scholarly journals A Nonstationary Mathematical Model for Acceleration Time Series

2021 ◽  
Vol 8 (2) ◽  
pp. 246-252
Author(s):  
Tahar Brahimi ◽  
Tahar Smain
Keyword(s):  
Time Series ◽  
Energy Demand ◽  
Spectral Response ◽  
Qualitative Description ◽  
Response Analysis ◽  
Model Parameters ◽  
Ductility Demand ◽  
Displacement Ductility ◽  
Acceleration Time ◽  
Hysteretic Energy

The choice of nonstationary stochastic models for the study is fully justified by the limitation of acceleration time series number. The three acceleration time series under consideration are used to generate a new, artificial series of ten per historical one using autoregressive moving average model. Subsequently, the average of nonlinear is utilized for the ten acceleration time series in order to obtain the spectral response of a system with single degree of freedom. Modeling of acceleration time series involves critical estimation of metrics that characterize nonstationary acceleration time series. Thus, for the stiffness degrading systems and bilinear systems, the metrics of hysteretic energy demand and displacement ductility demand during displacement are used. The applicability of artificially generated acceleration time series for the qualitative description of information was shown. More specifically, ARMA (2,2) showed the best results in the study for three accelerated time series through nonlinear response analysis. In addition, as a result, normalized hysteretic energy demand, empirically valid displacement ductility relationships, and model parameters were proposed.

The Use of ARMA Models in Earthquake Response Spectra

2006 ◽  
Author(s):  
Malek Brahimi ◽  
Sidi Berri
Keyword(s):  
Linear Response ◽  
Energy Demand ◽  
Arma Model ◽  
Response Spectra ◽  
Response Analysis ◽  
Arma Models ◽  
Maximum Displacement ◽  
Ductility Demand ◽  
Displacement Ductility ◽  
Hysteretic Energy

Structural design spectra are based on smoothed linear response spectra obtained from different events scaled by their peak values. Such an approach does not incorporate other characteristics of the excitation represented by measured data. This study investigate the use of non-stationary models which can be considered characteristic and representative of specific historical earthquakes. An earthquake record is regarded as a sample realization from a population of such samples, which could have been generated by the stochastic process characterized by an Autoregressive Moving Average (ARMA) model. ARMA models are developed for four major earthquakes after processing by a variance stabilizing transformation. Samples of acceleration records are generated for each event. In this earthquake modeling procedure, parameters describing the modulating function of the record and the stabilized series are estimated. Maximum displacement ductility demand and normalized hysteretic energy demand for linear and stiffness softening single degree of freedom system systems are computed for the samples generated for each event. The sensitivity and dependence of demand spectra on earthquake model characteristics are examined to develop a response prediction model. Non linear response analysis of the four events indicates that ARMA (2,1) process using samples of twenty simulated earthquakes provide a reliable description of the information contained within acceleration records. Empirical relationships for displacement ductility and Normalized hysteretic energy demand spectra are developed.

UNIFORM HAZARD SPECTRA BASED ON PARK-ANG DAMAGE INDEX

2008 ◽  
Vol 02 (03) ◽  
pp. 241-258 ◽  
Author(s):  
DEBARATI DATTA ◽  
SIDDHARTHA GHOSH
Keyword(s):  
Seismic Design ◽  
Energy Demand ◽  
Low Cycle Fatigue ◽  
Damage Index ◽  
Specific Site ◽  
Seismic Demand ◽  
Uniform Hazard Spectra ◽  
Ductility Demand ◽  
Displacement Ductility ◽  
Perfectly Plastic

The primary emphases in the performance-based seismic design (PBSD) philosophy are in the accounting for uncertainties in seismic demand/capacity and in the better quantification of seismic damage using suitable inelastic damage parameters. Uniform hazard spectra (UHS) provide probabilistic information regarding a seismic demand on a single degree oscillator for a specific site. UHS are very good tools for probabilistic hazard estimation as intended in PBSD. In the present work, UHS are generated for Park-Ang damage index of an elastic-perfectly plastic oscillator. Park-Ang damage index takes into account the effects of both displacement ductility demand and hysteretic energy demand in low-cycle-fatigue, and therefore is a demand parameter suitable for PBSD. The UHS are generated for a specific site using artificially generated ground motions. Two types of UHS plot are illustrated. A correlation between the probability of exceedance (of certain target damage index) and stated level of structural capacity is also established. Information provided by the UHS are proposed to be used, with the aid of equivalent systems, in the development of a reliability-based seismic design framework considering Park-Ang damage index as the seismic demand parameter.

