Identification of Uncertain Vibrating Beams through a Perturbation Approach

Struct Control Health Monit

Paolone

Ruta

2020

Damage, be it a material or a geometric degradation, modifies some features of the response foreseen by the original structural design. These variations, once the dependence on the damage causing them is established, can be used for identification purposes. In the literature, vibration-based approaches usually compare some responses of linear elastic structures with dissipative properties that are assumed proportional to the mass and stiffness measures. However, such an assumption is reasonable for new, undamaged structures, but can be unreliable in existing, potentially damaged structures, particularly for damages localised in narrow areas. The eigenmodes of a proportionally damped system can be reduced to the real ones of the relevant ideal undamped system. On the other hand, non-proportional damping exhibits complex eigenmodes that cannot be reduced to those of the ideal, or of the proportionally damped, structure. Thus, we may assume the complexity of the eigenmodes as a measure of nonproportional damping, hence of damage. On this basis, some contributions in the literature verified the relationship among presence of damage and amount of complexity. Here, we propose a perturbation approach and an objective function able to identify presence, location and amplitude of localised damages, intended as sources of non-proportionality in viscously damped linear systems. A prototype naturally discrete structure with four degrees-of-freedom is chosen to test and show capability and accuracy of the proposed method.

Section: Damage As a Perturbationmentioning

confidence: 99%

Dynamic damage identification using complex mode shapes

Struct Control Health Monit

Paolone

Ruta

2020

“…(10) leads to λ 0i = iπ/L, for the eigenvalues, and φ 0i = sin(λ 0i x), for the (unitary scaled) mode shapes; then, the perturbation approach, Eqs. (11)(12), furnishes the first and the second order eigensolutions. The first four couples (λ 0i ; φ 0i (x)) are shown in Fig.…”

Section: Case Studymentioning

confidence: 99%

“…In [12], a perturbation method has been proposed by some of the authors to derive the asymptotic eigensolution of a vibrating beam with uncertain damage. Then, the statistics of the random damage parameter have been obtained by means of an objective function minimizing the difference among analytical and experimental fractiles of the eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

Optimal Sensors Placement for Damage Detection of Beam Structures

Lecture Notes in Mechanical Engineering

Paolone

Pingaro

et al. 2020

Self Cite

This paper is dedicated to the identifiability of vibrating beam structures with uncertain damages. The probability of damage occurrence is computed assuming a Gaussian distributed random damage parameter. Then, we propose a technique for selecting an optimized solution of sensors placement based on the comparison among the probability of damage occurrence and the probability to detect the damage, where the latter is evaluated exploiting the closed-form asymptotic solution provided by a perturbation approach. This comparison must be intended as an investigation on the minimum number of sensors beyond which monitoring accuracy (estimated by an error function measuring the differences among the two probabilities) increases less than a 'small' predetermined threshold. The capabilities and efficiency of the technique are shown through a parametric analysis on a sample case study: a simply supported beam with a random parameter ruling the evolution of a non-localized damage. The relevant results are presented and discussed, showing which conditions (sensors network) properly characterizes the beam dynamics.

“…Damages are modeled as a perturbation of the healthy system and therefore a perturbation approach can properly describe the effect of the damage, both for standard [38] and state-space dynamic analysis [39,40]. In [41], a perturbation method has been proposed by some of the authors to derive the asymptotic eigensolution of a vibrating beam with uncertain damage. Then, the statistics of the random damage parameter have been obtained by means of an objective function minimizing the difference among analytical and experimental fractiles of the eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

Optimal Sensors Placement in Dynamic Damage Detection of Beams Using a Statistical Approach

Pingaro

Trovalusci

et al. 2020

J Optim Theory Appl

Self Cite

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.