An efficient approach for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations

An efficient approach is proposed for the equivalent linearization of frame structures with plastic hinges under nonstationary seismic excitations.The concentrated plastic hinges,described by the Bouc-Wen model,are assumed to occur at the two ends of a linear-elastic beam element.The auxiliary differential equations governing the plastic rotational displacements and their corresponding hysteretic displacements are replaced with linearized differential equations.Then,the two sets of equations of motion for the original nonlinear system can be reduced to an expanded-order equivalent linearized equation of motion for equivalent linear systems.To solve the equation of motion for equivalent linear systems,the nonstationary random vibration analysis is carried out based on the explicit time-domain method with high efficiency.Finally,the proposed treatment method for initial values of equivalent parameters is investigated in conjunction with parallel computing technology,which provides a new way of obtaining the equivalent linear systems at different time instants.Based on the explicit time-domain method,the key responses of interest of the converged equivalent linear system can be calculated through dimension reduction analysis with high efficiency.Numerical examples indicate that the proposed approach has high computational efficiency,and shows good applicability to weak nonlinear and medium-intensity nonlinear systems.

An Improved Second-Order Multisynchrosqueezing Transform for the Analysis of Nonstationary Signals

Second-order multisynchrosqueezing transform(SMSST),an effective tool for the analysis of nonstationary signals,can significantly improve the time-frequency resolution of a nonstationary signal.Though the noise energy in the signal can also be enhanced in the transform which can largely affect the characteristic frequency component identification for an accurate fault diagnostic.An improved algorithm termed as an improved second-order multisynchrosqueezing transform(ISMSST)is then proposed in this study to alleviate the problem of noise interference in the analysis of nonstationary signals.In the study,the time-frequency(TF)distribution of a nonstationary signal is calculated first using SMSST,and then aδfunction is constructed based on a newly proposed time-frequency operator(TFO)which is then substituted back into SMSST to produce a noisefree time frequency result.The effectiveness of the technique is validated by comparing the TF results obtained using the proposed algorithm and those using other TFA techniques in the analysis of a simulated signal and an experimental data.The result shows that the current technique can render the most accurate TFA result within the TFA techniques employed in this study.

Prestack nonstationary deconvolution based on variable-step sampling in the radial trace domain

The conventional nonstationary convolutional model assumes that the seismic signal is recorded at normal incidence. Raw shot gathers are far from this assumption because of the effects of offsets. Because of such problems, we propose a novel prestack nonstationary deconvolution approach. We introduce the radial trace （RT） transform to the nonstationary deconvolution, we estimate the nonstationary deconvolution factor with hyperbolic smoothing based on variable-step sampling （VSS） in the RT domain, and we obtain the high-resolution prestack nonstationary deconvolution data. The RT transform maps the shot record from the offset and traveltime coordinates to those of apparent velocity and traveltime. The ray paths of the traces in the RT better satisfy the assumptions of the convolutional model. The proposed method combines the advantages of stationary deconvolution and inverse Q filtering, without prior information for Q. The nonstationary deconvolution in the RT domain is more suitable than that in the space-time （XT） domain for prestack data because it is the generalized extension of normal incidence. Tests with synthetic and real data demonstrate that the proposed method is more effective in compensating for large-offset and deep data.

Modeling Nonstationary Time Series for Gyroscopic Drift Analysing

A state space aproach for modeling nonstationary time series is employed in analysing gyro transient process. Based on the concept of smoothness priors constraint, the overall model is using the Kalman filter and Akaike's AIC criterion.Some numerical results of gyro drift models are obtained for analysis of gyro system. As the trend and irregular components of the observed time series can be modeled simultaneously, it is statistically more accurate and efficient than that modeled separately.

Seismic noise attenuation using nonstationary polynomial fitting

We propose a novel method for seismic noise attenuation by applying nonstationary polynomial fitting （NPF）, which can estimate coherent components with amplitude variation along the event. The NPF with time-varying coefficients can adaptively estimate the coherent components. The smoothness of the polynomial coefficients is controlled by shaping regularization. The signal is coherent along the offset axis in a common midpoint （CMP） gather after normal moveout （NMO）. We use NPF to estimate the effective signal and thereby to attenuate the random noise. For radial events-like noise such as ground roll, we first employ a radial trace （RT） transform to transform the data to the time-velocity domain. Then the NPF is used to estimate coherent noise in the RT domain. Finally, the coherent noise is adaptively subtracted from the noisy dataset. The proposed method can effectively estimate coherent noise with amplitude variations along the event and there is no need to propose that noise amplitude is constant. Results of synthetic and field data examples show that, compared with conventional methods such as stationary polynomial fitting and low cut filters, the proposed method can effectively suppress seismic noise and preserve the signals.

