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Abstract

Although large ground motion databases are widely available today, in many occasions, the selection of ground motion records still hampers the use of nonlinear response history analysis in seismic engineering practice. This paper presents a novel optimization-based tool for creating subsets of ground motion records extracted from large databases. Existing heuristic methods select and/or scale ground motion records so that their mean spectrum fits a target spectrum, while methods that also consider the variability have been proposed. The paper presents a new and simple approach that selects and, if necessary, scales the ground motion records so that both their mean and variability optimally fit a target spectrum. The proposed approach is a multiobjective optimization methodology that can be solved quickly and efficiently with an evolutionary optimization algorithm. Contrary to other approaches, a Monte Carlo step is not required, while the proposed procedure is easy to implement and able to quickly search large databases. Furthermore, among the suite of optimum solutions (Pareto front) obtained, a criterion for choosing the most suitable design is proposed. The efficiency of the proposed tool is demonstrated with two numerical examples. In the first example, the target spectrum is a uniform hazard spectrum, while in the second example, a conditional mean spectrum (CMS) is adopted instead.

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... In that work, a thorough review of selection schemes is presented and the need for guidance regarding the use of metaheuristic optimization algorithms (such as GA) is emphasized, since they become more and more popular in GM selection applications. One more benefit in using GA for the process of GM selection, as pointed out in Ref. [43], is the elimination of Monte Carlo simulations along with the increased efficiency. The notion of efficiency in the optimization process is frequently used to describe that the resulting GM sets have a good match with the targets and that the optimization process is performed quickly. ...
... It is well understood that GM selection is an optimization problem that aims to find the optimal solution(s) that satisfy the objectives without exploring the entire solution space, as this is impractical, if not unfeasible. The number of solutions are the possible combinations of records given by the binomial coefficient, which leads to huge solution spaces, even for small databases with a few hundred records [41][42][43]. ...
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Ground motion record selection methodologies are commonly developed to ensure that the input excitation used in response history analyses embodies essential conditions such as spectral compatibility, hazard and intensity measure consistency, seismological and site-specific criteria, always performing in a computationally efficient manner. A methodology utilizing genetic algorithms is revisited here, expanded to select multi-component ground motions and satisfying the typically required selection objectives of earthquake engineering applications, while ensuring increased efficiency. Multi-objective optimization is performed, claimed to be superior in delivering robust results that account for spectral compatibility in first and second order statistics (mean and standard deviation) in a wide range of spectral values, as well as satisfying seismological and site-specific criteria. A unique contribution is the ability to include probability distribution targets in specific ordinates of the spectrum, on top of the mean and standard deviation, allowing for more refined ground motion sets that can be used to reduce the number of records required in response history analyses. Additionally, a novel benchmarking process to assess the efficiency of ground motion record methodologies is introduced here, in terms of providing sets that are globally-optimal solutions to the optimization problem. Through this benchmarking algorithm, the proposed methodology appears to be impeccable in extracting the best possible ground motion sets.
... HS is a kind of meta-heuristic search algorithm which tries to harmonize the improvisation process of musicians in finding together a pleasing harmony. The number of articles about ground motion record selection has grown in recent years [30][31][32][33] using meta-heuristic algorithms. Initial solution value for the decision variables are not required in HS and searching process is fully stochastic. ...
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Nonlinear time history analysis is an analytical method generally used in performance-based seismic design. With this method, seismic responses are obtained more realistically. Selection of ground motion records for nonlinear time history analysis is an important step since it strongly affects the analysis results. Therefore, it has always been a matter of curiosity to investigate the effect of the characteristics, content and number of the records on the analysis results. In this study, seismic responses of regular and irregular RC frames were investigated by varying the number of real ground motion records in a set. For this purpose, 13 different groups that contain three to hundred real ground motion records in size in a set have been considered and ten different earthquake record sets are obtained for each group. Ground motion selection procedure of Eurocode-8 was considered and a total of 130 sets were used for nonlinear response analysis of RC frames. Global drift ratio, maximum floor acceleration, inter-story drift ratio and six different intensity measures (IMs) were used to investigate the effect of the number of records. According to analysis results, nonlinear responses of RC frames are more stable and might be sufficient when the number of real records in a set is higher than seven according to Eurocode-8. Results indicate that if the number of real records in a set are lower than seven, conservative seismic responses can be found since the maximum rather than mean response values are used. It is observed that dispersion of seismic demands and mean to median ratios can be increased if the number of real records in a set is higher than ten. In addition, the correlation between some of IMs and seismic demands increase when the number of records in a set increased from three to seven and it remains stable from seven to hundred records. Furthermore, 7, 8, 15 and 22 records show the lowest error terms of considered engineering demand parameters for regular and irregular RC frames.
