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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. , 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 . ...
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  using meta-heuristic algorithms. Initial solution value for the decision variables are not required in HS and searching process is fully stochastic. ...
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.
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.
The accumulation of data on project management processes and standard solutions has made relevant research related to the use of knowledge engineering methods for a multi-criteria search for options that set optimal settings for project environment parameters. Purpose: Development of a method for searching and visualizing groups of projects that can be evaluated based on the concept of dominance and interpreted in terms of project variables and performance indicators. Methods: The enrichment of the sample while maintaining an implicit link between the project variables and performance indicators is carried out using a predictive neural network model. A set of genetic algorithms is used to detect the Pareto front in the multidimensional criterion space. The ontology of projects is determined after clustering options in the solution space and transforming the cluster structure into the criterion space. Automation of the search in the multidimensional space of the Pareto front greatest curvature zone, which determines the equilibrium design solutions, their visualization and interpretation are carried out using a tree map. Results: A tree map is constructed at any dimension of the criterion space and has a structure that has a topological correspondence with projections of shared cluster images from a multidimensional space onto a plane. For various types of transformations and correlations between performance indicators and project variables, it is shown that the areas of the Pareto front greatest curvature are determined either by the contents of the whole cluster or by part of the variants representing the "best" cluster. If an undivided rectangle of a cluster is adjacent to the upper right corner of a tree map, then its representatives in the criterion space are well separated from the rest of the clusters and, when maximizing performance indicators, are closest to the ideal point. All representatives of such a cluster are effective solutions. If the winning cluster contains dominant options inside the decision tree, then the ”best" cluster is represented by the remaining options that set the optimal settings for the project variables. Practical relevance: The proposed methods of searching and visualizing groups of projects can be used when choosing the conditions of resource and organizational and economic modeling of the project environment, ensuring the optimization of risks, cost, functional, and time criteria.
Historical structures are vulnerable to effect of earthquake, wind, flood, fire, etc. Considering the active seismic resources owned Turkey, earthquakes especially important threats for historical structures. Therefore, the structural response of historical structures should be investigation under seismic effects. The most important factor in investigation of seismic response is selection of appropriate earthquake ground motion records and scaling to target design spectrum. The aim of this paper is investigation of the seismic response of historical structure based on earthquake ground motion scaling method. The historical masonry clock tower in Çorum, Turkey, is selected as an example. This paper presents scaling of the real earthquake ground motion records selected from the region according to the target design spectrum by applying the time and frequency domain scaling methods specified in the 2018 Turkey Building Earthquake Code. Linear time history analyses of the clock tower are performed in unidirectional (only horizontal components on the 1st mode direction) and bidirectional (combination of horizontal and vertical component) by using scaled ground motion records. At the end of the analyses, the effect of vertical ground motion and ground motion scaling methods on the seismic response of the masonry clock tower is evaluated. The maximum displacement, principal stress and strain values are examined comparatively according to the relevant regulations. It is observed that earthquake ground motion records are matched the target design spectrum better by using frequency domain scaling method. The results also show that maximum displacement and principal stress values obtained by scaled records according to frequency domain scaling method are higher. It is seen that the vertical ground motion records should be taken into account in the evaluation of the seismic response of the structures.
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.
Structural damage identification is a scientific field that has attracted a lot of interest in the scientific community during the recent years. There have been many studies intending to find a reliable method to identify damage in structural elements both in location and extent. Most damage identification methods are based on the changes of dynamic characteristics and static responses, but the incompleteness of the test data is a great obstacle for both. In this paper, a structural damage identification method based on the finite element model updating is proposed, in order to provide the location and the extent of structural damage using incomplete modal data of a damaged structure. The structural damage identification problem is treated as an unconstrained optimization problem which is solved using the differential evolution search algorithm. The objective function used in the optimization process is based on a combination of two modal correlation criteria, providing a measure of consistency and correlation between estimations of mode shape vectors. The performance and robustness of the proposed approach are evaluated with two numerical examples: a simply supported concrete beam and a concrete frame under several damage scenarios. The obtained results exhibit high efficiency of the proposed approach for accurately identifying the location and extent of structural damage.
