Time-varying Standard Deviation Research Articles

Frequency-domain method for non-stationary stochastic vibrations of train-bridge coupled system with time-varying characteristics

When a train passes over a bridge, the vibrations of the vehicles and the bridge are the result of non-stationary stochastic processes due to the time-dependent characteristics of the coupled vehicle-bridge system. The aim of this study is to generalize the frequency domain method to investigate the non-stationary random vibration of the coupled system subjected to the excitation of track irregularities with consideration of time-dependent characteristics. To illustrate the method, a three-span simply supported bridge traversed by a single railway vehicle is adopted as an example. The time-dependent frequency response function (FRF) of the coupled system is theoretically derived through solving ordinary differential equations with variable complex coefficients, and the perturbation method is adopted to improve the calculation efficiency. By combining this with Priestley’s Evolutionary Spectra theory, the evolutionary power spectral density (PSD) of the non-stationary random response of the system is then derived. The transitions will occur when the wheels cross the joints between each bridge span and between the bridge and the adjacent roadway. By adopting mode shapes of the full structure, the change of states of the vehicle crossing multiple bridge spans and moving onto the roadway can be solved as a continuous process without separation. The proposed method is validated by comparisons with the Monte Carlo method, showing higher accuracy and efficiency when calculating the time-varying standard deviation of the response. It is found that the vibration of the vehicle is approximately stationary but with large variance due to the random track irregularities, while the bridge vibration follows a strongly non-stationary process with small randomness and is more related to the moving mass effect.

Evolutionary Spectra Estimation of a Nonstationary Process Based on a Single Sample

This paper proposes a novel method for estimating the evolutionary power spectral density (EPSD) of a nonstationary process based on a single sample. In the proposed method, a sample of a nonstationary process is decomposed into several components with a new binomial fitting decomposition (BFD). The EPSD of each component can be estimated using a newly proposed time-varying standard deviation estimation method and short-time Thomson multiple-window spectrum estimation method. The EPSD of the analyzed nonstationary sample is obtained by combining the EPSDs of all components. Via a comprehensive numerical study, the applicability of the proposed EPSD estimation method (for estimating the EPSD of a nonstationary process) is analyzed and compared with those by the Priestley method and wavelet-based method. The numerical results indicate that the estimated EPSD by the proposed method is more consistent with the corresponding theoretical one than those by the other two methods. Finally, the EPSDs of Storm Ampil, measured atop the Shanghai World Financial Center, are analyzed by the proposed method.

Estimation of peak factor and gust factor of nonstationary wind speed

This paper proposes a new method for estimating the peak factor and gust factor of nonstationary wind. In this method, the probability density function (PDF) of the largest value of a nonstationary wind speed is fitted using the PDF of the largest value of an equivalent stationary wind speed; subsequently the mean wind speed and standard deviation of the equivalent stationary wind speed, which are respectively defined as equivalent mean wind speed and equivalent standard deviation, are used to normalize the largest value of the nonstationary wind speed to calculate its gust factor and peak factor. The proposed method can be utilized in the field measurement of nonstationary wind speed to obtain peak factor and gust factor which might be applicable for predicting the largest value of a new nonstationary wind speed only using its time-varying mean wind speed and time-varying standard deviation. The applicability of the proposed method is verified using numerical simulation and wind speed data of three typhoons, which were measured atop the Shanghai World Financial Center (SWFC) at a height of 497 m. The three typhoons’ peak factor and gust factor estimated by the proposed method are also analyzed in this study.

Characterizing Nonstationary Wind Speed Using the ARMA-GARCH Model

AbstractThis paper aims to accurately calculate the time-varying standard deviation of nonstationary wind speed by modeling wind speed as a time-varying mean wind speed plus a uniformly modulated n...

A Multivariate Regression Reconstruction of the Quasi-Global Annual Precipitation on 1-Deg Grid From 1900 To 2015

This paper presents a multivariate linear regression reconstruction for the near-global annual precipitation anomalies with 1-deg latitude–longitude resolution from 1900 to 2015. The regression’s explanatory variables are the empirical orthogonal functions (EOFs), computed from the Global Precipitation Climatology Project (GPCP) dataset. The data for the regression’s dependent variable are from the station dataset of the Global Historical Climatology Network (GHCN). The data for the explanatory variables are the EOF data at the GHCN data locations. Compared to the earlier work of reconstruction at [Formula: see text] latitude–longitude resolution, our current reconstruction has two contributions. First, the spatial resolution is reduced to [Formula: see text] latitude–longitude. The finer resolution allows the data to be more useful in applications, such as historical drought assessment for a given region. Second, the multivariate regression is directly computed from linear regression models and hence includes the intercept term, which is not a coefficient of an EOF. The intercept enables a more realistic detection of the long-term trend of the spatial average. The trend of the global average annual precipitation from 1900 to 2015 is 0.133 (mm/day)/100a for the reconstruction with an intercept, and is 0.022 (mm/day)/100a without an intercept. The latter agrees with the trends of other models. The reconstruction error is assessed by a time-varying standard deviation.

