Showing papers by "Costas Papadimitriou published in 2019"

Structural health monitoring and fatigue damage estimation using vibration measurements and finite element model updating

Abstract: In this work, a computational framework is proposed for fatigue damage estimation in structural systems by integrating operational experimental measurements in a high-fidelity, large-scale finite e...

Modeling Error Estimation and Response Prediction of a 10-Story Building Model Through a Hierarchical Bayesian Model Updating Framework

Abstract: In this paper a hierarchical Bayesian model updating approach is proposed for calibration of model parameters, estimation of modeling error, and response prediction of dynamic structural systems. The approach is especially suitable for civil structural systems where modeling errors are usually significant. The proposed framework is demonstrated through a numerical case study, namely a 10-story building model. The ‘measured data’ include the numerically simulated modal parameters of a frame model which represents the true structure. A simplified shear building model with significant modeling errors is then considered for model updating with stiffness of different structural components (substructures) chosen as updating parameters. In the proposed hierarchical Bayesian framework, updating parameters are assumed to follow a known distribution model (normal distribution is considered here) and are characterized by the distribution parameters (mean vector and covariance matrix). The error function, which is defined as the misfit between model-predicted and identified modal parameters, is also assumed to follow a normal distribution with unknown parameters. The hierarchical Bayesian approach is applied to estimate the stiffness parameter distributions with mean and covariance matrix referred to as hyperparameters, as well as the modeling error which is quantified by the mean and covariance of error function. Joint posterior probability distribution of all updating parameters is derived from the likelihood function and the prior distributions. A Metropolis-Hastings within Gibbs sampler is implemented to evaluate the joint posterior distribution numerically. Two cases of model updating are studied with Case 1 assuming a zero mean for the error function, and Case 2 considering a non-zero error mean. The response time history of the building to a ground motion is predicted using the calibrated shear building model for both cases and compared with the exact response (simulated). Good agreements between predictions and measurements are observed for both cases with better accuracy in Case 2. This verifies the proposed hierarchical Bayesian approach for model calibration and response prediction and underlines the importance of considering and propagating the uncertainties of structural parameters and more importantly modeling errors.

Data-Driven Uncertainty Quantification and Propagation in Structural Dynamics through a Hierarchical Bayesian Framework

Abstract: In the presence of modeling errors, the mainstream Bayesian methods seldom give a realistic account of uncertainties as they commonly underestimate the inherent variability of parameters. This problem is not due to any misconception in the Bayesian framework since it is absolutely robust with respect to the modeling assumptions and the observed data. Rather, this issue has deep roots in users' inability to develop an appropriate class of probabilistic models. This paper bridges this significant gap, introducing a novel Bayesian hierarchical setting, which breaks time-history vibrational responses into several segments so as to capture and identify the variability of inferred parameters over multiple segments. Since computation of the posterior distributions in hierarchical models is expensive and cumbersome, novel marginalization strategies, asymptotic approximations, and maximum a posteriori estimations are proposed and outlined under a computational algorithm aiming to handle both uncertainty quantification and propagation tasks. For the first time, the connection between the ensemble covariance matrix and hyper distribution parameters is characterized through approximate estimations. Experimental and numerical examples are employed to illustrate the efficacy and efficiency of the proposed method. It is observed that, when the segments correspond to various system conditions and input characteristics, the proposed method delivers robust parametric uncertainties with respect to unknown phenomena such as ambient conditions, input characteristics, and environmental factors.

Detection of arterial wall abnormalities via Bayesian model selection

Abstract: Patient-specific modelling of haemodynamics in arterial networks has so far relied on parameter estimation for inexpensive or small-scale models. We describe here a Bayesian uncertainty quantificat...

