Structured model uncertainty

Jalayer E, Eranchin P, Pinto PE (2007b) Considering structural modelling uncertainty in seismic reliability analysis of RC frames use of advanced simulation methods. In Proceedings of the conference COMPDYN 2007, paper ID 1218, Crete, Greece, 13-16 June 2007... 

Jalayer E, lervolino I, Manfredi G (2010) Structural modeling uncertainties and their influence on seismic assessment of existing RC structures. Struct Saf... 

At each stage during the structure determination process, the current structural model gives an estimate of the prediction variance Z2 to be associated with the calculated amplitude. The contribution of the random part of the structure to this prediction variance decreases while the structure determination proceeds, and uncertainty is removed by the fit to the observations. Rescaling of Z2 would be needed during the optimisation of the Bayesian score. 

Summary. In this chapter the control problem of output tracking with disturbance rejection of chemical reactors operating under forced oscillations subjected to load disturbances and parameter uncertainty is addressed. An error feedback nonlinear control law which relies on the existence of an internal model of the exosystem that generates all the possible steady state inputs for all the admissible values of the system parameters is proposed, to guarantee that the output tracking error is maintained within predefined bounds and ensures at the same time the stability of the closed-loop system. Key theoretical concepts and results are first reviewed with particular emphasis on the development of continuous and discrete control structures for the proposed robust regulator. The role of disturbances and model uncertainty is also discussed. Several numerical examples are presented to illustrate the results. 

It is useful to distinguish between variability, parameter uncertainty, and model uncertainty, since they require different treatment in risk analysis (Suter and Barnthouse 1993). Variability refers to actual variation in real-world states and processes. Parameter uncertainty refers to imprecise knowledge of parameters used to describe variability or processes in a risk model this can arise from many sources including measurement error, sampling error, and the use of surrogate measurements or expert judgment. Model uncertainty refers to uncertainty about the structure of the risk model, including what parameters should be included and how they should be combined in the model equations. 

By retaining the groupings of overlapping reflections assumed by each author, their individual differences of judgement are retained and made to contribute to the uncertainties in the final structural model. The determination of the uncertainties caused by such differences of judgement is the main purpose of the present investigation... 

Why are these equations represented by 4th order polynomials and not 2nd order curves given that the vertical variation of temperature and vapor fraction are well approximated by second order functions The simple answer is that the transition from condensing water vapor to liquid water above 0 °C to condensing water ice below -20 °C, and the attendant affect on the fractionation factor (Fig. 2), results in additional structure not captured by 2nd or 3rd order curves. Each of the equations fit their respective model output with an R2 > 0.9997. The lack of symmetry of the modeled uncertainty reflects asymmetry in the probability density function and particularly the long tail toward lower values of T relative to the mean (see Fig. 2 of Rowley et al. 2001). The effect of this long tail is well displayed in both Figure 5 and 7. 

Realistic predichons of study results based on simulations can be made only with realistic simulation models. Three types of models are necessary to mimic real study observations system (drug-disease) models, covariate distribution models, and study execution models. Often, these models can be developed from previous data sets or obtained from literature on compounds with similar indications or mechanisms of action. To closely mimic the case of intended studies for which simulations are performed, the values of the model parameters (both structural and statistical elements) and the design used in the simulation of a proposed trial may be different from those that were originally derived from an analysis of previous data or other literature. Therefore, before using models, their appropriateness as simulation tools must be evaluated to ensure that they capture observed data reasonably well [19-21]. However, in some circumstances, it is not feasible to develop simulation models from prior data or by extrapolation from similar dmgs. In these circumstances, what-if scenarios or sensitivity analyses can be performed to evaluate the impact of the model uncertainty and the study design on the trial outcome [22, 23]. 

Another field where dielectric continuum models are extensively used is the statistical mechanical study of many particle systems. In the past decades, computer simulations have become the most popular statistical mechanical tool. With the increasing power of computers, simulation of full atomistic models became possible. However, creating models of full atomic detail is still problematic from many reasons (1) computer resources are still unsatisfactory to obtain simulation results for macroscopic quantities that can be related to experiments (2) unknown microscopic structures (3) uncertainties in developing intermolecular potentials (many-body correlations, quantum-corrections, potential parameter estimations). Therefore, creating continuum models, which process is sometimes called coarse graining in this field, is still necessary. 

Low-resolution optical spectroscopic measurements established that the PrPc—>PrPSc conversion is accompanied by a major decrease in a-helical content and an increase in (3-sheet structure [101-104]. However, the secondary structure of PrPSc remains controversial, with the estimated content of a-helical structure ranging from 0%, as assessed by circular dichroism spectroscopy [104], to 0-21%, as inferred from Fourier-transform infrared measurements [101-103, 105]. These low resolution spectroscopic measurements are subject to considerable uncertainty thus, caution should be exercised when using global secondary structure estimates for constructing specific high-resolution structural models of PrPSc. 

In the following, we compute the price of bond options assuming these two types of Random Fields as correlated sources of uncertainty, while dZ(t T) leads to anon-differential and dU (t, T) to a T-differential type of term structure model. Note that the computation of the particular option price differs only in the proposed type of correlation function. 

This updated robust probability of failure incorporates knowledge about 0 from C and from the updated information from the data. It is robust because the modeling uncertainties are taken into explicit account [198]. The updated structural reliability of the stmcture is P(5 P, C) = 1 - F(F D, C), where S denotes a safe status of the structure. 

Unfortunately there is much less structural information available in most other intercalated CPs [163,164] and, in these cases, structural modeling methods are often less quantitative and involve greater uncertainties. PANi is one of the few other intercalated CPs exhibiting crystalline phases sufficiently well developed to enable critical comparisons with structure factor calculations. The already dted 1991 paper by Pouget et al. [86] also identified the presence of structural polymorphism in HCl-doped PANi. Two basic structural motifs were observed and these were designated HCl ES-I and ES-II. This halogen anion is sufficiently small that these phases are, to first order, channel-hke in appearance (as aheady sketched in Figure 17.4). 

Reliability and Safety Data Collection and Analysis Fault Identification and Diagnostics Maintenance Modelling and Optimisation Structural Reliability and Design Codes Software Reliability Consequence Modelling Uncertainty and Sensitivity Analysis Safety Culture Organizational Learning Human Factors... 

Generally, the uncertainty in model predictions may derive from parameter or data uncertainties as well as from model uncertainties. Parameter or data uncertainty is defined as the lack of knowledge on parameter values or input data. Model uncertainty denotes uncertainty on the concept (accuracy, structure, completeness, suitability) of the model, on the mathematical model with its simplifications and approximations, and on the numerical model with its discretizations, coding errors, etc. (Gallegos Bonano 1993). 

ABSTRACT The determination of loads from accidental fires with realistic accuracy in the oil gas industry offshore and petrochemical industry onshore is important for the prediction of exposure of persoimel, equipment and structures to the fires. Standards, Codes of Practice and other similar publications refer to thermal loading from jet fires from 100 to 400kW/m and from 50 to 250kW/m for pool fires. The application of inappropriate fire loads may lead to incorrect predictions of fatalities, explosion of pressure vessels and collapse of structures. Further uncertainties are associated with heat transfer from the flame to pressure equipment and strucmres, and their behaviour when affected by accidental fires. The Paper presents results of a review of fire models from various Standards and Codes of Practice, and data obtained from full scale tests. A parametric study of the various methods used in the industry is presented. A simulation-based reliability assessment (SBRA) method has been applied to quantify potential accuracy range and its consequences to fire effects on structures. 

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