MS18.5 - System Identification and Damage Detection

When dealing with cable-suspended structures, it is essential to have an accurate estimation of the tensile force on cable elements. This is firstly to guarantee the structural safety of the structure but also to allow scheduling of the maintenance operations. Being the direct measurement often related to expensive and invasive operations, many indirect methods exist to solve the problem. Among them, the most popular are the ones based on vibration methods, able to relate the measured natural frequency with the tension force value through the taut string theory. However, in case the cable is part of a more complex system (like a suspended or cable-stayed bridges) or it is endowed with dampers, the vibration method based on the string theory may be inaccurate. This requires a more complex method able to include a detailed description of the cable geometry and constraints, along with modelling the effects of the dampers. To this purpose, referring to the cables of the Hovenring Bridge, a roundabout flyover for bicycles in Eindhoven (the Netherlands), a novel method is presented and applied to such structure. It is based on a combined experimental and numerical approach, where the experimentally based measure of the first natural frequency of the cable is combined with a FEM model of each cable to finally obtain an estimation of the tension force. Specifically, the FE model has been built by considering equivalent tensioned beam elements and it includes the modelling of threated bars and sockets that realize the constrains of the cable. Moreover, it is inclusive of the two Stockbridge type tuned mass dampers that are installed in each cable of the Hovenring Bridge, through equivalent mass-spring-damper systems. In the present paper, a complete description of the method will be carried out, together with the application to the 24 cables of the Hovenring Bridge. A validation of the proposed method is presented as well, through a comparison with a direct measurement of the tension force in 4 cables. Despite here presented with reference to a specific case, the method is suitable for generalization.

In the context of Structural Health Monitoring, the accurate estimation of the state of a structural system subjected to various sources of dynamic loads can be beneficial for assessing the current structural performance and for predicting the future one. In case of linear systems, for example, the estimation of the state can provide valuable information about unmeasured strains and corresponding stresses that, in turn, can favor the prediction of fatigue damage. Additionally, state estimation of structural systems responding in the nonlinear regime can facilitate the identification of damages that occurred during an extreme event (e.g., excessive wave, earthquake and strong wind). A major challenge in the state estimation task stems from the unavailability of the external input loads. Therefore, several joint input-state estimation techniques have been already developed in order to address this issue and, among them, the Augmented Kalman Filter (AKF) is one of the most commonly employed. Despite the advantages of the AKF, a critical aspect of this joint input-state estimation technique is associated with the instability that the estimation can experience when only noisy acceleration time series are available. Heretofore, several approaches have been proposed aiming to stabilize the estimation in case of linear systems. In this work, some of the most commonly employed approaches for stabilizing the AKF-based joint-input state estimation (e.g., dummy displacement measurements, dummy load measurements and Gaussian process latent force model) are adopted and thoroughly compared. Linear structural systems of varying size and complexity will be simulated and subjected to dynamic loads while the calculated responses will be used in order to assess and compare the performance of various existing techniques for stabilizing the estimation.

System identification on operational structures is made difficult by the lack of information regarding the structure and the input force. Output-only system identification methods exist as a way of inferring the system and input force, given the output of the system which can be readily measured. Within the context of identifying structural systems, the process of determining the properties of a system from output-only data falls under the banner of Operational Modal Analysis (OMA). This paper investigates the use of the Gaussian Process Convolution Model (GPCM) as an output only system identification tool for structural systems. The form of the model assumes a priori that the observed data arise as the result of a convolution between an unknown linear filter and an unobserved white noise process, where each of these are modelled as a GP. The GPCM infers both the linear time filter (which is the impulse response function, i.e. Green’s function, of the system) and driving white noise process in a Bayesian probabilistic fashion with an approximate posterior over both signals. The GPCM is demonstrated on a synthetic case study, and benchmarked against other available OMA techniques and against a non-dynamic GP model. It will additionally be shown how this uncertainty can be propagated onto the modal properties of the system.

The determination of the mass density of a taut vibrating membrane from measurements of resonant frequency values (eigenvalues) is a problem of practical interest in various areas of applied science, from structural mechanics to biology. The inverse problem that arises is of great mathematical difficulty and it is still open in many respects. Typically, for general domains and for arbitrary mass densities, uniqueness requires the knowledge of all the infinite eigenvalues and the trace of the normal derivative of the corresponding eigenfunctions at the boundary. It is expected that the requests on the data can be weakened for simple domains, such as rectangular ones. Although these latter conditions are of interest in applications, few general results are available in the literature for this simplified version of the problem. Things get even more complicated when as is the case considered in this work the available data are a finite number of resonant frequencies, a situation that always occurs in engineering applications. Despite the lack of well established theoretical framework, some encouraging results have been obtained in the reconstruction of small perturbations of a uniform mass density in a rectangular membrane with fixed boundary. All previous works, however, consider mass perturbations symmetric with respect to both the midlines of the domain [1]-[3]. The main objective of this work is to deal with general mass perturbations. Our reconstruction method is based on the fact that if the unknown mass density ρ= (ρo+r) is a small smooth perturbation of the uniform mass density ρo, then the differences between unperturbed and perturbed resonant frequencies are correlated with certain generalized Fourier coefficients of the unknown perturbation r. This property was recently applied in [4] for the determination of doubly symmetrical mass distributions from information on Dirichlet spectrum data only. Here we show that a detailed study of the linearized inverse problem around the uniform membrane is useful in selecting appropriate spectral data to be added to the Dirichlet spectrum to ensure a proper formulation and solution of the inverse problem. It turns out that, besides the Dirichlet spectrum, it is necessary to resort to three additional spectra. The method leads to an iterative algorithm based on successive linearizations of the inverse problem in a neighbourhood of the unperturbed membrane. The reconstruction technique has been validated on an extended series of numerical simulations. The results show a notable agreement between target and identified densities, even for perturbations with disconnected support. Moreover, a certain ability of the method also emerged in approximating mass distributions that do not necessarily fall within the small perturbations or that are less regular. The results obtained are valid under the hypothesis that the eigenvalues of the initial membrane are all simple. The analysis of cases with multiple eigenvalues is significantly more complex and is currently under study. [1] R. Knobel et al., Z. Angew. Math. Phys. (1994). [2] C. McCarthy, Appl. Anal. (2001). [3] Q. Gao et al., Comput. Math. Appl. (2015). [4] A. Kawano et al., Comput. Math. Appl. (2022).