Comparative ISS accelerometric analyses

Acta Astronautica 94 (2014) 681–689

Contents lists available at ScienceDirect

Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro

Comparative ISS accelerometric analyses$ N. Sáez a, X. Ruiz a,b, Jna. Gavaldà a,n, J. Pallarés c, V. Shevtsova d a

Departament de Química Física I Inorgànica, Universitat Rovira I Virgili, 43007 Tarragona, Spain Institut d'Estudis Espacials de Catalunya, IEEC, 43002 Barcelona, Spain c Departament d'Enginyeria Mecànica, Universitat Rovira I Virgili, 43007 Tarragona, Spain d Department of Chemical Physics, MRC, Université Libre Bruxelles, Brussels, Belgium b

a r t i c l e i n f o

abstract

Article history: Received 31 May 2013 Received in revised form 6 September 2013 Accepted 11 September 2013 Available online 27 September 2013

Two accelerometric records coming from the SAMSes es08 sensor in the Columbus module, the so-called Runs 14 and 33 in terms of the IVIDIL experiment, has been studied here using standard digital signal analysis techniques. The principal difference between both records is the vibrational state of the IVIDIL experiment, that is to say, during Run 14 the shaking motor of the experiment is active while that in Run 33 this motor is stopped. Identical procedures have been applied to a third record coming from the SAMSII 121f03 sensor located in the Destiny module during an IVIDIL quiescent period. All records have been downloaded from the corresponding public binary accelerometric files from the NASA Principal Investigator Microgravity Services, PIMS website and, in order to be properly compared, have the same number of data. Results detect clear differences in the accelerometric behavior, with or without shaking, despite the care of the designers to ensure the achievement of the ISS μg-vibrational requirements all along the experiments. & 2013 IAA. Published by Elsevier Ltd. All rights reserved.

Keywords: Accelerometric analyses Microgravity Gaussianity Spectrum

1. Introduction The experiment named Influence of VIbrations on DIffusion of Liquids, IVIDIL [1,2], was installed inside the Microgravity Science Glovebox, MSG, on September 23, 2009 by Frank de Winne (Expedition 21, ESA) and Robert Thirsk (Expedition 21, CSA). The Glovebox is one of the different ten International Standard Payload Racks (ISPRs) for research that can be accommodated in the European Columbus module [3]. The IVIDIL experiment began October 5, 2009 and it carried out more than 50 experimental runs until January 20, 2010. Finally, on January 28, 2010 was uninstalled by Soichi Noguchi (Expedition 22, JAXA). The scientific objective of the experiment was threefold. The first objective was to identify the limit level of vibrations below which g-jitter does not play a significant ☆

This paper was presented during the 63rd IAC in Naples. Corresponding author. Tel.: þ34 977 559518; fax: þ34 977 559563. E-mail addresses: [email protected], [email protected] (Jna. Gavaldà). n

role for onboard experiments. The second objective was to perform precise measurements of diffusion and thermodiffusion coefficients using two binary mixtures with positive and negative Soret coefficients. Finally, the third objective was the analysis of the influence of vibrations on the measured values of diffusion and thermodiffusion coefficients. This last goal also involved the study of vibration-induced convection and, particularly, heat and mass transfer under vibrations. Scientific data from the different IVIDIL runs have been provided by the E-USOC, the Spanish User Support and Operations Centre [4]. This paper presents a first attempt to characterize the accelerometric world [5,6] of the IVIDIL experiment. To do so, we analyze two signals from IVIDIL experiment. The first one, where the internal shaking is turned off, is the so-called Run 33 – thereafter IVIDIL1 signal – and comes from the SAMSes es08 sensor. The second signal the socalled Run 14 – thereafter IVIDIL2 – comes from the same sensor and it corresponds to an active period of operation of the experiment in which the internal shaking is turned on (2.8 Hz). Both signals have the same number of data.

