Model selection for a class of stochastic processes or random fields with bounded range

Field, Richard V.; Grigoriu, Mircea

doi:10.1016/j.probengmech.2008.08.003

Cited by 9 publications

(4 citation statements)

References 24 publications

(23 reference statements)

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“…Random vector X is defined by its joint cumulative distribution function, i.e., 10) where Pr(A 1 ∩ · · · ∩ A n ) is the probability that events A 1 , . .…”

Section: Joint Distribution and Densitymentioning

confidence: 99%

“…The two-sided spectral density function is the Fourier transform of the correlation function, i.e., 10) where i = √ −1. It is common to instead use the one-sided spectral density function defined for non-negative frequencies,…”

Section: Spectral Densitymentioning

confidence: 99%

“…(5.16) meaning that the covariance of Y (t) is not, in general, equal to ρ(τ ). There are many cases where the change to the covariance function is not significant and can be ignored; one example is when F is the CDF of a symmetric beta random variable (see [10]). Sometimes, however, the covariance functions of X and Y are very different, and this difference cannot be neglected.…”

Section: Memoryless Transformations Of Gaussian Processesmentioning

confidence: 99%

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Stochastic models: theory and simulation.

Field¹

2008

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Many problems in applied science and engineering involve physical phenomena that behave randomly in time and/or space. Examples are diverse and include turbulent flow over an aircraft wing, Earth climatology, material microstructure, and the financial markets. Mathematical models for these random phenomena are referred to as stochastic processes and/or random fields, and Monte Carlo simulation is the only general-purpose tool for solving problems of this type. The use of Monte Carlo simulation requires methods and algorithms to generate samples of the appropriate stochastic model; these samples then become inputs and/or boundary conditions to established deterministic simulation codes. While numerous algorithms and tools currently exist to generate samples of simple random variables and vectors, no cohesive simulation tool yet exists for generating samples of stochastic processes and/or random fields. There are two objectives of this report. First, we provide some theoretical background on stochastic processes and random fields that can be used to model phenomena that are random in space and/or time. Second, we provide simple algorithms that can be used to generate independent samples of general stochastic models. The theory and simulation of random variables and vectors is also reviewed for completeness.3

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“…Random vector X is defined by its joint cumulative distribution function, i.e., 10) where Pr(A 1 ∩ · · · ∩ A n ) is the probability that events A 1 , . .…”

Section: Joint Distribution and Densitymentioning

confidence: 99%

Section: Spectral Densitymentioning

confidence: 99%

Section: Memoryless Transformations Of Gaussian Processesmentioning

confidence: 99%

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Stochastic models: theory and simulation.

Field¹

2008

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“…The method was extended for general cases (Cheung & Beck, 2010;Ching & Chen, 2007). Field and Grigoriu (2009) studied the model selection problem of stochastic processes with bounded range. DiazDelaO, Garbuno-Inigo, Au, and Yoshida (2017) incorporated the subset simulation with Bayesian updating and model class selection for engineering reliability analysis.…”

Section: Introductionmentioning

confidence: 99%

Self‐calibrating Bayesian real‐time system identification

Yuen

Kuok

Dong

2019

Computer aided Civil Eng

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In this article, a novel Bayesian framework is proposed for real‐time system identification with calibratable model classes. This self‐calibrating scheme adaptively reconfigures the model classes to achieve reliable real‐time estimation for the system state and model parameters. At each time step, the plausibilities of the model classes are computed and they serve as the cue for calibration. Once calibration is triggered, all model classes will be reconfigured. Thereafter, identification will continue to propagate with the calibrated model classes until the next recalibration. Consequently, the model classes will evolve and their deficiencies can be corrected adaptively. This remarkable feature of the proposed framework stimulates the accessibility of reliable real‐time system identification. Examples are presented to demonstrate the efficacy of the proposed approach using noisy response measurement of linear and nonlinear time‐varying dynamical systems under stationary condition.

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Predicting laser weld reliability with stochastic reduced‐order models

Emery

Field

Foulk

et al. 2015

Numerical Meth Engineering

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Laser welds are prevalent in complex engineering systems and they frequently govern failure. The weld process often results in partial penetration of the base metals, leaving sharp crack-like features with a high degree of variability in the geometry and material properties of the welded structure. Accurate finite element predictions of the structural reliability of components containing laser welds requires the analysis of a large number of finite element meshes with very fine spatial resolution, where each mesh has different geometry and/or material properties in the welded region to address variability. Traditional modeling approaches cannot be efficiently employed. To this end, a method is presented for constructing a surrogate model, based on stochastic reduced-order models, and is proposed to represent the laser welds within the component. Here, the uncertainty in weld microstructure and geometry is captured by calibrating plasticity parameters to experimental observations of necking as, because of the ductility of the welds, necking -and thus peak load -plays the pivotal role in structural failure. The proposed method is exercised for a simplified verification problem and compared with the traditional Monte Carlo simulation with rather remarkable results.

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Model selection for a class of stochastic processes or random fields with bounded range

Cited by 9 publications

References 24 publications

Stochastic models: theory and simulation.

Stochastic models: theory and simulation.

Self‐calibrating Bayesian real‐time system identification

Predicting laser weld reliability with stochastic reduced‐order models

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