Efficient method for probabilistic fire safety engineering

A growing interest exists within the fire safety community for the topics of risk and reliability. However, due to the high computational requirements of most calculation models, traditional Monte Carlo methods are in general too time consuming for practical applications. In this paper a computationally very efficient methodology is for the first time applied to structural fire safety. The methodology allows estimating the probability density function which describes the uncertain response of the fire exposed structure or structural member, while requiring only a very limited number of model evaluations. The application of the method to structural fire safety is illustrated by two examples in the area of concrete elements exposed to fire

Bayesian learning of models for estimating uncertainty in alert systems: application to air traffic conflict avoidance

Alert systems detect critical events which can happen in the short term. Uncertainties in data and in the models used for detection cause alert errors. In the case of air traffic control systems such as Short-Term Conflict Alert (STCA), uncertainty increases errors in alerts of separation loss. Statistical methods that are based on analytical assumptions can provide biased estimates of uncertainties. More accurate analysis can be achieved by using Bayesian Model Averaging, which provides estimates of the posterior probability distribution of a prediction. We propose a new approach to estimate the prediction uncertainty, which is based on observations that the uncertainty can be quantified by variance of predicted outcomes. In our approach, predictions for which variances of posterior probabilities are above a given threshold are assigned to be uncertain. To verify our approach we calculate a probability of alert based on the extrapolation of closest point of approach. Using Heathrow airport flight data we found that alerts are often generated under different conditions, variations in which lead to alert detection errors. Achieving 82.1% accuracy of modelling the STCA system, which is a necessary condition for evaluating the uncertainty in prediction, we found that the proposed method is capable of reducing the uncertain component. Comparison with a bootstrap aggregation method has demonstrated a significant reduction of uncertainty in predictions. Realistic estimates of uncertainties will open up new approaches to improving the performance of alert systems

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

Uncertainty Analysis of the Adequacy Assessment Model of a Distributed Generation System

Due to the inherent aleatory uncertainties in renewable generators, the reliability/adequacy assessments of distributed generation (DG) systems have been particularly focused on the probabilistic modeling of random behaviors, given sufficient informative data. However, another type of uncertainty (epistemic uncertainty) must be accounted for in the modeling, due to incomplete knowledge of the phenomena and imprecise evaluation of the related characteristic parameters. In circumstances of few informative data, this type of uncertainty calls for alternative methods of representation, propagation, analysis and interpretation. In this study, we make a first attempt to identify, model, and jointly propagate aleatory and epistemic uncertainties in the context of DG systems modeling for adequacy assessment. Probability and possibility distributions are used to model the aleatory and epistemic uncertainties, respectively. Evidence theory is used to incorporate the two uncertainties under a single framework. Based on the plausibility and belief functions of evidence theory, the hybrid propagation approach is introduced. A demonstration is given on a DG system adapted from the IEEE 34 nodes distribution test feeder. Compared to the pure probabilistic approach, it is shown that the hybrid propagation is capable of explicitly expressing the imprecision in the knowledge on the DG parameters into the final adequacy values assessed. It also effectively captures the growth of uncertainties with higher DG penetration levels