Estimation Of Response Spectra Research Articles

Harmonic-wavelet approach for response spectrum estimation of vehicle and bridge systems with uncertain parameters subjected to stochastic excitation

Vehicle and bridge systems (VBSs) are subjected to stochastic excitations. Significant research effort has been devoted to the stochastic response analysis of VBSs. In most previous studies, VBSs have been treated as deterministic systems with certain parameters. However, the real VBSs always have uncertain parameters, such as the mass and spring stiffness of the vehicles and elastic modulus of the bridge material, which significantly affect the response power spectrum (RPS) estimation. Moreover, the equations of motion of the VBSs are essentially second-order differential equations with time-dependent and random coefficient matrices, and the excitation-response spectral relation cannot be directly described using the frequency response functions. These properties render the available methods unsuitable for the RPS estimation of the VBSs when both structural uncertainty and stochastic excitations are considered. In the present study, a harmonic-wavelet approach is proposed to estimate the time-varying RPSs of the VBSs with random parameters. The second-order differential equations of motion of VBSs with random parameters are first transformed into linear algebraic equations with random coefficient matrices using a harmonic-wavelet analysis technique; then, the excitation-response spectral relation of VBSs is derived based on these linear algebraic equations. Finally, the RPSs of VBSs with uncertain parameters are solved using the perturbation technique. The accuracy of the proposed method was verified by comparing it with the Monte Carlo method using a numerical example of railway VBS. The numerical simulation results show that the parameter uncertainties significantly affect the RPSs of the VBSs and increase the amplitude of the time-varying RPSs. The uncertainty of vehicle stiffness was the most sensitive factor for vehicle RPSs, and the bridge elastic modulus was the most sensitive factor for the bridge RPSs.

An adapted LSTM-DRRNet approach for predicting floor acceleration response spectrum

The floor response spectrum is an essential element in designing non-structural components (NSC) under earthquakes. However, most available approaches for floor response spectrum estimation involve complex modeling work, require intensive computational resources, and lack generalizability. To address these limitations, this paper proposes a novel deep-learning-based methodology to provide a generalized estimate of nonlinear floor response spectra, which is composed of a bidirectional convolutional long short-term memory network with an attention mechanism (ACN-BiLSTM) and a deep residual regression network (DRRNet). ACN-BiLSTM uses one-dimensional convolution to extract high-dimensional abstract features of ground motion spectrum in each period. The attention mechanism and multi-scale sliding time window are used to improve the network’s convergence speed and prediction accuracy. DRRNet uses deep one-dimensional convolution to build a residual shortcut connection, which delivers the proportional relationship between floor response spectrum at different heights. With the input of the ground motion acceleration spectrum and structural characteristics, the proposed method can estimate the nonlinear floor acceleration response spectrum on any floor of a building. To demonstrate its efficacy, the proposed approach is applied to a dataset that includes floor response spectra of 56 buildings subjected to 195 ground motions. The application results indicate that the proposed approach can effectively and reliably predict the nonlinear acceleration response spectrum with an accuracy of 97.29%. Such an efficient method is promising in advancing the seismic design of non-structural components.

A deep neural network framework for real‐time on‐site estimation of acceleration response spectra of seismic ground motions

AbstractVarious earthquake early warning (EEW) methodologies have been proposed globally for speedily estimating information (i.e., location, magnitude, ground‐shaking intensities, and/or potential consequences) about ongoing seismic events for real‐time/near real‐time earthquake risk management. Conventional EEW algorithms have often been based on the inferred physics of a fault rupture combined with simplified empirical models to estimate the source parameters and intensity measures of interest. Given the recent boost in computational resources, data‐driven methods/models are now widely accepted as effective alternatives for EEW. This study introduces a highly accurate deep‐learning‐based computational framework named ROSERS (i.e., Real‐time On‐Site Estimation of Response Spectra) to estimate the acceleration response spectrum (Sa(T)) of the expected on‐site ground‐motion waveforms using early non‐damage‐causing early p‐waves and site characteristics. The framework is trained using a carefully selected extensive database of recorded ground motions. Due to the well‐known correlation of Sa(T) with structures’ seismic response and resulting damage/losses, rapid and accurate knowledge of expected on‐site Sa(T) values is highly beneficial to various end‐users to make well‐informed real‐time and near‐real‐time decisions. The framework is thoroughly assessed and investigated through multiple statistical tests under three historical earthquake events. These analyses demonstrate that the overall framework leads to excellent prediction power and, on average, has an accuracy above 85% for hazard‐consistent early‐warning trigger classification.

