System identification (SI) for constructed structural systems has received a lot of attention with the continuous development of modern technologies. This thesis proposes a new nonlinear time series model for use in system identification (SI) of smart structures. The proposed model is implemented by the integration of a wavelet transform (WT) and nonlinear autoregressive moving average (NARMA) time series model. The approach demonstrates the efficient and accurate nonlinear SI of smart structures subjected to both ambient excitation and high impact load. To demonstrate the effectiveness of the wavelet-based NARMA modeling (WNARMA), smart structures equipped with magnetorheological (MR) dampers are investigated. The simulation results show that the computation of the WNARMA model is faster than that of the NARMA model without sacrificing the modeling accuracy. In addition, the WNARMA model is robust against noise in the data since it inherently has a denoising capacity.

This study focuses on implementing a log analysis strategy that combines a neural network algorithm and wavelet transform. Wavelet transform allows us to extract the important hidden information and features of the original time series log data and offers a precise framework for the analysis of input information. While neural network algorithm constitutes a powerfulnonlinear function approximation which can provide detection and prediction functions. The combination of the two techniques is based on the idea of using wavelet transform to denoise the log data by decomposing it into a set of coefficients, then feed the denoised data into a neural network. The experimental outputs reveal that this strategy can have a better ability to identify the patterns among problems in a log dataset, and make predictions with a better accuracy. This strategy can help the platform maintainers to adopt corresponding actions to eliminate risks before the occurrence of serious damages.

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.

This thesis presents an architecture and an FPGA implementation of the two dimensional discrete wavelet transformation (DWT) for applications where row-based raw image data is streamed in at high bandwidths and local buffering of the entire image is not feasible. The architecture is especially suited for multi-spectral imager systems, such as on board an imaging satellite, however can be used in any application where time to next image constraints require real-time processing of multiple images. The latency that is introduced as the images stream through the iii DWT module and the amount of locally stored image data, is a function of the image and tile size. For an n1 &times / n2 size image processed using (n1/k1) &times / (n2/k2) sized tiles the latency is equal to the time elapsed to accumulate a (1/k1) portion of one image. In addition, a (2/k1) portion of each image is buffered locally. The proposed hardware has been implemented on an FPGA and is part of a JPEG 2000 compression system designed as a payload for a low earth orbit (LEO) micro-satellite to be launched in September 2003. The architecture can achieve a throughput of up to 160Mbit/s. The latency introduced is 0.105 sec (6.25% of total transmission time) for tile sizes of 256&times / 256. The local storage size required for the tiling operation is 2 MB. The internal storage requirement is 1536 pixels. Equivalent gate count for the design is 292,447.

In this dissertation, I develop the theory and techniques for spatial and temporal image prediction with the magnitude and phase representation of the Complex Wavelet Transform (CWT) or the over-complete DCT to solve the problems of image inpainting and motion compensated inter-picture prediction. First, I develop the theory and algorithms of image reconstruction from the analytic magnitude or phase of the CWT. I prove the conditions under which a signal is uniquely specified by its analytic magnitude or phase, propose iterative algorithms for the reconstruction of a signal from its analytic CWT magnitude or phase, and analyze the convergence of the proposed algorithms. Image reconstruction from the magnitude and pseudo-phase of the over-complete DCT is also discussed and demonstrated. Second, I propose simple geometrical models of the CWT magnitude and phase to describe edges and structured textures and develop a spatial image prediction (inpainting) algorithm based on those models and the iterative image reconstruction mentioned above. Piecewise smooth signals, structured textures and their mixtures can be predicted successfully with the proposed algorithm. Simulation results show that the proposed algorithm achieves appealing visual quality with low computational complexity. Finally, I propose a novel temporal (inter-picture) image predictor for hybrid video coding. The proposed predictor enables successful predictive coding during fades, blended scenes, temporally decorrelated noise, and many other temporal evolutions that are beyond the capability of the traditional motion compensated prediction methods. The proposed predictor estimates the transform magnitude and phase of the desired motion compensated prediction by exploiting the temporal and spatial correlations of the transform coefficients. For the case of implementation in standard hybrid video coders, the over-complete DCT is chosen over the CWT. Better coding performance is achieved with the state-of-the-art H.264/AVC video encoder equipped with the proposed predictor. The proposed predictor is also successfully applied to image registration.

