Nonlinear Time-Frequency Control Theory with Applications

Nonlinear control is an important subject drawing much attention. When a nonlinear system undergoes route-to-chaos, its response is naturally bounded in the time-domain while in the meantime becoming unstably broadband in the frequency-domain. Control scheme facilitated either in the time- or frequency-domain alone is insufficient in controlling route-to-chaos, where the corresponding response deteriorates in the time and frequency domains simultaneously. It is necessary to facilitate nonlinear control in both the time and frequency domains without obscuring or misinterpreting the true dynamics. The objective of the dissertation is to formulate a novel nonlinear control theory that addresses the fundamental characteristics inherent of all nonlinear systems undergoing route-to-chaos, one that requires no linearization or closed-form solution so that the genuine underlying features of the system being considered are preserved. The theory developed herein is able to identify the dynamic state of the system in real-time and restrain time-varying spectrum from becoming broadband. Applications of the theory are demonstrated using several engineering examples including the control of a non-stationary Duffing oscillator, a 1-DOF time-delayed milling model, a 2-DOF micro-milling system, unsynchronized chaotic circuits, and a friction-excited vibrating disk. Not subject to all the mathematical constraint conditions and assumptions upon which common nonlinear control theories are based and derived, the novel theory has its philosophical basis established in the simultaneous time-frequency control, on-line system identification, and feedforward adaptive control. It adopts multi-rate control, hence enabling control over nonstationary, nonlinear response with increasing bandwidth ? a physical condition oftentimes fails the contemporary control theories. The applicability of the theory to complex multi-input-multi-output (MIMO) systems without resorting to mathematical manipulation and extensive computation is demonstrated through the multi-variable control of a micro-milling system. The research is of a broad impact on the control of a wide range of nonlinear and chaotic systems. The implications of the nonlinear time-frequency control theory in cutting, micro-machining, communication security, and the mitigation of friction-induced vibrations are both significant and immediate

Induction Motor Bearing Fault Detection Using a Fractal Approach

Fault detection is an important research area in mechanical engineering. Literature surveys indicate that bearing failures are considered the most common failure modes in motors. Various faults related to bearings can be categorized into single-point defects or generalized roughness defects. In many research studies, monitoring methods based on vibration signals are used to detect single-point bearing failures. Depending on which bearing surface contains the fault, the characteristic vibration frequencies can be calculated from the rotor speed and the bearing geometry. It also has been demonstrated that stator current monitoring can provide the same indication without requiring access to the motor. The combination of phase space reconstruction and fractal theory may provide an effective approach to detect bearing generalized roughness faults in induction motors by assembling the estimation of dynamic invariant properties of a nonlinear system. In mathematics, a delay embedding theorem gives the conditions under which a chaotic dynamical system can be reconstructed from a sequence of observations of the state of a dynamical system by lagging the time series to embed it in more dimensions. One can determine the delay time by calculating mutual information with equality distant space cells. False nearest neighbors provides a robust way to determine necessary embedding dimensions. Almost all chaotic systems have a quantifying measurement known as a fractal dimension which is extracted from the original or reconstructed phase space. There are many specific forms of fractal dimension. In this research, correlation dimension is used to estimate the dimension of attractors in nonlinear dynamical systems. Taking the result of Fourier based analysis as a reference for fault detection, experimental results show that the proposed method is as effective in detecting bearing generalized roughness faults in induction motors

