Status of the paper KATHOLIEKE UNIVERSITEIT LEUVEN

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1 FACULTEIT TOEGEPASTE WETENSCHAPPEN DEPARTEMENT BURGERLIJKE BOUWKUNDE AFDELING BOUWMECHANICA W. DE CROYLAAN B-3 HEVERLEE KATHOLIEKE UNIVERSITEIT LEUVEN Status of the paper B. PEETERS AND G. DE ROECK. One year monitoring of the z4-bridge: environmental influences versus damage events. In Proceedings of IMAC 8, the International Modal Analysis Conference, pp , San Antonio, Texas, USA, February. IR. BART PEETERS, RESEARCH ASSISTANT TEL. (+3 6) FAX (+3 6) bart.peeters@bwk.kuleuven.ac.be

2 ONE YEAR MONITORING OF THE Z4-BRIDGE: ENVIRONMENTAL INFLUENCES VERSUS DAMAGE EVENTS Bart Peeters, Guido De Roeck Department of Civil Engineering, Katholieke Universiteit Leuven W. de Croylaan, B-3 Heverlee, BELGIUM URL: ABSTRACT When using the analysis of vibration measurements as a tool for health monitoring of bridges, the problem arises of separating abnormal changes from normal changes in the dynamic behaviour. Normal changes are caused by varying environmental conditions such as humidity, wind and most important, temperature. The temperature may have an impact on the boundary conditions (frozen soil) and the Young s modulus of the material of which the structure consists. Abnormal changes on the other hand are caused by a loss of stiffness somewhere along the bridge. It is clear that the normal changes should not raise an alarm in the monitoring system (i.e. a false positive), whereas the abnormal changes may be critical for the structure s safety. This paper tries to give an answer to the question whether it is possible to separate the environmental influences from damage events. In the frame of the European SIMCES-project, the Z4-bridge in Switzerland was monitored during almost one year before it was artificially damaged; what makes it an excellent object to study methods that try to filter out the environmental influences. The paper presents the results of the measurements on the post-tensioned concrete bridge and shows that it is indeed possible to distinguish between abnormal and normal changes of its dynamic characteristics. NOMENCLATURE E f f x x ˆ x ˆ x x ˆ x x k u k y k Young s modulus frequency relative frequency difference damping ratio relative damping ratio difference variable mean of a variable estimated standard deviation of a variable estimated covariance between two variables estimated correlation between two variables discrete time instant input variable output variable e k i N a i, b i n a, n b n k AMA ARX EMS FPE MAC MACEC MISO SIMCES SISO SSI residual autocorrelations of residuals number of data points ARX model coefficients ARX model orders ARX time delay Automatic Modal Analysis Auto-Regressive exogeneous Environmental Monitoring System Final Prediction Error Modal Assurance Criterion Modal Analysis on Civil Engineering Constructions Multiple Input Single Output System Identification to Monitor Civil Eng. Struct. Single Input Single Output Stochastic Subspace Identification INTRODUCTION Since many years people are performing vibration tests on civil engineering structures. It became more and more clear that environmental parameters affect the dynamic behaviour of a structure. For instance, at low temperatures the eigenfrequencies of a concrete structure are significantly higher than at high temperatures. Damage detection is one of the main aims of vibration monitoring. A loss of stiffness is observed as a decrease of the eigenfrequencies. The problem is that changes due to damage can be completely masked by changes due to normal varying environmental parameters. Alampalli [] reports that eigenfrequency differences of a bridge due to freezing of the supports ( f = 4 5%) were an order of magnitude larger than changes due to damage ( f = 3 8%), in casu an artificial saw cut across the bottom flanges of both girders. It must be mentioned that the studied bridge was relatively small, with a span of 6.76 m and a width of 5.6 m. Roberts and Pearson [] are describing a monitoring program on a 9-span, 84 m long bridge. They found that normal environmental changes could account for - -