A decision support process is presented to accommodate selecting and scaling of earthquake motions as required for the time domain analysis of structures. Code-compatible suites of seismic motions are provided being, at the same time, prequalified through a multi-criterion approach to induce response parameters with reduced variability. The latter is imperative to increase the reliability of the average response values, normally required for the code-prescribed design verification of structures. Structural attributes like the dynamic characteristics as well as criteria related to variability of seismic motions and their compliance with a target spectrum are quantified through a newly introduced index, δsv–sc, which aims to prioritize motions suites for response history analysis. To demonstrate the applicability of the procedure presented, the structural model of a multi-story building was subjected to numerous suites of motions that were highly ranked according to both the proposed approach (δsv–sc) and the conventional one (δconv), that is commonly used for earthquake records selection and scaling. The findings from numerous linear response history analyses reveal the superiority of the proposed multi-criterion approach, as it extensively reduces the intra-suite structural response variability and consequently, increases the reliability of the design values. The relation between the target reliability in assessing structural response and the size of the suite of motions selected was also investigated, further demonstrating the efficiency of the proposed selection procedure to achieve higher response reliability levels with smaller samples of ground motion.
Although large ground motion databases are today widely available, the selection of records still hampers the use of nonlinear response history analysis in engineering practice. We propose a method that is based on a novel optimization algorithm in order to create subset of records chosen from a large database. Existing heuristic methods select and/or scale ground motion records so that their mean spectrum is close to a target/design design spectrum. The records obtained following this practice offer good estimates of the mean response but considerably underestimate the inherent response variability, thus providing no insight regarding the dispersion around the mean. The proposed method selects and scales the ground motion records so that their mean spectrum and the (period-depended) dispersion fit best a target spectrum and its dispersion. The problem is formulated as a two-objective optimization problem, where the record selection considers both the mean spectrum and its dispersion at the range of periods of interest. The problem is solved with the aid of the differential evolution algorithm which searches for potential record combinations whose mean and variance match the target spectral values (median and percentiles) obtained either from a code-compatible smooth spectrum or from a ground motion prediction equation (GMPE). The proposed procedure is efficient, easy to implement and able to quickly search a large pool of ground motion records, identifying record subsets that provide estimates of the response quantities of interest with a minimum number of ground motions. A three-storey moment frame building is considered as a benchmark problem in order to demonstrate the efficiency of the proposed optimization scheme .
We present ground motion prediction equations (GMPEs) for computing natural log means and standard deviations of vertical-component intensity measures (IMs) for shallow crustal earthquakes in active tectonic regions. The equations were derived from a global database with M 3.0–7.9 events. The functions are similar to those for our horizontal GMPEs. We derive equations for the primary M-and distance-dependence of peak acceleration, peak velocity, and 5%-damped pseudo-spectral accelerations at oscillator periods between 0.01–10 s. We observe pronounced M-dependent geometric spreading and region-dependent anelastic attenuation for high-frequency IMs. We do not observe significant region-dependence in site amplification. Aleatory uncertainty is found to decrease with increasing magnitude; within-event variability is independent of distance. Compared to our horizontal-component GMPEs, attenuation rates are broadly comparable (somewhat slower geometric spreading, faster apparent anelastic attenuation), V S30-scaling is reduced, nonlinear site response is much weaker, within-event variability is comparable, and between-event variability is greater.
This paper presents a new approach to selection of a set of recorded earthquake ground motions that in combination match a given site-specific design spectrum with minimum alteration. The scaling factors applied to se- lected ground motions are scalar values within the range specified by the user. As a result, the phase and shape of the response spectra of earthquake ground motions are not tampered with. Contrary to the prevailing scaling methods where a preset number of earthquake records (usually between a single component to seven pairs) are selected first and scaled to match the design spectrum next, the proposed method is capable of searching a set con- sisting of thousands of earthquake records and recommending a desired sub- set of records that match the target design spectrum. This task is achieved by using a genetic algorithm (GA), which treats the union of 7 records and cor- responding scaling factors as a single ''individual.'' The first generation of in- dividuals may include a population of, for example, 200 records. Then, through processes that mimic mating, natural selection, and mutation, new generations of individuals are produced and the process continues until an optimum individual (seven pairs and scaling factors) is obtained. The proce- dure is fast and reliable and results in records that match the target spectrum with minimal tampering and the least mean square of deviation from the tar- get spectrum. (DOI: 10.1193/1.1719028)
A new heuristic approach for minimizing possiblynonlinear and non-differentiable continuous spacefunctions is presented. By means of an extensivetestbed it is demonstrated that the new methodconverges faster and with more certainty than manyother acclaimed global optimization methods. The newmethod requires few control variables, is robust, easyto use, and lends itself very well to parallelcomputation.
