Kriging and Conditional Simulation of Gaussian Field

Hoshiya, Masaru

doi:10.1061/(asce)0733-9399(1995)121:2(181)

Cited by 50 publications

(14 citation statements)

References 2 publications

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“…While GRF conditional simulations constitute a standard and important topic in the literature of geostatistics (Chilès and Delfiner, 2012) with a variety of applications in geosciences and natural resources characterization (Delhomme, 1979;Chilès and Allard, 2005;Deutsch, 2002;Dimitrakopoulos, 2011;Journel and Kyriakidis, 2004), they have been increasingly used in engineering and related areas, where Gaussian random field models have been used as prior distributions on expensive-to-evaluation functions (Hoshiya, 1995;Santner et al, 2003;Villemonteix et al, 2009;Roustant et al, 2012;Binois et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

Fast Update of Conditional Simulation Ensembles

2014

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Gaussian random fields (GRF) conditional simulation is a key ingredient in many spatial statistics problems for computing Monte-Carlo estimators and quantifying uncertainties on non-linear functionals of GRFs conditional on data. Conditional simulations are known to often be computer intensive, especially when appealing to matrix decomposition approaches with a large number of simulation points. Here we study the settings where conditioning observations are assimilated batch-sequentially, i.e. one point or batch of points at each stage. Assuming that conditional simulations have been performed at a previous stage, we aim at taking advantage of already available sample paths and by-products in order to produce updated conditional simulations at minimal cost. We provide explicit formulas allowing to update an ensemble of sample paths conditioned on n ≥ 0 observations to an ensemble conditioned on n + q observations, for arbitrary q ≥ 1. Compared to direct approaches, the proposed formulas prove to substantially reduce computational complexity. Moreover, these formulas enable explicitly exhibiting how the q "new" observations are updating the "old" sample paths. Detailed complexity calculations highlighting the benefits of our approach with respect to state-of-the-art algorithms are provided and are complemented by numerical experiments.

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Section: Introductionmentioning

confidence: 99%

Fast Update of Conditional Simulation Ensembles

2014

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“…Application of the conditional simulation of ground motion records marked by nonstationary behavior are available in the literature, e.g., Vanmarcke and Fenton (1991), Hoshiya (1995), Shinozuka and Zhang (1996), Kameda and Morikawa (1994) and Heredia-Zavoni and Santa-Cruz (2000). These techniques are based on Kriging, conditional probability density function or their combination.…”

Section: Non-stationary Processesmentioning

confidence: 99%

“…Lumley (1970) and Armitt (1968) introduced this technique to address turbulence and wind-related problems, respectively, and it was later used by many researchers in describing pressure fluctuations on buildings and structures and a host of wind-related problems (e.g., Lee 1975; Kareem and Cermak 1984;Holmes 1992;Kareem 1999;Tamura et al 1999;Carassale et al 2001). In stochastic structural mechanics, the POD technique based on the covariance matrix has been utilized for the simulation of spatially varying correlated random variables (e.g., Yamazaki and Shinozuka 1990), stochastic finite element analysis (e.g., Ghanem and Spanos 1991), and stochastic dynamics (Li and Kareem 1989, 1995, Vasta and Schueller 2000.…”

Section: Proper Orthogonal Decompositionmentioning

confidence: 99%

Numerical simulation of wind effects: A probabilistic perspective

Kareem

2008

Journal of Wind Engineering and Industrial Aerodynamics

132

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Numerical simulations of wind loads and their effects are critical in the design of structures to ensure their safety under winds. The simulations range from generation of time histories of wind velocity, pressure and force fluctuations to structural response and assessment of attendant functionality and safety under service and design loads, respectively. Typically these schemes employ Monte Carlo based approaches that encompass model based simulations or information derived from observed data. The scope of simulations spans uni-variate to multivariate processes; uni-dimensional to multi-dimensional fields; Gaussian to non-Gaussian; stationary to non-stationary; conditional and unconditional cases. In order to accomplish these tasks, methods based on the time, frequency, or time-frequency domains are employed. This paper summarizes a historical perspective, recent developments and future challenges. Also included in the discussion are computational tools employed for data analysis, response analysis and its management, and prediction. Examples are presented to illustrate some of the topics discussed.

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“…They can be generated using a variety of methods, from matrix decomposition to spectral methods, as presented in [28,29,30,31]. Examples of such conditional simulations are displayed in Figure 1b.…”

Section: Conditional Simulationsmentioning

confidence: 99%

Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

Binois

Ginsbourger

Roustant

2015

European Journal of Operational Research

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Multi-objective optimization algorithms aim at finding Pareto-optimal solutions. Recovering Pareto fronts or Pareto sets from a limited number of function evaluations are challenging problems. A popular approach in the case of expensive-to-evaluate functions is to appeal to metamodels. Kriging has been shown efficient as a base for sequential multi-objective optimization, notably through infill sampling criteria balancing exploitation and exploration such as the Expected Hypervolume Improvement. Here we consider Kriging metamodels not only for selecting new points, but as a tool for estimating the whole Pareto Front and quantifying how much uncertainty remains on it at any stage of Kriging-based multi-objective optimization algorithms. Our approach relies on the Gaussian Process interpretation of Kriging, and bases upon conditional simulations. Using concepts from random set theory, we propose to adapt the Vorob'ev expectation and deviation to capture the variability of the set of non-dominated points. Numerical experiments illustrate the potential of the proposed workflow, and it is shown on examples how Gaussian process simulations and the estimated Vorob'ev deviation can be used to monitor the ability of Kriging-based multi-objective optimization algorithms to accurately learn the Pareto front.

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Kriging and Conditional Simulation of Gaussian Field

Cited by 50 publications

References 2 publications

Fast Update of Conditional Simulation Ensembles

Fast Update of Conditional Simulation Ensembles

Numerical simulation of wind effects: A probabilistic perspective

Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations

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