3 Figure : Location of the thermocouples. The variable i is the span number; i =,,3 [5]. Figure : The Z4-Bridge [5]. changes in eigenfrequencies of as much as 3 4% during the year. Farrar et al. [3] found that the first eigenfrequency of the Alamosa Canyon Bridge varies approximately 5% during a 4 hour time period. In a recent paper by Sohn et al. [4], the same bridge data is used to build a model that describes the variation of eigenfrequencies due to varying temperatures. This model is used to establish confidence intervals of the frequencies for a new temperature profile. This paper presents the results of (almost) one year monitoring of the Z4-Bridge. Interesting about this bridge is that it was artificially damaged at the end of the monitoring period. The paper is organized as follows. Next section describes the bridge and the monitoring system. Section 3 explains how the modal parameters are automatically extracted from the massive amount of vibration data. In section 4, we attempt to construct black-box models that explain the variation of the eigenfrequencies due to changing environmental influences. The models are found by applying system identification techniques to the data of the undamaged bridge. In section 5, the models are validated by using fresh data. These validation data also contain the artificial damage events. Section 6 concludes the paper. THE Z4-BRIDGE AND THE EMS The Z4-Bridge is located in Switzerland, connecting the villages Utzenstorf and Koppigen and overpassing the national highway A between Bern and Zürich. It is a classical posttensioned concrete box girder bridge with a main span of 3 m and side spans of 4 m (Figure ). Two rows of three pinned concrete columns are supporting the bridge at the end points and two concrete piers clamped into the girders are situated at the end points of the main span. The bridge is slightly skew: the axes of the piers are not perpendicular to the longitudinal axis of the bridge. Although there were no known structural problems with the bridge, it had to be demolished because a new railway next to the highway required a bridge with a larger side span. From November 997 till September 998, the bridge has been monitored. The aim of the environmental monitoring system (EMS) is to provide both environmental and vibrational data. 49 Sensors captured environmental parameters such as air temperature, wind characteristics, humidity, bridge expansion, soil temperatures at the boundaries and bridge concrete temperatures. The locations of the bridge thermocouples are shown on Figure. The sampling time is hour. Additionally, every hour during minutes, 8 accelerometers are capturing the vibrations of the bridge. More details on the bridge and the EMS can be found in Krämer at al. [5] and Rushton et al. [6]. 3 AUTOMATIC MODAL ANALYSIS (AMA) As indices for the dynamic behaviour of the structure, it seems natural to take the modal parameters: eigenfrequencies, damping ratios, mode shapes. Evidently, a realistic vibration monitoring system should be able to estimate the modal parameters from output-only data. There is no possibility of continuously exciting the bridge with a known force; so we have to use available but unmeasurable sources such as traffic and wind. An excellent method for the estimation of modal parameters from output-only data is stochastic subspace identification (SSI) [7,8]. The method is implemented in the toolbox MACEC [9] for use with Matlab []. Advantages of SSI over the widely used peak-picking method are: 6 The eigenfrequencies are objectively selected based on stabilization diagrams in stead of looking at peaks in the spectral densities of the signals. 6 The damping estimates are far more reliable. 6 True mode shapes are obtained in stead of operational deflection shapes. 6 Closely spaced modes can be separated. Especially this last advantage is important in case of Z4- Bridge, since two closely spaced modes are situated in the range Hz. The peak-picking method would fail to estimate both. SSI as it is implemented in MACEC requires some user interaction: the user has to select stable frequencies based on stabilization diagrams. This is a serious problem for the present case: there are CDs containing zipped acceleration - -

4 Table : Automatic modal analysis results. Mode Success Rate Eigenfrequency min [Hz] avg [Hz] max [Hz] max.diff. 98% % 93% % 3 96% % 4 77% % f [Hz] st Eigenfrequency vs. Wearing Surface Temperature data, measured at 565 time instants. The interpretation of 565 stabilization diagrams would take weeks and does not fit in a realistic monitoring system. Therefore an automatic modal analysis (AMA) procedure needed to be developed. A certain identified pole is considered as stable if the frequency, damping and mode shape deviations with respect to a pole identified at one model order lower, are within certain limits. This is nothing more yet than the classical way of constructing a stabilization diagram. The automatic procedure goes further and