The analysis of the fiber optic strain gages began by looking at Figure 5.21 and noting that up until sunrise and then after sunset there appeared to reasonable behavior in the compensated strain sensors. However, during the daylight hours, it was difficult to distinguish what was occurring. Compare Figure 5.21 showing the compensated strain to Figure 5.28 that shows the temperature for seven different fiber optic temperature sensors. As in the compensated strain plot, before sunrise and after sunset, the temperature as measured by all sensors is much more uniform than during the daylight hours. During the night, the plots exhibit an exponentially decaying trend and the difference in the measured temperatures is minimal. The exponential decay of the temperature matches the typical decay seen in the air temperature after the sunsets and the temperature begins to drop. Thus, Figure 5.28 would indicate that after the sunsets, the bridge reaches an equilibrium temperature with the surrounding night air.
To investigate whether the temperatures measured were reaching equilibrium with the environment after the sunset, the collected temperature data was compared to the reported air temperature. Table 5.5 shows the measured temperature for each sensor at three times during the night (civil dusk, midnight, and civil dawn)
Figure 5.29: Total strain, temperature, and compensated CMS strain from midnight to dawn.
for a dataset from April 2010. The minimum, maximum, and mean measured temperature have also been computed for each time. Table 5.5 also provides the air temperature as measured by the official weather station of Lock and Dam 15 at the Rock Island Bridge site. The installed fiber optic temperature sensors, on average, report the same temperature as the air temperature within the short-term accuracy (±1◦C) of the os4350 sensors. Sensor Temperature R9 does not follow the general trends of the other sensors and differs from the air temperatures not in just an offset, but the rate of decrease is accelerated.
As noted in Section 5.1.1, FBG strain sensors are highly temperature dependent on temperature. There- fore, the total strain as measured by the fiber optic strain gages can be informative about the behavior of the temperature sensors. In Section 5.5 it was determined that the trains and swings are the only significant source of mechanical strain so any changes in the total strain as measured by the strain gages is due to changes in the thermal strain. Therefore, the changes in the temperature should be mimicked by the change in the total strain if the temperature is measuring the temperature of the steel.
Figure 5.29 shows an example of the temperature compensated CMS strain and the total strain and temper- ature that were used to compute the CMS strain in ENLIGHT during the course of a night. The temperature
Table 5.5: Temperature (◦C) as measured by the temperature sensors on April 18-19, 2010. Civil Dusk Midnight Civil Dawn
Sensor 20:14 00:00 05:47 Minimum 11.10 5.47 0.47 Maximum 17.25 14.55 9.62 Mean 16.22 11.36 6.77 Air Temperature 16.66 11.11 6.66 Temperature R1 17.03 14.55 9.62 Temperature R2 16.13 10.98 6.13 Temperature R3 17.01 12.69 8.00 Temperature R4 16.72 11.25 6.63 Temperature R5 15.63 10.52 6.06 Temperature C6 16.05 11.09 6.36 Temperature R7 16.05 11.09 6.36 Temperature R8 16.32 11.51 7.46 Temperature R9 11.10 5.47 0.47 Temperature R10 16.42 11.79 7.80 Temperature R11 15.80 10.93 6.51 Temperature R12 16.57 12.13 8.38 Temperature L13 — — — Temperature L14 16.04 10.83 5.97 Temperature L15 16.87 12.49 7.85 Temperature L16 17.25 11.64 6.52 Temperature L17 16.64 11.32 6.29 Temperature L18 16.32 11.51 7.46 Temperature L19 16.90 11.51 6.39 Temperature L20 16.83 12.37 8.37 Temperature L21 16.68 11.61 6.79 Temperature L22 — — — Temperature L23 — — —
Note: Air temperatures are from the weatherunderground.com historical data- base for weather station MRCKI2 located at Lock and Dam 15. The station records the temperature in◦F to the nearest degree. The air temperatures in this table are the temperatures recorded closest to the given event and are therefore approximate.
Note: A dashed line (—) indicates that the given temperature sensor was not functioning when the data was collected.
