A Monte Carlo Method for Sensitivity Analysis and Parametric Optimization of Nonlinear Stochastic Systems: The Ergodic Case

1992 ◽  
Vol 30 (2) ◽  
pp. 440-464 ◽  
Author(s):  
Harold J. Kushner ◽  
Jichuan Yang
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Parametric Optimization ◽  
Stochastic Systems ◽  
Nonlinear Stochastic Systems

Model Validation: Model Parameter and Measurement Uncertainty

2005 ◽  
Vol 128 (4) ◽  
pp. 339-351 ◽  
Author(s):  
Richard G. Hills
Keyword(s):  
Experimental Data ◽  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Model Validation ◽  
Full Range ◽  
Correlated Data ◽  
Model Parameter ◽  
Test Models ◽  
Model Parameter Uncertainty

Our increased dependence on complex models for engineering design, coupled with our decreased dependence on experimental observation, leads to the question: How does one know that a model is valid? As models become more complex (i.e., multiphysics models), the ability to test models over the full range of possible applications becomes more difficult. This difficulty is compounded by the uncertainty that is invariably present in the experimental data used to test the model; the uncertainties in the parameters that are incorporated into the model; and the uncertainties in the model structure itself. Here, the issues associated with model validation are discussed and methodology is presented to incorporate measurement and model parameter uncertainty in a metric for model validation through a weighted r2 norm. The methodology is based on first-order sensitivity analysis coupled with the use of statistical models for uncertainty. The result of this methodology is compared to results obtained from the more computationally expensive Monte Carlo method. The methodology was demonstrated for the nonlinear Burgers’ equation, the convective-dispersive equation, and for conduction heat transfer with contact resistance. Simulated experimental data was used for the first two cases, and true experimental data was used for the third. The results from the sensitivity analysis approach compared well with those for the Monte Carlo method. The results show that the metric presented can discriminate between valid and invalid models. The metric has the advantage that it can be applied to multivariate, correlated data.

Probability and Sensitivity Analysis of Plate

2014 ◽  
Vol 617 ◽  
pp. 193-196 ◽  
Author(s):  
Katarina Tvrdá
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Flat Plate ◽  
Concrete Structures ◽  
Probability Analysis ◽  
Triangular Distribution ◽  
High Quality ◽  
Input Parameters ◽  
Concrete Solution

This paper deals with some problems of the ceiling plate, made of the Cobiax-system. Cobiax provides a system to produce voided, biaxial, flat plate slabs as a high-quality concrete solution for large spans and slim slabs. Plastic voids in the shape of spheres or flattened spheres are contained in steel cages and put into concrete structures to create longer spans and reduce vertical loads. The presented plate is made of cobiax balls with a diameter of 27 cm located outside the area of columns. Probability analysis of Monte-Carlo method in Ansys is presented. Input parameters are changing according to Gauss or triangular distribution.

Sensitivity Analysis of Manufacture Errors for Cable Dome

2010 ◽  
Vol 163-167 ◽  
pp. 822-827
Author(s):  
Jian Hua Zhang ◽  
Zhen Qing Wang ◽  
Yi Gang Zhang
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Numerical Model ◽  
Practical Problem ◽  
Structural Performance ◽  
Random Errors ◽  
Cable Length ◽  
Radial Bearing ◽  
Cable Dome

Construction control is the key technique for cable dome. During the actual engineering, however, it is difficult to ensure no difference between the real prestress distribution and the designed value due to existed construction errors. The practical problem for cable dome construction is to determine how much is allowable errors limit. To solve the problem, sensitivity analysis of manufacture errors of bearing and cable length are carried out in this paper. The random errors are simulated by Monte Carlo method. In a numerical model of cable dome with the diameter of 62m, the sensitivity of effect of bearing and cable length manufacture errors on structural performance is analyzed. Numerical results show that the manufacture errors of radial bearing, hoop cable 2, ridge cable 3, diagonal cable 3 and hoop cable 1 should be strictly controlled. Besides, the maximum allowable errors are proposed referring to the domestic existing specifications.

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