tries to incorporate the decisions that an experienced user would take. Only poles that are n s times stable are selected (to exclude accidentally stable poles) and the representative of a column of stable poles at a certain frequency is the one that is closest to the average of that column. The used criteria are: f # %, # %, % (&MAC) # 5% n s $ 5 () TP [ C] Figure 3: st Eigenfrequency vs. wearing surface temperature, TP. f [Hz] nd Eigenfrequency vs. Deck Soffit Temperature where f is the relative frequency difference, is the relative damping ratio difference and MAC is the MAC-value between two modes. From preliminary modal surveys [], we know that we can expect 4 modes in the range Hz. However due to the sometimes low excitation (especially at night when there is not much traffic) the AMA could not identify all 4 modes at every time instant. Table summarizes the AMA results. The Success Rate expresses the percentage of successful identifications of a certain mode. Except for mode 4, the rates are very high. The frequency information of Table is related to the monitoring period before any known damage took place. By consequence, the frequency differences ranging from 4 8% have to be explained by normal environmental changes. If we would wait until damage makes the eigenfrequencies to exceed the normal range, it would probably be too late TDS [ C] Figure 4: nd Eigenfrequency vs. deck soffit temperature, TDS. to observed environmental parameters. An alternative to this approach is a careful analysis of the physics that cause the eigenfrequencies to change. For instance a temperature change affects the Young s modulus of concrete and asphalt; and the eigenfrequencies are proportional to the square root of Young s modulus: f ~ E. Also freezing of the soil changes the boundary conditions of a structure [] and these affect again the eigenfrequencies. However, it may be clear that finding a quantitative description of all involved physical phenomena is far too complex. So we preferred the black-box system identification approach. In this section, the search for a good model that is able to describe the data is discussed. 4. Visual inspection of the data 4 BLACK-BOX MODELS: EIGENFREQUENCIES VERSUS TEMPERATURE From November till the end of July, we assume that the bridge remains intact. These EMS data are used to build experimental black-box models that relate the measured eigenfrequencies The first step in system identification is taking a look at the data. The st eigenfrequency versus the temperature of the wearing surface, TP, is represented in Figure 3. The nd eigenfrequency versus the temperature of the deck soffit, TDS, is represented in Figure 4. Roughly, the relation between temperature and frequency can be described by two - 3 -

5 5 4 Measurements at a warm period TP TWC TS f 3 Measurements at a very cold period TP TWC TS f 3 T and f (all normalized) T and f (all normalized) t [day], t = Nov 997 :: t [day], t = Nov 997 :: Figure 5: Normalized temperatures (TP,TWC,TS) and opposite of the st eigenfrequency (-f) during a warm period. lines, with the knee situated around C. This bilinear behaviour is observed for almost all combinations of frequency vs. temperature. Mode is somewhat an exception in the sense that its frequency increases with increasing temperatures (for positive temperatures). Some effort was spend in trying to find out the reason for the bilinear behaviour. Whereas the temperature versus time functions are very smooth; the frequency versus time functions are rather irregular. This can be observed on Figure 5, where 3 temperature readings and the opposite of the first eigenfrequency are plotted as a function of time. All quantities have been normalized. At first sight there seems to be no relation between frequency and temperature. On a larger time scale it is however clear that the frequency follows the main trends of the temperature data. If we look at the data of a cold period (Figure 6), the normalized opposite frequency is almost perfectly in line with the normalized temperature of the wearing surface (asphalt layer), TP. This explains the nonlinearity. At warm periods, the asphalt does not play any role, but during cold periods, it contributes significantly to the stiffness of the structure. The most evident approach to obtain a model is to apply (multiple) linear regression []: a linear relation between the frequency at a certain time instant and (some of) the temperatures at the same time instant is estimated by least squares. Because linearity is assumed, only data from periods where the