Simulation of Nonstationary Stochastic Processes by Spectral Representation

a b s t r a c tA powerful tool in computational stochastic mechanics is the stochastic finite element method (SFEM). SFEM is an extension of the classical deterministic FE approach to the stochastic framework i.e. to the solution of static and dynamic problems with stochastic mechanical, geometric and/or loading properties. The considerable attention that SFEM received over the last decade can be mainly attributed to the spectacular growth of computing power rendering possible the efficient treatment of large-scale problems. This article aims at providing a state-of-the-art review of past and recent developments in the SFEM area and indicating future directions as well as some open issues to be examined by the computational mechanics community in the future.

show abstract

“…[33,78,93,105,[167][168][169]. The simulation of the non-homogeneous fields is based on the notion of the evolutionary power spectrum [105,171].…”

Section: The Spectral Representation Methodsmentioning

confidence: 99%

The stochastic finite element method: Past, present and future

Stefanou

2009

Computer Methods in Applied Mechanics and Engineering

862

407

View full text Add to dashboard Cite

show abstract

“…6,31 Sample ground motion realizations based on a specified earthquake scenario can be simulated by the well-established Spectral Representation Method (SRM). [32][33][34][35] As shown in detail in the paper, the suggested ground motion model is exceptionally capable of representing strong non-stationarities of the ground motion and compares very efficiently with earthquake ground motion records and the state-of-the-art NGA-West2 GMPE models, 6,31 based on a variety of different earthquake scenarios.…”

Section: Introductionmentioning

confidence: 88%

Predictive model for site specific simulation of ground motions based on earthquake scenarios

Vlachos

Παπακωνσταντίνου

Deodatis

2017

Earthq Engng Struct Dyn

View full text Add to dashboard Cite

SummaryA predictive stochastic model is developed based on regression relations that inputs a given earthquake scenario description and outputs seismic ground acceleration time histories at a site of interest. A bimodal parametric nonstationary Kanai-Tajimi (K-T) ground motion model lies at the core of the proposed predictive model. The functional forms that describe the temporal evolution of the K-T model parameters can effectively represent strong non-stationarities of the ground motion. Fully non-stationary ground motion time histories can be generated through the powerful Spectral Representation Method. A Californian subset of the available NGA-West2 database is used to develop and calibrate the predictive model. Samples of the model parameters are obtained by fitting the K-T model to the database records, and the resulting marginal distributions of the model parameters are efficiently described by standard probability models. The samples are translated to the standard normal space and linear random-effect regression models are established relating the transformed normal parameters to the commonly used earthquake scenario defining predictors: moment magnitude M w , closest-to-site distance R rup , and average shear-wave velocity V S 30 at a site of interest. The random-effect terms in the developed regression models can effectively model the correlation among ground motions of the same earthquake event, in parallel to taking into account the location-dependent effects of each site. For validation purposes, simulated acceleration time histories based on the proposed predictive model are compared with recorded ground motions. In addition, the median and median plus/minus one standard deviation elastic response spectra of synthetic ground motions, pertaining to a variety of different earthquake scenarios, are compared to the associated response spectra computed by the NGA-West2 ground motion prediction equations and found to be in excellent agreement. KEYWORDSpredictive stochastic ground motion model, analytical evolutionary power spectrum, ground motion parametrization, random-effect regression, NGA-West2 database

show abstract

“…Conte and Peng [13] modeled the earthquake records using a bundle of waves with di erent arrival times using the evolutionary model of Priestly. Liang et al [28] used the Priestley's evolutionary model to derive a cosine series formula to simulate the non-stationary Gaussian processes based on spectral representation. They have proposed three methods to estimate the evolutionary energy content using short-time Fourier transform, wavelet transform, and Hilbert-Huang transform.…”

Section: Basic De Nitions 21 Frequency and Amplitude Non-stationarimentioning

confidence: 99%

On the Evolutionary Characteristics of the Acceleration Records Generated From Linear Time-Variant Systems

Waezi

Rofooei

2017

Scientia Iranica

View full text Add to dashboard Cite

Abstract. This paper discusses the time-varying characteristics of the output signals resulted from Linear Time Variant (LTV) systems using level-crossing properties. These systems, used for generating synthetic records based on a target record, contain two identi cation processes: 1) amplitude modulating function; and 2) time-varying Impulse Response Function (IRF) parameters. To track the IRF parameters e ciently, the zerocrossing and positive minima/negative maxima cumulative curves are usually utilized as the measures of the instantaneous spectral power. Using spectral moments, analytic relations for zero-crossing and positive minima/negative maxima cumulative count are developed with respect to the IRF's evolutionary power spectrum. In order to investigate the low-frequency components of the output records e ciently, the zero-crossing rate of the velocity and the displacement records are tracked and rigorous analytic equations for their descriptions are developed. Some of the issues concerning application of the developed equations are explored using two LVT models, and the limitations of the proposed procedures are explained. Through introduction of new compatibility measures, the necessity of implementing Monte Carlo simulations would no longer be needed, and it would be possible to generate synthetic acceleration records with desirable evolutionary characteristics with much shorter computation time.

show abstract

Simulation of Nonstationary Stochastic Processes by Spectral Representation

Cited by 186 publications

References 19 publications

The stochastic finite element method: Past, present and future

The stochastic finite element method: Past, present and future

Predictive model for site specific simulation of ground motions based on earthquake scenarios

On the Evolutionary Characteristics of the Acceleration Records Generated From Linear Time-Variant Systems

Contact Info

Product

Resources

About