Convergence and frequency-domain analysis of a discrete first-order model reference adaptive controller

SUMMARY We study the convergence properties of a direct model reference adaptive control system by applying techniques from numerical analysis. In particular, a first-order discrete system coupled to a minimal control synthesis algorithm discretized by the one-step one-stage zero-order-hold sampling is studied. This results in a strongly non-linear dynamic system owing to the adaptive mechanism where stability at steady state, i.e. at the operating point, equates to successful control. This paper focuses on the convergence analysis of the overall dynamical system for understanding accuracy, stability and performance at steadystate. The local stability of the steady state solution is considered by linearizing the system in the neighbourhood of an operating point when the input is a step function. This analysis allows us to specify two gain space domains which define the region of local stability. Moreover, both the accuracy and the frequency-domain analyses give insight into the range of adaptive control weightings that results in optimal performance of the minimal control synthesis algorithm and also highlights a possible approach to a priori selection of the time step and adaptive weighting values. The effectiveness of the proposed analysis is further demonstrated by simulations and experiments on a first-order plant. Copyright # 2006 John Wiley & Sons, Ltd

The analysis of the Generalized-a method for non-linear dynamic problems

International audienceThis paper presents the consistency and stability analyses of the Generalized-α methods applied to non-linear dynamical systems. The second-order accuracy of this class of algorithms is proved also in the non-linear regime, independently of the quadrature rule for non-linear internal forces. Conversely, the G-stability notion which is suitable for linear multistep schemes devoted to non-linear dynamic problems cannot be applied, as the non-linear structural dynamics equations are not contractive. Nonetheless, it is proved that the Generalized-α methods are endowed with stability in an energy sense and guarantee energy decay in the high-frequency range as well as asymptotic annihilation. However, overshoot and heavy energy oscillations in the intermediate-frequency range are exhibited. The results of representative numerical simulations performed on relatively simple single- and multiple-degrees-of-freedom non-linear systems are presented in order to confirm the analytical estimates

Partitioned time integration methods for hardware in the loop based on linearly implicit L-Stable Rosenbrock methods

Hardware in the loop based on dynamic substructuring was conceived to be a hybrid numerical-experimental technique to simulate the non-linear behaviour of an emulated structure. Its challenge is to ensure that both numerical and physical substructures interact in real time by means of actuators –transfer systems-. With this objective in mind, the development and implementation of partitioned real-time compatible Rosenbrock algorithms are presented in this paper. In detail, we shortly introduce monolithic linearly implicit L-stable algorithms with two stages; and in view of the analysis of complex emulated structures, we present a novel interfield partitioned algorithm. Both the stability and accuracy properties of the proposed algorithm are examined through analytical and numerical studies carried out on Single-DoF model problems. Moreover, a novel test rig conceived to perform both linear and nonlinear substructure tests is introduced, and tests on a two-DoF split-mass system are illustrated. The drawbacks of this algorithm are underlined and improvements are introduced on a companion solution procedure

The accuracy of the Generalized-α method in the time integration of non-linear Single- and Two-DOF forced systems

International audienceThis paper deals with the accuracy of a numerical time integration scheme, the implicit Generalized- α method, when applied near resonant conditions in periodic steady-state vibrations of elastic linear and nonlinear systems. In order to evaluate errors, analytical solutions of Frequency Response Functions (FRFs) are determined by using the Harmonic Balance method in single- and two-degrees-of-freedom viscously damped systems, where the non-linearity is introduced through hardening Duffing oscillators. Successively, the Generalized-α method is implemented in conjunction with the Harmonic Balance method to trace numerical solutions of FRFs. It is shown that the effective resulting algorithm, the Algorithmic Harmonic Balance-ρ∞ method, can define non-linear FRFs and allows the errors exhibited by the integration scheme near resonance in terms of frequency location and amplitude of the resonant peak to be quantified. The accuracy estimates demonstrate the robustness of the Generalized-α method also in the forced case and confirm its capability to reproduce amplitudes at resonance in the low frequency range and damp out them in the high frequency range

