A network approach to the modelling of active magnetic bearings

The modelling of active magnetic bearings based on a network approach is considered. Unlike in the standard modelling approach, where a linearization of the current-force relation for the centred shaft position is used, network models permit to include the position dependence of the bearing force in the force model. This becomes necessary when model based controllers are used to stabilize a magnetically supported shaft in tracking applications.

The approach is based on the well known application of network models to magnetic circuits. Further simplifying assumptions are discussed which allow one to obtain a network with a limited number of lumped parameters describing the magnetic behaviour of a magnetic bearing. The modelling of a combined radial and axial bearing serves as an example for the application of the proposed approach. Furthermore, the fitting of the network based model to measured characteristic force curves is discussed. In this context, a method for including saturation effects in the model is sketched.     

An approach to modelling industrial unit processes: application to a spiral concentrator for minerals

A suite of computer models which simulate process operations in common use in the minerals processing industry is being developed. Application of the models is described with reference to a particular process device, the spiral concentrator. The paper sets out to explain the basic strategy behind the unit process modelling approach and discusses in detail the overall model structure adopted. The model aims to provide a set of equations, with sufficient physical significance to give a reasonable fit to any specific data set, and which can be systematically adjusted (through auxiliary models, user judgement and experience) to provide meaningful performance predictions over a broad range of operating conditions. The approach is thought to be applicable to a wide variety of processes. The model has been tested using a variety of ores, separated on plant-scale equipment and practical examples are given. The scope and limitations of the method are reported, drawing on the results of parallel experimental work. The extent to which this kind of approach can be used as a predictive tool in process design applications and in the day-to-day running of mineral processing plant is discussed.     

Parsimonious modelling and forecasting of seasonal time series

Some seasonal time series models are considered which are appropriate for the univariate modelling and forecasting of many time series. The equivalent ARIMA forms of these models provide the basis for a critical examination of the Box-Jenkins approach to seasonal model-building. It is concluded that this approach is unsatisfactory and in particular can often result in over-differencing and the adoption of an inappropriate model. Two main reasons for this are discussed: (a) the inadequate class of models considered which rests on a restricted view of parsimony, and (b) the shortcomings of the basic approach to model identification.     

Categorical approach to modelling and to coupling of models

Solution of any engineering problem starts with a modelling process, which typically involves a choice among different kinds of models. To create a realistic model, one has to think carefully about the modelling process. Particularly in the case of coupled problems when several models are coupled together to represent a given physical phenomenon. This paper presents an approach based on the category theory that allows to describe this modelling process on a more abstract level. Using the advantages of abstract level, one can describe the coupling process in a concise way and introduce certain criteria to check consistency of a coupled model. The main idea of the proposed approach is to introduce a structure in the modelling process, which allows to see how different models interact without a precise look into them. Copyright © 2016 John Wiley & Sons, Ltd.     

Orders of Validation in Mathematical Modelling

Recent work on validation has demonstrated the paucity of validation in operational research projects. What little validation is done usually takes place when the modeller builds a model directly for a decision-maker. This paper begins by reviewing and exploring the processes of model-building and usage with different levels of separation between the model-builder and the ultimate user of the model outputs. The different types of validation that these levels of separation imply are then discussed, with emphasis on validation within linear programming. A checklist of validation questions is suggested. New modelling tools coming onto the market affect the levels at which mathematical modelling takes place and alter the ways in which this modelling should best be carried out in business.     

Modelling class hierarchies in the fuzzy object-oriented data model

In this paper we describe a fuzzy logic based approach to modelling uncertainty in class hierarchies. It is shown that the traditional view of class hierarchies is subsumed in this model as a special case. The problem of multiple inheritance in class hierarchies is discussed and analyzed. The membership value derivations in the inheritance hierarchy reflects the degree of fuzziness existing in the data values and the semantics of the situation being modelled. Thus a more realistic modelling of the universe of discourse is possible through this approach. This model is compatible with existing object-oriented data models.     

Modelling Intra-City Time-Dependent Travel Speeds for Vehicle Scheduling Problems

Many research papers have presented mathematical models for vehicle scheduling. Several of these models have been embedded in commercial decision support systems for intra-city vehicle scheduling for launderies, grocery stores, banks, express mail customers, etc. Virtually all of these models ignore the important issue of time-dependent travel speeds for intra-city travel. Travel speeds (and times) in nearly all metropolitan areas change drastically during the day because of congestion in certain parts of the city road network. The assumption of constant (time-independent) travel speeds seriously affects the usefulness of these models. This is particularly true when time windows (earliest and latest stop time constraints) and other scheduling issues are important. This research proposes a parsimonious model for time-dependent travel speeds and several approaches for estimating the parameters for this model. An example is presented to illustrate the proposed modelling approach. The issue of developing algorithms to find near-optimal vehicle schedules with time-dependent travel speeds is also discussed. The modelling approach presented in this paper has been implemented in a commercial courier vehicle scheduling system and was judged to be ‘very useful’ by users in a number of different metropolitan areas in the United States.     

