Adaptive Hessian-Based Nonstationary Gaussian Process Response Surface Method for Probability Density Approximation with Application to Bayesian Solution of Large-Scale Inverse Problems

2012 ◽  
Vol 34 (6) ◽  
pp. A2837-A2871 ◽  
Author(s):  
Tan Bui-Thanh ◽  
Omar Ghattas ◽  
David Higdon
Keyword(s):  
Inverse Problems ◽  
Gaussian Process ◽  
Probability Density ◽  
Response Surface ◽  
Response Surface Method ◽  
Large Scale ◽  
Density Approximation ◽  
Surface Method ◽  
Probability Density Approximation

scholarly journals Gaussian Process-Based Response Surface Method for Slope Reliability Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Hu ◽  
Guo-shao Su ◽  
Jianqing Jiang ◽  
Yilong Xiao
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Gp Model

A new response surface method (RSM) for slope reliability analysis was proposed based on Gaussian process (GP) machine learning technology. The method involves the approximation of limit state function by the trained GP model and estimation of failure probability using the first-order reliability method (FORM). A small amount of training samples were firstly built by the limited equilibrium method for training the GP model. Then, the implicit limit state function of slope was approximated by the trained GP model. Thus, the implicit limit state function and its derivatives for slope stability analysis were approximated by the GP model with the explicit formulation. Furthermore, an iterative algorithm was presented to improve the precision of approximation of the limit state function at the region near the design point which contributes significantly to the failure probability. Results of four case studies including one nonslope and three slope problems indicate that the proposed method is more efficient to achieve reasonable accuracy for slope reliability analysis than the traditional RSM.

Reliability Analysis of Suspension Bridge Using Gaussian Process Based Response Surface Method

2013 ◽  
Vol 860-863 ◽  
pp. 2970-2974
Author(s):  
Wei Zhao ◽  
Guo Shao Su ◽  
Li Hua Hu
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
High Efficiency ◽  
Gaussian Process Regression ◽  
Suspension Bridge ◽  
Surface Method ◽  
Complex Structural

Aiming to the problems of low precision using traditional response surface method for structural reliability analysis with high nonlinear implicit performance function, Gaussian process regression (GPR) model reconstructing response surface was hybridized into the checking design point method for solving the reliability. Then, an iterative algorithm is presented to reduce the errors of GPR response surface self-adaptively. Thus, a new method namely Gaussian process based response surface for reliability analysis of suspension bridge was proposed. The research results show that the proposed method is feasible. The proposed method has advantages of high efficiency and excellent adaptability for reliability analysis of the complex structural such as suspension bridge.

A Proposal of PSO with Presumption Function of the Solution Landscape by Response Surface Method

2014 ◽  
Vol 134 (9) ◽  
pp. 1293-1298
Author(s):  
Toshiya Kaihara ◽  
Nobutada Fuji ◽  
Tomomi Nonaka ◽  
Yuma Tomoi
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
Surface Method
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