Showing papers on "Mathematical model published in 1974"

Power system modeling

Abstract: A discussion of the philosophy of modeling of three-phase transmission lines, three-phase transformers, three-phase generators, and power system loads is presented. Although the topic is very basic, the material covered is not all conventional. Single-phase representation of a three-phase power system is discussed in detail. Assumptions usually employed in the power industry are stated. Also discussed is the mathematical representation of a non-symmetrical three-phase power system in which the symmetrical-component method is not applied. An important aspect is the study of the models used in present-day problems as well as the models that may be required in the near future.

Identification of human driver models in car following

Abstract: This paper presents the development of two new mathematical models of driver behavior in single-lane car following situations. Optimum parameter values in each of these models were obtained using standard parameter identification algorithms. The basic approach to model development was to derive the model structure using optimal control theory. The problem was formulated as a model-tracking problem and a quadratic cost function was minimized. Model parameters were optimized by comparing model behavior with freeway data obtained on Interstate 71 in Ohio by Clear and Treiterer. The results indicate that the models fit the data very well during acceleration and deceleration phases, but not during constant velocity regions. To obtain a better fit during transitions between acceleration and deceleration phases, a second model was postulated based on the hypothesis that the driver tracks not only the car directly in front of him, but also cars directly ahead of the lead car. An adaptive controller structure with a mode switching algorithm has been derived and its parameters optimized.

Admissible Scoring Systems for Continuous Distributions

Abstract: ABSTRACT The defining property of an admissible scoring system is that any individual perceives himself as maximizing his expected score by reporting his true subjective distribution. The use of admissible scoring systems as a measure of probabilistic forecasts is becoming increasingly well-known in those.cases where the forecast is a discrete distributicn over a finite number of alternatives. Most serious forecastS which are made in the real world seem to be forecasts of quantitieL rather than choices between a finite number of alternatives. In such cases as this, it seems much more natural to ask the forecaster to specify a continuous probability distribution which represents his expectations rather than trying to re-cast a basically continuous process into a discrete one. To construct an admissible scoring system for a continuous distribution, a collection of possiblid bets can be postulated on a continuous variable, and an admissible scoring system can be constructed as the net pay-off to a forecaster who takes all bets (and only those bets). which appear favorable on the basis of his reported distribution. Mathematical models for this and alternative systems are presentedlAuthor/BW)

Realistic Models in Population Ecology

Abstract: Publisher Summary This chapter discusses the realistic population models, based on the physiological, ecological and social behavior of individuals in the population, providing insight, and has predictive validity. They are useful in determining optimal strategies for pest control, harvesting, preservation of species etc. Simulation studies rely heavily on statistical considerations, for example, the probability of encountering a mate or predator. In contrast, the models discussed herein are primarily deterministic and such random events are taken into account as averages. Furthermore, in such models climate may be considered to vary according to some statistical distribution in its influence on births, deaths, and so on; however, the birth rate itself is not considered to be a random variable. In general, the approach employed here is based on partial and ordinary differential equations. Many algebraic models are, in fact, discrete approximations to partial differential equations, and certain integral formulations and branching processes can also be shown to be equivalent to partial differential equations. Currently, digital computers are routinely employed to obtain solutions to mathematical models. The results of some digital computer models are discussed.

A three dimensional vehicle-man model for collision and high acceleration studies.

Abstract: The basic elements of a mathematical analysis of a three-dimensional vehicle (cockpit)-- occupant simulation model are presented. The model employs Hanavan's finite segment human body model and possesses 31 degrees of freedom. The dynamical analysis is based upon Lagrange's form of d'Alembert's principle, which systematically provides for an efficient computer-oriented derivation of the governing dynamical equations of motion. The model possesses a broad range of application. An elementary study of a front-end collision is presented as an illustrative example.

Modeling of DC Motors for Control Applications

Abstract: Three different mathematical models of an armature-controlled dc motor are considered: (i) a precise nonlinear model, (ii) a piecewise linear model, and (iii) a second-order linear model. Experimental results are presented comparing the various models, and a range of applications for each is suggested.

Nonlinear Analysis of Solid Rocket Combustion Instability. Volume I.

