Time-varying Spectrum Research Articles

Time-frequency analysis of nonlinear structures under nonstationary excitation by directly solving structural dynamic equation through absolute displacement

The time-frequency evolution of seismic ground motion energy under strong earthquakes, which can be described by the evolutionary power spectral density (EPSD) matrix, will amplify the most unfavorable responses of members in nonlinear structural systems. However, the existing general finite element software fails to reduce the dimension of the EPSD matrix and then decouple time from frequency in frequency domain analysis. This failure greatly limits the simulation and calculation of multi-dimensional nonlinear structures with multiple degrees of freedom by the stochastic vibration theory. In this study, the pseudo excitation method (PEM), which can direct solve structural dynamic equations using absolute displacement, is used to derive the self-spectral and cross-spectral densities of seismic ground motions in one-dimensional and multi-dimensional cases. In MATLAB, the EPSD matrix is transformed into a four-dimensional uniform modulation excitation matrix independent of the time variable. Nonlinear iteration is conducted and the precise integration method (PIM) is employed through a transient analysis module. Furthermore, a simple one-dimensional example is presented to verify the correctness of the proposed algorithm herein. Finally, as an example, we select important parameters of the coherence model at different supports of a half-through three-span concrete-filled steel tubular (CFST) tied-arch bridge in view of real engineering conditions, and calculate the time-varying power spectrum and variance of the responses of arch ribs, arch feet and the bridge deck system. The results show that the theoretical derivation and the algorithm constructed in this paper can simulate the time-delay effect of the nonlinear structural system. This proves the feasibility of general finite element software in solving and analyzing random responses to multi-dimensional and multi-support non-stationary excitation of nonlinear structures.

Fatigue life analysis of scraper conveyor chain ring under different chain speeds and loads

This study aims to explore how different chain speeds and loads impact the fatigue life of the scraper conveyor chain ring. To achieve this, the study validates the reliability of a coupled simulation involving multi-body dynamics and the discrete element method. It also acquires time-varying tension load spectra under various operational conditions. The research evaluates the effects of distinct chain speeds and loads on parameters such as chain tension, vibration acceleration in the Y and Z-directions of the chain ring. Furthermore, finite element simulation is employed to examine stress distribution changes and fatigue life trends within the three-chain ring structure. The findings demonstrate that Y and Z-direction vibration accelerations of the chain ring correlate positively with the load. Additionally, the vibration acceleration in the Y-direction correlates positively with the chain speed. Across different chain speeds and loads, the maximum equivalent stress in the chain ring exhibits dynamic variations mirroring the load spectrum. Within the elastic deformation range of the chain ring, the highest stress within the transition region correlates linearly with chain tension. Load has a greater effect on the fatigue life of chain rings than chain speed. The fatigue life within the transition region of the chain ring decreases exponentially with increasing load at a constant chain speed. Conversely, at a constant load, chain ring life correlates positively with chain speed. Specifically, the fatigue life of the chain ring in LS 22 amounts to 32.64 days. When both chain speed and load are adjusted by 25%, the chain ring's lifespan reduces by 51.66% during simultaneous increments and increases by 39.26% with concurrent reductions in speed and load.

Impact of mental arithmetic task on the electrical activity of the human brain

Cognitive neuroscience investigates the intricate connections between brain function and mental processing to understand the cognitive architecture. Exploring the human brain, the epicenter of cognitive activity, offers valuable insights into underlying cognitive processes. To monitor brain states corresponding to various mental activities, appropriate measurement tools are essential. Electroencephalogram (EEG) signals serve as a valuable tool for recording patterns and changes in electrical brain activities. Leveraging non-linear signal processing techniques holds promise for advancing our understanding of brain activities during cognitive tasks. In this study, we analyze the electrical activity of the brain using EEG data collected from subjects engaged in a cognitive workload task. Employing wavelet-based analysis, we capture changes in the structure of EEG signals before and during a mental arithmetic task. Additionally, spectral analysis is conducted to discern alterations in the distribution of spectral contents of EEG signals. Our findings underscore the efficacy of wavelet-based analysis and spectral entropy in quantifying the time-varying and non-stationary nature of EEG recordings, offering effective frameworks for distinguishing between different cognitive activities. Consequently, these methods afford deeper insights into the cognitive architecture by tracking changes in the distribution of the time-varying spectrum.

