Performance-based post-earthquake decision making for instrumented buildings


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

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


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


Non-negative envelope function

\(\mathbf {K}\) :

Stiffness matrix

\(\mathbf {M}\) :

Mass matrix

n :

Number of degrees-of-freedom



\(\mathbf {P}\) :

State error covariance

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

Inter-story drift error covariance


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 :


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


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

Ground acceleration vector


Measurement noise


Process noise


Vector of auxiliary variables


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

\(\sigma ^2\) :


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

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

\(\omega\) :


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

Site dominant frequency

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

Normal distribution


American Society of Civil Engineers


Applied Technology Council




Collapse prevention


California Strong Motion Instrument Program


Damage measure


Degree of freedom


Decision variable


Engineering demand parameter


Extended Kalman filter


Finite element


Federal emergency management agency


Immediate occupancy


Inter-story drift


Kalman filter


Life safety




Nonlinear model-based observer


Performance-based assessment


Performance-Based Earthquake Engineering


Performance-based monitoring


Pacific Earthquake Engineering Research


Particle filters


Performance level


Power spectral density


Reinforced concrete




Unscented Kalman filter


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

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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).

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  • Decision making
  • Performance-based earthquake engineering
  • Seismic structural health monitoring
  • Dynamic response reconstruction
  • Instrumented buildings
  • Real-world validation