Detecting the position of non-linear component in periodic structures from the system responses to dual sinusoidal excitations

Based on the Nonlinear Output Frequency Response Functions (NOFRFs), a novel method is developed to detect the position of nonlinear components in periodic structures. The detection procedure requires exciting the nonlinear systems twice using two sinusoidal inputs separately. The frequencies of the two inputs are different; one frequency is twice as high as the other one. The validity of this method is demonstrated by numerical studies. Since the position of a nonlinear component often corresponds to the location of defect in periodic structures, this new method is of great practical significance in fault diagnosis for mechanical and structural systems

Nonlinear structural damage detection based on cascade of Hammerstein models

Structural damages can result in nonlinear dynamical signatures that can significantly enhance their detection. An original nonlinear damage detection approach is proposed that is based on a cascade of Hammerstein models representation of the structure. This model is estimated by means of the Exponential Sine Sweep Method from only one measurement. On the basis of this estimated model, the linear and nonlinear parts of the output are estimated, and two damage indexes (DIs) are proposed. The first DI is built as the ratio of the energy contained in the nonlinear part of an output versus the energy contained in its linear part. The second DI is the angle between the subspaces obtained from the nonlinear parts of two set of outputs after a principal component analysis. The sensitivity of the proposed DIs to the presence of damages as well as their robustness to noise are assessed numerically on spring-mass-damper structures and experimentally on actual composite plates with surface-mounted PZT-elements. Results demonstrate the effectiveness of the proposed method to detect a damage in nonlinear structures and in the presence of noise

Crack detection using nonlinear output frequency response functions - an experimental study

The new concept of Nonlinear Output Frequency Response Functions (NOFRFs) is introduced in this paper to detect cracks in beams using frequency domain information. The results show that the NOFRFs are a sensitive indicator of the presence of cracks providing the excitation is of an appropriate strength. The new results provide a novel and effective method for the detection of cracks in beams, with applications in structural fault diagnosis

Analysis of bilinear oscillators under harmonic loading using nonlinear output frequency response functions

In this paper, the new concept of Nonlinear Output Frequency Response Functions (NOFRFs) is extended to the harmonic input case, an input-independent relationship is found between the NOFRFs and the Generalized Frequency Response Functions (GFRFs). This relationship can greatly simplify the application of the NOFRFs. Then, beginning with the demonstration that a bilinear oscillator can be approximated using a polynomial type nonlinear oscillator, the NOFRFs are used to analyze the energy transfer phenomenon of bilinear oscillators in the frequency domain. The analysis provides insight into how new frequency generation can occur using bilinear oscillators and how the sub-resonances occur for the bilinear oscillators, and reveals that it is the resonant frequencies of the NOFRFs that dominate the occurrence of this well-known nonlinear behaviour. The results are of significance for the design and fault diagnosis of mechanical systems and structures which can be described by a bilinear oscillator model

New techniques for vibration condition monitoring: Volterra kernel and Kolmogorov-Smirnov

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.This research presents a complete review of signal processing techniques used, today, in vibration based industrial condition monitoring and diagnostics. It also introduces two novel techniques to this field, namely: the Kolmogorov-Smirnov test and Volterra series, which have not yet been applied to vibration based condition monitoring. The first technique, the Kolmogorov-Smirnov test, relies on a statistical comparison of the cumulative probability distribution functions (CDF) from two time series. It must be emphasised that this is not a moment technique, and it uses the whole CDF, in the comparison process. The second tool suggested in this research is the Volterra series. This is a non-linear signal processing technique, which can be used to model a time series. The parameters of this model are used for condition monitoring applications. Finally, this work also presents a comprehensive comparative study between these new methods and the existing techniques. This study is based on results from numerical and experimental applications of each technique here discussed. The concluding remarks include suggestions on how the novel techniques proposed here can be improved.Brunel University Department of Mechanical Engineering and CAPES, Fundacao Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior

Resonances and resonant frequencies for a class of nonlinear systems

Resonant phenomena for a class of nonlinear systems, which can be described by a SDOF model with a polynomial type nonlinear stiffness, are investigated using Nonlinear Output Frequency Response Functions (NOFRFs). The concepts of resonance and resonant frequencies are proposed for the first time for a class of nonlinear systems. The effects of damping on the resonances and resonant frequencies are also analyzed. These results produce a novel interpretation of energy transfer phenomena in this class of nonlinear systems and show how the damping effect influences the system resonant frequencies and amplitudes. The results are important for the design and fault diagnosis of mechanical systems and structures which can be described by the SDOF nonlinear model