Anti-aliasing nonstationary signals detecion algorithm based on interpolation in the frequency domain using the short time Fourier transform

To eliminate the aliasing that appeared during the measurement of multi-components nonstationary signals, a novel kind of anti-aliasing algorithm based on the short time Fourier transform （STFT） is brought forward. First the physical essence of aliasing that occurs is analyzed; second the interpolation algorithm model is setup based on the Hamming window; then the fast implementation of the algorithm using the Newton iteration method is given. Using the numerical simulation the feasibility of algorithm is validated. Finally, the electrical circuit experiment shows the practicality of the algorithm in the electrical engineering.

Damping Identification of Bridges Under Nonstationary Ambient Vibration

This research focuses on identifying the damping ratio of bridges using nonstationary ambient vibration data. The damping ratios of bridges in service have generally been identified using operational modal analysis （OMA） based on a stationary white noise assumption for input signals. However, most bridges are generally subjected to nonstationary excitations while in service, and this violation of the basic assumption can lead to uncertainties in damping identification. To deal with nonstationarity, an amplitude-modulating function was calculated from measured responses to eliminate global trends caused by nonstationary input. A natural excitation technique （NExT）-eigensystem realization algorithm （ERA） was applied to estimate the damping ratio for a stationarized process. To improve the accuracy of OMA-based damping estimates, a comparative analysis was performed between an extracted stationary process and nonstationary data to assess the effect of eliminating nonstationarity. The mean value and standard deviation of the damping ratio for the first vertical mode decreased after signal stationarization.

Modeling Monthly Spatial Distribution of Ommastrephes bartramii CPUE in the Northwest Pacific and Its Spatially Nonstationary Relationships with the Marine Environment

There are substantial spatial variations in the relationships between catch-per-unit-effort(CPUE) and oceanographic conditions with respect to pelagic species. This study examines the monthly spatiotemporal distribution of CPUE of the neon flying squid, Ommastrephes bartramii, in the Northwest Pacific from July to November during 2004–2013, and analyzes the relationships with oceanographic conditions using a generalized additive model(GAM) and geographically weighted regression(GWR) model. The results show that most of the squids were harvested in waters with sea surface temperature(SST) between 7.6 and 24.6℃, chlorophyll-a(Chl-a) concentration below 1.0 mgm^(-3), sea surface salinity(SSS) between 32.7 and 34.6, and sea surface height(SSH) between-12.8 and 28.4 cm. The monthly spatial distribution patterns of O. bartramii predicted using GAM and GWR models are similar to observed patterns for all months. There are notable variations in the local coefficients of GWR, indicating the presence of spatial non-stationarity in the relationship between O. bartramii CPUE and oceanographic conditions. The statistical results show that there were nearly equal positive and negative coefficients for Chl-a, more positive than negative coefficients for SST, and more negative than positive coefficients for SSS and SSH. The overall accuracies of the hot spots predicted by GWR exceed 60%(except for October), indicating a good performance of this model and its improvement over GAM. Our study provides a better understanding of the ecological dynamics of O. bartramii CPUE and makes it possible to use GWR to study the spatially nonstationary characteristics of other pelagic species.

Seismic spatial effects on long-span bridge response in nonstationary inhomogeneous random fields

The long-span bridge response to nonstationary multiple seismic random excitations is investigated using the PEM (pseudo excitation method). This method transforms the nonstationary random response analysis into ordinary direct dynamic analysis, and therefore, the analysis can be solved conveniently using the Newmark, Wilson-9 schemes or the precise integration method. Numerical results of the seismic response for an actual long-span bridge using the proposed PEM are given and compared with the results based on the conventional stationary analysis. From the numerical comparisons, it was found that both the seismic spatial effect and the nonstationary effect are quite important, and that both stationary and nonstationary seismic analysis should pay special attention to the wave passage effect.

