Regression analysis of spatial data

Many of the most interesting questions ecologists ask lead to analyses of spatial data. Yet, perhaps confused by the large number of statistical models and fitting methods available, many ecologists seem to believe this is best left to specialists. Here, we describe the issues that need consideration when analysing spatial data and illustrate these using simulation studies. Our comparative analysis involves using methods including generalized least squares, spatial filters, wavelet revised models, conditional autoregressive models and generalized additive mixed models to estimate regression coefficients from synthetic but realistic data sets, including some which violate standard regression assumptions. We assess the performance of each method using two measures and using statistical error rates for model selection. Methods that performed well included generalized least squares family of models and a Bayesian implementation of the conditional auto-regressive model. Ordinary least squares also performed adequately in the absence of model selection, but had poorly controlled Type I error rates and so did not show the improvements in performance under model selection when using the above methods. Removing large-scale spatial trends in the response led to poor performance. These are empirical results; hence extrapolation of these findings to other situations should be performed cautiously. Nevertheless, our simulation-based approach provides much stronger evidence for comparative analysis than assessments based on single or small numbers of data sets, and should be considered a necessary foundation for statements of this type in future.

A wavelet-based damage detection algorithm based on bridge acceleration response to a vehicle

Previous research based on theoretical simulations has shown the potential of the wavelet transform to detect damage in a beam by analysing the time-deflection response due to a constant moving load. However, its application to identify damage from the response of a bridge to a vehicle raises a number of questions. Firstly, it may be difficult to record the difference in the deflection signal between a healthy and a slightly damaged structure to the required level of accuracy and high scanning frequencies in the field. Secondly, the bridge is going to have a road profile and it will be loaded by a sprung vehicle and time-varying forces rather than a constant load. Therefore, an algorithm based on a plot of wavelet coefficients versus time to detect damage (a singularity in the plot) appears to be very sensitive to noise. This paper addresses these questions by: (a) using the acceleration signal, instead of the deflection signal, (b) employing a vehicle-bridge finite element interaction model, and (c) developing a novel wavelet-based approach using wavelet energy content at each bridge section which proves to be more sensitive to damage than a wavelet coefficient line plot at a given scale as employed by others.

Systolic array architectures for parameterised multiplexed IIR filters

Whilst conventional bit level pipelining introduces an m cycle delay, it does allow m separate computations to be processed at throughput rates comparable to that using word level systolic arrays. We concentrate on exploiting this delay and describe a systematic method for the design of high performance multiplexed IIR filters. Two multiply and accumulate structures are identified based on shift-and-add and carry-save data organisations which can be used as building blocks in the design of IIR filters. By replacing the word level multiply and accumulate units in word level systolic structures with their equivalent bit level circuits and introducing latches to ensure correct timing, numerous architectures can be designed that process multiplexed data directly without any additional circuit overhead.

SYSTOLIC IIR FILTERS WITH BIT LEVEL PIPELINING.

A novel bit-level systolic array architecture for implementing first-order IIR filter sections is presented. A latency of only two clock cycles is achieved by using a radix-4 redundant number representation, performing the recursive computation most-significant-digit first, and feeding back each digit of the result as soon as it is available.

Bit-level systolic architecture for very high performance IIR filters

A novel bit-level systolic array architecture for implementing bit-parallel IIR filter sections is presented. The authors have shown previously how the fundamental obstacle of pipeline latency in recursive structures can be overcome by the use of redundant arithmetic in combination with bit-level feedback. These ideas are extended by optimizing the degree of redundancy used in different parts of the circuit and combining redundant circuit techniques with those of conventional arithmetic. The resultant architecture offers significant improvements in hardware complexity and throughput rate.

Systematic methodology for the design of high performance recursive digital filters

A systematic design methodology is described for the rapid derivation of VLSI architectures for implementing high performance recursive digital filters, particularly ones based on most significant digit (msd) first arithmetic. The method has been derived by undertaking theoretical investigations of msd first multiply-accumulate algorithms and by deriving important relationships governing the dependencies between circuit latency, levels of pipe-lining and the range and number representations of filter operands. The techniques described are general and can be applied to both bit parallel and bit serial circuits, including those based on on-line arithmetic. The method is illustrated by applying it to the design of a number of highly pipelined bit parallel IIR and wave digital filter circuits. It is shown that established architectures, which were previously designed using heuristic techniques, can be derived directly from the equations described.

