Equivalence conditions for classes of linear and non-linear distributed parameter systems

Equivalence of certain classes of second-order non-linear distributed parameter systems and corresponding linear third-order systems is established through a differential transformation technique. As linear systems are amenable to analysis through existing techniques, this study is expected to offer a method of tackling certain classes of non-linear problems which may otherwise prove to be formidable in nature.

Fuzzy-expert approach for voltage-reactive power dispatch

The voltage stability control problem has become an important concern for utilities transmitting power over long distances. This paper presents an approach using fuzzy set theory for reactive power control with the purpose of improving the voltage stability of a power system. To minimize the voltage deviations from pre-desired values of all the load buses, using the sensitivities with respect to reactive power control variables form the basis of the proposed fuzzy logic control (FLC). Control variables considered are switchable VAR compensators, On Load Tap Changing (OLTC) transformers and generator excitations. Voltage deviations and controlling variables are translated into fuzzy set notations to formulate the relation between voltage deviations and controlling ability of controlling devices. The developed fuzzy system is tested on a few simulated practical Indian power systems and some IEEE standard test systems. The performance of the fuzzy system is compared with conventional optimization technique and results obtained are encouraging. Results obtained for a 24 - node equivalent EHV system of part of Indian southern grid and IEEE New England 39-bus system are presented for illustration purposes. The proposed Fuzzy-Expert technique is found suitable for on-line applications in energy control centre as the solution is obtained fast with significant speedups.

A note on the equivalence of shock manifold equations

The shock manifold equation is a first order nonlinear partial differential equation, which describes the kinematics of a shockfront in an ideal gas with constant specific heats. However, it was found that there was more than one of these shock manifold equations, and the shock surface could be embedded in a one parameter family of surfaces, obtained as a solution of any of these shock manifold equations. Associated with each shock manifold equation is a set of characteristic curves called lsquoshock raysrsquo. This paper investigates the nature of various associated shock ray equations.

On the alleged equivalence of certain field theories

Abstract. We critically examine some recent claims that certain field theories with and without boson kinetic energy terms are equivalent. We point out that the crucial element in these claims is the finiteness or otherwise of the boson wavefunction renormalisation constant. We show that when this constant is finite, the equivalence proof offered in the literature fails in a direct way. When the constant is divergent, the claimed equivalence is only a consequence of improper use of divergent quantities.

Two-dimensional fuzzy fault tree analysis for chlorine release from a chlor-alkali industry using expert elicitation

The hazards associated with major accident hazard (MAN) industries are fire, explosion and toxic gas releases. Of these, toxic gas release is the worst as it has the potential to cause extensive fatalities. Qualitative and quantitative hazard analyses are essential for the identification and quantification of these hazards related to chemical industries. Fault tree analysis (FTA) is an established technique in hazard identification. This technique has the advantage of being both qualitative and quantitative, if the probabilities and frequencies of the basic events are known. This paper outlines the estimation of the probability of release of chlorine from storage and filling facility of chlor-alkali industry using FTA. An attempt has also been made to arrive at the probability of chlorine release using expert elicitation and proven fuzzy logic technique for Indian conditions. Sensitivity analysis has been done to evaluate the percentage contribution of each basic event that could lead to chlorine release. Two-dimensional fuzzy fault tree analysis (TDFFTA) has been proposed for balancing the hesitation factor involved in expert elicitation. (C) 2010 Elsevier B.V. All rights reserved.

A new Fuzzy-LOGIC based Model for Chlorophyll-a in Pulicat Lagoon, India

Coastal lagoons are complex ecosystems exhibiting a high degree of non-linearity in the distribution and exchange of nutrients dissolved in the water column due to their spatio-temporal characteristics. This factor has a direct influence on the concentrations of chlorophyll-a, an indicator of the primary productivity in the water bodies as lakes and lagoons. Moreover the seasonal variability in the characteristics of large-scale basins further contributes to the uncertainties in the data on the physico-chemical and biological characteristics of the lagoons. Considering the above, modelling the distributions of the nutrients with respect to the chlorophyll-concentrations, hence requires an effective approach which will appropriately account for the non-linearity of the ecosystem as well as the uncertainties in the available data. In the present investigation, fuzzy logic was used to develop a new model of the primary production for Pulicat lagoon, Southeast coast of India. Multiple regression analysis revealed that the concentrations of chlorophyll-a in the lagoon was highly influenced by the dissolved concentrations of nitrate, nitrites and phosphorous to different extents over different seasons and years. A high degree of agreement was obtained between the actual field values and those predicted by the new fuzzy model (d = 0.881 to 0.788) for the years 2005 and 2006, illustrating the efficiency of the model in predicting the values of chlorophyll-a in the lagoon.