Auditory brainstem response (ABR) evaluation has been one of the most reliable methods for evaluating hearing loss. Clinically available methods for ABR tests require averaging for a large number of sweeps (~1000-2000) in order to obtain a meaningful ABR signal, which is time consuming.  This study proposes a faster new method for ABR filtering based on wavelet-Kalman filter that is able to produce a meaningful ABR signal with less than 500 sweeps. The method is validated against ABR data acquired from 7 normal hearing subjects with different stimulus intensity levels, the lowest being 30 dB NHL. The proposed method was able to filter and produce a readable ABR signal using 400 sweeps; other ABR signal criteria were also presented to validate the performance of the proposed method.

Magnetic Resonance Imaging (MRI) is a common medical imaging tool that have beenused in clinical industry for diagnostic and research purposes. These images are subjectto noises while capturing the data that can eect the image quality and diagnostics.Therefore, improving the quality of the generated images from both resolution andsignal to noise ratio (SNR) perspective is critical. Wavelet based denoising technique isone of the common tools to remove the noise in the MRI images. The noise is eliminatedfrom the detailed coecients of the signal in the wavelet domain. This can be done byapplying thresholding methods. The main task here is to nd an optimal threshold andkeep all the coecients larger than this threshold as the noiseless ones. Noise InvalidationDenoising technique is a method in which the optimal threshold is found by comparingthe noisy signal to a noise signature (function of noise statistics). The original NIDeapproach is developed for one dimensional signals with additive Gaussian noise. In thiswork, the existing NIDe approach has been generalized for applications in MRI imageswith dierent noise distribution. The developed algorithm was tested on simulated datafrom the Brainweb database and compared with the well-known Non Local Mean lteringmethod for MRI. The results indicated better detailed structural preserving forthe NIDe approach on the magnitude data while the signal to noise ratio is compatible.The algorithm shows an important advantageous which is less computational complexitythan the NLM method. On the other hand, the Unbiased NLM technique is combinedwith the proposed technique, it can yield the same structural similarity while the signalto noise ratio is improved.

The safety of pipelines distributed in the infrastructure of many industries has become very important since the industrial revolution. The guided ultrasonic wave technique can provide the possibility for rapid screening in long pipelines with corrosion. Especially the torsional mode T(0,1) of guided waves has been used in the cases of the pipe in the hidden region substantially. The ability of evaluating the inaccessible areas of the pipe makes the guided ultrasonic wave technique sit high on the roster of non-destructive testing tool for pipe inspection. However, the problem arises when attempting to detect the corrosions at the welded support bracket or under the bitumen coating on the pipe. The signal reflected from the corrosion will be covered by a large signal induced by the welded support or attenuated by the bitumen coating seriously. Therefore, the effects of welded support and bitumen coating on the T(0,1) mode are investigated by the experimental and the simulative methods. The continuous wavelet transform analysis is the signal processing method to extract the hidden signal of corrosion in this dissertation. There are five test pipes in the experiments. The response of the normal welded support is studied on the #1 test pipe. The #2 test pipe is used for attenuation investigation. The reflected signals of the features on the #3, #4, and #5 test pipes are measured and processed by continuous wavelet transform during defect detection process. In addition, the linear hexahedron elements are used to build the finite element models of the 6-inch steel pipe with support bracket and the pipe with bitumen coating. It is found that the effects of support bracket on the reflection comprise mode conversion, delayed appearance, trailing echoes, and frequency dependent behavior. When the T(0,1) mode impinges on to the support bracket, it will convert into the A0 mode inside the support due to the circumferential disturbance on the pipe surface. The reflection of the support bracket is identified as three parts formed by the direct echo, delayed echo and the trailing echo. The constructive interference of the A0 mode reflecting from the boundaries inside the support causes that the reflection spectrum shows two maxima peak at around 20-22 kHz (frequency regime of 0.0) and 32-34 kHz (frequency regime of 4.0) from both the experimental and simulated results. For the bitumen coating, the data collected from the welds and defects under the bitumen coating on the #2 test pipe show the attenuation effect on guided wave propagation and the difficulty of minor corrosion detection. In the finite element model of coated pipe, the results of predicted attenuation curves of T(0,1) mode indicate that the attenuation effect on guided wave propagation is aggravated with the increased value of the thickness, density or damping factor of the coated layer. Especially, in the case of 5-mm, the predicted attenuation curve shows a maximum point. Before this point, the attenuation increases with the operating frequency. For long range pipe inspection, it is the best way to avoid choosing the operating frequency around the corresponding frequency of the point. The measured data of corrosion affected by the welded support or the coated bitumen layer was processed by continuous wavelet transform to form a time-frequency analysis. The corrosion signals were identified in the contour map of the wavelet coefficient successfully. The understanding of the guided wave propagation on the pipe welded with support or pipe coated with bitumen is helpful to interpret the reflected signals. The use of continuous wavelet transform on signal processing techniques can improve the ability of defect detection on pipe with complex geometries.

