BRIDGE’S FREQUENCY RESULTING FROM TRAFFIC EXCITATION PLUS

6.12 BRIDGE’S FREQUENCY BY TRAFFIC EXCITATION WITHOUT EMO 6.13 CONCLUSIONS

6.14 ACKNOWLEDGMENTS 6.15 REFERENCES

Nota: O material desse artigo somente poderá pode ser utilizado para uso pessoal. Cada outro uso requer permis- são prévia da Sociedade Americana de Engenheiros Civis. Este material pode ser encontrado em [http://ascelibrary.org/doi/10.1061/%28ASCE%29SU.1943-5428.0000170].

Note: This material may be downloaded for personal use only. Any other use requires prior permission of the American Society of Civil Engineers. This material may be found at [http://ascelibrary.org/doi/10.1061/%28ASCE%29SU.1943-5428.0000170].

Dynamic Behavior of a Small Concrete Highway Bridge

Ana Paula C. Larocca, Ph.D.1; João Olympio de Araújo Neto2; Jorge Luiz Alves Trabanco, Ph.D.3; Marcelo Carvalho dos Santos, Ph.D.4; and Augusto Cesar Barros Barbosa, Ph.D.5

Abstract: This work presents the results of global positioning system (GPS) data processing using the phase residuals method (PRM)—L1 carrier phase from two satellites—to monitor the dynamic behavior of a small concrete bridge. The bridge tested, the Jaguari Bridge, is a small, curvd, reinforced concrete bridge. The bridge over the Jaguari River is a reinforced concrete bridge built in 1999, located on Fernão Dias Highway (BR 381), positioned at Kilometer 946, Minas Gerais, Brazil. The small concrete bridge was chosen for this study because its con- struction type is found in great numbers throughout Brazil. In parallel, there was a significant increase of pathologies in these structures as a result of lack of maintenance procedures. The detection of small vibrations of spans, for example, which is a good indicator of the health of a structure, can be monitored by GPS. The challenge in this case is trying to detect with GPS the dynamic displacement that has an amplitude close to 5 mm. Application of the PRM on GPS data allowed the detection of this very small dynamic vibration. In addition, this is thefirst case of success with applying GPS as a tool for monitoring the dynamic behavior of small concrete bridges. The experiment consisted of ses- sions conducted during 2 days and used two GPS receivers (with a 100-Hz recording rate) over the central span of the Jaguari Bridge in 2014. The continuous wavelet transform (CWT) was used as afilter technique to analyze the frequencies generated by residues from double-difference data processing.DOI:10.1061/(ASCE)SU.1943-5428.0000170. © 2016 American Society of Civil Engineers.

Introduction

The last decades presented a signiﬁcant growth of bridges and via- ducts in Brazil, which suffered from early deterioration caused by a lack of maintenance programs. Additionally, dynamic loading has become a particular concern within the civil engineering commu- nity, and the global positioning system (GPS) can offer direct meas- ures of dynamic displacements of large structures induced by traf- ﬁc, wind, and earthquake forces. Traditional civil engineering equipment, such as accelerometers and displacement transducers, are trusted tools for the registration of the structural dynamic behavior. However, studies conducted in the past decade have rated the GPS as an instrument to be considered for this purpose. Important studies have used GPS (sometimes added to another instrument) to

Chan et al. 2006;Watson et al. 2007;Psimoulis et al. 2008;Schaal and Larocca 2009;Moschas and Stiros 2015;Guo et al. 2014), and used wavelets applied to GPS data to provide better results for ana- lyzing structural behavior, such as those presented by Moschas and Stiros (2010) and Kaloop et al. (2013). The hypothesis in this paper is that the small concrete bridge vibrations mixed with random amplitude and frequency generated by electronic noise and multipath can be better detected with oversampled GPS data and using only two satellites (Schaal and Larocca 2001;Larocca 2004). The phase residuals method (PRM) uses the L1 carrier phase, which needs to be collected from only two satellites by receiver base and receiver rover (Larocca 2004;Larocca et al. 2009). This particular characteristic makes it different from the methods used in other studies.

