Research
Projects: Past Projects Effects of Ambient Temperature
on Modal Parameters
Research Team: Babak Moaveni (PI), Peter Moser (grad student)
Funding: N/A
Duration: 3/2010 – 6/2011
Relevant publications to date:
Moser, P., and Moaveni, B. (2011). "Environmental effects on the identified
natural frequencies of the Dowling Hall Footbridge."
Mechanical Systems and Signal Processing,
25(7), 23362357.
The modal parameters are often sensitive to changing environmental conditions
such as temperature, humidity, or excitation amplitude. Environmental conditions
can have as large an effect on the modal parameters as significant structural
damage, so these effects should be accounted for before applying damage
identification methods.
Figure 1 shows the identified natural frequencies of the six identified modes
versus the temperature of the northern abutment (C1) for the Dowling Hall
Footbridge at Tufts University campus. Correlation between natural frequencies
and temperatures is evident: higher natural frequencies generally occur at lower
temperatures. From this figure it can be observed that: (1) the identified
natural frequencies increase as temperatures decrease, (2) this effect is more
significant when the temperatures are below the freezing point resulting in a
nonlinear relationship, and (3) Modes 1, 3, and 4 show more clear correlation
with temperature while Modes 2, 5, and 6 show more scatter. One explanation for
the third observation is that Modes 2, 5, and 6 are identified with larger
estimation uncertainties as seen in Figure 10.
Figure 1. Identified natural frequencies versus western abutment temperature C1
Several nonlinear models are proposed to represent the relationship between the
identified natural frequencies and measured temperatures. Due to the high
correlation between some temperature records, only three records were used to
model the relationship between the identified six natural frequencies and the
measured temperatures. The three temperature measurements which gave the best
results for modeling were S3 (temperature of the steel frame), C2 (temperature
of the concrete deck) and C1 (temperature of the western abutment). The fact
that these three variables gave the best model suggests the structural frame,
the concrete deck, and the boundary conditions all significantly affect the
dynamics of this bridge. After evaluating many candidate models (including a
static linear model, an ARX model, a bilinear model, and polynomials of various
orders) a fourthorder polynomial static model was selected. The fourthorder
model with no cross terms was selected as the best practical model for the
relationship between natural frequencies and temperatures. Figure 2 compares the
identified natural frequencies with those simulated using the model, indicating
that the model fits the data well.
Figure 2. Timevariation of identified and fourthorder model simulated natural
frequencies of all six modes between January 25 and February 8, 2010
The fourthorder model presented can also be used to generate confidence
intervals around simulated natural frequencies based on the error variance and
the covariance of the temperature inputs. Figure 3 shows the identified and
simulated natural frequencies simulated using the fourthorder model during the
period between March 15 and March 29, together with the 95% confidence intervals
for the natural frequencies. The confidence intervals are indicated by the gray
shaded region, with the simulated natural frequency indicated by a darker gray
line. Data points which fall outside the confidence interval are shown with a
filled circle. Note that the width of the confidence interval compared to the
total variability in natural frequency is an indicator of the accuracy of the
model for each mode. Across the data shown, the simulated natural frequency and
confidence intervals generally match the data, and outliers are scattered rather
than concentrated.
Figure 3. Identified and simulated natural frequencies between March 15 and 29
using the fourthorder model without cross terms, together with the 95%
Confidence Interval (CI) and the outliers.
Confidence intervals provide a simple means of identifying damage: if a future
natural frequency develops a trend outside the confidence intervals established
for the corresponding temperatures it is likely that the bridge has experienced
structural change.
