### Abstract

The use of the posterior Cramér-Rao lower bound (PCRLB) as a lower bound for the mean-squared estimation error (MSEE) of progressive damage is investigated. The estimation problem is formulated in terms of a stochastic dynamic system model that describes the random evolution of damage and provides measurement uncertainty. Based on whether the system is linear or nonlinear, sequential Monte Carlo techniques are used to approximate the posterior probability density function and thus obtain the damage state estimate. The resulting MSEE is compared to the lower bound offered by the PCRLB that is obtained from the implied state transition probability density function and the measurement likelihood function. The progressive estimation results and the PCRLB are demonstrated for fatigue crack estimation in an aluminum compact-tension (CT) sample subjected to variable-amplitude loading.

Original language | English (US) |
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Title of host publication | Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2009, SMASIS2009 |

Pages | 589-595 |

Number of pages | 7 |

DOIs | |

State | Published - Dec 1 2009 |

Event | 2009 ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS2009 - Oxnard, CA, United States Duration: Sep 21 2009 → Sep 23 2009 |

### Publication series

Name | Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2009, SMASIS2009 |
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Volume | 2 |

### Other

Other | 2009 ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, SMASIS2009 |
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Country | United States |

City | Oxnard, CA |

Period | 9/21/09 → 9/23/09 |

### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials

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## Cite this

*Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2009, SMASIS2009*(pp. 589-595). (Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems 2009, SMASIS2009; Vol. 2). https://doi.org/10.1115/SMASIS2009-1454