Incremental Uncertainty Propagation with Multi-Fidelity Gaussian Process

2022 ◽  
Author(s):  
Bin Jia ◽  
Ming Xin
Keyword(s):  
Gaussian Process ◽  
Uncertainty Propagation

Frequency Response-Based Uncertainty Analysis of Vibration System Utilizing Multiple Response Gaussian Process

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Wangbai Pan ◽  
Guoan Tang ◽  
Jiong Tang
Keyword(s):  
Uncertainty Analysis ◽  
Gaussian Process ◽  
Frequency Response ◽  
Model Updating ◽  
Uncertainty Propagation ◽  
Multiple Response ◽  
Vibration System ◽  
Vector Fitting ◽  
Fitting Method ◽  
Small Set

This research concerns the uncertainty analysis and quantification of the vibration system utilizing the frequency response function (FRF) representation with statistical metamodeling. Different from previous statistical metamodels that are built for individual frequency points, in this research we take advantage of the inherent correlation of FRF values at different frequency points and resort to the multiple response Gaussian process (MRGP) approach. To enable the analysis, vector fitting method is adopted to represent an FRF using a reduced set of parameters with high accuracy. Owing to the efficiency and accuracy of the statistical metamodel with a small set of parameters, Bayesian inference can then be incorporated to realize model updating and uncertainty identification as new measurement/evidence is acquired. The MRGP metamodel developed under this new framework can be used effectively for two-way uncertainty propagation analysis, i.e., FRF prediction and uncertainty identification. Case studies are conducted for illustration and verification.

scholarly journals Identification and Prediction of Ship Maneuvering Motion Based on a Gaussian Process with Uncertainty Propagation

2021 ◽  
Vol 9 (8) ◽  
pp. 804
Author(s):  
Yifan Xue ◽  
Yanjun Liu ◽  
Gang Xue ◽  
Gang Chen
Keyword(s):  
Gaussian Process ◽  
Uncertainty Propagation ◽  
Model Identification ◽  
Economic Benefits ◽  
Vital Role ◽  
Training Data ◽  
Nonlinear Functions ◽  
Nonparametric Modeling ◽  
Ship Maneuvering ◽  
Vessel Scheduling

Maritime transport plays a vital role in economic development. To establish a vessel scheduling model, accurate ship maneuvering models should be used to optimize the strategy and maximize the economic benefits. The use of nonparametric modeling techniques to identify ship maneuvering systems has attracted considerable attention. The Gaussian process has high precision and strong generalization ability in fitting nonlinear functions and requires less training data, which is suitable for ship dynamic model identification. Compared with other machine learning methods, the most obvious advantage of the Gaussian process is that it can provide the uncertainty of prediction. However, most studies on ship modeling and prediction do not consider the uncertainty propagation in Gaussian processes. In this paper, a moment-matching-based approach is applied to address the problem. The proposed identification scheme for ship maneuvering systems is verified by container ship simulation data and experimental data from the Workshop on Verification and Validation of Ship Maneuvering Simulation Methods (SIMMAN) database. The results indicate that the identified model is accurate and shows good generalization performance. The uncertainty of ship motion prediction is well considered based on the uncertainty propagation technology.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

A Stochastic Model for the Inheritance of the Cancer Proneness Phenotype

1987 ◽  
Vol 26 (03) ◽  
pp. 117-123
Author(s):  
P. Tautu ◽  
G. Wagner
Keyword(s):  
Stochastic Model ◽  
Gaussian Process ◽  
Covariance Function ◽  
Neoplastic Disease ◽  
Disease Phenotype ◽  
Probabilistic Representation ◽  
Temporal Behaviour ◽  
Continuous Trait ◽  
Continuous Parameter ◽  
Level Zero

SummaryA continuous parameter, stationary Gaussian process is introduced as a first approach to the probabilistic representation of the phenotype inheritance process. With some specific assumptions about the components of the covariance function, it may describe the temporal behaviour of the “cancer-proneness phenotype” (CPF) as a quantitative continuous trait. Upcrossing a fixed level (“threshold”) u and reaching level zero are the extremes of the Gaussian process considered; it is assumed that they might be interpreted as the transformation of CPF into a “neoplastic disease phenotype” or as the non-proneness to cancer, respectively.

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