Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets: artificial and historic records

A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum (EPS). Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average (ARMA) filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals’ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice

A stochastic approach to synthesizing response spectrum compatible seismic accelerograms

Regulatory agencies require the use of artificial accelerograms satisfying specific criteria of compatibility with a given design spectrum, as input for certain types of analyses for the aseismic design of critical facilities. Most of the numerical methods for simulating seismic motions compatible with a specified design (target) spectrum proposed by various researchers require that a number of real recorded seismic accelerograms of appropriate frequency content is available. To by-pass this requirement, a previously established in the literature probabilistic approach to yield simulated earthquake records whose response spectrum achieves on average a certain level of agreement with a target spectrum is employed in the present paper. At the core of the above method lies the adoption of an appropriate parametric power spectrum model capable of accounting for various site-specific soil conditions. In this regard, the potential of two different, commonly, used spectral forms is evaluated for this purpose in context with the design spectrum defined by the European Code provisions. Next, an iterative wavelet-based matching procedure is applied to the thus acquired records to enhance, individually, the agreement of the corresponding response spectra with the targeted one. Special attention is paid to ensure that the velocity and the displacement time histories associated with the finally obtained artificial accelerograms are physically sound by means of appropriate baseline correction techniques

Joint time-frequency representation of simulated earthquake accelerograms via the adaptive chirplet transform

Seismic accelerograms are inherently nonstationary signals since both the intensity and frequency content of seismic events evolve in time. The adaptive chirplet transform is a signal processing technique for joint time-frequency representation of nonstationary data. Analysis of a signal via the adaptive chirplet decomposition in conjunction with the Wigner-Ville distribution yields the so-called adaptive spectrogram which constitutes a valid representation of the signal in the time-frequency plane. In this paper the potential of this technique for capturing the temporal evolution of the frequency content of strong ground motions is assessed. In this regard, simulated nonstationary earthquake accelerograms compatible with an exponentially modulated and appropriately filtered Kanai-Tajimi spectrum are processed using the adaptive chirplet transform. These are samples of a random process whose evolutionary power spectrum can be represented by an analytical expression. It is suggested that the average of the ensemble of the adaptive chirplet spectrograms can be construed as an estimate of the underlying evolutionary power spectrum. The obtained numerical results show, indeed, that the estimated evolutionary power spectrum is in a good agreement with the one defined analytically. This fact points out the potential of the adaptive chirplet analysis for as a tool for capturing localized frequency content of arbitrary data- banks of real seismic accelerograms

A Bayesian Framework for Estimating Seismic Wave Arrival Time

Because earthquakes have a large impact on human society, statistical methods for better studying earthquakes are required. One characteristic of earthquakes is the arrival time of seismic waves at a seismic signal sensor. Once we can estimate the earthquake arrival time accurately, the earthquake location can be triangulated, and assistance can be sent to that area correctly. This study presents a Bayesian framework to predict the arrival time of seismic waves with associated uncertainty. We use a change point framework to model the different conditions before and after the seismic wave arrives. To evaluate the performance of the model, we conducted a simulation study where we could evaluate the predictive performance of the model framework. The results show that our method has acceptable performance of arrival time prediction with accounting for the uncertainty

Assessment of wavelet-based representation techniques for the characterization of stochastic processes modelling pulse-like strong ground motions

Recently, the Meyer wavelet packets transform (MWPT), the harmonic wavelet transform (HWT), and the S-transform have been used to process recorded earthquake induced strong ground motions (GMs) in various earthquake engineering and engineering seismology applications. In this paper, the potential of these three wavelet-based time-frequency representation (TFR) techniques to identify and to characterize low-frequency pulse-like content in GMs is assessed. This is achieved by processing ensembles of simulated non-stationary time-histories with known energy content upon appropriately fine-tuning the considered TFRs. Next, the ensemble average wavelet transform is used to characterize the energy distribution of the time-histories on the time-frequency plane, within a Monte-Carlo analysis framework. Specifically, the considered time-histories are realizations of sums of uncorrelated uniformly modulated stochastic processes characterized by analytically known evolutionary power spectra (EPSDs). These EPSDs are judicially defined to model the frequency content of pulse-like GMs. Pertinent numerical results considering EPSDs compatible with the elastic design spectrum of the current European (EC8) aseismic code provisions are included, in which pre-specified pulse-type frequency content is introduced by adding low-frequency "patches of energy". The reported numerical data indicate that the HWT provides for smoother estimates of the considered EPSDs than the MWPT. Further, the S-transform is more accurate than both the HWT and the MWPT in identifying the time location and central frequency of the low frequency components contained in the considered artificial pulse-like accelerograms. Overall, this study sheds light into the challenges of detecting low frequency content “corrupted” by higher frequency components in artificial signals modelling pulse-like accelerograms in an effort to inform best practices in the application of TFR techniques to characterize low frequency pulses in recorded GMs

