A. G. Chassiakos

Identification of Nonlinear Dynamic Systems Using Neural Networks

This paper explores the potential of using parallel distributed processing methodologies (artificial neural networks) to identify the internal forces of structure unknown non linear dynamic systems

Development of adaptive modeling techniques for non-linear hysteretic systems

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.

Identification of the state equation in complex non-linear systems

Abstract Building on the basic idea behind the Restoring Force Method for the non-parametric identification of non-linear systems, a general procedure is presented for the direct identification of the state equation of complex non-linear systems. No information about the system mass is required, and only the applied excitation(s) and resulting acceleration are needed to implement the procedure. Arbitrary non-linear phenomena spanning the range from polynomial non-linearities to the noisy Duffing–van der Pol oscillator (involving product-type non-linearities and multiple excitations) or hysteretic behavior such as the Bouc–Wen model can be handled without difficulty. In the case of polynomial-type non-linearities, the approach yields virtually exact results for sufficiently rich excitations. For other types of non-linearities, the approach yields the optimum (in least-squares sense) representation in non-parametric form of the dominant interaction forces induced by the motion of the system. Several examples involving synthetic data corresponding to a variety of highly non-linear phenomena are presented to demonstrate the utility as well as the range of validity of the proposed approach.

On-Line Identification of Hysteretic Systems

Using adaptive estimation approaches, a method is presented for the on-line identification of hysteretic systems under arbitrary dynamic environments The availability of such an identification approach is crucial for the on-line control and monitoring of nonlinear structural systems to be actively controlled. In spite of the challenges encountered in the identification of the hereditary nature of the restoring force of such nonlinear systems, it is shown through the use of simulation studies and experimental measurements that the proposed approach can yield reliable estimates of the hysteretic restoring force under a very wide range of excitation levels and response ranges.

Robust Adaptive Neural Estimation of Restoring Forces in Nonlinear Structures

The availability of methods for on-line estimation and identification of structures is crucial for the monitoring and active control of time-varying nonlinear structural systems. Adaptive estimation approaches that have recently appeared in the literature for on-line estimation and identification of hysteretic systems under arbitrary dynamic environments are in general model based. In these approaches, it is assumed that the unknown restoring forces are modeled by nonlinear differential equations (which can represent general non-linear characteristics, including hysteretic phenomena). The adaptive methods estimate the parameters of the nonlinear differential equations on line. Adaptation of the parameters is done by comparing the prediction of the assumed model to the response measurement, and using the prediction error to change the system parameters. In this paper, a new methodology is presented which is not model based. The new approach solves the problem of estimating/identifying the restoring forces without assuming any model of the restoring forces dynamics, and without postulating any structure on the form of the underlying nonlinear dynamics. The new approach uses the Volterra/Wiener neural networks (VWNN) which are capable of learning input/output nonlinear dynamics, in combination with adaptive filtering and estimation techniques. Simulations and experimental results from a steel structure and from a reinforced-concrete structure illustrate the power and efficiency of the proposed method.

MODELLING UNKNOWN STRUCTURAL SYSTEMS THROUGH THE USE OF NEURAL NETWORKS

This paper explores the potential of using neural networks to identify the internal forces of typical systems encountered in the field of earthquake engineering and structural dynamics. After formulating the identification task as a neural network learning procedure, the method is applied to a representative chain-like system under deterministic and stochastic excitations. The neural network based identification method provides very good results for general classes of multi-degree-of-freedom structural systems. The range of validity of the approach is demonstrated, and some application issues are discussed for (a) partially known multi-degree-of-freedom systems and (b) completely unknown systems.

Identification of structural systems by neural networks

A method based on the use of neural networks is developed for the identification of systems encountered in the field of structural dynamics. The methodology is applied to the identification of linear and nonlinear dynamic systems such as the damped Duffing oscillator and the Van der Pol equation. The “generalization” ability of the neural networks is used to predict the response of the identified systems under deterministic and stochastic excitations. It is shown that neural networks provide high fidelity models of unknown structural dynamic systems, which are used in applications such as structural control, health monitoring of structures, earthquake engineering, etc.

Adaptive methods for identification of hysteretic structures

An adaptive method for the on-line identification of hysteretic structures under arbitrary dynamic environments is presented. In spite of the challenges encountered in the identification of the hereditary nature of the restoring force of hysteretic systems, it is shown that the proposed approach can yield reliable estimates of the hysteretic restoring force under a wide range of excitation levels and response ranges. The proposed method is verified through simulation studies and experimental tests conducted on a full-scale structural steel subassembly.

Neural network control of unknown systems

We show that for all unknown multi-input (MI) nonlinear systems that are affected by external disturbances, it is possible to construct a semi-global state-feedback stabilizer when the only information about the unknown system is that (A1) the system is robustly stabilizable, (A2) the state dimension of the system is known, (A3) the system vector-fields are at least C/sup 1/. The proposed stabilizer uses linear-in-the-weights neural networks whose synaptic weights are adaptively adjusted. Robust control Lyapunov functions (RCLF) and switching adaptive derivative feedback control are used. Using Lyapunov stability arguments, we show that the closed-loop system is stable and the state vector converges arbitrarily close to zero, provided that the controllers neural networks have a sufficiently large number of regressor terms, and that the controller parameters are appropriately chosen. It is worth noticing, that no growth conditions are imposed on the unknown system nonlinearities:also, the proposed approach does not require knowledge of the RCLF of the system. Moreover, although the proposed controller is a discontinuous one, the closed-loop system does not enter in sliding motions. However, the proposed controller might be a very conservative one and may result in very poor transient behavior and/or very large control inputs.