Abstract: : The primary objective of the current effort was to improve the utility, efficiency and accuracy of the previously developed nonlinear longitudinal combustion instability program. A finite difference procedure has been substituted for the method of characteristics solution of the governing equations of motion. The range of allowable motor and grain geometries has been greatly extended. In addition, the two-phase analysis has been extended to multiple particle sizes. A comparison with data from a small laboratory pulse motor has demonstrated that the present nonlinear model is capable of quantitatively predicting limiting amplitude when the combustion response of the propellant is adequately characterized. The program has also been modified to make it applicable to T-burners. A vent model which accounts for acoustic radiation losses has been developed. Separate nonlinear particle damping and uncoupled nonlinear combustion response studies have been carried out. (Modified author abstract)

Non-linear Disease Progress Curves

Abstract: This chapter is about mathematical models — formulae capable in some degree of describing natural events, usually by oversimplification. In particular, it is concerned with the process whereby collected data are approximated by some explicit mathematical function. We are of the opinion that there are two common attitudes towards this process. The more primitive is to consider the model simply as a means of fitting a line, a plane, or a hyperplane through a swarm of points to some optimum degree of closeness, commonly by minimizing the sum of squared deviations from the fitted function. The second, more sophisticated approach is to attempt to develop a function derived from some theory concerning the underlying natural processes which generated the data. The two approaches are not exclusive, for the second always leads to something like the first. But the first does not necessarily lead to the second, nor is there inherent in the first approach any guarantee of an improved understanding of natural phenomena.

Transient modeling of a catalytic converter to reduce nitric oxide in automobile exhaust

Abstract: Mathematical models are developed to study the catalytic reduction of nitric oxide contained in automobile exhaust in which the temperature, flow rate, and concentrations of various species vary widely with time. The quasi-static approximation is compared to the fully dynamic model. In the quasi-static model all processes are steady state except for the solid temperature and inlet conditions. Suggestions are given for deciding a priori if the quasi-static model is appropriate. Suggestions are also given for integrating the quasi-static equations in order to minimize errors compared to the dynamic model. The performance of three different catalysts is examined with the mathematical model, when the inlet conditions correspond to typical values of temperature, flow rate, and concentration when the automobile is operated according to the Federal Test Procedure.

Statistical ground excitation models for high speed vehicle dynamic analysis

Abstract: The method used to statistically describe a digitally defined ground roughness profile, based on measured data, is outlined and illustrated by reduction of the survey data of the Tracked Levitated Research Vehicle's (TLRV) Initial guideway section. The power spectral density (PSD) is the statistic of prime interest. Its use as the ground roughness excitation function in linear vehicle dynamic response analyses provides, the impetus. The PSD is not unique; therefore, when calculated for use in such analyses, the vehicle speed and suspension natural frequencies become critical parameters. The statistical estimates of the PSD and autocorrelation (AC) functions based on this TLRV data indicate a reasonable fit with mathematical models which consist of Fourier transform pairs. These PSD models contain less energy at low frequencies than the model presently used. A first-order vehicle dynamic response analysis incorporating one of these models results in substantial reductions of suspension stroke response. The roughness coefficient (A) of this section of thw TLRV guideway is approximately 1.2 x 10 to the minus 6th power feet-radians.

The Transportation Problem with Mixed Constraints

Abstract: A generalization of the standard transportation model in which the origin and destination constraints consist not only of equality but also inequality constraints is considered. It is shown that the model is equivalent to a standard transportation problem having only one additional origin and destination.

A theoretical model of pedestrian flow

Abstract: An entropy-maximizing model of a generalized pedestrian flow system is developed. This model is based on a fundamental conception of pedestrian traffic as being contained within a linear network. The model then maximizes the entropy of pedestrian flow within any given network, subject to a basic set of Kirchoff conditions. The resulting final equations are a special case of the gravity model. A general solution method is discussed and several numerical experiments with the model are described.

Stability of an Axial Flow Compressor with Steady Inlet Conditions

Abstract: A series of mathematical models of varying complexity which describe the dynamic behaviour of an axial flow compressor as a set of nonlinear differential equations are derived in a systematic way. These models are justified by comparing their stability with experimental surge data.

