An Extended Pearson System Useful In Reliability Analysis

In the present environment, industry should provide the products of high quality. Quality of products is judged by the period of time they can successfully perform their intended functions without failure. The cause of the failures can be ascertained through life testing experiments and the times to failure due to different cause are likely to follow different distributions. Knowledge of this distribution is essential to eliminate causes of failures and thereby to improve the quality and the reliability of products. The main accomplishment expected to the study is to develop statistical tools that could facilitate solution to lifetime data arising in such and similar contexts

Topological Invariants in Hydrodynamics and Hydromagnetics

In this thesis we are studying possible invariants in hydrodynamics and hydromagnetics. The concept of flux preservation and line preservation of vector fields, especially vorticity vector fields, have been studied from the very beginning of the study of fluid mechanics by Helmholtz and others. In ideal magnetohydrodynamic flows the magnetic fields satisfy the same conservation laws as that of vorticity field in ideal hydrodynamic flows. Apart from these there are many other fields also in ideal hydrodynamic and magnetohydrodynamic flows which preserves flux across a surface or whose vector lines are preserved. A general study using this analogy had not been made for a long time. Moreover there are other physical quantities which are also invariant under the flow, such as Ertel invariant. Using the calculus of differential forms Tur and Yanovsky classified the possible invariants in hydrodynamics. This mathematical abstraction of physical quantities to topological objects is needed for an elegant and complete analysis of invariants.Many authors used a four dimensional space-time manifold for analysing fluid flows. We have also used such a space-time manifold in obtaining invariants in the usual three dimensional flows.In chapter one we have discussed the invariants related to vorticity field using vorticity field two form w2 in E4. Corresponding to the invariance of four form w2 ^ w2 we have got the invariance of the quantity E. w. We have shown that in an isentropic flow this quantity is an invariant over an arbitrary volume.In chapter three we have extended this method to any divergence-free frozen-in field. In a four dimensional space-time manifold we have defined a closed differential two form and its potential one from corresponding to such a frozen-in field. Using this potential one form w1 , it is possible to define the forms dw1 , w1 ^ dw1 and dw1 ^ dw1 . Corresponding to the invariance of the four form we have got an additional invariant in the usual hydrodynamic flows, which can not be obtained by considering three dimensional space.In chapter four we have classified the possible integral invariants associated with the physical quantities which can be expressed using one form or two form in a three dimensional flow. After deriving some general results which hold for an arbitrary dimensional manifold we have illustrated them in the context of flows in three dimensional Euclidean space JR3. If the Lie derivative of a differential p-form w is not vanishing,then the surface integral of w over all p-surfaces need not be constant of flow. Even then there exist some special p-surfaces over which the integral is a constant of motion, if the Lie derivative of w satisfies certain conditions. Such surfaces can be utilised for investigating the qualitative properties of a flow in the absence of invariance over all p-surfaces. We have also discussed the conditions for line preservation and surface preservation of vector fields. We see that the surface preservation need not imply the line preservation. We have given some examples which illustrate the above results. The study given in this thesis is a continuation of that started by Vedan et.el. As mentioned earlier, they have used a four dimensional space-time manifold to obtain invariants of flow from variational formulation and application of Noether's theorem. This was from the point of view of hydrodynamic stability studies using Arnold's method. The use of a four dimensional manifold has great significance in the study of knots and links. In the context of hydrodynamics, helicity is a measure of knottedness of vortex lines. We are interested in the use of differential forms in E4 in the study of vortex knots and links. The knowledge of surface invariants given in chapter 4 may also be utilised for the analysis of vortex and magnetic reconnections.