Optimal sensor placement for artificial swimmers

Abstract: Natural swimmers rely for their survival on sensors that gather information from the environment and guide their actions. The spatial organization of these sensors, such as the visual fish system and lateral line, suggests evolutionary selection, but their optimality remains an open question. Here, we identify sensor configurations that enable swimmers to maximize the information gathered from their surrounding flow field. We examine two-dimensional, self-propelled and stationary swimmers that are exposed to disturbances generated by oscillating, rotating and D-shaped cylinders. We combine simulations of the Navier-Stokes equations with Bayesian experimental design to determine the optimal arrangements of shear and pressure sensors that best identify the locations of the disturbance-generating sources. We find a marked tendency for shear stress sensors to be located in the head and the tail of the swimmer, while they are absent from the midsection. In turn, we find a high density of pressure sensors in the head along with a uniform distribution along the entire body. The resulting optimal sensor arrangements resemble neuromast distributions observed in fish and provide evidence for optimality in sensor distribution for natural swimmers.

Bayesian Finite Element Model Updating

Abstract: In this chapter, the implementation of the reduced-order models within Bayesian finite element model updating is explored. The Bayesian framework for model parameter estimation, model selection, and robust predictions of output quantities of interest is first presented. Bayesian asymptotic approximations and sampling algorithms are then outlined. The framework is implemented for updating linear and nonlinear finite element models in structural dynamics using vibration measurements consisting of either identified modal frequencies or measured response time histories. For asymptotic approximations based on modal properties, the formulation for the posterior distribution is presented with respect to the modal properties of the reduced-order model. In addition, analytical expressions for the required gradients with respect to the model parameters are provided using adjoint methods. Two applications demonstrate that drastic reductions in computational demands can be achieved without compromising the accuracy of the model updating results. In the first application, a high-fidelity linear finite element model of a full-scale bridge with hundreds of thousands of degrees-of-freedom (DOFs) is updated using experimentally identified modal properties. In the second application, a nonlinear model of a base-isolated building is updated using acceleration response time histories.

Hierarchical Bayesian Calibration and Response Prediction of a 10-Story Building Model

Abstract: This paper presents Hierarchical Bayesian model updating of a 10-story building model based on the identified modal parameters. The identified modal parameters are numerically simulated using a frame model (exact model) of the considered 10-story building and then polluted with Gaussian white noise. Stiffness parameters of a simplified shear model~- representing modeling errors - are considered as the updating parameters. In the Hierarchical Bayesian framework, the stiffness parameters are assumed to follow a probability distribution (e.g., normal) and the parameters of this distribution are updated as hyperparameters. The error functions are defined as the difference between model-predicted and identified modal parameters of the first few modes and are also assumed to follow a predefined distribution (e.g., normal) with unknown parameters (mean and covariance) which will also be estimated as hyperparameters. The Metropolis-Hastings within Gibbs sampler is employed to estimate the updating parameters and hyperparameters. The uncertainties of structural parameters as well as error functions are propagated in predicting the modal parameters and response time histories of the building.

Optimal sensing for fish school identification

Abstract: Fish schooling implies an awareness of the swimmers for their companions. In flow mediated environments, in addition to visual cues, pressure and shear sensors on the fish body are critical for providing quantitative information that assists the quantification of proximity to other swimmers. Here we examine the distribution of sensors on the surface of an artificial swimmer so that it can optimally identify a leading group of swimmers. We employ Bayesian experimental design coupled with two-dimensional Navier Stokes equations for multiple self-propelled swimmers. The follower tracks the school using information from its own surface pressure and shear stress. We demonstrate that the optimal sensor distribution of the follower is qualitatively similar to the distribution of neuromasts on fish. Our results show that it is possible to identify accurately the center of mass and even the number of the leading swimmers using surface only information.

Fatigue Monitoring and Remaining Lifetime Prognosis Using Operational Vibration Measurements

