Frequency Nonstationarity Research Articles

Hybrid broadband simulation of long-period ground motion in far-field basins based on group delay model

Shallow seismic events often induce long-period ground motions in distant sedimentary basins, which can cause damage to structures. The current design earthquake input is usually based on amplitude, while the equally essential phase characteristics of far-field basin seismic waves are often ignored. To address this issue, this paper proposes a semi-empirical model based on group delay, which integrates the effects of source, path, local site, and basin on group delay, we characterize randomness of group delay through a parametric Gaussian probability framework, and approximates the frequency non-stationarity of positive and negative dispersion by introducing piecewise spline gradient regression. As an improvement of the stochastic finite fault method, the proposed method solves the problem that the original method cannot sufficiently reflect the phase characteristics and frequency non-stationarity of basin-induced seismic waves. Based on this model, the stochastic finite fault method and the spectral element method are combined to perform the hybrid simulation of basin ground motion, and the earthquake of 2003 Tokachi-Oki verifies the reliability of the proposed method.

Effect of Ground Motion Time–Frequency Non-Stationarity on Seismic Response of High-Speed Railway Simply Supported Bridge Based on Wavelet Packet Transform

Time–frequency non-stationarity is a ground motion characteristic which is frequently neglected in current seismic design and research. This paper studies its impact on the seismic response of high-speed railway simply supported bridge (HSRSSB). A method for generating time–frequency stationary earthquakes (TFSEs) and time–frequency non-stationary earthquakes (TFNSEs) using wavelet packet transform is proposed. A finite element model of a three-span HSRSSB is established using OpenSees. The seismic response is obtained through non-linear dynamic time history analysis, and the fragility curves of bridge components and system are calculated through incremental dynamic analysis. Finally, the reasons for the differences are analyzed by comparing the differences in seismic response of bridge, component fragility and system fragility under two groups of ground motion. The results show that the time–frequency non-stationarity of ground motion has an effect on the bridge response and fragility under strong earthquakes. TFNSE will lead to larger ground motion response, and the damage probability of bridge components and systems is higher. The reason is related to the damage and period extension of bridges under ground motion. Structures with prolonged period anti-seismic measures need to pay attention to this effect.

An Iterative PSD-Based Procedure for the Gaussian Stochastic Earthquake Model with Combined Intensity and Frequency Nonstationarities: Its Application into Precast Concrete Structures

Earthquakes cause severe damage to human beings and financial development, and they are commonly associated with a lot of uncertainties and stochastic factors regarding their frequency, intensity and duration. Thus, how to accurately select an earthquake record and determine an earthquake’s influence on structures are important questions that deserve further investigation. In this paper, the author developed an iterative power spectral density (PSD)-based procedure for the Gaussian stochastic earthquake model with combined intensity and frequency nonstationarities. In addition, they applied this procedure to five precast concrete structures for dynamic analysis and verification. The research proved the effectiveness of the iterative procedure for matching the target response spectra and for generating the required seismic records. The application examples verified the accuracy of the seismic design for the precast concrete structures and indicated the reliable dynamic demands of the precast concrete structures under the stochastic excitation of nonstationary earthquakes. In general, the research provided a meaningful reference for further stochastic earthquake selections, and it could play an effective role in further assessments of precast structures.

A Novel 3D Non-Stationary Massive MIMO Channel Model for Shortwave Communication Systems

In this paper, a novel three-dimensional (3D) non-stationary massive multiple-input multiple-output (MIMO) channel model for shortwave communication systems is proposed. Three transmission modes, i.e., groundwave, near vertical incident skywave (NVIS), and long-distance skywave are considered to eliminate the blind area and realize the full-coverage for shortwave communication. The ionospheric absorption loss and surface reflection loss during multi-hop transmissions are explored in the proposed channel model. In addition, new massive MIMO channel characteristics including the near-field spherical wavefront effect and spatial non-stationarity are considered. Temporal and frequency non-stationarities are also modeled due to the receiver (Rx) mobility and large relative bandwidth, respectively. The analytical and simulated space cross-correlation function (SCCF), time autocorrelation function (TACF), and frequency correlation function (FCF) of the proposed model are compared. The simulated path loss and singular value spread (SVS) are compared with those of the corresponding channel measurements, illustrating good fittings. In addition, the delay power spectral density (PSD) and Doppler PSD, and channel capacity are also simulated and analyzed. The proposed model can be used as a basis for the design and construction of shortwave communication systems.