Effect of pulse-like near-fault ground motions on utility-scale land-based wind turbines

Seismic response of a utility-scale land-based wind turbine to near-fault pulse-like ground motions is presented in this study. The structural model corresponds to the 5-MW prototype developed by National Renewable Energy Laboratory. Response parameters such as tower-top displacement, base shear, and overturning moment are calculated by time history analysis and response spectral analysis using different estimates of response spectra. The results show that peak ground velocity and the frequency of dominant pulse of the ground motion are critical parameters governing the response, while peak ground acceleration has very weak correlation to response. When the pulse period is in the vicinity of structural period, seismic response is found to be much larger than those imposed by extreme events in design wind loads. Response spectral analysis using the actual spectra obtained from actual ground motions yielded results close to those from time history analysis. The spectral model prescribed in Eurocode8 is found to be inadequate in representing near-fault seismic action on the wind turbine.

Development of a Web-GIS based Decision Support System for earthquake warning service in Vietnam

This paper describes the development of a Decision support system (DSS) for earthquake warning service in Vietnam using Web GIS technology. The system consists of two main components: (1) an on-line database of earthquakes recorded from the national seismic network of Vietnam, and (2) a set of tools for rapid seismic hazard assessment. Using an online earthquake database, the system allows creating a shake map caused by a newly recorded earthquake. In addition, the Web GIS environment allows any user, including non-professional to get useful information about a just-occurred event and the possible impact caused by the earthquake shortly after its occurrence. A fault-source model developed for Vietnam was used as a part of the hazard calculation and mapping procedure. All information and results obtained from the system are automatically included in the earthquake bulletins, which will be disseminated national wide afterward by the Vietnam earthquake information and tsunami warning Center.The shake maps produced by the DSS in terms of both Peak Ground Acceleration and intensity values are rapidly available via the Web and can be used for emergency response, public information, loss estimation, earthquake planning, and post-earthquake engineering and scientific analyses. Application of the online decision support system in earthquake warning service can mitigate the earthquake risk and reduce the losses and damages due to earthquakes in Vietnam in future.ReferencesBoore D.M., Joyner W.B. and Fumal T.E., 1994. Estimation of Response Spectra and Peak Acceleration from Wester North American earthquakes: an interim report, USGS open file report, 94-127, Menlo Park, California, United States Geological Survey.Boore D.M. and Atkinson G.M., 2008. 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Ground motion attenuation relationship for shallow strike-slip earthquakes in northern Vietnam based on strong motion records from Japan, Vietnam and adjacent regions, Structural Eng./Earthquake Eng., JSCE, 29, 23-39.Toro G.R., Abrahamson N.A. and Schneider J.F., 1997. Engineering Model of Strong Ground Motions from Earthquakes in the Central and Eastern United States, Seismological Research Letters, January/February.Wald D.J., Worden B.C., Quitoriano V. and Pankow K.L., 2006. ShakeMap Manual. Technical manual, users guide, and software guide.Wald D.L., Wald B. Worden and Goltz J., 2003. ShakeMap - a tool for earthquake response. U.S. Geological Survey Fact Sheet 087-03.Wells D.L. and Coppersmith K.J., 1994. New Empirical Relationships Among Magnitude, Rupture Length, Rupture Width, and Surface Displacement, Bulletin of the Seismological Society of America, 84, 974-1002.

Estimation of Response Spectra of Earthquake Ground Motion Based on an Attenuation Equation with Detailed Analysis of Source and Site Effects

Characterized Green’s function method (CGFM), a new approach for estimating the response spectra of earthquake ground motion, has been proposed by Oji et al. (2012). The CGFM is based on the concept that the spatial average of estimated results is equal to a conventional attenuation model. The site‐specific deviations can be modeled by the source rupture effects, such as directivity pulses and radiation patterns, which are represented by the frequency‐dependent factors obtained from a superposition of simple characterized waveforms obeying the omega‐square model. In this article, we expand the CGFM to include nonlinear site response at a specific site. This response is calculated using the estimated time history of ground motion on the engineering basement from the response spectrum and the simulated phase waveform obtained by the original CGFM. The proposed CGFM is verified by comparing the estimated results with the records from the 1995 Kobe and the 2007 Chuetsu‐Oki earthquakes, Japan.