0094-5765/$ - see front matter & 2013 IAA. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actaastro.2013.09.005

682

N. Sáez et al. / Acta Astronautica 94 (2014) 681–689

Table 1 Listing of the most potentially dangerous crew activities. IVIDIL2 (20/10/2009)

IVIDIL1 & NASA1 (10/12/2009)

Checking the aerosol filters at the Russian Elektron O2 generator. Work on the FIR installing the hardware. Work on the Lab THC/CCAA air conditioner, then closing the LAB1S6 MFCV and opening the LAB1P6 MFCV. Regular monthly maintenance of the TVIS. Regular 2-hr physical exercise.

Inspection & cleaning of the FDS and SDs in Node-2, Lab and Node-1. Preparations for an upcoming recharge of the KOB1 loop of the Russian SOTR. Regular systems maintenance. Regular 2hr physical exercise.

Also we use another signal – thereafter NASA1 – coming from the SAMS2 121f03 sensor on the Destiny module and, in order to be properly compared with the abovementioned IVIDIL1 it has the same starting/end time as well as the same number of data. All signals have been downloaded as binary data files from the NASA Principal Investigator Microgravity Services, PIMS website [7]. Remember that, as it is well-known, the NASA-GRC PIMS project has the responsibility of receive process and archive the acceleration measurements coming from the corresponding International Space Station sensors. Mention, at this respect, several exhaustive works concerning different increments of the station [8–11]. Additional complementary studies using data provided by Russian accelerometers have also been reported in the literature [12–14]. With the aim to correlate the accelerometric information with different events in the station we firstly investigate the crew activities during October the 20th (IVIDIL2) [15] and December the 10th (IVIDIL1 and NASA1) of 2009 [16]. Unfortunately our information is not precise enough in the sense that we know the activities but not when these activities were made. Also, no matching have been detected between the selected potentially dangerous activities of Table 1 and the corresponding (or similar) accelerometric fingerprints existing in the NASA accelerometric Handbook [17]. So, the above-mentioned initial strategy has been relaxed and the aim of the present work focused only on the accelerometric characterization itself making a comparative analysis of the three (IVIDIL1, IVIDIL2 and NASA1) signals over a span of 18 h, the standard duration of one experiment. The comparison will help to detect accelerometric differences between the two possible dynamic states of the IVIDIL experiment – with or without shaking – and also to investigate the differences between the two simultaneous accelerometric records coming from the Destiny and Columbus modules. Because both records corresponds to a quiescent period of the station, the information will also be useful to investigate if the ISS mg-vibrational requirements proposed by NASA [18] are accomplished or if any disturbances generated by some mechanical coupling between both modules of the station still exist and propagate during the experiments. 2. Additional details The position of the associated Cartesian references, which correspond to the ISS absolute coordinates {XA, YA, ZA} in both Destiny and Columbus modules [19], is sketched in Fig. 1.

Fig. 1. Cartesian reference from International Space Station.

Table 2 SAMS coordinate systems. Sensor

121f03 ES08

Location (in)

Orientation (degrees)

XA

YA

ZA

Roll

Pitch

Yaw

191.54 475.71

 40.54 235.22

135.25 160.27

0 0

30 90

 90  90

Table 3 Relationship between the SAMS sensors and the SSA coordinate systems. Sensor

Unit vector in Analysis Coordinates Axes

XA

YA

ZA

121f03

Xf03 Yf03 Zf03

0 1 0

 0.866 0  0.5

 0.5 0 0.866

ES08

XES08 YES08 ZES08

0 1 0

0 0 1

1 0 0

Tables 2 and 3 show sensor details. Each sensor has a defined coordinate system whose location and orientation are described regarding with the Space Station Analysis (SSA) coordinate system [20]. The shaking direction in the IVIDIL experiment is defined by the YES08 axis so, taking into account the information of Table 3, this direction is the same as the Yf03 and both coincides with the XA of the SSA system.

