10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska EVALUATION OF THE DYNAMIC RESPONSE OF STRUCTURES TO THE REAL, SYNTHETIC AND MODIFIED ACCELEROGRAMS USING S-TRANSFORM S.Arian Moghaddam 1 and M. Ghafory-Ashtiany 2 ABSTRACT Considering the important role of Non-linear Time History Analysis (NLTHA) in the assessment of the seismic demand imposed to the engineering structures; and that the lack of appropriate strong ground motion recordings in some regions has forced the earthquake engineers to select and modify a set of recordings from other available databases or use the artificial ones; the objective of this paper is to provide some insight for structural engineers who use modified or simulated accelerograms, as the input of NLTHA; in order to present a simple process to evaluate the influence of different ground motion modification and simulation techniques on the Engineering Demand Parameters (EDPs). Seismic demands of a range of single degree of freedom systems under real, modified and simulated accelerograms is obtained in terms of response histories and spectra; also, collapse capacity of a 6-story steel frame under real, modified and synthetic ground motions is estimated using Incremental Dynamic Analysis (IDA), while the change in time-frequency content of different types of ground motions after adjusting process is evaluated via S-Transform analysis. The correlation between observed response characteristics and time-frequency variations demonstrate that NLTHA users can predict possible changes in EDPs due to the adjusting processes just by checking time-frequency content of accelerograms. The results of study show that EDPs estimated using modified or simulated accelerograms in some cases can be overestimated. Also, one can simply make a reasonable prediction about changes in energy content of accelerograms and its impact on the response of structures by monitoring results of S-Transform analysis during the adjustment or simulation procedure. 1 Graduate Student, International Institute of Earthquake Engineering and Seismology, Tehran, Iran 2 Professor, International Institute of Earthquake Engineering and Seismology, Tehran, Iran Arian Moghaddam S, Ghafory-Ashtiany M; Evaluation of the dynamic response of structures to the real, synthetic and modified accelerograms using S-Transform. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.
Evaluation of the dynamic response of structures to the real, synthetic and modified accelerograms using S-Transform S.Arian Moghaddam 1 and M. Ghafory-Ashtiany 2 ABSTRACT Considering the important role of Non-linear Time History Analysis (NLTHA) in the assessment of the seismic demand imposed to the engineering structures, and that the lack of appropriate strong ground motion recordings in some regions; has forced the earthquake engineers to select and modify a set of recordings from other available databases or use the artificial ones. The objective of this paper is to provide some insight for structural engineers who use modified or simulated accelerograms, as the input of NLTHA; as well as presenting a simple process to evaluate the influence of different ground motion modification and simulation techniques on the Engineering Demand Parameters (EDPs). Seismic demands of some single degree of freedom systems under real, modified and simulated accelerograms are obtained in terms of response histories and spectra; and the ability of mentioned accelerograms in the determination of the collapse capacity of a 6-story steel frame is evaluated by Incremental Dynamic Analysis (IDA). While the S-Transform analysis help us asses the change in time-frequency variations of signals during adjusting process. The correlation between observed response characteristics and timefrequency variations demonstrate that NLTHA users can predict possible changes in EDPs due to the adjusting processes just by checking time-frequency content of accelerograms. The results of the study show that estimated EDPs using modified or simulated accelerograms in some cases can be overestimated. Also, one can simply make a reasonable prediction about changes in energy content of accelerograms and its impact on the response of structures by monitoring results of S- Transform analysis during the adjustment or simulation procedure. Introduction Input of Non-Linear Time History Analysis (NLTHA) Today, NLTHA is one of the key methods to estimate the dynamic behavior of engineering structures with adequate accuracy. Particularly, in the case of critical or special structures, irregular systems and tall buildings can be the best choice to compute the Engineering Demand Parameters (EDPs). Also, most of the existing seismic standards are providing the designers with a reduction in the conservatism when they select more complicated analysis types such as NLTHA; while new generation of seismic guidelines apply the NLTHA as an efficient tool in performance based earthquake engineering. 1 Graduate Student, International Institute of Earthquake Engineering and Seismology, Tehran, Iran 2 Professor, International Institute of Earthquake Engineering and Seismology, Tehran, Iran Arian Moghaddam S, Ghafory-Ashtiany M Evaluation of the dynamic response of structures to the real, synthetic and modified accelerograms using S-Transform. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.