Stochastic Analysis of a Large-Span Continuous Girder High-Speed Railway Bridge under Fully Non-Stationary Earthquake

The main objective of the present work is to evaluate the stochastic seismic response of a large-span continuous girder high-speed railway (CGHSR) bridge subjected to fully non-stationary seismic excitation. The stochastic ground motion is determined by a fully non-stationary ground acceleration model with both the time-varying intensity and frequency content. The stochastic seismic analysis of the large-span CGHSR bridge under a tri-directional earthquake, taking into consideration the wave passage effect, is performed using the pseudo excitation method (PEM) in frequency domain and the Monte Carlo sampling (MCS) method in time domain. A framework is proposed to determine the pseudo static displacement for the PEM under fully non-stationary seismic excitation, using the proper orthogonal decomposition (POD). A comparative study on the stochastic seismic response of the bridge is conducted using both the fully and modulated non-stationary ground acceleration. The results show that the structural nodal displacements estimated by the PEM agree well with those obtained by the MCS method. The proposed POD-based method works well in estimating the structural quasi-static displacement. Ignoring the frequency non-stationarity of the earthquake may underestimate the quasi-static displacement caused by the surface waves.

Quantifying the effect of ground-motion nonstationarity on the nonlinear dynamic responses of an ultra-high arch dam

Nonstationarity of a ground-motion time history refers to the changing frequency features over time. The frequency nonstationarity can greatly affect nonlinear structural responses, but is difficult to be captured realistically by current stochastic simulation methods. In this study, the ECSC-rho method is developed to generate synthetic earthquake ground motions through wavelet-packet characterization and optimization. Time and frequency properties of acceleration time histories are characterized using wavelet-packet analysis. The correlation between wavelet-packet coefficients in time and frequency domains is used as a simple proxy to represent nonstationarity in an acceleration time history. The basic idea is to adjust the wavelet-packet coefficients of a seed motion in both time and frequency domains to reconstruct an accelerogram, such that it matches a target spectrum, Arias intensity and nonstationarity feature. Compared with existing spectrum-matching techniques, the ECSC-rho method has distinctive advantages in simulating ground motions with prescribed nonstationarity, response spectra and energy build-up processes. The performance of the proposed ECSC-rho method is systematically validated using an ultra-high arch dam model, which incorporates highly nonlinear dam responses such as the opening of contraction joints and cumulative concrete damage. Extensive numerical simulations will highlight the effects of ground-motion nonstationarity on nonlinear dam responses, and provide practical guidelines for using spectrally-matched synthetic motions in dynamic dam analysis.

Evaluation and projection of the annual maximum streamflow in response to anthropogenic and climatic effects under nonstationary conditions in the Hanjiang River Basin, China