N. Sáez et al. / Acta Astronautica 94 (2014) 681–689

Consequently, in the next section we only present the results obtained in the above-mentioned directions, YES08 or Yf03, thereafter noted as Y. Notice finally that because IVIDIL1, IVIDIL2 and NASA1 are SAMS data the units are in g, the sampling rates are all 500 Hz and the cutoffs 200 Hz. The gains of the signals are a bit different, that is to say, 8.5 and 10 for the IVIDIL's and NASA records respectively. 3. Results First of all to eliminate possible instrument bias we have systematically demeaned all signals before any mathematical manipulation. A synthesis of the mathematical tools used here to quantitatively characterize these data is presented in Table 4. Calculations have been made using, in all cases, the Matlab package [21]. Fig. 2 shows the 10 s interval average of the three signals covering a total interval of 18 h of experiment. Analytically, for the y-axis is defined as,
 1 M N g avgk ¼ ∑ g ðk  1ÞM þ i k ¼ 1; 2:::; ð1Þ Mi¼1 M where g corresponds to gY (accelerometric Y component), M is the length of the interval and N the length of whole signal. Obviously this kind of plot enables to smooth the appearance of the raw signals and allows longer periods of time to be more clearly plotted. But, on the contrary, the information to be extracted is more restrictive because

interval averaged results are only useful for the identification of overall effects that tend to cause the change of the mean acceleration levels. In the present case, we can see that IVIDIL2 signal is noisier than IVIDIL1. This is generated by the shaking disturbances. Both signals present similar mean values. To complement the results of Fig. 2 having additional descriptive information about the smallest and largest data, the median, the lower/first quartile – 25% percentile – (Q1) and the upper/third quartile – 75% percentile – (Q3) we use a boxplot representation type (see Fig. 3). The length of the upper and lower whiskers in the figure has been calculated as U¼Q3þ1.5 (Q3 – Q1) and L ¼Q1–1.5 (Q3 – Q1) respectively. The factor (Q3 – Q1) is the so-called inter-quartile range (IQR), a robust measure of the statistical dispersion [22,23]. The quantitative values obtained are presented in Table 5. We can see that the mean and median values are practically coincident. The dispersion between both values (mean and median) is less than 0.5% in all the three set of data. This behavior can also be seen if we consider the mean position of the inter-quartile-range (IQR) because this value coincides with the median value. In addition, from Table 5 it is clear that the smallest and highest value of IQR corresponds to IVIDIL1 and IVIDIL2 respectively. The shaking process increases the data dispersion in the run up to roughly 5 times. Fig. 3 also shows the so-called outliers, points located over and below the U and L positions. In the present study

Table 4 Standard digital signal analysis techniques used here to characterize the accelerometric data. Display type Zero-order statistics Time domain

Frequency domain

683

Box plot Histogram Interval averaged acceleration Auto-correlation Cross-correlation Power spectral density. PSD Cumulative root mean squared acceleration. RMS Root sum of squares (RSS) one third octave RMS accel. Coherence

Fig. 2. Ten seconds interval average. Eighteen hours of data plot: (a) IVIDIL1, (b) NASA1 and (c) IVIDIL2.

684

N. Sáez et al. / Acta Astronautica 94 (2014) 681–689

Fig. 3. Boxplot of accelerometric signals: (a) IVIDIL1, (b) NASA1 and (c) IVIDIL2.

for Hanning window   n  W n ¼ 0:5 1  cos 2π N

Table 5 Values corresponds to the Fig. 3. Signal

Mean (mg)

Median (mg)

(Q3 – Q1) (mg)