Characterization of translating tornado-induced pressures and responses of a low-rise building frame based on measurement data

This study presents an analysis and characterization of dynamic wind pressures and internal forces of a low-rise building frame using measurement data obtained from a tornado simulator. The deterministic time-varying mean pressure component is extracted from the time history record using discrete wavelet transformation (DWT) approach. A continuous wavelet transformation (CWT) based approach is employed for determining the evolutionary power spectral density (EPSD) functions and time-varying standard deviation (STD) as well as co-variance of dynamic pressures. The results showed that the characteristics of dynamic pressures are strongly affected by the location of tornado, and are very different from those under straight-line wind. The pressure drop caused by tornado vortex plays a key role in defining the pressure characteristics. The building frame responses are also calculated from the statistics of pressures. The equivalent static wind loads (ESWLs) causing peak responses are defined by using the gust response factor approach. The effect of translation speed of tornado vortex is also investigated. The translating tornado vortex leads to a delay of occurrence of maximum time-varying mean and STD, and reduction in maximum STD thus peak response. It also makes the energy distribution of pressure fluctuations shifted to higher frequencies with a broader power spectrum. Finally, it is shown that the tornado-induced responses are significantly higher than those from ASCE 7-10.

Labor Market and Financial Shocks: A Time Varying Analysis

Motivated by the events of the Great Recession, we estimate a time-varying structural VAR model to analyze the effects of a financial shock on the labor market, focusing on the US. Our results indicate that a tightening of financial conditions is highly detrimental to the labor market. Moreover, we show that financial shocks have affected the unemployment rate asymmetrically in the last three decades, an implication that a standard VAR cannot capture: while negative financial shocks have been responsible for increases in unemployment, our model does not find significant contributions of financial shocks during periods of expansion. The source of this asymmetry is the time-varying standard deviation of the identified shock, which is higher in times of financial distress; on the other hand, we find the transmission mechanism is almost constant over time.

Labor Market and Financial Shocks: A Time-Varying Analysis

Motivated by the events of the Great Recession, we estimate a time-varying structural VAR model to analyze the effects of a financial shock on the labor market, focusing on the US. Our results indicate that a tightening of financial conditions is highly detrimental to the labor market. Moreover, we show that financial shocks have affected the unemployment rate asymmetrically in the last three decades, an implication that a standard VAR cannot capture: while negative financial shocks have been responsible for increases in unemployment, our model does not find significant contributions of financial shocks during periods of expansion. The source of this asymmetry is the time-varying standard deviation of the identified shock, which is higher in times of financial distress; on the other hand, we find the transmission mechanism is almost constant over time.

Temporal variability of spectro-temporal receptive fields in the anesthetized auditory cortex.

Temporal variability of neuronal response characteristics during sensory stimulation is a ubiquitous phenomenon that may reflect processes such as stimulus-driven adaptation, top-down modulation or spontaneous fluctuations. It poses a challenge to functional characterization methods such as the receptive field, since these often assume stationarity. We propose a novel method for estimation of sensory neurons' receptive fields that extends the classic static linear receptive field model to the time-varying case. Here, the long-term estimate of the static receptive field serves as the mean of a probabilistic prior distribution from which the short-term temporally localized receptive field may deviate stochastically with time-varying standard deviation. The derived corresponding generalized linear model permits robust characterization of temporal variability in receptive field structure also for highly non-Gaussian stimulus ensembles. We computed and analyzed short-term auditory spectro-temporal receptive field (STRF) estimates with characteristic temporal resolution 5–30 s based on model simulations and responses from in total 60 single-unit recordings in anesthetized Mongolian gerbil auditory midbrain and cortex. Stimulation was performed with short (100 ms) overlapping frequency-modulated tones. Results demonstrate identification of time-varying STRFs, with obtained predictive model likelihoods exceeding those from baseline static STRF estimation. Quantitative characterization of STRF variability reveals a higher degree thereof in auditory cortex compared to midbrain. Cluster analysis indicates that significant deviations from the long-term static STRF are brief, but reliably estimated. We hypothesize that the observed variability more likely reflects spontaneous or state-dependent internal fluctuations that interact with stimulus-induced processing, rather than experimental or stimulus design.

Error analysis and modifications to the short-time speech transmission index

The Speech Transmission Index (STI) predicts the intelligibility of speech degraded by noise and reverberation. Recently, Payton and Shrestha [J. Acoust. Soc. Am. 134, 3818–3827 (2013)] reported on a short-time speech-based STI (ssSTI) to predict time-varying intelligibility of speech using analysis windows shorter than 1 s. While the ssSTI generally tracked a theoretical STI calculated using octave-band signal-to-noise ratios, it deviated from the theoretical calculation for windows shorter than 0.3 s. The current work analyzes and improves the performance of the ssSTI for speech degraded by stationary speech-shaped noise. Using a cluster analysis, the time-varying standard deviation was determined to be inversely proportional to window length, octave band and speech envelope variance. Two ssSTI modifications are proposed to reduce the 0.3 s window limitation: A silence detection algorithm eliminates non-zero ssSTI values that occur during silence and a modified envelope extraction scheme reduces the standard deviation by increasing envelope bandwidth. Using the 0.3 s window as a performance benchmark, new octave-band specific window limitations, ranging from 151 ms to 21 ms, were established. The modified ssSTI also works with common octave-band window lengths as short as 30 ms when full envelope bandwidths are used in combination with the silence detector.

Approximate representation of the statistics for extreme responses of single degree-of-freedom system excited by non-stationary processes

The objective of this study is to estimate the statistics of the maximum response of a structural system excited by a non-stationary process. To provide basic information for the design of structures, the response of a single degree-of-freedom (SDOF) system subjected to a non-stationary Gaussian white noise is considered. For this purpose, we first derive the probabilistic properties of the maximum values of a non-stationary and zero-mean white noise, whose standard deviation varies temporally under some limited conditions. Then, using the obtained properties, we propose a method to estimate the stochastic properties of the maximum response of a given SDOF system excited by a non-stationary white noise whose time-varying standard deviation is known. The validity of the obtained results is confirmed through Monte Carlo simulation.