Predictive Maintenance of Circuit Breakers

For predictive maintenance of circuit breakers, a number of variables must be considered in order to assess the genuine working condition of a circuit breaker [CB]. This thesis selects vibration signatures obtained on the operating mechanisms and arcing chambers as a source of monitoring breaker conditions. The task of analyzing the behavior of a circuit breaker is perennial and difficult but the thesis has an attempt to tackle this problem. Experiments have been devised to monitor CBs; however, these have limitations details of which will be discussed. For example, each circuit breaker has its own unique vibration signature and the shape of the vibration may be different even though breakers confront similar problems. CBs have decades-long service life spans and failure rates are relatively low. Those that fail are not necessarily saved and there have been relatively few samples to base evidence upon. There are different vibration analysis algorithms available including Dynamic Time Warping [DTW], Resolution Ratio [RR], Discrete Envelope Statistics [DES], event time extraction, Chi-square based shape methods, and fractal theory. Some of these algorithms are based on acoustic properties of materials and rely on assessing extracted time component and the frequency components are extracted. This research applies multi-resolution analysis [MRA] to decomposed signals to in order to assess different sub-wave levels so that wave features may be captured and modeled. There are many ways to analyze the waves. This thesis uses optimizing fuzzy rules with genetic algorithm [GA] as the proposed method. The simuation part of the thesis uses spring performance as an example of how vibration signature analysis may be implemented. Spring vibrations are evaluated by two classification algorithms: Dynamic Time Warping [DTW] and multi-resolution analysis [MRA] with optimizing fuzzy rules with genetic algorithm [GA]. The first method is competent to identify the faulty cases from the normal ones by looking at the deviation of the vibration signature frequency content. In contrast, it is not capable to identify the degree of how bad it performs from looking at the frequency variation. For the second method, it is capable of not only classifying the abnormal cases from the normal cases, but also distinguishing the vibration signatures into different category so that the spring condition can be retrieved immediately. Fuzzy rules is capable of classify a new case to a category and genetic algorithm is an effective tool to minimize the applicable fuzzy rules. The accuracy of the identification is very satisfactory, which is over 90%. Consequently, the proposed algorithm is very useful for asset management purpose of breaker since the lifespan of the spring is known. Diagnostic technicians are able to make decision on the replacement scheme of the spring. There are some areas that this research uncovered that suggests further study is mandated. For example, there are other parameters that can be monitored and compared other than spring constant such as valve position in trip coil and close coil, acceleration parameter in changeover valves, damping in hydraulic cylinders and mechanical linkages, gas pressure in primary contacts and breaker resistance in line system

FaultFace: Deep Convolutional Generative Adversarial Network (DCGAN) based Ball-Bearing Failure Detection Method

Failure detection is employed in the industry to improve system performance and reduce costs due to unexpected malfunction events. So, a good dataset of the system is desirable for designing an automated failure detection system. However, industrial process datasets are unbalanced and contain little information about failure behavior due to the uniqueness of these events and the high cost for running the system just to get information about the undesired behaviors. For this reason, performing correct training and validation of automated failure detection methods is challenging. This paper proposes a methodology called FaultFace for failure detection on Ball-Bearing joints for rotational shafts using deep learning techniques to create balanced datasets. The FaultFace methodology uses 2D representations of vibration signals denominated faceportraits obtained by time-frequency transformation techniques. From the obtained faceportraits, a Deep Convolutional Generative Adversarial Network is employed to produce new faceportraits of the nominal and failure behaviors to get a balanced dataset. A Convolutional Neural Network is trained for fault detection employing the balanced dataset. The FaultFace methodology is compared with other deep learning techniques to evaluate its performance in for fault detection with unbalanced datasets. Obtained results show that FaultFace methodology has a good performance for failure detection for unbalanced datasets

A Review of Non-Invasive Techniques to Detect and Predict Localised Muscle Fatigue

Muscle fatigue is an established area of research and various types of muscle fatigue have been investigated in order to fully understand the condition. This paper gives an overview of the various non-invasive techniques available for use in automated fatigue detection, such as mechanomyography, electromyography, near-infrared spectroscopy and ultrasound for both isometric and non-isometric contractions. Various signal analysis methods are compared by illustrating their applicability in real-time settings. This paper will be of interest to researchers who wish to select the most appropriate methodology for research on muscle fatigue detection or prediction, or for the development of devices that can be used in, e.g., sports scenarios to improve performance or prevent injury. To date, research on localised muscle fatigue focuses mainly on the clinical side. There is very little research carried out on the implementation of detecting/predicting fatigue using an autonomous system, although recent research on automating the process of localised muscle fatigue detection/prediction shows promising results

Analysis and processing of mechanically stimulated electrical signals for the identification of deformation in brittle materials

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The fracture of brittle materials is of utmost importance for civil engineering and seismology applications. A different approach towards the aim of early identification of fracture and the prediction of failure before it occurs is attempted in this work. Laboratory experiments were conducted in a variety of rock and cement based material specimens of various shapes and sizes. The applied loading schemes were cyclic or increasing and the specimens were tested to compression and bending type loading of various levels. The techniques of Pressure Stimulated Current and Bending Stimulated Current were used for the detection of electric signal emissions during the various deformation stages of the specimens. The detected signals were analysed macroscopically and microscopically so as to find suitable criteria for fracture prediction and correlation between the electrical and mechanical parameters. The macroscopic proportionality of the mechanically stimulated electric signal and the strain was experimentally verified, the macroscopic trends of the PSC and BSC electric signals were modelled and the effects of material memory to the electric signals were examined. The current of a time-varying RLC electric circuit was tested against experimental data with satisfactory results and it was proposed as an electrical equivalent model. Wavelet based analysis of the signal revealed the correlation between the frequency components of the electric signal and the deformation stages of the material samples. Especially the increase of the high frequency component of the electric signal seems to be a good precursor of macrocracking initiation point. The additional electric stimulus of a dc voltage application seems to boost the frequency content of the signal and reveals better the stages of cracking process. The microscopic analysis method is scale-free and thus it can confront with the problems of size effects and material properties effects. The AC conductivity time series of fractured and pristine specimens were also analysed by means of wavelet transform and the spectral analysis was used to differentiate between the specimens. A non-destructive technique may be based on these results. Analysis has shown that the electric signal perturbation is an indicator of the forthcoming fracture, as well as of the fracture that has already occurred in specimens.The National Foundation of Scholarships (IKY) Greec

