Master of Science / Department of Mechanical and Nuclear Engineering / Warren N. White / As traditional resources are becoming scarce, renewable energy is a recent topic receiving greater concern. Among the renewable energies, wind power is a very popular type of energy extracted from wind which is readily available in the environment. The use of wind power all over the world is receiving increased attention. Horizontal axis wind turbines are the most popular equipment for extracting power form the wind. One of the problems of using wind turbines is how to maximize the wind power capture. In this paper, a method for maximizing the rotor power coefficient of a wind turbine is proposed. Simultaneous Perturbation Stochastic Approximation (SPSA) is an efficient way for extremum seeking. It is different from the classical gradient based extremum seeking algorithms. For maximizing the rotor power coefficient, it only needs two objective function measurements to take a step toward the next extremum approximation. The one measurement SPSA is a modification of SPSA method developed in this work. Instead of using measurements of two positions occurring at random directions away from the current position, it uses the measurement of one position in a random direction and the measurement of the current position to estimate the gradient. Usually, the rotor power coefficient is not easily measurable. For speed regulation, a nonlinear robust speed controller is used in this work. The controller produces an estimate of the aerodynamic torque of wind turbine. The quality of this estimate improves with time. From that, a good estimate of power coefficient can be obtained. Simulations in MATLAB are executed with a model of a wind turbine based on its dynamic equations. From simulations, it can be seen that the one measurement SPSA method works very well for the wind turbine. It changes the tip speed ratio and blade pitch simultaneously, and the power coefficient reaches its maximum value quickly in a reliable manner. The power capture optimization is then implemented in FAST, a turbine simulation model created by NREL which is used to test the 5MW NREL reference turbine. From the results, it is evident that the wind turbine reaches the maximum power coefficient rapidly.

This research investigates developing a training method for Restricted Hopfield Network (RHN) which is a subcategory of Hopfield Networks. Hopfield Networks are recurrent neural networks proposed in 1982 by John Hopfield. They are useful for different applications such as pattern restoration, pattern completion/generalization, and pattern association. In this study, we propose an enhanced training method for RHN which not only improves the convergence of the training sub-routine, but also is shown to enhance the learning capability of the network. Particularly, after describing the architecture/components of the model, we propose a modified variant of SPSA which in conjunction with back-propagation over time result in a training algorithm with an enhanced convergence for RHN. The trained network is also shown to achieve a better memory recall in the presence of noisy/distorted input. We perform several experiments, using various datasets, to verify the convergence of the training sub-routine, evaluate the impact of different parameters of the model, and compare the performance of the trained RHN in recreating distorted input patterns compared to conventional RBM and Hopfield network and other training methods.

During the last century, the number of car users has increased as an effect of the increasing population growth. To manage the environmental and infrastructural challenges that comes with a more congested traffic network, traffic planning has become of higher importance to analyze the current traffic state and to predict future capacity challenges and effects of investments. These analysis and evaluations are commonly performed in different traffic analysis tools, where updated and realistic traffic demand needs to be provided to ensure reasonable results. In this thesis, a macroscopic model of Norrköping municipality constructed in the traffic demand modelling software Visum and a daily Origin-Destination(OD)-matrix is considered. The goal of this thesis is to produce a method that modify the current daily demand matrix into hourly demand matrices, called hourly target matrices, that represents a typical weekday. The goal is also to implement and evaluate the OD-estimation algorithm Simultaneous Perturbation Stochastic Approximation (SPSA) to obtain updated and valid demand matrices for the network model of Norrköping. The method of dividing the daily demand matrix into hourly target matrices is based on the paper by Spiess %26 Suter (1990). The method makes use of the available daily trip purpose matrices combined with hourly link flow observations from 96 links in a multiple linear regression model to obtain 24 hourly demand matrices. The resulting matrices are compared with the link flow observations and has different levels of R^2-fit, the maximum fit is 85.79 % and the minimum fit is 55.89 %. The average R^2-value is 72 %. The OD-estimation based on SPSA is performed on the AM and PM peak hours. The algorithm is implemented in Python scripts that are called from Visum where the traffic assignments is calculated. The result is an increase in R^2-value since the link flow difference between estimated and observed link flow is decreased. In total, the estimated link flows are improved by 7.4 % in the AM peak hour and 15.6 % in the PM peak hour. The total absolute change in OD-demand is 3 871 trips for AM peak hour and 6 452 trips for the PM peak hour. The estimated OD-matrices are evaluated by qualitatively visualizing the difference in heat maps and in the quantitative measure structural similarity index. The result is no major structural change from the hourly target matrices which verifies that the information used when the target matrices is produced still is considered. The total demand increased in both hours, with 505 respectively 2 431 trips and flows in some OD-pairs has a very high percental change. This was restricted by adding a penalty term to the SPSA-algorithm on the PM peak hour. The result of penalized SPSA is a much less increase of total demand as well as less percental change of the OD-flows. Though, this to a cost of not decreasing the link flow difference in the same magnitude.

