Coherence Function Research Articles

Examples of the Application of the Coherence Function in the Tasks of Inspection of Stone Structures

Examples of the Application of the Coherence Function in the Tasks of Inspection of Stone Structures

Seeking Repeating Anthropogenic Seismic Sources: Implications for Seismic Velocity Monitoring at Fault Zones.

Seismic velocities in rocks are highly sensitive to changes in permanent deformation and fluid content. The temporal variation of seismic velocity during the preparation phase of earthquakes has been well documented in laboratories but rarely observed in nature. It has been recently found that some anthropogenic, high-frequency (>1Hz) seismic sources are powerful enough to generate body waves that travel down to a few kilometers and can be used to monitor fault zones at seismogenic depth. Anthropogenic seismic sources typically have fixed spatial distribution and provide new perspectives for velocity monitoring. In this work, we propose a systematic workflow to seek such powerful seismic sources in a rapid and straightforward manner. We tackle the problem from a statistical point of view, considering that persistent, powerful seismic sources yield highly coherent correlation functions (CFs) between pairs of seismic sensors. The algorithm is tested in California and Japan. Multiple sites close to fault zones show high-frequency CFs stable for an extended period of time. These findings have great potential for monitoring fault zones, including the San Jacinto Fault and the Ridgecrest area in Southern California, Napa in Northern California, and faults in central Japan. However, extra steps, such as beamforming or polarization analysis, are required to determine the dominant seismic sources and study the source characteristics, which are crucial to interpreting the velocity monitoring results. Train tremors identified by the present approach have been successfully used for seismic velocity monitoring of the San Jacinto Fault in previous studies.

Spectral adjustment for spatial confounding.

Adjusting for an unmeasured confounder is generally an intractable problem, but in the spatial setting it may be possible under certain conditions. We derive necessary conditions on the coherence between the exposure and the unmeasured confounder that ensure the effect of exposure is estimable. We specify our model and assumptions in the spectral domain to allow for different degrees of confounding at different spatial resolutions. One assumption that ensures identifiability is that confounding present at global scales dissipates at local scales. We show that this assumption in the spectral domain is equivalent to adjusting for global-scale confounding in the spatial domain by adding a spatially smoothed version of the exposure to the mean of the response variable. Within this general framework, we propose a sequence of confounder adjustment methods that range from parametric adjustments based on the Matérn coherence function to more robust semiparametric methods that use smoothing splines. These ideas are applied to areal and geostatistical data for both simulated and real datasets.

EEG biomarkers of activation of the lymphatic drainage system of the brain during sleep and opening of the blood-brain barrier

The lymphatic drainage system of the brain (LDSB) is the removal of metabolites and wastes from its tissues. A dysfunction of LDSB is an important sign of aging, brain oncology, the Alzheimer's and Parkinson's diseases. The development of new strategies for diagnosis of LDSB injuries can improve prevention of age-related cerebral amyloid angiopathy, neurodegenerative and cerebrovascular diseases. There are two conditions, such as deep sleep and opening of the blood-brain-barrier (OBBB) associated with the LDSB activation. A promising candidate for measurement of LDSB could be electroencephalography (EEG). In this pilot study on rats, we tested the hypothesis, whether deep sleep and OBBB can be an informative platform for an effective extracting of information about the LDSB functions. Using the nonlinear analysis of EEG dynamics and machine learning technology, we discovered that the LDSB activation during OBBB and sleep is associated with similar changes in the EEG θ-activity. The OBBB causes the higher LDSB activation vs. sleep that is accompanied by specific changes in the low frequency EEG activity extracted by the power spectra analysis of the EEG dynamics combined with the coherence function. Thus, our findings demonstrate a link between neural activity associated with the LDSB activation during sleep and OBBB that is an important informative platform for extraction of the EEG-biomarkers of the LDSB activity. These results open new perspectives for the development of technology for the LDSB diagnostics that would open a novel era in the prognosis of brain diseases caused by the LDSB disorders, including OBBB.

The consistency of invasive and non-invasive arterial blood pressure for the assessment of dynamic cerebral autoregulation in NICU patients.