Machine-Learning Methods for Earthquake Ground Motion Analysis and Simulation

This paper presents a novel method of data-based probabilistic seismic hazard analysis (PSHA) and ground motion simulation, verified using previously recorded strong-motion data and machine-learning techniques. The procedure consists of three parts: (1) selection of an orthonormal set of basis vectors called eigenquakes to represent characteristic earthquake records; (2) estimation of response spectra for the anticipated level of shaking for a scenario earthquake at a site using Gaussian process regression; and (3) optimal combination of the eigenquakes to generate time series of ground acceleration consistent with the response spectral ordinates obtained in the second part. The paper discusses the benefits of applying such machine-learning methods to strong-motion databases for PSHA and ground motion simulation, particularly in large urban areas where dense instrumentation is available or expected. The effectiveness of the proposed methodology is exhibited using four scenario examples for downtown Los Angeles. Advantages, disadvantages, and future research needs for this machine-learning approach to PSHA are discussed.

Response Spectrum Estimation for Fixed Offshore Structures With Inundation Effect Included: A Price’s Theorem Approach

Instead of a Volterra-series based method, a method based on Price’s theorem and Fourier Transforms is proposed for evaluating the nonlinear response power spectra of fixed offshore structures modeled as finite-memory systems. The numerical computation effort required for spectral estimations using the proposed method is significantly less than that of the Volterra-series method that requires multi-dimensional integrations. Nonlinear frequency-domain analyses of two jack-up platform structures are carried out to study the effects of inundation, cubic and quartic drag terms and polynomialization methods.

Complex seismic site effects in sediment‐filled valleys and implications on design spectra

AbstractEvidence of complex site effects in two‐dimensional geological configurations is illustrated first, and the related difficulties in interpreting ground motion observations are discussed, using weak motion data recorded in three alpine valleys in Northern Italy. While, on one hand, such valleys are mostly located in regions of low or moderate seismic hazard, where ground motion data are scarce, on the other hand investment in buildings and infrastructure has been substantial and may not always have been protected by adequate earthquake‐resistant provisions and zoning criteria. Moreover, experience and data obtained in regions hit by destructive earthquakes cannot be easily transferred to such a different context. The combined influence of one‐dimensional propagation effects on the dominant frequencies of motion, and of two‐dimensional effects on the amplification level and significant frequency band, are highlighted.Concerning design elastic spectra, estimates of response spectra on hard and soft soil are performed, using observed weak motion data and the empirical Green's functions method. Comparison of results with Eurocode 8 spectra shows that the latter may not be conservative at periods larger than 1 s. The relatively large response at such is related to the geological configuration of the valleys, which appear to require a reasonably accurate definition of their two‐dimensional geometry.

An analysis of the effects of the leg-spacing on spectral response of offshore structures

The authors have applied a computer-based model to perform spectral analysis of jacket platforms. The analysis is carried out in a consistent manner using the finite element method. The proper estimation of the phasing effects of the ocean waves on structural responses is dependent, inter alia, on the accurate calculation of nodal forces. Using the finite element approach the vector of nodal forces can be most accurately computed taking into account the varying distributed loads along the structural members. The model, developed by the first author, calculates cross-receptances of response for all degrees of freedom that enable the phase effects due to the spatial extent of the structure to be properly accounted for. This model includes the phase effects of wave loadings on the platform and it can thus give a more accurate estimation of response spectra which are generally required for design calculations; this is far more accurate than calculating wave loadings on an equivalent cantilever as is often done.

Validated Estimation of Response Spectra for the 1980 Irpinia Earthquake in the Eastern Area of Naples

The seismic ground motion of a test area in the eastern district of Naples is computed with a hybrid technique based on the mode summation and the finite difference methods. Synthetic seismograms are validated with the 1980 Irpinia earthquake, a good example of strong shaking for Naples, recorded 10km from the modeled sites. Realistic SH and P-SV wave seismograms are computed along geological cross sections representative of the area. As expected, the sedimentary cover causes an increase of the signal's amplitudes along the radial and transverse components. The spectral amplification of the vertical motion is generally negligible; instead, that of the horizontal motion ranges between 2 and 5 in the 0.7-2.2 Hz frequency range. Average and maximum spectral amplifications are considered along the different geological cross sections and acceleration response spectra for the Irpinia earthquake are evaluated in order to formulate appropriate design spectra and improvements to the building code.

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.

