Comprehensive stellar seismicanalysis
M. Farnir 1 M-A. Dupret 1 S.J.A.J. Salmon 1 A. Noels 1 G. Buldgen 2
1 Institut d’Astrophysique et Géophysique de l’Université de Liège, Allée du 6 août 17, 4000 Liège, Belgium 2 School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
Seismicanalysis of infilled frames
Kodur, V. K. R.; Erki, M. A.; Quenneville, J. H. P.
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hours or even days to carry out a single simulation. This makes the computational burden associated with the analysis impracticable, at times.
In this context, fast-running regression models, also called metamodels (such as Artificial Neural Networks (ANNs) [Zio, 2006; Cardoso et al., 2008; Beer and Spanos, 2009; Pedroni et al., 2010; Chojaczyk et al., 2015], Local Gaussian Processes (LGPs) [Bichon et al., 2008; Villemonteix et al., 2009] polynomial Response Surfaces (RSs) [Bucher and Most, 2008; Liel et al., 2009], polynomial chaos expansions [Ciriello et al., 2013; Sudret and Mai, 2015], stochastic collocations [Babuska et al., 2010], Support Vector Machines (SVMs) [Hurtado, 2007] and kriging [Bect et al., 2012; Dubourg and Sudret, 2014; Zhang et al., 2015]), can be built by means of input-output data examples to approximate the response of the original long-running FEMs without requiring a detailed physical understanding and modeling of the system process, and used for the seismicanalysis. Since the metamodel response is obtained quickly, the problem of high computational times is circumvented. However, the use of regression models in safety critical applications like NPPs still raises concerns as regards the control of their accuracy and precision.
gen over metals abundances Z/X 0 . The seismic indicators,
used as constraints, have been computed using the frequen- cies calculated by Davies et al. (2015) and corrected for the surface effects using Kjeldsen et al. (2008)’s prescription of which the coefficients a and b have been calibrated by Sonoi et al. (2015). We realised two independent calibrations, using either the metal mixture of AGSS09 (Asplund et al., 2009) or that of GN93 (Grevesse & Noels, 1993), for each of the com- ponents A and B of the 16 Cygni system. The models were calculated using the CLES (Scuflaire et al., 2008b) stellar evo- lution code and the theoretical frequencies were computed with the LOSC (Scuflaire et al., 2008a) oscillation code. The models used the FreeEOS software (Cassisi et al., 2003) to generate the equation of state table, the reaction rates pre- scribed by Adelberger et al. (2011) and the OPAL opacity ta- ble (Iglesias & Rogers, 1996) combined with that of Ferguson et al. (2005) at low temperatures. Moreover, the mixing in- side convective regions was computed according to the mix- ing length theory (Cox & Giuli, 1968) and using the value αMLT = l/H p = 1.82 (where l is the mixing length and
Notes. Bold values were used to determine the reference fitter. Frequency values in brackets were obtained by only a few fitters and have relatively
high uncertainties. (a) One fitter did not converge to the quoted value. (2 3 4 5 6 7) Indicates the number of fitters.
Fig. 5. Time-frequency diagram of HD 43587 around 1484 μHz.
= 1 mode around 2766 μHz (five fitters) and the = 2 mode around 2708 μHz (three fitters) were not fitted by the RF, and so we retained the results of the fitter whose set of frequencies leads to the minimum quadratic sum described in the previous subsec- tion. Note that for both cases, the results of all fitters are in agree- ment at the 1-sigma level. The last case is special as only two fit- ters gave estimates for an = 1 mode, while the spectrum clearly shows peaks well above the level of the noise. To check whether these peaks are a signature of the contamination mentioned in Sect. 2, we performed a time-frequency analysis around this fre- quency, for both HD 43587 and HD 43823, the latter being also contaminated, as mentioned in Sect. 2. Figure 5 clearly shows the signal, especially during the first 40–50 days. On the con- trary, the same diagram for HD 43823 does not show any fea- ture, apart from a quasi-horizontal straight line at 1467 μHz corresponding to a 24-h alias of the nineth orbital harmonic. We, therefore, concluded that the signal comes from the star it- self and not from the instrument, and retained a value rounded to 0.1 μHz, compatible at 1-sigma with the two determinations.
