Long-term monitoring and data analysis of the Tamar Bridge

TL;DR: In this paper, an extensive monitoring campaign of the Tamar Suspension Bridge as well as analysis carried out in an attempt to understand the bridge's normal condition are investigated. And the initial steps towards the development of a structural health monitoring system for the TAMAR Bridge are addressed.

About: This article is published in Mechanical Systems and Signal Processing.The article was published on 2013-02-01 and is currently open access. It has received 303 citations till now. The article focuses on the topics: Structural health monitoring.

Summary

1 Introduction

• Monitoring campaigns of long span bridges are becoming more and more common [1] as the research fields of structural health monitoring (SHM) and performance monitoring grow.
• On the way to developing rigorous and reliable procedures for SHM and performance monitoring for civil structures, the normal response of a system to changes in its environmental and operational conditions must first be ascertained.
• In the past, many researchers have investigated the effect of environmental and operational loads on classical bridge structures.
• Up to three years of dynamic, static and environmental data are now available.

1.1 History/specification

• The Tamar Bridge has been a vital transport link over the River Tamar carrying the A38 trunk road from Saltash in Cornwall to the city of Plymouth in Devon since its construction in 1961.
• The original bridge was designed as a conventional suspension bridge with symmetrical geometry, having a main span of 335 metres and side spans of 114 metres.
• The towers are constructed from reinforced concrete, and have a height of 73 metres with the deck suspended at half this height.
• The main suspension cables are 350mm in diameter, each consist of 31 locked-coil wire ropes and carry vertical locked-coil hangers at 9.1m intervals.
• The truss is 5.5 metres deep and composed of welded hollow steel boxes.

1.2 Upgrade

• When opened in 1961 Tamar Bridge was, for a short time, the longest suspension bridge in the UK and was also the first to be built after the end of World War II.
• In the late 1990’s, after nearly four decades of use, it was found that the bridge would not be able to meet a new European Union directive that bridges should be capable of carrying lorries up to 40 tonnes in weight.
• After considering a number of options, the appointed consultant proposed replacement of the main deck with a lightweight orthotropic steel deck, with construction of temporary relief lanes cantilevered either side of the bridge truss.
• The truss was strengthened by the installation of supplementary inverted U-shaped parallel elements fitted below the bottom chord and by welding additional steel plates at key locations.
• This upgrade gave rise to interest in the bridge performance, and various sensor systems have been installed to measure parameters such as tensions on the additional stays, wind velocity and structural temperature.

2 Monitoring the Tamar Bridge

• Currently three monitoring systems are in place and running at the Tamar Bridge.
• The sensors used in the SMS include: anemometers to measure wind speed and profile; a fluid pressure-based level sensing system to measure deck vertical displacement; temperature sensors for the main cable, deck steelwork and air temperature; extensometers and resistance strain gauges to measure loads in additional cables.
• Up until 2009, the Sheffield system recorded 64Hz-sampled time series in files at 10-minute intervals.
• This VI extracted modal parameters from the acceleration data using covariance-driven stochastic subspace identification (SSI) [2].
• The RTS, shown in Figure 3, was installed in September 2009 on the roof of the Tamar Bridge Office which sits close to the bridge on the Plymouth side bank of the river.

2.1 Approach to data mining

• From the three comprehensive monitoring systems described above, a huge amount of data is stored and processed daily.
• A Tamar Bridge SHM database has been created using the MySQL database engine to provide researchers with convenient and instant access to huge measurement sets.
• All the Fugro and Sheffield dynamic monitoring system data are stored and serviced in the database as well as processed modal parameters from acceleration measurements.
• Figure 5 shows a Tamar SHM database viewer that has been developed based on a MATLAB GUI.
• This viewer enables users to browse some of the important data sets (temperature, wind, traffic loadings) to find potential anomalies or understand general trends before pursuing a more detailed analysis.

