I. ABSTRACT
Structural failures like the I‐35W Mississippi River Bridge collapse on the first of August in 2007 is besides a huge economic loss often associated with personal suffer- ing and underlines yet again how quickly existing inspection and monitoring methods may fail. Engineering geodesy has always been providing an important contribution to monitoring and deformation analysis of man‐made structures.
In this contribution the potential and limitations of a low-cost accelerometer sen- sor system and a terrestrial laser scanner (TLS) for vibration analysis will be presented in practice. Therefore a suitable sensor setup has been determined and measurements have been carried out. In addition oscillations of a bridge for reference purposes were observed with the IBIS‐S system, which is based on the principle of microwave inter- ferometry with accuracy down to the sub‐millimetre and a sampling frequency of 200 Hz. This enables the possibility to determine real‐time deformations of bridges.
The data of all three sensors have been analysed in terms of natural frequencies and damping coefficients using least squares adjustment. Furthermore acceleration measurements have been integrated and appropriate filters were applied to derive dis- placements which have been compared with those from TLS and IBIS‐S. Hence this contribution provides information on which accuracies can be achieved for the de- rived parameters under real conditions which is fundamental for upcoming dynamic deformation analyses of structures.
II. INTRODUCTION
A multitude of sensors and sensor arrays as well as combinations of various meas- urement systems is currently in use for dynamic testing in the field of structural health monitoring (SHM) of bridges.A multitude of sensors and sensor arrays as well as combinations of various meas- urement systems is currently in use for dynamic testing in the field of structural health monitoring (SHM) of bridges.A multitude of sensors and sensor arrays as well as combinations of various meas- urement systems is currently in use for dynamic testing in the field of structural health monitoring (SHM) of bridges.
III. MEASURING SETUP AND SYSTEMS
The potential and limitations of different sensor systems for modal analysis of bridges will be investigated under real conditions. Therefore measurements have been carried out on a bridge near Braunschweig, Germany, which has been chosen due to its intense vibration characteristic. The observed bridge, which is shown in Figure 1, has a length of approx. 76 m and width of 13 m. Due to the requirements of the posi- tioning of the sensors and to ensure comparative measurements the sensors were placed close to the abutment indicated by a circle in Figure 1.
Figure 1. Observed bridge near Braunschweig, Germany
- Accelerometer Sensor System
The time synchronized acceleration measurements of at most 16 sensors can be transferred via USB connection to a computer over a distance up to 100 m. Accelerations can be measured with an accuracy of a = 20 µg⁄√Hz and a sampling rate up to 600 Hz.
- Terrestrial Laser Scanner
Terrestrial laser scanners (TLS) are active 3D measuring systems that are captur- ing distances to objects in equal increments of arc around the rotation and tilting axis. TLS are able to measure up to a million points per second with single point accuracies of a few millimeters but are usually not commonly used for modal analysis of struc- tures. However, some systems like the Zoller+Froehlich Imager 5003 are able to scan in a point mode which enables the possibility to perform distance measurements to a single point of an object with an extremely high sampling rate of 125 kHz. Hence measurements by using TLS can be relevant for modal analysis of structures.
- Terrestrial Interferometric Radar
The main principles concerning measurement and processing of satellite-based ra- dar interferometry are known in the field of radar remote sensing since many years. In the last years a transfer of these principles to ground-based measurement approaches happened. These terrestrial, interferometric radar systems are referred to as “terrestrial interferometric synthetic aperture radar (t-InSAR)”. With such systems the highly accurate determination of movements or change rates of local limited objects is possi- ble and has been shown by PIERACCINI et al. (2006), RIEDEL et al. (2011) and RÖDELSPERGER (2011).
Since 2006 such a system called IBIS (Image by Interferometric Survey), devel- oped by IDS (Ingegneria dei Sistemi), is available for the use in field of engineering geodesy. This system is available in different configurations. Beside the version for static monitoring (e.g. landslides, dams, etc.) a special version for the dynamic and static monitoring of structure vibrations exists, the IBIS-S which is depicted in Figure 2 on the outer right.
Figure 2. Low-cost accelerometer sensor system (left), TLS (middle) and IBIS-S (right)
IV. DATA ACQUISITION AND PREPERATION
The measurements are carried out during traffic and shall include sufficient evalu- able measurements for subsequent modal analysis. In particular the sections of ambi- ent vibrations, which occurred after excitation, are relevant for the determination of natural frequencies, damping coefficients and mode shapes that are called ambient windows. A detailed overview about ambient vibration monitoring can be found in.
