New Trends in Engineering Surveying Bridge Monitoring using TLS, Accelerometers and Ground-Based Radar Interferometry

Transcription

1 Invited lectures New Trends in Engineering Surveying Bridge Monitoring using TLS, Accelerometers and Ground-Based Radar Interferometry Ján Erdélyi 1, Peter Kyrinovič 1, Imrich Lipták 1, Alojz Kopáčik 1 1 Department of Surveying, Faculty of Civil Engineering, Slovak University of Technology in Bratislava, Vazovova 5, Bratislava, Slovakia, jan.erdelyi@stuba.sk, peter.kyrinovic@stuba.sk, imrich.liptak@stuba.sk, alojz.kopacik@stuba.sk Abstract. The weather conditions and the loading during operation cause changes in the spatial position and in the shape of engineering structures that affect static and dynamic function and reliability of these structures. Due to these facts, geodetic monitoring is an integral part of engineering structures diagnosis and gives important information about the current state (condition) of the structure. The development of the measuring instruments enables deformation monitoring of engineering structures using non-conventional surveying methods. For static deformation monitoring it is feasible to use the technology of terrestrial laser scanning, (TLS) if the selected parts of the monitored structure are approximated by single geometric entities (small planar surfaces). For dynamic deformation measurements (Structural Health Monitoring) of bridge structures ground-based radar interferometry and accelerometers are often used for the vibration mode determination using spectral analysis of frequencies. The paper deals with the experiences of researchers of The Department of Surveying, STU Bratislava in the field of deformation monitoring of bridge structures by nonconventional surveying methods. It describes the experimental deformation monitoring of the Liberty Bridge (Bratislava, Slovak Republic) performed using TLS, ground-based radar interferometry and accelerometers. The procedure of measurement, the data processing and the results of deformation monitoring are illustrated. Keywords: accelerometer, deformation monitoring, ground-based radar interferometry, structural health monitoring, terrestrial laser scanning. 1. Introduction Bridge structures are integral parts of the transport infrastructure in the Slovak Republic; their number in recent decades has increased by several times. The modernization of the transport infrastructure has caused the increase in traffic intensity, which is also reflected in the increased operating load of the bridges. This causes changes in the spatial position and the shape of the 27

2 SIG 2016 International Symposium on Engineering Geodesy, May 2016, Varaždin, Croatia constructions, which affect their static and dynamic functions and reliability. Due to these facts, geodetic measurements are integral parts of the bridge structure diagnosis. For static deformation monitoring of bridges, the technology of terrestrial laser scanning (TLS) could be used. The advantage of TLS over conventional surveying methods is the efficiency of the spatial data acquisition. TLS allows for a contactless determination of the spatial coordinates of points lying on the surface of the measured object. The scan rate of current scanners (up to 1 million points per second) allows for a significant reduction in the time necessary for the measurements; they respectively increase the quantity of the information obtained about the object measured. To increase the accuracy of the results, selected parts of the monitored structure can be approximated by single geometric entities using regression. In this case the position of the measured points is calculated from tens or hundreds of scanned points [Vosselman & Maas 2010]. Nowadays, the knowledge of the dynamic characteristics of a bridge structure s behaviour is also increasingly important. They are mainly caused by wind and by moving of the objects on the structure (pedestrians, cyclists, vehicles). These affect the resonant behaviour of the structure, which results in its dynamic deformation that is described by the modal characteristics of the structure s deformation (vibration modes). To achieve the safe operation of the structure it is necessary to design the deformations by computational modelling and to monitor them during the loading tests. Likewise, long-term monitoring of the structure using suitable methodologies is essential. The data obtained by dynamic monitoring significantly contribute to the stable and safe operation of the bridge and can be used for the calibration of a structural numerical model. For Structural Health Monitoring (SHM) of bridges, mainly accelerometers, ground-based radar interferometry, GNSS, tilt sensors and the like, are used. The dynamic characteristics of the monitored bridge are calculated using spectral analysis methods from the data (time series) acquired by the above mentioned technologies. 2. Deformation monitoring using TLS The determination of the displacements of structures from laser scanning data is relatively simple if the deformation is determined by differential models (as the difference between surfaces), or by measuring the coordinate difference between discrete measured points. In both cases the accuracy of the results depends on the accuracy of the position of scanned points (several millimetres). To increase the accuracy of the results, the measured points (monitored parts of the scanned structure) have to be modelled using regression. The vertical displacements of the measured points may be determined as the difference between the heights of these points in each measurement epoch. The height of the points could be calculated by modelling planes using orthogonal regression, while the position of the measured points in the XY plane can be defined by their coordinates in the plane [Figure 2.1]. 28