asphalt does not play any role is taken into account. In any case it would be difficult to make safety statements about the Z4-Bridge in very cold periods. As indicated on Figure 3, a large range of frequencies correspond to a temperature of - C. It is unlikely that a frequency decrease due to damage would exceed that range. In the following only positive temperature data are considered. Another problem with simple linear regression models is that the thermal dynamics of the bridge are not taken into account. As apparent from Figures 5-6, there are phase shifts from one temperature measurement location to another. This is due to Figure 6: Normalized temperatures (TP,TWC,TS) and opposite of the st eigenfrequency (-f) during a cold period. the thermal inertia of the asphalt and the concrete. So maybe we have to look at models that incorporate some dynamics in stead of simple static regression models that only try to relate simultaneously measured data. 4. Variable selection The visual inspection of the data provided already useful information for model building. In this subsection the number of model variables is reduced. The 4 eigenfrequencies are the output variables. There are 49 quantities available as input variables (cf. Section and [5,6]). Many quantities offer redundant information and not all of them should be included in the model. The high number of measured quantities is fine in a research project, but an economic monitoring system should operate with only a few environmental parameters. A first reduction is forced by circumstances. Some sensors failed during the monitoring period and the number of input candidates could already be reduced from 49 to 3. Also the humidity is excluded, because their was no clear relation between humidity and frequency. The air temperature and concrete temperatures are retained. In a next step the correlations between all inputs and outputs are determined. The correlation ˆ x x between two variables x and is x estimated as: ˆ x x = ˆ x x ˆ x ˆ x, ˆ x x = ˆ x = n n& j i' n n& j i' (x & x )(x & x ) (x & x ) The correlation is a value between - and. An absolute value close to, indicates a high linear association between the two variables. Input variables for which the correlation exceeds.99 are grouped together. Six groups are obtained. The input variable that has the largest correlation with most of the 4 eigenfrequencies is selected as representative for the group. () - 4 -

6 Table : Comparison between SISO models: TDT - eigenfrequency. Mode ARX-model static regression model.6.5 Autocorrelation of Residuals n a n b n k FPE n a n b n k FPE The retained variables are TWN, TP, TDT, TS, TSWN3 and the Air Temperature. Note that almost all representative variables are originating from the main span () of the bridge. 4.3 ARX models Having reduced the number of possible input candidates to 6, we are ready to build an input-output model. One of the simplest models described in the system identification literature (see for instance Ljung [3]) is the ARX model that consists of an Auto-Regressive output and an exogeneous input part: k +a y k& +...+a n a y k&na = b u k&nk +...+b nb u k&nk &n b % +e k (3) y k where is the output variable (i.c. an eigenfrequency) at time instant k; u k is the input variable (i.c. a temperature) and e k is a white noise term indicating that the input-output relation is not perfect. The ARX model is characterized by 3 numbers: n a, the auto-regressive order; n b, the exogeneous order and n k, the pure time delay between input and output. What makes ARX models so popular is that the coefficients a,...,a na and b,...,b nb can be estimated with the simple linear least squares method. A static regression model is an ARX model (with [n a,n b,n k ]=[,,]): y k = b u k +e k (4) Note that the means are removed from the input-output data; otherwise there would be an offset in equations (3-4). The advantage of using general ARX models over static regression models is that they include some dynamics: the current output and input are related to outputs and inputs at previous time instants. If more than input variable is included, equation (3) is still valid but u k is a column vector and the b coefficients are row vectors. With the 6 remaining input candidates and the possible choices for n a,n b,n k there are many different ARX models that can be fitted to the data. There are some criteria that can be used to assess and compare the quality of models. A first criterion is the value of the loss function, defined as: Time Lags [ ] Figure 7: Autocorrelation of the