Studies of the clinical application of dynamic cerebral autoregulation show considerable variations, and differences in blood pressure devices may be one of the reasons for this variation. Few studies have examined the consistency of invasive and non-invasive arterial blood pressure for evaluating cerebral autoregulation. We attempted to investigate the agreement between invasive and non-invasive blood pressure methods in the assessment of dynamic cerebral autoregulation with transfer function analysis. Continuous cerebral blood flow velocity and continuous invasive and non-invasive arterial blood pressure were simultaneously recorded for 15 min. Transfer function analysis was applied to derive the phase shift, gain and coherence function at all frequency bands from the first 5, 10, and 15 min of the 15-min recordings. The consistency was assessed with Bland-Altman analysis and intraclass correlation coefficient. The consistency of invasive and noninvasive blood pressure methods for the assessment of dynamic cerebral autoregulation was poor at 5 min, slightly improved at 10 min, and good at 15 min. The values of the phase shift at the low-frequency band measured by the non-invasive device were higher than those measured with invasive equipment. The coherence function values measured by the invasive technique were higher than the values derived from the non-invasive method. Both invasive and non-invasive arterial blood pressure methods have good agreement in evaluating dynamic cerebral autoregulation when the recording duration reaches 15 min. The phase shift values measured with non-invasive techniques are higher than those measured with invasive devices. We recommend selecting the most appropriate blood pressure device to measure cerebral autoregulation based on the disease, purpose, and design.

Comparing random dot motion in MATLAB vs. Inquisit Millisecond.

Random Dot Motion (RDM) displays refer to clouds of independently moving dots that can be parametrically manipulated to provide a perception of the overall cloud moving coherently in a specified direction of motion. As a well-studied probe of motion perception, RDMs have been widely employed to understand underlying neural mechanisms of motion perception, perceptual decision-making, and perceptual learning, among other processes. Despite their wide use, RDM stimuli implementation is highly dependent on the parameters and the generation algorithm of the stimuli; both can greatly influence behavioral performance on RDM tasks. With the advent of the COVID pandemic and an increased need for more accessible platforms, we aimed to validate a novel RDM paradigm on Inquisit Millisecond, a platform for the online administration of cognitive and neuropsychological tests and assessments. We directly compared, in the same participants using the same display, a novel RDM paradigm on both Inquisit Millisecond and MATLAB with Psychtoolbox. We found that psychometric functions of Coherence largely match between Inquisit Millisecond and MATLAB, as do the effects of Duration. These data demonstrate that the Millisecond RDM provides data largely consistent with those previously found in laboratory-based systems, and the present findings can serve as a reference point for expected thresholds for when these procedures are used remotely on different platforms.

Variation Characteristics of the Wind Field in a Typical Thunderstorm Event in Beijing

The understanding of wind field characteristics during thunderstorms is key to structural design for resistance to thunderstorms. In this paper, the directional thunderstorm wind model is adopted to analyze the characteristics of vertical variations of the wind field in a typical thunderstorm event in the Beijing urban area, based on the measured data. First, the longitudinal and lateral fluctuating wind speed components were decoupled and the change of direction was obtained. Then, variation of the wind speed, wind direction, turbulence intensity, turbulence integral length scale, and gust factor with the height and time were studied. The measured thunderstorm wind spectrum and the coherence function of horizontal longitudinal reduced turbulent fluctuations were analyzed and compared with empirical models. The results showed that the wind speed profile presented an obvious “nose shape” near the peak wind speed. The longitudinal turbulence integral scale was larger than the lateral one. The Von Karman spectrum is relatively effective in fitting the thunderstorm wind spectrum. Compared with synoptic winds, the gust factor during the pass of thunderstorm wind is larger, so it seems necessary to consider the influence of thunderstorm wind in engineering design.

Global reliability evaluation of a high-pier long-span continuous RC rigid frame bridge subjected to multi-point and multi-component stochastic ground motions

High-pier long-span continuous RC rigid frame bridges would be more vulnerable to seismic spatial variability and multi-component nature due to their large geometric dimension. However, research on seismic performance of these bridges subjected to multi-point and multi-component ground motions is sparse. In this study, the unified expression of spectral decomposition integrating spectral representation method and proper orthogonal decomposition based on coherency function matrix is derived. Then the dimension-reduction representation is developed for sample realization of multi-point and multi-component non-stationary stochastic ground motions with merely three elementary random variables, which bypasses the challenges of high-dimensional randomness degree and huge computation expense faced by the Monte Carlo simulation scheme. Thereafter the accurate seismic response analysis of a high-pier long-span bridge is numerically scrutinized combining with the probability density evolution method to further expound the effectiveness of the dimension-reduction model. Finally, a heuristic global reliability evaluation strategy employing relative displacement angle of bridge pier segments as criterion is proposed inspired by the idea of equivalent extreme-value event. Benefiting from this, both the refined reliability evaluation of bridge members and the structural global reliability can be accomplished, providing the possibilities of quantitative seismic performance assessment and earthquake resistance optimization design from an overall perspective.

