Sensor placement optimization and damage identification in a fuselage structure using inverse modal problem and firefly
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RESEARCH PAPER
Sensor placement optimization and damage identification in a fuselage structure using inverse modal problem and firefly algorithm Guilherme Ferreira Gomes1 · João Vitor Purcino Pereira1 Received: 12 August 2019 / Revised: 6 February 2020 / Accepted: 20 February 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The structural monitoring of mechanical systems is an extremely important task for ensuring its performance and structural health. To overcome limitations of traditional non-destructive inspections (NDIs), damage identification techniques have been developed from global indicators, mainly those based on modal data. In this study, damages are identified by solving an inverse problem. A fuselage model of an E190 aircraft is considered and the firefly algorithm (FA) metaheuristic is applied to solve the inverse problem in order to identify structural damages (location and severity). The method is then solved in two main fronts: (1) the direct problem using finite element analysis and (2) the inverse problem by minimizing an objective function. Evaluating modal response at many points on a large-scale structure can become prohibitive. For this, a method of optimizing sensors is performed using the Fisher information matrix (FIM). Results are compared considering the sensor placement optimization problem. It is noticed that optimized sensors contribute to an improvement in the identification of damages, mainly for complex and large-scale structures. The proposed optimized damage identification process using FIMFA has the potential to be extended to a wide range of SHM applications in complex structures. Hence, traditional NDIs have many shortcomings due to the complexity of large-scale structures as well as modern design structures and may not be practicable if the structure has restricted access. Accordingly, an enhanced damage identification method is developed in order to better handle measurement data to find structural changes (or damages) in complex aerospace structures. Keywords Damage identification · Inverse problem · Firefly algorithm · Fuselage · Sensor placement optimization List of symbols M Mass matrix ÿ (t) Acceleration K Stiffness matrix y(t) Displacement Y(y) Applied load n Number of degrees of freedom ϕj jth eigenvector λj jth eigenvalue m Total number of evaluated mode shapes ki Stiffness of the ith element Kd Damaged stiffnes matrix λdi jth eigenvalue of the damaged structure ϕdi jth eigenvector of the damaged structure * Guilherme Ferreira Gomes [email protected] 1
Mechanical Engineering Institute, Federal University of Itajubá – UNIFEI, Itajubá, Brazil
Δkj Stiffness of the jth damaged element βj Stiffness reduction factor of the jth damaged element Δ𝜆i Variation of the ith eigenvalue due to the damage Δ𝜙i Variation of the ith eigenvector due to the damage f (x) Objective function x Position vector I(r) Intensity of firefly brightness as a function of distance I0 Firefly brightness intensity at distance equal t
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