Nonstationary Earthquake Ground Motions Research Articles

Quantitative identification of pulse-like ground motions based on intrinsic time-scale decomposition technique

Pulse-like earthquake ground motions may cause great seismic demands in engineering structures, and identifying these ground motions is significant in earthquake engineering. The intrinsic time-scale decomposition (ITD) is a self-adaptive time-frequency decompaction method that decomposes signals into proper rotation components. The instantaneous frequency and amplitude of the components are well defined, and the temporal information of frequency and amplitude has the exact resolution with the time-scale of extreme of the original signal. ITD was introduced in this study to decompose the non-stationary earthquake ground motion signals. A procedure for filtering and extracting the low-frequency pulses was constructed, and a quantitative criterion for classifying the pulse-like ground motions was proposed. The proposed method was tested on many ground motions and compared with the existing classification methods. The proposed method was demonstrated as an effective way to identify the pulse-like ground motion records, which can be readily implemented in earthquake engineering practices.

Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations

It has long been one of the main challenges in science and engineering to capture the probabilistic response of high-dimensional nonlinear stochastic dynamic systems involving double randomness, i.e. randomness in both system parameters and excitations. For this purpose, a globally-evolving-based generalized density evolution equation (GE-GDEE) is established. Generally, for a multi-dimensional nonlinear system involving double randomness, if one single physical quantity as a response of the system is of interest, a GE-GDEE, as a two-dimensional partial differential equation (PDE) governing the probability density function (PDF), can be derived. The effective drift coefficients, which represent the physically driving force function in the GE-GDEE, can be determined based on the data from some representative deterministic dynamic analyses of the underlying physical system. A new estimator for effective drift coefficients is developed based on the vine copulas. Once the effective drift coefficients are determined, the GE-GDEE can be solved to capture the probability distributions of the quantities of interest. Several numerical examples, including linear and nonlinear multi-degree-of-freedom (MDOF) systems subjected to white noise or non-stationary earthquake ground motions, are presented to verify the effectiveness of the proposed method. Finally, problems for future investigations are discussed.

Probability distribution estimation for harmonisable loads and responses of linear elastic structures

In probabilistic distribution-based structural dynamics representing joint probability density functions (JPDFs) of loads and those of structural responses at any collection of time instants is a challenging and important issue. In this study, based on the mean square (m.s.) stochastic calculus, a novel method for estimating the JPDFs of external loads and those of structural responses is proposed. In particular, an external load is modelled as a harmonisable process, and its two approximate representations are proposed by the discrete Fourier transform. The JPDFs of the Fourier coefficients are directly estimated from multiple load samples. Using the load JPDFs in the frequency domain can estimate the JPDFs of the load at any finite time instants. By applying the load representations to the dynamic governing equation of linear elastic structures, the JPDFs of the structural responses at any finite time instants can be estimated. The two load representations are proved to converge in m.s. to the exact load process under certain conditions. Correspondingly, the estimated JPDFs of the load and those of structural responses in the time domain converge to their corresponding exact ones. The proposed method is numerically verified using a linear elastic structure under a nonstationary earthquake ground motion.

The smooth transition GARCH model for simulation of highly nonstationary earthquake ground motions

The aim of this paper is to extend a stochastic model for simulation of highly nonstationary ground motions (GMs). In this model, the dual-tree complex discrete wavelet transform (DT-CDWT) is applied to a recorded ground motion to extract its wavelet coefficients and then the Smooth Transition Generalized Autoregressive Conditional Heteroscedastic (ST-GARCH) model is used to simulate these coefficients. This model simulates nonstationary features of real GMs greatly, because the conditional variance estimated by this model changes compatibly with the amplitude nonstationary features of real GMs. Because of having asymmetric structure, this model also estimates sudden changes in the amplitude of ground motions. Some of the special capabilities of this model are the simulation of multiple increasing–decreasing cycles in the temporal amplitude of GMs, prediction of several peaks in the frequency spectrum of GMs, estimation of steps of their energy curve, and simultaneous simulation of all shocks of a GM sequence. Also, this model simulates the time–frequency energy distribution of both wide-frequency and narrow-frequency bandwidth GMs.

