Civil Engineering Reference
In-Depth Information
Table 14.1
Stochastic properties of 2D-truss bridge parameters
Stochastic properties
Mean
C.o.V. (
σ
/
μ
) (%)
Distribution
Young's modulus, GPa
70
8
Normal
Mass density, kg/m
3
2,800
4
Normal
Cross sectional area, m
2
0.0025
5
Normal
Fig. 14.2
Probability of sensor selection: EFI with stochastic Young's modulus
simulation is performed with the deterministic finite element code for the given number of samples. The natural
frequencies and mode shapes of the truss bridge are considered as the output response. The standard deviation of these
frequencies for different number of samples for the MCS is used to determine the number of samples required. In this
case, due to the stabilization of the standard deviation, 2,000 samples are chosen.
14.3.2 Sensor Placement Under Parametric Uncertainty
Initially, the effect of uncertain parameters on the sensor configuration is studied independently. Eleven sensor locations are
chosen out of the 28 DOFs available using the four OSP methods discussed in Sect.
14.2
. In MCS, the cross-sectional and
geometric properties vary with each sample. Therefore, the optimal locations of the 11 sensors also vary with each sample. The
probabilities of the DOFs chosen as optimal sensor locations for the case of stochastic Young's modulus, and for 2,000 samples
are shown in Fig.
14.2
. The results for all the stochastic variables show that there are several DOFs that are always chosen as an
optimal sensor location in every sample of the MCS. These sensor locations are of vital importance in the global configuration
and can be called as vital sensors. The results of EFIWMand KEMROmethodologies show similar sensor configurations due to
their theoretical similarities. In the case of the EFI method, DOFs 3, 6, 9, 25, and 27 have a probability of 1.0 when the Young's
modulus or cross section or mass density is considered as uncertain parameter. Therefore, these DOFs form five vital sensor
locations. The first 10 optimal sensor locations have much higher probabilities than the rest. However, the 11th and the next best
optimal choice have only small differences between their probabilities. For the EFIWMalgorithm, six sensors have a probability
of 1.0 and they are vital sensors. However, in this case the variability between the remaining sensors is higher. The KEMRO
algorithm shows a similar behaviour to EFIWM with seven vital sensors having a probability of 1.0 and small differences
between the remaining optimal sensors locations. Finally the SEMRO algorithm shows the highest number of vital sensors, with
eight having probabilities of 1.0, and has a large difference between the first 11 optimal locations and the others. The cumulative
effect of the three randomvariables on the OSP using the four methods show the number of vital sensors has decreased in all four
methodologies compared to the results with individual parameter uncertainty. Furthermore, all the algorithms show the same
vital sensors locations compared to the corresponding cases of individual stochastic variables, except in the case of EFI where
one of the sensors is different.