As the quality of asteroseismic data improves, due to space missions such as CoRoT (Baglin et al., 2009) and Ke- pler (Borucki et al., 2010), it becomes possible to study the frequency signature of acoustic glitches. Acoustic glitches are oscillating features visible in oscillation spectra due to a sharp variation in the stellar structure. It was first Vorontsov (1988) who showed that such a sharp variation can be directly observed in the frequencies. Subsequently, Gough (1990) showed that it is also visible in the second frequency differ- ences. Therefore, the detection and study of acoustic glitches may provide essential information to better constraint and understand the stellar structure. For example, constraints about the localisation of the base of the envelope convec- tive zone or the surface helium abundance may be derived. This has already been the subject of several studies (Mon- teiro et al. 2000; Basu et al. 2004; Verma et al. 2014, to name a few). However, it is of prime importance to take advan- tage of as much of the information available in the oscilla- tion spectrum as possible. Furthermore, the information has to be treated in a statistically relevant way. For these reasons, we developed a new method to analyse the whole oscillation spectrum (both smooth and oscillating – glitch – part) simul- taneously in a homogeneous and statistically relevant way. Using our method, we define new seismic indicators which are as uncorrelated to each other as possible. Those indi- cators may then be used as constraints for forward seismic modeling to provide improved models and the proper corre- lations between the resulting parameters for a given target.
In the present section, we describe the method we devel- oped. It aims at using as much as possible of the information available in the oscillation spectrum of a star. Therefore, both the oscillatory and smooth part of the spectrum are simultaneously analysed in a single adjustment. This avoids multiple usage of the same information to draw different in- ferences. The very strength of the proposed method is that the different parameters obtained will be independent of each other, i.e. their covariance matrix will be the identity matrix. This will allow to build indicators which also are independent of each other and draw statistically relevant inferences. The independence of the parameters will be en- sured by using Gram-Schmidt’s (Gram 1883; Schmidt 1907) algorithm. Then, the defined seismic indicators will be used as constraints to provide improved models in the frame- work of forward seismic modelling (see for example Miglio & Montalbán (2005) for one of the first use of Levenberg- Marquardt ’s algorithm to adjust a model to seismic and non-seismic observables). Finally, such models may be used as initial guesses for inverse seismic modelling. (see Rox- burgh & Vorontsov (2002a,b) for the application of the in- version technique on an artificial target, which shows the feasibility of such techniques, and Buldgen et al. (2016a,b) for examples of inversions in the case of 16 Cygni A.)
Consequently, the method of Figure 11 shows that there is no need to model the fluid domain while performing finite elements analyses. This considerably reduces the complexity of preliminary seismic analyses of lock gates. All these achievements are likely to help engineers in integrating the seismic action when pre-desingning lock gates. Nevertheless, this conclusion has to be nuanced, as one has always to bear in mind that the present approach is based on some simplifying assumptions (for example, the support conditions of the gate are somewhat idealized). For this reason, working with a refined model of the structure is still required, but only at the very last step of the design process. 5. REFERENCES
Given the high risk in the area, the seismic surveillance in the Virunga region started in the 1960s, but an operational network only emerged after the 2002 Nyiragongo eruption. Most of the seismic studies(Lukaya et al. 1992; Wafula et al. 1992; Mavonga et al. 2006, 2010; Tuluka 2010) have been dedicated to the location of long-period (LP) and volcano-tectonic (VT) events recorded during earthquake swarms preceding eruptions using classical methods. However, these methods are not efficient in the presence of emergent volcanic signals, especially with small seismic networks, resulting in large uncertainties with LP locations. A new network has been developed in the area since 2013, which permitted new initiatives to track the magmatic activity with seismic approaches. Recent efforts successfully located volcanic tremor using cross correlation functions(Barrière et al. 2017) .