The essential step in NLTHA is to select appropriate set of ground motions in order to achieve a reliable estimation of desired EDPs. The lack of suitable Strong Ground Motion records (SGMR) in some regions has forced the earthquake engineers to select and modify a set of recordings from other available databases or use the artificial ones. In other words, the NLTHA users have no choice but to modify a real accelerogram or generate an artificial one such that fulfills minimum code based requirements. The existing methods suggest the scaling, matching and artificial generation of accelerograms to ensure the compatibility with the design spectra. Although one can simply discern that all these methods are affecting the seismological characteristics of the accelerograms compared to real SGMR. Several studies have evaluated and shown the possible and unpredictable bias and errors in the structural response and estimation of EDPs under adjusted accelerograms [1, 2]. It should be noted that there are different SGM processing procedures that can affect the structural response accuracy, which are not in the scope of present paper. Time Frequency Representations (TFRs) The Earthquake ground motions are known to have non-stationary nature, both in their amplitude and frequency content [3]. The problem of inability of conventional spectral analysis using Fourier transform to describe the evolutionary spectral characteristics of non-stationary processes can be solved by using time-frequency spectral analysis [4]. One of the first Time-Frequency Representations (TFRs) providing required localization in time and frequency to establish a local spectrum for any time instant is Short Time Fourier Transform (STFT) [4, 5]. Shortcomings of STFT can be solved by using multi-resolutional techniques based on wavelet transform (WT), which uses a basis function that dilates and contracts with frequency [6]. Stockwell et al. [7] have proposed a time-frequency representation called S-Transform, as an extension of STFT and WT, which can be written as: i2 (, τ) = ( ) ( τ) π ft ST f x t g t e dt (1) Where f is frequency, g is the Gaussian window and τ controls the center of Gaussian window in time domain. Recently, a band variable filter having the ability of acting simultaneously in frequency and time domain has been applied to the analysis of non-linear dynamic behavior of soil and buildings [8, 9]. Also, Ghodrati Amiri and Arian Moghaddam have proposed an S- Transform-based signal decomposition technique to extract velocity pulses of near fault ground motions [6]. The S-Transform analysis is used in the simplification of accelerograms for rapid time history analysis of structures. S-Transform based filtering of time series [10] and generation of synthetic accelerograms has been examined by some researchers [11]. In this paper, the filter suggested by Ditommaso et al. [8] has been modified and used to monitor the time frequency variation of accelerograms before and after different adjustment procedures.
