Probabilistic response analysis

Examples of probabilistic response analysis using the mean-centred First-Order Second-Moment (FOSM) approximation, time-invariant (First- and Second-Order Reliability Methods, FORM and SORM) and time-variant (mean outcrossing rate computation) reliability analyses are provided to illustrate the methodology presented and its current capabilities and limitations. 

Simplified finite element probabilistic response analysis... 

Probabilistic response analysis consists of computing the probabilistic characterization of the response of a specific structure, given as input the probabilistic characterization of material, geometric and loading parameters. An approximate method of probabilistic response analysis is the mean-centred First-Order Second-Moment (FOSM) method, in which mean values (first-order statistical moments), variances and covariances (second-order statistical moments) of the response quantities of interest are estimated by using a mean-centred, first-order Taylor series expansion of the response quantities in terms of the random/uncertain model parameters. Thus, this method requires only the knowledge of the first- and second-order statistical moments of the random parameters. It is noteworthy that often statistical information about the random parameters is limited to first and second moments and therefore probabilistic response analysis methods more advanced than FOSM analysis cannot be fully exploited. 

MCS is a general and robust method for probabilistic response analysis, but it suffers two significant limitations (1) it requires knowledge of the full joint PDF of random parameters 0, which, in general, is only partially known, and (2) it requires performing a usually large number of FE response analyses, which could be computationally prohibitive. 

Figure 1 Comparison of probabilistic response analysis results for Usx obtained from FOSM and MCS (a) mean value one standard deviation and (b) standard deviation estimates.

The mean-centred First-Order Second-Moment (FOSM) method is presented as simplified FE probabilistic response analysis method. The FOSM method is applied to probabilistic nonlinear pushover analysis of a structural system. It is found that a DDM-based FOSM analysis can provide, at low computational cost, estimates of first- and second-order FE response statistics which are in good agreement with significantly more expensive Monte Carlo simulation estimates when the frame structure considered in this study experiences low-to-moderate material nonlinearities. 

The response sensitivity, probabilistic response and reliability analysis methods presented are based on nonlinear FE quasi-static pushover and time-history analyses, which are used extensively in earthquake engineering and referred to by structural design codes. 

A probabilistic safety analysis has been performed for all large US nuclear power plants in response to the need to perform Individual Plant Evaluations (IPEs). The NRC has issued a policy statement on the use of probabilistic analyses in the regulatoiy process. A recent document has been issued summarizing initial results from IPEs received and reviewed by the NRC. This document, NUREG-I560, Parts 1 and 2, also provides a discussion of the attributes that contribute to a high quality PSA. 

T.-P. Chang, T. Mochlo and E. Samaras, Seismic response analysis of nonlinear structures. Probabilistic Engineering Mechanics I, 157-166 (1986). 

In his section will be discussed probabilistic failure analysis made for previously selected pipe section with movable support. Probabilistic failure analysis combines deterministic and probabilistic analysis. Finite element method was used as deterministic method while the Monte Carlo Simulation and the combined Monte Carlo Simulation and Response Surface methods were used for the probabilistic analyses. 

They suggested the effect parameter the Critical Effect Dose (CED, a benchmark dose. Section 4.2.5) derived from the dose-response data by regression analysis. This CED was defined as the dose at which the average animal shows the Critical Effect Size (CES) for a particular toxicological endpoint, below which there is no reason for concern. The distribution of the CED can probabilistically be combined with probabilistic distributions of assessment factors for deriving standards... 

Stochastic analysis presents an alternative avenue for dealing with the inherently probabilistic and discontinuous microscopic events that underlie macroscopic phenomena. Many processes of chemical and physical interest can be described as random Markov processes.1,2 Unfortunately, solution of a stochastic master equation can present an extremely difficult mathematical challenge for systems of even modest complexity. In response to this difficulty, Gillespie3-5 developed an approach employing numerical Monte Carlo... 

What are the key sources of uncertainty in the exposure assessment This question can also be posed as Which exposure factors contribute the most to the overall uncertainty in the inventory This insight can be used, in turn, to target resources to reduce the largest and most important uncertainties. There are various ways to answer this question, including various forms of sensitivity analysis. For example, in the context of a probabilistic uncertainty simulation for an overall exposure assessment, various statistical methods can be used to determine which input distributions are responsible for contributing the most to the variance of the output. 

The local site effects play an important role in the evaluation of seismic hazard. The proper evaluation of the local site effects will help in evaluating the amplification factors for different locations. This article deals with the evaluation of peak ground acceleration and response spectra based on the local site effects for the study area. The seismic hazard analysis was done based on a probabilistic logic tree approach and the peak horizontal acceleration (PHA) values at the bed rock level were evaluated. Different methods of site classification have been reviewed in the present work. The surface level peak ground acceleration (PGA) values were evaluatedfor the entire study area for four different site classes based on NEHRP site classification. The uniform hazard response spectrum (UHRS) has been developed for the city of Bangalore and the details are presented in this work. 

Steidl, J. H. (2000). Site response in southern California for probabilistic seismic hazard analysis. 

Steidl, J. H. (2000). Site response in southern California for probabilistic seismic hazard analysis. Bulletin of the Seismological Society of America, 90, S149-S169. doi 10.1785/0120000504... 

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