Fatigue Damage Analysis of Steel Truss Suspension Bridge Under Non-Stationary and Non-Gaussian Buffeting

The wind field environment in mountainous zones is complex. If the wind field characteristics are regarded as stationary and Gaussian, the inaccurate response results of the structure will be obtained. In this paper, a fatigue evaluation method of steel truss suspension bridge members under non-stationary and non-Gaussian buffeting is proposed. This approach can solve the fatigue evaluation problem of steel truss suspension bridge members under mountain wind. Firstly, the normal wind speed (stationary and Gaussian) is obtained by the harmonic wave synthesis method. The wind speed considering non-stationary characteristics is obtained by adopting time-varying power spectrum. Secondly, through non-linear translation, the wind speed considering non-stationary characteristics is transformed into wind speed considering both non-Gaussian and non-stationary characteristics. Finally, combined with the Palmgren–Miner rule, the effects of three different buffeting responses on fatigue damage of suspension bridge members are studied. They are traditional buffeting response, buffeting response considering non-stationary characteristics and buffeting response considering both non-stationary and non-Gaussian characteristics. The results indicate that the fatigue damage of the main cable of the suspension bridge is the biggest at the mid-span. Under the same wind speed, considering two characteristics, the component fatigue damage will further increase.

Variation of Falcon 9 noise at far-field recording sites

The rapid launch cadence of SpaceX’s Falcon 9 rocket provides the opportunity to study the relative consistency of far-field noise propagation. Acoustical measurements of several Falcon 9 launches have been made on and near Vandenberg Space Force Base at a far-field location 8.4–14 km from the pad. This paper compares collocated measurements from different Falcon 9 missions to begin to understand data variability as a function of launch and environmental conditions at far-field locations. The 8.4 km location has been measured over 10 times, whereas other locations span subsets of launches. This comparative analysis includes time-varying levels, spectra, and waveform statistics, such as the pressure derivative skewness. Time periods of particular interest are liftoff, peak noise, and late into the launch when the vehicle is significantly downrange. [Work supported by USACE.]

Variation of Falcon 9 noise in the mid-field

The rapid launch cadence of SpaceX’s Falcon 9 rocket provides the opportunity to study the relative consistency of noise radiation. Acoustical measurements of several Falcon 9 launches have been made on and near Vandenberg Space Force Base within 1 km of the launch pad. This paper compares collocated mid-field measurements from different Falcon 9 missions to begin to understand data variability as a function of launch and environmental conditions. One location 395 m from the pad has been measured over 5 times. This comparative analysis includes time-varying levels, spectra, and waveform statistics such as the pressure derivative skewness. Time periods of particular interest are liftoff, peak noise, and late into the launch when the vehicle is significantly downrange. [Work supported by USACE.]

ANOPOW FOR REPLICATED NONSTATIONARY TIME SERIES IN EXPERIMENTS.

We propose a novel analysis of power (ANOPOW) model for analyzing replicated nonstationary time series commonly encountered in experimental studies. Based on a locally stationary ANOPOW Cramér spectral representation, the proposed model can be used to compare the second-order time-varying frequency patterns among different groups of time series and to estimate group effects as functions of both time and frequency. Formulated in a Bayesian framework, independent two-dimensional second-order random walk (RW2D) priors are assumed on each of the time-varying functional effects for flexible and adaptive smoothing. A piecewise stationary approximation of the nonstationary time series is used to obtain localized estimates of time-varying spectra. Posterior distributions of the time-varying functional group effects are then obtained via integrated nested Laplace approximations (INLA) at a low computational cost. The large-sample distribution of local periodograms can be appropriately utilized to improve estimation accuracy since INLA allows modeling of data with various types of distributions. The usefulness of the proposed model is illustrated through two real data applications: analyses of seismic signals and pupil diameter time series in children with attention deficit hyperactivity disorder. Simulation studies, Supplementary Materials (Li, Yue and Bruce, 2023a), and R code (Li, Yue and Bruce, 2023b) for this article are also available.

Time-lapse attenuation variations using distributed acoustic sensing vertical seismic profile data during CO2 injection at CaMI Field Research Station, Alberta, Canada

For seismic monitoring of geologic [Formula: see text] storage, it is useful to measure time-lapse (TL) variations of seismic attenuation. Seismic attenuation directly connects to different petrophysical parameters within the [Formula: see text] storage complex. We have developed an approach to derive smooth time-variant amplitude spectra from seismic signals by using the sparse strongest signal peaks, and then measuring two different attributes (conventional Q factor and its “geometric” counterpart) characterizing the path effects of seismic attenuation from the smooth spectra. This approach is straightforward and does not require sophisticated algorithms or parameterization schemes. We apply this approach to TL distributed acoustic sensing (DAS) vertical seismic profile (VSP) data from the Field Research Station (FRS) [Formula: see text] injection project in southern Alberta, Canada. High-quality stacked reflection records are obtained from the baseline and monitor DAS VSP surveys at the FRS and TL attenuation-attribute differences are derived from these reflection records. TL variations of attenuation are observed within the injection zone at the FRS, which are interpreted as being related to the injected [Formula: see text]. Although there is always a significant trade-off between the accuracy and temporal resolution of the measured attenuation parameters, reliable attenuation measurements around the injection zone are still achieved with an in-use reflection signal of a sufficient length and bandwidth. Attenuation attributes measured from this approach can be an advantageous tool for monitoring the distribution and migration of [Formula: see text] plumes.