IVIDIL1 NASA1 IVIDIL2

0.3538  0.0235 0.3537

0.3529  0.0236 0.3524

0.0686 0.1219 0.3422

the percentages of these outliers, calculated with respect to the total number of data in each signal, are very low, 1.3%, 0.5% and 5.5% in IVIDIL1, NASA1 and IVIDIL2, respectively. In addition, due to the existence of these outliers we have also calculated the trimmed mean, a special method of averaging that removes a percentage of the largest and smallest values before calculating the mean. However, quantitative results indicate that the differences between the maximum and minimum trimmed mean values in the tree cases are very low, that is to say 0.22%, 0.07% and 0.9% respectively. These values corroborate that the number of outliers is only a small percentage of the number of total values in each signal. The shaking process is also evident in the histograms of the signals (see Fig. 4). Data from IVIDIL1 and NASA1 indicate a normal behavior of both signals while that IVIDIL2 shows a distorted multimodal distribution. The power spectral density, equivalently the energy distribution for the different frequencies of the spectrum, has firstly been estimated using the periodogram [24]. Analytically, PSDK ¼

jFFT K j2 NUf N

ð2Þ

where FFTk is the fast Fourier transform of the signal (IVIDIL1, IVIDIL2 and NASA1), N the length of the signal (roughly 33 millions each one), fN the Nyquist frequency (in the present case 250 Hz) and U a window characteristic value obtained as U¼

1 N1 2 ∑ W Nn¼0 n

ð3Þ

0 r n rN

ð4Þ

But, in order to minimize its spectral variance, we use the Welch's method. As it is well known this method, specially recommended in the case of long signals, splits the data into overlapping segments, computes the corresponding periodogram of the overlapping segments and averages the resulting periodogram to produce a final power spectral density estimate [25] (Fig. 5). In the present cases the signals have been divided into 30 equal-length blocks with 50% overlap. These results have been obtained using a Hanning window because the literature ensures that this is the best strategy in microgravity windowing [26]. However, additional calculations using different kind of windows indicate that the frequency listing – obviously, not the amplitudes – is roughly invariant. Table 6 presents quantitative data about frequencies and amplitudes coming from Fig. 5. It can be observed that IVIDIL1 has a dominant frequency at 73.1 Hz and NASA1 at a different higher one, 141.7 Hz. Both high frequencies as well as the other appearing in the two firsts columns of this table probably correspond to life-support equipment or structural frequencies [26]. Also, notice that the values of the amplitudes associated with the other frequencies are in both cases very low. IVIDIL2 changes these tendencies increasing considerably the amplitudes and introducing a fundamental frequency of 2.8 Hz (shaking frequency). The other peaks that appear in the table are the different harmonics of this fundamental frequency. Table 6 also shows that the amplitude associated with 8.4 Hz is higher than the one corresponding to the value of the shaking frequency. This is an amazing situation, because 8.4 Hz is the third harmonic of 2.8 Hz. A plausible explanation of this fact is that the increasing is due to nonlinear phenomena [27]. We also found these frequencies in the x and z direction of the IVIDIL2, but, in these cases, their energy is smaller than the one existing in the shaking direction. Fig. 6 shows the cumulative root mean square, RMS, acceleration versus frequency for the Y component (shaking direction). As it is well known, this kind of plots quantifies the contribution of the spectral components at

N. Sáez et al. / Acta Astronautica 94 (2014) 681–689

685

Fig. 4. Accelerometric signal histograms: (a) IVIDIL1, (b) NASA1 and (c) IVIDIL2.

Fig. 5. Power spectral density. Data were calculated with Welch's method: (a) IVIDIL1, (b) NASA1 and (c) IVIDIL2.

