Seismic Accelerograms Research Articles

Modeling evolutionary power spectral density functions of strong earthquakes via copulas

This paper proposes a new approach for analyzing seismic accelerograms using the evolutionary Power Spectral Density function (EPSD). The accelerogram of an earthquake can be accurately modeled and simulated from its spectrogram, based on the oscillatory stochastic processes theory. To adequately characterize a spectrogram that is consistent with the response spectra, a parametric model with 16 parameters is proposed. This model describes the square of the amplitude spectrum, an envelope of the square of the accelerogram, and a copula that constructs a time–frequency model from the time and frequency marginals. The use of copulas to model a bivariate probability distribution is a common practice in statistics, particularly when the marginal distributions are known. The periodogram can be viewed as an unnormalized probability density function, where the total energy serves as the normalization constant, since the total energy of a seismic motion is always finite. Additionally, a reduced model consisting of only 10 parameters is presented, which may be especially valuable when only shear wave effects are relevant.

A Novel Stochastic Methodology for the Generation of Artificial Seismic Accelerograms

A Novel Stochastic Methodology for the Generation of Artificial Seismic Accelerograms

Probabilistic generation of hazard‐consistent suites of fully non‐stationary seismic records

AbstractA novel, practical, and computationally efficient probabilistic methodology for the stochastic generation of suites of fully non‐stationary artificial accelerograms is presented. The proposed methodology ensures that the produced ground motion suites match a given target spectral mean and target variability for the whole period range of interest. This is achieved by first producing an ensemble of random target spectra with the given mean and variability and then using them to generate artificial, target spectrum‐compatible, acceleration time‐histories with spectral representation techniques. Spectral correlation can also be assumed for the generated ground motion spectra. Based on the same backbone, two different formulations are proposed for generating spectrum‐compatible acceleration time‐histories of the non‐stationary kind. The distinction between these two variants lies in the techniques employed for modeling the temporal and spectral modulation, focusing on the site‐compatibility of the produced records. The first approach uses past‐recorded seismic accelerograms as seed records, and the second proposes and uses a new, probabilistic time‐frequency modulating function. The outcome of the proposed methodology is suites containing site‐compatible ground motion time‐histories whose spectral mean and variability match those obtained from any of the usually employed target spectra used in the earthquake engineering practice. An online tool implementing the proposed methodology is also freely provided.

Monte-Carlo Simulation for Moderate Seismic Zones Using Artificial Accelerograms

The present technical note deals with a new method to generate seismic accelerograms based on statistical characteristics and the classification of seismic waves. A short heterogeneous site- based analyse of these accelerograms is given with a seismic wave propagation code in 1D. After, a numerical simulation is done in order to obtain PGA using Newmark’s implicit scheme, and finally, Monte-Carlo simulation is used to determinate failure’s probability of structures localised in moderate seismic zones in hexagonal France

Fuzzy Multivariate Regression Models for Seismic Assessment of Rocking Structures

The assessment of rocking response is a challenging task due to its high nonlinearity. The present study investigates two methodologies to evaluate finite rocking rotations and overturn of three typical rocking systems. In particular, fuzzy linear regression (FLR) with triangular fuzzy numbers and a hybrid model combining logistic regression and fuzzy logic were adopted. To this end, three typical rocking structures were considered, and nonlinear time history analyses were performed to obtain their maximum response. Eighteen seismic intensity measures (IMs) extracted from recorded seismic accelerograms were considered to predict the responses. In the absence of rocking overturn, the finite rocking rotations and similarity ratios were calculated by adopting the FLR method. Moreover, extensive analysis was performed to evaluate the influence of each IM on the model’s predictions. On the other hand, rocking overturn was evaluated by logistic regression to compute the probability of collapse, followed by the FLR method to estimate the similarity between the different rocking-based structural systems. The root mean square error (RMSE) parameter and the log loss function were determined for every model to assess the predictions that emerged from the two fuzzy methods. As indicated, both methods demonstrated satisfactory results, presenting minimal deviations from the observed values. Finally, in the case of finite rocking rotation predictive models, remarkably high similarity ratios were observed among the various structures, with a median value of 0.96.