Proposed Method To evaluate the possible changes in the structural response and predict the mentioned bias, a simple yet effective procedure based on monitoring the time-frequency content of accelerograms during and after adjustment or generation methods is proposed. It is assumed that users are aware of natural period of vibration of the structure (T n ) that the accelerograms are intended to be applied in the NLTHA. The proposed method is summarized as: Identify the natural period of vibration of target structure (T n ). Compute the strong motion duration of adjusted (t d ) signal using any of the classic approaches such as significant, bracket, uniform duration or using the result of S- Transform analysis to detect when the amplitude of signals decays. Perform S-Transform to obtain time-frequency distribution of adjusted signal. An example of such distribution is presented in Fig. 1. Define the dimensions of Critical Zone (CZ) in terms of t d and T n, as highlighted in Fig.1 where the frequency band of 0.5-2 Hz around the natural frequency of structure is used. Extract the S-Transform amplitudes corresponding to the CZ. Compute the inverse S-Transform for the last step. Evaluate the CZ signal characteristics and/or compare them with original signal. Predict possible bias in the response of target structure under adjusted or generated accelerogram. Numerical Example As it is mentioned in the above sections, there are many requirements. Here, among different methods providing user with sufficient compatibility with target spectrum we are focusing on methods that directly change the frequency content of inputs to yield predefined level of compatibility with target response spectra. Therefore, a matched accelerogram generated by a well-known software, RSPmatch [12], an artificial accelerogram generated by stationary random process using SIMQKE1 [13] and a synthetic accelerograms generated by non-stationary signals via Belfagor [2] are selected to be evaluated. In this section, the proposed method has been used to examine the change in time variation of frequency content of the selected accelerograms. After extraction of critical zones in each case, typical ground motion parameters that describe intensity or energy content of signals have been computed, as shown in Table 1. The fault parallel component of recorded accelerogram in Elcentro earthquake is used as the real recording and the input of matching process. Fig. 2 depicts acceleration response spectrum of 5% damping for different accelerograms used in this paper. Different spectrum intensity measures, the majority of which to calculate the area under the elastic velocity spectrum in particular ranges of natural periods, have been suggested in the literature. Here, Housner Intensity which is believed to be an overall measure of the severity of the response of typical (velocity-controlled) engineering structures to the ground motions [14] is used based on Eq. 2:
2.5 HI = PSV ( T, ζ ) dt (2) 0.1 That the energy of the seismic wave motion at a site is proportional to the integral over time of absolute velocity [6], cumulative absolute velocity, given in Eq. 3, has been used as a measure of energy content of input motions. t CAV () t = V () t dt (3) 0 Also, the ratio of PGV and PGA and Arias Intensity are reported in this paper. Readers are referred to [18] for detailed information about them. Figure 1. Defining the critical zone in time-frequency domain computed by S-Transform analysis. Figure 2. Acceleration response spectrum of SIMQKE1 (Blue), Belfagor (Green), RSPmatch (Black) and Real (Dashed) accelerogram in comparison with Design spectrum (Red).
Table 2 shows the SGM parameters of CZ signals that are normalized to those of whole recordings. It shows that how important the CZ components are in constitution of original ground motions. For example, one could conclude that CZ didn t have a significant role in generation of Arias Intensity for real accelerogram compared to other cases. Table 3 and 4 compares the level of intensity measures in generated or adjusted signals compared to real ground motion. As an example, based on Table 4, all non-real accelerograms have higher energy content than real case (comparing CAV values) and this is more severe in case of SIMQKE1, while Table 3 implies that most of this energy is concentrated in CZs. In the next step, the collapse capacity of a 2D typical steel frame in 6 stories and 3 bays is estimated. The first mode period of vibration of structure is equal to 1.33s. This frame can be considered a flexible frame [15], while the details of modeling can be found in [16]. The single-record Incremental Dynamic Analysis (IDA) is applied using each accelerogram to estimate the collapse capacity of structure, as shown in Fig. 3. Table 1. Computed ground motion parameters in all cases and their CZs. PGV/PGA(s) AI(m/s) CAV(cm/s) HI(cm) Tp(s) * Tm(s) Real 0.11 1.80 1260 124.90 0.52 0.52 Real(CZ) 0.17 0.54 573 102.63 0.56 0.86 Belfagor 0.33 3.10 1401 282.80 0.40 0.90 Belfagor(CZ) 0.32 1.56 991 255.97 0.66 1.24 RSPmatch 0.21 3.82 1930 281.50 0.40 1.03 RSPmatch(CZ) 0.27 2.10 1285 252.90 0.68 1.35 SIMQKE1 0.23 4.48 2073 251.70 0.42 0.80 SIMQKE1(CZ) 0.23 2.32 1453 234.10 0.76 1.17 Predominant period Table 2. Evaluation of the importance of CZs in accelerograms. CZs Normalized to Original Recording Case PGV/PGA AI CAV HI Real 1.55 0.30 0.45 0.82 Belfagor 0.97 0.50 0.71 0.91 RSPmatch 1.29 0.55 0.67 0.90 SIMQKE1 1.00 0.52 0.70 0.93 Table 3. Comparison between real accelerogram and other cases in CZs.
