Abstract
The present paper deals with structural health monitoring of trusses, space frame and plate structure utilizing the Bayesian data fusion approach. The application of the proposed approach has been demonstrated on a 25-member plane truss, a 42-member space frame, a cantilever plate and a 120-member space truss. Different damage indexes of interest have been calculated for the damaged structure utilizing the natural frequency and modeshapes as damage indicators. Damage indexes used are modal strain energy (DIMSE), frequency response function strain energy dissipation ratio (FRFSEDR), flexibility strain energy damage ratio (FSEDR) and residual force-based damage index (RFBDI). Next, the Bayesian data fusion approach has been applied to these four damage indexes to find out the accurate damage location. The proposed approach reduces the number of suspected damaged elements in the structure significantly, thus reducing the computational time of optimization algorithm. Proposed algorithm has also shown encouraging performance in noisy environments. Overall present approach is found to be robust and computationally efficient, and thus can be applied for damage detection involving field evaluation of various structures.
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Appendix. Notation
Appendix. Notation
The following symbols are used in this paper:
f | = | Natural frequency (Hz); |
ϕ | = | Modeshape matrix; |
δ | = | Noise level parameter; |
M | = | Mass matrix; |
C | = | Damping matrix; |
K | = | Stiffness matrix |
F(t) | = | External excitation in time domain; |
x(t) | = | Time response; |
ω | = | Circular frequency; |
D | = | Damage index; |
Ω | = | Frequency of the harmonic excitation; |
F(Ω) | = | External excitation in frequency domain; |
x(Ω) | = | Frequency domain response; |
H(Ω) | = | Frequency response function (FRF); |
ζ | = | Modal damping ratio; |
R | = | Matrix containing modal residual vectors; |
S | = | Flexibility matrix; |
λ | = | Eigenvalues; |
P(X) | = | Damage prior probability; |
P(Y ) | = | Actual damage probability; |
Superscripts | ||
u | = | Parameter for undamaged structures |
d | = | Parameters for damaged structures |
ur | = | Updated response of damaged structure in each iteration |
ar | = | Actual response of the damaged structure |
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Barman, S.K., Mishra, M., Maiti, D.K. et al. Vibration-based damage detection of structures employing Bayesian data fusion coupled with TLBO optimization algorithm. Struct Multidisc Optim 64, 2243–2266 (2021). https://doi.org/10.1007/s00158-021-02980-6
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DOI: https://doi.org/10.1007/s00158-021-02980-6