Synthesizing Nonstationary Earthquake Ground Motion via Empirically Simulated Equivalent Group Velocity Dispersion Curves for Western Himalayan Region

Synthesizing Nonstationary Earthquake Ground Motion via Empirically Simulated Equivalent Group Velocity Dispersion Curves for Western Himalayan Region

Stochastic seismic response and stability reliability analysis of a vertical retaining wall in front of the pumping station of a nuclear power plant using the probability density evolution method

Vertical retaining walls are widely used to protect the water intake and drainage structures of nuclear power plants (NPPs); in particular, they are built as the inlet in front of the pumping station pool. It is of great significance to investigate the seismic behavior of the vertical retaining walls considering the uncertain nature of earthquakes according to the nuclear safety design requirements. The probability density evolution method (PDEM), which is a new and efficient methodology, is proposed here to study the stochastic seismic response and stability reliability of a vertical retaining wall in front of the pumping station pool of a NPP. Firstly, a set of representative acceleration time histories of non-stationary earthquake ground motions are generated by the spectral representation random function method according to the RG1.60 spectra for the NPP project design. Then, a series of deterministic stochastic seismic response analysis of a 26-m-high vertical retaining wall are performed. Finally, the probability information and seismic reliability of the vertical retaining wall under two seismic levels (SL-1 (operating-basis earthquake) and SL-2 (safety shutdown earthquake)) are obtained based on two physical parameters: the anti-sliding safety factor and anti-overturning safety factor. The results demonstrate that the proposed method of investigating the stochastic responses and seismic reliability of vertical retaining walls can provide more objective indices to evaluate the seismic safety during SL-1 and SL-2 seismic events. Furthermore, the proposed method can effectively investigate the ultimate seismic capacity of vertical retaining walls and other geo-structures in NPPs.

Stochastic seismic performance assessment of high CFRDs based on generalized probability density evolution method

Determining the failure probabilities of high concrete-faced rockfill dams (CFRDs) is an important component of seismic performance assessment, considering the randomness of earthquake ground motions. In this paper, a new efficient methodology that couples the recently developed generalized probability density evolution method (GPDEM) with the spectral representation-random function method is proposed to evaluate the seismic performance of high CFRDs from a stochastic perspective. A set of representative acceleration time histories of non-stationary earthquake ground motions with complete probability are generated based on an evolutionary power spectral density model through an iterative correction to produce a good fit between the average response spectrum and the code spectrum in China’s hydraulic structure seismic code. Then, a series of deterministic dynamic calculations for a 200-m CFRD based on a generalized plasticity model modified for rockfills and a generalized plasticity interface model are performed to solve the GPDEM equation. A new face-slab damage index that considers double physical parameters (demand capacity ratio and cumulative overstress duration based on stress) is presented and its probabilityinformation is determined by constructing a virtual random process. Finally, probability density functions and cumulative distribution functions are obtained under two seismic levels by considering three performance indices corresponding to deformation, stability of dam slope and safety of face-slabs. The failure probability of different failure grades demonstrates that this new method has a good applicability to seismic performance assessment of high CFRDs.

Probability Density Evolution of a Nonlinear Concrete Gravity Dam Subjected to Nonstationary Seismic Ground Motion

AbstractTo simulate fully nonstationary earthquake ground motion, an improved generalized evolutionary spectrum model derived from a counterpart of stationary seismic processes is proposed in the p...

Seismic fragility of base-isolated water storage tanks under non-stationary earthquakes

Seismic fragility curves for fixed-base and base-isolated liquid storage tanks are developed under non-stationary earthquakes, and their seismic performance are compared. The correlation between different earthquake intensity measure (IM) parameters and peak response quantities of the base-isolated liquid storage tanks are investigated. The failure criteria are chosen based on (1) the elastic buckling strength of the tank wall, which is defined in terms of critical base shear and critical overturning moment, and (2) in terms of the critical isolation displacement. The uncertainty involved is considered in the earthquake characteristics. Non-stationary earthquake ground motions are generated using Monte Carlo (MC) simulation. Influence of the isolator characteristic parameters and modeling approaches on the seismic fragility of the base-isolated liquid storage tanks is also investigated. Peak ground acceleration is found to be the well correlated IM parameter with the peak response quantities of the base-isolated liquid storage tanks. Substantial decrease in the seismic fragility of the base-isolated liquid storage tanks is observed as compared to the fixed-base tanks. Significant influence of the isolator characteristic parameters on the seismic fragility of the base-isolated liquid storage tanks are reported in the present study.

Time-Variant Reliability Analysis of Linear Elastic Systems Subjected to Fully Nonstationary Stochastic Excitations

AbstractThis paper presents closed-form solutions for the nongeometric spectral characteristics of nonstationary stochastic processes representing the response of linear elastic structural models subjected to fully nonstationary excitation processes. These spectral characteristics provide a complete description of the nonstationary stochastic processes representing the dynamic response of linear structural models when the input excitation is a Gaussian process. In particular, the nongeometric spectral characteristics can be used to evaluate the time-variant central frequency and bandwidth parameters of nonstationary stochastic processes. The closed-form solutions derived in this paper are used to evaluate the time-variant statistics and the first-passage probability of the response of single-degree-of-freedom and multidegree-of-freedom linear elastic structural models subjected to a well-known, fully nonstationary earthquake ground motion model. The new analytical results presented in this paper can be us...

