SIM/AtOMA: User’s Manual
4.6 Tutorial: Ponte sul Mincio, Verona
4.6.5 Tutorial: identification of the structure using AtOMA - AutoEFDD
Selection of input data Once AtOMA is launched, the check-box Au-toEFDD: New input data was selected. Then, in order to choose the folder where the measurement files were located the Browse button was pressed.
Figure 4.47: AutoEFDD: select input data
The parameters are chosen as displayed in Figure 4.47. Note that not all the channels available in the files were selected, since channels from 10 to 15 were excluded from the analysis.
The button Start is pressed in order to perform the first step of the FDD analysis (calculation of the cpsd matrices and singular value decomposition).
A progress bar will appear that allows you to watch the progress of the calcu-lations (Figure 4.48).
Figure 4.48: Progress bar.
Identification of the structural modes Once the calculation is com-pleted, it is required to perform the natural frequencies identification. The parameters are set as displayed in Figure 4.49
Figure 4.49: Natural frequencies identification.
A progress bar will inform you on the development of identification (Figure 4.50).
Figure 4.50: Progress bar.
The mean values of the results of the frequency identification are displayed in the text field in the Results Panel (Figure 4.51).
Figure 4.51: Mean values of the natural frequencies.
The development over time of the natural frequencies is displayed by pressing the Natural Frequencies Trend button (Figure 4.52).
Figure 4.52: Development of natural frequencies.
The auto-spectrum function is displayed by pressing the Singular values &
MAC Figure button. In Figure 4.53 the peaks corresponding to identified natural frequencies have been highlighted.
Figure 4.53: Singular values & MAC Figure.
The results are summarized in Table 4.2. It can be seen that the identification has been successfully held for almost every measurement file. The low standard deviation indicates that the frequencies are poorly dispersed.
Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6
fmax 2,173 4,077 4,590 6,177 9,741 11,572
fmin 2,100 4,028 4,517 6,128 9,692 11,523
fmean 2,130 4,064 4,548 6,139 9,719 11,561 std.dev 0,021 0,018 0,029 0,015 0,022 0,016 success% 96,4% 92,7% 98,2% 74,5% 76,4% 87,3%
Table 4.2: Frequency results of the monitoring using AutoEFDD.
Extraction of damping ratio Then, once the identification of the struc-tural modes is complete, damping ratio parameters must be calculated. First the parameters (MAC Threshold, Max Correlation and Min Correlation) are configured as shown in Figure 4.54.
Figure 4.54: Damping ratio calculation.
By pressing the Calculate Damping Ratio button the damping ratio parameters are extracted and their mean values are displayed in the text field in the Results panel (Figure 4.56).
Figure 4.55: Mean values of the damping ratios.
Validation of the results It is possible to launch the validation panel by pressing the Validate button. From this panel the user is allowed to observe the results obtained for each file and each structural mode. The tasks available through this panel are listed in Section 4.3.2.
Figure 4.56: Validation of the damping ratios.
The graphs for the first mode (2,124 Hz) of the file of the 24th July are dis-played in the following figures.
In Figure 4.57 is displayed the SDoF Auto-Spectral function for the first struc-tural mode. The selected frequency function shows good characteristics, as it is well defined and there is no noticeable noise.
Figure 4.57: SDoF Auto-Spectral function.
In Figure 4.57 the normalized auto-correlation function for the first structural mode is displayed. The behavior exhibited by the function is that of a typ-ical structural decay function and does not appear distinctive of a harmonic excitation.
Figure 4.58: Normalized auto-correlation function.
The logarithmic decrement shown in Figure 4.59 detaches itself, especially in the initial portion, from a linear trend.
Figure 4.59: Logarithmic decrement.
Therefore a lower value for the parameters Max Correlation and Min Corre-lation is chosen: Max CorreCorre-lation=0,6 and Min CorreCorre-lation=0.1. CalcuCorre-lation of the damping ratios is performed again by clicking the Calculate damping ra-tios button. The normalized auto-correlation function and the corresponding logarithmic decrement are shown in Figure 4.60.
Figure 4.60: Normalized auto-correlation function and logarithmic decre-ment with new parameters.
Figure 4.61 displays the correlation between the natural frequencies calculated using the EFDD analysis in frequency domain and those calculated, again using EFDD, in time domain. The values thus calculated are practically equal to each other.
Figure 4.61: Frequency (F) vs Frequency (T).
