Analysis and Extraction of Temperature Effects on Natural Frequencies of a Footbridge based on Continuous Dynamic Monitoring

Transcription

1 Analysis and Extraction of Teperature Effects on Natural Frequencies of a Footbridge based on Continuous Dynaic Monitoring Wei-Hua Hu, Carlos Moutinho, Filipe Magalhães, Elsa Caetano & Álvaro Cunha Faculty of Engineering of University of Porto (FEUP), Portugal ABSTRACT: The developent of efficient vibration based structural health onitoring systes requires distinguishing between abnoral changes in odal paraeters caused by structural daage and noral changes due to varying environental conditions. In this context, this paper is focused on the analysis and extraction of effects of teperature oscillations on natural frequencies of a footbridge, where a long-ter dynaic onitoring syste was installed by the Laboratory of Vibrations and Monitoring of the Faculty of Engineering of University of Porto. With that purpose, firstly, the teperature influence on the natural frequencies is reported, and correlations between easured teperatures and estiated natural frequencies are analyzed. Then, the Principal Coponent Analysis (PCA) and the Novelty Detection ethod are applied to identified natural frequencies: PCA effectively eliinates environental influence; Novelty analysis on the residual error of PCA predicted odel is used as a statistical indication of daage. The proposed procedure is illustrated using continuous dynaic data collected fro the footbridge during ore than one year. 1 INTRODUCTION Structural Health Monitoring (SHM) has becoe a ajor international research topic in recent years in civil engineering. One of the ain obstacles in the application of SHM is the environental and operational variations of structures. The so called daage sensitive features are also sensitive to changes in environental and operational conditions of structures, which often ask subtle structural changes caused by daage (Hoon Sohn 2007). Therefore, iportant issues in SHM are the analysis of influences of environental and operational variations, and the achieveent of daage indication based on the reoval of such effects. In this context, this paper is focused on the analysis and extraction of effects of environental and operational conditions on natural frequencies of a slender footbridge, where a long-ter dynaic onitoring syste was installed by the Laboratory of Vibrations and Monitoring (ViBest, ) of FEUP. Firstly, the teperature influence on natural frequencies is reported, and correlations between easured teperatures and estiated natural frequencies are analyzed. Then, the Principal Coponent Analysis and the Novelty Detection ethod are applied to identified natural frequencies. The proposed procedure is illustrated using continuous dynaic data collected fro the new Coibra footbridge.

2 56 IOMAC'09 3 rd International Operational Modal Analysis Conference 2 DESCRIPTION OF THE BRIDGE AND DYNAMIC MONITORING SYSTEM The new Pedro e Inês footbridge over Mondego River is located in the centre of the City Park of Coibra, recently developed along the two banks of the river and opened to public in April This new infrastructure, conceived to becoe a landark for the city and to contribute to the quality of a new leisure area, was designed by Adão da Fonseca (Adão da Fonseca et al 2005), leading a tea fro AFAssociados, in collaboration with Cecil Balond, leading the architectural tea fro Ove Arup. The bridge has a total length of 275 and is fored by a parabolic central arch with a span of 110 and two half lateral arches, in steel, supporting with total continuity a coposite steel concrete deck (Fig.1). The anti-syetry of both arch and deck cross-sections along the longitudinal axis of the bridge is a unique feature of this bridge, leading to the creation of a central square with 8 8 at id-span AV1 AV2 AV3 AV5 AV6 S3 S2 S west AT4 (a) Bridge plan and elevation, deployent of acceleroeters and sections (S1-S3) with teperature sensors east North South North TC TA South T2 T1 Section 1 (S1) T3 North AV5 AT4 Section 2 (S2) South T4 Section 3 (S3) (b) Sections (S1-S3) and teperature sensors Figure 1. Deployent of acceleroeters and teperature sensors Nuerical and experiental studies, developed by the Laboratory of Vibration and Monitoring fro FEUP, showed that this slender footbridge is prone to excessive vibrations caused by groups or streas of pedestrians. Therefore, six groups of tuned ass dapers (TMDs) were installed (Caetano, Cunha et al 2008). Aiing the peranent characterization of vibration levels after construction, the footbridge was also instruented with a dynaic onitoring syste, fored by signal acquisition, data counication and signal processing odules. The signal acquisition syste coprises six uniaxial piezoelectric acceleroeters installed in correspondence with the location of TMDs (Fig. 1). Five of the easure vertical accelerations (AV1-AV3, AV5-AV6), whereas another one easures lateral vibrations at id-span (AT4). All sensors are ounted inside the etallic deck and wired to the corresponding signal conditioners and digital coputer incorporating an analogue to digital converter and a UPS syste, located in one of the concrete abutents of the structure. An autoatic signal acquisition toolkit was developed in LabVIEW environent to record the acceleration signals and generate setup files every 20 inutes. The data counication syste sends peranently the ost recent collected data to a coputer located at FEUP using an ADSL line (Moutinho et al 2008). The signal processing syste is a toolkit developed in LabVIEW. It autoatically searches the latest data transitted fro the bridge in