The Impact of COVID-19 on the Relationship between Non-Renewable Energy and Saudi Stock Market Sectors Using Wavelet Coherence Approach and Neural Networks

In this study, we examine the impact of COVID-19 on the relationship between non-renewable energy and Saudi stock market sectors for the period 11 January 2017–22 January 2022. We apply wavelet coherence and Radial Basis Function Neural Network (RBFNN) models. Our results provide evidence that COVID-19 led to an increase in the strength of the relationship between oil as a main non-renewable energy source and Saudi stock market sectors and affected the nature and direction of this relationship. The relationships between oil and commercial and professional services, materials, banks, energy, and transportation sectors are the most affected. Our results will help hedge funds, mutual funds, and individual investors, forecast the direction of Saudi stock market sectors and the use of oil for hedging or diversification during periods of uncertainty and crisis. It will also help decision and policymakers in Saudi Arabia to make the necessary decisions and actions to maintain the stability of the stock market sectors during these periods.

Weighting function modification used for phase transform-based time delay estimation

Generalized cross-correlation is considered as the most straightforward time delay estimation algorithm. Depending on various weighting function, different methods were derived and a straightforward method, named phase transform (PHAT) has been widely used. PHAT is well-known for its robustness to reverberation and its sensitivity to noise, which is partly due to the fact that PHAT distributes same weights to the frequencies dominated by signal or noise. To alleviate this problem, two weighting functions are proposed in this paper. By taking a posteriori signal-to-noise ratio (SNR) into account to classify reliable and unreliable frequencies, different weights could be assigned. The first proposed weighting function borrows the idea of binary mask and distributes same weights to frequencies in same set, whereas, the second one assigns weights based on coherence function. Experiments showed the robustness of proposed methods to reverberation and noise for improving the performance of time delay estimation through various criteria.

The Mediating Role of Initiative Climate on the Relationship between Distributed Leadership and Organizational Resilience in Schools

This study investigated the mediating role of initiative climate on the relationship between distributed leadership and organizational resilience in schools. The study employed a cross-sectional design following quantitative methods. The sample consisted of 310 teachers recruited from different cities located in seven geographical regions of Turkey in 2020-2021 academic year using convenience sampling. Data were collected online (Google Forms) using the Distributed Leadership Inventory, Personal Initiative Scale, and Organizational Resilience Scale, all of which had acceptable validity and reliability. Participants “agreed” with initiative climate and organizational resilience in schools and school principals’ distributed leadership behaviors. There were positive correlations between the variables. The results showed that distributed leadership (leadership coherence and leadership functions) fosters initiative climate and organizational resilience in schools. Initiative climate also contributes to organizational resilience in schools. Lastly, it can be said that distributed leadership has a significant effect on schools’ resilience through initiative climate.

Use of S-transform and a new multi-taper S-transform for spectral and coherence estimates: With application to characterize and simulate multivariate non-Gaussian wind pressure coefficient

Obtaining a long duration time series of wind pressure coefficient from wind tunnel tests may not be economically feasible for some projects, and simulated synthetic time series of wind pressure coefficient can be used. In this study, we propose a new multi-taper S-transform (ST), where the discrete prolate spheroidal sequences are used for tapering, and ST is applied to each tapered time series. The proposed multi-taper ST is simple and efficient. The simulation results indicate that the proposed transform provides an unbiased estimate of the power spectral density (PSD) function with small variability. It is also shown that the use of the temporally-averaged results from ST or the proposed multi-taper ST leads to an unbiased estimate of the coherence function. As an application, we use the obtained PSD and coherence, and marginal probability distribution function (PDF) from the time series of the wind pressure coefficient as the targets to simulate univariate and multivariate processes. For the simulation of the non-Gaussian processes, we use the iterative power and amplitude correction but include a digital filter to consider sample-to-sample variability in the PSD function. We show that the PSD and coherence functions and the marginal PDF from the samples match their targets.