In code-based seismic design and assessment it is often allowed the use of real records as an input for nonlinear dynamic
analysis. On the other hand, international seismic guidelines, concerning this issue, have been found hardly applicable by
practitioners. This is related to both the difficulty in rationally relating the ground motions to the hazard at the site
and the required selection criteria, which do not favor the use of real records, but rather various types of spectrum matching
signals. To overcome some of these obstacles a software tool for code-based real records selection was developed. REXEL, freely
available at the website of the Italian network of earthquake engineering university labs (http://www.reluis.it/index_eng.html), allows to search for suites of waveforms, currently from the European Strong-motion Database, compatible to reference spectra
being either user-defined or automatically generated according to Eurocode 8 and the recently released new Italian seismic
code. The selection reflects the provisions of the considered codes and others found to be important by recent research on
the topic. In the paper, record selection criteria are briefly reviewed first, and then the algorithms implemented in the
software are discussed. Finally, via some examples, it is shown how REXEL can effectively be a contribution to code-based
real records selection for seismic structural analysis.
KeywordsEurocode 8-Hazard-Seismic design-Response spectrum
Differential Evolution (DE) is a simple but powerful evolutionary optimization algorithm with many successful applications.
In this paper we propose Differential Evolution for Multiobjective Optimization (DEMO) – a new approach to multiobjective
optimization based on DE. DEMO combines the advantages of DE with the mechanisms of Pareto-based ranking and crowding distance
sorting, used by state-of-the-art evolutionary algorithms for multiobjective optimization. DEMO is implemented in three variants
that achieve competitive results on five ZDT test problems.
The seismic behavior of asymmetric building structures is often complex and reductions to plane problems which can be analyzed with a single horizontal ground-motion component are often deemed unsatisfactory. As a consequence, dynamic structural analyses with both horizontal ground-motion components become more common, both in research as well as in practice. A review of code provisions regarding selection and scaling of ground motions for bi-directional analysis has, however, revealed that the guidelines provided are frequently inconsistent or are lacking transparency regarding the underlying assumptions. The aim of this study is to shed some light on a number of aspects involved when selecting and scaling records for bi-directional analysis and post-processing results of such analyses.
: This article discusses solving non-linear programming problems containing integer, discrete and continuous variables. The Part 1 of the article describes a novel optimization method based on Differential Evolution algorithm. The required handling techniques for integer, discrete and continuous variables are described including the techniques needed to handle boundary constraints as well as those needed to simultaneously deal with several non-linear and non-trivial constraint functions. In Part 2 of the article a mechanical engineering design related numerical example, design of a coil spring, is given to illustrate the capabilities and the practical use of the method. It is demonstrated that the described approach is capable of obtaining high quality solutions. The novel method is relatively easy to implement and use, effective, efficient and robust, which makes it as an attractive and widely applicable approach for solving practical engineering design problems. Keywords: evolutiona...
The consensual agreement that ground motion record selection plays an important role in the non-linear dynamic structural response has contributed to numerous research studies seeking the definition of accurate ground motion record selection techniques. However, most of the available tools only allow for record selection based on spectral compatibility between the mean response spectrum of a record suite and a target response spectrum. This paper presents SelEQ, a fully integrated framework that implements state-of-the art procedures for ground motion record selection and scaling. In addition to typical record selection procedures, SelEQ allows obtaining the Conditional Mean Spectrum (CMS) for the European territory, the latter making use of the open source platform OpenQuake and the recently proposed SHARE seismic hazard model. This important feature allows state-of-the-art record selection for probabilistic-based assessment and risk analysis. SelEQ incorporates a number of procedures available in the literature that facilitate preliminary record selection (e.g. disaggregation for a specific site) and that allow advanced selection criteria (e.g. control of mismatch of individual ground motion records). The framework makes use of the Adaptive Harmony Search meta-heuristic optimization algorithm in order to significantly minimize computational cost and analysis time, whilst still meeting the imposed selection constraints. Application examples of the framework indicate that it can accurately select suites of ground motion records for code-based and probabilistic-based seismic assessment.