Nonlinear System Identification of Neural Systems from Neurophysiological Signals

The human nervous system is one of the most complicated systems in nature. Complex nonlinear behaviours have been shown from the single neuron level to the system level. For decades, linear connectivity analysis methods, such as correlation, coherence and Granger causality, have been extensively used to assess the neural connectivities and input-output interconnections in neural systems. Recent studies indicate that these linear methods can only capture a small amount of neural activities and functional relationships, and therefore cannot describe neural behaviours in a precise or complete way. In this review, we highlight recent advances in nonlinear system identification of neural systems, corresponding time and frequency domain analysis, and novel neural connectivity measures based on nonlinear system identification techniques. We argue that nonlinear modelling and analysis are necessary to study neuronal processing and signal transfer in neural systems quantitatively. These approaches can hopefully provide new insights to advance our understanding of neurophysiological mechanisms underlying neural functions. These nonlinear approaches also have the potential to produce sensitive biomarkers to facilitate the development of precision diagnostic tools for evaluating neurological disorders and the effects of targeted intervention

Efficient Multidimensional Regularization for Volterra Series Estimation

This paper presents an efficient nonparametric time domain nonlinear system identification method. It is shown how truncated Volterra series models can be efficiently estimated without the need of long, transient-free measurements. The method is a novel extension of the regularization methods that have been developed for impulse response estimates of linear time invariant systems. To avoid the excessive memory needs in case of long measurements or large number of estimated parameters, a practical gradient-based estimation method is also provided, leading to the same numerical results as the proposed Volterra estimation method. Moreover, the transient effects in the simulated output are removed by a special regularization method based on the novel ideas of transient removal for Linear Time-Varying (LTV) systems. Combining the proposed methodologies, the nonparametric Volterra models of the cascaded water tanks benchmark are presented in this paper. The results for different scenarios varying from a simple Finite Impulse Response (FIR) model to a 3rd degree Volterra series with and without transient removal are compared and studied. It is clear that the obtained models capture the system dynamics when tested on a validation dataset, and their performance is comparable with the white-box (physical) models

A Control Systems Perspective to Condition Monitoring and Fault Diagnosis

Modern industrial processors, engineering systems and structures, have grown significantly in complexity and in scale during the recent years. Therefore, there is an increase in the demand for automatic processors, to avoid faults and severe break downs, through predictive maintenance. In this context, the research into nonlinear systems analysis has attained much interest in recent years as linear models cannot be used to represent some of these systems. In the field of control systems, the analysis of such systems is conducted in the frequency domain using methods of Frequency Response Analysis. Generalised Frequency Response Functions (GFRFs) and the Nonlinear Output Frequency Response Functions (NOFRFs) are Frequency Response Analysis techniques used for the analysis of nonlinear dynamical behaviour in the frequency domain. The problem of Condition Monitoring and Fault Diagnosis has been investigated in the perspective of modelling, signal processing and multivariate statistical analysis, data-driven methods such as neural networks have gained significant popularity. This is because possible faulty conditions related to complex systems are often difficult to interpret. In such a background, recently, a new data-driven approach based on a systems perspective has been proposed. This approach uses a controls systems analysis method of System Identification and Frequency Response Analysis and has been shown before as a potential technique. However, this approach has certain practical concerns regarding real-world applications. Motivated by these concerns in this thesis, the following contributions are put forward: 1. The method of evaluating NOFRFs, using input-output data of a nonlinear system may experience numerical errors. This is a major concern, hence the development of a method to overcome these numerical issues effectively. 2. Frequency Response Analysis cannot be used in its current state for nonlinear systems that exhibit severe nonlinear behaviour. Although theoretically, it has been argued that this is possible, even though, it has been impossible in a practical point of view. Therefore, the possibility and the manner in which Frequency Response Analysis can be conducted for these types of systems is presented. 3. Development of a System Identification methodology to overcome the issues of inadequately exciting inputs and appropriately capturing system dynamics under general circumstances of Condition Monitoring and Fault Diagnosis. In addition to the above, the novel implementation of a control systems analysis approach is implemented in characterising corrosion, crack depth and crack length on metal samples. The approach is applied to the data collected, using a newly proposed non-invasive Structural Health Monitoring method called RFID (Radio Frequency IDentification) wireless eddy current probing. The control systems analysis approach along with the RFID wireless eddy current probing method shows the clear potential of being a new technology in non-invasive Structural Health Monitoring systems