New results on the generalized frequency response functions of nonlinear volterra systems described by NARX model

In order that the nth-order Generalized Frequency Response Function (GFRF) for nonlinear systems described by a NARX model can be directly written into a more straightforward and meaningful form in terms of the first order GFRF and model parameters, the nth-order GFRF is now determined by a new mapping function based on a parametric characteristic. This can explicitly unveil the linear and nonlinear factors included in the GFRFs, reveal clearly the relationship between the nth-order GFRF and the model parameters, and also the relationship between the nth-order GFRF and the first order GFRF. Some new properties of the GFRFs can consequently be developed. These new results provide a novel and useful insight into the frequency domain analysis of nonlinear systems

A new method for the design of energy transfer filters

This paper is concerned with the development of a new method for the design of Energy Transfer Filters (ETFs). ETFs are a new class of nonlinear filters recently proposed by the authors, which employ nonlinear effects to transfer signal energy from one frequency band to a different frequency location. The new method uses the powerful Orthogonal Least Squares (OLS) algorithm to solve the Least Squares problem associated with the design and compared with previous methods achieves much better filtering performance

Mapping from parametric characteristics to generalized frequency response functions of nonlinear systems

Based on the parametric characteristic of the nth-order GFRF (Generalised Frequency Response Function) for nonlinear systems described by an NDE (nonlinear differential equation) model, a mapping function from the parametric characteristics to the GFRFs is established, by which the nth-order GFRF can directly be written into a more straightforward and meaningful form in terms of the first order GFRF, i.e., an ndegree polynomial function of the first order GFRF. The new expression has no recursive relationship between different order GFRFs, and demonstrates some new properties of the GFRFs which can explicitly unveil the linear and nonlinear factors included in the GFRFs, and reveal clearly the relationship between the nth-order GFRF and its parametric characteristic, and also the relationship between the nth-order GFRF and the first order GFRF. The new results provide a novel and useful insight into the frequency domain analysis and design of nonlinear systems based on the GFRFs. Several examples are given to illustrate the theoretical results

New Methods for Structural Health Monitoring and Damage Localization

Structural Health Monitoring (SHM) is traditionally concerned with fitting sensors inside structural systems and analyzing the features of signals from the sensor measurements using appropriate signal processing techniques in order to reveal the systems’ health status. A significant change of signal features is often considered to be an indication of damage. However, generally speaking, these techniques often cannot distinguish normal structural changes due to variations in system environmental or operating conditions from the changes which are induced by damage. For example, transmissibility analysis is a widely used signal analysis method for SHM. But traditional transmissibility is determined by the ratio of the spectra of two different system outputs, which generally depends on the location of loadings on the system and is, consequently, affected by system environmental conditions. In order to solve this challenge, a series of studies are conducted in this PhD project. The objectives are to develop new SHM and damage localization methods, which can effectively address the effects of changing system environmental or operational conditions and have potential to be applied in practice to more effectively solve practical SHM and damage localization problems. First, a general baseline model based SHM method is developed in this thesis. This method can be used to address a wide class of SHM problems via a baseline modelling and baseline model based analysis. The method can systematically take the effects of system’s operating or environmental conditions such as, e.g., environmental temperature etc. on signal analysis into account, and can therefore solve relevant challenges. Both simulation studies and field data analyses have been conducted to demonstrate the performance of the proposed new technique. Moreover, new transmissibility analysis methods are proposed for the detection and location of damage with nonlinear features in Multi-Degree-Of-Freedom (MDOF) structural systems. These methods extend the traditional transmissibility analysis to the nonlinear case. More importantly, the methods are independent from the locations of loading inputs to the systems and, to a great extent, provide effective solutions to the above mentioned problems with traditional transmissibility analysis. Again both numerical simulation studies and experimental data analysis have been conducted to verify the effectiveness and demonstrate potential practical applications of the new methods. Based on the results of nonlinearity detection and localization, new guidelines are proposed for the application of transmissibility analysis based modal identification method to nonlinear structural systems, which have potential to be further developed into a new approach to transmissibility based nonlinear modal analysis. In summary, the present study has addressed a series of fundamental problems with SHM, especially, problems associated with how to deal with the effects of changing system environmental or operational conditions on SHM results. Experimental studies have demonstrated the potential and significance of these results in practical engineering applications

Frequency domain theory of nonlinear Volterra systems based on parametric characteristic analysis.

The frequency domain methods tor linear systems are well accepted by engineers and have been widely applied in engineering practice because the transfer function of linear systems can always provide a coordinate-free and equivalent description for system characteristics and are convenient to be used for the system analysis and design. Although the analysis and design of linear systems in the frequency domain have been well established and the frequency domain methods for nonlinear systems have aheady been investigated for many years, the frequency domain analysis for nonlinear systems is far from being fully developed