Galerkin scheme based determination of first-passage probability of nonlinear system response

2013 ◽  
Vol 10 (10) ◽  
pp. 1285-1294 ◽  
Author(s):  
Pol D. Spanos ◽  
Ioannis A. Kougioumtzoglou
Keyword(s):  
Nonlinear System ◽  
System Response ◽  
First Passage ◽  
Galerkin Scheme ◽  
First Passage Probability

Galerkin Scheme-Based Determination of Survival Probability of Oscillators With Fractional Derivative Elements

2016 ◽  
Vol 83 (12) ◽  
Author(s):  
Pol D. Spanos ◽  
Alberto Di Matteo ◽  
Yezeng Cheng ◽  
Antonina Pirrotta ◽  
Jie Li
Keyword(s):  
Fractional Derivative ◽  
Survival Probability ◽  
Stochastic Averaging ◽  
Kolmogorov Equation ◽  
System Response ◽  
Statistical Linearization ◽  
Van Der Pol ◽  
Galerkin Scheme ◽  
Confluent Hypergeometric Functions

In this paper, an approximate semi-analytical approach is developed for determining the first-passage probability of randomly excited linear and lightly nonlinear oscillators endowed with fractional derivative elements. The amplitude of the system response is modeled as one-dimensional Markovian process by employing a combination of the stochastic averaging and the statistical linearization techniques. This leads to a backward Kolmogorov equation which governs the evolution of the survival probability of the oscillator. Next, an approximate solution of this equation is sought by resorting to a Galerkin scheme. Specifically, a convenient set of confluent hypergeometric functions, related to the corresponding linear oscillator with integer-order derivatives, is used as orthogonal basis for this scheme. Applications to the standard viscous linear and to nonlinear (Van der Pol and Duffing) oscillators are presented. Comparisons with pertinent Monte Carlo simulations demonstrate the reliability of the proposed approximate analytical solution.

Optimal Robust Fixture Configuration Design Using Computer Experiment

Manufacturing ◽  
2003 ◽  
Author(s):  
L. Shelley Xie ◽  
Agus Sudjianto
Keyword(s):  
Evaluation Method ◽  
Robustness Analysis ◽  
Optimal Solution ◽  
Computer Experiment ◽  
System Response ◽  
New Approach ◽  
New Information ◽  
Reliability Method ◽  
Fixture Configuration

A new FEA based design approach of optimal robust fixture configuration is proposed in this paper, which employs a surrogate model through computer experiment to significantly reduce the intensive computing effort involving numerous FEA system response evaluations. The effects of the fixture variability to the workpiece performance variability are assessed through an efficient robustness evaluation method, First Order Reliability Method (FORM), based on the surrogate computer model. Not restricted to primary datum surface, this new approach enables simultaneous determination of robust locator/clamp locations and clamping forces for a deformable workpiece and thus captures interaction between locating and clamping. The effectiveness of this approach is illustrated though an application example. The results of robustness analysis reveal new information and suggest that the optimal solution resulted from deterministic optimization may not be the best solution when the design is subjected to variability.

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