| Περίληψη: | Vibration-based damage detection has been investigated extensively whereas the localization of Single-Site Damages (SSDs) and Multi-Site Damages (MSDs) has been explored to a lesser extent. The methods employed for vibration-based localization may be categorized into two main families, the Finite Element Model (FEM) based methods and the data-based methods. The FEM based methods employ the test structure’s detailed and large in size FEM needing update with signals from several sensors and they treat the problem of damage localization as a problem of precise localization whose solution requires the precise estimation of the SSD and MSD Cartesian coordinates on an investigated continuous structural topology, assuming that damage may occur anywhere on the specified topology. The data-based methods employ data-based structural models exclusively identified from a limited number of measured signals (a single measurement may be sometimes sufficient) and they treat the SSD and MSD localization as a classification problem, a problem much simpler than the problem of precise localization, where an unknown SSD or MSD is roughly classified to one of a number of pre-specified damages or to the nearest sensors.
Recently, SSD precise localization was achieved through the Functional Model Based Method (FMBM) based on the innovative class of data–based Functional Models (FMs), appropriate data pooling techniques, and proper estimation procedures. The FM parameters depend on a scheduling parameter such as the SSD location’s coordinate and thus an FM is capable of representing the considered (partial) structural dynamics for an SSD incurred anywhere on a given structural topology. Univariate FMs, such as the Vector dependent Functionally Pooled -ARX (VFP-ARX) models, were used for SSD localization on a laboratory aircraft skeleton structure consisting of 1D structural elements (1D continuous structural topologies) with a single sensor and with a FM determined for each element. However a number of issues are left open such as the damage precise localization with the FMBM on structures consisting of 2D and 3D elements, the identification of a single FM representing the dynamics of all structural elements, the damage precise localization with the FMBM based on more than one sensor and the precise localization of MSDs.
The current thesis addresses the aforementioned open issues regarding the use of the FMBM for damage localization, with the main goal being the extension and use of FMs for the precise localization of SSDs and MSDs on continuous structural topologies. Chapter II addresses the problem of vibration- based precise localization of SSDs anywhere on any structure, consisting of any number of 1D, 2D or 3D elements. This is achieved through a generalization of the FMBM which employs a single VFP-ARX model for incorporating the whole structural topology and describing the structural dynamics under any damage. The damage coordinates may be incorporated into the model parameters through a 3D scheduling vector whose containing Cartesian coordinates are properly constrained to reflect a given topology. In the context of the FMBM, the localization of an unknown SSD is based on the estimation of the Cartesian coordinates of an unknown damage location within the VFP-ARX model structure and the bounds of the specific structural topology, so that the location estimate and its constructed uncertainty bounds (confidence intervals) are bound within the structural topology and of statistically optimal accuracy. The effectiveness of the postulated method is demonstrated via precise localization of SSDs on a relatively complex 3D lab-scale truss structure consisting of 1D structural elements. An SSD corresponds to loosening of any single bolt and damage localization is investigated based on the use of a single acceleration response sensor within a very low and narrow frequency bandwidth. The results show that SSD localization of high accuracy is possible on a 3D structure through the Generalized FMBM.
Chapter III investigates (i) the extension of the original scalar FMBM to its vector form in order to exploit multiple structural responses for achieving SSD localization of higher precision (compared to the scalar form) on structures consisting of 1D structural elements and (ii) its comparison with the previously developed scalar version (Chapter I). The new version is equipped with a VFP-Vector ARX (VFP-VARX) model which constitutes an extension of the previously used, scalar, VFP-ARX model and is capable of representing the structural dynamics as viewed from multiple measurement positions, while also accounting for their interrelations. Based on this model form, precise estimation of the damage coordinates is achieved within a nonlinear optimization framework with constraints representing the structural topology, and corresponding damage confidence intervals are constructed. The size of a VFP-VARX model is larger compared to that of a VFP-ARX model thus increasing the FMBM’s computational complexity and time. The vector version of the FMBM is assessed through the precise localization of SSDs on a 3D lab-scale truss structure, the use of two acceleration response sensors within a very low and narrow frequency bandwidth and detailed comparisons with the previous scalar version (Chapter II). An SSD corresponds to loosening of any single bolt and the results demonstrate that the vector version of the method leads to improved localization accuracy.
The focus of Chapter IV is on assessing, for the first time, the achievable damage localization accuracy of the Generalized FMBM (Chapter II) on a 2D structural element. Localization of SSDs is addressed on a lab-scale aircraft stabilizer structure, a 2D structural element, under practical limitations relating to potential in-flight implementation such as constraints on the number of deployed sensors and the excitation bandwidth, which must be limited and low frequency. The method handles the specific 2D structural topology through a representation of the trapezoidal structure as a simple rectangle based on a transformed coordinate system, thus formulating the estimation of the Cartesian coordinates of an unknown SSD location as an optimization problem with simple (as opposed to functional) boundary constraints. In this context, a VFP-VARX model characterized by a 2D scheduling vector is employed. The assessment is based on the use of only two vibration sensors in a limited, low frequency bandwidth and the various examined SSD scenarios simulate local stiffness reduction via the addition of a small mass at any point on the structure. The vector version of the Generalized FMBM (Chapter III) is used due to the multiple employed sensors. The results show that SSD localization of high accuracy is indeed possible on a 2D structural element.
Chapter V addresses the problem of MSD precise localization, that is the estimation of the exact MSD coordinates on various structural topologies via a proper extension of the vibration-based FMBM. More specifically, two versions of the method are introduced: i) A 2M version employing two separate FMs, one FM for the representation of the structural dynamics under any SSD and one FM for the representation of the structural dynamics under any MSD and ii) a 1M version employing a single FM for representing the structural dynamics under SSDs and MSDs. In both versions, an unknown damage is characterized as an SSD or MSD through statistical hypothesis tests and subsequently the estimate of the MSD Cartesian coordinates along with the uncertainty bounds are obtained. The employment of two FMs increases the FMBM’s computational complexity but on the other hand the higher modelling accuracy through distinct models offers better damage localization accuracy whereas the employment of a single FM leads to a simpler training procedure in the method’s baseline phase. The performance of the FMBM’s versions on MSD precise localization under a reduced number of experiments (corresponding to MSDs) in their training is also investigated. The two versions of the extended FMBM are assessed through precise localization of SSDs and MSDs (double) on the right wing of a lab–scale Garteur aircraft skeleton. The wing is considered as a 1D structural element in 1D space and a single acceleration response sensor within a very low and narrow frequency bandwidth is employed. SSDs and MSDs are simulated via small mass attachment. The damage characterization results show that both versions of the FMBM are capable of successfully characterizing an unknown damage as an SSD or MSD. The results show that SSD and MSD localization of high accuracy is possible through the two versions of the FMBM with the 2M version exhibiting a slightly better performance for SSDs.
Finally, Chapter VI contains the concluding remarks and future perspectives of the thesis.
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