Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

Advanced analysis of steel frame structures comprising non-compact sections

During the past decade, a significant amount of research has been conducted internationally with the aim of developing, implementing, and verifying "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures. Application of these methods permits comprehensive assessment of the actual failure modes and ultimate strengths of structural systems in practical design situations, without resort to simplified elastic methods of analysis and semi-empirical specification equations. Advanced analysis has the potential to extend the creativity of structural engineers and simplify the design process, while ensuring greater economy and more uniform safety with respect to the ultimate limit state. The application of advanced analysis methods has previously been restricted to steel frames comprising only members with compact cross-sections that are not subject to the effects of local buckling. This precluded the use of advanced analysis from the design of steel frames comprising a significant proportion of the most commonly used Australian sections, which are non-compact and subject to the effects of local buckling. This thesis contains a detailed description of research conducted over the past three years in an attempt to extend the scope of advanced analysis by developing methods that include the effects of local buckling in a non-linear analysis formulation, suitable for practical design of steel frames comprising non-compact sections. Two alternative concentrated plasticity formulations are presented in this thesis: the refined plastic hinge method and the pseudo plastic zone method. Both methods implicitly account for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the methods for the analysis of steel frames comprising non-compact sections has been established by comparison with a comprehensive range of analytical benchmark frame solutions. Both the refined plastic hinge and pseudo plastic zone methods are more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations. For example, the pseudo plastic zone method predicts the ultimate strength of the analytical benchmark frames with an average conservative error of less than one percent, and has an acceptable maximum unconservati_ve error of less than five percent. The pseudo plastic zone model can allow the design capacity to be increased by up to 30 percent for simple frames, mainly due to the consideration of inelastic redistribution. The benefits may be even more significant for complex frames with significant redundancy, which provides greater scope for inelastic redistribution. The analytical benchmark frame solutions were obtained using a distributed plasticity shell finite element model. A detailed description of this model and the results of all the 120 benchmark analyses are provided. The model explicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. Its accuracy was verified by comparison with a variety of analytical solutions and the results of three large-scale experimental tests of steel frames comprising non-compact sections. A description of the experimental method and test results is also provided.

Bearing damage analysis by calculation of capacitive coupling between inner and outer races of a ball bearing

Bearing damage in modern inverter-fed AC drive systems is more common than in motors working with 50 or 60 Hz power supply. Fast switching transients and common mode voltage generated by a PWM inverter cause unwanted shaft voltage and resultant bearing currents. Parasitic capacitive coupling creates a path to discharge current in rotors and bearings. In order to analyze bearing current discharges and their effect on bearing damage under different conditions, calculation of the capacitive coupling between the outer and inner races is needed. During motor operation, the distances between the balls and races may change the capacitance values. Due to changing of the thickness and spatial distribution of the lubricating grease, this capacitance does not have a constant value and is known to change with speed and load. Thus, the resultant electric field between the races and balls varies with motor speed. The lubricating grease in the ball bearing cannot withstand high voltages and a short circuit through the lubricated grease can occur. At low speeds, because of gravity, balls and shaft voltage may shift down and the system (ball positions and shaft) will be asymmetric. In this study, two different asymmetric cases (asymmetric ball position, asymmetric shaft position) are analyzed and the results are compared with the symmetric case. The objective of this paper is to calculate the capacitive coupling and electric fields between the outer and inner races and the balls at different motor speeds in symmetrical and asymmetrical shaft and balls positions. The analysis is carried out using finite element simulations to determine the conditions which will increase the probability of high rates of bearing failure due to current discharges through the balls and races.

The feasibility of vibration analysis as a technique to detect osseointegration of transfemoral implants

