, power-spectral density, and multiscale sample entropy—and contrast to an alternative framework in terms of finite-time dynamics of networks of time-dependent cyclic processes. In time-independent systems, the net effect of a large number of individually intractable contributions may be considered as noise; we show that time-dependent oscillator systems with only a small number of contributions may appear noise-like when analysed according to the traditional framework using power-spectral density estimation. However, methods characteristic of the time-dependent finite-time-dynamics framework, such as the wavelet transform and wavelet bispectrum, are able to identify the determinism and provide crucial information about the analysed system. Finally, we compare these two frameworks for three sets of experimental data. We demonstrate that while techniques based on the traditional framework are unable to reliably detect and understand underlying time-dependent dynamics, the alternative framework identifies deterministic oscillations and interactions.

Spectral Variability in Fixed Windows using Fractional Fourier Transform: Application in Power Spectral Density Estimation

In statistical signal processing, power spectral density estimation is a frequency domain analysis in which power contents of a signal are measured with respect to frequency components of that signal. The power estimation of a signal can be carried out more precisely by using a window with a narrower 3-dB bandwidth and higher side-lobe attenuation. Theoretically, these two spectral parameters show trade-off in variable windows and remain constant in fixed windows. In this work, spectral behavior of fixed windows has been elaborated using Fractional Fourier Transform (FRFT) keeping their inherent time domain behavior intact. The FRFT is an extension of conventional Fourier transform with an additional variable parameter, known as rotation angle, which makes it more flexible and useful in various signal processing applications viz. power estimation and designing of tunable transition band FIR filters. In this article, variability in 3-dB bandwidth and sidelobe attenuation of fixed windows has been achieved by exploiting the available flexibility in FRFT and obtained variability has been applied in the estimation of signal power. Simulation results demonstrate that both of these two spectral parameters are improved and hence, trade-off problem between resolution and spectral leakage in the power spectral density estimation is overcome upto an extent.

Spatial and Spectral Components of the BOLD Global Signal in Rat Resting-State Functional MRI.

In resting-state fMRI (rs-fMRI), the global signal average captures widespread fluctuations related to unwanted sources of variance such as motion and respiration, as well as widespread neural activity; however, relative contributions of neural and non-neural sources to the global signal remain poorly understood. This study sought to tackle this problem through the comparison of the BOLD global signal to an adjacent non-brain tissue signal, where neural activity was absent, from the same rs-fMRI scan obtained from anesthetized rats. In this dataset, motion was minimal and ventilation was phase-locked to image acquisition to minimize respiratory fluctuations. Data were acquired using three different anesthetics: isoflurane, dexmedetomidine, and a combination of dexmedetomidine and light isoflurane. A power spectral density estimate, a voxel-wise spatial correlation via Pearson's correlation, and a co-activation pattern analysis were performed using the global signal and the non-brain tissue signal. Functional connectivity was calculated using Pearson's linear correlation on default mode network (DMN) regions. We report differences in the spectral composition of the two signals and show spatial selectivity within DMN structures that show an increased correlation to the global signal and decreased intra-network connectivity after global signal regression. All of the observed differences between the global signal and the non-brain tissue signal were maintained across anesthetics. These results show that the global signal is distinct from the noise contained in the tissue signal, as support for a neural contribution. This study provides a unique perspective to the contents of the global signal and their origins.

Colinear focused laser differential interferometry and self-aligned focusing schlieren.

A colinear focused laser differential interferometer (FLDI) and self-aligned focusing schlieren (SAFS) system has been assembled and tested in the laboratory, using a turbulent jet of compressed air issuing from a small needle nozzle to provide a high frequency density object. Measurements verified that the coupling of the SAFS system onto the optical axis of the FLDI system had negligible influence on the FLDI system's data, including tests that assessed the influence of the inclusion of dichroic mirrors, dichroic mirror reflection angle, dichroic mirror positioning relative to the Wollaston prisms of the FLDI system, and SAFS light propagation direction. A qualitative comparison of the focusing ability of the two systems was made, and FLDI power spectral density estimates and SAFS spectral proper orthogonal decomposition were used for quantitative comparisons of the acoustic frequency of the jet, with good agreement between the two. The success of the system integration and resulting jet testing demonstrates the utility of this colinear, simultaneous FLDI/SAFS measurement system.

Correction to: Formalism for power spectral density estimation for non-identical and correlated noise using the null channel in Einstein Telescope

Correction to: Formalism for power spectral density estimation for non-identical and correlated noise using the null channel in Einstein Telescope

A neural network-supported two-stage algorithm for lightweight dereverberation on hearing devices

A two-stage lightweight online dereverberation algorithm for hearing devices is presented in this paper. The approach combines a multi-channel multi-frame linear filter with a single-channel single-frame post-filter. Both components rely on power spectral density (PSD) estimates provided by deep neural networks (DNNs). By deriving new metrics analyzing the dereverberation performance in various time ranges, we confirm that directly optimizing for a criterion at the output of the multi-channel linear filtering stage results in a more efficient dereverberation as compared to placing the criterion at the output of the DNN to optimize the PSD estimation. More concretely, we show that training this stage end-to-end helps further remove the reverberation in the range accessible to the filter, thus increasing the early-to-moderate reverberation ratio. We argue and demonstrate that it can then be well combined with a post-filtering stage to efficiently suppress the residual late reverberation, thereby increasing the early-to-final reverberation ratio. This proposed two-stage procedure is shown to be both very effective in terms of dereverberation performance and computational demands, as compared to, e.g., recent state-of-the-art DNN approaches. Furthermore, the proposed two-stage system can be adapted to the needs of different types of hearing-device users by controlling the amount of reduction of early reflections.