Real-time Loss Estimation for Instrumented Buildings

Motivation. A growing number of buildings have been instrumented to measure and record earthquake motions and to transmit these records to seismic-network data centers to be archived and disseminated for research purposes. At the same time, sensors are growing smaller, less expensive to install, and capable of sensing and transmitting other environmental parameters in addition to acceleration. Finally, recently developed performance-based earthquake engineering methodologies employ structural-response information to estimate probabilistic repair costs, repair durations, and other metrics of seismic performance. The opportunity presents itself therefore to combine these developments into the capability to estimate automatically in near-real-time the probabilistic seismic performance of an instrumented building, shortly after the cessation of strong motion. We refer to this opportunity as (near-) real-time loss estimation (RTLE). Methodology. This report presents a methodology for RTLE for instrumented buildings. Seismic performance is to be measured in terms of probabilistic repair cost, precise location of likely physical damage, operability, and life-safety. The methodology uses the instrument recordings and a Bayesian state-estimation algorithm called a particle filter to estimate the probabilistic structural response of the system, in terms of member forces and deformations. The structural response estimate is then used as input to component fragility functions to estimate the probabilistic damage state of structural and nonstructural components. The probabilistic damage state can be used to direct structural engineers to likely locations of physical damage, even if they are concealed behind architectural finishes. The damage state is used with construction cost-estimation principles to estimate probabilistic repair cost. It is also used as input to a quantified, fuzzy-set version of the FEMA-356 performance-level descriptions to estimate probabilistic safety and operability levels. CUREE demonstration building. The procedure for estimating damage locations, repair costs, and post-earthquake safety and operability is illustrated in parallel demonstrations by CUREE and Kajima research teams. The CUREE demonstration is performed using a real 1960s-era, 7-story, nonductile reinforced-concrete moment-frame building located in Van Nuys, California. The building is instrumented with 16 channels at five levels: ground level, floors 2, 3, 6, and the roof. We used the records obtained after the 1994 Northridge earthquake to hindcast performance in that earthquake. The building is analyzed in its condition prior to the 1994 Northridge Earthquake. It is found that, while hindcasting of the overall system performance level was excellent, prediction of detailed damage locations was poor, implying that either actual conditions differed substantially from those shown on the structural drawings, or inappropriate fragility functions were employed, or both. We also found that Bayesian updating of the structural model using observed structural response above the base of the building adds little information to the performance prediction. The reason is probably that Real-Time Loss Estimation for Instrumented Buildings ii structural uncertainties have only secondary effect on performance uncertainty, compared with the uncertainty in assembly damageability as quantified by their fragility functions. The implication is that real-time loss estimation is not sensitive to structural uncertainties (saving costly multiple simulations of structural response), and that real-time loss estimation does not benefit significantly from installing measuring instruments other than those at the base of the building. Kajima demonstration building. The Kajima demonstration is performed using a real 1960s-era office building in Kobe, Japan. The building, a 7-story reinforced-concrete shearwall building, was not instrumented in the 1995 Kobe earthquake, so instrument recordings are simulated. The building is analyzed in its condition prior to the earthquake. It is found that, while hindcasting of the overall repair cost was excellent, prediction of detailed damage locations was poor, again implying either that as-built conditions differ substantially from those shown on structural drawings, or that inappropriate fragility functions were used, or both. We find that the parameters of the detailed particle filter needed significant tuning, which would be impractical in actual application. Work is needed to prescribe values of these parameters in general. Opportunities for implementation and further research. Because much of the cost of applying this RTLE algorithm results from the cost of instrumentation and the effort of setting up a structural model, the readiest application would be to instrumented buildings whose structural models are already available, and to apply the methodology to important facilities. It would be useful to study under what conditions RTLE would be economically justified. Two other interesting possibilities for further study are (1) to update performance using readily observable damage; and (2) to quantify the value of information for expensive inspections, e.g., if one inspects a connection with a modeled 50% failure probability and finds that the connect is undamaged, is it necessary to examine one with 10% failure probability

