Chapters authored
Discretization of Random Fields Representing Material Properties and Distributed Loads in FORM Analysis
The reliability analysis of more complicated structures usually deals with the finite element method (FEM) models. The random fields (material properties and loads) have to be represented by random variables assigned to random field elements. The adequate distribution functions and covariance matrices should be determined for a chosen set of random variables. This procedure is called discretization of a random field. The chapter presents the discretization of random field for material properties with the help of the spatial averaging method of one-dimensional homogeneous random field and midpoint method of discretization of random field. The second part of the chapter deals with the discretization of random fields representing distributed loads. In particular, the discretization of distributed load imposed on a Bernoulli beam is presented in detail. Numerical example demonstrates very good agreement of the reliability indices computed with the help of stochastic finite element method (SFEM) and first-order reliability method (FORM) analyses with the results obtained from analytical formulae.
Part of the book: Dependability Engineering
On Risk and Reliability Studies of Climate-Related Building Performance
A design strategy based on integration of the building form and structure with its external environment in order to take advantage of natural forces (wind and buoyancy effects) has been evaluated in terms of risk and reliability measures. Tools for the probabilistic analysis (First-Order Reliability Method (FORM), Monte Carlo) have been presented and applied in the probabilistic modelling and sensitivity analysis of the response function of the studied building physics problem. Sensitivity analysis of the influence of basic random variables on the probability distribution of a response function is straightforward in FORM methodology. The case-based studies of probabilistic modelling of uncertainties coupled to wind speed and temperature difference through the specified building/environment system have been presented (i.e., the distribution models of the air change rate ACH and the dynamic U value characterising thermal performance of dynamic insulation). Sensitivities of the probability model of ACH to the parameters of wind speed and temperature distributions have been estimated for the consecutive values of the air change rate using FORM methodology. Reliability of ACH turned out to be most sensitive to the shape parameter of the wind speed distribution (in two-parameter Weibull model). The probabilistic risk analysis along with the effective tools for sensitivity analysis can be used to support design decisions and also to develop better models for evaluation of building performance.
Part of the book: Risk Assessment