A design method for seismic retrofit of reinforced concrete frame buildings using aluminum shear panels

Despite significant progress in research and development of aluminum shear panels in recent decades, their implementation for seismic retrofit of existing reinforced concrete (RC) buildings can still be significantly extended. Their application is limited by the general lack of relatively simple and effective design criteria and proper guidelines. This paper develops a design method for the seismic retrofit of reinforced concrete buildings using aluminum multi-stiffened shear panels as dampers. Both the nonlinearity in the structure and the dampers-structure interaction are considered to give an optimal distribution of the shear panels over the height of the building. The analytical laws refer to dissipative aluminum shear panels recently tested and analyzed by the authors. The proposed procedure has been described in detail. Its applicability has been demonstrated by analyzing two typical RC buildings having drift capacity-to-demand ratios ranging from 0.505 to 0.624. The design value of the panel-to-frame stiffness ratio has been found to range from 0.594 to 1.432 as a function of the lateral stiffness of the existing building. The verification of the proposed procedure has been carried out by checking the validity of the design assumptions. The first one (i.e., the mode shapes remain the same before and after retrofit) has been checked using the modal assurance criterion that gives values ranging from 0.992 to 0.998. The second one (i.e., uniform yield drift distribution over the building height) has been checked by comparing the yield drifts with their average value giving a standard deviation ranging from about 11 to 15%. The effectiveness of the design method has been finally validated through nonlinear time-history analysis for different seismic accelerograms and hysteresis models. The results show that the seismic retrofit design procedure is effective in significantly reducing inter-story drift (maximum inter-story drift ratio demands ranging from 1.04 to 2.07%) thus satisfying the acceptance criteria of the building, and avoiding drift concentration and consequential weak story collapse.

Enhancing tunability of liquid storage tanks to function as deep tuned liquid dampers by use of a submerged stretched membrane

This is a study on a deep, liquid-containing tank, such as an overhead water tank on a building, with a vertically submerged stretched membrane (SSM). Here, instead of the sloshing mode, which can become detuned and also affords a low damper mass ratio, the impulsive liquid–membrane interacting system is designed to serve as a dynamic vibration absorber. The requirement of tuning the frequency of the impulsive liquid–membrane interacting system to the structural frequency can be achieved without any imposition on the tank dimensions, which are generally fixed from the tank's functional requirements. The system frequency would remain unchanged so long the membrane would remain submerged below a minimum liquid depth, thereby allowing fluctuation of liquid level within a prescribed range of the tank depth. The formulation for obtaining the frequency of the impulsive liquid–membrane interacting system is derived, using the sub-domain partition approach. It is seen that through suitable adjustment of the design parameters of the membrane, the proposed tank damper can be tuned to both short-period and to long-period structures. Further, the impulsive liquid mass, which otherwise has no role to play in the damping mechanism of a tuned liquid damper (TLD), is here utilized to absorb and dissipate the vibrational energy. Through a time-domain study considering recorded seismic accelerograms, the significant control effectiveness of the proposed damper system is illustrated. Further, the results obtained from the equivalent mechanical model of the structure–damper system are compared with those from a finite element analysis of the fluid–structure system in the ANSYS Workbench environment.

Reliability-based optimum design of multiple tuned mass dampers for minimization of the probability of failure of buildings under earthquakes

This work proposes a methodology for reliability-based optimum design of multiple tuned mass dampers (MTMD) for installation in buildings situated in seismic regions. Unlike works that disregard uncertainties and perform deterministic optimizations, the approach proposed in this work aims to minimize the probability of failure of buildings under earthquakes taking the uncertainties into account. For this purpose, a modern optimization technique, the Whale Optimization Algorithm (WOA), is employed. Actual records of seismic accelerograms that occurred in the site of interest are used to characterize the seismic risk, determining the expected value of the peak ground acceleration (PGA) annual exceedance rate. Thus, the seismic risk is estimated by fitting probability distribution functions of the PGA for periods of one and fifty years, to assess, via numerical simulation, the building’s reliability. The proposed methodology is illustrated considering two buildings located in the city of Cúcuta, Colombia, where earthquake data are available. Robust estimators of the system reliability are calculated using a database of seismic records with notably different features. The results confirm that the proposed methodology for optimization of MTMD considerably increases the reliability of both buildings, highlighting the effectiveness of MTMD in minimizing the probability of failure of buildings situated in regions with significant seismic activity.

