Vibration-based Bayesian model updating of civil engineering structures applying Gaussian process metamodel

Structural health monitoring plays a significant role in providing information regarding the performance of structures throughout their life spans. However, information that is directly extracted from monitored data is usually susceptible to uncertainties and not reliable enough to be used for structural investigations. Finite element model updating is an accredited framework that reliably identifies structural behavior. Recently, the modular Bayesian approach has emerged as a probabilistic technique in calibrating the finite element model of structures and comprehensively addressing uncertainties. However, few studies have investigated its performance on real structures. In this article, modular Bayesian approach is applied to calibrate the finite element model of a lab-scaled concrete box girder bridge. This study is the first to use the modular Bayesian approach to update the initial finite element model of a real structure for two states—undamaged and damaged conditions—in which the damaged state represents changes in structural parameters as a result of aging or overloading. The application of the modular Bayesian approach in the two states provides an opportunity to examine the performance of the approach with observed evidence. A discrepancy function is used to identify the deviation between the outputs of the experimental and numerical models. To alleviate computational burden, the numerical model and the model discrepancy function are replaced by Gaussian processes. Results indicate a significant reduction in the stiffness of concrete in the damaged state, which is identical to cracks observed on the body of the structure. The discrepancy function reaches satisfying ranges in both states, which implies that the properties of the structure are predicted accurately. Consequently, the proposed methodology contributes to a more reliable judgment about structural safety.

Reduced order numerical modeling for calibration of complex constitutive models in powder pressing simulations

Numerical simulations of different ceramic production phases often involve complex constitutive models, with difficult calibration process, relying on a large number of experiments. Methodological developments, proposed in present paper regarding this calibration problem can be outlined as follows: assessment of constitutive parameters is performed through inverse analysis procedure, centered on minimization of discrepancy function which quantifies the difference between measurable quantities and their computed counterpart. Resulting minimization problem is solved through genetic algorithms, while the computational burden is made consistent with constraints of routine industrial applications by exploiting Reduced Order Model (ROM) based on proper orthogonal decomposition. Throughout minimization, a gradual enrichment of designed ROM is used, by including additional simulations. Such strategy turned out to be beneficial when applied to models with a large number of parameters. Developed procedure seems to be effective when dealing with complex constitutive models, that can give rise to non-continuous discrepancy function due to the numerical instabilities. Proposed approach is tested and experimentally validated on the calibration of modified Drucker-Prager CAP model, frequently adopted for ceramic powder pressing simulations. Assessed values are compared with those obtained by traditional, time-consuming tests, performed on pressed green bodies.

Investigation of the Effectiveness of Multi-Fidelity Surrogates on Extrapolation

Surrogates have been used as an approximate tool to emulate simulation responses based on a handful of response samples. However, for high fidelity simulations, often only a small number samples are affordable, and this increases the risk of extrapolation using surrogates. Frequently, most of the sampling domain is not in the interpolation domain (called coverage), usually defined as the convex hull of these samples. For example, when we build a surrogate with 20 samples in six-dimensional space, the coverage is merely 2% of the sampling domain. Multi-fidelity surrogates (MFS) may mitigate this problem, because they use large number of low fidelity simulations, so that most of the domain is covered with at least some simulations. This paper explores the extrapolation capability of MFS frameworks through examples including algebraic functions. To examine the effects of different MFS frameworks, we consider six MFS frameworks in terms of their functional forms and frameworks for fitting the forms to data. We consider three different functional forms based on different approaches: 1) a model discrepancy function, 2) model calibration, and 3) both. Bayesian MFS frameworks based on the functional forms are considered. We include also their counterparts in simple frameworks, which have the same functional form but can be built with ready-made surrogates. We examined the effect of the high fidelity sample coverage on extrapolation while the number of high fidelity samples remains the same. The root mean square errors (RMSE) of the interpolation and extrapolation domains are calculated to see their effectiveness on the overall RMSE of whole MFS. For the examples considered, we found that the presence of a regression scalar could be important to extrapolation. Bayesian framework is useful to find a good regression scalar, which simplifies the discrepancy function.

Remarks on Parameter Calibration and Model Validation Based on Sensitivity

In this paper, different approaches to parameter calibration and model validation were compared to understand the accuracy and robustness, especially when only a small number of data are available. Conventional one-point calibration, two-point calibration, sensitivity-based calibration, discrepancy-based calibration methods are compared when the number of data is less than three. An analytical example as well as a cantilever beam model are used to demonstrate the performance and accuracy of different methods. Numerical examples indicate that the conventional calibration method that does not account for the discrepancy function may lead to biased parameter and prediction models. It also can be seen that accurate parameter can be identified only when the form of discrepancy function is accurate.

Imaging from Internal Data

This chapter introduces efficient methods for reconstructing both the shape and the elasticity parameters of an inclusion using internal displacement measurements. It first considers the inverse problem of recovering the shape and the (constant) shear modulus of an inclusion from internal measurements. The small-volume asymptotic framework is used to separate the information in the measurements into a near-field and a far-field part. A discrepancy function is then presented and a regularization is discussed. The chapter proceeds by describing the more general case of shear distributions, taking into account the discrepancy between the measured and computed displacement fields. In order to write down a descent gradient scheme in the case of a heterogeneous shear distribution, the derivative of the discrepancy function with respect to the shear modulus is computed.

New KEMIRA Method for Determining Criteria Priority and Weights in Solving MCDM Problem

This study presents a new KEmeny Median Indicator Ranks Accordance (KEMIRA) method for determining criteria priority and selection criteria weights in the case of two separate groups of criteria for solving multiple criteria decision making (MCDM) problem. Kemeny median method is proposed to generalize experts' opinion. Medians are calculated applying three different measure functions. Criteria weights are calculated and alternatives ranking accomplished by solving optimization problem — minimization of ranks discrepancy function calculated for two groups of criteria. A numerical example for solving specific task of elite selection from security personnel is given to illustrate the proposed method.