ETD Collection

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    Spectral shaping in DC-DC converters using maximum entropy random pulse width modulation
    (2018) Dove, Albert
    This work investigates the impact of probability distribution functions (PDF) on spreading the harmonic power in the power density spectrum (PSD) of Random PWM (RPWM) switching signals. Periodic switching is known to result in conducted electromagnetic interference (EMI) in switched-mode power converters. The main benefit of using RPWM signals is the ability to reduce the amplitudes of harmonics that cause conducted EMI. This helps in minimizing the dependence on sophisticated EMI filters that are typically used for mitigating this problem. This contributes to reduced volume and cost of power converters. With these benefits, a RPWM signal with the ’most reduced’ harmonics, and results in the desired power conversion, can be considered an ideal switching signal. In the PSD of RPWM signals, the reduction in the amplitude of harmonics does not imply that their harmonic power is lost. Instead, it is spread throughout the spectrum. This phenomenon establishes the relation that spreading out harmonic power reduces the high amplitude harmonics. As a result, it can be similarly said that maximally spreading out harmonic power in the PSD is an ideal requirement. This requirement is a key property that this research seeks to achieve, while ensuring that the RPWM signal maintains its properties that allow it to be used in a DC-DC converter the same way a traditional PWM would be used to convert electrical power. This is a constraint that is mostly governed by the duty ratio and, in the case of RPWM signals, by the nominal duty ratio. RPWM behaviour is governed by probability distribution functions that determine the nominal behaviour of the signal. This means that by using PDFs, the ability to alter both the time-domain nominal properties and frequency domain properties (in the PSD) is granted. The Method of Maximum Entropy in itself grants the very ability to obtain a PDF that has a maximally spread out distribution of probability while maintaining those time-domain nominal switching constraints. This idea ignited the initial investigation into how Maximum Entropy probability distributions result in the maximal spreading out of the PSD, given time-domain constraints. Before this, an investigation into the relationship between spreading out of probability in the PDFs and spreading out of harmonic power in the PSD is presented. Where it was found that increasing spreading of probability (quantified by entropy) of RPWM causes more spreading out of harmonic power in the PSD. This finding then qualified the use of Maximum Entropy (MaxEnt) PDFs to maximally spread out harmonic power, while maintaining time-domain constraints. With this, a method for computing MaxEnt PDFs given the time domain constraints - was formulated, and their ability to spread out harmonic power and yet maintain the constraints - was demonstrated. Additionally, MaxEnt PDFs coupled with varying the strength of time-domain constraints, revealed the limitations of spectral spreading using RPWM PDFs. Wherein stronger time-domain constraints of the PDFs restricted the maximum spreading level that can be obtained in the PSD.
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    Hydrological data interpolation using entropy
    (2006-11-17T07:40:07Z) Ilunga, Masengo
    The problem of missing data, insufficient length of hydrological data series and poor quality is common in developing countries. This problem is much more prevalent in developing countries than it is in developed countries. This situation can severely affect the outcome of the water systems managers’ decisions (e.g. reliability of the design, establishment of operating policies for water supply, etc). Thus, numerous data interpolation (infilling) techniques have evolved in hydrology to deal with the missing data. The current study presents merely a methodology by combining different approaches and coping with missing (limited) hydrological data using the theories of entropy, artificial neural networks (ANN) and expectation-maximization (EM) techniques. This methodology is simply formulated into a model named ENANNEX model. This study does not use any physical characteristics of the catchment areas but deals only with the limited information (e.g. streamflow or rainfall) at the target gauge and its similar nearby base gauge(s). The entropy concept was confirmed to be a versatile tool. This concept was firstly used for quantifying information content of hydrological variables (e.g. rainfall or streamflow). The same concept (through directional information transfer index, i.e. DIT) was used in the selection of base/subject gauge. Finally, the DIT notion was also extended to the evaluation of the hydrological data infilling technique performance (i.e. ANN and EM techniques). The methodology was applied to annual total rainfall; annual mean flow series, annual maximum flows and 6-month flow series (means) of selected catchments in the drainage region D “Orange” of South Africa. These data regimes can be regarded as useful for design-oriented studies, flood studies, water balance studies, etc. The results from the case studies showed that DIT is as good index for data infilling technique selection as other criteria, e.g. statistical and graphical. However, the DIT has the feature of being non-dimensionally informational index. The data interpolation iii techniques viz. ANNs and EM (existing methods applied and not yet applied in hydrology) and their new features have been also presented. This study showed that the standard techniques (e.g. Backpropagation-BP and EM) as well as their respective variants could be selected in the missing hydrological data estimation process. However, the capability for the different data interpolation techniques of maintaining the statistical characteristics (e.g. mean, variance) of the target gauge was not neglected. From this study, the relationship between the accuracy of the estimated series (by applying a data infilling technique) and the gap duration was then investigated through the DIT notion. It was shown that a decay (power or exponential) function could better describe that relationship. In other words, the amount of uncertainty removed from the target station in a station-pair, via a given technique, could be known for a given gap duration. It was noticed that the performance of the different techniques depends on the gap duration at the target gauge, the station-pair involved in the missing data estimation and the type of the data regime. This study showed also that it was possible, through entropy approach, to assess (preliminarily) model performance for simulating runoff data at a site where absolutely no record exist: a case study was conducted at Bedford site (in South Africa). Two simulation models, viz. RAFLER and WRSM2000 models, were then assessed in this respect. Both models were found suitable for simulating flows at Bedford.