On the Selection of Wavelet Models in the Simulation of Seismic Accelerograms through Evolutionary Optimization

A numerical procedure, based on an evolutionary optimization algorithm, has been proposed by the authorsfor the simultaneous generation of the three components of the seismic ground acceleration. The methodology allowsthe determination of a train of seismic waves modeled by three different waveforms, for the generation of groundseismic acceleration components. The parameters of each wave, i.e., amplitude, frequency, duration, arrival time anddirection, are determined using an evolutionary optimization algorithm. Although no theoretical justification is knownby the authors for the generation, at the seismic source, of specific initial waveforms, both in case of fracture or ofsliding with friction, waveform acceleration components that satisfy the condition of zero final velocity should inprinciple be preferred. The latter is a physical restriction that is automatically satisfied by anti-symmetrical functions,thus eliminating the need to correct the baseline of simulated accelerograms. The error of fit of simulated accelerogramsgenerated by three different waveforms proposed in the literature was herein determined by comparison with actualseismic records. On that basis, estimations of the expected error of the evolutionary optimization algorithm inengineering applications are presented.

Decomposing seismic accelerograms with optimized window and its application for generating artificial fully non-Gaussian and nonstationary ground motion time histories

In the present study, we propose a framework to simulate artificial seismic ground motion time histories for a given target record based on the time-frequency decomposition with an optimized window. The considered time-frequency decomposition technique is the S-transform (ST), where the optimized window is determined based on an energy concentration measure (ECM). For the evaluation of ECM for S-transform, we propose to use the time-frequency power spectral density function rather than the ST coefficients. Depending on the adopted assumption, the use of the iterative power and amplitude correction algorithm (IPAC) or the spectral represent method is suggested. The use of IPAC could also preserve the non-Gaussian characteristics of the target record. The proposed framework to simulate the artificial seismic ground motion time histories can capture the irregular pockets of power concentration in the time-frequency domain, and no assumptions on the functional forms of the spectra are required. The use of the proposed framework in simulating the time histories is illustrated by numerical examples, showing that the zero-upcrossing rate, the power distribution in time and in frequency, and the spectral acceleration of the simulated time histories match well their corresponding targets.

Simultaneous simulation of the three components of seismic accelerograms at locations around seismological stations

Simultaneous simulation of the three components of seismic accelerograms at locations around seismological stations

Assessment and Localization of Structural Damage in r/c Structures through Intelligent Seismic Signal Processing

ABSTRACT In this work, a novel approach in post-earthquake structural damage estimation is investigated. The approach is formulated as a problem of both damage approximation and localization. The inter-story drift ratio and the global damage index of Park/Ang (DIG,PA) are the estimated damage indicators for each floor of the structure. Artificial neural networks (ANNs), random forests (RFs), support vector machines (SVMs) with linear and radial basis function (RBF) kernels and adaptive neuro-fuzzy inference systems (ANFISs) are tested to predict the seismic damage state of each floor of an 8-storey reinforced concrete (r/c) building subjected to 155 natural and artificially generated seismic accelerograms. The damage potential of the accelerograms is described by three seismic parameters extracted from the response of the structure. The set of seismic accelerograms is defined by combining two outlier detection techniques, isolation forests and Z-score, while the set of seismic parameters is confirmed by minimum redundancy maximum relevance (mRMR) feature selection algorithm. Optimization methods are used to fine-tune the performance of all networks. Results indicate RFs and ANNs among the models with optimal performances, reaching average correct classification rates of up to 96.87% and 91.87% with RFs, and 96.25% and 90.12% with ANNs, for DIG,PA and ISDR, respectively.