Channel Prediction With Time-Varying Doppler Spectrum in High-Mobility Scenarios: A Polynomial Fourier Transform Based Approach and Field Measurements

Beamforming for multi-antenna wireless communication systems has been widely studied and applied in practice. However, its performance in high mobility scenarios deteriorates dramatically due to severe channel aging. This issue stimulates the research of channel prediction in high mobility scenarios. This paper studies the general high-mobility Doppler domain wireless channel characterization and reveals that: 1) the Doppler frequency of the cluster corresponding to the near scatterers varies approximately linearly over short periods; 2) the linear-fitting characteristics of autoregressive model leads to poor channel prediction performance; 3) the parameter estimation algorithms of the chirp model which encompasses the characteristics are particularly complex. Given the shortcomings of existing works, this paper adopts the short-time Fourier transform to pre-estimate the parameter range and leverages the polynomial Fourier transform to obtain the initial values of the parameters. The downhill simplex algorithm is used to search for the fine-grained values of the parameters. In addition, the orthogonal matching pursuit algorithm is utilized to reconstruct the sparse signal. Evaluation results under the COST2100 channel model and a channel measurement campaign indicate that the proposed scheme can enhance the channel prediction accuracy or reduce the computing overhead compared to the existing matrix completion and polynomial iteration method.

The time invariant beamformer for Doppler spread suppression in high‐mobility transmission

AbstractBeamforming network with the Doppler suppression scheme reducing the channel time‐varying effects has attracted much research interests in high‐mobility massive MIMO communications. However, the current time‐varying beamforming network still suffers from high volatility peak‐to‐average power ratio (PAPR) fluctuations. For this reason, a time invariant compensation optimized beamformer is proposed to mitigate the peak‐to‐average power ratio high volatility and the channel time variation in the high‐mobility uplink transmission. To attain the Doppler spread and implement the Doppler spread suppression scheme, a time‐varying spectrum (TVS) is proposed and its statistical properties of time‐varying spectrum is analyzed. The simulation results are provided to verify the proposed studies.

Comparing acoustical measurements from Falcon 9 launches

The Falcon 9 rocket has successfully launched nearly 300 orbital missions, providing the opportunity to study noise radiation and propagation variability. Acoustical measurements of several Falcon 9 launches have been made on and near Vandenberg Space Force Base, ranging 0.5 to 14 km from the launch pad. This paper’s purpose is to compare collocated measurements from different Falcon 9 launches to begin to understand data variability as a function of launch and environmental conditions. One far-field location, at a distance of 8.4 km, has been measured across all launches, whereas several other locations spanned subsets of launches. This comparative analysis includes time-varying levels, spectra, and waveform statistics such as the pressure derivative skewness. Time periods of particular interest are liftoff, peak noise, and late into the launch when the vehicle is significantly downrange. [Work supported in part by the NSF REU program and by USACE.]

Improving vertical resolution of vintage seismic data by a weakly supervised method based on cycle generative adversarial network

Seismic vertical resolution is critical for accurately identifying subsurface structures and reservoir properties. Improving the vertical resolution of vintage seismic data with strongly supervised deep learning is challenging due to scarce or costly labels. To remedy the label-lacking problem, we develop a weakly supervised deep-learning method to improve vintage seismic data with poor resolution by extrapolating from nearby high-resolution seismic data. Our method uses a cycle generative adversarial network with an improved identity loss function. In addition, we contribute a pseudo-3D training data construction strategy that reduces discontinuity artifacts caused by accessing 3D field data with a 2D network. We determine the feasibility of our method on 2D synthetic data and achieve results comparable to the classic time-varying spectrum whitening method on field poststack migration data while effectively recovering more high-frequency information.

