Abstract
Civil engineering structures are especially complex due to their size, geometric and physical uniqueness, intrinsic nonlinearity, and also due to the variations of their properties as a function of environmental or operational loadings and support conditions. While overloading can produce severe but recoverable changes in modal properties, in the order of 30%, environmental conditions like temperature and humidity can produce state changes, particularly in supporting soils and boundary conditions, that have been observed to impose changes of 50% on modal properties without the presence of damage. Some of these variations are abrupt while others are slow, yet regardless of their speed they impose challenges on the experimental setups and identifications techniques. The basic civil structural instrumentation is mainly based on accelerometers and displacements sensors, being their characteristics described in the present chapter. The environmental excitations are in general nonstationary and input excitations are usually not measured. So, response is generally analyzed using Operational Modal Analysis (OMA) techniques, even if Experimental Modal Analysis (EMA) have also been extensively used. The most commonly applied technique for identification is the Stochastic Identification algorithm in their covariance and data-driven versions. In order to observe the complexities of civil infrastructure, examples are given for buildings under environmental and earthquake loads and bridges under environmental and traffic loads. Identification and automatic tracking algorithm are presented theoretically and with examples.
Abbreviations
- [A]:
-
System state matrix
- a gi :
-
Base acceleration
- a P :
-
Acceleration at position p
- \( {a}_i^{(k)} \) :
-
Average distance between the i-th object of a cluster and the remaining object of the same cluster
- ADC:
-
Analog to digital
- ARX:
-
Auto-regressive model with exogenous input
- \( {b}_i^{(k)} \) :
-
Average distance between the i-th object of a cluster and the objects assigned to other clusters
- B(PK):
-
Overall between-cluster distance measured from a partition P of k clusters
- [C]:
-
Observation matrix
- COV:
-
Reference to covariance-driven in SSI
- C k :
-
k-th cluster of partition PK
- d(xi,xj):
-
Distance between observations i and j measured for quantity x
- DAS:
-
Data acquisition systems
- EFDD:
-
Enhanced frequency domain decomposition
- EMD:
-
Empirical mode decomposition
- ERA:
-
Eigensystem realization algorithm
- FDD:
-
Frequency domain decomposition
- FFT:
-
Fast Fourier transform
- [H]:
-
Hankel matrix
- ITD:
-
Ibrahim time domain decomposition
- K :
-
Number of clusters in cluster partition
- [L]:
-
Matrix obtained from LQ decomposition
- LVDT:
-
Linear variable differential transformer
- MAC:
-
Modal assurance criterion
- MIMO:
-
Muitiple input multiple output
- MOESP:
-
Multivariate output-error state space
- MP:
-
Mean phase
- MPD:
-
Mean phase deviation
- MPC:
-
Mean phase collinearity
- Next-ERA:
-
Natural excitation technique eigensystem realization algorithm
- [O]:
-
Observability matrix
- P k :
-
Cluster partition containing k clusters
- PP:
-
Peak picking
- [Q]:
-
Matrix obtained from LQ decomposition
- R XX, RXY:
-
Cross-correlation
- SIL(Pt):
-
Silhouette width of partition P containing t clusters
- S/N:
-
Signal-to-noise ratio
- SHM:
-
Structural Health Monitoring
- \( {s}_i^{(k)} \) :
-
Silhouette width of the i-th object assigned to a cluster
- s k :
-
Silhouette width of cluster k
- SSI:
-
Stochastic subspace identification
- STFT:
-
Short-time Fourier transform
- SVD:
-
Singular value decomposition
- S XX, SXY:
-
Periodogram
- T :
-
Overall distance measured from a cluster partition
- [T]:
-
Toeplitz matrix
- [U]:
-
Hankel matrix of observations
- UPS:
-
Uninterruptable power supply
- v(t):
-
Decay response
- W(PK):
-
Overall within-cluster distance measured from a partition P of k clusters
- {y}:
-
Response vector
- \( \dot{y},\ddot{y} \) :
-
First and second time derivatives of y
- [Y]:
-
Hankel matrix of response
- {z}:
-
State space vector
- β t :
-
Damping of mode t
- γ 2 :
-
Coherence
- λ :
-
Eigenvalue
- ω, f:
-
Natural frequency of mode t
- [Σ]:
-
Singular values matrix
- [ϕ]:
-
Modal shape matrix
- [ψ]:
-
Eigenvector matrix
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Acknowledgments
The authors would like to acknowledge all the support given by the Department of Civil Engineering, of the University of Chile, and by the Structures Department of the Portuguese National Laboratory for Civil Engineering (LNEC).
In addition, the authors would also like to acknowledge the support given by Conicyt and Fondecyt Chile, projects 1950629, 1000912, 1070319, and the Portuguese Foundation for Science and Technology (FCT) through the SAFESUSPENSE project – POCI-01-0145-FEDER-031054 (funded by COMPETE2020, POR Lisboa and FCT).
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Boroschek, R., Santos, J.P. (2020). Civil Structural Testing. In: Allemang, R., Avitabile, P. (eds) Handbook of Experimental Structural Dynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-6503-8_29-1
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