Methodology

The PRM, under development since 2000 (Schaal and Larocca 2002;Schaal et al. 2012), is based on interferometer principle and uses the L1 carrier phase, which needs to be collected from only two satellites by receiver base and receiver rover with a phase angle of approximately 90° and a constellation no larger than four satellites. This particular characteristic makes it different from the methods used in other studies published up to now, and this paper presents the ﬁrst results obtained for small concrete bridges.

To measure vertical displacement, for example, it is necessary for one satellite to be close to the zenith and another to be close to the horizon (Fig. 1). In the processing of the double-difference phase, the lowest satellite is the reference satellite, allowing collection of the vector of residuals from the highest satellite, called the satellite measurer here. With this conﬁguration, there is a greater contribution in theﬁnal data-processing results of double-phase difference (residuals) due to changes in the phase detected with the movement of the GPS antenna (rover).

1_Professor, _Measuring _Laboratory, _Dept. _of _{Transportation}

Engineering, Sao Carlos Engineering School, Univ. of Sao Paulo, Av. Trabalhador Saocarlense, 400, Sao Carlos-SP-CEP 13566-590, Brazil (corresponding author). E-mail: [email protected]

2_{Ph.D. Candidate, Univ. of Campinas, SP-CEP 13083-970, Brazil;}

Lecturer, Federal Institute of South Minas Gerais–Campus Inconﬁdentes, Praça Tiradentes, 416–Centro–Inconﬁdentes–MG–CEP 37576-000, Brazil. E-mail: [email protected]

3_{Associate Professor, Dept. of Civil Engineering, State Univ. of}

Campinas, Rua Saturnido de Brito, 224, Campinas–SP–CEP 13083-889, Brazil. E-mail: [email protected]

4_{Full Professor, Dept. of Geodesy and Geomatics Engineering, Univ.}

of New Brunswick, 3 Bailey Dr., Fredericton NB E3B 5A3, Canada. E-mail: [email protected]

5_{Professor, Center of Science and Technology, Ceara State Univ., Av.}

Dr. Silas Muguba, 1700 Campus do Itaperi, Fortaleza–CE 60740-000, Brazil. E-mail: [email protected]

Note. This manuscript was submitted on April 3, 2014; approved on November 5, 2015; published online on February 8, 2016. Discussion period open until July 8, 2016; separate discussions must be submitted for individual papers. This paper is part of the Journal of Surveying Engineering, © ASCE, ISSN 0733-9453.

The residuals incorporate all phase deviations from the adjusted double-difference position during the observation. These phase deviations are a result of electronic receiver noise, multipath, small dynamic antenna movements, and other error sources. Converting the residuals in the frequency domain by the continuous wavelet transform (CWT), it is possible to see the different behaviors of the receiver phase noise, multipath, and periodic oscillations of a bridge span, allowing the distinction between interferences and structural behavior. These residuals were generated through processing with

Justin Javad2.107.

It is important to make clear that theﬁrst task for obtaining the phase residuals from the raw data is to verify the data quality, look- ing for phase jumps and missing epochs. This can be done by look- ing at the data continuity of the chosen satellites. The loss of some sporadic epoch from the GPS signal and any small phase jump that stays within the noise level will not compromise the results. In the case of a large phase jump, the data must be disregarded and a proper window must be selected, as no phase jump correction is performed.

The observable L1 double-difference phase is given by Leick (2004) wpq km;1ð Þ ¼t f cr pq km t p ð Þ þ Npq km;1ð Þ þ I1 km;1;pq wð Þ þt f cT pq kmð Þt þ dpq km;1;wð Þ þ ɛt pqkm;1;w (1) Multiplying both sides of Eq. (1) by L1 wavelengthλ1

λ1wpq_km;1ðtÞ ¼rpq_kmð Þ þ λtp 1N_km;1pq ð Þ þ λ1 1I_km;1;pq _wð Þ þ Tt _kmpqð Þt

þ λ1dpq_km;1;_wð Þ þ λt 1ɛpq_km;1;_w

(2) Thefirst term of the right side of Eq. (2) is the double difference of topocentric distances between p, q satellites and k, m receivers. The second term is thefirst epoch ambiguity, and it has no time dependence. The time dependence of the third and fourth terms, respectively, related to the ionosphere and troposphere, can be sepa- rated in two behaviors. For a short baseline, one is almost a steady state and the second will depend on the noncorrelation among the ionosphere and troposphere scintillation, with a random time behavior. Thefifth term is any time-dependent phase disturbance. Finally,

the last term is related to the receiver phase noise with a random behavior.

