## Abstract

Structural health monitoring requires engineers to understand the state of a structure from its observed response. When this information is uncertain, Bayesian probability theory provides a consistent framework for making inferences. However, structural engineers are often unenthusiastic about Bayesian logic and prefer to make inference using heuristics. Here we propose a quantitative method for logical inference based on a formal analogy between linear elastic mechanics and Bayesian inference with linear Gaussian variables. We start by discussing the estimation of a single parameter, by assuming that all of the uncertain quantities have a Gaussian distribution and that the relationship between the information and the parameter is linear. With these assumptions, the analogy is stated as follows: The expected value of the parameter corresponds to the position of a bar with one degree of freedom; uncertain information on the parameter is modelled as linear elastic springs in series or parallel. If we want to extend the analogy to N parameters, we prove that we must simply express the potential energy of the mechanical system, with N degrees of freedom, associated to the inference problem in question. We apply the mechanical equivalent to a real-life case study: The elongation of a cable belonging to Adige Bridge, a cable-stayed bridge North ofTrento, Italy, in the case of two and three parameters to estimate.

Original language | English |
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Title of host publication | Transforming the Future of Infrastructure through Smarter Information |

Subtitle of host publication | Proceedings of the International Conference on Smart Infrastructure and Construction Construction, 27–29 June 2016 |

Editors | RJ Mair, K Soga, Y Jin, AK Parlikad, JM Schooling |

Pages | 393-398 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 6 Jul 2016 |

Event | 2016 International Conference on Smart Infrastructure and Construction, ICSIC 2016 - Cambridge, United Kingdom Duration: 27 Jun 2016 → 29 Jun 2016 |

### Conference

Conference | 2016 International Conference on Smart Infrastructure and Construction, ICSIC 2016 |
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Country/Territory | United Kingdom |

City | Cambridge |

Period | 27/06/16 → 29/06/16 |

## Keywords

- health monitoring
- Bayesian probability theory
- logical inference