Proposed Framework of Building Nonlinear Models: A Study using the Bouc-Wen Hysteretic Model

Nonlinear models are useful tools in current engineering practice for benefits such as cost savings and improved safety features, especially for testing, designing and maintenance of engineering services. Such models have been widely used for understanding the physics of systems and structures, predictions of abnormalities, predictions of specific scenarios to enable control and for planning of production. Having the correct fit-for-purpose model is very important for the model to be utilised in any of the functions as required, which enables accurate understanding and predictions of the real system to be modelled.
The work presented in this thesis is concerned with proposing a framework for building a fit-for-purpose nonlinear model using the Bouc-Wen model of hysteresis as an example nonlinear model to be identified.
The proposed framework is presented with steps suggested for the understanding of the requirements and purpose of building a nonlinear model. This is the main idea of the thesis where sufficient initial understanding of a problem will lead to experimental design to be able to provide the right sets of data to fit the purpose of the model to be built.
Using a variant of the Differential Evolution algorithm, the inputs of data sets for identification or parameter estimation were investigated. The investigation compared the input magnitudes, input types and noise levels to show that the result of identification can be misleading without a real understanding of the model requirements. This shows the importance of the specification of model requirements suggested in the framework. A measure of Improvement Ratio is also suggested to improve confidence of nonlinear parameter estimation by way of evaluation against linear parameter estimates.
Finally, a Volterra series approximation method for nonlinear polynomial models is used to estimate the parameters of the Bouc-Wen hysteretic model. It is shown that only linear parameters can be identified accurately in the presence of noise. Another key finding relates the nonlinear parameters to parameters of a nonlinear polynomial model to show some physical resemblance to the nonlinear polynomial damping and stiffness term, further work is required to truly understand this.