## Abstract

The Proper Orthogonal Decomposition (POD) method has been employed to extract the important signatures of the random field presented in an engineering product or process. Our preliminary study found that coefficients of the signatures are statistically uncorrelated but may be dependent. In general, the statistical dependence of the coefficients is ignored in the random field characterization for probability analysis and design. This paper thus proposes an effective approach to characterize the random field for probability analysis and design while accounting for the statistical dependence among the coefficients. The proposed approach is composed of two technical contributions. The first contribution is to develop a generic approximation scheme of random field as a function of the most important field signatures while preserving prescribed approximation accuracy. The coefficients of the signatures can be modeled as random field variables and their statistical properties are identified using the Chi-Square goodness-of-fit test. Second, the Rosenblatt transformation is employed to transform the statistically dependent random field variables into statistically independent random field variables. There exist so many transformation sequences when the number of random field variables becomes large. It was found that an improper selection of a transformation sequence may introduce high nonlinearity into system responses, which causes inaccuracy in probability analysis and design. Hence, a novel procedure is proposed for determining an optimal transformation sequence that introduces the least degree of nonlinearity to the system response after the Rosenblatt transformation. The proposed random field characterization can be integrated with one of the

Original language | English (US) |
---|---|

Title of host publication | ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010 |

Pages | 1133-1148 |

Number of pages | 16 |

Edition | PARTS A AND B |

DOIs | |

State | Published - 2010 |

Externally published | Yes |

Event | ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010 - Montreal, QC, Canada Duration: Aug 15 2010 → Aug 18 2010 |

### Publication series

Name | Proceedings of the ASME Design Engineering Technical Conference |
---|---|

Number | PARTS A AND B |

Volume | 1 |

### Other

Other | ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2010 |
---|---|

Country/Territory | Canada |

City | Montreal, QC |

Period | 8/15/10 → 8/18/10 |

## All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Mechanical Engineering
- Computer Science Applications
- Computer Graphics and Computer-Aided Design

## Keywords

- Eigenvector dimension reduction
- Probability analysis and design
- Proper orthogonal decomposition
- Random field