A high-frequency magnitude scale

Abstract A high-frequency magnitude scale (m) is proposed: m=2log⁡a˜hf+3, where ãhf is the high-frequency level of the Fourier amplitude spectrum of acceleration in cm/sec (average or random horizontal component), at a hypocentral or closest fault distance of 10 km. m can be determined from either instrumental data or the felt area of an earthquake. The definition of m has been arranged such that m = M (moment magnitude) for events of “average” stress drop, in both eastern North America (ENA) and California. m provides a measure of the stress drop if M is also known. The observed relationship between m and M indicates that the average stress drop is about 150 bars for ENA earthquakes, and about 70 bars for California earthquakes. The variability of stress drop is much larger in ENA than in California. The chief justification for the m scale is its utility in the interpretation of the large preinstrumental earthquakes that are so important to seismic hazard estimation in eastern North America. For such events, m can be determined more reliably than can M or mN (Nuttli magnitude), and forms a much better basis for estimating high-frequency ground motions. When used as a pair, m and M provide a good index of ground motion over the entire engineering frequency band. If both of these magnitudes can be defined for an earthquake then a ground-motion model, such as the stochastic model, can be used to obtain reliable estimates of response spectra and peak ground motions.

Estimation of near-source ground motions from a teleseismically derived rupture model of the 1989 Loma Prieta, California, earthquake

Abstract A rupture model for the 1989 Loma Prieta earthquake obtained from inversion of teleseismic body waves is used to calculate the mainshock, near-source, strong ground motions. The effectiveness of both synthetic and empirical (aftershock) Green9s functions is evaluated in terms of velocity response spectra over the period range from 0.1 to 10 sec. A strictly deterministic approach is used in the simulation of near-source ground motion with both the synthetic and aftershock Green9s functions. A deterministic method has advantages in that it is simple to apply and there is no stochastic element to introduce variability in the solution. Response spectral values are very sensitive to the choice of the mainshock source-time function. Using a 1.0-sec triangular time function obtained from the teleseismic study gives good estimates of response spectra from 1- to 2-sec period for aftershock Green9s functions and from 1- to 10-sec period for synthetic Green9s functions. The limited long-period response of the aftershock summations is due to the restricted bandwidth of the recording sensor. Using a 0.5-sec Kostrov time function extends the bandwidth of validity of the aftershock summations to 0.1- to 2-sec period and the synthetic Green9s function summations to 0.3- to 10-sec period. The limited short-period bandwidth of the synthetic Green9s function summations is due to the lower-frequency content (5 Hz) and absence of accurate high-frequency propagation effects in the synthetic seismograms. Although the teleseismic study could not distinguish between a 1.0-sec triangular time function and a 0.5-sec Kostrov time function, we feel justified in using the Kostrov function because it lies within our broader knowledge of earthquake source-time functions.

A note on the fast computation of response spectra estimates

AbstractAn algorithm is presented for fast computation of estimates of response spectra. It is based on the formalism of random vibration theory. Numerical results show that estimates are reliable and useful for practical applications.

On the Motion and Relative Water Surface of a Moored Semisubmersible Platform under Combined Conditions of Irregular Waves and Winds

Generally the critical motions and relative water surface of a moored semisubmersible are very complicate under combined external disturbances ; namely steady wind, dynamic variable winds and irregular waves. This paper deals with the steady and variable parts using frequency domain approach. The analysis is done for wave frequency and very low frequency. Theoretical predictions are compared to experimental results and a good agreement is obtained.Also the effect of the damping coefficient on the response spectrum estimation of very low frequency is discussed, and the cause for scattered statistical values estimated from response spectrum is investigated. Finally, a practical method for total prediction for motion and relative motion including the very slowly varying phenomena and steady drift parts is introduced.

An application of cokriging for estimation of tripartite earthquake response spectra

A tripartite earthquake response spectrum exhibits peak values of acceleration, velocity, and displacement in concert, each as a function of natural frequency of vibration. Because cokriging is a regionalized variable technique for multiple variable estimation, it was employed to jointly estimate peak values of acceleration, velocity, and displacement through a frequency discretization process. The objective of this application was to develop a technique for estimation of response spectra at uninstrumented locations. Because magnitudes of the three response variables differed, these data were normalized prior to cokriging. This process simply involved dividing each type of variable by its maximum value for a given frequency; hence, values of each type of variable ranged between zero and one. This allowed better accuracy in developing cross-variograms. Cokriging proved to be an efficient and accurate technique to use for the estimation of tripartite response spectra.