Begell House Inc.
International Journal for Uncertainty Quantification
IJUQ
2152-5080
2
2
2012
PREFACE
ii
10.1615/Int.J.UncertaintyQuantification.v2.i2.10
Nicholas
Zabaras
Department of Mechanical and Aerospace Engineering, Department of Applied and Computational Mathematics and Statistics University of Notre Dame, Notre Dame, IN; University of Warwick Coventry CV4 7AL United Kingdom
USA/SOUTH AMERICA SYMPOSIUM ON STOCHASTIC MODELING AND UNCERTAINTY QUANTIFICATION, LEBLON BEACH, RIO DE JANEIRO, BRAZIL, AUGUST 1-5, 2011
ROBUST STOCHASTIC DESIGN OF BASE-ISOLATED STRUCTURAL SYSTEMS
95-110
10.1615/Int.J.UncertaintyQuantification.v2.i2.20
Hector
Jensen
Departmento de Obras Civiles, Universidad Tecnica Federico Santa Maria, Valparaiso, Chile
Juan
Sepulveda
Departmento de Obras Civiles, Universidad Tecnica Federico Santa Maria, Valparaiso, Chile
Luis
Becerra
Departmento de Obras Civiles, Universidad Tecnica Federico Santa Maria, Valparaiso, Chile
approximation strategies
base-isolated structural systems
common random numbers
nonlinear optimization
robust reliability
sensitivity analysis
simulation methods
stochastic optimization
The development of a general framework for robust reliability-based design of base-isolated structural systems under uncertain conditions is presented. The uncertainties about the structural parameters as well as the variability of future excitations are characterized in a probabilistic manner. Isolation elements composed of nonlinear lead rubber bearings are used to model the isolation system. The optimal design problem is formulated as a nonlinear constrained minimization problem involving multiple design requirements, including reliability constraints related to the structural performance. Failure events defined by a large number of random variables are used to characterize the reliability of the system. A sequential optimization approach based on global conservative, convex, and separable approximations is implemented for solving the optimization problem. An example problem that considers a 10-story building under stochastic ground excitation illustrates the beneficial effects of base-isolation systems in reducing the superstructure response.
STOCHASTIC DRILL-STRING DYNAMICS WITH UNCERTAINTY ON THE IMPOSED SPEED AND ON THE BIT-ROCK PARAMETERS
111-124
10.1615/Int.J.UncertaintyQuantification.v2.i2.30
Thiago G.
Ritto
Department of Mechanical Engineering, Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro, 21945-970, Brazil
R.
Sampaio
Department of Mechanical Engineering, PUC-Rio, Rio de Janeiro, 22453-900, Brazil
drill-string dynamics
stochastic dynamics
uncertainty quantification
bit-rock interaction
A drill string is a slender structure with nonlinear dynamics; it is an equipment used in the oil industry to drill rock in the search of oil and gas. The aim of this paper is to model the uncertainties related to the speed imposed at the top and uncertainties related to the bit-rock parameters, and to investigate how these uncertainties propagate throughout the system. The continuum system is linearized about the prestressed configuration, the finite-element model is applied to discretize the system, and then a reduced-order model is constructed using normal modes of the linearized system; only torsional and axial vibrations are considered in the analysis. A constant rotational speed is imposed at the top and a nonlinear bit-rock interaction acts at the bottom. A probabilistic approach is used to model the uncertainties and the Monte Carlo method is used to approximate the stochastic differential equations.
FORWARD AND BACKWARD UNCERTAINTY PROPAGATION FOR DISCONTINUOUS SYSTEM RESPONSE USING THE PADÃ‰-LEGENDRE METHOD
125-143
10.1615/Int.J.UncertaintyQuantification.v2.i2.40
Tonkid
Chantrasmi
Department of Mechanical and Aerospace Engineering, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
Gianluca
Iaccarino
Department of Mechanical Engineering Institute for Computational Mathematical Engineering Stanford University Bldg 500, RM 500-I, Stanford CA 94305 - USA
uncertainty quantification
Pade-Legendre reconstruction
discontinuity
Bayesian inference
The Pade-Legendre method has been introduced as an effective approach to characterize uncertainties in the presence of strongly non-linear or discontinuous system responsesthus, it supports forward propagation. The method is based on the construction of a ratio of polynomials that approximate the available data. Two criteria for the choice of the best approximant are considered and an optimization approach is proposed. Moreover, the approach is applied in a case in which the discontinuity in the system response is due to limited data, to demonstrate how the successive addition of data transforms the rational approximant into a simple polynomial interpolant (the denominator becomes a constant). Finally, the present method is applied to estimate an input parameter characterized by a sharp discontinuity, using Bayesian inference starting from observations of the system responsethus, it also supports backward propagation.