The Use of Stochastic Models to Measure Damage Potential in Acceleration Time Series

2009 ◽  
Author(s):  
Malek Brahimi ◽  
Sidi Berri ◽  
Abdelrazak Menasseri ◽  
Abdelrachid Boulaouad
Keyword(s):  
Energy Demand ◽  
Structural Response ◽  
Response Spectra ◽  
Linear Displacement ◽  
Damage Potential ◽  
Ductility Demand ◽  
Displacement Ductility ◽  
Earthquake Records ◽  
Seismic Records ◽  
Mean And Variance

ARMA models are obtained with parameters chosen to fit real accelerograms of different earthquake records. The maximum likelihood technique is used to estimate the parameters. A random set of earthquakes is generated for each event and used to establish statistically valid structural response spectra. From a sample of earthquakes, the mean and variance of response spectral ordinates are obtained for damage predictors namely peak linear displacement, ductility demand and hysteretic energy demand and compared to spectra based on single earthquake records. These Models are used to assess the damage potential in seismic records.

Selective Linear Segmentation for Detecting Relevant Parameter Changes*

2020 ◽  
Author(s):  
Arnaud Dufays ◽  
Elysee Aristide Houndetoungan ◽  
Alain Coën
Keyword(s):  
Time Series ◽  
Hedge Fund ◽  
Expectation Maximization Algorithm ◽  
Model Parameters ◽  
Relevant Parameter ◽  
Time Varying ◽  
Long Time ◽  
Model Selection Uncertainty ◽  
Penalized Likelihood Approach ◽  
Changes Over Time

Abstract Change-point (CP) processes are one flexible approach to model long time series. We propose a method to uncover which model parameters truly vary when a CP is detected. Given a set of breakpoints, we use a penalized likelihood approach to select the best set of parameters that changes over time and we prove that the penalty function leads to a consistent selection of the true model. Estimation is carried out via the deterministic annealing expectation-maximization algorithm. Our method accounts for model selection uncertainty and associates a probability to all the possible time-varying parameter specifications. Monte Carlo simulations highlight that the method works well for many time series models including heteroskedastic processes. For a sample of fourteen hedge fund (HF) strategies, using an asset-based style pricing model, we shed light on the promising ability of our method to detect the time-varying dynamics of risk exposures as well as to forecast HF returns.

A statistical study on artificially generated earthquake records

1976 ◽  
Vol 3 (1) ◽  
pp. 11-19
Author(s):  
W. K. Tso ◽  
B. P. Guru
Keyword(s):  
Statistical Study ◽  
Spectral Response ◽  
Flexible Structures ◽  
Time History ◽  
Maximum Response ◽  
Response Analysis ◽  
Seismic Region ◽  
Natural Period ◽  
Earthquake Records ◽  
Time History Response

A statistical study has been done to investigate (i) the variation of spectral responses of structures due to artificially generated earthquake records with identical statistical properties, (ii) the effect of duration of strong shaking phase of artificial earthquakes on the response of structures, and (iii) the number of earthquake records needed for time-history response analysis of a structure in a seismic region. The results indicate that the flexible structures are more sensitive to the inherent statistical variations among statistically identical earthquake records. Consequently several records must be used for time-history response analysis. A sample of eight or more records appear to provide a good estimate of mean maximum response. The duration of strong shaking can significantly affect the maximum response. Based on the results, it is suggested that for the purpose of estimating peak response, the strong shaking duration of the input earthquake motion should be at least four times the natural period of the structure. The maximum responses due to statistically identical ground motion records are observed to fit approximately the type 1 extreme value distribution. Thus, it is rationally possible to choose a design value based on the mean, standard deviation of the spectral response values and tolerable probability of exceedance.

