Linear-wavelet networks

This paper proposes a nonlinear regression structure comprising a wavelet network and a linear term. The introduction of the linear term is aimed at providing a more parsimonious interpolation in high-dimensional spaces when the modelling samples are sparse. A constructive procedure for building such structures, termed linear-wavelet networks, is described. For illustration, the proposed procedure is employed in the framework of dynamic system identification. In an example involving a simulated fermentation process, it is shown that a linear-wavelet network yields a smaller approximation error when compared with a wavelet network with the same number of regressors. The proposed technique is also applied to the identification of a pressure plant from experimental data. In this case, the results show that the introduction of wavelets considerably improves the prediction ability of a linear model. Standard errors on the estimated model coefficients are also calculated to assess the numerical conditioning of the identification process.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.

Ensemble clustering in deterministic ensemble Kalman filters

Ensemble clustering (EC) can arise in data assimilation with ensemble square root filters (EnSRFs) using non-linear models: an M-member ensemble splits into a single outlier and a cluster of M−1 members. The stochastic Ensemble Kalman Filter does not present this problem. Modifications to the EnSRFs by a periodic resampling of the ensemble through random rotations have been proposed to address it. We introduce a metric to quantify the presence of EC and present evidence to dispel the notion that EC leads to filter failure. Starting from a univariate model, we show that EC is not a permanent but transient phenomenon; it occurs intermittently in non-linear models. We perform a series of data assimilation experiments using a standard EnSRF and a modified EnSRF by a resampling though random rotations. The modified EnSRF thus alleviates issues associated with EC at the cost of traceability of individual ensemble trajectories and cannot use some of algorithms that enhance performance of standard EnSRF. In the non-linear regimes of low-dimensional models, the analysis root mean square error of the standard EnSRF slowly grows with ensemble size if the size is larger than the dimension of the model state. However, we do not observe this problem in a more complex model that uses an ensemble size much smaller than the dimension of the model state, along with inflation and localisation. Overall, we find that transient EC does not handicap the performance of the standard EnSRF.

Femtosecond pulse shaping using differential evolutionary algorithm and wavelet operators

Evolutionary meta-algorithms for pulse shaping of broadband femtosecond duration laser pulses are proposed. The genetic algorithm searching the evolutionary landscape for desired pulse shapes consists of a population of waveforms (genes), each made from two concatenated vectors, specifying phases and magnitudes, respectively, over a range of frequencies. Frequency domain operators such as mutation, two-point crossover average crossover, polynomial phase mutation, creep and three-point smoothing as well as a time-domain crossover are combined to produce fitter offsprings at each iteration step. The algorithm applies roulette wheel selection; elitists and linear fitness scaling to the gene population. A differential evolution (DE) operator that provides a source of directed mutation and new wavelet operators are proposed. Using properly tuned parameters for DE, the meta-algorithm is used to solve a waveform matching problem. Tuning allows either a greedy directed search near the best known solution or a robust search across the entire parameter space.

Cooled infrared filters and dichroics for the sea and land surface temperature radiometer (SLSTR)

The Sea and Land Surface Temperature Radiometer (SLSTR) is a nine channel visible and infrared high precision radiometer designed to provide climate data of global sea and land surface temperatures. The SLSTR payload is destined to fly on the Ocean and Medium-Resolution Land Mission for the ESA/EU Global Monitoring for Environment and Security (GMES) Programme Sentinel-3 mission to measure the sea and land temperature and topography for near real-time environmental and atmospheric climate monitoring of the Earth. In this paper we describe the optical layout of infrared optics in the instrument, spectral thin-film multilayer design, and system channel throughput analysis for the combined interference filter and dichroic beamsplitter coatings to discriminate wavelengths at 3.74, 10.85 & 12.0 μm. The rationale for selection of thin-film materials, deposition technique, and environmental testing, inclusive of humidity, thermal cycling and ionizing radiation testing are also described.

Wavelet-based ULF wave diagnosis of substorm expansion phase onset

Using a discrete wavelet transform with a Meyer wavelet basis, we present a new quantitative algorithm for determining the onset time of Pi1 and Pi2 ULF waves in the nightside ionosphere with ∼20- to 40-s resolution at substorm expansion phase onset. We validate the algorithm by comparing both the ULF wave onset time and location to the optical onset determined by the Imager for Magnetopause-to-Aurora Global Exploration (IMAGE)–Far Ultraviolet Imager (FUV) instrument. In each of the six events analyzed, five substorm onsets and one pseudobreakup, the ULF onset is observed prior to the global optical onset observed by IMAGE at a station closely conjugate to the optical onset. The observed ULF onset times expand both latitudinally and longitudinally away from an epicenter of ULF wave power in the ionosphere. We further discuss the utility of the algorithm for diagnosing pseudobreakups and the relationship of the ULF onset epicenter to the meridians of elements of the substorm current wedge. The importance of the technique for establishing the causal sequence of events at substorm onset, especially in support of the multisatellite Time History of Events and Macroscale Interactions During Substorms (THEMIS) mission, is also described.

