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. 2019 Oct 8;19(19):4341.
doi: 10.3390/s19194341.

Structural Damage Identification Based on AR Model with Additive Noises Using an Improved TLS Solution

Cai Wu  1 , Shujin Li  2 , Yuanjin Zhang  3
Affiliations

Structural Damage Identification Based on AR Model with Additive Noises Using an Improved TLS Solution

Cai Wu et al. Sensors (Basel). .

Abstract

Structural damage is inevitable due to the structural aging and disastrous external excitation. The auto-regressive (AR) based method is one of the most widely used methods for structural damage identification. In this regard, the classical least-squares algorithm is often utilized to solve the AR model. However, this algorithm generally could not take all the observed noises into account. In this study, a partial errors-in-variables (EIV) model is used so that both the current and prior observation errors are considered. Accordingly, a total least-squares (TLSE) solution is introduced to solve the partial EIV model. The solution estimates and accounts for the correlations between the current observed data and the design matrix. An effective damage indicator is chosen to count for damage levels of the structures. Both mathematical and finite element simulation results show that the proposed TLSE method yields better accuracy than the classical LS method and the AR model. Finally, the response data of a high-rise building shaking table test is used for demonstrating the effectiveness of the proposed method in identifying the location and damage degree of a model structure.

Keywords: auto-regressive model; damage identification; total least-squares method.

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Conflict of interest statement

The authors declare that there is no conflict of interest regarding the publication of this paper.

Figures

Figure 1
Figure 1
Size of the beam: (a) Cross-sectional view of the beam; (b) Distribution of the sensors.
Figure 2
Figure 2
Acceleration power spectral density (PSD) of testing point 5: (a) Before damage; (b) 50% damage.
Figure 3
Figure 3
Damage identification results: (a) Point 4; (b) Condition 4.
Figure 4
Figure 4
Observed signal with 30 dB Noises: (a) Before damaged; (b) Condition 3.
Figure 5
Figure 5
Damage identification results (a) Point 4; (b) Point 6.
Figure 6
Figure 6
Identification results along the beam in condition 4.
Figure 7
Figure 7
Picture of the model.
Figure 8
Figure 8
Damage after the test (52nd floor).
Figure 9
Figure 9
PSD figures for acceleration outputs of the top floor: (a) Before the earthquake excitations; (b) After the earthquake excitations.
Figure 10
Figure 10
IFs of some floors after different earthquake intensities: (a) 8th floor; (b) 14th floor; (c) 41st floor; (d)Top floor.
Figure 11
Figure 11
Identification factors (Ifs) along with stories: (a) Frequent 6; (b) Rare 7.
Figure 12
Figure 12
Comparison between least square (LS) solution with total least-squares (TLSE) solution: (a) 8th story; (b) 50th story.
Figure 13
Figure 13
Comparison along with stories after Moderate 6.
See this image and copyright information in PMC

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