Optimal Sensors Placement in Dynamic Damage Detection of Beams Using a Statistical Approach
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Optimal Sensors Placement in Dynamic Damage Detection of Beams Using a Statistical Approach Egidio Lofrano1 · Marco Pingaro1 Achille Paolone1
· Patrizia Trovalusci1
·
Received: 9 June 2020 / Accepted: 26 September 2020 © The Author(s) 2020
Abstract Structural monitoring plays a central role in civil engineering; in particular, optimal sensor positioning is essential for correct monitoring both in terms of usable data and for optimizing the cost of the setup sensors. In this context, we focus our attention on the identification of the dynamic response of beam-like structures with uncertain damages. In particular, the non-localized damage is described using a Gaussian distributed random damage parameter. Furthermore, a procedure for selecting an optimal number of sensor placements has been presented based on the comparison among the probability of damage occurrence and the probability to detect the damage, where the former can be evaluated from the known distribution of the random parameter, whereas the latter is evaluated exploiting the closed-form asymptotic solution provided by a perturbation approach. The presented case study shows the capability and reliability of the proposed procedure for detecting the minimum number of sensors such that the monitoring accuracy (estimated by an error function measuring the differences among the two probabilities) is not greater than a control small value. Keywords Sensors placement · Perturbation approach · Damage detection · Uncertain stiffness · Vibrating beam Mathematics Subject Classification 47A55 · 70L05 · 74A45 · 74E35 · 74H10 · 74K10
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Egidio Lofrano [email protected] Marco Pingaro [email protected] Patrizia Trovalusci [email protected] Achille Paolone [email protected]
1
Sapienza University of Rome, Rome, Italy
123
Journal of Optimization Theory and Applications
1 Introduction Strategic constructions, such as bridges and tower buildings, during their lifetime are inexorably subjected to degradation and damage of various kinds. For this reason, careful monitoring is required for profitable maintenance and for activation of safety protocols in case of danger (“early warning” systems). The main problem, that discourages the use of large-scale structural health monitoring (SHM) system, is its high cost, directly related to the cost of the instrumentation and in particular the number of sensors used. In this framework, dynamic approaches—mainly concerned with output-only techniques—have been successfully adopted to locate and quantify structural damages for historical [1,2] and recent construction [3,4]. Other methods have been proposed for the damage detection such as data-driven [5,6] and statistical method [7]. As reported by many authors, when structural responses of dynamic systems are exploited to trace the signature of the damage, one deals with an inverse problem, where damage influence is recognized starting from its effect. On the one hand, techniques not model based, see for instance [8,9], are able to directl
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