Finite Element Model Updating for Civil Engineering Structures: Applying convex optimization

Any modern society depends on its infrastructure network to function and prosper. Large civil engineering structures are critical nodes within any infrastructure network and, therefore, their structural integrity is of utmost importance. Structural health monitoring (SHM) is the engineering field encompassing all the techniques dedicated to providing information about the physical state of structures. Originally, the main tool to analyze the integrity of a structure was periodical visual inspection, but the inception of the digital age opened the door for researchers and professionals to investigate and design advanced computer based SHM systems. These systems have a great potential to provide timely accurate information for a safe and efficient management of civil engineering structures.

One of the primary tasks of modern SHM systems is the identification of dynamic properties by processing vibration test data measured in the monitored structure. Then, finite element (FE) model updating seeks to translate the identified dynamic properties into information about the structural condition. Ideally, FE model updating could enable the capacity for damage location and quantification during the lifespan of large structures which in turn would greatly enhance the usefulness of SHM systems.

The FE model updating problem can be described mathematically as an inverse problem to estimate unknown physical quantities using indirect dynamic data. To solve this inverse problem, the dominant approach in FE model updating relies on the linear least-squares method and it is often called sensitivity model updating. It is well-known that updating problems resulting from sensitivity model updating are prone to be ill-posed and this affects the robustness of the method. As an alternative, this thesis introduces a novel FE model updating approach based on the convex optimization framework. Convex optimization is a mathematical field that has broader capabilities than the linear least-squares method to model engineering problems. Moreover, convex optimization has been successfully used in other areas of structural engineering such as finite element limit analysis and topology optimization.

In this thesis, the premise for the development of the new updating approach is that the updating process should be carried out in small steps due to the highly nonlinear dependencies between the structural dynamics and the physical parameters. Therefore, the proposed FE model updating approach consists in the sequential solution of updating steps. As the core of the approach, the updating step is defined as a convex optimization problem that insures a limited change for the physical parameters to be updated. Furthermore, convex optimization enables the possibility to incorporate prior knowledge about the modelled structural system into the updating problem by adding constraints and regularization.

The effectiveness and robustness of the proposed convex optimization based updating approach are demonstrated using numerous examples. The proposed approach provides precise solutions for determined updating problems, i.e. equal number of available data points and unknown quantities. Also, it is shown that precise solutions for underdetermined updating problems (less data points than unknown quantities) can be obtained by adding constraints and regularization based on engineering insight. Furthermore, due to the noisy nature of the dynamic properties estimated in SHM systems, a detailed study of the updating performance, using noise perturbed dynamic data, is presented. This study shows the capability and robustness of convex optimization model updating to provide accurate information about damage detection for considerable levels of noise perturbation. Also, along this analysis, the updating performance of the novel approach is compared to the performance of the sensitivity model updating. It is shown that the convex optimization based model updating approach unambiguously provides a superior updating performance.

In conclusion, this Ph.D. thesis presents a new FE model updating methodology that is simple to implement, offers flexibility to incorporate engineering insight mathematically and delivers a better performance than the dominant model updating methodology.