Uncertain variables and their applications for a class of uncertain systems

This paper presents definitions and basic properties of uncertain variables and shows how they may be applied to the analysis and decision making in static systems with unknown parameters in their mathematical models. The unknown parameters are assumed to be uncertain variables described by certainty distributions given by an expert. Two versions of the uncertain variables are described. The uncertain variable in the first version may be considered as a special case of the fuzzy number with a specific interpretation. Two forms of systems are considered in the paper: a system described by a function (functional system) and a system described by a relation (relational system). In both cases the statements and general solutions of the analysis and decision problems are presented. Simple examples illustrating the application of the uncertain variables are included.     

Evaporation rate and separation factor of molecular distillation in a falling film apparatus

During molecular distillation in a falling film apparatus, temperature and concentration of the more volatile components undergo a marked decrease in axial and radial directions, due to the distillation in vacuo. The gradients produce changes in the rate of surface evaporation and separation efficiency along the flow path. A theoretical study of this problem is presented for binary mixtures. The respective differential equations for heat and mass transfer in the liquid film are solved numerically. As the results demonstrate, the aspect ratio of an apparatus should be large when a high separation is required and small when a high distillation rate is more important.     

Initial cutting conditions by abrasive grain fixed flexibly

In the paper, the initial cutting conditions by an abrasive grain fixed flexibly have been described. These conditions have been determined by incision angle at the beginning of machining zone as well as the occurring phenomena resulting from a mechanical cooperation of abrasive grain with machined material. It has been revealed that the incision angle may affect the direction of changes of roughness of the smoothed surface, making it possible to forecast this output magnitude. The dependences of this angle on the machining parameters have been derived for the conditions of forward and backward machining. They make it possible to choose these parameters as a rationale for the smoothing effects of finishing. The presented considerations and the conclusions coming out of them have been verified by experiment, and some exemplary proofs of these cognitive actions are described in the paper.     

Numerical analysis of erosion of the rotor labyrinth seal in a geothermal turbine

Excessive erosion of the labyrinth seal of a 110 MW geothermal turbine has been investigated. This study used computational fluid dynamics (CFD) and aims to identify one cause of erosion and a possible solution for substantially reducing it. The predictions were based upon a numerical calculation using a CFD model of the labyrinth seal with a water/steam flow containing hard solid particles and solved with a commercial CFD code: Fluent V5.0. The results confirmed the existence of flow conditions that play a major role in the rotor labyrinth seal erosion. Afterwards, the flow path was simulated with changes of rotor labyrinth seal geometry, which are indeed feasible of being implemented. The results confirmed that it is possible to reduce the erosion process by approximately 80% by incorporating a steam flow deflector in the fourth stage diaphragm, which changes the steam flow direction in the inlet zone to the rotor labyrinth seal channel, resulting in a reduction in steam volumetric mass flow and hard particle velocity by about 44%.     

Modification of technological properties of fish protein concentrates

Fish protein concentrates are mixtures of cross‐linked and aggregated molecules of different muscle proteins. The final conformation of the components of the mixtures is formed as a result of procedures applied to convert the raw material into a product of desirable and stable sensory properties, containing less than 0.1% of lipids. To achieve this end usually extraction with hot organic solvents, mainly isopropyl alcohol and 1,2‐dichloroethane, followed by air drying are employed. These conditions bring about denaturation of many of the proteins followed by aggregation of the molecules due to the interaction of reactive functional groups in extended polypeptide chains. In the final product a large proportion of hydrophobic groups is exposed to the solvent and the proteins exhibit an extremely low water affinity. Such concentrates, although valuable as protein supplements, have only limited suitability as active components of various processed foods, as they have poor technological value. They are insoluble or have a very low water dispersibility and swelling ability, do not form gels after heating, or have any significant fat‐emulsifying capacity. Changing the dissociation or number of ionic groups of the molecules prior to extraction, e.g., by acidifying or acylating, can partially reduce the denaturing effect of heat and organic solvents and thus improve the functional properties of the product. An upgrading of the quality of concentrates produced by hot extraction can be achieved by partial enzymatic or chemical deaggregation, hydrolysis followed by the plastein reaction, or formation of suitable derivatives. The best results have been obtained by partial hydrolysis of acylated proteins or precipitation of the aggregated products using sodium hexametaphosphate. The functional properties of such products are comparable to those of vegetable protein isolates used as meat extenders. Various protein products of high technological value can be also obtained by enzymatic hydrolysis of the raw material, followed by separation of the lipids without organic solvent extraction. Such products, however, have a distinct odor and flavor and must be stabilized because of residual lipids.     

Numerical modeling of gland seal erosion in a geothermal turbine

Excessive erosion of the low-pressure rotor end gland seal of a 25 MWe geothermal turbine produced a partial loss of turbine vacuum that degraded cycle efficiency. This study used computational fluid dynamics (CFD) to identify the causes of erosion and the optimal steam seal system flow conditions for reducing the erosion problem. The predictions were based upon a numerical calculation using a commercial CFD code (Adapco Star-CD) to model the rotor end gland seal with a steam flow containing hard solid particles. The results confirmed that flow conditions play a major role in rotor gland seal erosion. By changing steam seal flow pressures to vary flow, it was confirmed that there is a threshold seal flow condition below which erosion does not occur, or is minimized. Optimizing the rotor end gland seal supply pressure and intercondenser pressure reduced the turbulent flow kinetic energy by 49%, with a corresponding decrease in the erosion rate of the rotor gland seal surface. The erosion rate is related directly to the particle velocity and turbulent flow kinetic energy. Recommendations are provided for adjusting the rotor end gland seal system to avoid erosion.     

VAGUENESS AND UNCERTAINTY: A ROUGH SET PERSPECTIVE

Vagueness and uncertainty have attracted the attention of philosophers and logicians for many years. Recently, AI researchers contributed essentially to this area of research. Fuzzy set theory and the theory of evidence are seemingly the most appealing topics. On this note we present a new approach, based on the rough set theory, for looking to these problems. The theory of rough sets seems a suitable mathematical tool for dealing with problems of vagueness and uncertainty. This paper is a modified version of the author's lecture titled "An inquiry into vagueness and uncertainty," which was delivered at the AI Conference in Wigry (Poland), 1994.     

Mixed-Mode Oscillations in a Modified Chua’s Circuit

We consider a singularly perturbed system of differential equations of the form ε u′=g(u,v,λ), v′=f(u,v,λ), where (u,v)∈R ³, 0<ε?1, and λ is a set of parameters. Such a system describes a modified Chua’s circuit with mixed-mode oscillations (MMOs). MMOs consist of a series of small-amplitude oscillations (canard solutions) and large-amplitude relaxations. In the paper we provide a series of both numerical and analytical analyses of the singularly perturbed system for the modified Chua’s circuit with nonlinear f and g. In particular, we analyze the occurrence of the Farey sequence $\it L^{s}$ , where $\it L$ and $\it s$ are the numbers of large and small oscillations, respectively.