Differentiable approximations to Brownian motion on manifolds

The main part of this thesis is devoted to generalised Ornstein-Uhlenbeck processes. We show how to construct such processes on 2-uniformly smooth Banach spaces. We give two methods of constructing Ornstein-Uhlenbeck type processes on manifolds with sufficient structure, including on finite dimensional Riemannian manifold where we actually construct a process on the orthonormal bundle 0(M) and project down to M to obtain the required process. We show that in the simplest case on a finite dimensional Riemannian manifold the two constructions give rise to the same process. We construct the infinitesimal generator of this process. We show that, given a Hilbert space and a Banach space E with W a Brownian motion on E whose index set includes [0,R], and X: H->L(E;H), V:H->H satisfying sufficient boundedness and Lipschitz conditions, the solutions of the family of o.d.e.'s dxβ=X(xβ)vβdt+V(xβ)dt (where vβ is an O-U velocity process on E), indexed by weΩ where Ω is the probability space over which W is defined, converges in L2-norm to a solution of dx=X(x)dW+V(x)dt, both solutions having the same starting point. We show that the convergence is uniform over [O, R] in probability, and include a proof of Elworthy, from 'Stochastic Differential Equations on Manifolds' (Warwick University preprint, 1978) to show that convergence still occurs when the processes are constructed on suitable manifolds (Elworthy's proof is for piecewise linear approximations). We extend our results to include 0-U processes in 'force-fields'. We follow the method of Elworthy to show the uniform convergence of the flows of the constructed processes. Finally we prove similar convergence theorems for piecewise-linear approximations, following the proofs of Elworthy

A real-time capable mixing controlled combustion model for highly diluted conditions

A new real-time capable heat release rate model is presented that captures the high dilution effects of exhaust gas recirculation (EGR). The model is a Mixing Controlled Combustion type with enhancements to account for wall impingements, pilot injections, charge dilution caused by EGR at part load. The model was parameterised in two steps using a small set of measured data: the majority of model parameters were identified without EGR before identifying additional EGR related constants. The model performance was assessed based on key metrics: start of combustion; peak heat release and point of peak heat release and cylinder pressure. The model was evaluated over the full engine speed, load and EGR operating envelope and cylinder pressure metrics were predicted with R2 values above 0.94. With EGR, the model was able to predict qualitatively and quantitively the performance whilst being parameterised by only by a small dataset. The model can be used to enable the engineering of robust new control algorithms and controller hardware for future engines using offline processes

An improved rate of heat release model for modern high speed diesel engines

To meet the increasingly stringent emissions standards, diesel engines need to include more active technologies with their associated control systems. Hardware-in-the-loop (HiL) approaches are becoming popular where the engine system is represented as a real-time capable model to allow development of the controller hardware and software without the need for the real engine system. This paper focusses on the engine model required in such approaches. A number of semi-physical, zero-dimensional combustion modeling techniques are enhanced and combined into a complete model, these include—ignition delay, premixed and diffusion combustion and wall impingement. In addition, a fuel injection model was used to provide fuel injection rate from solenoid energizing signals. The model was parameterized using a small set of experimental data from an engine dynamometer test facility and validated against a complete data set covering the full engine speed and torque range. The model was shown to characterize the rate of heat release (RoHR) well over the engine speed and load range. Critically, the wall impingement model improved R2 value for maximum RoHR from 0.89 to 0.96. This was reflected in the model's ability to match both pilot and main combustion phasing, and peak heat release rates derived from measured data. The model predicted indicated mean effective pressure and maximum pressure with R2 values of 0.99 across the engine map. The worst prediction was for the angle of maximum pressure which had an R2 of 0.74. The results demonstrate the predictive ability of the model, with only a small set of empirical data for training—this is a key advantage over conventional methods. The fuel injection model yielded good results for predicted injection quantity (R2 = 0.99) and enabled the use of the RoHR model without the need for measured rate of injection.</jats:p

Accuracy of Diesel Engine Combustion Metrics over the Full Range of Engine Operating Conditions