One of the main causes of above knee or transfemoral amputation (TFA) in the developed world is trauma to the limb. The number of people undergoing TFA due to limb trauma, particularly due to war injuries, has been increasing. Typically the trauma amputee population, including war-related amputees, are otherwise healthy, active and desire to return to employment and their usual lifestyle. Consequently there is a growing need to restore long-term mobility and limb function to this population. Traditionally transfemoral amputees are provided with an artificial or prosthetic leg that consists of a fabricated socket, knee joint mechanism and a prosthetic foot. Amputees have reported several problems related to the socket of their prosthetic limb. These include pain in the residual limb, poor socket fit, discomfort and poor mobility. Removing the socket from the prosthetic limb could eliminate or reduce these problems. A solution to this is the direct attachment of the prosthesis to the residual bone (femur) inside the residual limb. This technique has been used on a small population of transfemoral amputees since 1990. A threaded titanium implant is screwed in to the shaft of the femur and a second component connects between the implant and the prosthesis. A period of time is required to allow the implant to become fully attached to the bone, called osseointegration (OI), and be able to withstand applied load; then the prosthesis can be attached. The advantages of transfemoral osseointegration (TFOI) over conventional prosthetic sockets include better hip mobility, sitting comfort and prosthetic retention and fewer skin problems on the residual limb. However, due to the length of time required for OI to progress and to complete the rehabilitation exercises, it can take up to twelve months after implant insertion for an amputee to be able to load bear and to walk unaided. The long rehabilitation time is a significant disadvantage of TFOI and may be impeding the wider adoption of the technique. There is a need for a non-invasive method of assessing the degree of osseointegration between the bone and the implant. If such a method was capable of determining the progression of TFOI and assessing when the implant was able to withstand physiological load it could reduce the overall rehabilitation time. Vibration analysis has been suggested as a potential technique: it is a non destructive method of assessing the dynamic properties of a structure. Changes in the physical properties of a structure can be identified from changes in its dynamic properties. Consequently vibration analysis, both experimental and computational, has been used to assess bone fracture healing, prosthetic hip loosening and dental implant OI with varying degrees of success. More recently experimental vibration analysis has been used in TFOI. However further work is needed to assess the potential of the technique and fully characterise the femur-implant system. The overall aim of this study was to develop physical and computational models of the TFOI femur-implant system and use these models to investigate the feasibility of vibration analysis to detect the process of OI. Femur-implant physical models were developed and manufactured using synthetic materials to represent four key stages of OI development (identified from a physiological model), simulated using different interface conditions between the implant and femur. Experimental vibration analysis (modal analysis) was then conducted using the physical models. The femur-implant models, representing stage one to stage four of OI development, were excited and the modal parameters obtained over the range 0-5kHz. The results indicated the technique had limited capability in distinguishing between different interface conditions. The fundamental bending mode did not alter with interfacial changes. However higher modes were able to track chronological changes in interface condition by the change in natural frequency, although no one modal parameter could uniquely distinguish between each interface condition. The importance of the model boundary condition (how the model is constrained) was the key finding; variations in the boundary condition altered the modal parameters obtained. Therefore the boundary conditions need to be held constant between tests in order for the detected modal parameter changes to be attributed to interface condition changes. A three dimensional Finite Element (FE) model of the femur-implant model was then developed and used to explore the sensitivity of the modal parameters to more subtle interfacial and boundary condition changes. The FE model was created using the synthetic femur geometry and an approximation of the implant geometry. The natural frequencies of the FE model were found to match the experimental frequencies within 20% and the FE and experimental mode shapes were similar. Therefore the FE model was shown to successfully capture the dynamic response of the physical system. As was found with the experimental modal analysis, the fundamental bending mode of the FE model did not alter due to changes in interface elastic modulus. Axial and torsional modes were identified by the FE model that were not detected experimentally; the torsional mode exhibited the largest frequency change due to interfacial changes (103% between the lower and upper limits of the interface modulus range). Therefore the FE model provided additional information on the dynamic response of the system and was complementary to the experimental model. The small changes in natural frequency over a large range of interface region elastic moduli indicated the method may only be able to distinguish between early and late OI progression. The boundary conditions applied to the FE model influenced the modal parameters to a far greater extent than the interface condition variations. Therefore the FE model, as well as the experimental modal analysis, indicated that the boundary conditions need to be held constant between tests in order for the detected changes in modal parameters to be attributed to interface condition changes alone. The results of this study suggest that in a clinical setting it is unlikely that the in vivo boundary conditions of the amputated femur could be adequately controlled or replicated over time and consequently it is unlikely that any longitudinal change in frequency detected by the modal analysis technique could be attributed exclusively to changes at the femur-implant interface. Therefore further development of the modal analysis technique would require significant consideration of the clinical boundary conditions and investigation of modes other than the bending modes.

Shakedown stress analysis of insulated rail joint (IRJ)

A finite element numerical simulation is carried out to examine stress distributions on railhead in the cicinity of the endpost of an insulated rail joint. The contact patch and pressure distribution are considered using modified Hertzian simulation. A combined elasto-plastic material modelling available in Abaqus is employed in the simulation. A dynamic load factor of 1.21 is considered in modelling for the wheel load based on a previous study as part of this on going research. Shakedown theorem is employed in this study. A peak pressure load which is above the shakedown limit is determined as input load. As a result, a progressive damage in the railhead has been captured as depicted in the equivalent plastic strain plot.