This dissertation aims to improve the performance of existing assignment-based dynamic origin-destination (O-D) matrix estimation models to successfully apply Intelligent Transportation Systems (ITS) strategies for the purposes of traffic congestion relief and dynamic traffic assignment (DTA) in transportation network modeling. The methodology framework has two advantages over the existing assignment-based dynamic O-D matrix estimation models. First, it combines an initial O-D estimation model into the estimation process to provide a high confidence level of initial input for the dynamic O-D estimation model, which has the potential to improve the final estimation results and reduce the associated computation time. Second, the proposed methodology framework can automatically convert traffic volume deviation to traffic density deviation in the objective function under congested traffic conditions. Traffic density is a better indicator for traffic demand than traffic volume under congested traffic condition, thus the conversion can contribute to improving the estimation performance. The proposed method indicates a better performance than a typical assignment-based estimation model (Zhou et al., 2003) in several case studies. In the case study for I-95 in Miami-Dade County, Florida, the proposed method produces a good result in seven iterations, with a root mean square percentage error (RMSPE) of 0.010 for traffic volume and a RMSPE of 0.283 for speed. In contrast, Zhou’s model requires 50 iterations to obtain a RMSPE of 0.023 for volume and a RMSPE of 0.285 for speed. In the case study for Jacksonville, Florida, the proposed method reaches a convergent solution in 16 iterations with a RMSPE of 0.045 for volume and a RMSPE of 0.110 for speed, while Zhou’s model needs 10 iterations to obtain the best solution, with a RMSPE of 0.168 for volume and a RMSPE of 0.179 for speed. The successful application of the proposed methodology framework to real road networks demonstrates its ability to provide results both with satisfactory accuracy and within a reasonable time, thus establishing its potential usefulness to support dynamic traffic assignment modeling, ITS systems, and other strategies.

Optimization problems involving uncertainties are common in a variety of engineering disciplines such as transportation systems, manufacturing, communication networks, healthcare and finance. The large number of input variables and the lack of a system model prohibit a precise analytical solution and a viable alternative is to employ simulation-based optimization. The idea here is to simulate a few times the stochastic system under consideration while updating the system parameters until a good enough solution is obtained. Formally, given only noise-corrupted measurements of an objective function, we wish to end a parameter which minimises the objective function. Iterative algorithms using statistical methods search the feasible region to improve upon the candidate parameter. Stochastic approximation algorithms are best suited; most studied and applied algorithms for funding solutions when the feasible region is a continuously valued set. One can use information on the gradient/Hessian of the objective to aid the search process. However, due to lack of knowledge of the noise distribution, one needs to estimate the gradient/Hessian from noisy samples of the cost function obtained from simulation. Simple gradient search schemes take much iteration to converge to a local minimum and are heavily dependent on the choice of step-sizes. Stochastic Newton methods, on the other hand, can counter the ill-conditioning of the objective function as they incorporate second-order information into the stochastic updates. Stochastic Newton methods are often more accurate than simple gradient search schemes. We propose enhancements to the Hessian estimation scheme used in two recently proposed stochastic Newton methods, based on the ideas of random directions stochastic approximation (2RDSA) [21] and simultaneous perturbation stochastic approximation (2SPSA-31) [6], respectively. The proposed scheme, inspired by [29], reduces the error in the Hessian estimate by (i) Incorporating a zero-mean feedback term; and (ii) optimizing the step-sizes used in the Hessian recursion. We prove that both 2RDSA and 2SPSA-3 with our Hessian improvement scheme converges asymptotically to the true Hessian. The key advantage with 2RDSA and 2SPSA-3 is that they require only 75% of the simulation cost per-iteration for 2SPSA with improved Hessian estimation (2SPSA-IH) [29]. Numerical experiments show that 2RDSA-IH outperforms both 2SPSA-IH and 2RDSA without the improved Hessian estimation scheme.

