Development of adaptive modeling techniques for non-linear hysteretic systems

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Abstract

Adaptive estimation procedures have gained significant attention by the research community to perform real-time identification of non-linear hysteretic structural systems under arbitrary dynamic excitations. Such techniques promise to provide real-time, robust tracking of system response as well as the ability to track time variation within the system being modeled. An overview of some of the authors’ previous work in this area is presented, along with a discussion of some of the emerging issues being tackled with regard to this class of problems. The trade-offs between parametric-based modeling and non-parametric modeling of non-linear hysteretic dynamic system behavior are discussed. Particular attention is given to (1) the effects of over- and under-parameterization on parameter convergence and system output tracking performance, (2) identifiability in multi-degree-of-freedom structural systems, (3) trade-offs in setting user-defined parameters for adaptive laws, and (4) the effects of noise on measurement integration. Both simulation and experimental results indicating the performance of the parametric and non-parametric methods are presented and their implications are discussed in the context of adaptive structures and structural health monitoring.

Section snippets

Motivation

Problems involving the identification of structural systems exhibiting inelastic restoring forces with hereditary characteristics are widely encountered in the applied mechanics field. Representative examples include buildings under strong earthquake excitations, aerospace structures incorporating joints, and computer disk drives. Due to the hysteretic nature of the restoring force in such situations, the non-linear force cannot be expressed in the form of an algebraic function involving the

Problem formulation

The fundamental problem which will be considered here is the prediction of the restoring force of non-linear hysteretic structural elements, and the adaptive estimation of either a non-parametric or parametric model which describes the elements’ dynamic behavior. The prediction and parameter estimation is conducted based on the system's measured dynamic response (usually acceleration measurements).

The structural topologies which will be considered range in complexity from the simple SDOF system

Applications

Several applications of parametric and non-parametric identification are presented in the context of civil structures during strong excitations.

Integration of measured data and a priori assumptions

The adaptive identification schemes discussed here depend on measured data from the structural system response. Generally, only one of these signals is measured (usually acceleration), and the other two are obtained by integration and/or differentiation schemes. This is an old problem in the identification of both linear and non-linear systems, and has been considered by others. The problem is particularly important in the context of non-linear identification, because the non-linear restoring

Conclusions

The authors’ work in the area of adaptive modeling of non-linear hysteretic systems has been reviewed in general terms, with an emphasis on fundamental concepts which dictate needed developments in this important area of research. The advantages and disadvantages of parametric and non-parametric modeling approaches are presented and their complementary features discussed. The need for additional sensor information, such as direct velocity or displacement data in addition to the usual

Acknowledgements

This study was supported in part by grants from the US Air Force Office of Scientific Research, the National Science Foundation, and the Federal Emergency Management Agency.

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