Response Analysis of Wood Structures Under Natural Hazard Dynamic Loads

The basic requirements needed for response analysis of wood structures against natural hazards are reviewed. A method for stochastic dynamic analysis of wood structures, which allows investigations into their performance and safety under natural hazards such as earthquakes and severe winds, is presented. To illustrate the method, earthquake ground motions are modeled as a stochastic process with Gaussian white noise properties. A single-degree-of-freedom wood structural system is modeled by a hysteretic constitutive law that produces a smoothly varying hysteresis. It models previously observed behavior of wood joints and structural systems, namely, (1) nonlinear, inelastic behavior, (2) stiffness degradation, (3) strength degradation, and (4) pinching. The constitutive law takes into account the experimentally observed dependence of wood joints' response to the input and response at an earlier time (known as memory). Hysteresis shapes produced by the proposed model compare favorably with common wood joints. The hysteresis model can produce a wide variety of hysteresis shapes, degradations, and pinching behavior to model a whole gamut of possible combinations of materials and joint configurations in wood construction. The nonstationary response statistics of a single-degree-of-freedom wood building subjected to white noise excitations are obtained by Monte Carlo simulation and stochastic equivalent linearization. The latter is shown to give a reasonably accurate prediction of the system's response statistics, which may be used in calculating design response values. The method of analysis is general and may be used to study the response of various kinds of structural systems, including multi-degree-of-freedom systems, as long as appropriate structural models are available and appropriate hysteresis model parameters for these systems are known

Damage classification and estimation in experimental structures using time series analysis and pattern recognition

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Improving Loss Estimation for Woodframe Buildings. Volume 2: Appendices

This report documents Tasks 4.1 and 4.5 of the CUREE-Caltech Woodframe Project. It presents a theoretical and empirical methodology for creating probabilistic relationships between seismic shaking severity and physical damage and loss for buildings in general, and for woodframe buildings in particular. The methodology, called assembly-based vulnerability (ABV), is illustrated for 19 specific woodframe buildings of varying ages, sizes, configuration, quality of construction, and retrofit and redesign conditions. The study employs variations on four basic floorplans, called index buildings. These include a small house and a large house, a townhouse and an apartment building. The resulting seismic vulnerability functions give the probability distribution of repair cost as a function of instrumental ground-motion severity. These vulnerability functions are useful by themselves, and are also transformed to seismic fragility functions compatible with the HAZUS software. The methods and data employed here use well-accepted structural engineering techniques, laboratory test data and computer programs produced by Element 1 of the CUREE-Caltech Woodframe Project, other recently published research, and standard construction cost-estimating methods. While based on such well established principles, this report represents a substantially new contribution to the field of earthquake loss estimation. Its methodology is notable in that it calculates detailed structural response using nonlinear time-history structural analysis as opposed to the simplifying assumptions required by nonlinear pushover methods. It models physical damage at the level of individual building assemblies such as individual windows, segments of wall, etc., for which detailed laboratory testing is available, as opposed to two or three broad component categories that cannot be directly tested. And it explicitly models uncertainty in ground motion, structural response, component damageability, and contractor costs. Consequently, a very detailed, verifiable, probabilistic picture of physical performance and repair cost is produced, capable of informing a variety of decisions regarding seismic retrofit, code development, code enforcement, performance-based design for above-code applications, and insurance practices