A STOCHASTIC COLLOCATION APPROACH FOR UNCERTAINTY QUANTIFICATION IN HYDRAULIC FRACTURE NUMERICAL SIMULATION
145-160
10.1615/Int.J.UncertaintyQuantification.v2.i2.50
Souleymane
Zio
Mechanical Engineering, COPPE, Federal University of Rio de Janeiro, P.O. Box 68503, 21941972, Rio de Janeiro, Brazil
Fernando A.
Rochinha
COPPE, Universidade Federal
do Rio de Janeiro Brazil
hydraulic fracture
uncertainty quantification
stochastic collocation
The exploitation of oil and gas can be stimulated through hydraulic fractures (HF), which are discontinuities in the rock formation induced by the injection of high pressurized viscous fluids. Because there exists considerable variability in geologic formations, such as oil and gas reservoirs, the computational models, and, consequently, the predictions drawn from simulations, might lead to misleading conclusions, despite the use of efficient and robust numerical schemes. In order to take into account uncertainties on the numerical results due to the variability in the input data, a stochastic analysis of HF is presented here. The elasticity modulus of the rock and the confining stress are assumed to be described by random variables, and therefore, the equations governing the fracture propagation are recast as stochastic partial differential equations (SPDEs). In order to solve the resulting problem, among several alternatives available in the literature, a stochastic collocation method is adopted. The elasticity modulus probability distributions are constructed using two different approaches, both using a small amount of information. A number of numerical simulations are presented in order to illustrate the impact of the uncertainties in the data input on the fracture propagation.
RELATIONSHIP BETWEEN BAYESIAN AND FREQUENTIST SIGNIFICANCE INDICES
161-172
10.1615/Int.J.UncertaintyQuantification.v2.i2.60
Marcio
Diniz
Department of Statistics, Federal University of Sao Carlos, Rod. Washington Luis, km 235, Sao Carlos, SP, 13565-905, Brazil
Carlos A. B.
Pereira
Mathematics and Statistics Institute, University of Sao Paulo, Sao Paulo, SP, Brazil
Adriano
Polpo
Department of Statistics, Federal University of Sao Carlos, Rod. Washington Luis, km 235, Sao Carlos, SP, 13565-905, Brazil
Julio M.
Stern
Mathematics and Statistics Institute, University of Sao Paulo, Sao Paulo, SP, Brazil
Sergio
Wechsler
Mathematics and Statistics Institute, University of Sao Paulo, Sao Paulo, SP, Brazil
Bayesian test
likelihood ratio
e-value
p-values
significance test
The goal of this paper is to illustrate how two significance indicesthe frequentist p-value and Bayesian e-value have a straight mathematical relationship. We calculate these indices for standard statistical situations in which sharp null hypotheses are being tested. The p-value considered here is based on the likelihood ratio statistic. The existence of a functional relationship between these indices could surprise readers because they are computed in different spaces: p-values in the sample space and e-values in the parameter space.
A BAYES NETWORK APPROACH TO UNCERTAINTY QUANTIFICATION IN HIERARCHICALLY DEVELOPED COMPUTATIONAL MODELS
173-193
10.1615/Int.J.UncertaintyQuantification.v2.i2.70
Angel
Urbina
Optimization and Uncertainty Quantification, Sandia National Laboratories, P.O. Box 5800, MS 1318, Albuquerque, New Mexico 87185-1320, USA
Sankaran
Mahadevan
Civil and Environmental Engineering Department, Vanderbilt University, Nashville, Tennessee 37235, USA
Thomas L.
Paez
Thomas Paez Consulting, Durango, CO 80301
uncertainty quantification
Markov chain Monte Carlo
Bayesian inference
hierarchical model development
structural dynamics
Performance assessment of complex systems is ideally accomplished through system-level testing, but because they are expensive, such tests are seldom performed. On the other hand, for economic reasons, data from tests on individual components that are parts of complex systems are more readily available. The lack of system-level data leads to a need to build computational models of systems and use them for performance prediction in lieu of experiments. Because their complexity, models are sometimes built in a hierarchical manner, starting with simple components, progressing to collections of components, and finally, to the full system. Quantification of uncertainty in the predicted response of a system model is required in order to establish confidence in the representation of actual system behavior. This paper proposes a framework for the complex, but very practical problem of quantification of uncertainty in system-level model predictions. It is based on Bayes networks and uses the available data at multiple levels of complexity (i.e., components, subsystem, etc.). Because epistemic sources of uncertainty were shown to be secondary, in this application, aleatoric only uncertainty is included in the present uncertainty quantification. An example showing application of the techniques to uncertainty quantification of measures of response of a real, complex aerospace system is included.