In structural analysis, it is common practice to construct a finite element (FE) model of
an as-built structure using nominal material properties and idealized boundary
conditions. However, behaviors of the FE model generally differ from the as-built
structure in the field. To minimize the differences, selected parameters of the FE model
can be updated using experimental measurements from the as-built structure. This
paper investigates the FE model updating of a full-scale concrete frame structure with
over a thousand degrees-of-freedom. Given experimental measurements obtained
during a shaker test, frequency-domain modal properties of the concrete structure are
identified. A non-convex optimization problem is then formulated to update parameter
values of the FE model by minimizing the difference between the experimentally
identified modal properties and those generated from the FE model. The selected
optimization variables include concrete elastic moduli of the columns, beams and slabs.
Upon model updating, the modal properties of the FE model can match better with the
experimentally identified modal properties.
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A Comparative Study of Frequency-domain Finite Element Updating Approaches Using Different Optimization Procedures
In order to achieve a more accurate finite element (FE) model for an as-built structure, experimental data collected from the actual structure can be used to update selected parameters of the FE model. The process is known as FE model updating. This research compares the performance of two frequency-domain model updating approaches. The first approach minimizes the difference between experimental and simulated modal properties, such as natural frequencies and mode shapes. The second approach minimizes modal dynamic residuals from the generalized eigenvalue equation involving stiffness and mass matrices. Both
model updating approaches are formulated as an optimization problem with selected updating parameters as optimization variables. This research also compares the performance of different optimization procedures, including a nonlinear least-square, an interior-point and an iterative linearization procedure. The comparison is conducted using a numerical example of a space frame structure. The modal dynamic residual approach shows better performance than
the modal property difference approach in updating model parameters of the space frame structure.
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- Award ID(s):
- 1634483
- NSF-PAR ID:
- 10181590
- Date Published:
- Journal Name:
- EWSHM
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This paper describes a MATLAB package for structural model updating, named SMU. The SMU package updates parameter values of a finite element model by solving optimization problems utilizing modal properties obtained from sensor measurements. In particular, the package offers three model updating formulations, namely, (1) the modal assurance criterion value approach, (2) the eigenvector difference approach, and (3) the modal dynamic residual formulation. The first two belong to the family of modal property difference formulations. For each formulation, the analytical Jacobian derivative of the objective function is derived and implemented in SMU. Since the formulated optimization problems are generally nonconvex, the global optimality of the solution cannot be guaranteed using off-the-shelf optimization algorithms. In order to increase the chance of finding a better local minimum, the SMU package can perform gradient search from randomly generated starting points. Several examples for the model updating of as-built structures are included in the GitHub package. This paper demonstrates the SMU functionality through model updating of an 18-DOF model and a concrete building frame model.
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Numerical modeling of actual structural systems is a very complex task mainly due to the lack of complete knowledge on the involved parameters. Simplified assumptions on the uncertain geometry, material properties and boundary conditions make the numerical model response differ from the actual structural response. Improvements of the finite element (FE) models to obtain accurate response predictions can be achieved by vibration based FE model updating which uses experimental measures to minimize the differences between the numerical and experimental modal features (i.e. natural frequencies and mode shapes). Within this context, probabilistic model updating procedures based on the Bayes’ theorem were recently proposed in the literature in order to take into account the uncertainties affecting the structural parameters and their influence on the structural response. In this paper, a novel framework to efficiently estimate the posterior marginal PDF of the selected model parameters is proposed. First, the main dynamic parameters to be used for model updating are identified by ambient vibration tests on an actual structural system. Second, a first numerical FE model is developed to perform initial sensitivity analysis. Third, a surrogate model based on polynomial chaos is calibrated on the initial FE model to significantly reduce computational costs. Finally, the posterior marginal PDFs of the chosen model parameters are estimated. The effectiveness of the proposed method is demonstrated using a FE numerical model describing a curved cable-stayed footbridge located in Terni (Umbria Region, Central Italy).more » « less
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Numerical modeling of actual structural systems is a very complex task mainly due to the lack of complete knowledge on the involved parameters. Simplified assumptions on the uncertain geometry, material properties and boundary conditions make the numerical model response differ from the actual structural response. Improvements of the finite element (FE) models to obtain accurate response predictions can be achieved by vibration based FE model updating which uses experimental measures to minimize the differences between the numerical and experimental modal features (i.e. natural frequencies and mode shapes). Within this context, probabilistic model updating procedures based on the Bayes’ theorem were recently proposed in the literature in order to take into account the uncertainties affecting the structural parameters and their influence on the structural response. In this paper, a novel framework to efficiently estimate the posterior marginal PDF of the selected model parameters is proposed. First, the main dynamic parameters to be used for model updating are identified by ambient vibration tests on an actual structural system. Second, a first numerical FE model is developed to perform initial sensitivity analysis. Third, a surrogate model based on polynomial chaos is calibrated on the initial FE model to significantly reduce computational costs. Finally, the posterior marginal PDFs of the chosen model parameters are estimated. The effectiveness of the proposed method is demonstrated using a FE numerical model describing a curved cable-stayed footbridge located in Terni (Umbria Region, Central Italy).more » « less
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ABSTRACT: This paper explores the use of cyber-physical systems (CPS) for optimal design in wind engineering. The approach combines the accuracy of physical wind tunnel testing with the ability to efficiently explore a solution space using numerical optimization algorithms. The approach is fully automated, with experiments executed in a boundary layer wind tunnel (BLWT), sensor feedback monitored by a high-performance computer, and actuators used to bring about physical changes in the BLWT. Because the model is undergoing physical change as it approaches the optimal solution, this approach is given the name “loop-in-the-model” testing. The building selected for this study is a low-rise structure with a parapet wall of variable height. Parapet walls alter the location of the roof corner vortices, alleviating large suction loads on the windward facing roof corner and edges and setting up an interesting optimal design problem. In the BLWT, the model parapet height is adjusted using servo-motors to achieve a particular design. The model surface is instrumented with pressure taps to measure the envelope pressure loading. The taps are densely spaced on the roof to provide sufficient resolution to capture the change in roof corner vortex formation. Experiments are conducted using a boundary BLWT located at the University of Florida Natural Hazard Engineering Research Infrastructure (NHERI) Experimental Facility. The proposed CPS approach enables the optimal solution to be found quicker than brute force methods, in particular for complex structures with many design variables. The parapet wall provides a proof-of-concept study with a single design variable that has a non-monotonic influence on a structure’s wind load. This study focuses on envelope load effects, seeking the parapet height that minimizes roof and parapet wall suction loading. Implications are significant for more complex structures where the optimal solution may not be obvious and cannot be reasonably determined with traditional experimental or computational methods. KEYWORDS: Cyber-physical systems, optimization, boundary-layer wind tunnel, parapet wall, NHERImore » « less
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Accepted Manuscript1.0
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