3 Invited lectures The advantage of this procedure is that the position of the measured points does not change with the thermal expansion of the structure. The heights of the measured points are calculated by projecting the points onto regression planes. Figure 2.1 Determination of the height of measured points Orthogonal regression is calculated from the general equation of a plane: =0 (1) where: a, b and c are the parameters of the normal vector of the plane, X, Y and Z are the coordinates of the point lying in the plane, d is the scalar product of the normal vector of the plane and the position vector of any point of the plane. Singular Value Decompensation is used for the calculation of the elements of the normal vector [Čepek et al. 2009]: = (2) where: A is the design matrix, with dimensions nx3, and n is the number of points used for the calculation. The column vectors of U nxn are normalized eigenvectors of matrix AA T. The column vectors of V 3x3 are normalized eigenvectors of A T A. The matrix Σ nx3 contains eigenvalues on the diagonals. Then the normal vector of regression plane is the column vector of V corresponding to the smallest eigenvalue from Σ. The design matrix has the form: ( ) ( ) ( ) ( = ) ( ) ( ) (3) ( ) ( ) ( ) where: ( ), ( ) and ( ) are the coordinates of the point cloud reduced to a centroid. The position of the observed points in XY plane is defined as fixed. The Z coordinates (heights) of the measured points are calculated by projecting the points onto regression planes [Figure 2.1] using formula: = The standard deviations of the results are calculated using uncertainty propagation law, from the standard deviation of the vertical component of the transformation error and the standard deviation of the regression plane. (4) 29

4 SIG 2016 International Symposium on Engineering Geodesy, May 2016, Varaždin, Croatia The transformation of the point clouds in each measurement epoch is needed to obtain data in a common coordinate system in each measurement epoch. The accuracy of the transformation is given by the differences (ΔX, ΔY, ΔZ) between the identical reference points succeeding the transformation of the scanned point cloud of the current measurement epoch into the coordinate system of the initial measurement epoch. The standard deviation of the regression planes is calculated from the orthogonal distance of the points of the point cloud from these planes. Dispersion of the points around the plane mainly reflects the random error (noise) of the distance measurement by TLS (coordinate determination). To eliminate the effects of the systematic errors, it is recommended to perform the measurements in the same conditions in each epoch (position of the scanner, temperature, etc.). The effect of the systematic errors is included in the accuracy of determination of coordinates of the reference points (stable objects in each epoch). To get a better imagination about the behaviour of the monitored structure, the vertical displacements can be transformed into the direction of the normal vectors of the regression planes. An application based on software MATLAB Displacement_TLS [Figure 2.2] was developed for automated data processing. The aforementioned computational procedure is performed and controlled with help of the graphical user interface of the application. The application was created as a standalone app; however, the Matlab Runtime is necessary to be installed. 30 Figure 2.2 Print screen of the Displacement_TLS dialog window 3. Deformation monitoring using accelerometer measurements Accelerometers generate an output signal in the form of a time series of the accelerations. Determining relative displacements can be accomplished by several

