A discontinuous extended Kalman filter for non-smooth dynamic problems

Problems that result into locally non-differentiable and hence non-smooth state-space equations are often encountered in engineering. Examples include problems involving material laws pertaining to plasticity, impact and highly non-linear phenomena. Estimating the parameters of such systems poses a challenge, particularly since the majority of system identification algorithms are formulated on the basis of smooth systems under the assumption of observability, identifiability and time invariance. For a smooth system, an observable state remains observable throughout the system evolution with the exception of few selected realizations of the state vector. However, for a non-smooth system the observable set of states and parameters may vary during the evolution of the system throughout a dynamic analysis. This may cause standard identification (ID) methods, such as the Extended Kalman Filter, to temporarily diverge and ultimately fail in accurately identifying the parameters of the system. In this work, the influence of observability of non-smooth systems to the performance of the Extended and Unscented Kalman Filters is discussed and a novel algorithm particularly suited for this purpose, termed the Discontinuous Extended Kalman Filter (DEKF), is proposed

Preface

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Special Issue on Uncertainty Quantification and Propagation in Structural Systems

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Editorial: Robust Monitoring, Diagnostic Methods and Tools for Engineered Systems

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Fatigue monitoring and remaining lifetime prognosis using operational vibration measurements

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. © The Society for Experimental Mechanics, Inc. 2019

Fatigue assessment in steel railway bridges using output only vibration measurements and partial structural information

A novel methodological framework for the online fatigue lifetime assessment of steel railway bridges is presented in this paper. By adopting a simply supported beam model amenable to a moving force at a constant velocity, the framework presumes the availability of noise-corrupted structural vibration acceleration response measurements and formulates an online estimator that identifies the unknown (i) excitation force, (ii) structural information, which herein pertains to the modal damping ratio, and (iii) modal displacements and velocities. The estimated information is subsequently applied to the calculation of stresses in both measured and unmeasured locations and, thus, to the residual fatigue life estimation of the structure. The numerical results provide a significant indication of effectiveness and suggest further investigation. © Civil-Comp Press, 2016

Input-state-parameter estimation of structural systems from limited output information

A successive Bayesian filtering framework for addressing the joint input-state-parameter estimation problem is proposed in this study. Following the notion of analytical, rather than hardware redundancy, the envisaged scheme, (i) adopts realistic assumptions on the sensor network capacity; and (ii) allows for a certain degree of uncertainty in the structural information available throughout the life-cycle of the monitored structure. This uncertainty is quantitatively expressed via a parameter vector of known functional relationship to the structural matrices. An observer is accordingly established, which recombines the dual and unscented Kalman filters. The former aims at tackling the unknown structural excitations, while the latter solves the state and parameter estimation problem via an augmented state-space. An extensive parametric study on simulated structural systems under different measurement setups, excitation types and structural properties demonstrates the method's effectiveness. © 2019 Elsevier Lt

A general substructure-based framework for input-state estimation using limited output measurements

This paper presents a general framework for estimating the state and unknown inputs at the level of a system subdomain using a limited number of output measurements, enabling thus the component-based vibration monitoring or control and providing a novel approach to model updating and hybrid testing applications. Under the premise that the system subdomain dynamics are driven by the unknown (i) externally applied inputs and (ii) interface forces, with the latter representing the unmodeled system components, the problem of output-only response prediction at the substructure level can be tailored to a Bayesian input-state estimation context. As such, the solution is recursively obtained by fusing a Reduced Order Model (ROM) of the structural subdomain of interest with the available response measurements via a Bayesian filter. The proposed framework is without loss of generality established on the basis of fixed- and free-interface domain decomposition methods and verified by means of three simulated Wind Turbine (WT) structure applications of increasing complexity. The performance is assessed in terms of the achieved accuracy on the estimated unknown quantities. © 2020 The Author(s

EACS 2016 paper - LQR–UKF SEMI–ACTIVE CONTROL OF UNCERTAIN STRUCTURES

<div>EACS 2016 Paper No. 161</div><div><br></div>A novel semi-active control strategy for the effective vibration mitigation of structural systems of uncertain properties is introduced in this study. The implemented approach emerges through fusion of the Unscented Kalman filter (UKF), as a nonlinear observer, with the linear-quadratic regulator (LQR). The UKF is implemented towards the establishment of an adaptive joint state and parameter estimation problem, taking into account that numerical models of structural systems are often inadequate due to inherent uncertainties, such as noise and modeling errors, unknown system properties and influence of varying operational conditions. The improved state-space representation is accordingly fed into the LQR and a semi-active control scheme that utilizes clipping is applied. Since both estimation and control are executed within the same loop, particular attention is attributed to the derivation of the appropriate LQR strategy, pertaining to both the selection of optimal weight matrices and the real-time tuning of the control parameters. A simulated five-story shear-frame subject to earthquake motion serves as a case-study for validating the proposed methodology. The promising results encourage further investigation of the developed strategy, especially in regards to its real-time experimental implementation using semi-active actuators, such as magnetorheological dampers

Resonant metabarriers as seismic attenuators in granular media

Arrays of surface resonators forming so-called metabarriers are capable of converting seismic Rayleigh waves into less dangerous shear waves traveling in the bulk, attenuating the ground motion at the surface. However, this phenomenon pertains to resonant materials inserted in homogeneous media which feature properties rather different to those of natural soils. In this work, we experimentally investigate the ability of a resonant metabarrier embedded below the surface of an inhomogenous medium, i.e. a granular unconsolidated material, to attenuate the incoming surface waves. Although unable to diverge their propagation into the bulk, we find that surface resonators in granular media achieve attenuation of Rayleigh waves by up to 50 % around their resonant frequency. The findings can be used as a starting point for future real-scale implementations for seismic protection systems in stratified soils presenting an inhomogeneous stiffness profile at the seismic Rayleigh waves scale