Rearranging Eq. (2) joining terms with similar time behavior: λ1wpqkm;1ðtÞ ¼rpqkm t

ð Þ þ S þ λ1dpqkm;1;wð Þ þ Nt (3) where S = stationary components; and N = random phase noise. The topocentric distance, as a function of time, between satellite p and receiver k is given by the expression

rp k t p ð Þ ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixpð Þ x_tp k ð Þ2 þ ypð Þ y_tp k 2 þ zpð Þ z_tp k ð Þ2 q (4) The same expressions are used for the other three distances. The double difference among topocentric distances in a short baseline as a function of time can be represented by a polynomial function

rpq km t p ð Þ ¼ anð Þtp n þ an1ð Þtp n1þ a0 (5)

Substituting Eq. (5) in Eq. (3) λ1wpqkm;1ð Þ ¼ at nð Þtp

þ an1ð Þtp n1þ a0þ S

þ λ1dpq_km;1;_wðtÞ þ NðtÞ (6)

In Eq. (6), the coefﬁcient a0can be added to the steady-sate com-

ponents (S), and the time behavior of observed double difference can beﬁtted to the polynomial function, the residuals of which contain the time-dependent phase disturbances and random phase noise. Eq. (7) gives the phase residuals [R(t)] in meters

R tð Þ ¼ λ1dpqkm;1;wð Þ þ N tt ð Þ ¼ λ1wpqkm;1ð Þ at nð Þtp n

þ an1ð Þtp n1þ a0þ S (7)

The polynomialﬁt can be done by the parametric minimum least-squares method (Leick 2004). With this approximation, it is possible to obtain directly the phase residual from the raw data, independent of a regular data-processing program, to be analyzed in the frequency domain by the CWT, as previously mentioned.

Fig. 1. Satellite conﬁguration in relation to a GPS rover and base measuring vertical displacements

ments of a large structure are difﬁcult to separate from the random noise, degrading the precision of the measurement. One way to improve the signal-to-noise ratio is the autocorrelation technique. Autocorrelation enhances periodic functions and lessens random values. The autocorrelation of data of n samples is converted to a half-time sample because the delay can only be shifted by half the original sample. Eq. (8) presents the applied autocorrelation function with the delay (t) ranging from 0 to n/2 (Patrick 2005)

Rð Þ ¼t X

n=2 t¼0

R tð Þ Rðt þtÞ (8)

Spectral Analysis of GPS Data

The wavelet analysis was the tool chosen to perform the analysis of the double-difference phase residuals, using Justin Javad software and interferometry technique, in the frequency domain and, conse- quently, to identify the corresponding frequencies resulting from periodic displacements. The spectrum also presents frequencies resulting from multipath, noise, and other sources (e.g., the effects of variation of the antenna’s phase center), which are accentuated in highly reﬂective environments and in nonstatic observations (Leick 2004).

The wavelet analysis involves an operation linear that can be used in the analysis of nonstationary signals for extracting information of variations in frequency, and it allows the detection of periodic phenomena located in time or space. This technique has been used widely in various areas of research and studies, such as geo- physics, hydrology, climate data analysis, medicine, study of sound, and GPS data analysis (Meyer 1993;Larocca et al. 2010;Kaloop et al. 2013).

