Performance-based post-earthquake decision making for instrumented buildings
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ORIGINAL PAPER
Performance‑based post‑earthquake decision making for instrumented buildings Milad Roohi1 · Eric M. Hernandez2 Received: 9 December 2019 / Revised: 26 May 2020 / Accepted: 8 June 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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 postearthquake 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). Keywords Decision making · Performance-based earthquake engineering · Seismic structural health monitoring · Dynamic response reconstruction · Instrumented buildings · Real-world validation List of symbols arg min Argument of the minimum 𝐛1 Spatial distribution of excitation 𝐛2 Spatial distribution of process noise c2 Output location matrix 𝐂𝜉 Damping matrix e State error 𝔼 Expected value E Viscous damping coefficient 𝐄 Feedback matrix 𝐄opt Optimal feedback matrix F(t) Corrective force fc′ Compressive strength of concrete fR (.) Restoring force function * Milad Roohi [email protected] Eric M. Hernandez [email protected] 1
Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, CO 80523, USA
Department of Civil and Environmental Engineering, University of Vermont, Burlington, VT 05405, USA
2
G0 Constant power spectral density intensity hk Height of the kth story I(t) Non-negative envelope function 𝐊 Stiffness matrix 𝐌 Mass matrix n Number of degrees-of-freedom p[.] Probability 𝐏 State error covariance 𝐏ISD Inter-story drift error covariance q(t) Displacement vector q̂ (t) Displacement vector estimate q(t) ̇ Velocity vector q(t) ̈ Acceleration vector Sü ∗ ü ∗ (𝜔) Kanai–Tajimi power spectral density t Time tr(.) Trace ü g (t) Ground acceleration vector v(t) Measurement noise w(t) Process noise z(t) Vector of auxiliary variables y(t) Measured displacement vector y(t) ̇ Measured velocity vector ÿ (t) Measured acce
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