Original Ground Motion Research Articles

Modification of ground motions using wavelet transform and VPS algorithm

In this paper a simple approach is presented for spectral matching of ground motions utilizing the wavelet transform and a recently developed metaheuristic optimization technique. For this purpose, wavelet transform is used to decompose the original ground motions to several levels, where each level covers a special range of frequency, and then each level is multiplied by a variable. Subsequently, the vibrating particles system (VPS) algorithm is employed to calculate the variables such that the error between the response and target spectra is minimized. The application of the proposed method is illustrated through modifying 12 sets of ground motions. The results achieved by this method demonstrate its capability in solving the problem. The outcomes of the VPS algorithm are compared to those of the standard colliding bodies optimization (CBO) to illustrate the importance of the enhancement of the algorithm.

Synthesis of Spatially Correlated Earthquake Ground Motions Based on Hilbert Transform

A simplified method for synthesizing spatially correlated earthquake ground motions is developed based on Hilbert transform and a reference earthquake record. In this method, one reference earthquake record is treated as the original ground motion, based on a series of generated ground motions. This procedure uses the instantaneous amplitude and the instantaneous phase of the record obtained using Hilbert transform to achieve the nonstationarity of ground motion. To establish the coherency between generated ground motions, an incoherence model is employed to describe the relation between the instantaneous phase at the present station and the instantaneous phases at previous stations. This type of phase is defined as the instantaneous coherence phase. In addition, time lag is included in the instantaneous coherence phase to prescribe the wave passage effect. The proposed Hilbert-transform-based method is efficient and avoids cumbersome parameter estimations as well as other drawbacks involved in some traditional synthesizing methods. Applications of this method demonstrate that the generated ground motions are statistically analogous with the reference record.

A classification method for pulse-like ground motions based on S-transform

This article presents a new identification procedure to detect pulse-like ground motion based on the S-transform. The S-transform is utilized as an effective tool for time-frequency representation of ground motions. It is shown that plots of the S-transform in the time-frequency domain named as the S-feature provide useful information for initial detection of pulses in the velocity time history of the ground motions. To perfect identification of pulse-like motions, a method is presented for extraction of pulses from original ground motions based on the convolution theorem. The proposed procedure is applied for classification of pulse-like near-fault ground motions owing to directivity effects in a data set of selective earthquakes. The period of velocity pulses, as an important parameter in structural engineering, is also determined from extracted pulses. The results of this study provide a suitable platform for selecting pulse-like records, when seismic analyses of structures in near-fault areas are of primary interest.

A new method for modification of ground motions using wavelet transform and enhanced colliding bodies optimization

In this paper a simple and robust approach is presented for spectral matching of ground motions utilizing the wavelet transform and an improved metaheuristic optimization technique. For this purpose, wavelet transform is used to decompose the original ground motions to several levels, where each level covers a special range of frequency, and then each level is multiplied by a variable. Subsequently, the enhanced colliding bodies optimization technique is employed to calculate the variables such that the error between the response and target spectra is minimized. The application of the proposed method is illustrated through modifying 12 sets of ground motions. The results achieved by this method demonstrate its capability in solving the problem. The outcomes of the enhanced colliding bodies optimization (ECBO) are compared to those of the standard colliding bodies optimization (CBO) to illustrate the importance of the enhancement of the algorithm.

A Simple and Quantitative Algorithm for Identifying Pulse‐Like Ground Motions Based on Zero Velocity Point Method

Pulse‐like ground motions, which are mainly concentrated in near‐fault regions, can induce severe damage on structures. This article presents a simple and effective method used for quantitatively identifying pulse‐like ground motions. First, zero velocity point method is proposed based on the properties of trigonometric functions. This method can reveal the time‐domain characteristics of ground‐motion velocity time history and can be used to detect the potential velocity pulse which is included in corresponding original ground motion. Second, pulse‐like ground motions are classified into two classes: single‐pulse‐like and multi‐pulse‐like ground motions. Further, single‐pulse‐like is divided into significant‐single‐pulse‐like and non‐significant‐single‐pulse‐like, while multi‐pulse‐like is divided into double‐pulse‐like, three‐pulse‐like, and four‐pulse‐like. Third, energy method is adopted to formulate the identification criterion for each type of pulse‐like ground motion. Finally, the energy parameters of the detected potential velocity pulse for a large number of ground motions are calculated, and the proposed identification criteria are applied to identify whether these ground motions are pulse‐like or not. A comparison of the methodology proposed in this study with previous identification methods is presented. Analysis results indicate that the methodology proposed in this study can accurately distinguish pulse‐like and non‐pulse‐like ground motions.

