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Mechanical Equivalent of Logical Inference for Structural Health Monitoring



Structural health monitoring requires engineers to assess the state parameters of a structure based on empirical data provided by a monitoring system. When the information is affected by one or more sources of uncertainty, Bayesian probability theory provides a consistent framework to make statistical inference. However, structural engineers are often unenthusiastic of Bayesian logic, finding its application complicated and burdensome. In this contribution, we propose a quantitative, rational, method for statistical inference based on a formal analogy between linear elastic mechanics and Bayesian inference with linear Gaussian variables. More specifically, we investigate the case of single parameter estimation and we show how using this analogy we can easily reproduce a complex inference scheme, including multiple source of information and correlated data, in the form of a model made of parallel or in-series springs. The solution of that mechanical model is obtained thanks to the classical structural mechanics, but it provides the same outcome of the equivalent statistical inference.

doi: 10.12783/SHM2015/293

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