Determination of the Response Amplitude Operator of a tidal turbine as a spectral transfer function

A transfer function determination method is proposed in this study to predict the unsteady fluctuations of the performance of a tidal turbine model. This method is derived from the Response Amplitude Operator (RAO) applied in the offshore industry to predict linear wave-induced loads on large structures. It is based on a spectral approach and requires the acquisition of a turbine parameter (e.g. torque, thrust, power or root-blade force) in synchronization with an upstream flow velocity measurement. On the frequency range where the causality between these two signals is proven, the transfer function is established using the ratio between the cross-spectral density and the spectral density of the incoming velocity.The linearity is verified using the coherence function, which shows validity for the turbine power in the lowest frequencies only. This transfer function is then used to reconstruct the power fluctuations which is compared to the recorded one for a particular flow condition with bathymetry generated turbulence. The result shows the dependence on the accurate location of the velocity measurement point used for the reconstruction. This point must exactly correspond to the expected turbine location, i.e. where the turbine response needs to be processed. Bearing in mind its limits, the method can be used to predict the loadings of extreme events on the turbine structure and the performance variations corresponding to the unsteady characteristics of a turbulent flow, for a better grid integration.

Analytical Simulation of 3D Wind-Induced Vibrations of Rectangular Tall Buildings in Time Domain

The Monte Carlo simulation method for along-wind loads on tall buildings performed in the time and space domain may be the only analytical viable option for specific problems such as nonlinearity behavior, nonclassically damping, and detailed structural models in commercial software. However, both across-wind and torsional-wind loads due to vortex shedding are not usually simulated in time domain because the vertical decay constants are unknown or the empirical coherence functions cannot be applied in Monte Carlo simulation methods. In this paper, the spectral representation (SR) method is used to simulate in time domain the along-wind, across-wind, and torsional-wind loads on rectangular tall buildings considering the vertical correlation between the signals. The Krenk root-coherence function is used for the normalized cross-spectrum on the along-wind direction, whereas the Davenport root-coherence function is used for the other two types of wind loads. For both across-wind and torsional-wind loads, the Davenport root-coherence function was assessed at the vortex shedding frequency by changing the vertical decay constants until converge between the Davenport model and the Liang empirical coherence model was achieved. Based on a three‐dimensional model with two translational and one torsional degree of freedom for each floor, the proposed vertical decay constants were validated by comparing the elastic response between frequency domain and time domain approaches. Generally speaking, the results show that peak displacements are significantly underestimated for both across-wind and torsional directions when vertical correlation is neglected. In addition, the advantages of time domain simulation were shown by performing a nonlinear time history analysis considering a bilinear isotropic material hardening model in both translational directions.

Direction of arrival estimation using Gaussian process interpolation

Gaussian processes (GP) have been used to predict acoustic fields by interpolating under-sampled field observations. Using GP interpolation to predict fields is advantageous due to its ability to denoise measurements, and for its prediction of likely field outcomes given a certain field coherence, or in GP terminology, a kernel. While there are many design options for a coherence function, in this study we examine using the radial basis function kernel, the physically based plane wave kernel, and a composition of plane wave kernels representing a certain angular interval of directions. The composite kernel is relevant in ocean acoustics where it is often the case that arrivals can only be within a narrow direction of arrival. We demonstrate that an array sampled with spacing larger than a half wavelength can benefit from GP interpolation, giving less root mean squared error.

Nonlinear dynamic response of sea-crossing bridges to 3D correlated wind and wave loads

Long span sea-crossing bridges are often slender and sensitive to wind and wave loads. Nonlinear dynamic response analysis of the bridges under three-dimensional (3D) correlated wind and wave loads is performed in this study in consideration of both geometric and aerodynamic nonlinearities. An optimized C-vine copula is first used to construct a 3D joint probability distribution and environmental contour of mean wind speed, significant wave height and peak wave period. Multi-point fluctuating wind loads with Davenport coherence function and random wave loads with pile group effect are then determined using wind and wave spectra respectively. The nonlinear wind-wave-bridge system considering geometric and aerodynamic nonlinearities is solved by the Newmark-β method with the 3D correlated wind and wave parameters as an input. The proposed approach is finally applied to a real sea-crossing cable-stayed bridge with the measured wind and wave data. The results show that the nonlinear response of the bridge is higher than its linear response with the same input. The bridge response is significantly reduced if the 3D correlated wind and wave loads other than conventional uncorrelated wind and wave loads are considered.