Design and implementation of the symmetrically extended 2-D wavelet transform

The inclusion of the Discrete Wavelet Transform in the JPEG-2000 standard has added impetus to the research of hardware architectures for the two-dimensional wavelet transform. In this paper, a VLSI architecture for performing the symmetrically extended two-dimensional transform is presented. This architecture conforms to the JPEG-2000 standard and is capable of near-optimal performance when dealing with the image boundaries. The architecture also achieves efficient processor utilization. Implementation results based on a Xilinx Virtex-2 FPGA device are included.

Wavelet packet transforms for system-on-chip applications

A methodology for the production of silicon cores for wavelet packet decomposition has been developed. The scheme utilizes efficient scalable architectures for both orthonormal and biorthogonal wavelet transforms. The cores produced from these architectures can be readily scaled for any wavelet function and are easily configurable for any subband structure. The cores are fully parameterized in terms of wavelet choice and appropriate wordlengths. Designs produced are portable across a range of silicon foundries as well as FPGA and PLD technologies. A number of exemplar implementations have been produced.

Comparison of Wavelet Transform and Time-Domain Analysis of Second Trimester Uterine Artery Doppler Waveforms in Screening for Pre-Eclampsia

The aim of this study was to compare time-domain waveform analysis of second-trimester uterine artery Doppler using the resistance index (RI) with waveform analysis using a mathematical tool known as wavelet transform for the prediction of pre-eclampsia (PE). This was a retrospective, nested case-cohort study of 336 women, 37 of whom subsequently developed PE. Uterine artery Doppler waveforms were analysed using both RI and waveform analysis. The utility of these indices in screening for PE was then evaluated using receiver operating characteristic curves. There were significant differences in uterine artery RI between the PE women and those with normal pregnancy outcome. After wavelet analysis, significant difference in the mean amplitude in wavelet frequency band 4 was noted between the 2 groups. The sensitivity for both Doppler RI and frequency band 4 for the detection of PE at a 10% false-positive rate was 45%. This small study demonstrates the application of wavelet transform analysis of uterine artery Doppler waveforms in screening for PE. Further prospective studies are needed in order to clearly define if this analytical approach to waveform analysis may have the potential to improve the detection of PE by uterine artery Doppler screening.

3D Analysis of Seepage under Hydraulic Structures with Intermediate Filters

Seepage flow under hydraulic structures provided with intermediate filters has been investigated. The flow through the banks of the canal has been included in the model. Different combinations of intermediate filter and canal width were studied. Different lengths of the floor, differential heads, and depths of the sheet pile driven beneath the floor were also investigated. The introduction of an intermediate filter to the floor of hydraulic structures reduced the uplift force acting on the downstream floor by up to 72%. The maximum uplift reduction occurred when the ratio of the distance of filter location downstream from the cutoff to the differential head was 1. Introducing a second filter in the downstream side resulted in a further reduction in the exit hydraulic gradient and in the uplift force, which reached 90%. The optimum locations of the two filters occurred when the first filter was placed just downstream of the cutoff wall and the second filter was placed nearly at the middistance between the cutoff and the end toe of the floor. The results showed significant differences between the three-dimensional (3D) and the two-dimensional (2D) analyses.

Analysis of Fixed-Speed Wind Farm Low-Frequency Power Pulsations using a Wavelet-Prony Method

The increasing penetration of wind generation on the Island of Ireland has been accompanied by close investigation of low-frequency periodic pulsations contained within the active power flow from different wind farms. A primary concern is excitation of existing low-frequency oscillation modes already present on the system, particularly the 0.75 Hz mode as a consequence of the interconnected Northern and Southern power system networks. Recently grid code requirements on the Northern Ireland power system have been updated stipulating that wind farms connected after 2005 must be able to control the magnitude of oscillations in the range of 0.25 - 1.75 Hz to within 1% of the wind farm's registered output. In order to determine whether wind farm low-frequency oscillations have a negative effect (excite other modes) or possibly a positive impact (damping of existing modes) on the power system, the oscillations at the point of connection must be measured and characterised. Using time - frequency methods, research presented in this paper has been conducted to extract signal features from measured low-frequency active power pulsations produced by wind farms to determine the effective composition of possible oscillatory modes which may have a detrimental effect on system dynamic stability. The paper proposes a combined wavelet-Prony method to extract modal components and determine damping factors. The method is exemplified using real data obtained from wind farm measurements.

A Wavelet Approach to the Selective Computation of Eigenvalues for Small Signal Stability Analysis

This paper proposes a method to assess the small signal stability of a power system network by selective determination of the modal eigenvalues. This uses an accelerating polynomial transform, designed using approximate eigenvalues
obtained from a wavelet approximation. Application to the IEEE 14 bus network model produced computational savings of 20%,over the QR algorithm.