Some Comments on the Use of Mathematical Models in Anthropology

Abstract: It has become increasingly apparent that mathematical models may play a significant role in anthropological methodology. Less apparent is the fact that such models have an important place in formulation of theory as well. At the same time, many errors appear in attempts to use mathematical models. This paper attempts to indicate the nature of such errors and a methodology by which they can be avoided. A case study is presented showing the relationship of mathematical models to anthropological theory. Department of Anthropology University of California, Los Angeles December, 1972 AS IS THE CASE for students in other disciplines, anthropologists are becoming increasingly aware that the use of mathematical models can be a very powerful tool in the analysis of data and the formulation of theory. Mathematics is useful if for no other reason than that the very nature of a mathematical model requires precise definitions, exact statements of relationships between variables, and quantification of data. In a mathematical model, it is not sufficient simply to state that variable A is correlated with variable B, but the precise way in which B changes as A changes-for example, linearly, exponentially, or otherwise-must be stated. Such rigor in defining relationships necessitates a scrutiny of data and a rethinking of theory that might not occur without the formulation of a mathematical model. A mathematical model thus provides a concise way to state relationships among variables. In addition, the attempt to establish a model for use in a particular instance may itself facilitate the process of understanding and explaining the phenomena under observation. This important aspect of mathematical models has, unfortunately, been little exploited. The purpose of this paper is to explore the ways in which mathematical models can be and have been used in this manner. In the anthropological literature, there are many examples that could be cited that demonstrate the usefulness of mathematical models for explication. White's An anatomy of kinship (1963), for instance, shows the power that formal mathematical models have if a set of basic (and exhaustive) definitions for a system can be stated explicitly. By first deriving such a set of definitions for an exogamous marriage system, he was able to demonstrate that the resulting structure has a particular mathematical form, known as a group, and hence can be analyzed by the concepts and theory of that branch of mathematics known as group theory. At the same time that this makes the structure of the marriage system so defined apparent, it also makes equally obvious any sources of error in the model should its conclusions be untenable, for errors can only lie in the basic set of definitions. These can then be modified and, if necessary, a new structure developed. In the absence of such explicit definitions and well-defined theory, the result can be near chaos-witness the debate in the early 1960's over the validity of Levi-Strauss' purported distinction between marriage systems built on "prescription" versus those derived from "preference." Without precise definitions of these terms, it becomes extremely difficult to resolve the validity of the distinction implied by the terms. While Ackerman (1964) tried to do this statistically, it is clear that in part his efforts could not be wholly convincing. He was obliged to test not just an explicit definition, but also his interpretation of Levi-Strauss' term, which need not have been the same as one by Needham. And Needham in turn does not appear to agree with Levi-Strauss (Harris 1968:512). Most mathematical models used in anthropology, though, are statistical in nature. These are the simplest to formulate and, generally speaking, most easily adapted to traditional ways of anthropological analysis. Such statistical models often lack precision, in the sense of formally showing the nature of the relationship between variables. However, there are implicit assumptions

Identification of Aircraft Stability and Control Coefficients for the High Angle-of-Attack Regime.

Abstract: : A central problem of the stall/post-stall flight regime is the identification of nonlinear aerodynamic coefficients whose adverse characteristics may produce severe handling quality degradation. This identification problem is twofold: determination of the nonlinear aerodynamic models and estimation of the coefficients of these models. An integrated parameter identification procedure based on maximum likelihood methods is presented to resolve these problems with verification results based on a nonlinear six-degree-of-freedom digital aircraft simulation. The identification procedure consists of the sequential application of a model determination algorithm and a maximum likelihood identification method. Input design and measurement system specification techniques are combined with this application to form the integrated parameter identification process. The model determination algorithm is based on least squares subset regression techniques. This structure and parameter estimation procedure is applied to the response of an advanced fighter. Results of the application of the identification procedure to these data have shown that the model structure and parameters of the nonlinear regime can be successfully identified, even in the presence of high levels of process and measurement noise. It is further shown that the estimates obtained from a data length with a given input can be used to successfully predict the response of the aircraft to another input in the same flight regime. The procedures established and verified are highly flexible and may be readily applied to modeling other classes of nonlinear vehicles from test data.