5 Invited lectures methodologies. The most common method is the double integration of the acceleration by a rectangular or trapezoidal rule [Sangbo 2010]. Generally, this problem can be described by the formula ( ) = ( ) (5) The selection of the appropriate sample rate has a significant effect on the accuracy of the calculations. In this case it is recommended to provide the measurement with a sample rate at least twice that of the highest significant frequency of the vibration of the structure. Another important factor influencing the accuracy of the integration of the measurements is the implementation of a high-pass filter. By using a suitable filter, the long-term components of the measured signal (e.g., drift) can be eliminated. Therefore, it is necessary to design a filter with a minimum frequency and magnitude response. The effect of the filter seen on the raw measurements can be analysed by a transfer function. 4. Deformation monitoring using ground based radar Ground-based radar is an innovative measurement approach for the dynamic deformation monitoring of large structures such as bridges [Bernardini et al. 2007], [Pieraccini et al. 2007]. Radar measurements use the Stepped Frequency Continuous Wave (SF-CW) technique. This approach enables the detection of target displacements in the radar s line of sight. The basic principle of the technique is the transmission of a set of sweeps that consist of a number of electromagnetic waves at different frequencies. A pulse radar generates short-term duration pulses to obtain a range resolution that is related to the pulse durations according to = (6) where c is the speed of light in a free space, and τ is the time of the pulse s flight. At each time interval of the measurements, the components of the received signals represent a frequency response measured at the number of discrete frequencies. The application of an Inverse Fourier Transformation frequency response is transformed to a time domain. The system then builds a onedimensional image a range profile, where the reflectors are resolved with a range resolution according to their distance from the radar [Figure 4.1]. When the range profile is generated, the displacements of the targets are detected by the Differential Interferometry technique. This approach compares the phase delay of the emitted and reflected microwaves Radial displacement is therefore linked with the phase delay Δφ by the following = Δ (7) where λ is the wavelength of the signal. Radial displacements of the targets can be transformed into vertical displacements according to figure

6 SIG 2016 International Symposium on Engineering Geodesy, May 2016, Varaždin, Croatia Figure 4.1 Radar range resolution principle 32 Figure 4.2 Radial displacement and projected displacement 5. Spectral analysis of the measured data In the case of determining bridge vibration modes, spectral analysis methods are used. The most often used is the Fourier transformation. This approach describes a time-dependent signal by harmonic functions that can be used to transition the signal from the time to the frequency domain. The signal can be expressed continuously or in a discrete form. In practical applications a finite number of the data is analyzed by the numerical method of the Fourier transformation, known as the discrete Fourier transformation (DFT). Calculation of the DFT can be realized by several algorithms. In the case of the dynamic deformation of bridges, the fast Fourier transformation (FFT) is most often used. The FFT is defined as ( ) = ( ) ( ) / (8) where ( ) is the autocorelation function, and ( ) is the spectral window function [Cooley & Tukey 1965]. An alternative is the application of the Welch method that uses the FFT algorithm. In this case, the spectral density of the time series is computed from the overlapped segments. These segments are analysed by the FFT method. The results give a smooth periodogram and better accuracy of the frequencies

7 Invited lectures determined. However, the resolution of the magnitude spectrum is unfortunately lower [Welch 1967]. A cross-spectral analysis of two-time series (signals) is used for the crosscorrelation and the time delay between them. It can be described as a different dynamic response to external effects (wind, pedestrians, cyclists, etc.). The crossspectral density of the two-time series can be estimated by the FFT of the crosscorrelation function as ( ) = ( ) ( ) / (9) where ( ) is the cross-corelation function, and ( ) is the spectral window function [Bracewell 1965]. The correlation of two time-synchronized signals at a specific period can be defined by their coherence. The significant frequencies of the signals are determined by Fisher s periodicity test. The amplitudes and phase shifts of the signals can be estimated by the least squares method. 6. Liberty Bridge (Slovakia) The Liberty Bridge is part of a cycling route between the Bratislava district of Devínska Nová Ves (the Slovak Republic) and Schlosshof (Austria). It crosses the river Morava at the river kilometre 4.31, where a transverse cycling route, a stagnant pool of the river Stará mláka, the ruins of the old bridge, and a border fortification bunker are located. The bridge is built over an inundation area on both sides in a protected floodplain forest [Figure 6.1]. The total length of the bridge structure is m [Agócs & Vanko 2011]. The substructure consists of reinforced-concrete pillars in which the supports of the main structure are anchored. The main structure consists of a steel structure with a triangular truss beam suspended over the river Morava and the inundation bridges on both sides of the river. Figure 6.1 Liberty bridge, suspended structure (left) and inundation bridge (right) The measurements were focused on determining any displacements of the suspended bridge; it consisted of 3 sections with spans of 30.0 m m m = m over the river. The reinforcing girder is a tubular triangle shaped with an orthotropic deck. The middle section has the shape of a circular 33