Analysis of Span-Directional Coherence Function and Buffeting Response of a Long-Span Natural Gas Pipeline Suspension Bridge under a Turbulent Wind Field

A long-span natural gas pipeline suspension bridge is prone to buffeting under the action of a turbulent wind field. In order to accurately calculate the buffeting response of the structure under a turbulent wind field, the 1 : 15 segment model wind tunnel test is used to obtain the aerodynamic coefficient and flutter derivative of the bridge deck structure. According to the test results, the buffeting force coherence functions under five different span-directional spacing are fitted. The results show that the buffeting force coherence function corresponding to different wind attack angles has a peak at the corresponding wing grid vibration frequency in the low-frequency region; when the spacing increases to r = 0.51 m or above, the amplitude of coherence function decreases significantly; for the spacing of r = 0.17 m , the buffeting force coherence functions in different directions are obviously different but the corresponding coherence functions of resistance, lift, and torque show a similar curve trend between different wind attack angles. Based on the Scanlan buffeting force correction model, the buffeting response under the reference wind speed of 30.1 m/s is analyzed in the frequency domain and compared with the wind tunnel test results of the whole bridge. The results show that the buffeting response calculated in this paper is in good agreement with the wind tunnel test results of the whole bridge and the buffeting response law is consistent. The maximum value of vertical buffeting response is located near the 1/4 span, and the maximum values of lateral and torsional response are located in the middle of the span. The lateral buffeting displacement response is significantly greater than the vertical buffeting displacement response. Under different wind attack angles, the vertical, lateral, and torsional buffeting displacement responses of the bridge deck structure increase nonlinearly with the increase of wind speed.

Earthquake response analysis of nuclear facilities subjected to incoherent seismic waves based on the random-vibration-theory methodology

In this study, based on the random-vibration-theory (RVT) methodology, an earthquake response analysis of a nuclear facility with a rigid foundation on rock/soil sites is considered when incoherent seismic waves are incident on the system. Using the coherency function of seismic waves, the power spectral density (PSD) matrix for six-degree-of-freedom motions of the rigid foundation is calculated. The stochastic earthquake responses of the soil–structure interaction system are obtained, and the PSD function for the pseudo-acceleration of equipment on one floor of the structure is derived. Peak factors of random vibrations are employed to estimate the spectral acceleration or in-structure response spectrum (ISRS) of the equipment. The accuracy of the proposed RVT methodology is verified for nuclear power plant structures on hard rock, soft rock, and layered soil acted upon by coherent and incoherent seismic waves. Because the ISRS outcomes are found to decline at high frequencies, reduction factors due to incoherency are obtained from the proposed RVT methodology. These factors can be applied to earthquake responses to coherent ground motions to consider the effects of incoherent seismic waves.

Vibration characteristics of mineral composite beams by experimental modal test method

Abstract Some machines, such as heavy presses and rammers, can be exposed to big shock and inertial forces under dynamic severe working conditions. Even if vibration isolation to the foundations of machines operating under dynamic loads is applied, the exposure of these machines to shock and resonance loads may not be adequately prevented. The sensitivity of these machines, the product quality, or life span can also incredibly decrease. Therefore, it is essential to know the vibration behaviors of machine bodies and parts. This study investigates vibration characteristics of polymer matrix composite (PMC) materials by the experimental modal test method. Nine different composite beam samples having sizes of 20 × 25 × 480 mm were produced for modal tests. Composite beams contain different ratios of aggregate and epoxy resin. Each composite beam’s natural frequencies and damping ratios were defined with frequency response and coherence functions taken from the experimental modal tests. The results from the modal analysis revealed that the most influential parameter on the vibration properties was the gravel ratio. As a result of the experimental study, it was concluded that while epoxy-resin, gravel and fine-sand additives increased the stiffness of PMC beam, gravel and fine sand additives also increased the damping rate of PMC beam.

Phase-space quantum Wiener-Khintchine theorem.

We derive a quantum version of the classical-optics Wiener-Khintchine theorem within the framework of detection of phase-space displacements with a suitably designed quantum ruler. A phase-space-based quantum mutual coherence function is introduced that includes the contribution of the detector. We obtain an universal equality linking resolution with coherence. This is illustrated with the case of Gaussian states and number states.