Lucia Faravelli

Fuzzy control of structural vibration. An active mass system driven by a fuzzy controller

The authors are engaged in a long-term research project studying the potential of fuzzy control strategies for active structural control in civil engineering applications. The advantage of this approach is its inherent robustness and its ability to handle the non-linear behaviour of the structure. Moreover, the computations for driving the controller are quite simple and can easily be implemented into a fuzzy chip. In this paper attention is focused on the response of a three-storey frame, subjected to earthquake excitation, controlled by an active mass driver located on the top floor. The design and the implementation of the controller driving the AMD system are discussed.

Control of nonlinear structures using the fuzzy control approach

Active control of structures against environmental loads, such as earthquakes and wind, has received much attention in the last decade. Much of this research has involved development of control algorithms based on the assumption of exact knowledge of the system parameters, a condition that does not always exist in real-life applications. In addition, most of this research effort has focused upon linear control. Few active control strategies can effectively handle control of nonlinear behavior.Fuzzy logic control provides a promising opportunity for this purpose. This paper discusses the motivations for using a Fuzzy Logic Controller (FLC) and the guidelines for its design. A brief description of a FLC is first outlined to introduce the appropriate definitions. The application of fuzzy control to nonlinear structures is then illustrated. Some numerical examples are presented to study the controlled response of a hysteretic plane frame under earthquake loading.

A new philosophy for stochastic equivalent linearization

Abstract An extension, to the time-dependent situation, of what is known in static structural reliability as the ‘normal tail approximation’ is presented. This is pursued within the classical stochastic equivalent linearization scheme. Duffing and hysteretic oscillators are studied in detail.

Stochastic finite elements for crash problems

Abstract A stochastic finite element technique, based on the association of a response surface scheme with the “impact” finite-element code PAMCRASH , is implemented. The actual response is modelled by a piecewise idealization which combines several response surface interpolations. In such a way greater accuracy is obtained in the tails of the response probability distribution; the latter plays a basic role in reliability assessment. Crash problems are studied by analysing a structure representative, for frontal impact, of a classical automobile system. The structure is assumed to have stochastic properties and is studied during the crash against a rigid obstacle. The response variable of interest is the maximum value of the force on the rigid trolley-truck to which the system is connected.

Nonlinear State Observation for Cable Dynamics

We explore the applicability of non-linear state observation to cable dynamics. The aim is to capture from the minimal number of measurements a larger description of the state to be employed in active or semi-active control policies. To this end, a non-linear state observer is designed analytically, in the space of modal amplitudes, following relevant literature results. The main theory of non-linear state observation is preliminary reviewed and the applicability to the dynamics of structural cables is discussed, including asymptotic stability and minimal number of measurements. Next a sample non-resonant cable is considered and numerical simulations are carried out in order to test the observation error stability under different conditions. A non-collocated feedback control strategy, based on transversal actuation, is finally considered, in which the control algorithm is based on the estimated state variables. The with-observer control solution is compared with the ideal case in which the entire state of the system is known, thus highlighting the limits and potentialities of the proposed approach.

Log-likelihood maximization and response surface in reliability assessment

Nonlinear dynamics problems can generally be solved only in a numerical way. This prevents from a direct application of standard reliability methods. A technique which makes use of iterated response-surface analytical approximations of the system performance function was therefore proposed in view of reliability assessment. The limitation of this technique was of working in a standard normalized space, so that appropriate space transformations are preliminarly required.This paper shows how this response-surface iterative scheme can also be used in the original space of the random variables, provided a maximum log-likelihood constrained optimization problem is solved. Moreover, asymptotic theory also provides a better estimate of the probability of failure of the dynamical system against any assigned limit state.

Vulnerability assessment for medieval civic towers

The seismic vulnerability of an ancient civic bell tower is studied. Rather than seeing it as an intermediate stage towards a risk analysis, the assessment of vulnerability is here pursued for optimising the retrofit design. Vulnerability curves are drawn by carrying out a single time history analysis of a model calibrated based on experimental data. From the results of this analysis, the medians of three selected performance parameters are estimated, and they are used to compute, for each of them, the probability of exceeding or attaining the three corresponding levels of light, moderate and severe damage. For future development, the same model can be used to numerically implement the effects of different retrofitting solutions and to re-estimate the associated vulnerability curves. The ultimate goal is to provide a numerical tool able to drive the optimisation process of a retrofit design by the comparison of the vulnerability estimates associated with the different retrofitting solutions.

Reliability based stability analysis for actively controlled structures

Abstract The long-term goal of the research activity in progress is the optimization of control strategies under reliability objectives. Different control concepts and different reliability target formulations can be compared. In particular, reliability criteria based on crossing rates and on direct approximations of the maxima of random fields could be adopted. The direct method is based on an approximation of the underlying field by a finite expansion of shape functions. Stability is a basic property of a closed-loop system, it guarantees that the system will reach an equilibrium state after external or internal disturbances. In this paper, attention is focused on the stability analysis of a nonlinear control scheme. For this purpose, the significant values of the response variables are the ones at the time the external excitation stops. Measures of stability are derived by FORM/SORM methods as probabilities of starting the free vibration within an assigned region in the phase space. Sensitivity factors for the various system parameters are derived. The sensitivities are given in terms of the limit state functions at the maximum likelihood point.

Energy Dissipation in Shape Memory Alloy Devices

A way of reasoning to reduce the response of a structural system under dynamic excitation is to think in terms of energy dissipation via plastic deformation devices. The concept of recoverable plastic deformation opens the way to the application of smart materials and, in particular, of shape memory alloys (SMAs). The characterization of the Ti Ni alloy structural component, with a complete definition of its mechanical properties and assembling features, is discussed.

Methods of non-linear stochastic dynamics for the assessment of structural fragility☆

Abstract Some of the external events which can significantly contribute to the overall risk of a nuclear power plant, give rise to a dynamic excitation of the structural components which form the plant. The computation of the risk associated with these external events requires an investigation of the behaviour of the structural components beyond the elastic limit. The stochastic nature of the excitation, then, leads one to deal with a non-linear stochastic dynamic problem. No general method of solution exists for such a problem when large structural systems are considered, although classical methods of propagating uncertainty have been successfully employed. This paper investigates the possibility of formulating an approach founded on a suitable equivalent linearization technique. In particular the authors make operative a new method of fragility analysis to be applied directly to the linearized system. The numerical example considers a framed structural component: its aim is to show the degree of accuracy that can be reached by the approach formulated in the paper.