Figure 5.30: Total strain, temperature, and compensated CMS strain during afternoon with swing events.
shows the exponential decay that has been previously discussed as the temperature dropped about five de- grees over the course of the night. The total stain shows both the changes in mechanical strain caused by the swing events13that occurred during the night and the change in strain due to the change in temperature. At midnight, the bridge is in the open position and then soon closes so that the stairs on the upstream side of the bridge. At 06:00, the bridge, after making a series of swings, is once again locked with the stairs on the upstream side. When the bridge is in the same position, the contributions to the total strain from the me- chanical strain should be the same and any change in strain is caused by the thermal strains. Equation (5.9) predicts that for a five degree change in temperature, the thermal strain should change about 91.5µ. The strain change seen in the total strain in Figure 5.29 conforms to this estimate. Therefore, when the tempera- ture compensation is performed, the result is a straight line broken by the swing events. This shows that at night the temperature measurements are likely properly measuring the temperature of the steel.
However, during the day, the influence of the sun can cause the temperature sensors to measure a tem- perature that does not wholly represent the temperature in the steel. For example, Figure 5.30 shows an
Figure 5.31: Total strain, temperature, and compensated CMS strain during an afternoon swing event.
example the temperature compensated CMS strain and the total strain and temperature that were used to compute the CMS strain in ENLIGHT during an afternoon. The total strain in the figure shows that the bridge is in the open position at noon, closes soon after, opens for nearly forty minutes for a swing, then a train crosses the bridge at 13:30, and then two more swings occur later in the afternoon. The strain tran- sitions between the events are generally straight, smooth lines that can increase and decrease at times over the course of the afternoon. This strain pattern indicates that the temperature in the steel changed gradually over the course afternoon. However, the temperature record for the same period shows three distinct peaks and a wide amount of variation between those peaks.
The third peak in temperature that ends at about 15:00 in Figure 5.30 has been isolated in Figure 5.31.14 This isolated swing event shows a change of about eight degrees between its maximum temperature and the minimum temperature. Again using Equation (5.9), the change in temperature should correspond to a change in strain of 146.4µ. The total strain does not exhibit this expected response.
What the total strain does show is that just before the start of the third temperature spike, the bridge
14The total strain has been offset by -100 microstrain from the total strain in Figure 5.30 and the scales have been changed for clarity.
unlocked and began to swing. The swing does cause the temperature of the steel to increase as seen in the rise in strain while in the open position but the amount and rate of change does not match that indicated by the temperature sensor. As a result, the compensated CMS strain shows the initial strain increase due to the bridge unlocking but once the measured temperature and the steel temperature are mismatched, there is a large decrease in the compensated strain because the formula is over compensating with the measured temperature.
This peak demonstrates that during the day it is possible that the temperature sensor is no longer measur- ing the temperature of just the steel. A clue as to what is happening is that the bridge is rotating and the sun at this period in the afternoon is highly directional. When the bridge opens and begins to swing, the sensors and the steel eye-bar they are attached to moves from a position of shadow to one of direct sunlight exposure. The solar radiation causes the temperature of the black painted steel to rise increasing the total strain but it also affects the temperature sensor. As noted in Section 5.2.1, the os4350 sensors are enclosed in an anodized aluminum casing. The specific heat of aluminum is 0.91 kJ/(kg·C) at ambient temperatures while that of steel is 0.49 kJ/(kg·C). When the sensors and member are swung into the sun they are exposed to an amount of solar radiation which has units of W/m2which is equivalent to J/(s·m2) for the same amount of time. The ratio of exposure area to mass for the aluminum clad sensor is 0.0315 m2/kg while that for the eye-bar the strain sensor is attached to is 0.0027 m2/kg. Thus for the same solar input, the aluminum would be expected to experience a rise in temperature about 6.28 times greater than that of the steel.
Given that the steel saw a thermal induced strain increase of 13 µ, according to Equation (5.9), the steel experienced only a 0.71◦C rise in temperature. However, the temperature sensor recorded a rise in temperature of 8.13◦C which is 6.28 times greater than the temperature rise in the steel. The difference could be attributed to a combination of the different absorption levels of the radiation and the ability of the steel to radiate heat to the air while the temperature sensor is restricted due to its protective covering. The protective coating may also account for the slight delay in the start of the rise in temperature seen in the measured temperature record.
