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Performance-based post-earthquake decision making for instrumented buildings

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Abstract

This paper develops a decision making framework for post-earthquake assessment of instrumented buildings in a manner consistent with performance-based design criteria. This framework is achieved by simultaneously combining and advancing existing knowledge from seismic structural health monitoring and performance-based earthquake engineering paradigms. The framework consists of (1) measurement, (2) uncertainty modeling, (3) dynamic response reconstruction, (4) damage estimation, and (5) performance-based assessment and decision making. In particular, the main objective is to reconstruct inter-story drifts with a probabilistic measure of exceeding performance-based acceptance limits and determine the post-earthquake re-occupancy classification of the instrumented building of interest. Since the proposed framework is probabilistic, the outcome can be used to obtain the probability of losses based on the defined decision variables and be integrated into a risk-based decision making process by city officials, building owners, and emergency managers. The framework is illustrated using data from the Van Nuys hotel testbed, a seven-story reinforced concrete building instrumented by the California Strong Motion Instrumentation Program (CSMIP Station 24386).

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Abbreviations

\(\mathrm{arg}\,\mathrm{min}\) :

Argument of the minimum

\(\mathbf {b}_1\) :

Spatial distribution of excitation

\(\mathbf {b}_2\) :

Spatial distribution of process noise

\(c_2\) :

Output location matrix

\(\mathbf {C}_\xi\) :

Damping matrix

e :

State error

\({\mathbb {E}}\) :

Expected value

E :

Viscous damping coefficient

\(\mathbf {E}\) :

Feedback matrix

\(\mathbf {E}_{\text {opt}}\) :

Optimal feedback matrix

F(t):

Corrective force

\(f'_{\text {c}}\) :

Compressive strength of concrete

\(f_{\text {R}}(.)\) :

Restoring force function

\(G_0\) :

Constant power spectral density intensity

\(h_k\) :

Height of the kth story

I(t):

Non-negative envelope function

\(\mathbf {K}\) :

Stiffness matrix

\(\mathbf {M}\) :

Mass matrix

n :

Number of degrees-of-freedom

p[.]:

Probability

\(\mathbf {P}\) :

State error covariance

\(\mathbf {{P}}_{\mathrm{ISD}}\) :

Inter-story drift error covariance

q(t):

Displacement vector

\(\hat{q}(t)\) :

Displacement vector estimate

\(\dot{q}(t)\) :

Velocity vector

\(\ddot{q}(t)\) :

Acceleration vector

\(S_{\ddot{u}^*\ddot{u}^*(\omega )}\) :

Kanai–Tajimi power spectral density

t :

Time

\({\text {tr}}(.)\) :

Trace

\(\ddot{u}_{\text {g}}(t)\) :

Ground acceleration vector

v(t):

Measurement noise

w(t):

Process noise

z(t):

Vector of auxiliary variables

y(t):

Measured displacement vector

\(\dot{y}(t)\) :

Measured velocity vector

\(\ddot{y}(t)\) :

Measured acceleration vector

\(\xi _{\text {g}}\) :

Site dominant damping coefficient

\(\sigma\) :

Standard deviation

\(\sigma ^2\) :

Variance

\(\varvec{\varPhi }(\omega )\) :

Power spectral density

\(\varvec{\varPhi }_{ee}(\omega )\) :

Error spectral density matrix

\(\varvec{\varPhi }_{vv}(\omega )\) :

Power spectral density of measurement noise

\(\varvec{\varPhi }_{ww}(\omega )\) :

Power spectral density of uncertain inputs

\(\omega\) :

Frequency

\(\omega _{\text {g}}\) :

Site dominant frequency

\({\mathcal {N}}\) :

Normal distribution

ASCE:

American Society of Civil Engineers

ATC:

Applied Technology Council

C:

Collapse

CP:

Collapse prevention

CSMIP:

California Strong Motion Instrument Program

DM:

Damage measure

DoF:

Degree of freedom

DV:

Decision variable

EDP:

Engineering demand parameter

EKF:

Extended Kalman filter

FE:

Finite element

FEMA:

Federal emergency management agency

IO:

Immediate occupancy

ISD:

Inter-story drift

KF:

Kalman filter

LS:

Life safety

M:

Measurement

NMBO:

Nonlinear model-based observer

PBA:

Performance-based assessment

PBEE:

Performance-Based Earthquake Engineering

PBM:

Performance-based monitoring

PEER:

Pacific Earthquake Engineering Research

PF:

Particle filters

PL:

Performance level

PSD:

Power spectral density

RC:

Reinforced concrete

RMS:

Root-mean-square

UKF:

Unscented Kalman filter

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Acknowledgements

Support for this research provided, in part, by award No. 1453502 from the National Science Foundation is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, CO, 80523, USA

    Milad Roohi

  2. Department of Civil and Environmental Engineering, University of Vermont, Burlington, VT, 05405, USA

    Eric M. Hernandez

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  1. Milad Roohi
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Correspondence to Milad Roohi.

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Roohi, M., Hernandez, E.M. Performance-based post-earthquake decision making for instrumented buildings. J Civil Struct Health Monit 10, 775–792 (2020). https://doi.org/10.1007/s13349-020-00416-1

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