A knowledge-based multi-role decision support system for ore blending cost optimization of blast furnaces

Literature illustrates the difficulties in obtaining the lowest-cost optimal solution to an ore blending problem for blast furnaces by using the traditional trial-and-error method in iron and steel enterprises. To solve this problem, we developed a cost optimization model which we have implemented in a multi-role-based decision support system (DSS). On the basis of analyzing the business flow and working process of ore blending, we propose an architecture of DSS which is built based on multi-roles. This DSS construction pre-processes the data for materials and elements, builds a general database, abstracts the related optimal operations research models and introduces the reasoning mechanism of an expert system. A non-linear model of ore blending for blast furnaces and its solutions are provided. A database, a model base and a knowledge base are integrated into the expert system-based multi-role DSS to meet the different demands of data, information and decision-making knowledge for the various roles of users. A comparison of the results for the DSS and the trial-and-error method is provided. The system has produced excellent economic benefits since it was implemented at the Xiangtan Iron & Steel Group Co. Ltd., China.     

An Interactive Aid to Financial Planning

The problem of producing financial plans for the subsidiary of a multinational corporation is one which is critical, especially in uncertain times. In addition there is always a pressing time constraint. This paper describes a suite of models which are in use by Caltex Oil South Africa to assist in this area. The approach adopted was to provide simple models which work interactively. The financial planning analysts were able to be very involved in the project because a high level modelling language was used which they could easily comprehend. The tremendous benefits of this type of approach in terms of user acceptance and in other areas are examined.     

A structure-conveying modelling language for mathematical and stochastic programming

We present a structure-conveying algebraic modelling language for mathematical programming. The proposed language extends AMPL with object-oriented features that allows the user to construct models from sub-models, and is implemented as a combination of pre- and post-processing phases for AMPL. Unlike traditional modelling languages, the new approach does not scramble the block structure of the problem, and thus it enables the passing of this structure on to the solver. Interior point solvers that exploit block linear algebra and decomposition-based solvers can therefore directly take advantage of the problem’s structure. The language contains features to conveniently model stochastic programming problems, although it is designed with a much broader application spectrum.     

Modelling to optimise consumptive use of game

There has been a rapid increase in the number of private game ranches established in South Africa in recent years. These ranches are good for conservation but many are driven by the profit motive. A number of models have been used to help managers formulate strategies for achieving their economic objectives. These models are discussed and their use illustrated.A detailed sex and age structured model is presented first with an illustration of its use in attaining two different management objectives. For a given management objective this model generates the returns per unit of food consumed for each species. These returns are then fed into a model to determine the relative abundance of each species in a multispecies herbivory that is required to maximise income.Finally, some problems with the use of these models are discussed. Suggestions and current modelling activities towards improving the tools available to African game ranch managers are presented.     

Wind-excited vibrations of transmission lines: A comparison of different mathematical models

In this paper, the modelling of wind-excited vibrations of conductor cables in overhead transmission lines is discussed. Only oscillations in the frequency range from 10 Hz to 50 Hz due to vortex shedding are considered. Different mathematical models are proposed for the cables, for the aerodynamic forces and for the dampers. The models are compared and their relative merits are summarized. Finally, a relatively simple approach is proposed for the calculation of the bending strains in the cables of a transmission line with dampers. The problem is an example of how mathematical modelling at different levels combines mathematical tools with engineering insight into the physical problem.     

A self-similar premixed turbulent flame model

This paper is devoted to premixed combustion modelling in turbulent flow. First, we derive a model for the turbulent flame velocity based on the observed self-similarity of the turbulent flame. The model uses the local flame brush width as a fundamental parameter and, therefore, we show how it can be retrieved for numerical implementation. The diffusive property of the brush width is treated in such a way as to theoretically let the brush have a clearly defined boundary propagating at finite velocity. The model, implemented in Star-CD CFD software through user programming, is then numerically tested on three configurations for which another model, the Turbulent Flame Closure model, is known to give very good agreement. Some effects of numerics are commented and results for both models are compared. While based on very different approaches the two models lead to substantially similar results. In this way, we have shown that the local brush width can effectively be used, giving an additional degree of freedom for premixed turbulent combustion modelling.     