The analyses for detecting the frequency resulting from the small dynamic vibration were done by applying the CWT with the Morlet wavelet, which deserves a short description (Morettin 2013;Mallat 2008). Choosing the best mother wavelet is not a simple task. Usually, there are more than a couple of alternatives (Indrusiak et al. 2005). In this research, which aimed to study the frequency in the time domain from GPS data that have the contribution of electronic noise and multipath, the Morlet wavelet was one of the most efficient at identifying the signs of the frequencies expected as a result of a signal with a variation in peak-to-peak amplitude up to 5 mm in the low-frequency region. Thefirst study the authors devel- oped using CWT was published in 2009, and details can be found in Larocca et al. (2009). A particular wavelet, Morlet, was used and is defined by Eq. (9) as

coðhÞ ¼ p1=4eiwohe1=2h

(9) whereco= dimension less frequency; andh = dimensionless time.

When using wavelets for feature extraction purposes, the Morlet wavelet is a good choice because it provides a good balance between time and frequency localization.

The idea behind the CWT is to apply the wavelet as a band-pass ﬁlter to the time series. The CWT of a time series ½f ðtÞ; t ¼ 1; :::; N with uniform time steps (dt) is deﬁned as the convolution of fðtÞ with the complex combination of the mother wavelet scaled and normalized [see Eq. (10)]

Wj;kðtÞ ¼ _j t¼1

fðtÞc0 _j dt (10)

where Wj;kðtÞ = similarity between the wavelet function and the ana-

lyzed time series [fðtÞ] [i.e., the higher the value of Wj;kðtÞ, the

greater the similarity between the analyzed function and mother wavelet function that modulates the signal analyzed].

The idea behind the CWT is to apply the wavelet as a band-pass ﬁlter to the time series.

Field Experiments on a Small Concrete Bridge

Field experiments were carried out to verify the consistency of the method for monitoring the dynamic behavior of small concrete bridges.

Instrumentation Layout

The instrumentation used consisted of a pair of GPS JAVAD receivers (Sigma 100-Hz data rate with choke ring antennas, model RegAnt_DD_E). Therefore, Fig.2(a)illustrates the layout of the instruments used (the rover GPS antenna over the middle of the large span with 30 m, Jaguari Bridge's draft), and Fig.2(b)shows the monitored bridge with the positioning of the GPS antenna in- stalled over the top of a reinforced concrete New Jersey barrier.

Fig.3illustrates the static antenna over a pillar 300 m away from the Jaguari Bridge (baseline). As the baseline is short, most of the GPS errors are canceled when using a double-differencing data- processing technique, and errors remaining in the background noise are mainly a result of a multipath effect (Leick 2004;Chan et al. 2006).

If a control point is not nearby and is required to perform the post-processing with data from a dual-frequency GPS receiver, a possible option would be to use the method absolute plus loop- based solution accumulated time-relative (APLAT) (Liu et al. 2013). Although this is possible, this method has not been tested with the proposed method.

Data Analysis

The accelerometer (Spectrum Ac1) was the instrument of compari- son with GPS data, and measurements made by Ac1 on the bridge presented frequencies between 4 and 8 Hz, as shown in Fig.4. The geotechnical instrumentation of the bridge occurred in March 2013 (Andrade et al. 2013). It was not possible to perform the geodetic instrumentation at the same time.

However, the data collected with GPS clearly indicated the detection of the span’s natural frequency and its harmonics resulting from trafﬁc, which remained open during the data collection.

Zero-Baseline Test

A zero-baseline test was performed to determine the correct operation of a GPS receiver, associated antennas, and cabling. The objec- tive was to verify the amplitude of electronic noise of the GPS receiver. If the receivers presented an electronic noise higher than 3 mm, the detection was impaired. One-minute data were collected for this investigation. Fig.5shows the residual of an L1 double-difference phase.

J. Surv. Eng., 04016008

Preliminary Test

This test was carried out to test the hypothesis that GPS data under PRM analysis permit the detection of vibration with an amplitude under 5 mm. GPS JAVAD receivers (Sigma 100 Hz) and an electro- mechanical oscillator (EMO) were used, as shown in Fig.6.

The ﬁeld test using the EMO applied a well-known vertical vibration on a GPS rover antenna with a frequency of 0.4 Hz and 3.8 mm peak-to-peak. This step precedes the bridge's analysis and was used for testing and calibrating the detection with GPS.

