Nonstationary First Threshold Crossing Reliability for Linear System Excited by Modulated Gaussian Process

Greco, Rita; Marano, Giuseppe Carlo; Fiore, Alessandra; Vanzi, Ivo

doi:10.1155/2018/3685091

Cited by 3 publications

(3 citation statements)

References 27 publications

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“…These systems face either steady or fluctuating forces. This study considers both scenarios to evaluate how structural responses vary statistically, employing the covariance approach [13,14].…”

Section: Linear Elastic Mdof Subject To Non-stationary Random Vibrationmentioning

confidence: 99%

“…The main objective of this research is to introduce a numerical technique for evaluating response covariance in the time domain for linear structures subjected to non-stationary stochastic loads. This method is tailored for a generic scenario where the input involves a non-stationary modulated filtered white noise process, capable of simulating various real physical loads like earthquakes [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs

Domaneschi,

Cucuzza,

Sardone

et al. 2024

Computation

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Random vibration analysis is a mathematical tool that offers great advantages in predicting the mechanical response of structural systems subjected to external dynamic loads whose nature is intrinsically stochastic, as in cases of sea waves, wind pressure, and vibrations due to road asperity. Using random vibration analysis is possible, when the input is properly modeled as a stochastic process, to derive pieces of information about the structural response with a high quality (if compared with other tools), especially in terms of reliability prevision. Moreover, the random vibration approach is quite complex in cases of non-linearity cases, as well as for non-stationary inputs, as in cases of seismic events. For non-stationary inputs, the assessment of second-order spectral moments requires resolving the Lyapunov matrix differential equation. In this research, a numerical procedure is proposed, providing an expression of response in the state-space that, to our best knowledge, has not yet been presented in the literature, by using a formal justification in accordance with earthquake input modeled as a modulated white noise with evolutive parameters. The computational efforts are reduced by considering the symmetry feature of the covariance matrix. The adopted approach is applied to analyze a multi-story building, aiming to determine the reliability related to the maximum inter-story displacement surpassing a specified acceptable threshold. The building is presumed to experience seismic input characterized by a non-stationary process in both amplitude and frequency, utilizing a general Kanai–Tajimi earthquake input stationary model. The adopted case study is modeled in the form of a multi-degree-of-freedom plane shear frame system.

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Section: Linear Elastic Mdof Subject To Non-stationary Random Vibrationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs

Domaneschi,

Cucuzza,

Sardone

et al. 2024

Computation

View full text Add to dashboard Cite

show abstract

“…14. The statistical properties of zero crossings for a stochastic process are, however, largely unsolved and there is no closed-form solution for the probability density function for the level crossing of a stochastic process [5,22,[26][27][28][29][30]. Level and zero crossings are studied in [5,22,[27][28][29] for a sine wave with ergodic white Gaussian noise.…”

Section: Statistical Errors In Zero Crossings Of the Modal Auto-correlation Functionmentioning

confidence: 99%

The statistical errors in the estimated correlation function matrix for operational modal analysis

Tarpø

Friis

Georgakis

et al. 2020

Journal of Sound and Vibration

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Given the random vibration of a linear and time-invariant system, the correlation function matrix is equivalent to free decays when the system is excited by Gaussian white noise. Correlation-driven Operational Modal Analysis utilises these properties to identify modal parameters from systems in operation based on the response only. Due to the finite length of the system response, the correlation function matrix must be estimated and this introduces statistical errors. This article focuses on the statistical errors due to this estimation process and the effect it has on the envelope and zero crossings of the estimated correlation function matrix. It is proven that the estimated correlation function matrix is a Gaussian stochastic process. Furthermore, it is proven that the envelope of the modal correlation function matrix is Rice distributed. This causes the tail region of the correlation function to become erroneous -called the noise tail. The zero crossings are unbiassed, but the random error related to the crossings increases fast in the noise tail. The theory is tested on a simulated case and there is a high agreement between theory and simulation. A new expression for the minimal time length is introduced based on the bias error on the envelope.

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Method of non-stationary random vibration reliability of hydro-turbine generator unit

Li,

Liu,

Cai

et al. 2024

Acta Mech. Sin.

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Nonstationary First Threshold Crossing Reliability for Linear System Excited by Modulated Gaussian Process

Cited by 3 publications

References 27 publications

Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs

Numerical Covariance Evaluation for Linear Structures Subject to Non-Stationary Random Inputs

The statistical errors in the estimated correlation function matrix for operational modal analysis

Method of non-stationary random vibration reliability of hydro-turbine generator unit

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