Generation of fully non-stationary random processes consistent with target seismic accelerograms

In this paper, a method for generating samples of a fully non-stationary zero-mean Gaussian process, having a target acceleration time-history as one of its own samples, is presented. The proposed method requires the following steps: i) divide the time axis of the target accelerogram in contiguous time intervals in which a uniformly modulated process is introduced as the product of a deterministic modulating function per a stationary zero-mean Gaussian sub-process, whose power spectral density (PSD) function is filtered by two Butterworth filters; ii) estimate, in the various time intervals, the parameters of modulating functions by least-square fitting the expected energy of the proposed model to the energy of the target accelerogram; iii) estimate the parameters of the PSD function of the stationary sub-process, once the occurrences of maxima and of zero-level up-crossings of the target accelerogram, in the various intervals, are counted; iv) obtain the evolutionary spectral representation of the fully non-stationary process by adding the various contribution evaluated in the various intervals.

Generation of seismic excitations compatible with target spectrum: application to Eurocode 8

PurposeThis paper aims to artificially generate seismic accelerograms compatible with the response spectrum imposed as a function of the given environmental parameters such as magnitude, epicentral distance and type of soil. This study is necessary for the non-linear dynamic analysis of structures in regions where real seismic records are not available.Design/methodology/approachFirst, a stochastic iterative method is used to estimate the spectral densities of acceleration power from the respective target response spectra. Thereafter, based on the superposition of seismic waves, a subsequent iterative procedure, which implicitly takes into account the non-stationary character of temporal intensity content of strong ground motions, is developed to synthesize, from these power spectral density, the corresponding acceleration time histories. The phase contents of the ground acceleration samples, thus obtained, are generated using a probability density function of phase derivatives with characteristic parameters estimated from seismological considerations. When based on seismic codes spectrum compatible criteria, this procedure can be used to generate strong ground motions for structural design.FindingsThe results found show that the forms of acceleration of the target and the simulated signals have similar characteristics in terms of strong motion durations, the peak ground acceleration values, corresponding time of occurrence and also, the corresponding cumulative energy functions follow practically the same pattern of variations.Originality/valueThe aim of this study is to generate seismic accelerograms compatible with regulatory spectra by the composition of the three acceleration duration segments based on environmental parameters (magnitude, epicentral distance and type of soil) and which subsequently serves to control the time envelope of the generated signals, and therefore the random generation of phase derivatives, which has not been previously treated.

Seismic damage potential described by intensity parameters based on Hilbert-Huang Transform analysis and fundamental frequency of structures

This study aims to present new frequency-related seismic intensity parameters (SIPs) based on the Hilbert-Huang Transform (HHT) analysis. The proposed procedure is utilized for the processing of several seismic accelerograms. Thus, the entire evaluated Hilbert Spectrum (HS) of each considered seismic velocity time-history is investigated first, and then, a delimited area of the same HS around a specific frequency is explored, for the proposition of new SIPs. A first application of the suggested new parameters is to reveal the interrelation between them and the structural damage of a reinforced concrete frame structure. The index of Park and Ang describes the structural damage. The fundamental frequency of the structure is considered as the mentioned specific frequency. Two statistical methods, namely correlation analysis and multiple linear regression analysis, are used to identify the relationship between the considered SIPs and the corresponding structural damage. The results confirm that the new proposed HHT-based parameters are effective descriptors of the seismic damage potential and helpful tools for forecasting the seismic damages on buildings.

Seismic Behavior Analysis of Seismic Isolated Structure by Spectrum-compatible Bi-directional Seismic Accelerograms

Seismic Behavior Analysis of Seismic Isolated Structure by Spectrum-compatible Bi-directional Seismic Accelerograms

Novel Hilbert spectrum-based seismic intensity parameters interrelated with structural damage

