New Methods for Analysis of Nonlinear Systems in the Frequency Domain with Applications in Condition Monitoring and Engineering Systems

The study of nonlinear systems has received great attention in recent years because of the necessity of dealing with practical problems that cannot be modelled by linear representations. Although the availability of greater computational power and advances in the field of system identification have allowed significant progresses towards modelling real world processes, a systematic method for understanding the systems characteristics is still an open problem. In this context, as has been demonstrated in many studies, the extension of the well-known concept of linear Frequency Response Function (FRF) to nonlinear systems are a significant potential solution. The condition monitoring problem is closely associated with the analysis of systems characteristics and can therefore be considered as part of this scenario. Modern industrial processes have grown significantly in both size and complexity, creating the demand for automatic systems that can aid human operators in the important task of recognising when the process is experiencing malfunctions. Although this problem has been studied from the perspective of a wide scope of disciplines, such as modelling, signal processing, intelligent systems and statistical analysis, in many cases, data oriented methods or generic problem solvers (such as neural networks) often have to be applied. This is because complicated system behaviours are often difficult to interpret so as to associate them with possible faulty conditions.nonlinear system analysis in the frequency domain, and studies the application of these new methods for solving condition monitoring problems. The principle is based on the idea that a nonlinear system formulation can be used to deal with situations of practical interest where nonlinear behaviour cannot be neglected and that the frequency domain analysis approach can be applied to conduct an in-depth study of the system properties for the purpose of characterising systems faulty behaviours. In order to apply this principle, several issues need to be addressed, including the evaluation of the frequency characteristics of nonlinear systems and the generation of useful features that allow an effective characterisation of faulty system conditions. Motivated by these needs, the following research studies are conducted in this thesis: In order to address these challenges, this thesis proposes new methods for nonlinear system analysis in the frequency domain, and studies the application of these new methods for solving condition monitoring problems. The principle is based on the idea that a nonlinear system formulation can be used to deal with situations of practical interest where nonlinear behaviour cannot be neglected and that the frequency domain analysis approach can be applied to conduct an in-depth study of the system properties for the purpose of characterising systems faulty behaviours. In order to apply this principle, several issues need to be addressed, including the evaluation of the frequency characteristics of nonlinear systems and the generation of useful features that allow an effective characterisation of faulty system conditions. Motivated by these needs, the following research studies are conducted in this thesis: 1 - Development of new methods that allow an eficient extraction of the frequency domain representations of nonlinear systems, namely, Generalised Frequency Response Functions (GFRFs) and Nonlinear Output Frequency Response Functions (NOFRFs). The thesis first derives a comprehensive methodology that allows an efficient and systematic extraction of GFRFs from a polynomial NARX (Nonlinear Auto-Regressive with eXogenous inputs) model. Then the same idea is used for addressing issues regarding the computation of NOFRFs, providing efficient algorithms that allow an effective determination of the NORRFs in both numerical and analytical forms. 2- Establishment of a condition monitoring framework based on the new GFRFs/NOFRFs evaluation methods. This framework is constructed over a practical background where physical knowledge about the system is scarce, although process history data is available. In this context, black-box models can be built and the system properties can be extracted by computing the system's GFRFs/NOFRFs via the newly proposed methods. These functions provide fundamental information for deriving useful features that can be used for characterising faults and building effective diagnosis systems. The effectiveness of the proposed methods has been verified by both simulation studies and real data analysis tests, demonstrating the advantage of the new condition monitoring framework for engineering applications. These studies significantly improve current frequency analysis methods for nonlinear systems and, at the same time, provide effective condition monitoring approaches for a wide range of engineering systems