and below a given frequency to the overall RMS acceleration level. Taking into account the Parseval's theorem this magnitude can be calculated as, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g YcumRMSk ¼

k

∑ PSDi ðg Y Þ=ΔF

i¼0

ð5Þ

The International Space Station vibratory limit requirements are defined in terms of the RMS acceleration for each one of 31 one third octave bands between 0.1 and 200 Hz [10]. The RMS calculations presented here are defined as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u f highðkÞ u g YRMSk ¼ t ∑ PSDi ðg Y ÞΔF ð6Þ i ¼ f lowðkÞ

where fhigh and flow are the maximum and minimum values of the corresponding band. Similar expressions exist for the rest of components. Finally the RMS acceleration is computed as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g RMSk ¼ g 2XRMSK þ g 2YRMSK þg 2ZRMSK ð7Þ Fig. 7 shows the RMS acceleration in one-third-octave frequency intervals of the three signals analyzed. We also

include for comparison the above-mentioned ISS vibratory limits which defines the so-called ISS microgravity mode [28,29]. We can see that IVIDIL1 and NASA1 are below the theoretical limits. On the contrary, IVIDIL2 is closer of the limit curve crossing it in 2.8 and 8.4 Hz bands obviously related with the external shaking. It is clear that if the internal motor is running, the Columbus module is not operating in a strict microgravity mode. To close the present second order statistical analyses we also present the second order moments of the three discrete signals, that is to say, their auto-correlation functions. As it is well known the auto-correlation functions show the dependence of the values of the time series against itself offset in time by one to several time steps, the corresponding lag. The auto-correlation coefficient at a particular lag L is defined here as [30], NL

∑ ðg k ððj  1ÞΔtÞÞðg k ððj 1 þ LÞΔtÞÞ

C 2gk ðL ΔtÞ ¼

j¼1

N

ð8Þ

∑ ðg k ððj 1ÞΔtÞÞ2

j¼1

where L is the number of points, Δt is 0.002 s and gk is the signal under study (IVIDIL1, IVIDIL2 and NASA1).

686

N. Sáez et al. / Acta Astronautica 94 (2014) 681–689

Table 6 Frequencies obtained from power spectral density. Frequency (Hz)

2.8 5.6 7.8 8.4 14 19.6 20 39.2 40 60 72.8 73.1 75.6 98.3 110 140 141.7 182.6 187.7

Amplitude (g2/Hz) IVIDIL1

NASA1

IVIDIL2

– – 1.15  10  9 – – – 2.99  10  10 – 2.31  10  10 – 1.77  10  7 2.36  10  6 – 6.10  10  10 – 4.43  10  10 – 6.50  10  8 1.51  10  7

– – – – – – 1.46  10  9 – 7.29  10  8 5.47  10  8 – – 5.58  10  10 9.15  10  8 6.63  10  8 – 3.79  10  5 – 1.24  10  10

1.75  10  3 1.40  10  6 – 2.76  10  3 1.00  10  4 2.07  10  4 – 3.28  10  5 – – 9.86  10  5 – 1.59  10  4 – – 9.32  10  5 – – 2.92  10  7

Positive auto-correlation might be considered a tendency for a system to remain in the same state from one observation to the next. The three correlograms, that is to say, the plots of the auto-correlation functions as a function of the lag are presented in Figs. 8 and 9. Cases (a) and (c) exhibit alternated sequences of positive and negative values decaying with time. Case (a) decays quickly showing a nice beating behavior while that in the case (c) the decrease is more progressive. This implies medium/weak (a) and strong (c) correlations. The (c) pattern is characteristic to come from underlying sinusoidal models. However, the correlogram (b) quickly decays to zero with time indicating that, in this case, the values of the signal are totally uncorrelated. Notice that Fig. 9 shows a beating behavior also in case (b). It is interesting to mention that correlograms are a commonly-used tool for checking randomness in a data set. This randomness is ascertained by computing auto correlations for data values at varying time lags. If random, such auto correlations should be near zero for any or all time-lag separations. So, taking into account the information

Fig. 6. Cumulative RMS of the Y component (shaking direction): (a) IVIDIL1, (b) NASA1 and (c) IVIDIL2.

Fig. 7. RMS acceleration versus one-third-octave frequency bands: (a) IVIDIL1, (b) NASA1 and (c) IVIDIL2. Bold line is current ISS vibratory requirements curve.