ON THE VARIATION OF MAXIMUM ISOLATOR DISPLACEMENTS DUE TO GROUND MOTION DIRECTIONALITY

In most of the cases, code specifications dictate the use of nonlinear response history analyses (NRHA) to estimate maximum isolator displacements (MIDs) of a seismically isolated structure (SIS). For this purpose, a set of ground motion records with similar characteristics needs to be selected. Then, the structure is analyzed bidirectionally by considering both orthogonal horizontal components of these records. However, there is not any provision regarding the ground motion directionality effect in the codes but simply use of as-recorded motions is encouraged. This study investigates the effect of ground motion directionality on variation of MIDs in case of bidirectional NRHA. Thus, a typical SIS, where the isolator units are composed of lead rubber bearings (LRBs), is subjected to ground motions rotated from their as-recorded original form by increments of 10o up to 360o. Here, LRBs are modelled by a deteriorating hysteretic representation in which the strength of the isolator reduces gradually due to the applied loading. In the analyses, first, the original as-recorded ground motion is applied to the SIS and the corresponding MID is noted. Then, the same structure is subjected to rotated versions of the same motion and again the MIDs are noted. To quantify the variation in the isolator displacement, analytically obtained MIDs are compared. Results showed that there is an amplification in MIDs due to change in ground motion direction.

Study on Low-Frequency Characterizations of Pulse-Type Ground Motions through Multi-Resolution Analysis

This article makes an attempt to investigate the low-frequency characterizations of pulse-type ground motions through ground motion components instead of original records. A decomposed method based on multi-resolution analysis is introduced in this article. The accuracy and validity of the method is tested in frequency domain, time domain and dynamic response. A dataset of 398 low-frequency components is obtained after the decomposition of 91 typical pulse-type records. A probabilistic model to describe the proportion of low-frequency components in corresponding original ground motions is established. At last, the decomposed method is used to investigate the impulsive characterizations of pulse-type ground motions.

ON INELASTIC RESPONSE SPECTRA OF PULSE‐TYPE GROUND MOTION BASED ON DECOMPOSITION METHOD

AbstractThis article aims to investigate the influence of different frequency components on the amplitude parameters and inelastic response spectral characterizations of pulse‐type ground motions. 53 pulse‐type ground motions selected from 12 large earthquakes are utilized in this study. First, the high frequency components (HFC) and low frequency components (LFC) of these ground motions are obtained based on multi‐scale decomposed method. To compare with the results obtained by traditional methods, the predominant component (PC) which can be used as the representation of the dominant velocity pulse and the residual component (RC) which is obtained by removing the PC from original ground motion are analyzed. Second, the comparison of the amplitude parameters and the inelastic response spectra between original ground motions and four kinds of ground motion components (HFC, LFC, PC, and RC) is performed in order to investigate the influence of ground motion components on the amplitude parameters and inelastic response spectral characterizations of the corresponding original ground motions. Finally, a harmonic ground motion model is used to explore the reasons for the special inelastic response spectral characterizations for pulse‐type ground motions. Analysis results show that low‐frequency component is not only the major factor that influences the velocity and displacement amplitude of pulse‐type ground motion but also can cause considerable influence on the acceleration amplitude of original ground motion. It is also the immediate causes of the larger inelastic displacement ratio and the smaller inelastic strength reduction factor for pulse‐type ground motions. That will result in higher displacement and strength demands for building structure when the structure is subjected to pulse‐type ground motions.

Effects of near-fault ground motions on the nonlinear behaviour of reinforced concrete framed buildings