Seismic Response of Base-Isolated High-Rise Buildings under Fully Nonstationary Excitation

Stochastic seismic responses of base-isolated high-rise buildings subjected to fully nonstationary earthquake ground motion are computed by combining the pseudoexcitation and the equivalent linearization methods, and the accuracy of results obtained by the pseudoexcitation method is verified by the Monte Carlo method. The superstructure of a base-isolated high-rise building is represented by a finite element model and a shear-type multi-degree of freedom model, respectively. The influence of the model type and the number of the modes of the superstructure participating in the computation of the dynamic responses of the isolated system has been investigated. The results of a 20-storey, 3D-frame with height to width ratio of 4 show that storey drifts and absolute accelerations of the superstructure for such a high-rise building will be substantially underestimated if the shear-type multi-degree of freedom model is employed or the higher modes of the superstructure are neglected; however, this has nearly no influence on the drift of the base slab.

A UNIVARIATE PHASE SPECTRUM MODEL FOR SIMULATION OF NONSTATIONARY EARTHQUAKE GROUND MOTIONS

A family of simulation methods for nonstationary earthquake ground motions is proposed. It employs a univariate model of phase spectrum built up on a time argument associated with the concept of starting-time of phase evolution of frequency components. This phase model allows a feasible phase spectrum just using few variables of the starting-time in numerical implementation. In order to reduce the computational effort of the starting-time, a wave-group propagation formulation is also introduced. Two observed ground motions at the type-II site, i.e. Northridge and Chi-Chi waves, are investigated for illustrative purposes. Inspired from the proposed method, a numerical technique for the spatial variation of ground motions is also developed, and the investigation of coherency function between the example ground motions observed at different stations is carried out. Numerical results prove the validity and applicability of the simulation scheme. This methodology provides a new perspective towards the representation of nonstationary stochastic ground motions.

Modeling and Simulation of Nonstationary Processes Utilizing Wavelet and Hilbert Transforms

AbstractAn approach is proposed for modeling and simulating nonstationary earthquake ground motions that utilizes stationary wavelet and Hilbert transforms. The proposed model is based on the time-frequency representation of a process, which is essential for capturing the nonstationary characteristics of earthquake ground motions. Stationary wavelet transform is first utilized to decompose a sample of a multicomponent nonstationary random process into a set of monocomponent signals. These signals are subsequently transformed to analytic signals using the Hilbert transform, which yields the instantaneous amplitudes and frequencies. Without the customary assumption of piecewise stationarity or reliance on an assumed modulation function, this approach is able to simulate nonstationary random processes, such as earthquake ground motion, based on a sample realization of the process and its instantaneous features. The method is extended to the simulation of multivariate random processes utilizing the proper ort...

Modeling of non-stationary ground motion using the mean reverting stochastic process

This paper presents a new method for modeling amplitude and frequency non-stationary earthquake ground motions using a scalar first order dynamic mean reverting stochastic differential equation driven by Brownian motion with parametric time varying coefficients. It determines the proper relationship between these time varying parametric coefficients and presents the statistical and probability distribution characteristics of the response solution. It demonstrates the applicability of the method by presenting some simulations of amplitude and frequency non-stationary earthquake ground motions. The verification of the amplitude and frequency non-stationary contents of the mean reverting stochastic ground motions is demonstrated using the Hilbert–Huang transform method. Also a corresponding interpretation between the coefficients of the proposed model and the coefficients of the usual oscillatory second order differential equation driven by white Gaussian noise is presented along with some comments how it can be applied to simulate ground motions consistent with acceleration target records such as boxcar, trapezoidal, other exponential functions, or compound and target records at source, near field, and far field distances.