Stochastic modelling of reservoir operations

The nature of hydrologic parameters in reservoir management models is uncertain. In mathematical programming models the uncertainties are dealt with either indirectly (sensitivity analysis of a deterministic model) or directly by applying a chance-constrained type of formulation or some of the stochastic programming techniques (LP and DP based models). Various approaches are reviewed in the paper. Moran's theory of storage is an alternative stochastic modelling approach to mathematical programming techniques. The basis of the approach and its application is presented. Reliability programming is a stochastic technique based on the chance-constrained approach, where the reliabilities of the chance constraints are considered as extra decision variables in the model. The problem of random event treatment in the reservoir management model formulation using reliability programming is addressed in this paper.     

Choice of modelling technique for evaluating health care interventions

Economic evaluation, such as cost effectiveness analysis, provides a method for comparing healthcare interventions. These evaluations often use modelling techniques such as decision trees, Markov processes and discrete event simulations (DES). With the aid of examples from coronary heart disease, the use of these techniques in different health care situations is discussed. Guidelines for the choice of modelling technique are developed according to the characteristics of the health care intervention.The choice of modelling technique is shown to depend on the acceptance of the modelling technique, model ‘error’, model appropriateness, dimensionality and ease and speed of model development. Generally decision trees are suitable for acute interventions but they cannot model recursion and Markov models are suitable for simple chronic interventions. It is further recommended that population based models be used in order to provide health care outcomes for the likely cost, health benefits and cost effectiveness of the intervention. The population approach will complicate the construction of the model. DES will allow the modeller to construct more complex, dynamic and accurate systems but these may involve a corresponding increase in development time and expense. The modeller will need to make a judgement on the necessary complexity of the model in terms of interaction of individuals and model size and whether queuing for resources, resource constraints or the interactions between individuals are significant issues in the health care system.     

Knowledge-based time-critical dynamic decision modelling

Recent interests in dynamic decision modelling have led to the development of several representation and inference methods. These methods however, have limited application under time-critical conditions where a trade-off between model quality and computational tractability is essential. This paper presents a knowledge-based approach to time-critical dynamic decision modelling. A knowledge representation and modelling method, called the time-critical dynamic influence diagram, is proposed. The proposed approach has the ability to represent space-temporal abstraction in dynamic decision models. Several algorithms from different classes for solving time-critical dynamic influence diagrams are described. A knowledge-based meta-reasoning approach is proposed for the purpose of selecting the best abstracted model and algorithm that provide the optimal trade-off between model quality and model tractability. The approach is applied to solve a time-critical medical decision problem. An outline of the knowledge-based model construction procedure is also provided.     

Three-dimensional modelling of NOx and particulate traps using CFD: A porous medium approach

Lean burn after-treatment systems are the current focus for reducing emissions from diesel exhaust. The trend is for commercial CFD packages to use a single channel modelling approach. Due to computational demands, this necessitates specification of representative channels for modelling, implying prior knowledge of the flow field. This paper investigates a methodology for applying the porous medium approach to lean burn after-treatment systems. This approach has proved successful for three-way catalysis modelling and has the advantage that the flow field is predicted. Chemical kinetic rates for NO_x trapping and regeneration in the model are based on information available in the open literature. Similarly, filtration information based on mass accumulation and soot combustion kinetics are also readily available. Modification of the source terms in a commercial CFD package enables prediction of trapping and release of NO_x. This is an effective way to model a NO_x trap after-treatment system and provides simultaneous 3D modelling of the flow field. With diesel, particulate filtration is required. In the case of particulate traps, however, because of channel geometry, some assumptions are necessary for use of the porous medium approach and these are discussed in this paper. Both models produce qualitatively correct output and have parameters that can be tuned to conform to experimental data. Data to validate the NO_x trap model is to be measured. The particulate trap model, on the other hand, is a feasibility study for modelling the complete diesel after-treatment system using the porous medium approach.     

Modelling and prediction of machining errors using ARMAX and NARMAX structures

Forecasting compensatory control, which was first proposed by Wu [ASME J. Eng. Ind. 99 (1977) 708], has been successfully employed to improve the accuracy of workpieces in various machining operations. This low-cost approach is based on on-line stochastic modelling and error compensation. The degree of error improvement depends very much on the accuracy of the modelling technique, which can only be performed on-line in a real-time recursive manner. In this study, the effect of the control input (i.e. the cutting force) is considered in the development of the error models, and the formulation of recursive exogenous autoregressive moving average (ARMAX) models becomes necessary. The nonlinear ARMAX or NARMAX model is also used to represent this nonlinear process. ARMAX and NARMAX models of different autoregressive (AR), moving average (MA) and exogenous (X) orders are proposed and their identifications are based on the recursive extended least square (RELS) method and the neural network (NN) method, respectively. An analysis of the computational results has confirmed that the NARMAX model and the NN method are superior to the ARMAX model and the RELS method in forecasting future machining errors, as indicated by its higher combined coefficient of efficiency.