Normalized to Real(CZ) Case PGV/PGA AI CAV HI Tp Tm Belfagor(CZ) 1.88 2.89 1.73 2.49 1.18 1.44 RSPmatch(CZ) 1.59 3.89 2.24 2.46 1.21 1.57 SIMQKE1(CZ) 1.35 4.30 2.54 2.28 1.36 1.36 Table 4. Comparison between real accelerogram and other cases in whole time-frequency domain. Normalized to Real Case PGV/PGA AI CAV HI Tp Tm Belfagor 3.00 1.72 1.11 2.26 0.77 1.73 RSPmatch 1.91 2.12 1.53 2.25 0.77 1.98 SIMQKE1 2.09 2.49 1.65 2.02 0.81 1.54 Discussion The main question of this study is trying to answer : Can NLTHA users predict possible bias in the result of the analysis due to the application of non-real accelerograms (modified or simulated), before performing the time consuming analysis, and consequently avoid using accelerograms with most possible biased results? To answer this question, the ability of signals corresponding to critical zones in time-frequency domain in excitation of target structure is evaluated quantitatively. Figure 3. IDA based collapse capacity curves using different accelerograms.
Figure 4. Comparison of PSV value around the natural period of structure (1.33s) From Table 1 to 4, it can be concluded that based on the computed parameters all nonreal cases will impose overestimated demand to the structure. This is in accordance with the result of IDA curve in Fig. 3. The energy based evaluation of signals suggest that SIMQKE1 will carry or represent most of the seismic energy in terms of CAV and AI; while Belfagor and RSPmatch will import more seismic energy to the SDOF oscillators in term HI. Accordingly, one could expect that minimum collapse capacity should be attributed to the SIMQKE1 or Belfagor. But, the matched accelerogram via RSPmatch cause the most severe damage to the target steel frame based on Fig. 3. The aforementioned paradox can be resolved by using mean periods of ground motions [17]. In other words, that the computed energy is carried by signals in what frequency range should be determined. More close are the mean period (T m ) of CZ signals to the natural period of target frame; more severe is the damage due to the seismic excitation. The ratio between mean period of critical zones of ground motions and natural period of structure is reported in Fig. 3 in the vicinity of each IDA curve. One can simply notice that the order of most damaging cases in term of IDA curves corresponds to the order of computed ratios. Assuming that the imported energy to a structure during seismic motion is related to the area under pseudo velocity response spectrum; Fig. 4 will confirm this conclusion, while the RSPmatch shows higher energy level, in term of PSV, around the natural period of structure. Fig. 5 depicts response history of a non-linear SDOF with 5% damping and Elastic Perfect Plastic (EPP) behavior that the natural period of which is 0.5s. Based on Fig. 5 one should conclude that the most nonlinear displacement is caused by SIMQKE1. Comparing the time-frequency content of signals; users can monitor and detect the most affected zones and predict the tendency of structural response in other structures. In this case, Fig. 6 shows the affected zones compared to real ground motion. For example, SIMQKE1 impose stationary high frequency content to the accelerograms which is expected to excite stiff structures and cause large dynamic response.
Conclusions A simple method, based on the monitoring of gradual change in the frequency content of signals during strong motion duration has been proposed to evaluate the influence of ground motion modification and generation methods on the response of structures. Comparison between computed parameters of original ground motions and those of adjusted accelerograms is used to predict the possible bias in the estimation of collapse capacity of structures. Most important results are: Engineering demand parameters computed using artificial or modified accelerograms can be highly overestimated in comparison with those calculated based on the real accelerograms. The bias of the NLTHA due to the selection of input, can be assessed before the structural analysis. Energy based intensity measures such as CAV, HI, etc. can be used to predict possible bias in the structural response more efficiently. None of the ground motion single parameters can correlate with the collapse capacity of structure adequately. Combination of spectral energy content and ratio between mean period of critical zone in an accelerogram and natural period of vibration of the structure can be a better predictor of the dynamic behavior It is possible to detect the affected zones of accelerogram in time-frequency domain and evaluate the effectiveness of simulated or modified accelerograms in yielding reliable estimation of response characteristics. Figure 5. Nonlinear response history of SDOF system under different cases in this paper.