residuals for the TDT - f models: - -, ARX4;, ARX. e k where is a residual of the data and the model (3). Other criteria include penalties for model complexity like Akaike s final prediction error (FPE) criterion or Rissanen s minimum description length criterion [3]. Our strategy to find a good model is the following. For all 4 eigenfrequencies and all 6 input candidates, SISO ARX models are estimated. A good and simple (i.e. with only a few coefficients) model is selected for all 4 input-output combinations. Next, the input is selected that yields on the average the best models for all 4 frequencies. The best models have the lowest and FPE values. It turned out that the model based on TDT performed best; but it must be added that not much quality loss was observed when using other temperatures. The results are represented in Table. Note that the input and output data were normalized before the models were identified. The model for the first mode seems to be much better than the models for the other 3 modes. The static regression results are also represented. Especially for the first modes, the improvements of an ARX model over a static model are spectacular. Afterwards input variables were added to the SISO models, but it was observed that the models hardly improved. For instance, the quality measures of a MISO ARX4 model, that includes all 6 input variables and has the first eigenfrequency as output, are: =.4, FPE =.43. These values have to be compared with the values on the first line of Table. For a static MISO ARX model that includes all input variables, we have: =.87, FPE =.88. Another quality criterion for a model is provided by the autocorrelation function of the residuals. The lag i autocorrelation is defined as: = N j N e k (5) i = N N j e k%i e k (6) k= k= - 5 -

7 3 Mode 4 Mode 3 ESTIMATION VALIDATION 3 ESTIMATION VALIDATION Residuals Residuals t [day], t = Nov 997 :: t [day], t = Nov 997 :: Figure 8: Residuals of the ARX4 model for TDT - f and the 95% confidence intervals. In order to justify the least squares approach to find the model coefficients, it was assumed that e k is white noise. In Figure 7, the autocorrelation functions for the SISO ARX4 and ARX models are plotted. The residuals of the static model are not white noise at all. This is an indication that more information could be extracted from the data. 5 VALIDATION: IS DAMAGE DETECTION POSSIBLE? Once a good model is obtained, it can be used for prediction. The least squares method does not only provide an estimate of the ARX model coefficients, but also of the covariance matrix of the coefficients. The square roots of the diagonal elements of this matrix are estimates of the standard deviations of individual model coefficients. With this covariance matrix, it is also possible to estimate the standard deviations of a new observation. New environmental data are fed to the models of Section 4. The models predict the corresponding eigenfrequencies and also the standard deviations of this frequencies. The standard Figure : Residuals of the ARX model for TDT - f3 and the 95% confidence intervals. deviations can be used to establish confidence intervals around the predicted values. For instance, if ŷ is the predicted output and ˆ y the estimated standard deviation on a new observation, the (& )% confidence interval on ŷ is given by: [ŷ&t /, ˆ y, ŷ+t /, ˆ y] ; where the value t /, is found from a statistical table of the Student s T distribution. For a large number of data points and =.5 (leading to 95% confidence intervals), we have t /, =.96. If the measured eigenfrequencies are not enclosed by the confidence intervals, there is a high probability that other than the normal environmental parameters are influencing the frequencies. It is for instance possible that the bridge has been damaged. The ARX models for the 4 eigenfrequencies, determined in Section 4, are now used for prediction. In Figures 8-, the residuals of these models are given. Remember that the residuals are defined as the measured values minus the predicted values. Also the 95% confidence intervals are represented. If a residual exceeds the interval, it is likely that something happened with the bridge. The vertical lines on the figures split the residuals in two parts: an estimation and a 5 Mode 4 Mode 4 ESTIMATION VALIDATION 3 ESTIMATION VALIDATION Residuals Residuals t [day], t = Nov 997 :: t [day], t = Nov 997 :: Figure 9: Residuals of the ARX3 model for TDT - f and the 95% confidence intervals Figure : Residuals of the ARX model for TDT - f4 and the 95% confidence intervals.