Measuring and analyzing combustion is a critical part of the development of high efficiency and low emitting engines. Faced with changes in legislation such as real driving emissions (RDE) and the fundamental change in the role of the combustion engine with the introduction of hybrid-electric powertrains, it is essential that combustion analysis can be conducted accurately across the full range of operating conditions. In this work, the sensitivity of five key combustion metrics is investigated with respect to eight necessary assumptions used for single zone diesel combustion analysis. The sensitivity was evaluated over the complete operating range of the engine using a combination of experimental and modeling techniques. This provides a holistic understanding of combustion measurement accuracy. For several metrics, it was found that the sensitivity at the mid-speed/load condition was not representative of sensitivity across the full operating range, in particular at low speeds and loads. Peak heat release rate and indicated mean effective pressure (IMEP) were found to be most sensitive to the determination of top dead center (TDC) and the assumption of in-cylinder gas properties. An error of 0.5 deg in the location of TDC would cause on average a 4.2% error in peak heat release rate. The ratio of specific heats had a strong impact on peak heat release with an error of 8% for using the assumption of a constant value. A novel method for determining TDC was proposed which combined a filling and emptying simulation with measured data obtained experimentally from an advanced engine test rig with external boosting system. This approach improved the robustness of the prediction of TDC which will allow engineers to measure accurate combustion data in operating conditions representative of in-service applications.</p

Characterisation and Optimisation of a Real-Time Diesel engine model

Accurate real-time engine models are an essential step to allow the development of control algorithms in parallel to the development of engine hardware using hardware-in-the-loop applications. A physics-based model of the engine high-pressure air path and combustion chamber is presented. The model was parameterised using data from a small set of carefully selected operating conditions for a 2.0 l diesel engine. The model was subsequently validated over the complete engine operating map with exhaust gas recirculation and without exhaust gas recirculation. A high level of fit was achieved with R2 values above 0.94 for the mean effective pressure and above 0.99 for the air flow rate. The model run time was then reduced for real-time application by using forward differencing and single-precision floating-point numbers and by calculating the in-cylinder prediction for only a single cylinder. A further improvement of 25% in the run time was achieved by improving the submodels, including the strategic use of one-dimensional and two-dimensional look-up tables with optimised resolution. The model exceeds the performance of similar models in the literature, achieving a crank angle resolution of 0.5° at 4000 r/min. This simulation step size still yields good accuracy in comparison with a crank angle resolution of 0.1° and was validated against the experimental results from a New European Driving Cycle. The real-time model allows the development of control strategies before the engine hardware is available, meaning that more time can be spent to ensure that the engine can meet the performance and the emissions requirements over its full operating range

Age grading \u3cem\u3eAn. gambiae\u3c/em\u3e and \u3cem\u3eAn. arabiensis\u3c/em\u3e using near infrared spectra and artificial neural networks

Background Near infrared spectroscopy (NIRS) is currently complementing techniques to age-grade mosquitoes. NIRS classifies lab-reared and semi-field raised mosquitoes into \u3c or ≥ 7 days old with an average accuracy of 80%, achieved by training a regression model using partial least squares (PLS) and interpreted as a binary classifier. Methods and findings We explore whether using an artificial neural network (ANN) analysis instead of PLS regression improves the current accuracy of NIRS models for age-grading malaria transmitting mosquitoes. We also explore if directly training a binary classifier instead of training a regression model and interpreting it as a binary classifier improves the accuracy. A total of 786 and 870 NIR spectra collected from laboratory reared An. gambiae and An. arabiensis, respectively, were used and pre-processed according to previously published protocols. The ANN regression model scored root mean squared error (RMSE) of 1.6 ± 0.2 for An. gambiae and 2.8 ± 0.2 for An. arabiensis; whereas the PLS regression model scored RMSE of 3.7 ± 0.2 for An. gambiae, and 4.5 ± 0.1 for An. arabiensis. When we interpreted regression models as binary classifiers, the accuracy of the ANN regression model was 93.7 ± 1.0% for An. gambiae, and 90.2 ± 1.7% for An. arabiensis; while PLS regression model scored the accuracy of 83.9 ± 2.3% for An. gambiae, and 80.3 ± 2.1% for An. arabiensis. We also find that a directly trained binary classifier yields higher age estimation accuracy than a regression model interpreted as a binary classifier. A directly trained ANN binary classifier scored an accuracy of 99.4 ± 1.0 for An. gambiae and 99.0 ± 0.6% for An. arabiensis; while a directly trained PLS binary classifier scored 93.6 ± 1.2% for An. gambiae and 88.7 ± 1.1% for An. arabiensis. We further tested the reproducibility of these results on different independent mosquito datasets. ANNs scored higher estimation accuracies than when the same age models are trained using PLS. Regardless of the model architecture, directly trained binary classifiers scored higher accuracies on classifying age of mosquitoes than regression models translated as binary classifiers. Conclusion We recommend training models to estimate age of An. arabiensis and An. gambiae using ANN model architectures (especially for datasets with at least 70 mosquitoes per age group) and direct training of binary classifier instead of training a regression model and interpreting it as a binary classifier

An investigation of the individual differences of the students at Palmer Memorial Institute, Sedalia, North Carolina, in the language arts.

Thesis (M.A.)--Boston Universit