The objective of this study is to propose new seismic intensity parameters based on the Hilbert spectrum and to associate them with the seismic damage potential. In recent years the assessment of even more seismic features derived from the seismic acceleration time-histories was associated with the structural damage. For a better insight into the complex seismic acceleration time-history, Hilbert-Huang Transform (HHT) analysis is utilized for its processing, and the Hilbert spectrum is obtained. New proposed seismic intensity parameters based on the Hilbert spectrum are derived. The aim is to achieve a significant estimation of the seismic damage potential on structures from the proposed new intensity parameters confirmed by statistical methods. Park-Ang overall structural damage index is used to describe the postseismic damage status of structures. Thus, a set of recorded seismic accelerograms from all over the word is applied on a reinforced concrete frame structure, and the Park-Ang indices through nonlinear dynamic analysis are provided and considered subsequently as reference numerical values. Conventional seismic parameters, with well-known seismic structural damage interrelation, are evaluated for the same set of excitations. Statistical procedures, namely correlation study and multilinear regression analysis, are applied on the set of the conventional parameters and the set of proposed new parameters separately, to confirm their interrelation with the seismic structural damage. The regression models are used for the evaluation of the structural damage indices for every set of parameters, respectively. The predicted numerical values of the structural damage indices evaluated from the two sets of seismic intensity parameters are inter-compared with the reference values. The numerical results confirm the ability of the proposed Hilbert spectrum based new seismic intensity parameters to approximate the postseismic structural damage with a smaller Standard Error of Estimation than this accomplished of the conventional ones.

Seismic Performance of Damper Installed In High-Rise Steel Building In Bangladesh

This research paper describes the results of analysis of the seismic behavior of a thirty story steel building with and without damper under different earthquake acceleration signals. The proposed procedure placed the various types of damper like friction damper, bilinear damper and exponential damper on the top three floors of the building. The study compares the different performances such as the joint displacement, joint acceleration, the base force of structure with and without damper for a thirty-story steel building using ETAB2015. The study further performs time history analysis for different seismic accelerograms to observe the actual time domain responses of the structure. Linear time-history analysis on this steel building structure indicates that maximum displacement, maximum base force, and maximum acceleration effectively reduce in the presence of damper at top three floors of the building.

Time-response functions of mechanical networks with inerters and causality

This paper derives the causal time-response functions of three-parameter mechanical networks that have been reported in the literature and involve the inerter-a two-node element in which the force-output is proportional to the relative acceleration of its end-nodes. This two-terminal device is the mechanical analogue of the capacitor in a force-current/velocity-voltage analogy. The paper shows that all frequency-response functions that exhibit singularities along the real frequency axis need to be enhanced with the addition of a Dirac delta function or with its derivative depending on the strength of the singularity. In this way the real and imaginary parts of the enhanced frequency response functions are Hilbert pairs; therefore, yielding a causal time-response function in the time domain. The integral representation of the output signals offers an attractive computational alternative given that the constitutive equations of the three-parameter networks examined herein involve the third derivative of the nodal displacement which may challenge the numerical accuracy of a state-space formulation when the input signal is only available in digital form as in the case of recorded seismic accelerograms.

A novel stochastic linearization framework for seismic demand estimation of hysteretic MDOF systems subject to linear response spectra

This paper proposes a novel computationally economical stochastic dynamics framework to estimate the peak inelastic response of yielding structures modelled as nonlinear multi degree-of-freedom (DOF) systems subject to a given linear response spectrum defined for different damping ratios. This is accomplished without undertaking nonlinear response history analyses (RHA) or, to this effect, constructing an ensemble of spectrally matched seismic accelerograms. The proposed approach relies on statistical linearization and enforces pertinent statistical conditions to decompose the inelastic d-DOF system into d linear single DOF oscillators with effective linear properties (ELPs): natural frequency and damping ratio. Each such oscillator is subject to a different stationary random process compatible with the excitation response spectrum with damping ratio equal to the oscillator effective critical damping ratio. This equality is achieved through a small number of iterations to a pre-specified tolerance, while peak inelastic response estimates for all DOFs of interest are obtained by utilization of the excitation response spectrum in conjunction with the ELPs. The applicability of the proposed framework is numerically illustrated using a 3-storey Bouc-Wen hysteretic frame structure exposed to the Eurocode 8 elastic response spectrum. Nonlinear RHA involving a large ensemble of non-stationary Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed approach in a Monte Carlo-based context. The novel feature of iterative matching between the excitation response spectrum damping ratio and the ELP damping ratio enforces the required compatibility in the damping properties of the effective linear oscillators and the imposed elastic response spectra. It is found that this latter feature reduces drastically the error of the estimates (i.e., by an order of magnitude) obtained by a non-iterative application of the framework.