The design provisions of current seismic codes are generally not very accurate for assessing effects of near-fault ground motions on reinforced concrete (r.c.) spatial frames, because only far-fault ground motions are considered in the seismic codes. Strong near-fault earthquakes are characterized by long-duration (horizontal) pulses and high values of the ratio α PGA of the peak value of the vertical acceleration, PGAV, to the analogous value of the horizontal acceleration, PGAH, which can become critical for girders and columns. In this work, six- and twelve-storey r.c. spatial frames are designed according to the provisions of the Italian seismic code, considering the horizontal seismic loads acting (besides the gravity loads) alone or in combination with the vertical ones. The nonlinear seismic analysis of the test structures is performed using a step-by-step procedure based on a two-parameter implicit integration scheme and an initial stress-like iterative procedure. A lumped plasticity model based on the Haar-Karman principle is adopted to model the inelastic behaviour of the frame members. For the numerical investigation, five near-fault ground motions with high values of the acceleration ratio α PGA are considered. Moreover, following recent seismological studies, which allow the extraction of the largest (horizontal) pulse from a near-fault ground motion, five pulse-type (horizontal) ground motions are selected by comparing the original ground motion with the residual motion after the pulse has been extracted. The results of the nonlinear dynamic analysis carried out on the test structures highlighted that horizontal and vertical components of near-fault ground motions may require additional consideration in the seismic codes.

A nonlinear signal-based control method and its applications to input identification for nonlinear SIMO problems

The problem of control system design can be conceptualised as identifying an input signal to a plant (the system to be controlled) so that the corresponding output matches that of a pre-defined reference signal. Primarily, this problem is solved via well-known techniques based upon the principle of feedback design, an essential component for ensuring stability and robustness of the controlled system. However, feedforward design techniques also have a large part to play, whereby (in the absence of feedback control and assuming that the plant is stable) a model of the plant dynamics can be used to modify the reference signal so that the resultant feedforward input signal generates a plant output signal that is sufficiently close to the original reference signal.The principal objective of this paper is to introduce a new nonlinear control method, called nonlinear signal-based control (NSBC) that can be executed as an on-line technique of feedforward compensation (used synonymously here with the phrase ‘input identification’) and an off-line technique of feedback compensation. NSBC determines the feedforward input signal to the plant by using an error signal, determined from the difference between the output signals from a linear model of the plant and from the nonlinear plant, under the same input signal. The efficacy of NSBC is examined via numerical examples using Matlab/Simulink and compared with alternative well-known methods based upon inverse transfer function compensation and also the method of high gain feedback control.NSBC was found to provide the most accurate input identification in all the examined cases of linear or nonlinear single-input, single-output and single-input, multi-output (SIMO) systems. Furthermore, in problems of structural and earthquake engineering, NSBC was also found to be particularly effective in estimating the original ground motion from a nonlinear SIMO system and its response.

Fully Nonstationary Spatially Variable Ground Motion Simulations Based on a Time-Varying Power Spectrum Model

By analyzing the evolutionary spectrum method for multivariate nonstationary stochastic processes, a simulation method for fully nonstationary spatially variable ground motion is proposed based on the Kameda time-varying power spectrum model. This method can properly simulate nonstationary spatially variable ground motion based on a target response spectrum. Two numerical examples, in which the Kameda time-varying power spectra are calculated for different conditions, are presented to demonstrate the capabilities of the proposed method. In the first example, the nonstationary spatially variable ground motion that satisfies the time-frequency characteristics and response characteristics of the original ground motion is simulated by identifying the parameters of the given time-varying power spectrum. In the second example, the ground motion that satisfies the design response spectra is simulated by defining the parameters of the time-varying power spectrum directly. The results demonstrate that the method can effectively simulate nonstationary spatially variable ground motion, which implies that the proposed method can be used in engineering applications.

On Near‐Fault Ground Motion Characteristics Through Multi‐Scale Method

AbstractGround motion recorded in near‐fault regions that possesses long‐period pulse is a special destructive ground motion. For further research on the constituent of low‐frequency component and its pulse characteristics, a decomposition method based on multi‐scale analysis method in wavelet theory is proposed. Accordingly, an intact ground motion can be decomposed into multiple components having different frequency contents. Firstly, the validity and accuracy of this decomposition method are elaborated in three aspects which are the frequency domain, time domain and the dynamic response. Secondly, a suite of 53 typical near‐fault ground motions recorded from 12 recent major earthquakes are decomposed through this method, then a total of 266 ground motion components are obtained. Thirdly, a quantitative statistical study of the variation of the long period components contained in near‐fault ground motions with the impact of site and rupture distance is carried out in this paper. Lastly, predominant component is used as the simplified model of dominant pulse, and the variation of velocity amplitude and pulse period with the impact of magnitude and rupture distance is presented. It is concluded that: the period of the component which is the main ingredient of near‐fault ground motions is within 0.2∼2 s; the long‐period component contained in soil ground motions is richer than in rocks; in near‐fault area where the rupture distance is 0∼15 km, the proportion of the long period component decreases along with rupture distance increase; PGVp, the velocity amplitude of predominant component, is about 0.6 times of PGV, the velocity amplitude of original ground motion, and a clear linear relation is found between them; PGVp decreases as rupture distance increases, and will be larger in great earthquakes; logarithm of the pulse periods Tp increases linearly as magnitude increases.