Abstract The flood regimes have been changing due to the climate change and human activities. Evaluating the flood risk under nonstationarity is critical to water resource management authorities in disaster reduction. In this study, the annual maximum streamflow (AMS) was used to analyze the nonstationarity in flood frequency in the Hanjiang River (HJR) Basin. A Generalized Additive Model for Location, Scale and Shape (GAMLSS) is employed to characterize nonstationarity in the AMS with time, as well as climatic and anthropogenic factors. Additionally, changes of the AMS in response to future climate change and human activity are also investigated. Results indicate that flood behavior can be better described by the nonstationary model with physically based covariates than that with time and the stationary model, implying that flood regimes of the HJR Basin are mainly influenced by anthropogenic and climatic factors including reservoir, precipitation and temperature. The precipitation and temperature projected by the Statistical Downscaling Model (SDSM) under two climate scenarios (RCP2.6 and RCP4.5) in the HJR Basin are characterized by an increasing trend over the period of 2006–2100. Furthermore, an increasing trend was found in the AMS during 2051–2100, indicating that flood risk is likely to increase in the future in the HJR Basin due to the climate change alone without further changes in hydrological engineering and flood management. The results quantified the flood frequency under nonstationarity conditions with physically based covariates and provided information to the decision-makers to address the potential risks posed to the HJR Basin.

A Novel B5G Frequency Nonstationary Wireless Channel Model

Frequency nonstationarity is an important statistical property of beyond fifth generation wireless communication channels due to extremely large bandwidths used in millimeter wave (mmWave) and teraherz communications. In this article, a general averaged power delay profile method is first introduced as a metric to determine the stationarity regions of wireless channels in the time, frequency, and spatial domains. Then, we apply this method to determine the frequency stationarity regions (FSRs) of channel measurements in a sub-6-GHz frequency band (2-4 GHz) and two mmWave frequency bands (14-16 GHz and 28-30 GHz). Frequency nonstationary (FnS) properties are found from all of the three bands. A novel FnS channel model is then proposed to model wireless channels in all frequency bands. We first split a FnS channel into a few frequency stationary (FS) subband channels and model them one by one, which are finally combined as an FnS channel model considering the cluster evolution in the frequency domain and the frequency consistency of subband channels. Simulation results show that the frequency correlation functions of the proposed FnS channel model fit well those of the measured FnS channels.

Анализ Пространственно-Временной Мезодинамики: Окрестность «Тяжелых Хвостов Распределения» Помехи, Медианный Подход, Пакет Вейвлет-Преобразований (Analysis of Time and Spatial Meso-Dynamics: Neighborhood of the Residuals Heavy-Tailed Distribution, Median Approach, Wavelet Transformation Package)

Russian Abstract: Препринт представляет новые результаты анализа мезодинамики показателей 12 основных отраслей динамики на данных ежемесячной статистики по 82 российским регионам с января 2005 по декабрь 2020 гг. Решение задачи сбалансированного и устойчивого пространственного развития регионов и России в целом требует отказа от постулирования нормального распределения помехи в нелинейной мезодинамике. Следует обеспечить адекватность моделей, увеличить точность моделирования и, главное, прогнозирования оценок трендов и отраслевых циклов мезодинамики, рассматривая окрестность помехи с распределением «с тяжелыми хвостами», а также обосновать преимущество предложенного инструментария по сравнению с известными. Исследование выполнено в методологии эконофизики. Увеличена сложность моделей объектов анализа за счет рассмотрения новых структур взаимодействия регулярных компонент траекторий (в том числе комплекса логистических трендов) между собой и с помехой. Для помехи рассмотрено применение мод, медиан при реконструкции регулярных компонент траекторий, обеспечивающих свойство робастности, не требующее знания параметров моделей помехи и стационарности законов распределения. Предложено моделирование отраслевых циклов авторским пакетом вейвлет-преобразований, позволяющим учесть нестационарность временной и частотной неоднородности пространственных траекторий мезодинамики. Разработанный инструментарий реализован в виде программного кода в открытой бесплатной среде R, с использованием как общедоступных пакетов и функций, так и авторских решений. Получены репрезентативные, устойчивые и синхронизированные во времени аналитические оценки компонент динамики отраслей мезо- и макропоказателей экономики России. Превышены известные результаты по точности моделирования и, главное, прогнозирования оценок нестационарной и неоднородной мезодинамики при помехе с «тяжелыми хвостами» распределения. Принятая методология и предложенный инструментарий позволили обеспечить возможность формирования базы знаний для экономической практики и теории нелинейной динамики, сбалансированности и устойчивости регионального развития в среднесрочной перспективе, перейти к формированию атласа отраслевых циклов экономики России, к анализу бифуркаций и «детерминированного хаоса». English abstract: English Abstract: The Preprint provides new results on meso-dynamics analysis of 12 main economic branches in 82 Russian regions from January 2005 till December 2020. The problem of balanced and sustainable spatial development of the Russian regions and Russia as a whole leads to rejection of normal distribution of the non-linear models' residuals. The models should be adequate and have high fitting and forecasting accuracy for both the trend and cycles. For this purpose the authors consider neighborhood of the residuals' heavy-tailed distribution, increased the models' complexity using new structures (including a set of logistic trends). For the residuals there is considered usage of mods, medians which provide robustness and not need the knowledge about the residuals' distribution nor its stationarity. The industries' cycles are modeled using authors' package of wavelet transformations to consider time and frequency non-stationarity of spatial meso-dynamics trajectories. The tools are applied in program code in R language using both common libraries and functions and the authors' solutions. Representative, stable and synchronized analytical components estimates of the dynamics of meso and macro-industries of Russia are obtained. The tools are compared to common solutions by their accuracy on test forecasting samples and its advantages are proved. So the chosen methodology and proposed tools allow to create knowledge base for economical theory and practice, balanced and sustainable regional development in mid-term as well to begin design an 'atlas' of industries' cycles in the Russian regions, bifurcation analysis and 'deterministic chaos'.