Generalized Demodulation Transform for Bearing Fault Diagnosis Under Nonstationary Conditions and Gear Noise Interferences

It is a challenging issue to detect bearing fault under nonstationary conditions and gear noise interferences. Meanwhile, the application of the traditional methods is limited by their deficiencies in the aspect of computational accuracy and e ciency, or dependence on the tachometer. Hence, a new fault diagnosis strategy is proposed to remove gear interferences and spectrum smearing phenomenon without the tachometer and angular resampling technique. In this method, the instantaneous dominant meshing multiple(IDMM) is firstly extracted from the time-frequency representation(TFR) of the raw signal, which can be used to calculate the phase functions(PF) and the frequency points(FP). Next, the resonance frequency band excited by the faulty bearing is obtained by the band-pass filter. Furthermore, based on the PFs, the generalized demodulation transform(GDT) is applied to the envelope of the filtered signal. Finally, the target bearing is diagnosed by matching the peaks in the spectra of demodulated signals with the theoretical FPs. The analysis results of simulated and experimental signal demonstrate that the proposed method is an e ective and reliable tool for bearing fault diagnosis without the tachometer and the angular resampling.

A Recent Approach Incorporating External Forces To Predict Nonstationary Processes

Most real-world time series have some degree of nonstationarity due to external perturbations of the observed system; external driving forces are the essential reason that leads to the nonstationarity of dynamics system. In this paper, the authors present a novel technique in which the authors incorporate external forces to predict nonstationary time series. To test the effect, the authors also examined two prediction experiments with an ideal time series from a logistic map and a proxy climate dataset for the past millennium. The preliminary results show that the resulting algorithm has better predictive ability than the one that does not consider the external forces.

Machine learning based online fault prognostics for nonstationary industrial process via degradation feature extraction and temporal smoothness analysis

Fault degradation prognostic, which estimates the time before a failure occurs and process breakdowns, has been recognized as a key component in maintenance strategies nowadays. Fault degradation processes are, in general,slowly varying and can be modeled by autoregressive models. However, industrial processes always show typical nonstationary nature, which may bring two challenges: how to capture fault degradation information and how to model nonstationary processes. To address the critical issues, a novel fault degradation modeling and online fault prognostic strategy is developed in this paper. First, a fault degradation-oriented slow feature analysis(FDSFA) algorithm is proposed to extract fault degradation directions along which candidate fault degradation features are extracted. The trend ability assessment is then applied to select major fault degradation features. Second, a key fault degradation factor(KFDF) is calculated to characterize the fault degradation tendency by combining major fault degradation features and their stability weighting factors. After that, a time-varying regression model with temporal smoothness regularization is established considering nonstationary characteristics. On the basis of updating strategy, an online fault prognostic model is further developed by analyzing and modeling the prediction errors. The performance of the proposed method is illustrated with a real industrial process.

Nonstationary Time Series Prediction by Incorporating External Forces

Almost all climate time series have some degree of nonstationarity due to external forces of the observed system. Therefore, these external forces should be taken into account when reconstructing the climate dy- namics. This paper presents a novel technique in predicting nonstationary time series. The main difference of this new technique from some previous methods is that it incorporates the driving forces in the pre- diction model. To appraise its effectiveness, three prediction experiments were carried out using the data generated from some known classical dynamical models and a climate model with multiple external forces. Experimental results indicate that this technique is able to improve the prediction skill effectively.

Bayesian track-before-detect algorithm for nonstationary sea clutter

Radar detection of small targets in sea clutter is a particularly demanding task because of the nonstationary characteristic of sea clutter.The track-before-detect(TBD)filter is an effective way to increase the signal-to-clutter ratio(SCR),thus improving the detection performance of small targets in sea clutter.To cope with the nonstationary characteristic of sea clutter,an easily-implemented Bayesian TBD filter with adaptive detection threshold is proposed and a new parameter estimation method is devised which is integrated into the detection process.The detection threshold is set according to the parameter estimation result under the framework of information theory.For detection of closely spaced targets,those within the same range cell as the one under test are treated as contribution to sea clutter,and a successive elimination method is adopted to detect them.Simulation results prove the effectiveness of the proposed algorithm in detecting small targets in nonstationary sea clutter,especially closely spaced ones.

Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

This paper studies a low order mixed finite element method （FEM） for nonstationary incompressible Navier-Stokes equations. The velocity and pressure are approximated by the nonconforming constrained Q1^4ot element and the piecewise constant, respectively. The superconvergent error estimates of the velocity in the broken H^1-norm and the pressure in the L^2-norm are obtained respectively when the exact solutions are reasonably smooth. A numerical experiment is carried out to confirm the theoretical results.