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Selection of appropriate ground motion (GM) records for nonlinear dynamic analysis (NDA) of structures plays a crucial role to estimate structural responses reasonably. In this study, a multi-functional solution model utilizing stochastic harmony search (HS) algorithm is proposed to obtain scaled or unscaled real GM component sets for uni-directional analysis of two-dimensional structural models and GM component pair sets for bi-directional analysis of three-dimensional structural models. The solution model allows to consider compatibility between target spectrum and both mean spectrum and individual spectra besides desired spectral variability. Uniform hazard spectrum, conditional mean spectrum or scenario-based spectrum can be selected as target spectrum. Combined response spectra of selected component pairs such as SRSS, geometric mean and maximum directional can also be handled by the solution model. To demonstrate the efficiency of the solution model, various examples were presented. In addition, a sensitivity analysis was performed to evaluate the effect of HS parameters on the solution accuracy. Results show that the proposed solution model can be regarded as efficient to obtain appropriate GM record sets to be used for NDAs within a probabilistic seismic design and/or performance assessment framework.
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Existing earthquake ground motion (GM) selection methods for the seismic assessment of structural systems focus on spectral compatibility in terms of either only central values or both central values and variability. In this way, important selection criteria related to the seismology of the region, local soil conditions, strong GM intensity and duration as well as the magnitude of scale factors are considered only indirectly by setting them as constraints in the pre-processing phase in the form of permissible ranges. In this study, a novel framework for the optimum selection of earthquake GMs is presented, where the aforementioned criteria are treated explicitly as selection objectives. The framework is based on the principles of multi-objective optimization that is addressed with the aid of the Weighted Sum Method, which supports decision making both in the pre-processing and post-processing phase of the GM selection procedure. The solution of the derived equivalent single-objective optimization problem is performed by the application of a mixed-integer Genetic Algorithm and the effects of its parameters on the efficiency of the selection procedure are investigated. Application of the proposed framework shows that it is able to track GM sets that not only provide excellent spectral matching but they are also able to simultaneously consider more explicitly a set of additional criteria.
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Dynamic structural analysis often requires the selection of input ground motions with a target mean response spectrum. The variance of the target response spectrum is usually ignored or accounted for in an ad hoc manner, which can bias the structural response estimates. This manuscript proposes a computationally efficient and theoretically consistent algorithm to select ground motions that match the target response spectrum mean and variance. The selection algorithm probabilistically generates multiple response spectra from a target distribution, and then selects recorded ground motions whose response spectra individually match the simulated response spectra. A greedy optimization technique further improves the match between the target and the sample means and variances. The proposed algorithm is used to select ground motions for the analysis of sample structures in order to assess the impact of considering ground-motion variance on the structural response estimates. The implications for code-based design and performance-based earthquake engineering are discussed. [DOI: 10.1193/1.3608002]
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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.
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Suites of earthquake ground motions play an important role in the seismic design and analysis process. A semi-automated procedure is described that selects and scales ground motions to fit a target acceleration response spectrum, while at the same time the procedure controls the variability within the ground motion suite. The basic methodology selects motions based on matching the target spectral shape, and then fits the amplitude and standard deviation of the target by adjusting the individual scale factors for the motions. The selection of motions from a larger catalog of motions is performed through either a rigorous method that tries each possible suite of motions or an iterative approach that considers a smaller set of potential suites in an effort to find suites that provide an acceptable fit to the target spectrum. Guidelines are provided regarding the application of the developed procedures, and example applications are described.
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Seismic input to nonlinear dynamic analyses of structures is usually defined in terms of acceleration time series whose response spectra are compatible with a specified target response spectrum. Time domain spectral matching used to generate realistic design acceleration time series is discussed in this paper. A new and improved adjustment function to be used in modifying existing accelerograms while preserving the nonstationary character of the ground motion is presented herein. The application of the new adjustment wavelet ensures stability, efficiency and speed of the numerical solution and prevents drift in the resulting velocity and displacement time series. [DOI: 10.1193/1.3459159]
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The problem of selecting a suite of earthquake accelerograms for time-domain analyses is of particular practical and academic interest. Research in this field has led to numerous approaches for compiling suites of accelerograms that may be used to robustly estimate the median structural response. However, many applications in earthquake engineering require the estimation of the full distribution of a structural response parameter for a particular predefined scenario. This article presents an efficient procedure whereby the distributions of interstory or roof drifts may be well approximated. The procedure makes use of three-point approximations to continuous distributions and the strong correlation that exists between the spectral acceleration at the initial fundamental period of the structure and the drift response. The distributions obtained under the proposed approach are compared with a reference distribution assumed to represent the true underlying distribution of drift response. The reference distribution is defined through a regression analysis conducted on the results of time-domain analyses of a six-story reinforced-concrete frame building subjected to 1,666 unscaled natural accelerograms. The results indicate that robust estimates of the first and second moments of the distribution of logarithmic drift may be obtained by subjecting the structure to several accelerograms scaled to match three target spectra over a range of periods. The target spectra are defined by the numbers of standard deviations above or below the median 5%-damped spectral acceleration and correspond to the roots of a third-order Hermite polynomial. The results demonstrate that consideration of fifth-order Hermite polynomials does not lead to a significantly improved performance of the approach.