When the bridge turns back to its original position, the measured temperature begins an exponential decay as it approaches equilibrium with the temperature of the steel as seen between 15:00 and 15:05 in Figure 5.31. Thus undoing the effects of direct solar radiation exposure to the temperature sensor and the steel member. The process of solar heating caused the temperature sensor to record a temperature other than the temperature of the steel in the other swing events shown in Figure 5.30. Note that during the brief train event at 13:30, the strain record shows no significant temperature differential because the bridge has not
Figure 5.32: Total strain, temperature, and compensated CMS strain from dawn to early morning.
changed position.
Also note that the dip in temperature at about 13:00 during the first swing event could be caused by the shadows of a cloud. The aluminum also has a thermal conductivity that is greater than that of steel (205 and 36 W/(m·C) respectively). This means that it takes steel longer to heat up or cool down then aluminum. Thus, reductions in the degree of solar exposure or temperature in general will affect the aluminum more than it will the steel. During the night when the steel temperature is above the ambient temperature, the sensitivity of the aluminum allows the temperature sensor to track the steel temperature well, because the steel will lag the temperature. However, when the ambient temperature is greater than the temperature of the steel or solar exposure is present, the aluminum (and therefore the measured temperature) will lead the steel temperature causing the compensation problems.
Figure 5.32 shows the effect of the leading versus lagging effect in the temperature measurement and as a result the temperature compensation. In the pre-dawn hours, the temperature and total strain are well matched and the compensation is adequate. However, after sunrise, the same total strain and temperature that were previously well matched are not any longer. The measured temperature increases faster and greater
than the temperature of the steel during the swing events causing problems in the compensation. At 09:00 a spike occurs in the measured temperature that does not appear in the total strain record. This spike of unknown origin is not evidence of a sensor misbehaving (it is doing what it is supposed to do – measure the temperature of the aluminum casing), because no evidence of such behavior exists in the same sensor during the night.
5.6.1 Conclusions
The analysis of the temperature sensors concludes that during the night hours, when the temperature of the steel lags the ambient temperature, the aluminum encased fiber optic sensors can adequately record the tem- perature of the steel. However, during the daylight hours where the sensors can be exposed to solar radiation that adds heat to the equation of thermal equilibrium at different rates due to the mismatched specific heat values of the steel and aluminum, the os4350 temperature sensors are not measuring the temperature of the steel.
As a result of this analysis, the uncompensated strain measurements are used in the integrated SHM pro- gram. This choice is acceptable because the event detection algorithm that lies at the heart of the integrated program is looking for changes in strain that occur over a short period of time. As the period of time de- creases the change in temperature approaches zero and therefore so does the thermal strain component of the total strain measured. In addition, the statistics used to determine the bridge condition will be conservatively restricted to those events that fall between nautical dusk an nautical dawn when solar radiation is less likely to affect the sensors.
Researchers in other fields have also noticed the effects of direct solar radiation on fiber optic sensors. Neilson et al. [101] performed studies that submersed fiber optic temperature sensors in water that impedes the penetration of the solar radiation. The fiber optic sensors exhibited measurable differences in heating due to solar radiation as a function of the depth of the sensor in the water column. The net effects of the radiation seen in the Neilson study were small because the sensors were placed in a moving stream whose flow cooled the sensors. They also determined that close to the stream beds, the heat conduction of the concrete stream bed could dominate the thermodynamics contributing to the temperature measured by the fiber optic sensors. The thermodynamic principles are the same for the stream bed as they are for the Rock Island Bridge. Placing the Rock Island temperature sensors on black painted steel and not allowing cooling other than conduction to the steel substrate exacerbates the radiative effects on the bridge sensors.
effects might not be eliminated. Nakamura and Mahrt [102] developed a model to correct for the observed radiative error in temperature measurements that were shielded with naturally ventilated shields that ideally are supposed to prevent shortwave radiation penetration. However, the correction method depends on the measurement of the wind speed and the net radiation. On the Rock Island Bridge by properly shielding the fiber optic temperature sensors, the error effects might be minimal enough that the heat conduction from the steel would be the dominant influence on the sensors.