Reinforcement Learning Approaches to Power System Scheduling

One major component of power system operation is generation scheduling. The objective of the work is to develop efficient control strategies to the power scheduling problems through Reinforcement Learning approaches. The three important active power scheduling problems are Unit Commitment, Economic Dispatch and Automatic Generation Control. Numerical solution methods proposed for solution of power scheduling are insufficient in handling large and complex systems. Soft Computing methods like Simulated Annealing, Evolutionary Programming etc., are efficient in handling complex cost functions, but find limitation in handling stochastic data existing in a practical system. Also the learning steps are to be repeated for each load demand which increases the computation time.Reinforcement Learning (RL) is a method of learning through interactions with environment. The main advantage of this approach is it does not require a precise mathematical formulation. It can learn either by interacting with the environment or interacting with a simulation model. Several optimization and control problems have been solved through Reinforcement Learning approach. The application of Reinforcement Learning in the field of Power system has been a few. The objective is to introduce and extend Reinforcement Learning approaches for the active power scheduling problems in an implementable manner. The main objectives can be enumerated as:(i) Evolve Reinforcement Learning based solutions to the Unit Commitment Problem.(ii) Find suitable solution strategies through Reinforcement Learning approach for Economic Dispatch. (iii) Extend the Reinforcement Learning solution to Automatic Generation Control with a different perspective. (iv) Check the suitability of the scheduling solutions to one of the existing power systems.First part of the thesis is concerned with the Reinforcement Learning approach to Unit Commitment problem. Unit Commitment Problem is formulated as a multi stage decision process. Q learning solution is developed to obtain the optimwn commitment schedule. Method of state aggregation is used to formulate an efficient solution considering the minimwn up time I down time constraints. The performance of the algorithms are evaluated for different systems and compared with other stochastic methods like Genetic Algorithm.Second stage of the work is concerned with solving Economic Dispatch problem. A simple and straight forward decision making strategy is first proposed in the Learning Automata algorithm. Then to solve the scheduling task of systems with large number of generating units, the problem is formulated as a multi stage decision making task. The solution obtained is extended in order to incorporate the transmission losses in the system. To make the Reinforcement Learning solution more efficient and to handle continuous state space, a fimction approximation strategy is proposed. The performance of the developed algorithms are tested for several standard test cases. Proposed method is compared with other recent methods like Partition Approach Algorithm, Simulated Annealing etc.As the final step of implementing the active power control loops in power system, Automatic Generation Control is also taken into consideration.Reinforcement Learning has already been applied to solve Automatic Generation Control loop. The RL solution is extended to take up the approach of common frequency for all the interconnected areas, more similar to practical systems. Performance of the RL controller is also compared with that of the conventional integral controller.In order to prove the suitability of the proposed methods to practical systems, second plant ofNeyveli Thennal Power Station (NTPS IT) is taken for case study. The perfonnance of the Reinforcement Learning solution is found to be better than the other existing methods, which provide the promising step towards RL based control schemes for practical power industry.Reinforcement Learning is applied to solve the scheduling problems in the power industry and found to give satisfactory perfonnance. Proposed solution provides a scope for getting more profit as the economic schedule is obtained instantaneously. Since Reinforcement Learning method can take the stochastic cost data obtained time to time from a plant, it gives an implementable method. As a further step, with suitable methods to interface with on line data, economic scheduling can be achieved instantaneously in a generation control center. Also power scheduling of systems with different sources such as hydro, thermal etc. can be looked into and Reinforcement Learning solutions can be achieved.

An assessment of potential public health risk associated with the extended survival of indicator and pathogenic bacteria in freshwater lake sediments

Microcosm studies were performed to evaluate the survival of Escherichia coli, Salmonella paratyphi and Vibrio parahaemolyticus in water and sediment collected from the freshwater region of Vembanad Lake (9 35◦N 76 25◦E) along the south west coast of India. All three test microorganisms showed significantly (p < 0.01) higher survival in sediment compared to overlying water. The survival in different sediment types with different particle size and organic carbon content revealed that sediment with small particle size and high organic carbon content could enhance their extended survival (p < 0.05). The results indicate that sediments of the Lake could act as a reservoir of pathogenic bacteria and exhibit a potential health hazard from possible resuspension and subsequent ingestion during recreational activities. Therefore, the assessment of bacterial concentration in freshwater Lake sediments used for contact and non contact recreation has of considerable significance for the proper assessment of microbial pollution of the overlying water, and for the management and protection of related health risk at specific recreational sites. Besides, assessment of the bacterial concentration in sediments can be used as a relatively stable indicator of long term mean bacterial concentration in the water column above