AF-MNS: A Novel AM-FM Based Measure of Non-Stationarity

Robust signal processing in any application depends on the representation and the understanding of the signals in hand. There is a plethora of signal processing methods, wherein choosing a method over others would depend on the attributes of the signals and their intended application. As of now, only spectral stationarity is discussed for the deterministic signals. This letter presents a novel amplitude-modulation-frequency-modulation (AM-FM) based measure of non-stationarity of the deterministic signals by extracting AM-FM components using the Fourier decomposition method (FDM). FDM generates analytic signal representation, where the real and imaginary parts are the Hilbert transform pairs. Simple and intuitive measures of amplitude and frequency non-stationarity are presented to quantitatively assess the extent of non-stationarity. Both these measures are zero for stationary signals, while at least one of them is positive for the non-stationary signals. Important observations regarding the stationarity of a signal are made with the help of some examples. The utility of the concept is demonstrated via an application of EEG signal classification.

A General 3D Space-Time-Frequency Non-Stationary Model for 6G Channels

In this paper, a general three-dimensional (3D) space-time-frequency non-stationary model is proposed for sixth generation (6G) channels. From the proposed model, a novel method, so-called correlated cluster based birth-death (BD) process method, is developed to efficiently and jointly mimic the 3D channel space-time-frequency non-stationarity. In this developed method, the frequency non-stationarity is properly captured by correlated clusters, which are obtained via an unsupervised learning algorithm in machine learning, i.e., K-Means clustering algorithm. Additionally, the developed method involves the cluster based space-time non-stationary modeling. Based on the correlation coefficient of clusters, the BD probabilities on the array and time axes are reasonably modified by the linear weight method and matrix iteration algorithm. Therefore, interactions among the space, time, and frequency non-stationary modeling are sufficiently considered. Important channel statistical properties are derived and thoroughly investigated. Simulation results demonstrate that the channel non-stationarity in space-time-frequency domains can be sufficiently characterized. Finally, the excellent agreement between the simulation results and measurements further verifies the accuracy of the proposed model.