another application is the quantification of anomalies by using probabilities. Once we know that observed seismic velocity changes statistically obey Gaussian distribution, we can assign a probability to each daily seismic velocity change. Then we can quantitatively judge if a current seismic velocity change is normal or abnormal. Figure 18 is similar to Figure 3, but the vertical axis is the seismic velocity change normalized by its standard deviation during the normal period. Red horizontal lines show +/- four times the standard deviation. According to the Gaussian distribution, a probability of exceeding +/- four times the standard deviation is only about 10^-4 (0.01%). Therefore, we can quantify how often a seismic velocity change exceeds this threshold with this probability. If the seismic velocity change exceeds the threshold for two successive days, the probability becomes as low as 10^-8. In the top three panels, seismic velocity changes exceed -4 times the standard deviation associated with the Tohoku-Oki earthquake on March 11, 2011. According to the results, we can quantitatively evaluate how rare such a large seismic velocity change is. Such quantification also helps monitor seismic velocity changes and detect some anomalies automatically without human intervention.
To address such issue, we intend to answer to the two first Structural Health Monitoring (SHM) levels namely: damage detection and damage localization using Modal Operational Analysis (MOA) coupled with numerical modelling by Finite Element (FE). To illustrate such methodology, a concrete building located in Andorre la Vieille (Andorra) is numerically modelled. The structural behaviour of the building is studied through frequency computation method in order to identify its undamaged behaviour. A seismic event is next simulated by a non-linear dynamic computation method to create damage within the structure. Numerical results (eigen frequency, modal shapes and damage location) allow to highlight damaged zones induced by the earthquake and quantify degradation level in these areas. Some discussion is also provided according to the results sensitivity to materials properties and damage evolution law.
The widespread brittle failure of welded beam-to-column connections caused by the 1994 Northridge and 1995 Kobe earthquakes highlighted the need for retrofitting measures effective in reducing the strength demand imposed on connections under cyclic loading. Researchers presented the reduced beam section (RBS) as a viable option to create a weak zone away from the connection, aiding the prevention of brittle failure at the connection weld. More recently, an alternative connection known as a reduced web section (RWS) has been developed as a potential replacement, and initial studies show ideal performance in terms of rotational capacity and ductility. This study performs a series of non-linear static pushover analyses using a modal load case on three steel moment-resisting frames of 4-, 8-, and 16-storeys. The frames are studied with three different connection arrangements; fully fixed moment connections, RBSs and RWSs, in order to compare the differences in capacity curves, inter-storey drifts, and plastic hinge formation. The seismic-resistant connections have been modeled as non-linear hinges in ETABS, and their behavior has been defined by moment-rotation curves presented in previous recent research studies. The frames are displacement controlled to the maximum displacement anticipated in an earthquake with ground motions having a 2% probability of being exceeded in 50 years. The study concludes that RWSs perform satisfactorily when compared with frames with fully fixed moment connections in terms of providing consistent inter-storey drifts without drastic changes in drift between adjacent storeys in low- to mid-rise frames, without significantly compromising the overall strength capacity of the frames. The use of RWSs in taller frames causes an increase in inter-storey drifts in the lower storeys, as well as causing a large reduction in strength capacity (33%). Frames with RWSs behave comparably to frames with RBSs and are deemed a suitable replacement.
separated by a distance of 960 (m), filtered between 0.08 and 0.5 (Hz).
Figure 5(a) shows the power spectral density x ð!Þ of
the vertical displacement at various places in the LHC tunnel. Below 1 Hz, all the curves are superimposed. Above that, the power spectral density varies by a factor up to 10 000, i.e., the level of the signal varies by a factor 100. These sources are responsible of what is known as the technical noise. They can have two origins: either a varia- tion of the level of vibration as a function of the abscissa of the tunnel, due to local excitation sources (e.g. cooling systems or ventilation), or a variation of the amplitude corresponding to the different times of measurements. In the latter case, the variations should also be visible on the signals from the geophone which stays always at the same location. Such variations have not been noticed. A detailed analysis of these local sources would require a synchro- nous monitoring of the ground vibrations at all these points in the tunnel, during several nights. This is hardly realiz- able, and anyway not currently feasible because the LHC machine is running. However, our experience is that the level of ground vibrations, measured at the same place and roughly the same time shows, under the same environmen- tal conditions, roughly the same signals. For this reason, the most probable origin of these high variations of the technical noise is a variation of the level as a function of the abscissa of the tunnel.