8 validation part. The estimation data (only partially represented) were already used to estimate the ARX model, whereas the validation data are fresh data. Concerning mode, damage is observed from day 77 on (5-Aug-998). Around this date, the damage scenario Settlement of a pier, 8 mm was realized [5]. The preceding scenarios, settlements of and 4 mm, seem to have no large influence on mode. For the other modes,3 and 4, damage is observed from day 69, 7 on (7,8-Aug-998). Around these dates, the settlement system was installed. The bridge was not yet settled and there were no cracks in the bridge girders. However, to install the settlement system one of the piers needed to be cut [5]. Damaging the pier clearly affects the frequencies of mode to 4. The frequency decrease of mode is very spectacular. Further, the residuals of mode and are clearly passing the confidence limits at days (7,8-July-998). We have however no idea what the cause of that frequency drop could be. 6 CONCLUSIONS In this paper we presented a method to distinguish normal eigenfrequency changes from abnormal changes due to damage. ARX models were fitted to data from the healthy structure. It is evident that an ARX model that includes the thermal dynamics of the bridge, is superior to a static regression model. Also, it turned out that a temperature measurement at one location was sufficient to find an accurate model. The ARX models are used for prediction. If a new observation lies outside the confidence intervals on the prediction, it is likely that the bridge is damaged. In case of the Z4-Bridge and the applied damage scenarios, we could successfully detect damage. The low temperature data were disregarded in this paper. Future research will focus on a description of the nonlinear behaviour so that we can also make safety statements about the bridge in cold periods. The proposed method for filtering out environmental influences should be validated on other bridges too. ACKNOWLEDGEMENTS The data for this research were obtained in the framework of the BRITE-EURAM Programme CT96 77, SIMCES with a financial contribution by the European Commission. Partners in the project were: K.U.Leuven, Aalborg University, EMPA, LMS International, WS Atkins, Sineco, T.U.Graz. REFERENCES [] ALAMPALLI, S. Influence of in-service environment on modal parameters. In Proceedings of IMAC 6, 6, Santa Barbara, CA, USA, February 998. Proceedings of ISMA 3, the International Conference on Noise and Vibration Engineering, Leuven, Belgium, September 998. [3] FARRAR, C.R., DOEBLING, S.W., CORNWELL, P.J. AND STRASER, E.G. Variability of modal parameters measured on the Alamosa Canyon Bridge. In Proceedings of IMAC 5, 57 63, Orlando, FL, USA, February 997. [4] SOHN, S., DZONCZYK, M., STRASER, E.G., KIREMIDJIAN, A.S., LAW, K.H. AND MENG, T. An experimental study of temperature effect on modal parameters of the Alamosa Canyon Bridge. Earthquake Engineering and Structural Dynamics, 8, , 999. [5] KRÄMER, C., DE SMET, C.A.M. AND DE ROECK, G. Z4- Bridge damage detection tests. In Proceedings of IMAC 7, Kissimmee, FL, USA, February 999. [6] RUSHTON, A., PEARSON, A.J. AND ROBERTS G.P. Brite- EuRam project SIMCES (CT96-77), task A: bridge testing, environmental monitoring of Z4-Bridge. Technical Report AM3548/R4, WS Atkins, Bristol, UK, 999. [7] VAN OVERSCHEE, P. AND DE MOOR, B. Subspace identification for linear systems: theory - implementation - applications. Kluwer Academic Publishers, Dordrecht, The Netherlands, 996. [8] PEETERS, B. AND DE ROECK, G. Reference-based stochastic subspace identification for output-only modal analysis. Mechanical Systems and Signal Processing. Accepted August 999. [9] PEETERS, B., VAN DEN BRANDEN, B., LAQUIÈRE, A. AND DE ROECK, G. Output-only modal analysis: development of a GUI for Matlab. In Proceedings of IMAC 7, Kissimmee, FL, USA, 49 55, 999. [ [] THE MATHWORKS. Using MATLAB, version 5.3. Natick, MA, USA, 999. [] PEETERS, B., DE ROECK, G., HERMANS, L., WAUTERS, T., KRÄMER, C., DE SMET, C.A.M. Comparison of system identification methods using operational data of a bridge test. In Proceedings of ISMA 3, 93 93, K.U.Leuven, Belgium, September 998. [] MONTGOMERY, D.C. AND PECK, E.A. Introduction to linear regression analysis. Wiley, New York, USA, 99. [3] LJUNG L. System identification: theory for the user. Prentice-Hall, Englewood Cliffs, New Jersey, USA, 987. [] ROBERTS, G.P. AND PEARSON, A.J. Health monitoring of structures - towards a stethoscope for bridges. In - 7 -