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As urban population across the globe increases, the demand for adequate transportation grows. Several strategies have been suggested as a solution to the congestion which results from this high demand outpacing the existing supply of transportation facilities. High –Occupancy Toll (HOT) lanes have become increasingly more popular as a feature on today’s highway system. The I-95 Express HOT lane in Miami Florida, which is currently being expanded from a single Phase (Phase I) into two Phases, is one such HOT facility. With the growing abundance of such facilities comes the need for indepth study of demand patterns and development of an appropriate pricing scheme which reduces congestion. This research develops a method for dynamic pricing on the I-95 HOT facility such as to minimize total travel time and reduce congestion. We apply non-linear programming (NLP) techniques and the finite difference stochastic approximation (FDSA), genetic algorithm (GA) and simulated annealing (SA) stochastic algorithms to formulate and solve the problem within a cell transmission framework. The solution produced is the optimal flow and optimal toll required to minimize total travel time and thus is the system-optimal solution. We perform a comparative evaluation of FDSA, GA and SA non-linear programming algorithms used to solve the NLP and the ANOVA results show that there are differences in the performance of the NLP algorithms in solving this problem and reducing travel time. We then conclude by demonstrating that econometric iv forecasting methods utilizing vector autoregressive (VAR) techniques can be applied to successfully forecast demand for Phase 2 of the 95 Express which is planned for 2014

In Chapter 2, we propose several two-timescale simulation-based actor-critic algorithms for solution of infinite horizon Markov Decision Processes (MDPs) with finite state-space under the average cost criterion. On the slower timescale, all the algorithms perform a gradient search over corresponding policy spaces using two different Simultaneous Perturbation Stochastic Approximation (SPSA) gradient estimates. On the faster timescale, the differential cost function corresponding to a given stationary policy is updated and averaged for enhanced performance. A proof of convergence to a locally optimal policy is presented. Next, a memory efficient implementation using a feature-vector representation of the state-space and TD (0) learning along the faster timescale is discussed. A three-timescale simulation based algorithm for solution of infinite horizon discounted-cost MDPs via the Value Iteration approach is also proposed. An approximation of the Dynamic Programming operator T is applied to the value function iterates. A sketch of convergence explaining the dynamics of the algorithm using associated ODEs is presented. Numerical experiments on rate based flow control on a bottleneck node using a continuous-time queueing model are presented using the proposed algorithms. Next, in Chapter 3, we develop three simulation-based algorithms for finite-horizon MDPs (FHMDPs). The first algorithm is developed for finite state and compact action spaces while the other two are for finite state and finite action spaces. Convergence analysis is briefly sketched. We then concentrate on methods to mitigate the curse of dimensionality that affects FH-MDPs severely, as there is one probability transition matrix per stage. Two parametrized actor-critic algorithms for FHMDPs with compact action sets are proposed, the ‘critic’ in both algorithms learning the policy gradient. We show w.p1convergence to a set with the necessary condition for constrained optima. Further, a third algorithm for stochastic control of stopping time processes is presented. Numerical experiments with the proposed finite-horizon algorithms are shown for a problem of flow control in communication networks. Towards stochastic optimization, in Chapter 4, we propose five algorithms which are variants of SPSA. The original one measurement SPSA uses an estimate of the gradient of objective function L containing an additional bias term not seen in two-measurement SPSA. We propose a one-measurement algorithm that eliminates this bias, and has asymptotic convergence properties making for easier comparison with the two-measurement SPSA. The algorithm, under certain conditions, outperforms both forms of SPSA with the only overhead being the storage of a single measurement. We also propose a similar algorithm that uses perturbations obtained from normalized Hadamard matrices. The convergence w.p.1 of both algorithms is established. We extend measurement reuse to design three second-order SPSA algorithms, sketch the convergence analysis and present simulation results on an illustrative minimization problem. We then propose several stochastic approximation implementations for related algorithms in flow-control of communication networks, beginning with a discrete-time implementation of Kelly’s primal flow-control algorithm. Convergence with probability1 is shown, even in the presence of communication delays and stochastic effects seen in link congestion indications. Two relevant enhancements are then pursued :a) an implementation of the primal algorithm using second-order information, and b) an implementation where edge-routers rectify misbehaving flows. Also, discrete-time implementations of Kelly’s dual algorithm and primal-dual algorithm are proposed. Simulation results a) verifying the proposed algorithms and, b) comparing stability properties with an algorithm in the literature are presented.