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

Meshless TL and UL approaches for large deformation analysis

To accurately and effectively simulate large deformation is one of the major challenges in numerical modeling of metal forming. In this paper, an adaptive local meshless formulation based on the meshless shape functions and the local weak-form is developed for the large deformation analysis. Total Lagrangian (TL) and the Updated Lagrangian (UL) approaches are used and thoroughly compared each other in computational efficiency and accuracy. It has been found that the developed meshless technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming. In addition, the TL has better computational efficiency than the UL. However, the adaptive analysis is much more efficient using the UL approach than using in the TL approach.

Theoretical analysis of serrated chip formation based on ideal models in high speed cutting

In this paper, two ideal formation models of serrated chips, the symmetric formation model and the unilateral right-angle formation model, have been established for the first time. Based on the ideal models and related adiabatic shear theory of serrated chip formation, the theoretical relationship among average tooth pitch, average tooth height and chip thickness are obtained. Further, the theoretical relation of the passivation coefficient of chip's sawtooth and the chip thickness compression ratio is deduced as well. The comparison between these theoretical prediction curves and experimental data shows good agreement, which well validates the robustness of the ideal chip formation models and the correctness of the theoretical deducing analysis. The proposed ideal models may have provided a simple but effective theoretical basis for succeeding research on serrated chip morphology. Finally, the influences of most principal cutting factors on serrated chip formation are discussed on the basis of a series of finite element simulation results for practical advices of controlling serrated chips in engineering application.

Vibration of L-shaped plates under a deterministic force or moment excitation : a case of statistical energy analysis application

Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary

Computational fluid dynamics analysis of a flat plate photocatalytic reactor for storm and wastewater reuse

A computational fluid dynamics (CFD) analysis has been performed for a flat plate photocatalytic reactor using CFD code FLUENT. Under the simulated conditions (Reynolds number, Re around 2650), a detailed time accurate computation shows the different stages of flow evolution and the effects of finite length of the reactor in creating flow instability, which is important to improve the performance of the reactor for storm and wastewater reuse. The efficiency of a photocatalytic reactor for pollutant decontamination depends on reactor hydrodynamics and configurations. This study aims to investigate the role of different parameters on the optimization of the reactor design for its improved performance. In this regard, more modelling and experimental efforts are ongoing to better understand the interplay of the parameters that influence the performance of the flat plate photocatalytic reactor.

Elasto-plastic stress analysis of an insulated rail joint (IRJ) with a loading below shakedown limit

A finite element numerical simulation is carried out to examine stress distributions on railhead in the vicinity of the endpost of a insulated rail joint. The contact patch and pressure distribution are considered using modified Hertzian formulation. A combined elasto-plastic material modelling available in Abaqus is employed in the simulation. A dynamic load factor of 1.21 is considered in modelling for the wheel load based on a previous study as part of this on going research. Shakedown theorem is employed in this study. A peak pressure load which is above the shakedown limit is determined as input load. As a result, a progressive damage in the railhead has been captured as depicted in the equivalent plastic strain plot.

Determination of stress-strain characteristics of railhead steel using image analysis

True stress-strain curve of railhead steel is required to investigate the behaviour of railhead under wheel loading through elasto-plastic Finite Element (FE) analysis. To reduce the rate of wear, the railhead material is hardened through annealing and quenching. The Australian standard rail sections are not fully hardened and hence suffer from non-uniform distribution of the material property; usage of average properties in the FE modelling can potentially induce error in the predicted plastic strains. Coupons obtained at varying depths of the railhead were, therefore, tested under axial tension and the strains were measured using strain gauges as well as an image analysis technique, known as the Particle Image Velocimetry (PIV). The head hardened steel exhibit existence of three distinct zones of yield strength; the yield strength as the ratio of the average yield strength provided in the standard (σyr=780MPa) and the corresponding depth as the ratio of the head hardened zone along the axis of symmetry are as follows: (1.17 σyr, 20%), (1.06 σyr, 20%- 80%) and (0.71 σyr, > 80%). The stress-strain curves exhibit limited plastic zone with fracture occurring at strain less than 0.1.

Numerical analysis of the time variable fractional order mobile-immobile advection-dispersion model

Many physical processes exhibit fractional order behavior that varies with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider the time variable fractional order mobile-immobile advection-dispersion model. Numerical methods and analyses of stability and convergence for the fractional partial differential equations are quite limited and difficult to derive. This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the fractional order mobile immobile advection-dispersion model. In the paper, we use the Coimbra variable time fractional derivative which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems. An implicit Euler approximation for the equation is proposed and then the stability of the approximation are investigated. As for the convergence of the numerical scheme we only consider a special case, i.e. the time fractional derivative is independent of time variable t. The case where the time fractional derivative depends both the time variable t and the space variable x will be considered in the future work. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.