Influence of Earthquake Frequency Nonstationarity on Seismic Structural Response

Earthquake ground acceleration records exhibit nonstationarity in both amplitude and frequency content. In order to simplify the random vibration analysis, most earthquake models have often neglected the temporal variation of the frequency content. This is partly because it is difficult to incorporate this variation in ground motion models and also partly because it was believed that it had no substantial effect on structure response. The aim of this paper is to identify the temporal variation in frequency content effects, characterizing the earthquake strong ground motions, on structures. Two comparative stochastic earthquake ground motion models based on the concept of physical spectrum are used to characterize and simulate from a selected ground acceleration record two sets of artificial earthquakes exhibiting similar phases distribution and different frequency contents: the first set presents a time-variant frequency content, and the second has a time-invariant frequency content. Three hysteretic models have been considered, elasto-plastic model (bilinear), Clough’s stiffness degrading model and maximum point-oriented bilinear model. Comparative results are presented to quantify the effects of the time-variant frequency content of earthquake ground motion on the structural response of elastic and inelastic simple systems. It is found that the characteristics of elastic and inelastic structural response depend strongly on the time variation of the frequency content in the seismic input.

Stochastic simulation of fully nonstationary aftershock ground motions from known preceding main shock

Aftershocks can cause significant additional damage to a structure that already got damaged during the preceding main shock. Past studies showed that the ground motion characteristics of an aftershock, in statistical sense, are related to those of the preceding main shock. Hence, statistical assessment of additional damage during future aftershocks given a main shock requires conditional simulation of aftershock ground motions. In the present study, a methodology is proposed to obtain an ensemble of fully nonstationary aftershock ground motions at a site of interest from the known seismic scenarios of both the main shock and the anticipated aftershock. The proposed method is based on the Priestley process assumption in order to characterize both amplitude and frequency nonstationarities via some frequency-dependent deterministic amplitude modulations. The amplitude modulations of a probable aftershock process belonging to the anticipated aftershock seismic scenario are considered to be statistically dependent on those of the recorded main shock process. Since the amplitude modulation is obtained from the frequency-dependent energy arrival curves, a conditional scaling model for the energy arrival of aftershocks is newly proposed. An improved methodology is also proposed in order to extract the frequency-dependent amplitude modulations from the energy arrival curves, obtained either via the scaling model or from a recorded motion, as well as to generate process-specific random samples from the knowledge of such modulations. It is found that the simulated ground motion ensemble shows better agreement with the recorded aftershock process, especially for larger aftershocks, when the aftershock's dependency on its main shock (via the conditional scaling model) is considered than what it shows when the dependency is not considered.

Recent Developments and Future Challenges in Channel Measurements and Models for 5G and Beyond High-Speed Train Communication Systems

The fast developments of high-speed train (HST) and growing communication demands of users pose new challenges for HST communication systems. To provide reliable communication services, key 5G communication technologies, such as millimeter-wave (mmWave) and massive multiple-input multiple-output (MIMO), and potential architectures, such as coordinated multipoint and mobile relay station, are considered in future railway communications. New technologies and architectures will bring new channel propagation characteristics. Accurate channel models that can capture these channel characteristics play a critical role in the design and test of future railway communication systems. This article reviews the HST channel measurements conducted in different scenarios and frequency bands, and the advanced HST channel models. Then a novel HST channel model incorporating the mmWave and massive MIMO propagation characteristics is presented, and its frequency non-stationarity is analyzed. Finally, some future directions are discussed.

Adaptive water infrastructure planning for nonstationary hydrology

Abstract The uncertainty of a changing climate raises challenges for water infrastructure planning and design. Not accounting for nonstationarity may result in under-designed structures that fail too frequently, or over-designed structures that are economically inefficient. This concern is magnified by uncertainty in the long-term frequency and magnitude of future extreme events. Planning strategies that allow adaptations over a structure's life could improve both reliability and economic efficiency. This study develops a method to inform adaptive water infrastructure planning with uncertain hydrologic and other forms of nonstationarity, applied to levee system planning. A stochastic dynamic programming model including a Markov process is developed for infrastructure planning with uncertain nonstationarity in flood frequency. Bayes' theorem is used to update peak flow probabilities conditioned on observed past peak flows and to update expected residual flood damages over time. A levee system planning problem with a numerical example from California illustrates the approach to derive optimal levee heights over time, and economic values of adapting to uncertain nonstationary flood risk. The projected range of probabilistic hydrology scenarios affects the optimal results, particularly in later planning stages as hydrology scenarios diverge with time. Adaptive planning strategies allowing more levee upgrades over time slightly lowers the overall cost and provides better flood protection than one-time construction under nonstationary hydrology for any climate in the example. Compared to a known future nonstationary hydrology, incorporating uncertain nonstationary climate results in higher levees being planned for observed severe hydrology scenarios in later stages. The overall present value cost with uncertain nonstationary climate depends on rates of change in peak flow distribution parameters in future hydrology scenarios.

