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Models for Risk Assessment, Management, and Design
Published in Winston Chow, Katherine K. Connor, Peter Mueller, Ronald Wyzga, Donald Porcella, Leonard Levin, Ramsay Chang, Managing Hazardous Air Pollutants, 2020
A Monte Carlo sampling scheme was used as the basis for preparing the stochastic analysis and evaluating the uncertainty in the worst-case risks. In brief, a Monte Carlo analysis uses a random number generator and a series of mathematical equations to sample values from specified distributions; distributions are described by a mean and standard deviation with an indication of distribution type. For each variable included in the stochastic analysis, a value is selected from the distribution. Exposure and risk is calculated for the first sample set and the results are stored. The process is then repeated a thousand or more times until a large distribution of risk outcomes is developed. Statistical calculations are then performed on the risk distribution to identify confidence limits and risk percentiles.
EXCURSION PROBABILITIES OF LINEAR AND NONLINEAR SYSTEMS
Published in W. Q. Zhu, G.Q. Cai, R.C. Zhang, Advances in Stochastic Structural Dynamics, 2003
Helmut J. Pradlwarter, Gerhart I. Schuëller
Simulation offers an alternative approach to study the complexity related with the dynamics of the structural model. Deterministic structural analysis is nowadays well developed and complex structural models with linear and nonlinear behavior can be computed straight forward in most cases. It is therefore natural to employ available deterministic methods also for the stochastic analysis. Monte Carlo simulation can be regarded as a bridge between deterministic and stochastic analysis. Monte Carlo simulation (MCS) is quite general. The generality, however, is usually inversely proportional to the efficiency In other words, the efficiency depends strongly on the introduced apriori information about the considered problem Regarding efficiency, general procedures such as controlled MCS [8. 7] or subset simulation |1|, are not competitive when compared with methods which succeed to extract and exploit the most essential properties of the considered problem. A recently published work |2| is a typical example for the latter. It introduces a MCS procedure with
Uncertainty Quantification in Composite Structures
Published in Sudip Dey, Tanmoy Mukhopadhyay, Sondipon Adhikari, Uncertainty Quantification in Laminated Composites, 2018
Sudip Dey, Tanmoy Mukhopadhyay, Sondipon Adhikari
In general, composites are heterogeneous materials, which can be tailored according to their intended applications. Composites are widely used for various applications (aerospace, automotive, construction, marine, mechanical and many other industries) due to the fact that composites have high specific modulus, specific strength, low thermal conductivity, and high temperature resistance which are stochastic in nature. For example, about 25% to 50% of their total weight is made of composites in modern aircrafts such as Airbus A380 and Boeing 787 respectively (refer to Fig. 2.1) (Mallick 2007). A comprehensive description of the applications of composite materials can be found in Mallick (2007). In the past few decades, stochastic analyses in engineering fields have gained immense attentions from many researchers. The main focus of stochastic analysis is projected to determine the variability in responses due to uncertain randomness in material and geometrical properties and operational cum environment conditions. The stochastic analysis is not a new concept, rather it started before 1990s to develop the methods of digitally generating sample functions of the stochastic field by using the Monto Carlo Simulation (MCS) for dynamic analysis of non-linear structures (Shinozuka and Deodatis 1988, Oberkampf 2000, 2001). Stochastic simulations typically include four steps: quantifying the input variable uncertainties (probabilistic characteristics of the input stochastic input parameters); development of a stochastic model which represents the variability of uncertain input parameters; implementation of a model to propagate uncertainty from the input level to the output level (global responses of the system); and finally quantifying the output parameters uncertainty (Padmanabhan and Pitchumani 1999). The propagation of uncertainty can be addresses in two ways: through simulation techniques and non-simulation techniques. Simulation techniques imply solving the deterministic system for a given number of parameter combinations and can therefore can be computationally very expensive. These samples can be used to obtain a surrogate model of the system, i.e., an equation relating the uncertain parameters to the response, whose expression is simpler and efficient to evaluate than the original equation. Thereby the surrogate model can be used for uncertainty quantification following a non-intrusive approach. Non-simulation techniques can be based on perturbation methods, which imply that the results are only valid for small variations of the uncertain parameters. Otherwise, they can be based on spectral methods, which imply solving a system of equations of size several times the size of the deterministic system.
Inelastic static and dynamic seismic response assessment of frames with stochastic properties
Published in Structure and Infrastructure Engineering, 2021
Georgios Balokas, Michalis Fragiadakis
The stochastic analysis accounts for uncertainty in several parameters, including material properties, geometry and loads, which are represented by stochastic fields. A stochastic (or random) field is a mapping from a random outcome to a function of space (or time). If is the expected value of the model parameter of interest k (e.g. Young’s modulus E, yield stress σy), the spatial uncertainty is provided by the following random field: where is a zero-mean field. There are few experimental databases for the statistical characterisation of material properties, while it is common belief that their probabilistic characteristics are closer to non-Gaussian rather than Gaussian. In order to generate such a field, a Gaussian one has to be first generated and then it should be transformed to non-Gaussian.
Ethanol production from food waste in West Attica: evaluation of investment plans under uncertainty
Published in Biofuels, 2020
A. Konti, P. Papagiannakopoulou, D. Mamma, D. Kekos, D. Damigos
Sensitivity analysis, however, like other traditional methods of uncertainty such as scenario approaches, is not effective to handle problems at which multiple eventualities occur, given that the analysis is performed on a ceteris paribus basis. Thus, in order to cope with the uncertainty and ambiguity stemming from multiple parameters simultaneously, a stochastic analysis (also known as risk analysis) needs to be carried out by means of Monte Carlo simulation. Monte Carlo simulation is among the most frequently used methods for the treatment of this type of uncertainty [18]. It presents a robust approach to model the uncertainty of the input and to account for the uncertainties characterized using probability distributions [19]. The primary output of Monte Carlo simulation in investment analysis is a histogram of NPV (or IRR) values, which represents the distribution of all possible outcomes and estimates the probability of success for the project (i.e. the probability that NPV will be greater than zero) along with critical statistics. In this way, it allows analysts to better understand and visualize risk and uncertainty in DCF analysis. Monte Carlo simulation could, also, be considered the easiest way to value real options of complex projects since it does not require formulation of cash flow through differential equations or trees [20].
Reliability-based design optimization with frequency constraints using a new safest point approach
Published in Engineering Optimization, 2018
R. El Maani, A. Makhloufi, B. Radi, A. El Hami
To quantify and account for the effects of uncertainties, such as stochastic variations in operating conditions, stochastic analysis methods need to be developed and integrated into the design process. For single-field problems, particularly in the field of structural mechanics, stochastic analysis has been well explored and integrated into RBDO methods (Frangopol and Maute 2003, 2004). However, design optimization procedures for coupled multi-physics problems that account for uncertainties are still in their infancy (Allen and Maute 2002; Pettit, Canfield, and Ghanem 2002) and only a limited amount of work has been done on formal methods to include reliability analyses in the RBDO design of aerospace systems, and aeroelastic structures in particular.