8 SIG 2016 International Symposium on Engineering Geodesy, May 2016, Varaždin, Croatia arc with a radius of m. The deck is composed of a metal plate, steel girders that are positioned in a transverse direction, and of the longitudinal reinforcements. The cross slope of the deck is 2% from the longitudinal axis of the bridge to the edges; the clearance width is equal to the width of the 4.0 m traffic lane. The structure of the main construction is suspended on four pylons that are designed as dual - hinged rectangular frames. The diameter of the pylons is m; their height is 17.7 m [Figure 6.1]. 7. Deformation monitoring using TLS, accelerometers and interferometric radar The monitoring using TLS was performed in 3 measurement epochs; i.e., in November 2012, March 2013 and November 2013, using Leica ScanStation2. The bottom side of the middle section of the suspended structure was scanned from a single position of the scanner. The scanner was positioned on the Slovak side of the river approximately at the longitudinal axis of the bridge, thus the whole bottom side of the structure could be scanned [Figure 7.1]. The reference network consists of four control points. Due to the fact that the bridge is built in the natural reservation, there are no possibilities to make observation sites. Due to this restriction two of the control points were stabilized on the base of the pillars on the Slovak side by metallic fasteners and another two were on the points of the original setting-out network of the bridge and stabilized by observational pillars. All of the control points were signalized by Leica HDS targets. 34 Figure 7.1 Position of the scanner and control points The data obtained by the TLS were transformed to the local coordinate system of the bridge as defined by the control points. The data processing was focused on determining the vertical displacements of the observed points positioned on the bottom side of the bridge deck.

9 Invited lectures The vertical displacements of the observed points were determined by the methodology proposed in the Chapter 2 using the app Displacement_TLS. During the data processing, square fences of m x m were defined on the bottom side of the bridge deck (these defines approximately the same set of points in each epoch). The observed points were positioned on the bottom of the transverse girders between the diagonal reinforcements of the supporting girders on both sides of the bridge. The total number of observed points was 46. The figure 7.2 shows the displacements of the observed points selected. The measurements show the displacement of all of the observed points except for the points on the ends of the suspended structure. These points have not changed their position, because the structure is anchored to the supporting structure at these parts. The standard deviation of the displacements calculated using uncertainty propagation law varies from 1.3 mm to 1.8 mm. The displacements towards the centre of the bridge are increasing and have negative values. In the middle of the bridge they reach values of -13 mm respectively, -10 mm in March This is partly caused by the lower temperature of the structure in the control epoch of the measurement and partly by the load of a 10 cm layer of snow. Figure 7.2 Vertical displacements Liberty bridge For the dynamic deformation monitoring of the bridge two HBM B12/200 one-axial accelerometers, that are supported by an HBM Spider 8 A/D transducer and a ground-based IBIS-S interferometric radar was used. The accelerometers measure the acceleration in vertical direction. These inductive sensors have an operating frequency of up to 200 Hz and measuring range of up to 200 ms -2. The accuracy of the sensors is defined by a relative error of up to ±2%. The measured signal is digitized by a HBM Spider 8 A/D transducer and saved to the computer by Catman Easy software. The sensors are positioned in the middle of the suspended structure and at the anchorage of the suspension cables [Figure 7.3]. 35