Development and validation of a computational method to predict unintended auditory brainstem response during transcranial ultrasound neuromodulation in mice

BackgroundTranscranial ultrasound stimulation (TUS) is a promising noninvasive neuromodulation modality. The inadvertent and unpredictable activation of the auditory system in response to TUS obfuscates the interpretation of non-auditory neuromodulatory responses. ObjectiveThe objective was to develop and validate a computational metric to quantify the susceptibility to unintended auditory brainstem response (ABR) in mice premised on time frequency analyses of TUS signals and auditory sensitivity. MethodsUltrasound pulses with varying amplitudes, pulse repetition frequencies (PRFs), envelope smoothing profiles, and sinusoidal modulation frequencies were selected. Each pulse's time-varying frequency spectrum was differentiated across time, weighted by the mouse hearing sensitivity, then summed across frequencies. The resulting time-varying function, computationally predicting the ABR, was validated against experimental ABR in mice during TUS with the corresponding pulse. ResultsThere was a significant correlation between experimental ABRs and the computational predictions for 19 TUS signals (R2 = 0.97). ConclusionsTo reduce ABR in mice during in vivo TUS studies, 1) reduce the amplitude of a rectangular continuous wave envelope, 2) increase the rise/fall times of a smoothed continuous wave envelope, and/or 3) change the PRF and/or duty cycle of a rectangular or sinusoidal pulsed wave to reduce the gap between pulses and increase the rise/fall time of the overall envelope. This metric can aid researchers performing in vivo mouse studies in selecting TUS signal parameters that minimize unintended ABR. The methods for developing this metric can be adapted to other animal models.

Chirp cyclic moment for chirp cyclostationary processes: Definitions and estimators

In high-mobility wireless communications and radar systems, a higher carrier frequency and higher moving speed/acceleration of terminals enhance the impact of the time-varying Doppler effect. This effect alters the cyclostationarity of the transmitted signal and characterizes the received signal as a chirp cyclostationary (CCS) signal. The generalized cyclic statistics of CCS signals are defined based on Fourier analysis, which is either zero-value or non-bandlimited, and is thus inefficient. In this study, the linear canonical transform (LCT), a generalized form of the Fourier transform, was used to address these issues. The moment function is a k-dimensional variable comprising a single time variable and k−1 lag variables. The chirp cyclic moment and the time-varying canonical spectrum were designed as the LCT of the moment with respect to the time and lag variables, respectively. Furthermore, an estimator of the chirp cyclic moment was defined, which is demonstrated to be asymptotic unbiased, asymptotic mean-square-consistent and asymptotic complex normal. Applications of the chirp cyclic moment in radar parameter estimation and electrocardiogram signal characterization were verified using simulated and real-life data.

Vibro-acoustic sensing of tissue-instrument-interactions allows a differentiation of biological tissue in computerised palpation

Background:The shift towards minimally invasive surgery is associated with a significant reduction of tactile information available to the surgeon, with compensation strategies ranging from vision-based techniques to the integration of sensing concepts into surgical instruments. Tactile information is vital for palpation tasks such as the differentiation of tissues or the characterisation of surfaces. This work investigates a new sensing approach to derive palpation-related information from vibration signals originating from instrument-tissue-interactions. Methods:We conducted a feasibility study to differentiate three non-animal and three animal tissue specimens based on palpation of the surface. A sensor configuration was mounted at the proximal end of a standard instrument opposite the tissue-interaction point. Vibro-acoustic signals of 1680 palpation events were acquired, and the time-varying spectrum was computed using Continuous-Wavelet-Transformation. For validation, nine spectral energy-related features were calculated for a subsequent classification using linear Support Vector Machine and k-Nearest-Neighbor. Results:Indicators derived from the vibration signal are highly stable in a set of palpations belonging to the same tissue specimen, regardless of the palpating subject. Differences in the surface texture of the tissue specimens reflect in those indicators and can serve as a basis for differentiation. The classification following a supervised learning approach shows an accuracy of >93.8% for the three-tissue classification tasks and decreases to 78.8% for a combination of all six tissues. Conclusions:Simple features derived from the vibro-acoustic signals facilitate the differentiation between biological tissues, showing the potential of the presented approach to provide information related to the interacting tissue. The results encourage further investigation of a yet little-exploited source of information in minimally invasive surgery.

Estimation and interpreting instantaneous frequency of signals in non-stationary measurement sensor systems: An overview

The basic concepts and methods of joint time-frequency distributions are discussed. The primary purpose is to demonstrate how a signal's spectral composition alters over time as well as to modify the underlying physical and mathematical concepts of a time-varying spectrum. Main intent is to generate energy or intensity of signal distribution which was represented in both time and frequency. Over last 40 years, fundamental ideas have been developed steadily so that significant advances have occurred. The variety of ideas and motivations that have led to the development of the concepts are highlighted in this review, which is written with non-specialists in mind. An overview of several attempts to determine instantaneous frequency (IF) was given. Numerous characteristics, including the product of bandwidth time (BT), analytic signal as well as the link between time frequency distribution and IFs are explored. Finally, discussions of mono-component, multi-component, and instantaneous bandwidth signals are presented. It is shown that the context of the put forth theory adequately describes each of these ideas. These estimation and interpreting schemes find immediate applications like biomedical signal analysis, speech processing, health care sensor systems.

