Abstract
In civil and mechanical engineering, Bayesian inverse methods may serve to calibrate the uncertain input parameters of a structural model given the measurements of the outputs. Through such a Bayesian framework, a probabilistic description of parameters to be calibrated can be obtained; this approach is more informative than a deterministic local minimum point derived from a classical optimization problem. In addition, building a response surface surrogate model could allow one to overcome computational difficulties. Here, the general polynomial chaos expansion (gPCE) theory is adopted with this objective in mind. Owing to the fact that the ability of these methods to identify uncertain inputs depends on several factors linked to the model under investigation, as well as the experiment carried out, the understanding of results is not univocal, often leading to doubtful conclusions. In this paper, the performances and the limitations of three gPCE-based stochastic inverse methods are compared: the Markov Chain Monte Carlo (MCMC), the polynomial chaos expansion-based Kalman Filter (PCE-KF) and a method based on the minimum mean square error (MMSE). Each method is tested on a benchmark comprised of seven models: four analytical abstract models, a one-dimensional static model, a one-dimensional dynamic model and a finite element (FE) model. The benchmark allows the exploration of relevant aspects of problems usually encountered in civil, bridge and infrastructure engineering, highlighting how the degree of non-linearity of the model, the magnitude of the prior uncertainties, the number of random variables characterizing the model, the information content of measurements and the measurement error affect the performance of Bayesian updating. The intention of this paper is to highlight the capabilities and limitations of each method, as well as to promote their critical application to complex case studies in the wider field of smarter and more informed infrastructure systems.
Highlights
In recent decades, increasing effort has been devoted to the identification of constructed systems
Structural identification (St-Id) is a subfield of system identification, which originated in electrical engineering in relation to circuit and control theory; it has been defined as “the parametric correlation of structural response characteristics predicted by a mathematical model with analogous quantities derived from experimental measurements” [1]
Models that might be updated can be classified in two main classes: physics-based models, such as mathematical physics and discrete geometric models and non-physicsbased models, such as inter alia probabilistic, statistical and meta-models
Summary
In recent decades, increasing effort has been devoted to the identification of constructed systems. Discrete geometric models include finite element (FE) models, commonly used in civil, bridge and structural engineering to analyze, e.g., the internal forces and displacements of structures in several limit states, or to predict the response of the system to dynamic actions such as earthquakes, wind and traffic. It must be emphasized, on the one hand, that the input parameters of the model (material properties, geometric properties, boundary conditions, load conditions, etc.) are affected by different sources of uncertainty; on the other, that simplifying modelling assumptions regarding the model structure are often required or implicitly made. All these issues may significantly decrease the quality and accuracy of the numerical model, which needs suitable updating
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