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 inference.
However, structural engineers are often unenthusiastic about Bayesian logic and prefer to make inference using
heuristics. Herein we propose a quantitative method for logical inference based on a formal analogy between linear
elastic mechanics and Bayesian inference with Gaussian variables. We start by discussing the estimation of a single
parameter under the assumption that all of the uncertain quantities have a Gaussian distribution and that the relationship
between the observations and the parameter is linear. With these assumptions, the analogy is stated as follows: the
expected value of the considered parameter corresponds to the position of a bar with one degree of freedom and
uncertain observations of the parameter are modelled as linear elastic springs placed in series or parallel. If we want to
extend the analogy to multiple parameters, we simply have to express the potential energy of the mechanical system
associated to the inference problem. The expected value of the parameters is then calculated by minimizing that potential
energy. We conclude our contribution by presenting the application of mechanical equivalent to a real-life case study in
which we seek the elongation trend of a cable belonging to Adige Bridge, a cable-stayed bridge located North of Trento,
Carlo Cappello, Denise Bolognani, and Daniele Zonta, "Mechanical equivalent of Bayesian inference from monitoring data," Proc. SPIE 9803, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2016, 98031O (Presented at SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring: March 22, 2016; Published: 20 April 2016); https://doi.org/10.1117/12.2218762.
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