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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.
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Ground motion models (or "attenuation relationships") describe the probability distribution of spectral acceleration at an individual period, given a set of predictor variables such as magnitude and distance, but they do not address the correlations between spectral acceleration values at multiple periods or orientations. Those correlations are needed for several calculations related to seismic hazard analysis and ground motion selection. Four NGA models and the NGA ground motion database are used here to measure these correlations, and predictive equations are fit to the results. The equations are valid for periods from 0.01 seconds to 10 seconds, versus similar previous equations that were valid only between 0.05 and 5 seconds and produced unreasonable results if extrapolated. Use of the new NGA ground motion database also facilitates a first study of correlations from intra- and inter-event residuals. Observed correlations are not sensitive to the choice of accompanying ground motion model, and intra-event, inter-event, and total residuals all exhibit similar correlation structure. A single equation is thus applicable for a variety of correlation predictions. A simple example illustrates the use of the proposed equations for one hazard analysis application. DOI: 10.1193/1.2857544
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A common goal of dynamic structural analysis is to predict the response of a structure subjected to ground motions having a specified spectral acceleration at a given period. This is important, for example, when coupling ground motion hazard curves from probabilistic seismic hazard analysis with results from dynamic structural analysis. The prediction is often obtained by selecting ground motions that match a target response spectrum, and using those ground motions as input to dynamic analysis. The commonly used Uniform Hazard Spectrum (UHS) is shown here to be an unsuitable target for this purpose, as it conservatively implies that large-amplitude spectral values will occur at all periods within a single ground motion. An alternative, termed a Conditional Mean Spectrum (CMS), is presented here. The CMS provides the expected (i.e., mean) response spectrum, conditioned on occurrence of a target spectral acceleration value at the period of interest. It is argued that this is the appropriate target response spectrum for the goal described above, and is thus a useful tool for selecting ground motions as input to dynamic analysis. The Conditional Mean Spectrum is described, its advantages relative to the UHS are explained, and practical guidelines for use in ground motion selection are presented. Recent work illustrating the impact of this change in target spectrum on resulting structural response is briefly summarized.
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This paper reviews alternative selection procedures based on established methods for incorporating strong ground motion records within the framework of seismic design of structures. Given the fact that time history signals recorded at a given site constitute a random process which is practically impossible to reproduce, considerable effort has been expended in recent years on processing actual records so as to become ‘representative’ of future input histories to existing as well as planned construction in earthquake-prone regions. Moreover, considerable effort has been expended to ensure that dispersion in the structural response due to usage of different earthquake records is minimized. Along these lines, the aim of this paper is to present the most recent methods developed for selecting an ‘appropriate’ set of records that can be used for dynamic analysis of structural systems in the context of performance-based design. A comparative evaluation of the various alternatives available indicates that the current seismic code framework is rather simplified compared to what has actually been observed, thus highlighting both the uncertainties and challenges related to the selection of earthquake records.
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Multi-objective evolutionary algorithms (MOEAs) that use non-dominated sorting and sharing have been criticized mainly for: (1) their O(MN<sup>3</sup>) computational complexity (where M is the number of objectives and N is the population size); (2) their non-elitism approach; and (3) the need to specify a sharing parameter. In this paper, we suggest a non-dominated sorting-based MOEA, called NSGA-II (Non-dominated Sorting Genetic Algorithm II), which alleviates all of the above three difficulties. Specifically, a fast non-dominated sorting approach with O(MN<sup>2</sup>) computational complexity is presented. Also, a selection operator is presented that creates a mating pool by combining the parent and offspring populations and selecting the best N solutions (with respect to fitness and spread). Simulation results on difficult test problems show that NSGA-II is able, for most problems, to find a much better spread of solutions and better convergence near the true Pareto-optimal front compared to the Pareto-archived evolution strategy and the strength-Pareto evolutionary algorithm - two other elitist MOEAs that pay special attention to creating a diverse Pareto-optimal front. Moreover, we modify the definition of dominance in order to solve constrained multi-objective problems efficiently. Simulation results of the constrained NSGA-II on a number of test problems, including a five-objective, seven-constraint nonlinear problem, are compared with another constrained multi-objective optimizer, and the much better performance of NSGA-II is observed
of Dissemination of European strong-motion data
  • N Ambraseys
  • J Douglas
  • D Rinaldis
  • C Berge-Thierry
  • P Suhadolc
  • G Costa
  • R Sigbjörnsson
  • P Smit
Ambraseys, N., J. Douglas, D. Rinaldis, C. Berge-Thierry, P. Suhadolc, G. Costa, R. Sigbjörnsson, and P. Smit. 2004. Vol. 2 of Dissemination of European strong-motion data. Swindon, UK: Engineering and Physical Sciences Research Council.
Optimized earthquake time history and response spectra (user's guide)
  • J Ferritto
Ferritto, J. 1992. Optimized earthquake time history and response spectra (user's guide). Rep. No. UG-0025. Port Hueme, CA: Naval Civil Engineering Laboratory.