Submarine Impact With the Oseberg Jacket

1992 ◽  
Vol 114 (1) ◽  
pp. 1-8
Author(s):  
T. C. Thuestad ◽  
F. G. Nielsen
Keyword(s):  
Time Series ◽  
Initial Level ◽  
Progressive Collapse ◽  
Structural Safety ◽  
Acceleration Time ◽  
The North ◽  
Structural Capacity ◽  
Collapse Analysis ◽  
The North Sea ◽  
Progressive Collapse Analysis

The Oseberg jacket was installed at the Oseberg field in the North Sea during the summer of 1987 and the production started on December 1, 1988. On March 6, 1988, a submarine accidentally impacted with the Oseberg jacket. This paper presents results from the evaluation of the importance of the damage to the overall structural safety. A nonlinear progressive collapse analysis is applied for the safety check. The theoretical computations are verified through evaluation of strain and acceleration time series recorded during the submarine impact. The reduction in the overall structural capacity of the jacket was in the order of 10 percent. However, the local member capacity was significantly reduced and it was necessary to remove the damaged member in order to obtain the initial level of safety.

scholarly journals Recurrence time distribution and temporal clustering properties of a cellular automaton modelling landslide events

2013 ◽  
Vol 20 (6) ◽  
pp. 1071-1078 ◽  
Author(s):  
E. Piegari ◽  
R. Di Maio ◽  
A. Avella
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Cellular Automaton ◽  
Time Window ◽  
Fano Factor ◽  
Recent Analysis ◽  
Recurrence Time ◽  
Model Parameters ◽  
Reasonable Prediction ◽  
First Time

Abstract. Reasonable prediction of landslide occurrences in a given area requires the choice of an appropriate probability distribution of recurrence time intervals. Although landslides are widespread and frequent in many parts of the world, complete databases of landslide occurrences over large periods are missing and often such natural disasters are treated as processes uncorrelated in time and, therefore, Poisson distributed. In this paper, we examine the recurrence time statistics of landslide events simulated by a cellular automaton model that reproduces well the actual frequency-size statistics of landslide catalogues. The complex time series are analysed by varying both the threshold above which the time between events is recorded and the values of the key model parameters. The synthetic recurrence time probability distribution is shown to be strongly dependent on the rate at which instability is approached, providing a smooth crossover from a power-law regime to a Weibull regime. Moreover, a Fano factor analysis shows a clear indication of different degrees of correlation in landslide time series. Such a finding supports, at least in part, a recent analysis performed for the first time of an historical landslide time series over a time window of fifty years.

Hysteretic Poisson INGARCH model for integer-valued time series

2017 ◽  
Vol 17 (6) ◽  
pp. 401-422 ◽  
Author(s):  
Buu-Chau Truong ◽  
Cathy WS Chen ◽  
Songsak Sriboonchitta
Keyword(s):  
Time Series ◽  
Model Comparison ◽  
Monte Carlo Sampling ◽  
Information Criteria ◽  
Model Parameters ◽  
Modelling Framework ◽  
South Wales ◽  
Proposed Model ◽  
Over Dispersion ◽  
Ingarch Model

This study proposes a new model for integer-valued time series—the hysteretic Poisson integer-valued generalized autoregressive conditionally heteroskedastic (INGARCH) model—which has an integrated hysteresis zone in the switching mechanism of the conditional expectation. Our modelling framework provides a parsimonious representation of the salient features of integer-valued time series, such as discreteness, over-dispersion, asymmetry and structural change. We adopt Bayesian methods with a Markov chain Monte Carlo sampling scheme to estimate model parameters and utilize the Bayesian information criteria for model comparison. We then apply the proposed model to five real time series of criminal incidents recorded by the New South Wales Police Force in Australia. Simulation results and empirical analysis highlight the better performance of hysteresis in modelling the integer-valued time series.

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