OMA Research of Sky Tower in Wrocław, Poland

Sky Tower is a skyscraper in Wrocław, Poland. Construction began in December 2007 with the demolition of the 24-story Poltegor structure, until then the tallest building in the city. Sky Tower is the tallest residential building in Poland in the category of height to roof and category of highest floor but is shorter than the Palace of Culture and Science. On the 49 floor is a publicly accessible viewpoint. Operational Modal Analysis (OMA) of Sky Tower was done in 2012 when the tower was almost completed. No excitations with the exception of ambient excitations were used 8 eigenfrequencies and eigenforms were detected.


Subject of study
The Sky Tower is a skyscraper in Wrocław, Poland, Figure 1.The Sky Tower complex consists of 3 connected buildings: B1 -3-storey platform, in which the shopping gallery is located.B2 -50-storey tower, levels from 28 to 48 contain 184 apartments and the remaining levels provide office space.B3 -19-storey "sail" containing 52 apartments on levels from 11 to 18, as well as offices.The highest tower with spire was originally planned to be 258 m tall (roof height 221 m).The construction of a reinforced concrete structure was completed in September 2011, and its final height is 205.82 m.Total building height is 212 m.

Measurements
Measurements were made at the end of the construction works.Measurements were carried out using practically all the available measuring equipment.Fifteen seismic accelerometers were connected to two system PULSE cassettes.
Two variants of dynamic research were prepared: the first variant included the connection of two system PULSE cassettes and their full synchronization via 2 optical fibre junction stations.However, due to their weight, it proved impossible to carry the suitcases containing the optical fibre stations so high and the availability of lifts was very limited.the second variant included connecting two PULSE system cassettes and synchronizing them directly without the optical fibre station using a long LAN cable.
The second variant was finally realized.Signals from fifteen accelerometers mounted in the horizontal direction were recorded.Three DeltaTron 8430 accelerometers were installed on each of the selected floors -three measurements on each level identify the movement of the floor as a rigid plane body.2, where the dotted line indicates the outline of the B2 building (tower), the dashed line schematically shows the elevator-stair shaft.The solid line shows the shaft that forms the geometric model in the OMA analysis.
Because the vibration were measured mainly for OMA, the measurements were long -60 minutes.The distribution and assembly of the equipment took much longer than the measurements itself.Nevertheless, the entire measuring system was mounted, applied to measurements and disassembled during one day.

Results
Table 1 summarizes OMA analysis results obtained using the stochastic methods SSI-PC.In order to compare the eigenforms and check for their linear dependence on each other, the value of the Modal Assurance Criterion (MAC) was calculated.The results of this analysis are shown in Fig. 3 and in Table 2.Because of the very large value of the MAC (0.9), it was considered that the forms N o 4 and N o 5 are one eigenform of (MAC = 0.91).The result of the comparison of eigenforms N o 7 and N o 8 (MAC = 0.96) were interpreted similarly -compare Table 3.
It should be noted that the above eigenforms have been identified using stochastic methods SSI-PC.The use of identification methods in frequency domain allowed the identification of only one eigenfrequency in the region up to 3 Hz -1.545 Hz.Deeper analysis showed that the incidence of 1.545 Hz corresponds to the same form that has been detected by the SSI-PC method, i.e. form N o 7 and N o 8, which was previously considered to be one form that corresponds to the frequency (1,538-1,539) Hz.
The final results of the OMA analysis within the scope of the detected eigenfrequencies and the corresponding damping ratios are shown in Table 3.The eigenforms corresponding to the detected eigenfrequecies are shown in the Fig. 4, Fig. 5 and Fig. 6.

Conclusions
Based on the analysis of the results obtained, it is clear that stochastic methods are the more efficient methods of OMA analysis of a tall buildings.Within the analyzed range up to 3 Hz, 8 eigenfrequencies were detected.The use of frequency domain identification methods allowed for the detection of only one eigenfrequency in the range up to 3 Hz, which was consistent with one of eigenfequencies detected by the stochastic method.This confirms the correctness of the operation of the stochastic algorithms, but at the same time demonstrates the essential advantage of using stochastic methods in the detection of relatively low eigenfrequencies of large construction and engineering structures.
According to the authors, OMA modal analysis methods based on stochastic algorithms should be the standard for modal analysis of large structures, especially high and very high buildings.

Fig. 2 .
Fig. 2. The placement of accelerometers in the Sky Tower in Wrocław (OMA scheme).

Table 1 .
The results of Operational Modal Analysis (SSI-PC methods).

Table 3 .
The final results of Operational Modal Analysis.