3 57 Coibra, detects axiu vibration aplitudes and akes statistical treatent of acceleration tie series, generates waterfall plots to depict the frequency coponent distribution and identifies odal paraeters using autoated EFDD and SSI-COV techniques (Hu et al 2008). Besides the acceleroeters, 6 teperature sensors (Fig. 1) were also installed by the Laboratory for Concrete Technology and Structural Behaviour of FEUP to provide environental data, including the abient teperature (TA), concrete slab teperature (TC), and teperature in different steel sections (T1-T4), which were well selected by the designer in order to provide an adequate representation of the bridge behaviour (Diande et al 2008). The set of entioned coponents can be considered as a siple dynaic structural health onitoring syste that has been operating since the 1 st of June 2007 till now, except for a stop fro the 1 st of Septeber 2007 to the 13 th of October EFFECT OF TEMPERATURE ON NATURAL FREQUENCIES In this study, the teperature data fro the 6 teperature sensors exhibit siilar trend and therefore the average teperature is used to represent environental variation. Fig. 2 depicts annual variation of one-hour average teperature during day light tie. It is observed that the average teperature at the footbridge ranges fro 0.19 C to C. Figure 2. Variation of one-hour average teperatures fro 1 st June 2007 to 31 st May 2008 (The onitoring syste was not operating fro 1 st Sep 2007 to 13 th Oct 2007) frequency daily average frequency frequency daily average frequency (a) 1 st natural frequency identified by EFDD frequency daily average frequency (b) 2 nd natural frequency identified by EFDD frequency daily average frequency (c) 1 st natural frequency identified by SSI-COV (d) 2 nd natural frequency identified by SSI-COV Figure 3. Variation of identified odal frequencies by both EFDD and SSI-COV ethods fro 1 st June 2007 to 31 st May 2008 (The onitoring syste was not operating fro 1 st Sep 2007 to 13 th Oct 2007)

4 58 IOMAC'09 3 rd International Operational Modal Analysis Conference The structure natural frequencies have been autoatically identified by the signal processing syste for each hour. Fig. 3 shows the annual variation of the first two natural frequencies estiated by the used ethods. To further illustrate the annual tendency, the daily average frequency curve is also displayed. It is observed fro Figs. 2-3 that the frequency doain EFDD and the tie doain SSI-COV ethods produce siilar results, and the first two natural frequencies are inversely related to changes in easured teperature. The relation between natural frequencies and teperature ay be further clarified by Fig. 4. As shown, the first two natural frequencies identified by different ethods both decrease as teperature rises. Fro a statistical point of view, the relations between teperature and natural frequencies can be assued as linear. Therefore, a linear regression odel was developed to represent the first two natural frequencies as function of the average teperature, which can be atheatically described as f i =a+bt i, where a and b are coefficients to be estiated, t i are the saples of average teperature and f i are corresponding natural frequencies. f 1 = t f 2 = t (a) Natural frequencies identified by EFDD versus average teperature f 1 = t f 2 = t (b) Natural frequencies identified by SSI-COV versus average teperature Figure 4. Natural frequency versus average teperature According to Fig. 4, it ay be concluded that the frequencies identified by both EFDD and SSI-COV ethods can reflect siilar global effect of teperature, despite the better perforance of SSI-COV, which allows a better frequency resolution of the estiates. Although other environental and operational factors such as wind, huidity and traffic loading ay also affect the natural frequencies, fro the viewpoint of long ter onitoring, teperature ay be considered the ain environental factor. Statistical analysis of these two natural frequencies shows that the noral teperature change produces variations of 1.7% and 1.4%, which ay ask the change of natural frequency caused by structural daage. To establish a baseline for long ter structural health onitoring, such effect induced by teperature should be eliinated effectively, and features which are sensitive to daage yet insensitive to environental change are necessary.

