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

A New Reflecting Microscope Objective with Two Concentric Spherical Mirrors

[none

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

Efficient Real Space Solution of the Kohn-Sham Equations with Multiscale Techniques

We present a multigrid algorithm for self consistent solution of the Kohn-Sham equations in real space. The entire problem is discretized on a real space mesh with a high order finite difference representation. The resulting self consistent equations are solved on a heirarchy of grids of increasing resolution with a nonlinear Full Approximation Scheme, Full Multigrid algorithm. The self consistency is effected by updates of the Poisson equation and the exchange correlation potential at the end of each eigenfunction correction cycle. The algorithm leads to highly efficient solution of the equations, whereby the ground state electron distribution is obtained in only two or three self consistency iterations on the finest scale.Comment: 13 pages, 2 figure

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

E2/M1 ratio from the Mainz p(γ⃗,p)π0p(\vec \gamma, p)\pi^0 data

We suggest that the error quoted in the Mainz determination of the E2/M1 ratio (at the resonance energy) should be enlarged. A term dropped in expressions used by this group could be significant.Comment: 2 pages of text. Submitted to the Comments section of PR