Modeling and Quantification of Physical Systems Uncertainties in a Probabilistic Framework

Cunha, Americo

doi:10.1007/978-3-319-55852-3_8

Cited by 25 publications

(28 citation statements)

References 59 publications

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“…To construct the probabilistic model, the PDFs of the random parameters were determined through the maximum entropy principle [56,57]. Considering that the linear stiffness and the damping coefficient can not be negative, we assumed the interval ð0; 1Þ as the support of these random variables.…”

Section: Stochastic Version Of the Nonlinear Systemmentioning

confidence: 99%

Damage detection in uncertain nonlinear systems based on stochastic Volterra series

Villani

Silva

Cunha

2019

Mechanical Systems and Signal Processing

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The damage detection problem in mechanical systems, using vibration measurements, is commonly called Structural Health Monitoring (SHM). Many tools are able to detect damages by changes in the vibration pattern, mainly, when damages induce nonlinear behavior. However, a more difficult problem is to detect structural variation associated with damage, when the mechanical system has nonlinear behavior even in the reference condition. In these cases, more sophisticated methods are required to detect if the changes in the response are based on some structural variation or changes in the vibration regime, because both can generate nonlinearities. Among the many ways to solve this problem, the use of the Volterra series has several favorable points, because they are a generalization of the linear convolution, allowing the separation of linear and nonlinear contributions by input filtering through the Volterra kernels. On the other hand, the presence of uncertainties in mechanical systems, due to noise, geometric imperfections, manufacturing irregularities, environmental conditions, and others, can also change the responses, becoming more difficult the damage detection procedure. An approach based on a stochastic version of Volterra series is proposed to be used in the detection of a breathing crack in a beam vibrating in a nonlinear regime of motion, even in reference condition (without crack). The system uncertainties are simulated by the variation imposed in the linear stiffness and damping coefficient. The results show, that the nonlinear analysis done, considering the high order Volterra kernels, allows the approach to detect the crack with a small propagation and probability confidence, even in the presence of uncertainties.

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Section: Stochastic Version Of the Nonlinear Systemmentioning

confidence: 99%

Damage detection in uncertain nonlinear systems based on stochastic Volterra series

Villani

Silva

Cunha

2019

Mechanical Systems and Signal Processing

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“…Since they are the critical parameters for the brake system efficiency, studying the effect of such variabilities on the braking force is essential for a good design. In this way, a parametric probabilistic approach [15,16] is employed here to construct a consistent stochastic model for uncertain parameters a and F s .…”

Section: Mathematical Modelmentioning

confidence: 99%

“…Thus, if the uncertain parameters a and F s are represented by the known random vector X, the braking force becomes the random variable Y ¼ MðXÞ, for which the distribution must be estimated. The process of determining the distribution of Y, once the probabilistic law of X is known, is dubbed uncertainty propagation problem [15,16], being addressed in this paper via the Monte Carlo simulation [19,20].…”

Section: Uncertainty Propagationmentioning

confidence: 99%

“…This result is at the least curious and unexpected, since the angular dependencies introduced in the mechanical model by Eqs. (15) and (17) define a structure of multiplicative uncertainty between a and F s , what should make F h not invariant with respect to the input distribution. This result suggests that the nonlinearity associated with the alpha parameter is very weak, which causes F h to behave as an affine map of F s , and thus to preserve the form of its distribution.…”

Section: Uncertainty Quatificationmentioning

confidence: 99%

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Robust optimization and uncertainty quantification in the nonlinear mechanics of an elevator brake system

et al. 2019

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This paper deals with nonlinear mechanics of an elevator brake system subjected to uncertainties. A deterministic model that relates the braking force with uncertain parameters is deduced from mechanical equilibrium conditions. In order to take into account parameters variabilities, a parametric probabilistic approach is employed. In this stochastic formalism, the uncertain parameters are modeled as random variables, with distributions specified by the maximum entropy principle. The uncertainties are propagated by the Monte Carlo method, which provides a detailed statistical characterization of the response. This work still considers the optimum design of the brake system, formulating and solving nonlinear optimization problems, with and without the uncertainties effects.

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“…where ( ) and for = 0,1, … , are known real functions and values, respectively with 0 ( ) = 1 and 0 = 1. The maximization problem is solved using the Lagrange multipliers for = 0,1, … , as [12], [13]…”

Section: Uncertainty Quantification Schemementioning

confidence: 99%

Probabilistic Design and Uncertainty Quantification of the Structure of a Monopile Offshore Wind Turbine

Nispel

Ekwaro-Osire

Dias

et al. 2019

Volume 13: Safety Engineering, Risk, and Reliability Analysis

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Despite the increasing demand for offshore energy, structural components of offshore wind turbines (OWT), such as the tower and foundation, are considered the most critical parts of the turbine. In fact, uncertainties regarding load conditions, soil and structural properties highly undermine the OWT structural reliability. In this scenario, in order to obtain more accurate results, rigorous probabilistic analyses are necessary. In this study, a probabilistic analysis of the dynamic response of a monopile OWT is conducted by using a systematic uncertainty quantification (UQ) framework to deal with the uncertainty assessment of the model input parameters. The proposed dynamic model computes the dynamic response of the turbine due to wind and waves loads on the monopile structure utilizing a simple cantilever beam analytical model. The distributions of the model input parameters are determined using (1) nonparametric statistics for a large dataset, and (2) the maximum entropy principle for a small dataset. Monte Carlo simulations are performed to propagate the uncertainties of the model inputs and to determine the system reliability expressed in terms of their probability of failure for the serviceability limit state design criterion. Finally, to demonstrate the shortcomings of traditional approaches that assume standard distributions to model uncertainties, a UQ approach modeling the uncertainties of the parameters using normal distributions is contrasted with our framework. From the results, significant differences between the distribution shape and values of the probability of failure can be observed; thus, it demonstrates the importance of developing probabilistic frameworks with systematic UQ to have more realistic approximations of the reliability of the OWT structure.

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Modeling and Quantification of Physical Systems Uncertainties in a Probabilistic Framework

Cited by 25 publications

References 59 publications

Damage detection in uncertain nonlinear systems based on stochastic Volterra series

Damage detection in uncertain nonlinear systems based on stochastic Volterra series

Robust optimization and uncertainty quantification in the nonlinear mechanics of an elevator brake system

Probabilistic Design and Uncertainty Quantification of the Structure of a Monopile Offshore Wind Turbine

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