Figure 6. Detection of affected zones of in time-frequency domain for a) Belfagor, b) RSPmatch and c) SIMQKE1
References 1. Luco N, Bazzurro P. Does amplitude scaling of ground motion records result in biased nonlinear structural drift responses? Earthquake Engineering & Structural Dynamics 2007; 36(13):1813-1835. 2. De Luca F, Iervolino I, Cosenza E. Compared seismic response of degrading systems to artificial and real records. In. Proc of 14th European Conference on Earthquake Engineering: 2010. 3. Mukherjee S, Gupta VK. Wavelet-based characterization of design ground motions. Earthquake Engineering & Structural Dynamics 2002, 31(5):1173 1190. 4. Gurley K, Kareem A. Applications of wavelet transforms in earthquake, wind and ocean engineering. Engineering Structures 1999, 21(2):149 167. 5. Cohen L. Time-frequency analysis: theory and applications. Prentice-Hall: New Jersey, 1995. 6. GhodratiAmiri G, Arian moghaddam S: Extraction of forward-directivity velocity pulses using S-Transformbased signal decomposition technique. Bulletin of Earthquake Engineering 2014, 1-32. 7. Stockwell RG, Mansinha L, Lowe R. Localisation of the complex spectrum: the S transform. IEEE Trans Signal Processing 1996, 44:998-1001. 8. Ditommaso R, Mucciarelli M, Ponzo F. S-Transform based filter applied to the analysis of nonlinear dynamic behaviour of soil and buildings. In: 14th European conference on earthquake engineering. vol. Proceedings Volume. Ohrid, Republic of Macedonia; 2010. 9. Puglia R, Ditommaso R, Pacor F, Mucciarelli M, Luzi L, Bianca M. Frequency variation in site response as observed from strong motion data of the L Aquila (2009) seismic sequence. Bulletin of Earthquake Engineering 2011, 9(3):869-892. 10. Hosseini M, Arian moghaddam S, Motovali emami S. A method for simplification of earthquake accelerograms for rapid time history analysis based on time-frequency. In: The 11th Biennial International Conference on Vibration Problems, Lisbon; 2013. 11. Fan J, Dong P. Simulation of artificial near-fault ground motions based on the S-transform In: Congress on Image and Signal Processing. 2008. 12. Hancock J, Watson-Lamprey J, Abrahamson NA, Bommer JJ, Markatis A, McCOY E, Mendis R. An improved method of matching response spectra of recorded earthquake ground motion using wavelets. Journal of Earthquake Engineering 2006, 10(spec01):67-89. 13. Vanmarcke E, Gasparini, D. Simulated earthquake motions compatible with prescribed response spectra. R76-4, Dept. of Civil Engineering, Massachusetts Inst. of Technology Cambridge, 1976. 14. Elnashai AS, DiSarno L. Fundamentals of Earthquake Engineering. Wiley: New York, 2008. 15. Medina RA, Krawinkler H. Evaluation of drift demands for the seismic performance assessment of frames. Journal of Structural Engineering 2005, 131(7):1003-1013. 16. Dimopoulos AI, Bazeos N, Beskos DE. Seismic yield displacements of plane moment resisting and x-braced steel frames. Soil Dynamics and Earthquake Engineering 2012, 41:128-140. 17. Rathje EM, Abrahamson NA, Bray JD. Simplified frequency content estimates of earthquake ground motions.journal of Geotechnical and Geoenvironmental Engineering 1998, 124(2):150-159.