Application of an evolutionary fuzzy system for the estimation of workforce deployment and cross-training in an assembly environment

Owing to the increased customer demands for make-to-order products and smaller product life-cycles, today assembly lines are designed to ensure a quick switch-over from one product model to another for companies' survival in market place. The complexity associated with the decisions pertaining to the type of training and number of workers and their exposition to the different tasks especially in the current era of customized production is a serious problem that the managers and the HRD gurus are facing in industry. This paper aims to determine the amount of cross-training and dynamic deployment policy caused by workforce flexibility for a make-to-order assembly. The aforementioned issues have been dealt with by adopting the concept of evolutionary fuzzy system because of the linguistic nature of the attributes associated with product variety and task complexity. A fuzzy system-based methodology is proposed to determine the amount of cross-training and dynamic deployment policy. The proposed methodology is tested on 10 sample products of varying complexities and the results obtained are in line with the conclusions drawn by previous researchers.

Data rectification and detection of trend shifts in jet engine path measurements using median filters and fuzzy logic

Filtering methods are explored for removing noise from data while preserving sharp edges that many indicate a trend shift in gas turbine measurements. Linear filters are found to be have problems with removing noise while preserving features in the signal. The nonlinear hybrid median filter is found to accurately reproduce the root signal from noisy data. Simulated faulty data and fault-free gas path measurement data are passed through median filters and health residuals for the data set are created. The health residual is a scalar norm of the gas path measurement deltas and is used to partition the faulty engine from the healthy engine using fuzzy sets. The fuzzy detection system is developed and tested with noisy data and with filtered data. It is found from tests with simulated fault-free and faulty data that fuzzy trend shift detection based on filtered data is very accurate with no false alarms and negligible missed alarms.

Fuzzy logic intelligent system for gas turbine module and system fault isolation

A fuzzy logic intelligent system is developed for gas-turbine fault isolation. The gas path measurements used for fault isolation are exhaust gas temperature, low and high rotor speed, and fuel flow. These four measurements are also called the cockpit parameters and are typically found in almost all older and newer jet engines. The fuzzy logic system uses rules developed from a model of performance influence coefficients to isolate engine faults while accounting for uncertainty in gas path measurements. It automates the reasoning process of an experienced powerplant engineer. Tests with simulated data show that the fuzzy system isolates faults with an accuracy of 89% with only the four cockpit measurements. However, if additional pressure and temperature probes between the compressors and before the burner, which are often found in newer jet engines, are considered, the fault isolation accuracy rises to as high as 98%. In addition, the additional sensors are useful in keeping the fault isolation system robust as quality of the measured data deteriorates.

Health monitoring,of a helicopter rotor in forward flight using fuzzy logic

A fuzzy logic system is developed for helicopter rotor system fault isolation. Inputs to the fuzzy logic system are measurement deviations of blade bending and torsion response and vibration from a "good" undamaged helicopter rotor. The rotor system measurements used are flap and lag bending tip deflections, elastic twist deflection at the tip, and three forces and three moments at the rotor hub. The fuzzy logic system uses rules developed from an aeroelastic model of the helicopter rotor with implanted faults to isolate the fault while accounting for uncertainty in the measurements. The faults modeled include moisture absorption, loss of trim mass, damaged lag damper, damaged pitch control system, misadjusted pitch link, and damaged flap. Tests with simulated data show that the fuzzy system isolates rotor system faults with an accuracy of about 90-100%. Furthermore, the fuzzy system is robust and gives excellent results, even when some measurements are not available. A rule-based expert system based on similar rules from the aeroelastic model performs much more poorly than the fuzzy system in the presence of high levels of uncertainty.

Machine-tool selection and operation allocation in FMS: solving a fuzzy goal-programming model using a genetic algorithm

The decision-making process for machine-tool selection and operation allocation in a flexible manufacturing system (FMS) usually involves multiple conflicting objectives. Thus, a fuzzy goal-programming model can be effectively applied to this decision problem. The paper addresses application of a fuzzy goal-programming concept to model the problem of machine-tool selection and operation allocation with explicit considerations given to objectives of minimizing the total cost of machining operation, material handling and set-up. The constraints pertaining to the capacity of machines, tool magazine and tool life are included in the model. A genetic algorithm (GA)-based approach is adopted to optimize this fuzzy goal-programming model. An illustrative example is provided and some results of computational experiments are reported.

A fuzzy control for network overload alleviation

This paper presents a prototype of a fuzzy system for alleviation of network overloads in the day-to-day operation of power systems. The control used for overload alleviation is real power generation rescheduling. Generation Shift Sensitivity Factors (GSSF) are computed accurately, using a more realistic operational load flow model. Overloading of lines and sensitivity of controlling variables are translated into fuzzy set notations to formulate the relation between overloading of line and controlling ability of generation scheduling. A fuzzy rule based system is formed to select the controllers, their movement direction and step size. Overall sensitivity of line loading to each of the generation is also considered in selecting the controller. Results obtained for network overload alleviation of two modified Indian power networks of 24 bus and 82 bus with line outage contingencies are presented for illustration purposes.