Damping ratio results Once the validation is complete, results of the calcu-lation can be displayed by pressing the buttons Damping vs Frequency (Figure 4.62), Mean damping vs Frequencies, Box plot (Figure 4.63) and Damping vs time (Figures 4.64, 4.65 and 4.66).
In Figure 4.62 the extracted modal parameters are displayed for all the files.
Mode 1 and 4 are the structural modes that have allowed a better identification of the damping ratio, although presenting some dispersion in the results.
Figure 4.62: Damping vs frequency figure.
The box-plot description shown in Figure 4.63 is actually useful only for mode 1, 4 and 5 as they are the only modes to possess a sufficient success rate.
Figure 4.63: Box plot description of damping ratio results.
In Figures 4.64, 4.65, 4.66 are shown the extracted damping ratio values for each structural mode over time. It is clear that modes 2, 3 and 6 do not have a sufficient number of results and the correspondent damping ratio can not be used, at this stage, for model updating operations.
Since the time span for the monitoring was too narrow, it was not possible to observe any type of seasonal fluctuation of the results.
Figure 4.64: Trend over time of damping ratios for mode 1, 2.
Figure 4.65: Trend over time of damping ratios for mode 3, 4.
Figure 4.66: Trend over time of damping ratios for mode 5, 6.
It can be seen from Table 4.3 that damping ratio results for this structure are affected by a high level of uncertainty, which is confirmed by the low success rate for modes 2, 3, 5, 6 and the high dispersion of the results especially for mode 4. Therefore it is required to perform a validation of the results using AutoSSI method.
Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 ζmax 4,747% 3,799% 4,070% 7,111% 3,562% 1,629%
ζmin 1,164% 1,462% 1,901% 0,827% 0,891% 0,920%
ζmean 2,314% 2,152% 3,003% 3,500% 2,069% 1,373%
std.dev 0,864% 0,975% 0,858% 1,608% 0,935% 0,324%
success% 89,1% 9,1% 9,1% 58,2% 20,0% 7,3%
Table 4.3: Damping results of the monitoring using AutoEFDD.
Saving the template If the parameters used to configure the analysis (NFFT, Channels, MAC threshold for frequency, Frequency sensibility, MAC Thresh-old for damping, Max and Min Correlation) are considered to be the ones that provide the best results for the structure, then it is possible to save a Template file. The template file contains information about the position of the modal domains of the structure, therefore, subsequent analysis are carried out to con-firm the presence of a mode of vibration around the modal domain previously defined.
Figure 4.67: Save template button.
To save a template file, press the Save template file button. A dialog requires the user to specify some details of the analysis. By pressing OK the tem-plate is automatically saved inside the Temtem-plate folder of the program. The name of the template file is automatically defined by the name of the template set by the user: if the template is called Mincio OK, the file name will be T emplate_M incio_OK.ef dd.
Save results To save the results of the analysis, press the Save results but-ton.
Figure 4.68: Save results button.
If a template file was previously saved, the program automatically saves the results file inside the Results folder corresponding to the template. Otherwise, a dialog asks the user to specify the folder where the file will be saved.
Analysis using AutoSSI To perform a SSI analysis, press Browse to select the folder containing the files and set the channels to use in the analysis. For the current analysis, the chosen channels are 1,2,3,4,5,6,7,8,9 as shown in Figure 4.69.
Figure 4.69: Analysis using SSI.
Then, press Start SSI in order to launch the analysis. Note that AutoSSI procedure requires requires much more time and processing power higher than AutoEFDD.
Once the analysis is finished, the user is asked to save the SSI results file.
The results given by AutoSSI procedure are displayed in Tables 4.4 and 4.5.
AutoSSI analysis could not identify the 6th structural mode at 11,56 Hz, prob-ably due to the calibration of the internal parameters of the model.
Mode 1 Mode 2 Mode 3 Mode 4 Mode 5
fmax 2,165 4,279 4,710 6,111 9,751
fmin 2,098 4,199 4,310 5,988 9,735
fmean 2,126 4,235 4,553 6,057 9,743 std.dev 0,021 0,027 0,132 0,047 0,011 success% 100,0% 72,7% 90,9% 54,5% 18,2%
Table 4.4: Frequency results of the monitoring using AutoSSI.
Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 ζmax 3,551% 3,613% 7,329% 4,252% 3,734%
ζmin 1,451% 1,692% 2,464% 2,496% 2,606%
ζmean 2,755% 2,700% 4,590% 3,253% 3,170%
std.dev 0,723% 0,596% 1,474% 0,700% 0,798%
success% 100,0% 72,7% 90,9% 54,5% 18,2%
Table 4.5: Damping results of the monitoring using AutoSSI.
The reason why these results are of interest resides in the possibility to com-pare them with those extracted by the method AutoEFDD. By pressing the Validate AutoEFDD results button in the SSI panel, it is possible to compare the results obtained with the two different procedures. The program asks the user to select the AutoEFDD and AutoSSI results files to compare. Then Ta-bles 4.6 and 4.7 are displayed, which contain the results for both AutoEFDD and AutoSSI, including the relative error between the results.
In Table 4.6 are shown the natural frequencies extracted using the two proce-dures. The results are very close, except for the mode 6 which is not identified by the method AutoSSI.
Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6
f (EF DD) 2.128 4.067 4.547 6.146 9.720 11.564
Success%(EF DD) 100% 92.7% 98.2% 90.9% 76.4% 87.3%
f (SSI) 2.126 4.230 4.554 6.057 9.743
-Success%(SSI) 100% 81.8% 90.9% 54.5% 18.2%
-Error 0.1% 3.9% 0.1% 1.5% 0.2%
-Table 4.6: Comparision of the natural frequencies extracted using Au-toEFDD and AutoSSI.
In Table 4.7 are displayed the damping ratios obtained with the two procedures.
AutoSSI presents a higher success rate than AutoEFDD for modes 2, 3, 5.
The average results show an error ranging from 9% to 44%. These errors are considerable acceptable, given the structural differences of the models. The
order of magnitude of the parameters is in fact confirmed, and these values could be used for the calibration of a FE model.
Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 ζ(EF DD) 2.236% 2.152% 3.003% 3.545% 2.034% 1.373%
Success%(EF DD) 89.1% 9.1% 9.1% 60.0% 20.0% 7.3%
ζ(SSI) 2.755% 2.700% 4.590% 3.253% 3.170%
-Success%(SSI) 100% 72.7% 90.9% 54.5% 18.2%
-Error 20.8% 22.6% 41.8% 8.6% 43.7%
-Table 4.7: Comparision of the damping ratios extracted using AutoEFDD and AutoSSI.
Overall, it can be said that the identification made by using the AutoEFDD is validated.
New AutoEFDD analysis using template To start an analysis based on a previous one, select from the drop-down menu File → New from template.
Then, select the template file previously saved (for example T emplate_M incio _OK.ef dd).
In the Input data panel, select the check-box AutoEFDD: New input data and press Browse to select the folder containing the measurement files, then press Start. The program will automatically process all the steps of the anal-ysis, since no user input is required. When the calculation of the damping ratios is completed, the program saves the results inside the template’s Re-sults folder (in this case, ReRe-sults/M incioOk/ and merges the new results file with the other files in the folder (if any). The merged results file is called current_sequence.mat and it can be opened using the View results button.
Schedule functions To set up the automatic execution of the template-driven analysis, select Schedule → New Schedule from the drop-down menu.
The panel shown in figure 4.70 displays a typical configuration of the schedule.
Figure 4.70: New Schedule.
In this case, the chosen template is T emplate_M incio_OK.ef dd, and the folder is the one in which the program that handles the measurements of the structure puts new files. Since new files are usually stored at 10:45 and 17:45, the analysis is programmed to automatically start at 11:00 and 18:30.
Pressing Save, the scheduled task is saved as a configuration file inside the schedule folder, whose name is sch_M incio.schedule.
In order to enable the scheduler, select from the drop-down menu Schedule → Schedule launcher. The user is asked to choose the configuration file, in this case sch_M incio.schedule. A dialog displays the next scheduled analysis.
Figure 4.71: Schedule launcher.
Pressing OK, the scheduler is disabled.
When the specified time is reached, the analysis is performed automatically without user intervention, and once completed, the system gets back waiting for the next run.
Conclusions With the perspective of the program user, an analysis of the dynamic identification of the bridge over the Mincio was developed, demon-strating the reliability of the results obtained by the procedure AutoEFDD by the procedure AutoSSI also available as a ATOMA.
At the current state, it is necessary to rely on other software in to correlate the modal shapes of the FE model with those identified with modal testing.
For other expected future developments for the program, look at 5.6.