Abstract: A framework is presented for real-time monitoring of fatigue damage accumulation and prognosis of the remaining lifetime at hotspot locations of new or existing structures by combining output-only vibration measurements from a permanently installed, optimally located, sparse sensor network with the information build into high-fidelity computational mechanics models. To produce fatigue damage accumulation maps at component and/or system level, valid for the monitoring period, the framework integrates developments in (a) fatigue damage accumulation (FDA) and (b) stress time histories predictions under loading and structural modeling uncertainties based on monitoring information (Papadimitriou et al., Struct Control Health Monit 18(5):554–573, 2011). Methods and computational tools include, but are not limited to, the use of Kalman-type filters for state and stress response reconstruction based on the sensor information (Eftekhar Azam et al., Mech Syst Signal Process 60:866–886, 2015; Lourens et al., Mech Syst Signal Process 29:310–327, 2012), as well as stress cycle counting techniques, S-N curves and fatigue damage accumulation laws (Miner, Appl Mech Trans (ASME) 12(3):159–164, 1945; Palmgren, VDI-Z 68(14):339–341, 1924) to estimate fatigue from the reconstructed stress time histories at numerous hot spot locations. The FDA maps provide realistic fatigue estimates consistent with the actual operational conditions experienced by an individual structure. Combined with models of future loading events and their uncertainties, assumed or rationally estimated during the long-term monitoring period, the continuously updated FDA maps can be used to predict the remaining fatigue lifetime maps and associated uncertainties. Developments are valuable for planning cost-effective maintenance strategies, eventually reducing the life-cycle maintenance cost.

Implications of subsoil-foundation stiffness on the dynamic characteristics of a monitored bridge

Abstract: Model updating based on system identification (SI) results is a well-established procedure to evaluate the reliability of a developed numerical model. In this inverse assessment problem, soil-found...

Reliability Analysis of Dynamical Systems

Abstract: The use of reduced-order models in the context of reliability analysis of dynamical systems under stochastic excitation is explored in this chapter. A stochastic excitation model based on a point-source model is introduced, and it is used for the generation of ground motions. The corresponding reliability analysis represents a high-dimensional reliability problem whose solution is carried out by an advanced simulation technique. Two application problems are considered in order to evaluate the effectiveness of the proposed model reduction technique. The first example consists of a two-dimensional frame structure, while the second example considers an involved nonlinear finite element building model. The results show that an important reduction in computational effort can be achieved without compromising the accuracy of the reliability estimates.

On the Potential of Dynamic Sub-structuring Methods for Model Updating

Abstract: While purely data-driven assessment is feasible for the first levels of the Structural Health Monitoring (SHM) process, namely damage detection and arguably damage localization, this does not hold true for more advanced processes. The tasks of damage quantification and eventually residual life prognosis are invariably linked to availability of a representation of the system, which bears physical connotation. In this context, it is often desirable to assimilate data and models, into what is often termed a digital twin of the monitored system. One common take to such an end lies in exploitation of structural mechanics models, relying on use of Finite Element approximations. proper updating of these models, and their incorporation in an inverse problem setting may allow for damage quantification and localization, as well as more advanced tasks, including reliability analysis and fatigue assessment. However, this may only be achieved by means of repetitive analyses of the forward model, which implies considerable computational toll, when the model used is a detailed FE representation. In tackling this issue, reduced order models can be adopted, which retain the parameterisation and link to the parameters regulating the physical properties, albeit greatly reducing the computational burden. In this work a detailed FE model of a wind turbine tower is considered, reduced forms of this model are found using both the Craig Bampton and Dual Craig Bampton methods. These reduced order models are then used and compared in a Transitional Markov Chain Monte Carlo procedure to localise and quantify damage which is introduced to the system.

Model Reduction Techniques for Structural Dynamic Analyses

Abstract: This chapter presents a model reduction technique based on substructure coupling for dynamic analysis. The dynamic behavior of the substructures is described by a set of dominant fixed-interface normal modes along with a set of interface constraint modes that account for the coupling at each interface where the substructures are connected. Based on these modes, the corresponding reduced-order matrices are derived. The internal dynamic behavior of the substructures is then enhanced by consideration of the contribution of residual fixed-interface normal modes. Next, the interface degrees of freedom are reduced by consideration of a small number of characteristic constraint modes. Pseudo-codes are provided in order to illustrate how the reduced-order matrices are constructed, by including dominant and residual fixed-interface normal modes as well as interface reduction. Finally, the dynamic response of reduced-order models is discussed.