Nonstationary inversion-based directional deconvolution of airgun array signature

Airgun arrays are widely used in marine seismic exploration because signatures excited by airgun arrays have high energy and high-peak bubble ratio, whereas the considerable length and width of the array and ghost reflections make the airgun array signature directional. As a result, the relation of the reflection amplitude with the incident and azimuth angles is variable. This means that the directivity of the airgun array results in a nonstationary wavelet and distorts the relation of the amplitude variation with the incident and azimuth angles. To remove the directivity effect, we propose a nonstationary inversion-based directional deconvolution. At fi rst, the signature as a function of take-off angle and azimuth angle is calculated using the spatial configuration of the airgun array and the near-field signatures. Then, based on the velocity model, the time-variant take-off angles are estimated and directional fi lters are designed using the take-off angles. Finally, the directivity-dependent signatures are shaped to the signature right below the airgun array using nonstationary inversion in the directional deconvolution.

Nonstationary signal inversion based on shaping regularization for random noise attenuation

Prediction filtering is one of the most commonly used random noise attenuation methods in the industry;however,it has two drawbacks.First,it assumes that the seismic signals are piecewise stationary and linear.However,the seismic signal exhibits nonstationary due to the complexity of the underground structure.Second,the method predicts noise from seismic data by convolving with a prediction error filter(PEF),which applies inconsistent noise models before and after denoising.Therefore,the assumptions and model inconsistencies weaken conventional prediction filtering's performance in noise attenuation and signal preservation.In this paper,we propose a nonstationary signal inversion based on shaping regularization for random noise attenuation.The main idea of the method is to use the nonstationary prediction operator(NPO)to describe the complex structure and obtain seismic signals using nonstationary signal inversion instead of convolution.Different from the convolutional predicting filtering,the proposed method uses NPO as the regularization constraint to directly invert the eff ective signal from the noisy seismic data.The NPO varies in time and space,enabling the inversion system to describe complex(nonstationary and nonlinear)underground geological structures in detail.Processing synthetic and field data results demonstrate that the method eff ectively suppresses random noise and preserves seismic refl ection signals for nonstationary seismic data.

Wavelet-Based Nonstationary Wind Speed Model in Dongting Lake Cable-Stayed Bridge

The wind-rain induced vibration phenomena in the Dongting Lake Bridge (DLB) can be observed every year, and the field measurements of wind speed data of the bridge are usually nonstationary. Nonstationary wind speed can be decomposed into a deterministic time-varying mean wind speed and a zero-mean stationary fluctuating wind speed component. By using wavelet transform (WT), the time-varying mean wind speed is extracted and a nonstationary wind speed model is proposed in this paper. The wind characteristics of turbulence intensity, integral scale and probability distribution of the bridge are calculated from the typical wind samples recorded by the two anemometers installed on the DLB using the proposed nonstationary wind speed model based on WT. The calculated results are compared with those calculated by the empirical mode decomposition (EMD) and traditional approaches. The compared results indicate that the wavelet-based nonstationary wind speed model is more reasonable and appropriate than the EMD-based nonstationary and traditional stationary models for characterizing wind speed in analysis of wind-rain-induced vibration of cables.

Nonstationary probability densities of system response of strongly nonlinear single-degree-of-freedom system subject to modulated white noise excitation

The nonstationary probability densities of system response of a single-degree- of-freedom system with lightly nonlinear damping and strongly nonlinear stiffness subject to modulated white noise excitation are studied. Using the stochastic averaging method based on the generalized harmonic functions, the averaged Fokl^er-Planck-Kolmogorov equation governing the nonstationary probability density of the amplitude is derived. The solution of the equation is approximated by the series expansion in terms of a set of properly selected basis functions with time-dependent coefficients. According to the Galerkin method, the time-dependent coefficients can be solved from a set of first-order linear differential equations. Then, the semi-analytical formulae of the nonstationary probability density of the amplitude response as well as the nonstationary probability density of the state response and the statistic moments of the amplitude response can be obtained. A van der Pol-Duffing oscillator subject to modulated white noise is given as an example to illustrate the proposed procedures. The effects of the system parameters, such as the linear damping coefficient and the nonlinear stiffness coefficient, on the system response are discussed.

THE COUPLING OF BOUNDARY ELEMENT AND FINITE ELEMENT METHODS FOR THE EXTERIOR NONSTATIONARY NAVIER-STOKES EQUATIONS

In this paper, we represent a new numerical method for solving the nonstationary Stokes equations in an unbounded domain. The technique consists in coupling the boundary integral and finite element methods. The variational formulation and well posedness of the coupling method are obtained. The convergence and optimal estimates for the approximation solution are provided.