3.1 Dynamic response

• As previously described, dynamic data for the Tamar Bridge is extracted from accelerometer data using a data-driven SSI technique (add reference to one of Ki’s monitoring papers).
• Principal component analysis takes a multivariate data set and projects it on to a new set of variables, or ‘principal components,’ which are linear combinations of the old variables.
• Previously, little attention has been given to the effect of traffic loading on modal parameters.
• (1) This type of model is called a response surface model [10], the idea being originally developed by Box and Wilson [11] for modelling chemical processes.
• Figure 9 demonstrates the effect of including an additional temperature dependent variable in the model of the third modal frequency.

3.1.1 Deck Acceleration

• Closely linked to the wind profile, and also the dynamics of traffic loading is the acceleration of the deck.
• This amplitude dependency indicates that the system is nonlinear, which is not unexpected for such a complex structure.
• This bi-functional relationship must be considered with any attempt to model the bridge’s behaviour with respect to deck acceleration.
• It does not necessarily follow that this should be reflected in the relationship between deck acceleration and modal frequency; it is possible that one regime could define the acceleration-frequency relation.
• On inspection of Figure 14, there generally appears to be two different trends roughly separable by wind speed and direction, namely, the frequencies appear to act under a different regime when high wind speeds from a southerly direction are recorded.

3.1.2 Mathematical Models of Modal Frequencies

• Based on the above analysis, more complex models to predict modal frequency change can now be contrived.
• Indeed, inputs based on deck acceleration should take into account the two possible response regimes discovered, which occur most likely because of differing wind patterns.
• These methods are known to have powerful prediction capabilities, however, no knowledge of the physical system can be gained directly from these non-parametric approaches.
• A normalised mean-squared error (MSE) will be used as a performance index for each model, which is defined here as 𝑀𝑆𝐸 = 100∑(𝑚𝑜𝑑𝑒𝑙 𝑒𝑟𝑟𝑜𝑟𝑠)2 𝑛 (𝜎[𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑜𝑛𝑠])2 (3) where n is the number of data points predicted and σ denotes standard deviation.
• For the traffic loading, this most likely suggests that the model will benefit from a more sophisticated traffic loading estimate than can be provided by a single parameter, it is unlikely that the traffic on the bridge half an hour previously actually affects the modal frequencies at the time.

3.1.3 Tentative steps towards Damage Detection

• For a working SHM system there must be a mechanism for detecting the occurrence of damage.
• Indeed this is considered one of the largest stumbling blocks for the transferral of SHM to civil structures [14].
• Figure 15 plots the errors of the model described above for the first modal frequency, with confidence limits at plus and minus three standard deviations of the errors from the training period.
• Errors clearly depart significantly from the confidence interval during the time of the suspected sensor fault.

4 Summary

• The current paper has introduced and described the substantial monitoring campaign being carried out on the Tamar Suspension Bridge in the Southwest of England.
• Three monitoring systems currently in place have provided a wealth of data detailing the static and dynamic behaviour of the bridge deck and cables, as well as the operational and environmental factors affecting them.
• Traffic loading was found to be a dominant driver of daily frequency fluctuation, whilst temperature was found to have more of a seasonal effect than daily.
• Finally, response surface models have been fitted in attempt to predict the modal frequency changes of the bridge deck given the measured environmental/operational conditions.
• The higher modal frequencies can also be predicted with similar models, although with less accuracy.

Figures

Figure 1: Tamar suspension bridge

Figure 9: (a) linear model of the third deck modal frequency with traffic loading input.

Figure 13: RMS of vertical deck acceleration plotted according to estimated traffic loading

Figure 6: Deck Modal Frequencies plotted with respect to traffic loading, wind speed and temperature

Figure 8: Linear model of first deck modal frequency with traffic loading input only.

Figure 12. Vertical and horizontal deck acceleration plotted with respect to wind speed and sorted by wind direction.

Figure 2: Cantilever lanes added in the upgrade

Table 1. Parameter coefficients for models predicting the first and second modal frequencies.

Figure 11. Above: model estimate of first modal frequency at high wind speed with traffic and temperature inputs only.

Figure 7: First two principal component scores of frequency data sorted according to temperature, wind speed and traffic loading.