10 SIG 2016 International Symposium on Engineering Geodesy, May 2016, Varaždin, Croatia Figure 7.3 Position of the radar and the accelerometers The radar measures the dynamic displacements by comparing the phase shifts of the reflected radar waves collected at the same time intervals. Displacement is measured in a radial direction (line of sight). The minimal range resolution of the radar is 0.5 m. The accuracy of the measured displacements is at a level of 0.01 mm, but it depends on the range and the quality of the reflected signal. The measurements and data registration are managed by the IBIS-S operational software installed in a PC (notebook). The dynamic measurements were performed during different types of the structure loading that were designed on the basis of the finite element method (FEM) model of the bridge [Agócs & Vanko 2011]. Four loading epochs were defined as follows: the first without loading, the second 1 person, walking, the third 1 person running, the fourth 1 person jumping at the centre of the structure. Each epoch was performed in 3 phases. In the first phase, the measurements had started before the loading of the structure. The second phase continued at the time of the loading and the last phase was realized after the loading of the structure during its damping phase. Each epoch lasted approximately 2 minutes. The frequency of the data registration by the accelerometers and ground-based radar were realized on the level of 100 Hz due to the requirements to achieve a higher degree of accuracy of the relative displacements and the occurrence of significant frequencies of the structural deformations that were higher than 10 Hz rd phase (structure dumping) Figure 7.4 Vertical displacements determined by radar (left) and accelerometers (right) during Epoch No. 4 The data processing consisted of the determination of the relative displacements, auto-spectral analysis of the accelerometer and the ground-based radar data, as well as of cross-spectral analysis of the data obtained by both methods. Determining the relative displacements by the accelerometers was realized by the double integration of the accelerations measured. The accelerometer drift and integration errors were eliminated by a Butterworth high st phase (before structure loading) 2 nd phase (structure loading) Epoch

11 Invited lectures pass filter with a cut-off frequency at the level of 0.5 Hz. This filter attenuates the magnitude of the spectrum at the frequency of 1 Hz by 0.7%, which has no significant influence on the displacements determined. The filter was applied before and after the first integration of the velocities. Raw displacement data from radar are measured in a radial direction (direction in the line of sight). The first step in the data processing of the radar measurements is setting the geometry of the structure and defining the position of the radar and the measured points. We can define the measured points manually using corner reflectors or by finding parts on the structure that have acceptable reflection parameters. In our case the second option was chosen. A good reflection of the signal from the structure defines the range bin profile [Figure 7.5]. Figure 7.5 Range bin profiles The selected peaks (P01 and P02) correspond to the position of the accelerometers stabilized on the structure. The figure 7.5 shows the estimated signal to the ratio (SNR) of the signal s reflection, depending on the structure s range. The effect of pedestrians walking has a minimum influence on the vertical displacements. The rapid movement of pedestrians affects the maximum vertical displacements twice more than during the loading by a standard pedestrian s walking. The harmonic jumping of pedestrians affects the maximum displacements at a level of around 2.50 mm (P01) and 4.85 mm at the centre (P02) of the structure. Before the spectral estimation of the accelerations, each measured time series of the accelerations was filtered by the Butterworth highpass filter with a cut-off frequency of 0.1 Hz. This filter attenuates the signal amplitudes with a 1 Hz frequency on the level of 0.2%. This has a minimum influence on the estimation of the expected dominant frequencies of the structural deformations. Determining the natural frequencies of the structural deformations at each measured point (P01 and P02) was realized by an auto-spectral analysis using the FFT method. The same method was used for the cross-spectral analysis of the time series measured by the acceleration sensors and interferometric radar at the points P01 and P02. The estimation parameters were the same as during the auto-spectral estimation at these points. In the next step, the phase shifts of both signals and their coherence were determined. During the measurement without the structure s load, the frequency of deformation at the level of 1.52 HZ has been determined. only by radar 37

