The Bouc-Wen hysteretic or memory-dependent model [1,2] is well known and very powerful because of its versatility and simplicity. It is a very concise model governed by a single non-linear differential equation that can be easily applied in several hysteretic phenomena in the fields of magnetism, electricity, materials and elasto-plasticity of solids. Examples include the response of reinforced concrete (RC) sections, steel sections, bolted connections, lead rubber bearings (LRB), friction pendulum systems (FPS) etc.

The common form of a one-degree-of-freedom Bouc-Wen model includes eight parameters that govern the size and shape of the hysteretic loops. It is shown that some plausible assumptions can reduce the number of parameters to six; however, the parameters may increase if the model is extended to include other phenomena, for example strength deterioration, stiffness degradation and pinching as for example in the response of RC sections.

A variety of methods have been applied to the identification problem, such as genetic algorithms, differential evolution, extended Kalman filters, reduced gradient methods, simplex methods, etc. Genetic algorithms (GAs) rovide a promising solution for two main reasons: first, GAs use only "payoff" data i.e. no derivative data, for the evolution of the population and second, they feature an inherent capability for massive parallel computing.

In this work a new variant genetic algorithm, the so-called sawtooth GA, is applied to the above problem. This GA combines a variable population size and periodic partial reinitialization of the population in a synergistic way to enhance performance. The algorithm is combined with a hill climbing technique for the best individual in order to calculate the final local optimum effectively.

It is shown that, although the complexity of the problem is significant, the above GA can quickly examine the search space and provide very good results for engineering purposes.

1

R.Bouc, "Forced vibration of mechanical systems with hysteresis", Proceedings of the Fourth Conference on Non-linear oscillation, Prague, Czechoslovakia, 1967.

2

Y.K. Wen, "Method for random vibration of hysteretic systems", J. Eng. Mech. ASCE 102, 249-263, 1976.

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