Civil Engineering Reference
In-Depth Information
The number of sensors can also be selected if a desired level of accuracy is required. Sensors configurations become very
expensive as the number of sensors increases. Furthermore, a procedure is required to estimate the exact number of sensors
needed. In particular, for similar levels of accuracy measured in terms of MAC rms error, big differences could exist in the
number of sensors employed. To illustrate this methodology suppose we wish to select the number of sensors between 11 and
14. The effects of the noise are also considered. In this case the EFI algorithm is applied to determine the best sensor
configuration for the case of 11 and 14 sensors. After these configurations are fixed, the MCS is run with uncertain
parametric variables (Young's modulus, cross section and mass density) to assess the performance in terms of MAC rms
error. If noise is added the MAC rms error increases from the case of low noise. The MAC rms errors are similar for 11 and
14 sensors in the case of no noise, but show higher differences with high noise.
14.4 Conclusions
This paper investigates the influence of parametric uncertainties on the OSP methodologies for modal analysis of structures.
Four OSP algorithms were used for numerical studies. A truss type bridge structure is considered as the test case to study the
effects of parametric uncertainties on the OSP. Geometric (cross section) and material properties (Young's modulus and
mass density) were considered as uncertain variables. Monte Carlo simulation was performed to evaluate the optimal sensor
locations under uncertainty. This was propagated through a finite element model of the truss bridge structure. The natural
frequencies show considerable scatter due to uncertainty. In addition, the mode shapes also show considerable variations due
to uncertainty and therefore affect the optimal sensor locations. Initially, the effects of uncertainty in individual variables on
the sensor configurations were examined. The numerical results show that some sensor locations were always chosen even
with the uncertainty. These sensors are called vital sensors due to their high probabilities of occurrence. When the
cumulative effect of uncertain variables are considered, the MCS shows similar results and retains the vital sensors of the
individual uncertainty results. In order to compare the optimal sensor configurations obtained from four OSP methodologies,
three assessment criteria were established. These criteria were applied to the sensor configurations identified by the four OSP
algorithms considered in this work. Furthermore, due to the importance of noise in real applications, different levels of
signal-to-noise-ratios were considered. The noise was incorporated into the finite element model to simulate its effects on the
mode shapes of truss bridge. Three different levels of noise were considered and the corresponding sensor configurations
were compared. Finally, these numerical results demonstrate that uncertainties in geometric and material properties play a
significant role in the optimal sensor placement methodologies.
Acknowledgements
We express special thanks to the Spanish Ministry of Education, Culture and Sport for Grant Number FPU-AP2009-3475
and to the Junta de Andaluc´a for the Research Project P09-TEP-5066.
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