12 SIG 2016 International Symposium on Engineering Geodesy, May 2016, Varaždin, Croatia measurements. Signals from both measuring points are low coherent with relatively high phase delay at the level of around The dominant frequencies of the deformations that were determined during the walking of 1 person corresponds with the 22 nd vibration mode of the structure (from the FEM model). The estimated frequencies approximately at the level of 2.10 Hz corresponds with the frequency of the pedestrian s steps during standard walking. The phase shift at the level around 23.0 is caused by a short delay in the structure s response at points P01 and P02 that were influenced by the pedestrian s walking. The third loading epoch shows the resonant oscillation of the structure affected by running at the range from 2.50 Hz to 3.00 Hz, which corresponds to the frequency of the impact of feet on the structure during running. The signals at the 44 th vibration mode at the level around 3.80 Hz have a minimum phase delay at the range from 0 to 3. The 4 th load was realized during the synchronized jumping by one person at the centre of the structure. The structural oscillation at the frequency level of 1.81 Hz and the minimum phase shift are affected only by this activity. The estimated frequency is similar to the 22 nd natural frequency defined by FEM model. 8. Conclusion The paper deals with the deformation monitoring of the bridge structures by non-conventional surveying methods: terrestrial laser scanning, accelerometers and by the ground-based radar interferometry. The basic principles of deformation monitoring using the mentioned methods have been described. The paper also describes the experimental deformation monitoring of the Liberty Bridge (Bratislava, Slovak Republic). Acknowledgement This work was supported by the Slovak Research and Development Agency under the contract No. APVV References Agócs, Z.; Vanko, M. (2011). Devínska Nová Ves Schloshof Cycling bridge, Cyklomost Devínska Nová Ves Schlosshof, Technical Documentation. Bratislava: INGSTEEL, spol.s.r.o. Bernardini, G.; De Pasquale, G.; Bicci, A.; Marra, M.; Coppi, F.; Ricci, P. (2007). Microwave Interferometer for Ambient Vibration Measurements on Civil Engineering Structures: 1. Principles of the radar technique and laboratory tests, EVACES 07. Bracewell, R. (1956). Pentagram Notation for Cross Correlation, The Fourier Transform and Its Applications, New York: McGraw-Hill, Cooley, J. W.; Tukey, J. W. (1965). An Algorithm for the Machine Calculation of Complex Fourier series, Mathematic Computation, 19 (90),

13 Invited lectures Čepek, A.; Pytel, J. (2009). A note on numerical solutions of least squares adjustment in GNU project gama, In Pilz J., editor, Interfacing Geostatistics and GIS, Springer Berlin Heidelberg, Pieraccini, M.; Parrini, F.; Fratini, M.; Atzeni, C.; Spinelli, P.; Micheloni, M. (2007). Static and Dynamic Testing of Bridges through Microwave Interferometry, NDT&E Int, 40, Sangbo, H. (2010). Measuring Displacement Signal with an Accelerometer, Journal of Mechanical Science and Technology, 24(6), Vosselman, G.; Maas, H. G. (2010). Airborne and Terrestrial Laser Scanning, Dunbeath: Whittles Publishing. Welch, P. D. (1967). The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms, IEEE Transactions on Audio Electroacoustics,

14 SIG 2016 International Symposium on Engineering Geodesy, May 2016, Varaždin, Croatia Novi trendovi u inženjerskoj geodeziji monitoring mosta pomoću TLS-a, akcelerometra i terestričke radarske interferometrije Sažetak. Vremenski utjecaji i opterećenja koja djeluju na građevinu uzrokuju promjene u položaju i obliku građevine, što ima utjecaja na statičku i dinamičku funkciju i pouzdanost tih građevina. Iz tih razloga, geodetski monitoring je sastavni dio praćenja građevina koji daje važne informacije o trenutnom stanju građevine. Razvoj mjernih instrumenata omogućuje monitoring pomaka i deformacija građevina korištenjem nekonvencionalnih metoda mjerenja. Za monitoring statičkih pomaka moguće je koristiti tehnologiju terestričkoga laserskog skeniranja (TLS), ako se odabrani dijelovi građevine aproksimiraju jednim geometrijskim entitetom (malim ravnim plohama). Za monitoring dinamičkih pomaka mostova često se koristi terestrička radarska interferometrija i akcelerometri za određivanje vibracija pomoću spektralne analize frekvencija. U radu je opisano iskustvo znanstvenika sa Zavoda za geodeziju, STU Bratislava u području monitoringa pomaka i deformacija mostova pomoću nekonvencionalnih metoda mjerenja. Opisan je eksperimentalni monitoring Mosta slobode (Bratislava, Slovačka) korištenjem TLS-a, terestričke radarske interferometrije i akcelerometra. Prikazani su postupci mjerenja, obrade podataka i rezultati monitoringa pomaka. Ključne riječi: akcelerometar, monitoring pomaka, monitoring građevina, terestrička radarska interferometrija, terestričko lasersko skeniranje. *scientific paper 40