Hurricane damage assessment for residential construction considering the non-stationarity in hurricane intensity and frequency

Natural hazards such as hurricanes may cause extensive economic losses and social disruption for civil structures and infrastructures in coastal areas, implying the importance of understanding the construction performance subjected to hurricanes and assessing the hurricane damages properly. The intensity and frequency of hurricanes have been reported to change with time due to the potential impact of climate change. In this paper, a probability-based model of hurricane damage assessment for coastal constructions is proposed taking into account the non-stationarity in hurricane intensity and frequency. The non-homogeneous Poisson process is employed to model the non-stationarity in hurricane occurrence while the non-stationarity in hurricane intensity is reflected by the time-variant statistical parameters (e.g., mean value and/or standard deviation), with which the mean value and variation of the cumulative hurricane damage are evaluated explicitly. The Miami-Dade County, Florida, USA, is chosen to illustrate the hurricane damage assessment method proposed in this paper. The role of non-stationarity in hurricane intensity and occurrence rate due to climate change in hurricane damage is investigated using some representative changing patterns of hurricane parameters.

Simulation and generation of spectrum-compatible ground motions based on wavelet packet method

This paper deals with the problem of generating spectrum-compatible artificial accelerograms for seismic dynamic analysis of engineering projects. A wavelet-packet-based, two-step procedure for the issue is proposed. The first step is to generate acceleration time history that could account for temporal and frequency non-stationarities of recorded ground motions. The second step is to decompose it into a desired number of wavelet packet vectors with high frequency resolution and non-overlapping frequency contents. Then each wavelet packet vector is scaled suitably and iteratively for the response spectrum of the simulated accelerogram to fit a specified design spectrum. The advantages of this procedure are that it can simulate user-specified acceleration time history with only 6 input parameters and the adjusted accelerogram has similar characteristics to the recorded one. The proposed procedure has been illustrated by simulating and modifying acceleration time history that are compatible with two different design spectrums for nuclear power plants. In addition, iterative efficiency of the method is investigated by simulating and adjusting acceleration time history for 100 successive times. The maximum relative error of the 76 period control points can reach 6% or below. Results show that the proposed method is effective and practical to generate and find spectrum-compatible ground motions with both stochastic and deterministic aspects.

An Improved Approach for Nonstationary Strong Ground Motion Simulation

A new stochastic ground motion model for generating a suite of ground motion time history with both temporal and frequency nonstationarities for specified earthquake and site characteristics is proposed based on the wavelet method. This new model is defined in terms of 6 key parameters that characterize the duration, evolving intensity, predominant frequency, bandwidth and frequency variation of the ground acceleration process. All parameters, except for peak ground acceleration (PGA), are identified manually from a database of 2444 recorded horizontal accelerations. The two-stage regression analysis method is used to investigate the inter- and intra-event residuals. For any given earthquake and site characteristics in terms of the fault mechanism, moment magnitude, Joyner and Boore distance and site shear-wave velocity, sets of the model parameters are generated and used, in turn, by the stochastic model to generate strong ground motion accelerograms, which can capture and properly embody the primary features of real strong ground motions, including the duration, evolving intensity, spectral content, frequency variation and peak values. In addition, it is shown that the characteristics of the simulated and observed response spectra are similar, and the amplitude of the simulated response spectra are in line with the predicted values from the published seismic ground motion prediction equations (SGMPE) after a systematic comparison. The proposed method can be used to estimate the strong ground motions as inputs for structural seismic dynamic analysis in engineering practice in conjunction with or instead of recorded ground motions.