N. Sáez et al. / Acta Astronautica 94 (2014) 681–689

687

Fig. 8. Correlograms: (a) IVIDIL1, (b) NASA1 and (c) IVIDIL2.

Fig. 9. Correlogram's details of Fig. 8.

Table 7 Frequencies obtained from the analyses of auto-correlation functions. IVIDIL1

8  10 7.8 73.1

4

Autocorrelation frequency (Hz) NASA1

IVIDIL2

14.2 141.7

2.8 8.4 75.6

that the dominant frequencies obtained before also appear in the present autocorrelation analyses. The cross-correlation function is a standard quantitative method which estimates the degree of dependence between the values of two time series offset in the time by one to several steps. The normalized cross-correlation coefficient at a generic lag (L) is defined analytically [31,32], NL

∑ ðg k ððj  1ÞΔtÞÞðg r ððj 1 þLÞΔtÞÞ

j¼1

shown in Figs. 8 and 9 it is clear that the randomness assumption seems to fail here only in the labeled case c). Additionally we analyze the more relevant frequency presents in the autocorrelation (see Table 7). In the case of IVIDIL1 and NASA1 and taking into account the information contained in Figs. 8a and 9b, we have detected two near frequencies at 73 Hz and 100 Hz (see Table 6), the differences are 8  10  4 Hz in Fig. 8a and 14.2 Hz in Fig. 9b, which are responsible to produce the beatings observed in both figures. Also the comparison of Tables 6 and 7 shows

C gkgr ðL ΔtÞ ¼ sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi N

∑ ðg k ððj  1ÞΔtÞÞ2

j¼1

N

∑ ðg r ððj  1 þ LÞΔtÞÞ2

j¼1

ð9Þ As the cross-correlation is normalized, the limits (  1 and 1) indicate maximum correlation and 0 indicate no correlation at all. Fig. 10 shows the cross-correlation functions calculated for the couples, IVIDIL1-NASA1, IVIDIL1-IVIDIL2 and IVIDIL2NASA1, – labeled as (a), (b) and (c) respectively. Despite the

688

N. Sáez et al. / Acta Astronautica 94 (2014) 681–689

Fig. 10. Cross-correlation functions: (a) IVIDIL1-NASA1, (b) IVIDIL1-IVIDIL2 and (c) IVIDIL2-NASA1.

Fig. 11. Coherence functions: (a) IVIDIL1-NASA1, (b) IVIDIL1-IVIDIL2 and (c) IVIDIL2-NASA1.

different shapes of these functions it is clear that because all maxima are very low – of the order of 10  3 – there is no correlation between the signals of any of the three couples considered. On the other side, the Fourier transform of the crosscorrelation function is the cross-spectral density function. Normalizing it, we finally obtain the coherence function as [33], C XY ðf Þ ¼

jP XY ðf Þj P XX ðf ÞP YY ðf Þ 2

ð10Þ

The coherence is thus a frequency function that measures the degree of lineal dependency between two signals by testing whether they contain similar frequency components. The magnitude of coherence ranges from zero to one. If the coherence is equal to one the two signals are considered to be related linearly. Conversely, a coherence which is equal to 0 suggests that the signals are totally unrelated at that frequency. Fig. 11 shows the coherence functions calculated for the three above-mentioned couples. Because the low values of the three signals, and reinforcing the previous crosscorrelation results, it can be concluded that there are no

common frequencies in any couple. In particular, cases (a) and (c) indicate that, under conditions of the present work, there is no coupling between the two different racks containing the SAMS sensor inside the Columbus and Destiny modules. 4. Conclusions As a preliminary delivery of a wider study about the accelerometric environment of the IVIDIL experiment the present results concern the comparative analysis of three accelerometric signals. Two of them correspond to different runs of the experiment (with – IVIDIL2 – and without – IVIDIL1 – shaking) and the third one corresponds to the same interval of time as the second one but coming from SAMS sensors located in the Destiny Module – NASA1. The first general conclusion is that the statistical techniques used here have been able to successfully characterize, from an accelerometric point of view, the three runs analyzed. More in deep, the vibrational characterization suggests that the high values – but not equal – of the frequencies found in IVIDIL1 and NASA1 can be correlated with life-support equipments or structural movements all along the experiment. On the contrary,

