Bayesian Updating, Model Class Selection and Robust Stochastic Predictions of Structural Response

A fundamental issue when predicting structural response by using mathematical models is how to treat both modeling and excitation uncertainty. A general framework for this is presented which uses probability as a multi-valued conditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. The fundamental probability models that represent the structure’s uncertain behavior are specified by the choice of a stochastic system model class: a set of input-output probability models for the structure and a prior probability distribution over this set that quantifies the relative plausibility of each model. A model class can be constructed from a parameterized deterministic structural model by stochastic embedding utilizing Jaynes’ Principle of Maximum Information Entropy. Robust predictive analyses use the entire model class with the probabilistic predictions of each model being weighted by its prior probability, or if structural response data is available, by its posterior probability from Bayes’ Theorem for the model class. Additional robustness to modeling uncertainty comes from combining the robust predictions of each model class in a set of competing candidates weighted by the prior or posterior probability of the model class, the latter being computed from Bayes’ Theorem. This higherlevel application of Bayes’ Theorem automatically applies a quantitative Ockham razor that penalizes the data-fit of more complex model classes that extract more information from the data. Robust predictive analyses involve integrals over highdimensional spaces that usually must be evaluated numerically. Published applications have used Laplace's method of asymptotic approximation or Markov Chain Monte Carlo algorithms

Two-step Bayesian Structure Health Monitoring Approach for IASC-ASCE Phase II Simulated and Experimental Benchmark Studies

This report uses a two-step probabilistic structural health monitoring approach to analyze the Phase II simulated and experimental benchmark studies sponsored by the IASC-ASCE Task Group on Structural Health Monitoring. The studies involve damage detection and assessment of the test structure using simulated ambient-vibration data and experimental data generated by various excitations. The two-step approach involves modal identification followed by damage assessment using the pre- and post-damage modal parameters based on the Bayesian updating methodology. An Expectation-Maximization algorithm is proposed to find the most probable values of the parameters. The results of the analysis show that the probabilistic approach is able to detect and assess most damage locations involving stiffness losses of braces in the braced frame cases, while the success of the approach in detecting rotational stiffness losses of the beam-column connections in the untraced cases may rely on sufficient prior information for the column stiffness

Synergistic combination of systems for structural health monitoring and earthquake early warning for structural health prognosis and diagnosis

Earthquake early warning (EEW) systems are currently operating nationwide in Japan and are in beta-testing in California. Such a system detects an earthquake initiation using online signals from a seismic sensor network and broadcasts a warning of the predicted location and magnitude a few seconds to a minute or so before an earthquake hits a site. Such a system can be used synergistically with installed structural health monitoring (SHM) systems to enhance pre-event prognosis and post-event diagnosis of structural health. For pre-event prognosis, the EEW system information can be used to make probabilistic predictions of the anticipated damage to a structure using seismic loss estimation methodologies from performance-based earthquake engineering. These predictions can support decision-making regarding the activation of appropriate mitigation systems, such as stopping traffic from entering a bridge that has a predicted high probability of damage. Since the time between warning and arrival of the strong shaking is very short, probabilistic predictions must be rapidly calculated and the decision making automated for the mitigation actions. For post-event diagnosis, the SHM sensor data can be used in Bayesian updating of the probabilistic damage predictions with the EEW predictions as a prior. Appropriate Bayesian methods for SHM have been published. In this paper, we use pre-trained surrogate models (or emulators) based on machine learning methods to make fast damage and loss predictions that are then used in a cost-benefit decision framework for activation of a mitigation measure. A simple illustrative example of an infrastructure application is presented

Factors Contributing to the Catastrophe in Mexico City During the Earthquake of September 19, 1985

The extensive damage to high‐rise buildings in Mexico City during the September 19, 1985 earthquake is primarily due to the intensity of the ground shaking exceeding what was previously considered credible for the city by Mexican engineers. There were two major factors contributing to the catastrophe, resonance in the sediments of an ancient lake that once existed in the Valley of Mexico, and the long duration of shaking compared with other coastal earthquakes in the last 50 years. Both of these factors would be operative again if the Guerrero seismic gap ruptured in a single earthquake

Application of Subset Simulation to Seismic Risk Analysis

This paper presents the application of a new reliability method called Subset Simulation to seismic risk analysis of a structure, where the exceedance of some performance quantity, such as the peak interstory drift, above a specified threshold level is considered for the case of uncertain seismic excitation. This involves analyzing the well-known but difficult first-passage failure problem. Failure analysis is also carried out using results from Subset Simulation which yields information about the probable scenarios that may occur in case of failure. The results show that for given magnitude and epicentral distance (which are related to the ‘intensity’ of shaking), the probable mode of failure is due to a ‘resonance effect.’ On the other hand, when the magnitude and epicentral distance are considered to be uncertain, the probable failure mode correspondsto the occurrence of ‘large-magnitude, small epicentral distance’ earthquakes

Simplified PBEE to Estimate Economic Seismic Risk for Buildings

A seismic risk assessment is often performed on behalf of a buyer of large commercial buildings in seismically active regions. One outcome of the assessment is that a probable maximum loss (PML) is computed. PML is of limited use to real-estate investors as it has no place in a standard financial analysis and reflects too long a planning period for what-if scenarios. We introduce an alternative to PML called probable frequent loss (PFL), defined as the mean loss resulting from an economic-basis earthquake such as shaking with 10% exceedance probability in 5 years. PFL is approximately related to expected annualized loss (EAL) through a site economic hazard coefficient (H) introduced here. PFL and EAL offer three advantages over PML: (1) meaningful planning period; (2) applicability in financial analysis (making seismic risk a potential market force); and (3) can be estimated by a rigorous but simplified PBEE method that relies on a single linear structural analysis. We illustrate using 15 example buildings, including a 7-story nonductile reinforced-concrete moment-frame building in Van Nuys, CA and 14 buildings from the CUREE-Caltech Woodframe Project

Compressive sampling for accelerometer signals in structural health monitoring

In structural health monitoring (SHM) of civil structures, data compression is often needed to reduce the cost of data transfer and storage, because of the large volumes of sensor data generated from the monitoring system. The traditional framework for data compression is to first sample the full signal and, then to compress it. Recently, a new data compression method named compressive sampling (CS) that can acquire the data directly in compressed form by using special sensors has been presented. In this article, the potential of CS for data compression of vibration data is investigated using simulation of the CS sensor algorithm. For reconstruction of the signal, both wavelet and Fourier orthogonal bases are examined. The acceleration data collected from the SHM system of Shandong Binzhou Yellow River Highway Bridge is used to analyze the data compression ability of CS. For comparison, both the wavelet-based and Huffman coding methods are employed to compress the data. The results show that the values of compression ratios achieved using CS are not high, because the vibration data used in SHM of civil structures are not naturally sparse in the chosen bases