Detection and attribution of non-stationarity in intensity and frequency of daily and 4-h extreme rainfall of Hyderabad, India

Summary The high intensity rainfall has a significant contribution in urban area flooding and understanding this high intensity rainfall over urban areas may help us to reduce the damage caused by urban floods. In this study, the changes in Hyderabad city daily and sub-daily (4-h) extreme rainfall are analyzed using various climate change detection indices. Our analysis indicates that there is increasing trend in intensity and frequency of Hyderabad city daily extreme rainfall. In addition, increasing trend in intensity and frequency of monsoon months’ (June–August) 1 a.m. to 4 a.m., 5 p.m. to 8 p.m. and 9 p.m. to 12 a.m. and non-monsoon months’ 5 p.m. to 8 p.m. extreme rainfall is also observed. Based on recent theoretical development in the Extreme Value Theory (EVT), the changes in extreme rainfall of Hyderabad city are further attributed through modelling the non-stationarity (trend) present in the extreme rainfall intensity and frequency. The extreme rainfall intensity is modelled with peaks-over-threshold (POT) based Generalized Pareto Distribution (GPD) and frequency is modelled using inhomogeneous Poisson distribution. The trend is incorporated as covariate in the scale parameter (σ) of the GPD and the rate parameter (λ) of the Poisson distribution. In this study, four physical processes, i.e. Urbanization, El Nino-Southern Oscillation (ENSO) cycle, local temperature changes, and global warming are used as covariates. Further, the combinations of these covariates are also considered for modelling the non-stationarity. Based on covariates and their combinations, fifteen non-stationary models and one stationary model are constructed and the best model is chosen based on the corrected Akaike Information Criterion (AICc) value. The covariate(s) in the best chosen non-stationary statistical model is/are attributed as the most significant physical process/processes which causes non-stationarity in the series. The study results indicate that the non-stationarity in daily extreme rainfall of Hyderabad city is mostly associated with global processes, i.e. ENSO cycle and global warming and the non-stationarity in sub-daily (4-h) extreme rainfall is mostly associated with local processes, i.e. Urbanization and local temperature changes. It is also observed that, in most of the cases, the stationary model is not even considerable based on AICc value.

Effects of time lag and frequency matching on phase-based connectivity

The time- and frequency-varying dynamics of how brain regions interact is one of the fundamental mysteries of neuroscience. In electrophysiological data, functional connectivity is often measured through the consistency of oscillatory phase angles between two electrodes placed in or over different brain regions. However, due to volume conduction, the results of such analyses can be difficult to interpret, because mathematical estimates of connectivity can be driven both by true inter-regional connectivity, and by volume conduction from the same neural source. Generally, there are two approaches to attenuate artifacts due to volume conduction: spatial filtering in combination with standard connectivity methods, or connectivity methods such as the weighted phase lag index that are blind to instantaneous connectivity that may reflect volume conduction artifacts. The purpose of this paper is to compare these two approaches directly in the presence of different connectivity time lags (5 or 25ms) and physiologically realistic frequency non-stationarities. The results show that standard connectivity methods in combination with Laplacian spatial filtering correctly identified simulated connectivity regardless of time lag or changes in frequency, although residual volume conduction artifacts were seen in the vicinity of the “seed” electrode. Weighted phase lag index under-estimated connectivity strength at small time lags and failed to identify connectivity in the presence of frequency mismatches or non-stationarities, but did not misidentify volume conduction as “connectivity.” Both approaches have strengths and limitations, and this paper concludes with practical advice for when to use which approach in context of hypothesis testing and exploratory data analyses.