Generation of Nonstationary Artificial Ground Motion Based on the Hilbert Transform

Abstract In this paper, a synthesizing method based on the Hilbert transform is proposed to generate artificial earthquake ground‐motion samples, the nonstationary features of which are similar to those of given natural seismic recordings. With this aim in mind, the given natural seismogram, assumed to be a sample of some underlying random process, is first processed by the Hilbert transform to obtain its instantaneous amplitude and instantaneous phase functions. The instantaneous amplitude function is treated as an invariant variable for which the value will be preserved into the synthetic samples, whereas the instantaneous phase function is treated stochastically to address the randomness of the underlying ground‐motion process. By establishing the stochastic model for the instantaneous phase function, the underlying ground‐motion random process can be determined, and a series of its samples can be generated numerically. Synthetic examples demonstrate that the ground‐motion samples generated by the proposed method can maintain the general time‐variant features of original natural ground motions, and the method has application potential either in the engineering practice or in earthquake engineering research.

Effect of Ground Motion Modification Technique on Seismic Geotechnical Engineering Analyses

Ground motion modification (or spectral matching) has been criticized, but has many appealing characteristics and is widely used in practice. Modification of ground motions can be performed in either the time domain or the frequency domain. Depending on the choice of modification technique, modified ground motions can be significantly different from each other as well as from the original ground motion. This paper studies the impact of these differences on seismic geotechnical analyses for two different site profiles using two earthquake scenarios and a total of 20 ground motions. This study shows that the final results are influenced by many factors such as the original (seed) ground motion, the target spectrum, and the local site conditions, in addition to the ground motion modification technique used. The results also show that while both techniques can significantly modify the original ground motion, neither technique is consistently more conservative than the other. Therefore, a general conclusion that a particular technique results in ground motions that yield the largest intensity parameters cannot be made a priori.

Selecting and scaling real ground motion records using harmony search algorithm

In this study, a solution model is proposed to obtain input ground motion datasets compatible with given design spectra based on meta-heuristic harmony search algorithm. The utility of the solution model is demonstrated by generating ground motion datasets matching the Eurocode-8 design spectra for different soil types out of an extensive database of recorded motions. A total of 352 records are selected from the Pacific Earthquake Engineering Center (PEER) Strong Motion Database based on magnitude, distance, and site conditions to form the original ground motion domain. Then, the proposed harmony search based solution algorithm is applied on the pre-selected 352 time-series to obtain the ground motion record sets compatible with design spectra. The results demonstrate that the proposed HS based solution model provides an efficient way to develop input ground motion record sets that are consistent with code-based design spectra.

A shift approach for the dynamic response of rigid‐plastic systems

AbstractA shift approach is presented for evaluating and interpreting the response of rigid‐perfectly plastic single‐degree‐of‐freedom systems to dynamic loading. Scaling laws for such systems are, as the term suggests, multiplicative in nature, relating peak dynamic response to products of key problem parameters such as linear spectral coordinates, force reduction coefficient and peak values of the excitation and its time derivatives. Contrary to classical laws, the proposed approach is additive, imposing a shift in the ordinates and the abscissa of the excitation function by means of a set of parameters uniquely related to the yielding resistance of the system. The dynamic response is then obtained by integrating the modified excitation function in a linear‐like manner within a particular yielding branch, for the nonlinearity is incorporated into the forcing term. The mathematical validity of the approach is demonstrated analytically and its importance is highlighted for systems with symmetric yielding resistance subjected to near‐fault earthquake motions. The modified excitation function may be discontinuous between different yielding branches and relates uniquely to the development of plastic deformation. It is thereby referred to as Plastic Input Motion (PIM). It is shown that the ordinates and the duration of this function may be significantly (yet not necessarily) smaller than those of the original ground motion depending on yield strength. The relationship of the proposed approach to the existing methods and parameters of earthquake engineering such as Newmark's sliding block and relative ground acceleration, is discussed. Copyright © 2010 John Wiley & Sons, Ltd.