Ensemble transform Kalman-Bucy filters

Two recent works have adapted the Kalman–Bucy filter into an ensemble setting. In the first formulation, the ensemble of perturbations is updated by the solution of an ordinary differential equation (ODE) in pseudo-time, while the mean is updated as in the standard Kalman filter. In the second formulation, the full ensemble is updated in the analysis step as the solution of single set of ODEs in pseudo-time. Neither requires matrix inversions except for the frequently diagonal observation error covariance. We analyse the behaviour of the ODEs involved in these formulations. We demonstrate that they stiffen for large magnitudes of the ratio of background error to observational error variance, and that using the integration scheme proposed in both formulations can lead to failure. A numerical integration scheme that is both stable and is not computationally expensive is proposed. We develop transform-based alternatives for these Bucy-type approaches so that the integrations are computed in ensemble space where the variables are weights (of dimension equal to the ensemble size) rather than model variables. Finally, the performance of our ensemble transform Kalman–Bucy implementations is evaluated using three models: the 3-variable Lorenz 1963 model, the 40-variable Lorenz 1996 model, and a medium complexity atmospheric general circulation model known as SPEEDY. The results from all three models are encouraging and warrant further exploration of these assimilation techniques.

The effect of (mis-specified) GARCH filters on the finite sample distribution of the BDS test

This paper considers the effect of using a GARCH filter on the properties of the BDS test statistic as well as a number of other issues relating to the application of the test. It is found that, for certain values of the user-adjustable parameters, the finite sample distribution of the test is far-removed from asymptotic normality. In particular, when data generated from some completely different model class are filtered through a GARCH model, the frequency of rejection of iid falls, often substantially. The implication of this result is that it might be inappropriate to use non-rejection of iid of the standardised residuals of a GARCH model as evidence that the GARCH model ‘fits’ the data.

Wavelet based detection of changes in the composition of RLC networks

The current work discusses the compositional analysis of spectra that may be related to amorphous materials that lack discernible Lorentzian, Debye or Drude responses. We propose to model such response using a 3-dimensional random RLC network using a descriptor formulation which is converted into an input-output transfer function representation. A wavelet identification study of these networks is performed to infer the composition of the networks. It was concluded that wavelet filter banks enable a parsimonious representation of the dynamics in excited randomly connected RLC networks. Furthermore, chemometric classification using the proposed technique enables the discrimination of dielectric samples with different composition. The methodology is promising for the classification of amorphous dielectrics.

Smart-phone based electrocardiogram wavelet decomposition and neural network classification

This paper discusses ECG classification after parametrizing the ECG waveforms in the wavelet domain. The aim of the work is to develop an accurate classification algorithm that can be used to diagnose cardiac beat abnormalities detected using a mobile platform such as smart-phones. Continuous time recurrent neural network classifiers are considered for this task. Records from the European ST-T Database are decomposed in the wavelet domain using discrete wavelet transform (DWT) filter banks and the resulting DWT coefficients are filtered and used as inputs for training the neural network classifier. Advantages of the proposed methodology are the reduced memory requirement for the signals which is of relevance to mobile applications as well as an improvement in the ability of the neural network in its generalization ability due to the more parsimonious representation of the signal to its inputs.

On the application of optimal wavelet filter banks for ECG signal classification

This paper discusses ECG signal classification after parametrizing the ECG waveforms in the wavelet domain. Signal decomposition using perfect reconstruction quadrature mirror filter banks can provide a very parsimonious representation of ECG signals. In the current work, the filter parameters are adjusted by a numerical optimization algorithm in order to minimize a cost function associated to the filter cut-off sharpness. The goal consists of achieving a better compromise between frequency selectivity and time resolution at each decomposition level than standard orthogonal filter banks such as those of the Daubechies and Coiflet families. Our aim is to optimally decompose the signals in the wavelet domain so that they can be subsequently used as inputs for training to a neural network classifier.

Spectral design of temperature-invariant narrow bandpass filters for the mid-infrared

The ability of narrow bandpass filters to discriminate wavelengths between closely-separated gas absorption lines is crucial in many areas of infrared spectroscopy. As improvements to the sensitivity of infrared detectors enables operation in uncontrolled high-temperature environments, this imposes demands on the explicit bandpass design to provide temperature-invariant behavior. The unique negative temperature coefficient (dn/dT<0) of Lead-based (Pb) salts, in combination with dielectric materials enable bandpass filters with exclusive immunity to shifts in wavelength with temperature. This paper presents the results of an investigation into the interdependence between multilayer bandpass design and optical materials together with a review on invariance at elevated temperatures.