Seismic stratigraphy and attenuation of gas-hydrate zones within Hikurangi and Gondwana margins, eastern New Zealand

SUMMARY Gas hydrates that occur on many continental margins have received global attention. In reflection seismic imaging, the bottom-simulating reflector (BSR) is a common indicator of gas hydrates. However, it is difficult to identify gas hydrates and quantify their amounts through the BSR alone. For gas-hydrate characterization, it is therefore useful to measure seismic stratigraphic and attenuation attributes. Short-scale patterns of layering that contain information about the amount and mechanism of gas hydrates can be identified through stratigraphic and attenuation attributes. We measure the complete time-variant spectra by using sparse strongest peaks, and the spectral differences at different times through attenuation parameters Q–1 and γ. The traditional Q–1 is associated with the attenuation of the frequency-dependent part of wavefield, and the γ characterizes the frequency-independent attenuation. The measurement approach is straightforward and requires no sophisticated inverse algorithm and is applied to surface seismic data acquired over the Hikurangi and Gondwana margins, eastern New Zealand. High-quality spectral and attenuation images are obtained. Spectral attributes correlate with BSRs and large positive Q–1 and negative γ-values are below and above the BSRs, which are interpreted as being related to free-gas and gas-hydrate accumulations. These results will aid the quantification of gas hydrates and the assessment of their roles as an energy resource, as a potential geological hazard, and in climate change and ocean warming.

Quantifying reserve capabilities for designing flexible electricity markets: An Australian case study with increasing penetrations of renewables

Across several power systems with market frameworks, policy-makers are proposing that balancing flexibility requirements emerging during energy transition be addressed through new reserve product markets. However, these may introduce additional costs, constraints and complexity, and even encroach upon the functions of existing operational practices. Thus, policy-makers need to assess and compare flexibility design options, and quantifying system flexibility capabilities based on current and expected resource mixes can assist in achieving this. In this article, we offer a practical method to quantify the time-varying spectrum of upwards and downwards flexibility capabilities in systems, and subsequently apply it to historical and projected resource mixes in two regions of the Australian National Electricity Market. Our results suggest that with higher penetrations of renewable energy: (1) downwards flexibility margins can be exhausted around noon if wind and solar are unable or unwilling to provide it, (2) upwards flexibility becomes more scarce during morning and evening peak demand events and (3) a greater portion of upwards flexibility is provided by energy-limited resources. Given these trends, we recommend that policy-makers examine how existing operational practices can be augmented to elicit upwards flexibility provision, and that duration specifications and sustained footroom procurement be considered for reserve products.

Extended harmonic input method for response spectrum determination of vehicle–bridge systems

The calculation of response power spectral densities (PSDs) from the excitation PSDs of vehicle–bridge (VB) systems is crucial for the safety evaluation of operating vehicles, bridge fatigue analysis, and vibration control optimization. However, calculations using the available methods result in considerable computational errors when applied to evaluate the response PSDs of VB systems. Hence, an extended harmonic input method (HIM) is proposed to compute the time-varying response spectrum in VB systems. First, the unique characteristics of VB systems that may cause the inapplicability of conventional methods are systematically analyzed. Subsequently, an extended version of the HIM is mathematically established to calculate the time-varying response spectrum of VB systems via the representation of inputs and decomposition of responses. Finally, a numerical example of an actual high-speed railway bridge subjected to track irregularities or seismic excitations is presented to illustrate the efficacy of the novel method.

Time-Variant Spectrum Mapping via Reduced Basis Representation and Greedy Sampling Locations Optimization

Spectrum mapping has been increasingly important in various wireless communication applications, such as spectrum management, network planning, power control, dynamic spectrum access etc. In this letter, we consider the problem of time-varying spectrum situation map reconstruction using a small amount of sampled data. In contrast to traditional assumption that the statistical signal propagation model is known, we infer spatial propagation characteristics from the spectrum data. Then, a greedy optimization is applied to calculate the sampling locations with the reduced spatial spectrum situation basis representation, which also converts the original underdetermined problem of spectrum situation recovery into a least squares problem with spatial smoothness constraint, thus greatly reducing the matrix operations. Simulations confirm the superiority of our proposed algorithm in reconstruction performance and computational efficiency in online spectrum mapping tasks.