Parametrization of Reduced-Order Models Based on Global Interface Reduction

Abstract: An interpolation scheme for approximating the interface modes in terms of the model parameters is presented in this chapter. The approximation scheme involves a set of support points in the model parameters space and a number of interpolation coefficients that are determined by the singular value decomposition technique. The approximate interface modes are combined with the parametrization scheme introduced in Chap. 2 to derive the corresponding reduced-order matrices. Pseudo-codes are provided to illustrate how the interface modes are approximated and how the parametrization of the reduced-order matrices is constructed based on interface reduction.

Reliability-Based Design Optimization

Abstract: The solution of reliability-based design optimization problems by using reduced-order models is considered in this chapter. Specifically, problems involving high-dimensional stochastic dynamical systems are analyzed. The design process is formulated in terms of a constrained nonlinear optimization problem, which is solved by a class of interior point algorithms based on feasible directions. Search directions are estimated in an efficient manner as a by-product of reliability analyses. The design process generates a sequence of steadily-improved feasible designs. Three numerical examples are presented to evaluate the performance of the interior point algorithm and the effectiveness of reduced-order models in the context of complex reliability-based optimization problems. High speedup values can be obtained for the design process without changing the accuracy of the final designs.

Reliability Sensitivity Analysis of Dynamical Systems

Abstract: The reliability sensitivity analysis of systems subjected to stochastic loading is considered in this chapter. In particular, the change that the probability of failure undergoes due to changes in the distribution parameters of the uncertain model parameters is utilized as a sensitivity measure. A simulation-based approach that corresponds to a simple post-processing step of an advanced sampling-based reliability analysis is used to perform the sensitivity analysis. In particular, subset simulation, introduced in the previous chapter, is applied in the present formulation. The analysis does not require any additional system response evaluations. The feasibility and effectiveness of the approach is demonstrated on a finite element model of a bridge under stochastic ground excitation. The sensitivity analysis is carried out in a reduced space of generalized coordinates. The computational effort involved in the reliability sensitivity analysis of the reduced-order model is significantly decreased with respect to the corresponding analysis of the full finite element model. The reduction is accomplished without compromising the accuracy of the reliability sensitivity estimates.

Quantification of Aleatory Uncertainty in Modal Updating Problems using a New Hierarchical Bayesian Framework

Abstract: Financial support from the Hong Kong research grants councils under grant numbers 16234816 and 16212918 is gratefully appreciated. The last author gratefully acknowledges the European Commission for its support of the Marie Sklodowska Curie program through the ETN DyVirt project (GA 764547). This paper is completed as a part of the second author’s PhD dissertation conducted jointly at Sharif University of Technology and the Hong Kong University of Science and Technology. The second author would like to gratefully appreciate kind support and supervision of Professor Fayaz R. Rofooei at Sharif University of Technology. We would also like to express our sincere appreciation to Professor Chih-chen Chang for generously sharing sensors, prototypes, and laboratory facilities.

A New Online Bayesian Approach for the Joint Estimation of State and Input Forces using Response-only Measurements

Abstract: Financial support from the Hong Kong research grants councils under grant numbers 16234816 and 16212918 is gratefully appreciated. The last author gratefully acknowledges the European Commission for its support of the Marie Sklodowska Curie program through the ETN DyVirt project (GA 764547). This paper is completed as a part of the second authors PhD dissertation conducted jointly at Sharif University of Technology and the Hong Kong University of Science and Technology. The second author would like to gratefully appreciate kind support and supervision of Professor Fayaz R. Rofooei at Sharif University of Technology.

Parametrization of Reduced-Order Models Based on Normal Modes

Abstract: This chapter deals with the parametrization of reduced-order models based on dominant and residual fixed-interface normal modes, in terms of model parameters. The division of the original structure is guided by a parametrization scheme, which assumes that the substructure matrices for each of the introduced linear substructures depend on only one of the model parameters. Based on this assumption, a global parametrization of the reduced-order matrices is provided. Invariant issues are discussed that are related to the matrices that account for the contribution of residual normal modes. A pseudo-code is then provided in order to illustrate how the parametrization of the reduced-order matrices is constructed.