5 59 4 ELIMINATION OF THE TEMPERATURE EFFECT 4.1 Theory of Principal Coponent Analysis and Novelty Detection technique Principle coponent analysis (PCA) is a ulti-variate statistical ethod. Under the assuption that the environental conditions have a linear effect on the identified paraeters, PCA ethodology can eliinate such effect. In the current study, PCA analysis is used to reove teperature effect. Subsequently, novelty detection technique ay be used to detect possible daage. The basic idea of novelty detection is first to build an internal representation of the structure s baseline in noral condition, and then exaine subsequent data to see if they significant depart fro a noral condition. n N Let us consider the atrix Y R whose colun vectors y k are the identified n-order natural frequencies at tie t k,(k=1,2,..,n, N is the nuber of saples). A singular value decoposition of the covariance atrix of Y is YY Σ = T T = UΣU (3) Σ Σ 2 where U is an orthonoral atrix ( UU T = I ), whose coluns define the principal coponents and for a subspace spanning the data, Σ is the singular value atrix representing the active energy of the associated principal coponents. Matrix Σ can be split in two parts: Σ 1 = diag( σ1, σ 2... σ ) is a diagonal atrix with the square of the first singular values on the diagonal, ranked by decreasing order, and Σ = diag(, σ... σ ). Define the indicator: 2 I i i σ n n = = 1σ i = σ i (5) and deterine as the lowest integer such that I > e(%), where e is a threshold value (i.e. 95%). The eaning of this threshold is as following: unobserved factors contribute to e% of the variance in the observed data (Deraeaeker et al 2007). The first coluns of U are the principal coponents, which are associated with the ost influencing unobserved factors and constitute a transforation atrix T (loading atrix). T can project the frequency atrix Y into the environental-factor characterized space X (scores atrix) X=T T Y (6) The new data can be re-apped into original space Y ˆ = TX (7) The residual error E due to the loss of inforation while perforing the two-way projection can be calculated as E = Y Yˆ (8) The new feature vector is given by E, it corresponding to the dynaic features fro which the environental effects have been reoved. Applying the novelty detection technique to the residual error E, the Novelty Index (NI) can be defined using the Mahalanobis nor NI k 1 = E R E (9) T k k where R=(YY T )/N is the covariance atrix of frequency atrix Y. To detect possible daage, an X-bar control chart (Yan et al 2005; Diego et al 2005) is constructed by drawing two lines: a centre line (C L ) and an additional horizontal line corresponding to an upper liit (UCL), these are: C L = NI (10) (4)

6 60 IOMAC'09 3 rd International Operational Modal Analysis Conference UCL = NI + ασ (11) where NI and σ is the ean value and standard deviation of NI in the reference healthy state.α is taken as 3, which corresponding to 99.7% confidence. Two criteria can be eployed as daage warning (Deraeaeker et al 2007; Yan et al 2005; Diego et al 2005): (1) outlier analysis, counting for the percentage of the NI lying outside the UCL and (2) ratio of NI between healthy and daage state. In the healthy state, the new vibration features should stay in the hyperplane spanned by the features in reference state. Percentage of the NI overpassing UCL is rather sall and ratio of NI 1. On the contrary, with the eergence of daage, the new vibration features will depart fro hyperplane in the reference healthy state, which will cause a significant increase of outliers and relatively large ratio of NI. 4.2 Application of Principal Coponent Analysis and Novelty Detection Methodology PCA and novelty detection have been already applied in nuerical and laboratory odels (Deraeaeker et al 2007; Yan et al 2005; Diego et al 2005). In this paper, this ethod is used for the long ter onitoring results of Coibra footbridge. According to Fig. 4, it can be assued that teperature has a linear effect on the first two natural frequencies. Teperature linear effect on frequencies can be also reflected by linear relation between different frequencies, as shown in Fig. 5. These two natural frequencies identified by EFDD ethod constitute atrix Y= [y 1, y 2 ]. Substituting Y into Eqs. (3-5), one obtains the singular values and 3.751E-6 with I > 99.9%, which indicates that only one environental factor arkedly affects the variation of natural frequencies. In the following part, two sets of frequencies identified by EFDD ethod both in winter tie and in suer tie are investigated to illustrate the potential of reoving the teperature effect. (a) EFDD results (b) SSI-COV results Figure 5. Correlation between the first two natural frequencies fro 1 st, June 2007 to 31 st, May 2008 Fig. 6 shows two sets of consecutive saples both in suer and winter. The corresponding average teperature varies fro º C to º C in suer, whereas changes fro 0.19 º C to º C in winter. It is clear that ost of the two natural frequencies estiates in winter tie are higher than those in suer tie because of teperature effect. PCA and Novelty Detection are applied to these data and results are shown in Fig. 7. It can be observed that NI in both two sets stay in the sae level, the results of outlier analysis are siilar and the ratio of NI 1. The effect of teperature is efficiently reoved. This footbridge is new and no daage is reported fro 1 st June, 2007 to 31 st May, A baseline healthy state of this footbridge has been constructed based on the onitoring results during this period. The successive onitored data fro 1 st June 2008 to 1 st Deceber 2008 is used to copare with baseline state. The corresponding results of NI are displayed in Fig. 8. Copared with baseline healthy state, the NI during the period 1 st June 2008 to 1 st Deceber 2008 still reain sall, outlier analysis exhibits siilar results and ratio NI are still close to 1, which eans that the footbridge is still in a healthy stage and no daage occurred, as expected.