Fig.7. shows a well-known region inside the cone of inﬂuence

with a high level of energy at 0.4 Hz, indicating the detection of vibration applied with 3.8 mm. This controlled result encouraged the authors to perform the tests on the bridge.

Data Collected at Jaguari Bridge

The GPS observation campaign on the bridge was held in the after- noon between 1,320 and 1,335 hrs. on June 17, 2013. The total observation period was 15 min, and the interval with the highest satellite (SV11) remained near the zenith—between 78 and 908 and a storage ratio of 100 observations per second. The baseline has an azimuth of 1858. The weather conditions at the time of observations were favorable, with an average temperature of 20° C, wind speed of 17 km/h, and 61% moisture. Trafﬁc conditions were normal without any restriction of trafﬁc lanes. Justin Javid 2.107 was used for the post-processing, which lets one choose the reference satellite and the satellite measurer, such as suggested by the proposed methodology. SV11 was used as the reference satellite, because it was close to the horizon. As the measurer satellite, SV14 was used (located around the zenith; Fig.8). The residues used to apply CWT were from measurer Satellite SV14.

Bridge’s Frequency Resulting from Traffic Excitation plus EMO

Fig.9shows a well-known region inside the cone of inﬂuence with a high level of energy resulting from the EMO, set for an applied os- cillation of 0.4 Hz, and the bridge's frequency resulting from trafﬁc excitation—frequencies between 4 and 8 Hz, approximately. It is also possible to see the high level of energy resulting from multipath accentuated by the passage of trucks with body on steel or aluminum elements that contribute to the multipath increase.

Bridge’s Frequency by Traffic Excitation without EMO Fig. 10 shows a zoomed-in image of the region that presents a high concentration of energy, which is consistent with the frequencies displayed by the Ac1 accelerometer: frequencies close to 4 and 8 Hz (approximately 4.29 and 7.75 Hz). The 5% signif- icance (95% confidence) level for signal wave information is limited by a thick contour. It is important to mention that the region that represents the detection (thick contour) is not continuous (as in Fig. 7) because traffic was not controlled—traffic was freeflowing at that time.

Fig.11shows shows distinct regions with a high level of energy, on a timescale, from vehicles of signiﬁcant weight crossing the

Fig. 2. (a) Unscaled draft of the bridge monitored, adapted from the original design; (b) GPS antenna on Jaguari Bridge (image by authors)

Fig. 3. Static antenna over a pillar 300 m away from the Jaguari Bridge

Fig. 4. Acceleration spectrum (frequency) in the vertical direction for monitoring the normal trafﬁc on October 10, 2011 from accelerometer (data fromAndrade et al. 2013)

Fig. 5. Zero baseline 100-Hz data rate residuals of an L1 double-difference phase

Fig. 6. GPS antenna over the EMO and details of the EMO (images by João Olympio de Araújo Neto)

Fig. 7. Morlet CWT of time series (1 min) of residuals with 0.4-Hz sine wave with 3.8-mm amplitude; the 5% signiﬁcance level of sine wave detection is shown as a thick contour and in the upper position; the values of raw residuals (Conbings) are compressed between−2 and 2 (StandAnom.) for better viewing

bridge and presented expected frequency—close to 4, 5, and 8 Hz from 5 min of GPS observations. It is important to show the wavelet image with all observations (30,000) because it can be seen that the frequencies from the bridge's oscillations are compressed between 4 and 8 Hz. Then it is necessary to observe by zoomed-in imaging into smaller intervals, to lighten the response frequency between 4 and 8 Hz. The aggressive effect of multipath is also observed at spe- ciﬁc intervals of lower frequency as a result of the passage of trucks with the body on steel or aluminum elements that contribute to multipath increase.

Conclusions

Only a few dozen seconds of observation with a high-rate GPS receiver allow the use of the simpliﬁed model of expression for this phase and a third-degree polynomial to perform an adjustment of the raw data.

Both sets of tests showed that the GPS phase observable by a satellite closely aligned to the direction of a periodic displacement can

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