Pulse extraction and displacement response evaluation for long-period ground motions

Long-period ground motions with directivity and/or path effects are often characterised by the presence of velocity and acceleration pulses in the lowermost frequency range. An objective of this article is to present a discrete-time signal processing method for isolating these pulses. In this method, the velocity and the acceleration pulses are identified by applying a low-pass discrete-time filter Hlp (ω) at a suitable cut-off frequency f c to the Fourier transforms of the original velocity and acceleration ground motion time histories, respectively. Another objective of this article is to present a mathematical expression for evaluating the linear displacement response of a single degree-of-freedom (SDF) system by simultaneous application of two frequency modulators, Hlp (ω) and Hu (ω), to the original ground excitation. By using only the pulse component of the ground motion as the excitation force, it is shown that the displacement response of the SDF system with natural period exceeding a certain valu...

Estimating the size of an earthquake using short-period seismograms of the first three seconds: A simulated experiment using the 1999 Chi-Chi earthquake sequence

Most of the present earthquake early warning systems are based on broadband or strong motion recordings. However, the short-period instruments are still deployed. It is well-known that short-period recordings have saturation problems for large earthquakes when estimating the size of an earthquake. Thus, it is necessary to make clear the magnitude at which saturation starts to occur for the commonly used τc and Pd measurements, respectively. To investigate the possibility of using short-period seismic recordings for earthquake early warning, we conducted a simulated experiment using the strong motion data of the 1999 Chi-Chi earthquake sequence including its main shock and 31 aftershocks, with magnitude span from 4 to 7.6. The strong motion acceleration recordings were convolved with the instrument response of short-period seismographs in northern China to simulate short-period seismograms. Parameters τc and Pd from the first-three-second seismograms were calculated for the simulated short-period recordings and compared with that obtained by the original strong ground motion recordings. The result showed that to some extent, short-period recordings can be used for threshold earthquake early warning, while the magnitude saturation of Pd estimation can be up to 6.5, better than τc estimation.

Quantitative Classification of Near-Fault Ground Motions Using Wavelet Analysis

A method is described for quantitatively identifying ground motions containing strong velocity pulses, such as those caused by near-fault directivity. The approach uses wavelet analysis to extract the largest velocity pulse from a given ground motion. The size of the extracted pulse relative to the original ground motion is used to develop a quantitative criterion for classifying a ground motion as “pulselike.” The criterion is calibrated by using a training data set of manually classified ground motions. To identify the subset of these pulselike records of greatest engineering interest, two additional criteria are applied: the pulse arrives early in the ground motion and the absolute amplitude of the velocity pulse is large. The period of the velocity pulse (a quantity of interest to engineers) is easily determined as part of the procedure, using the pseudoperiods of the basis wavelets. This classification approach is useful for a variety of seismology and engineering topics where pulselike ground motions are of interest, such as probabilistic seismic hazard analysis, ground- motion prediction (“attenuation”) models, and nonlinear dynamic analysis of structures. The Next Generation Attenuation (nga) project ground motion library was processed using this approach, and 91 large-velocity pulses were found in the fault- normal components of the approximately 3500 strong ground motion recordings considered. It is believed that many of the identified pulses are caused by near-fault directivity effects. The procedure can be used as a stand-alone classification criterion or as a filter to identify ground motions deserving more careful study.

Using the total least squares method for seismic correction of recordings from unknown instruments

This paper describes the correction or recovery of the original ground motion acceleration time histories from accelerometer digital records. It deals specifically with the situation where the recording accelerometer instrument is unknown. This is the case with some older (legacy) records. The term instrument implies all processes that have modified the time history in some way, such as the accelerometer response transfer function, anti-alias filters used in A/D conversion, digital quantisation, etc. The total least squares (TLS) method is used to identify the unknown system (instrument) that must be used to de-convolute the recorded time histories. This approach is compared and contrasted with the recursive least squares method (QR-RLS) and a standard second order, single-degree-of-freedom, idealised instrument de-convolution. A range of seismic events from Iceland and Taiwan (SMART-1 array) are considered. These data sets include a number of different strong motion accelerometers, from Iceland: the SMA-1, DCA-333, A-700, SSA-1 instruments and the SA-3000 used in the SMART-1 array. Without any assumed information about the instrument the TLS is shown to provide a reasonable estimate of its characteristics from just the recorded time history data.