7 61 winter suer winter suer (a) 1 st frequency (b) 2 nd frequency Figure 6. Coparison of the first two natural frequencies both in suer (18.17 º C º C) and winter (0.19 º C º C) winter outlier analysis: 1 % suer outlier analysis: 1% NI w /NI s =0.977 Figure 7. Residual error of data in suer (18.17 º C º C) and winter (0.19 º C º C) Set I outlier analysis: 0.8 % Set II outlier analysis: 1.3% NI / NI =0.991 I II Figure 8. Coparison of residual error of data in Set I:1 st June, st May, 2008 and Set II: 1 st June, st Deceber, CONCLUSION This paper ainly discusses the effect of teperature on natural frequencies of a new footbridge based on long ter dynaic onitoring data. Firstly, results fro appropriate data processing confir that teperature is an iportant environental factor that originates a linear effect on identified natural frequencies. To reove this effect, PCA and Novelty Detection techniques were introduced. The potential of this ethodology is illustrated by two sets of data in winter and suer tie. Finally, long ter onitoring data collected during the first year is used to construct a baseline healthy state. The reaining data is processed and copared with this baseline state to detect possible daages. As this footbridge is quite new, the ratios between averaged NI reained close to one, as expected. In the future, possible daage will be

8 62 IOMAC'09 3 rd International Operational Modal Analysis Conference nuerically siulated and the potential of PCA and Novelty Detection techniques will be further investigated. ACKNOWLEDGMENTS The authors acknowledge the financial support provided by the Portuguese Foundation for Science and Technology (FCT) in ters of Basic Funding of CEC / FEUP, as well as the Ph.D. Scholarship provided to the first author. REFERENCE Hoon Sohn Effects of environental and operational variability on structural health onitoring. Phil.Trans.R.Soc.A (365), p Adão da Fonseca.A and Balond.C Conceptual design of a footbridge over river Mondego, Coibra. Footbridge 2005,Venice,Italy. Caetano, E., Cunha, A., Moutinho, C. & Magalhães, F Lessons fro the practical ipleentation of a passive control syste at the new Coibra footbridge, Keynote Lecture at the Third International Conference Footbridge 2008, Porto, Portugal. Moutinho, C., Hu, W.-H., Caetano, E. & Cunha, A Ipleentation of a dynaic onitoring syste at Coibra footbridge, XXVI Int. Modal Analysis Conference (IMAC-XXVI), Orlando, Florida, USA. Moutinho, C., Hu, W.-H., Caetano, E. & Cunha. A Analysis of the levels of vibration easured by a dynaic onitoring syste at Coibra footbridge, Fourth European Conference on Structural Control, St. Petersburg, Russia. Hu, W.-H., Moutinho, C., Cunha, A. & Caetano, E A signal processing, result anageent and visualization syste for evaluation of long ter dynaic behavior of bridges, Fourth European Workshop on Structural Health Monitoring, Cracow, Poland. Hu, W.-H., Cunha, A., Caetano, E, Magalhães, F. & Moutinho, C LabVIEW toolkits for outputonly odal identification and long-ter dynaic structural onitoring, Journal of Structure and Infrastructure Engineering, accepted for publication. Diande, A., Pientel, M., Félix, C. & Figueiras, J Monitoring and nuerical analysis of the new footbridge over the Mondego river. Int. Conference on Challenges for Civil Construction, Porto, Portugal. Deraeaeker, A. et al Vibration-based structural health onitoring using output-only easureent under changing environent. Mechanical Systes and Signal Processing, (22-1). P Yan, A.-M., Kershen, G., De Boe, P. & Golinval. J.-C Structural daage diagnosis under varying environental conditions - Part I: A linear analysis, Mechanical Systes and Signal Processing, (19). P Diego, F.G., Shirley, J. D. & Juan, M. C Daage detection accoodating varying environental conditions, Structure Health Monitoring, (5-2).P