An improved equivalent force control algorithm for hybrid seismic testing of nonlinear systems

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Performance-based Earthquake Evaluation of a Full-Scale Petrochemical Piping System

Assessment of seismic vulnerability of industrial petrochemical and oil & gas piping systems can be performed, beyond analytical tools, through experimental testing as well. Along this line, this paper describes an experimental test campaign carried out on a full-scale piping system in order to assess its seismic behaviour. In particular, a typical industrial piping system, containing several critical components, such as elbows, a bolted flange joint and a Tee joint, was tested under different levels of realistic earthquake loading. They corresponded to serviceability and ultimate limit states for support structures as suggested by modern performance-based earthquake engineering standards. The so called hybrid simulation techniques namely, pseudo-dynamic and real time testing with dynamic substructuring, were adopted to perform seismic tests. Experimental results displayed a favorable performance of the piping system and its components; they remained below their yielding, allowable stress and allowable strain limits without any leakage even at the Near Collapse limit state condition for the support structure. Moreover, the favourable comparison between experimental and numerical results, proved the validity of the proposed hybrid techniques alternative to shaking table tests

Identification of the hysteretic behaviour of a partial-strength steel-concrete moment-resisting frame structure subject to pseudodynamic tests

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Seismic vulnerability of above-ground storage tanks with unanchored support conditions for Na-tech risks based on Gaussian process regression

AbstractThis paper aims to investigate the seismic vulnerability of an existing unanchored steel storage tank ideally installed in a refinery in Sicily (Italy), along the lines of performance-based earthquake engineering. Tank performance is estimated by means of component-level fragility curves for specific limit states. The assessment is based on a framework that relies on a three-dimensional finite element (3D FE) model and a low-fidelity demand model based on Gaussian process regression, which allows for cheaper simulations. Moreover, to approximate the system response corresponding to the random variation of both peak ground acceleration and liquid filling level, a second-order design of experiments method is adopted. Hence, a parametric investigation is conducted on a specific existing unanchored steel storage tank. The relevant 3D FE model is validated with an experimental campaign carried out on a shaking table test. Special attention is paid to the base uplift due to significant inelastic deformations that occur at the baseplate close to the welded baseplate-to-wall connection, offering extensive information on both capacity and demand. As a result, the tank performance is estimated by means of component-level fragility curves for the aforementioned limit state which are derived through Monte Carlo simulations. The flexibility of the proposed framework allows fragility curves to be derived considering both deterministic and random filling levels. The comparison of the seismic vulnerability of the tank obtained with probabilistic and deterministic mechanical models demonstrates the conservatism of the latter. The same trend is also exhibited in terms of risk assessment

Finite element model updating of a semi‐rigid moment resisting structure

Partial-strength composite steel–concrete moment-resisting frame structures can be designed to develop a ductile response in components of beam-to-column joints and column bases, including flexural yielding of beam end plates, shear yielding of column web panel zones and yielding of anchors. To evaluate the performance of a statically indeterminate structure under different earthquake intensities, a series of pseudo-dynamic, quasi-static cyclic and vibration tests were carried out at the European Laboratory for Structural Assessment of the Joint Research Centre at Ispra, Italy. The identified modal parameters from forced vibration tests at three different damage levels were used in order to quantify local and global damage indices by updating a 3D FE model of the structure with the non-linear Powell's Dog-Leg optimization method. Then, the Latin Hypercube Sampling technique, a variant of the Monte Carlo method, was employed to study the sensitivity of the updated parameters of the 3D model to modal inputs, caused by measurement noise. Rotations of beam-to-column joints and column bases, storey displacements and forces were employed during the final cyclic test in order to update a 2D FE model of the test structure. To avoid numerical instabilities during the detection of the non-linear behaviour of the structure, a novel technique based on the transformation of the origin coordinates in each half cycle was implemented. The identified joint behaviours allowed low-cycle fatigue energy-based damage indices to be applied. Copyright © 2009 John Wiley & Sons, Ltd