Analysis of stationary and non-stationary phenomena in turbulent subcritical flow behind two parallel cylinders

This study presents the analysis of the bistable phenomenon for turbulent flows around two cylinders side-by-side using two methods for data analysis and chaos theory for dynamic analysis. The experimental data were acquired for various Reynolds numbers and pitch-todiameter ratio p/D of 1.16, 1.26, and 1.60, cylinders diameter was 25.1 mm. The experimental technique consists of measuring the velocity fluctuations in an aerodynamic channel using hot-wire anemometry. The study presents the application of the Hilbert-Huang transform (HHT) as a tool of analysis for non-stationary and non-linear signals. The method was first validated using single cylinders and then extended for two cylinders side-by-side. Results show that the HHT method may provide information about particular events in timefrequency space and about the physics of flow scales. The statistical analysis of the experimental data is performed to identify statistical patterns that can be used to characterize the bistable flow. The signals are scanned by a moving window for the statistical analysis, creating blocks of probability density functions (PDFs). The four first statistical moments of each PDF are calculated, and a tendency of behavior based on their variations is established. The dynamics of the bistable flow system are studied applying chaos theory tools, like the largest Lyapunov exponent. The strange attractors of the velocity-time series are reconstructed, and their topology is useful to understand the physics of the bistable system. Each flow wake mode is analyzed separately. A general model of the bistable flow is reconstructed using probability functions. The application of a set of tools in the analysis of the turbulent wake behind cylinders is useful for the comprehension of turbulent phenomena, producing meaningful results and allowing the identification of turbulent structures and flow scales, and a better understanding of the system dynamics.Este estudo apresenta a análise do fenômeno da biestabilidade no escoamento em torno de dois cilindros lado a lado usando dois métodos para análise de sinais, e teoria do caos para a análise da dinâmica. Os dados experimentais foram adquiridos para vários números de Reynolds e várias razões de aspecto p/D de 1,16, 1,26 e 1,60, o diâmetro dos cilindros é de 25,1 mm. A técnica experimental utilizada consiste em medir as flutuações de velocidade em um canal aerodinâmico utilizando anemometria de fio quente. O estudo apresenta a aplicação da transformada de Hilbert-Huang (HHT) como ferramenta de análise para sinais não estacionários e não lineares. O método é primeiramente validado utilizando sinais experimentais para um cilindro sobre escoamento turbulento e após aplicado ao escoamento sobre dois cilindros lado a lado. Resultados mostram que o método de HHT fornece não só uma definição mais precisa de eventos específicos no espaço tempo-frequência, mas também permite uma interpretação física mais significativa dos processos dinâmicos das escalas do escoamento. A análise estatística dos dados experimentais é feita com o objetivo de identificar padrões estatísticos que possam ser utilizados para caracterização do escoamento biestável. Para a análise estatística os dados são varridos por uma janela móvel, criando blocos de funções densidade de probabilidade (PDFs). Os quatro primeiros momentos estatísticos são calculados e é possível estabelecer uma tendência de comportamento baseada em suas variações. A dinâmica do sistema biestável é estudada aplicando ferramentas da teoria do caos, como o maior expoente de Lyapunov. O atrator estranho da série temporal da velocidade é reconstruído e sua topologia é utilizada para melhor compreensão do comportamento físico do fenômeno da biestabilidade. Cada esteira do escoamento biestável é analisada separadamente. Um modelo geral do escoamento biestável é reconstruído utilizando funções de probabilidade. A aplicação de um conjunto de ferramentas para a análise da turbulência das esteiras dos cilindros é útil para a melhor compreensão de fenômenos turbulentos, produzindo resultados significativos e permitindo a identificação de estruturas turbulentas e escalas do escoamento e um entendimento sobre a dinâmica do sistema