Many hydrocarbon detection techniques have been developed for decades and one of the most efficient techniques for hydrocarbon exploration in recent years is well known as amplitude versus offset analysis (AVO). However, AVO analysis does not always result in successful hydrocarbon finds because abnormal seismic amplitude variations can sometimes be caused by other factors, such as alternative lithology and residual hydrocarbons in certain depositional environments. Furthermore, not all gas fields are associated with obvious AVO anomalies. Therefore, new techniques should be applied to combine with AVO for hydrocarbon detection. In my thesis, I, through case studies, intend to investigate and validate the wave decomposition technique as a new tool for hydrocarbon detection which decomposes seismic wave into different frequency contents and may help identify better the amplitude anomalies associated with hydrocarbon occurrence for each frequency due to seismic attenuation. The wavelet decomposition analysis technique has been applied in two geological settings in my study: clastic reservoir and carbonate reservoir. Results from both cases indicate that the wavelet decomposition analysis technique can be used for hydrocarbon detection effectively if the seismic data quality is good. This technique can be directly applied to the processed 2D and 3D pre-stack/post-stack data sets (1) to detect hydrocarbon zones in both clastic and carbonate reservoirs by analyzing the low frequency signals in the decomposed domain and (2) to identify thin beds by analyzing the high frequency signals in the decomposed domain. In favorable cases, the method may possibly help separate oil from water in high-porosity and high-permeability carbonate reservoirs deeply buried underground. Therefore, the wavelet analysis would be a powerful tool to assist geological interpretation and to reduce risk for hydrocarbon exploration.

The Ultra-Wideband (UWB) communication technology has been extensively attended in recent years. In this thesis, we propose the improved selective-Rake receiver and analyze the performance on UWB channels. The UWB transmission channels are modeled with statistical methods and its fading characteristics are discussed. Different impulse radio properties for the UWB communication system are analyzed. The system performance and design complexity issues of selective-Rake receiver (SRake) are studied. Rake receiver has difficulties achieving desired system performance in the dense multipath environment. The main ideas of SRake receiver are to obtain the SNR level on known multipath channel and to determine the desired number of Rake fingers. Matched filters and maximum likelihood detectors are utilized in the implementation of the SRake to estimate the signal time delay. The CLEAN algorithm is then used in selecting the paths with relatively high energy. Furthermore, we also propose a noise cancellation scheme for performance improvement in the SRake receiver. In the noise cancellation scheme, the multiresolution property of wavelet transform is used for filtering the noise interference caused by the rapid fluctuation factor. In addition, a two-stage search is combined with the original CLEAN algorithm to increase the accuracy of path selection. From our simulation results on the UWB channels, the improved SRake receiver, with noise cancellation and two-stage search, indeed has high SRake output SNR and better path accuracy than the original SRake receiver.