Pulse‐like seismic records constitute a special category of ground motions, because they are capable of causing significant damage to several structures. In this article, a new pulse indicator (PI) for the characterization of seismic motions as pulse‐like or non‐pulse‐like is proposed, which is set equal to the cross‐correlation factor of the significant pulse and the original record. It is suggested that records for which PI is greater than 0.65 are characterized as pulse‐like, whereas records with PI less than 0.55 are characterized as non‐pulse‐like. The method is applied to a total of 221 records that have been characterized in the literature as pulse‐like, non‐pulse‐like, or ambiguous, and the comparison of the new PI with previously proposed indicators is performed. It is also shown that the proposed PI is related to the inelastic response of structures, because records characterized as pulse‐like produce, in general, inelastic displacements larger than the elastic ones. In the presented examples, the Mavroeidis and Papageorgiou wavelet is used for the mathematical representation of the predominant pulse inherent in a record; however, other types of wavelets could also be used.
Electronic Supplement:Tables of classification of considered records and proposed pulse indicator (PI) index for records characterized as pulse‐like.
This paper describes an algorithm to efficiently select ground motions from a database while matching a target mean, variance and correlations of response spectral values at a range of periods. The approach improves an earlier algorithm by Jayaram et al. (2011). Key steps in the process are to screen a ground motion database for suitable motions, statistically simulate response spectra from a target distribution, find motions whose spectra match each statistically simulated response spectrum, and then perform an optimization to further improve the consistency of the selected motions with the target distribution. These steps are discussed in detail, and the computational expense of the algorithm is evaluated. A brief example selection exercise is performed, to illustrate the type of results that can be obtained. Source code for the algorithm has been provided, along with metadata for several popular databases of recorded and simulated ground motions, which should facilitate a variety of exploratory and research studies.
This study proposes a method for selecting ground motions from a ground motion library with response spectra that match the target response spectrum mean, variance and correlation structures. The proposed method is conceptually simple and straightforward. In this method, a desired number of ground motions are sequentially selected from first to last. The accuracy and consistency of the proposed method are verified through comparisons of the ground motions selected using the proposed method with those selected using conventional methods. This study shows that the seismic responses of the frames vary according to ground motion selection and correlation structures.
The purpose of this study is to propose an accurate and efficient method for selecting and scaling ground motions matching target response spectrum mean and variance, which does not require excessive computation and simulation. In the proposed method, a desired number of ground motions are sequentially scaled and selected from a ground motion library without iterations. Copyright
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]
A prototype expert system was developed for selecting site-specific design accelerograms from a database of earthquake records according to a set of rules and heuristics. The expert system was devised using the shell builder M.1 (Knowledge Base Building Tool, Teknowledge Inc., Palo Alto, CA) along with external routines written in C and FORTRAN for computing the required characteristics of the ground motion. The expert system combines objective and subjective approaches to select a time history for a given site/structure system. It uses the information supplied by the user about the site and the structure under consideration to explore the database and proposes a list of candidate time histories. The time histories are then ranked in different ways according to their expected damage potential. The criteria used to assess the damage potential are the type of structure considered, the subsurface geology at the site, and the ground motion characteristics. This bears on the effect of the recommended time history characteristics such as its dominant period, peak ground acceleration or velocity, and duration. If the system cannot find a recorded accelerogram within the database for the given site, it asks the user for additional information about the site and proposes recommended parameters for the generation of synthetic accelerogram.
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.
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.
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]
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.
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.
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
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.
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.
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
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)
Ferritto, J. 1992. Optimized earthquake time history and response spectra
(user's guide). Rep. No. UG-0025. Port Hueme, CA: Naval Civil