N. Sáez et al. / Acta Astronautica 94 (2014) 681–689

the spectrum of IVIDIL2 shows a dominant frequency and their harmonics indicating that the internal movement dominates the signal breaking also its Gaussianity. In addition, the RMS acceleration levels versus one-thirdoctave frequency intervals show that NASA μg vibrational standard requirements are not accomplished if IVIDIL is in vibrational mode, that is to say, with the shaking motor turned on. Auto and cross-correlation analyses indicate that only IVIDIL2 shows a significant degree of auto-correlation. Also, the cross-correlation and the coherence functions show no-significant values. So, under the conditions of the present work, there is not mechanical coupling between the two different racks containing the SAMS sensors inside the Columbus and Destiny modules. Acknowledgments This work was supported by the MICINN under Project AYA2010–11917-E which partially covers our participation in the two active ESA projects HSF-US/2010-042 and HSF-US/2010-041. We also thank Drs. D. Melnikov and A. Mialdun of the Microgravity Research Center (Université Libre de Bruxelles) for their invaluable help in the early stages of the work. References [1] V. Shevtsova, IVIDIL experiment on-board the ISS, Adv. Space Res. 46 (2010) 672–679. [2] V. Shevtsova, A. Mialdun, D. Melinkov, I. Ryzhkov, Y. Gaponenko, Z. Saghir, Y. Lyubimova, J.C. Legros, The IVIDIL experiment on-board the ISS: thermodiffusion in the presence of controlled vibrations, C. R. Mec. 339 (2011) 310–317. [3] National Aeronautics and Space Administration, NASA, Reference Guide to the International Space Station, 2010. [4] A. Rodríguez, J. Rodríguez, A. Laverón-Simavilla, V. Lapuerta, Results and experiences from the SODI-IVIDIL experiment on the ISS, in: Proceedings of the 61st International Astronautical Congress (IAC), Prague, CZ, 2010. [5] A.V. Oppenheim, R.W. Shafer, Digital Signal Processing, Prentice Hall, Inc., Englewood Cliffs, 1975. [6] E.C. Ifeachor, B.W. Jervis, Digital Signal Processing – A practical Approach, Addison-Wesley Publishing Co., Wokingham, England, 1993. [7] 〈http://pims.grc.nasa.gov/html/ISSAccelerationArchive.html〉. [8] K. McPherson, Principal Investigator Microgravity Services Role in ISS Acceleration Data Distribution, in: Proceedings of the 38th AIAA Aerospace Sciences Meeting & Exhibit (ASME), Reno, Nevada, 2000 (AIAA – 2000–0572). [9] K. McPherson, K. Hrovat, E. Kelly, Acceleration data distribution capabilities and initial microgravity environment analysis from onboard the International Space Station, in: Proceedings of the 52nd International Astronautical Congress (IAC), Toulouse, France, 2001 (IAF – 01 – J.5.02). [10] K. Jules, K. McPherson, K. Hrovat, E. Kelly, T. Reckart, A status report on the characterization of the microgravity environment of the International Space Station, Acta Astronaut. 55 (2004) 335–364.