Figure 4: Reflector installed on Bridge Deck

Figure 3: RTS installed on the roof of Tamar Bridge Office

Figure 10: Modal frequency plotted according to RMS of vertical deck accelerations (above) and horizontal deck accelerations (below).

Figure 16: Model Errors of the prediction for the first modal frequency including period of suspected sensor fault

Figure 15: Model Errors of the prediction for the first modal frequency

Figure 5. Tamar SHM Database viewer based on MATLAB GUI

Figure 14: Variations of first and second modal frequencies plotted according to rms of deck acceleration.

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Long-term monitoring and data analysis of the tamar bridge" ?

The current paper outlines the extensive monitoring campaign of the Tamar suspension bridge as well as analysis carried out in the attempt to understand the bridge ’ s normal condition. 

Q2. How can the authors interpret the results of the response surface models?

One of the main advantages of polynomial response surface models is their simplicity; they are easily fitted using least-squares methods, and they are very easy to interpret, as coefficient values can indicate the significance of a parameter (as long as input variables are normalised prior to use). 

Q3. What is the first monitoring system installed at the Tamar Bridge?

The first is a Structural Monitoring System (SMS) installed by Fugro Structural Monitoring, which is used to monitor cable loads, structural and environmental temperatures and wind speed and profile. 

Q4. How can a simple response surface model predict the change in the first modal frequency?

It was found that a simple response surface model with input parameters based on the estimated traffic loading, temperature and deck acceleration (in turn dependent on the wind speed and direction) can predict the change in the first modal frequency to a good degree of accuracy. 

Q5. What was the effect of wind speed on the response of a long span bridge?

The response of a long span bridge to high and low wind speeds was investigated in [6], where it was concluded that the modal frequencies decreased with increased response amplitude levels directly caused by increased wind speed. 

Q6. How does the frequency of the second mode change with temperature?

For the frequency that appears most sensitive to temperature (the second, which corresponds to the first lateral symmetric mode), the frequency decreases by approximately 4.5% over a 20°C change in temperature. 

Q7. What is the way to predict the modal frequency of a bridge?

If the simple models used above in an attempt to better understand the bridge’s normal condition are capable of predicting the modal frequency change to a good and most importantly consistent degree, their prediction errors would be a good candidate for a damage indicator that is not affected by environmental and operational conditions. 

Q8. What are the two feature parameters for each of the vertical and horizontal deck acceleration measurements?

Two feature parameters for each of the vertical and horizontal deck acceleration measurements are included; one where only acceleration values occurring when high wind speeds hitting the deck side on are recorded (zero at all other times), the other for acceleration values occurring in all other wind conditions. 

Q9. What other approaches have been explored for similar problems?

Alternative approaches such as neural networks and support-vector machines have previously been explored in the literature for similar problems [12,13]. 

Q10. How many new cables were installed to supplement the original suspension system?

Eighteen new locked-coil cables were installed and stressed to supplement the original suspension system, primarily to help carry the additional dead load of the new cantilever lanes and associated temporary works (Figure 2). 

Q11. What is the effect of adding a temperature variable on the general fit to all recorded data?

Over short time periods (as illustrated in the inset figures) the addition of a temperature variable has no visible effect, however, the general fit to all recorded data (main figures) appears to be improved, which suggests that the temperature has more of a seasonal influence than daily, for this mode at least. 

Q12. Why did the model fail to perform well on the second modal frequency?

This was due, as explained previously, to the fact that large drops occur in the time history of the second modal frequency that the model cannot recreate, which are thought to be caused by traffic patterns. 

Q13. What is the effect of adding a variable dependent on the wind speed on the bridge?

As the bridge is orientated east-west, the increasing response with increased wind speed occurs, not surprisingly, when the wind hits the bridge side on. 

Q14. How many tonnes of traffic is on the bridge during the week?

From toll counts and web cam images, the instantaneous traffic loading on the bridge is estimated to increase by between 100 to 200 tonnes during very busy periods, which occur around 8am on weekdays.