The single point accuracy of the used terrestrial laser scanner (TLS) Z+F Imager 5003 is technically not high enough to detect displacements smaller than a millimetre. The only way to detect such small displacements is to perform measurements with a high sampling rate and to average the measurements afterwards. Therefore a sampling rate of 7812 Hz was used in order to achieve a reasonable accuracy for the averaged distance measurements.
Afterwards 100 filtered distance measurements were averaged which resulted in a theoretical sampling rate of 78.12 Hz for the TLS time series. Furthermore trend and offset were removed by subtracting an adjusted straight line from the post-processed TLS data as well as of the raw displacements obtained from IBIS-S and acceleration measurements. The resulting ambient window of the TLS measurements is depicted in Figure 6. The maximum amplitude of the oscillation is approximately 0.4 mm and shows a smooth behaviour for the first 15 seconds while the rest is noisier. The damp- ing characteristic is visible with some deviations from a smooth damped harmonic oscillation.
Figure 3. Ambient window derived from TLS.
The ambient window obtained from accelerometer measurements is shown in Figure 4 where the vibration and damping characteristic of the bridge are clearly visi- ble. Although in comparison to post-processed TLS or raw IBIS-S data the signal it- self is much noisier.
Figure 4. Ambient window obtained from accelerometer.
Due to the high accuracy of the IBIS-S measurements the observed oscillation with maximum amplitude of nearly 0.5 mm is very smooth and reveals an explicit damping characteristic, which can be seen in Figure 5.
Figure 5. Ambient window obtained from IBIS-S
- Natural Frequency and damping coefficient
The ambient window obtained from each sensor were used to determine the first natural frequency and damping coefficient using least squares adjustment, see e.g. MIKHAIL (1976), with the functional model for a damped harmonic oscillation including amplitude a , frequency f , phase shift j and damping coefficient d as unknown parameters. The adjusted first natural frequency and damping coefficient as well as their standard deviations are listed in Table 1.
The difference between the calculated first natural frequencies of all sensors is smaller than 0.6 mHz, also the damping coefficient derived from accelerometer and IBIS-S are nearly equal and differ by only 0.06 %. The damping coefficient deter- mined from TLS measurements is remarkably different from those derived via accel- erometer or IBIS-S measurements. The pre-processing of the TLS measurements hardly influenced the determination of the damping coefficient but on the natural fre- quency. The different damping coefficient needs to be clarified in further investiga- tions.
The high accuracy of the IBIS-S is also reflected in the standard deviations of the first natural frequency and damping coefficient which is approximately five times smaller than the achieved value for the standard deviations using accelerometers or TLS. Hence it is justified to regard IBIS-S as a reference sensor.
V. CONCLUSION AND OUTLOOK
This contribution provides information about accuracy and reliability of modal pa- rameters derived from low-cost accelerometer sensor system, TLS and IBIS-S under real measurement conditions. The used low-cost accelerometer sensor system is a suitable sensor for modal analysis of structures. Natural frequencies, damping coeffi- cients as well as derived displacements could be determined with high accuracy.
Besides poor single point accuracy of TLS measurements such systems are reveal- ing great potential for modal analysis of structures. A maximum sampling rate of 125 kHz could have been applied for the measurements using the presented TLS although a relatively small sampling rate of 7812 Hz was used which led to a standard devia- tion smaller than 0.05 mm for the obtained displacements. Increasing the sampling rate will lead to a more precise determination of natural frequencies and displace- ments while different results for damping coefficient still need to be clarified in fur- ther investigations. Furthermore some TLS are able to scan in a profile mode which enables the possibility to observe the whole length of a bridge at once with a sampling rate up to 50 Hz. The accuracy and reliability of derived modal parameters from TLS measurements scanning in profile mode still needs to be analysed.
For an upcoming dynamic deformation analysis of structures the correlation be- tween measurements as well as the applicability of existing statistical tests on derived modal parameters needs to be determined.
The implementation of geodetic strategies for deformation analysis of a combined geometric and dynamic monitoring of structures will offer a much more significant and reliable tool for damage detection which will provide a substantial contribution to structural health monitoring.