Reliability problems in eartquake engineering

This monograph deals with the problem of reliability analysis in the field of Earthquake Engineering. Chapter 1 is devoted to a summary of the most widely used reliability methods, with emphasis on Monte Carlo and solver surrogate techniques used in the subsequent chapters. Chapter 2 presents a discussion of the Monte Carlo from the viewpoint of Information Theory. Then, a discussion is made in Chapter 3 on the selection of random variables in Earthquake Engineering. Next, some practical methods for computing failure probabilities under seismic loads are reported in Chapter 4. Finally, a method for reliability-based design optimization under seismic loads is presented in Chapter 5

Uncertainty Propagation and Feature Selection for Loss Estimation in Performance-based Earthquake Engineering

This report presents a new methodology, called moment matching, of propagating the uncertainties in estimating repair costs of a building due to future earthquake excitation, which is required, for example, when assessing a design in performance-based earthquake engineering. Besides excitation uncertainties, other uncertain model variables are considered, including uncertainties in the structural model parameters and in the capacity and repair costs of structural and non-structural components. Using the first few moments of these uncertain variables, moment matching requires only a few well-chosen point estimates to propagate the uncertainties to estimate the first few moments of the repair costs with high accuracy. Furthermore, the use of moment matching to estimate the exceedance probability of the repair costs is also addressed. These examples illustrate that the moment-matching approach is quite general; for example, it can be applied to any decision variable in performance-based earthquake engineering. Two buildings are chosen as illustrative examples to demonstrate the use of moment matching, a hypothetical three-story shear building and a real seven-story hotel building. For these two examples, the assembly-based vulnerability approach is employed when calculating repair costs. It is shown that the moment-matching technique is much more accurate than the well-known First-Order-Second-Moment approach when propagating the first two moments, while the resulting computational cost is of the same order. The repair-cost moments and exceedance probability estimated by the moment-matching technique are also compared with those by Monte Carlo simulation. It is concluded that as long as the order of the moment matching is sufficient, the comparison is satisfactory. Furthermore, the amount of computation for moment matching scales only linearly with the number of uncertain input variables. Last but not least, a procedure for feature selection is presented and illustrated for the second example. The conclusion is that the most important uncertain input variables among the many influencing the uncertainty in future repair costs are, in order of importance, ground-motion spectral acceleration, component capacity, ground-motion details and unit repair costs

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 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 degreeof-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. It is found that the novel feature of iterative matching between the excitation response spectrum damping ratio and the ELP damping ratio reduces drastically the error of the estimates (i.e., by an order of magnitude) obtained by non-iterative application of the framework

Seismic vulnerability of above-ground storage tanks with unanchored support conditions for Na-tech risks based on Gaussian process regression

AbstractThis paper aims to investigate the seismic vulnerability of an existing unanchored steel storage tank ideally installed in a refinery in Sicily (Italy), along the lines of performance-based earthquake engineering. Tank performance is estimated by means of component-level fragility curves for specific limit states. The assessment is based on a framework that relies on a three-dimensional finite element (3D FE) model and a low-fidelity demand model based on Gaussian process regression, which allows for cheaper simulations. Moreover, to approximate the system response corresponding to the random variation of both peak ground acceleration and liquid filling level, a second-order design of experiments method is adopted. Hence, a parametric investigation is conducted on a specific existing unanchored steel storage tank. The relevant 3D FE model is validated with an experimental campaign carried out on a shaking table test. Special attention is paid to the base uplift due to significant inelastic deformations that occur at the baseplate close to the welded baseplate-to-wall connection, offering extensive information on both capacity and demand. As a result, the tank performance is estimated by means of component-level fragility curves for the aforementioned limit state which are derived through Monte Carlo simulations. The flexibility of the proposed framework allows fragility curves to be derived considering both deterministic and random filling levels. The comparison of the seismic vulnerability of the tank obtained with probabilistic and deterministic mechanical models demonstrates the conservatism of the latter. The same trend is also exhibited in terms of risk assessment

Nonlinear effects in ground motion simulations: modeling variability, parametric uncertainty and implications in structural performance predictions