Closed-Form Solutions for the Response of Linear Systems to Fully Nonstationary Earthquake Excitation

New explicit closed-form solutions are derived for the evolutionary correlation and power spectral–density (PSD) matrices characterizing the nonstationary response of linear elastic, both classically and nonclassically damped, multi-degree-of-freedom (MDOF) systems subjected to a fully nonstationary earthquake ground motion process. The newly developed earthquake ground motion model considered represents the temporal variation of both the amplitude and the frequency content typical of real earthquake ground motions. To illustrate the analytical results obtained, a three-dimensional unsymmetrical building equipped with viscous bracings is considered with a single-component ground motion acting obliquely with respect to the building principal directions. These new analytical solutions for structural response statistics are very useful in gaining physical insight into the nonstationary response behavior of linear dynamic systems subjected to realistic stochastic earthquake ground motion models. Furthermore, the evolution in time of the cross-modal correlation coefficients is examined and compared with the classical stationary solution for white-noise ground motion excitation. The effects of cross-modal correlations on various mean-square response quantities also are investigated using the analytical solutions obtained.

Statistical insight into constant-ductility design using a non-stationary earthquake ground motion model

A recently developed earthquake ground motion model non-stationary in both intensity and frequency content is validated at the inelastic Single-Degree-Of-Freedom (SDOF) structural response level. For the purpose of this study, the earthquake model is calibrated for two actual earthquake records. The objective of a constant (or target) displacement ductility used in conventional earthquake-resistant design is examined from the statistical viewpoint using this non-stationary earthquake model. The non-linear hysteretic structural behaviour is modelled using several idealized hysteretic SDOF structural models. Ensemble-average inelastic response spectra corresponding to various inelastic SDOF response (or damage) parameters and conditioned on a constant displacement ductility response are derived from the two identified stochastic ground motion models. The effects of the type of hysteretic behaviour, the structural parameters, the target displacement ductility factor, and the ground motion model on the statistics of the inelastic response parameters are thoroughly investigated. The results of this parametric study shed further light on the proper interpretation and use of inelastic response or damage parameters in earthquake-resistant design in order to achieve the desirable objective of ‘constant-damage design’. © 1997 by John Wiley & Sons, Ltd.

Estimation of response spectra and simulation of nonstationary earthquake ground motions

Abstract Italian strong-motion data were used to study the attenuation of response spectra and to simulate artificial accelerograms as a function of magnitude, distance, and site geology. The database has already been utilized for the study of the attenuation of peak ground acceleration (PGA) and velocity and consists of 95 accelerograms from 17 earthquakes of magnitudes ranging from 4.6 to 6.8. Using multiple regressions, we developed empirical predictive equations for the vertical and horizontal components of response spectra corresponding to 14 frequencies ranging from 0.25 to 25 Hz. Predictive equations, aimed at the ground-motion simulation, were also estimated for time-dependent frequency parameters, strong ground motion duration, and Arias intensity. The shape of the predicted spectra is strongly dependent on magnitude and nearly independent of distance. Alluvium sites show an amplification effect, with respect to stiff sites, in different frequency ranges according to the thickness of the soil deposit. The vertical/horizontal spectral ratio in far field varies, with magnitude and frequency, from 0.35 to 0.85. The resulting response spectra are compared with the predictions of some recent attenuation relationships and with those proposed by the Eurocode EC8. The simulation of nonstationary strong ground motions is achieved through an empirical method where time and frequency features of the motion are represented through the physical spectrum, extending the spectral moments theory to the nonstationary case. The simulated time histories fit the recorded accelerograms in terms of several ground-motion amplitude measures, such as peak acceleration, peak velocity, Fourier spectra, and response spectra. The principal advantage of the proposed method consists in correlating the simulation parameters with earthquake magnitude, source distance, and soil conditions.

Random Vibration of Rotating Machines under Earthquake Excitations

Random vibration of rotating machines subjected to seismic excitations is analyzed in which the six‐component earthquake ground motions are modeled as nonstationary random processes. The six‐component earthquake inputs including the rotational components of base excitations, result in not only nonhomogeneous excitations but also parametric excitations. Thus, the classical spectral analysis of random vibration is not applicable. Furthermore, both nonhomogeneous and parametric random excitations are correlated random processes, making the problem even more difficult to solve analytically. To date random vibration of such a complicated problem has not been investigated. The method of Monte Carlo simulation is used to simulate the six‐component nonstationary earthquake ground motions and to determine the statistics of the response of rotating machines. The significance of seismic base rotations on the overall structural response is examined. A numerical example is worked out to demonstrate the methodology employed.

Simulating and analyzing artificial nonstationary earthquake ground motions

Abstract This paper describes models used to simulate earthquake accelerograms and analyses of these artificial accelerogram records for use in structural response studies. The artificial accelerogram records are generated by a class of linear linear difference equations which have been previously identified as suitable for describing ground motions. The major contributions of the paper are the use of Kalman filters for estimating time-varying model parameters, and the development of an effective nonparametric method for estimating the variance envelopes of the accelerogram records.