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Vibration-based Model Updating and Identification of Multiple Axial Forces in Truss Structures
(2016)
Safety assessment of existing iron and steel truss structures requires the determination of the axial forces and corresponding stresses in truss structural members. The results of the axial force determination can be integrated as part of a structural health monitoring scheme for existing trusses. In this work, a methodology is proposed to identify multiple axial forces in members of a truss structure based on the modal parameters. Vibration test allows the identification of the natural frequencies and mode shapes, globally of the truss structure as well as locally of the individual bars. The method calibrates the numerical model of the truss structure using a genetic algorithm and strategic validation criteria. The validation criteria are based on the identified natural frequencies and global mode shapes of the truss structure as well as information of the axial forces in the individual bars of the truss, which are estimated from the natural frequencies and five amplitudes of the corresponding local mode shapes of the single bars based on an analytical-based algorithm. The calibration allows the identification of the axial forces in all bars of the truss structure. For mode pairing strategy, a technique makes use of the enhanced modal assurance criteria with the calculation of the modal strain energies. Moreover, the modal strain energies are also used to select the relevant local mode shape of the individual bars. The feasibility and accuracy of the proposed methodology is verified by laboratory experiments on several truss structures. In situ tests on existing trusses are intended. The results from one of the laboratory tested structures, i.e. a two-bar system, are presented.
The inverse identification of the stress state in axially loaded slender members of iron and steel truss structures using measured dynamic data is discussed. A methodology is proposed based on the finite element model updating coupled with nature-inspired optimization techniques, in particular the particle swarm optimization. The numerical model of truss structures is calibrated using natural frequencies and mode shapes from vibration tests, as well as additional information of the axial forces in selected truss members based on the experimentally identified modal parameters. The results of the identification are the axial forces or corresponding stresses in truss structures and the joint rigidity in relation to pinned and rigid conditions.
The main challenge in using numerical models as digital twins in real applications for prognosis purposes, such as reliability analysis, is the calibration and validation of the models based on uncertain measurement data. Uncertainties are not limited to the measurement data, but the numerical model itself will not be perfect due to the modelling assumptions.
In this contribution, a probabilistic inference method for model calibration, based on the Bayes’ Theorem, is used to face that issue. Such inference approaches include uncertainties on the data as well as on the model parameters, allowing to compute an a posteriori distribution for the model parameters as well as a noise term reflecting the measured data. However, such probabilistic inference methods require a lot of evaluations of the numerical forward model for different model parameters. An improvement of the efficiency is obtained by replacing the forward model with a reduced model. Model reduction, e.g. the proper generalized decomposition (PGD) method, is a popular concept to decrease the computational effort, where each evaluation of the reduced forward model is a pure less costly function evaluation.
The heterogeneous spatial distribution of material parameters in the forward model is described by a lognormal random field. This allows identifying a variable stiffness over the spatial directions by identifying the random field variables with given measurement data. These changes can e.g. be caused by damage. The lognormal field is approximated as series expansion for the PGD problem.
The derived efficient model identification procedure is shown using a real reinforced prestress demonstrator bridge and stereophotogrammetry measurement data. A digital twin for that demonstrator bridge is build up using a set of measurement data and verified by testing additional measurement data. PGD model error against the FEM model is discussed based on an importance sampling analysis computing the Bayes Factor.
Numerical simulators, such as finite element models, have become increasingly capable of predicting the behaviour of structures and components owing to more sophisticated underlying mathematical models and advanced computing power. A common challenge lies, however, in calibrating these models in terms of their unknown/uncertain parameters. When measurements exist, this can be achieved by comparing the model response against measured data. Besides uncertain model parameters, phenomena like damage can give rise to further uncertainties; in particular, quasi-brittle materials, like concrete, experience damage in a heterogeneous manner due to various imperfections, e.g. in geometry and boundary conditions. This hardens an accurate prediction of the damaged behaviour of real structures that comprise such materials.
In this study, which draws from a data-driven approach, we use the force-version of the finite element model updating method (FEMU-F) to incorporate measured displacements into the identification of the damage parameters, in order to cope with heterogeneity. In this method, instead of conducting a forward evaluation of the model and comparing the model response (displacements) against the data, we impose displacements to the model and compare the resulting force residuals with measured reaction forces. To account for uncertainties in the measurement of displacements, we endow this approach with a penalty term, which reflects the discrepancy between measured and imposed displacements, where the latter is assumed as unknown random variables to be identified as well. A Variational Bayesian approach is used as an approximating tool for computing posterior parameters. The underlying damage model considered in this work is a gradient-enhanced damage model.
We first establish the identification procedure through two virtual examples, where synthetic data (displacements) are generated over a certain spatially-dense set of points over the domain. The procedure is then validated on an experimental case-study; namely a 3-point bending experiment with displacement measurements resulting from a digital image correlation (DIC) analysis.
The Bundesanstalt für Materialforschung und -prüfung (BAM) collaborates with TNO to develop a software framework for automated calibration of structural models based on monitoring data. The ultimate goal is to include such models in the asset management process of engineering structures. As a basis for developing the framework, a multi-span road bridge consisting of ten simply supported steel box girders was selected as a test case. Our group measured output-only vibration data from one box girder under ambient conditions. From the data, we determined eigenfrequencies and mode shapes. In parallel, we developed a preliminary structural model of the box girder for the purpose of predicting its modal properties. In this contribution, we provide an overview of the measurement campaign, the operational modal analysis, the structural modeling and qualitatively compare the identified with the predicted modes. As an outlook, we discuss the further steps in the calibration process and future applications of the calibrated model.