While site effects are accounted for in most modern U.S. seismic design codes for building structures, there exist no standardized procedures for the computationally efficient integration of nonlinear ground response analyses in broadband ground motion simulations. In turn, the lack of a unified methodology affects the prediction accuracy of site-specific ground motion intensity measures, the evaluation of site amplification factors when broadband simulations are used for the development of hybrid attenuation relations and the estimation of inelastic structural performance when strong motion records are used as input in aseismic structural design procedures. In this study, a set of criteria is established, which quantifies how strong nonlinear effects are anticipated to manifest at a site by investigating the empirical relation between nonlinear soil response, soil properties, and ground motion characteristics. More specifically, the modeling variability and parametric uncertainty of nonlinear soil response predictions are studied, along with the uncertainty propagation of site response analyses to the estimation of inelastic structural performance. Due to the scarcity of design level ground motion recording, the geotechnical information at 24 downhole arrays is used and the profiles are subjected to broadband ground motion synthetics. For the modeling variability study, the site response models are validated against available downhole array observations. The site and ground motion parameters that govern the intensity of nonlinear effects are next identified, and an empirical relationship is established, which may be used to estimate to a first approximation the error introduced in ground motion predictions if nonlinear effects are not accounted for. The soil parameter uncertainty in site response predictions is next evaluated as a function of the same measures of soil properties and ground motion characteristics. It is shown that the effects of nonlinear soil property uncertainties on the ground-motion variability strongly depend on the seismic motion intensity, and this dependency is more pronounced for soft soil profiles. By contrast, the effects of velocity profile uncertainties are less intensity dependent and more sensitive to the velocity impedance in the near surface that governs the maximum site amplification. Finally, a series of bilinear single degree of freedom oscillators are subjected to the synthetic ground motions computed using the alternative soil models, and evaluate the consequent variability in structural response. Results show high bias and uncertainty of the inelastic structural displacement ratio predicted using the linear site response model for periods close to the fundamental period of the soil profile. The amount of bias and the period range where the structural performance uncertainty manifests are shown to be a function of both input motion and site parameters.Ph.D.Committee Chair: Dominic Assimaki; Committee Member: Bruce R. Ellingwood; Committee Member: Glenn J. Rix; Committee Member: Karim Sabra; Committee Member: Zhigang Pen

A Geostatistical Approach toward Shear Wave Velocity Modeling and Uncertainty Quantification in Seismic Hazard

The ground motion parameters such as amplitude, frequency content and the duration can be affected by the local site condition and may result in amplification or de-amplification to the original bedrock motion. Shear wave velocity is an important site parameter to describe the site condition and is widely used in estimating site response, classifying sites in recent building codes and loss estimation. This dissertation is aimed at: modeling the spatial variation of shear wave velocity using geostatistical tools; improve the random field framework for estimating soil properties to account for multiple sources of data; develop finite element model to qualify the uncertainty propagation in dynamic site response; introduce the response surface concept into seismic hazard analysis and quantifying the uncertainty propagation in dynamic site response caused by the variation of shear wave velocity and design parameters. To model the spatial variation of shear wave velocity, a multiscale random field-based framework is presented and applied to map Vs30 - the time-averaged shear wave velocity in the top 30 meters of subsurface material - over extended areas. In this framework, the random field concept is employed to model the horizontal variation of shear wave velocity. Suzhou Site is selected as the research area and its measured shear wave velocity data is combined with the U.S. Geological Survey (USGS) slope-based Vs30 map for mapping the Vs30 around whole research area. Moreover, a different method of integrating multiple sources of data is used and tested based on a synthetic digital field. To quantify the uncertainty propagation in dynamic site response caused by the variation of shear wave velocity, the finite element method (FEM) is developed and combined with random field realizations of shear wave velocity profiles. A viscoelastic constitutive model is implemented in the FEM model to account for the non-linear hysteresis response of subsurface materials under cyclic loadings. The analyzed site responses, as well as the input parameters generated with Monte Carlo simulations (MCS), are then used to study the peak acceleration at site surface subjected to a given input seismic wave. Finally, the response surface method and the first order second-moment method (FOSM) are integrated into dynamic site response analysis to characterize the variation of site performance caused by spatial variation of shear wave velocity. Through illustrative examples, the effectiveness, advantage, practicability, and significance of improved random field framework and developed uncertainty propagation evaluation methodology are demonstrated