689

[11] K. Jules, K. McPherson, K. Hrovat, E. Kelly, Initial characterization of the microgravity environment of the International Space Station: increments 2 through 4, Acta Astronaut. 55 (2004) 855–887. [12] D.A. Zavalishin, M.Yu Belyaev, V.V. Sazonov, Estimation of dynamic characteristics of the International Space Station from measurements of microaccelerations, Cosmic Res. 47 (2009) 173–184. [13] D.A. Zavalishin, M.Yu Belyaev, V.V. Sazonov, Determination of characteristic frequencies of elastic oscillations of the International Space Station construction, Cosmic Res. 48 (2010) 352–361. [14] M. Yu Belyaev, E.V. Babkin, S.B. Ryabukha, A.V. Ryazantsev, Microperturbations on the international space station during physical exercises of the crew, Cosmic Research 49 (2011) 160–174. [15] 〈http://www.spaceref.com/news/viewsr.html?pid=32632〉. [16] 〈http://www.spaceref.com/news/viewsr.html?pid=33004〉. [17] Principal Investigator Microgravity Services, PIMS ISS, Acceleration Handbook, NASA Microgravity Science Division/Microgravity Environment Program Glenn Research Center, 2004. [18] R. DeLombard, K. Hrovat, E. Kelly, B. Humphreys, Interpreting the International Space Station microgravity environment, in: Proceedings of the 43rd AIAA Aerospace Sciences Meeting and Exhibit (ASME), Reno, Nevada, 2005 (AIAA – 2005–0727). [19] Principal Investigator Microgravity Services. International Space Station, PIMS Acceleration Data File Description Document, NASA Glenn Research Center, Cleveland, Ohio, 2002 (PIMS – ISS – 101). [20] K. Jules, K. Hrovat, E. Kelly, T. Reckart, International Space Station Increment – 6/8. Microgravity Environ. Summary Rep., 2006 (NASA/ TM – 2006–213896). [21] 〈http://www.mathworks.es/〉. [22] R. McGill, J.W. Tukey, W.A. Larsen, Variations of boxplot, Am. Stat. 32 (1) (1978) 12–16. [23] L.S. Nelson, Evaluating overlapping confidence intervals, J. Qual. Technol. 21 (1989) 140–141. [24] G. Heinnzel, A. Rüdigher, R. Schilling, Spectrum and spectral density estimation by the Discrete Fourier Transform (DFT) including a comprehensive list window functions and some new flat-top windows, Max-Planck-Inst. Gravitations Phys. (2002) 15–16. [25] M.J.B. Rogers, K. Hrovat, K. McPherson, M.E. Moskowitz, T. Reckart, Accelerometer Data Analysis and Presentation Techniques, NASA Lewis Research Center, Cleveland, Ohio, 1997. [26] K. Jules, K. Hrovat, E. Kelly, T. Reckart, International Space Station Increment 2, Quick look Rep., 2002 (NASA/TM – 2002–211200). [27] N. Sáez, Jna. Gavaldà, X. Ruiz, V. Shevtsova, On the vibrational environment of the “influence of vibrations on diffusion of liquids” experiment, in: Proceedings of the 11th International Conference on Vibrational Problems (ICOVP), Lisbon, Portugal, 9–12 September 2013. [28] B.V. Tryggvason, R.F. Redden, R.A. Herring, W.M.B. Duval, R.W. Smith, K.S. Rezkallah, S. Varma, The vibration environment on the International Space Station: its significance to fluid-based experiments, Acta Astronaut. 48 (2–3) (2001) 59–70. [29] N.J. Penley, C.P. Schafer, J.-D.F. Bartoe, The International Space Station as a microgravity research platform, Acta Astronaut. 50 (11) (2002) 691–696. [30] P.L. O'Neil, D. Nicolaides, D. Honnery, J. Soria, Autocorrelation functions and the determination of integral length with reference to experimental and numerical data, Department of Mechanical Engineering, Monash University, Australia, 2004. [31] B.C. Song, A fast normalized cross correlation-based block matching algorithm using multilevel Cauchy–Schwartz inequality, ETRI Journal 33 (3) (2011). [32] J.P. Lewis, Fast normalized cross correlation, 1995. [33] M. DosSantos Mesquita, S. Halldórsdóttir, Data analysis: filtering, crosscorrelation, coherence and applications to geophysical data using matlab, 2005.