Integrated modelling and numerical treatment of freeway flow

The effectiveness of macroscopic dynamic freeway flow models at both uninterrupted and interrupted flow conditions is tested. Model implementation is made by finite difference methods developed here for solving the system's governing equations. These schemes are more effective than existing numerical methods, particularly when generation terms are introduced. The modelling alternatives and numerical solution algorithms are compared by employing a data base generated through microscopic simulation. Despite the effectiveness of the proposed numerical treatments, substantial deviations from the data at interrupted flows are still noticeable. In order to improve performance when flow is interrupted, we develop a modelling methodology that takes into account the ramp-freeway interactions so that all freeway components are treated as a system. We show that the coupling effects of the merging traffic streams are significant. Finally, the incremental benefits of using the more sophisticated high-order continuum models are assessed.     

Psychological aspects of equation-based modelling

Psychological aspects of equation-based modelling languages like Modelica are under-represented in literature. This does not reflect the growth of the corresponding userbase. In this paper we try to close this gap by tackling the problem from three sides: we conduct expert interviews, we conduct an experiment based on self-reported timings to analyse the effects of inheritance on understandability, and we conduct an online experiment to analyse the effects of model representations on the performance at modelling tasks. The expert interviews suggest that experienced modelling experts tend to develop their models from the top-down, while novices do the opposite. Results from the second experiment indicate that the effect of inheritance on the time to understand a model is both significant and large. The results of the last experiment imply that graphical representations outperform block-diagrams for several metrics. These results open a broad research field on the theory of good modelling practice.     

Mathematical modelling and dynamic simulation of multi-effect falling-film evaporator for milk powder production

Multiple-effect evaporators are widely used in dairies and food industries because they are appropriately suited for concentrating food solutions. Some mathematical models for multi-effect evaporators are reported in previous studies. But most of them are steady-state models, and there are no extensive studies on the dynamic behaviour of these evaporators. In this paper, two types of dynamic model, lumped and distributed, are developed for an industrial four-effect falling-film evaporator which is used to concentrate whole milk. These models are validated with data from an industrial unit. The results show that the distributed model has slightly better predictions than the lumped model, but the lumped model has comparable performance because its structure is simple and the needed simulation time is short in comparison with the distributed model.     

Object-oriented modelling and simulation of heat exchangers with finite element methods

The paper describes the derivation of finite-element models of one-dimensional fluid flows with heat transfer in pipes, using the Galerkin/least-squares approach. The models are first derived for one-phase flows, and then extended to homogeneous two-phase flows. The resulting equations have then been embedded in the context of object-oriented system modelling; this allows one to combine the fluid flow model with a model for other phenomena such as heat transfer, as well as with models of other discrete components such as pumps or valves, to obtain complex models of heat exchangers. The models are then validated by simulating a typical heat exchanger plant.     

Toward a formalism of modeling and simulation using model theory

This article proposes a Modeling and Simulation (M&S) formalism using Model Theory. The article departs from the premise that M&S is the science that studies the nature of truth using models and simulations. Truth in models and simulations is relative as they seek to answer specific modeling questions. Consequently, truth in M&S is relative because every model is a purposeful abstraction of reality. We use Model Theory to express the proposed formalism because it is built from the premise that truth is relative. The proposed formalism allows us to: (1) deduce formal definitions and explanations of areas of study in M&S, including conceptual modeling, validity, and interoperability, and (2) gain insight into which tools can be used to semi‐automate validation and interoperation processes. © 2013 Wiley Periodicals, Inc. Complexity 19: 56–63, 2014     

Dynamic modelling and simulation of a hot strip finishing mill

Hot rolling is an essential industrial process in the production of sheet steel, a widely used product in manufacturing and construction. A finishing mill performs a set of operations in a hot strip rolling mill, and is a complex unit including many processes and control loops. Its modelling is a challenging task due to the variety of phenomena that occur within the mill, and variable transport delays. Model validation is also challenging due to a scarcity of measurements. On the other hand, a dynamic model that adequately reflects the numerous interactions between the mill units can be very useful for tasks such as high performance control design or vibration analysis. In this study, a one-dimensional model has been developed and validated against real plant data. The end use of the model is intended to be looper control analysis, but the model is kept sufficiently general so that it can be used or easily extended for other applications.     

A unified approach to the modelling of holonomic and nonholonomic mechanical systems

An alternative technique, called projection method, for solving constrained system problems is presented. This approach can be used to derive equations of motion of both holonomic and nonholonomic systems, and the dynamic equations can be expressed in generalized velocities and/or quasi-velocities. Compared against the other methods of classical mechanics (Lagrange's, Gibbs-Appell, Kane's,...), the present method turns out to be extraordinarily short, elementary and general. As such, it deserves to be promoted as a generally accepted method in academic and engineering applications. Three examples are reported to illustrate advantages of the technique     

Efficiency measure,modelling and estimation in combined array designs

In off‐line quality control, the settings that minimize the variance of a quality characteristic are unknown and must be determined based on an estimated dual response model of mean and variance. The present paper proposes a direct measure of the efficiency of any given design‐estimation procedure for variance minimization. This not only facilitates the comparison of different design‐estimation procedures, but may also provide a guideline for choosing a better solution when the estimated dual response model suggests multiple solutions. Motivated by the analysis of an industrial experiment on spray painting, the present paper also applies a class of link functions to model process variances in off‐line quality control. For model fitting, a parametric distribution is employed in updating the variance estimates used in an iteratively weighted least squares procedure for mean estimation. In analysing combined array experiments, Engel and Huele (Technometrics, 1996; 39:365) used log‐link to model process variances and considered an iteratively weighted least squares leading to the pseudo‐likelihood estimates of variances as discussed in Carroll and Ruppert (Transformation and Weighting in Regression, Chapman & Hall: New York). Their method is a special case of the approach considered in this paper. It is seen for the spray paint data that the log‐link may not be satisfactory and the class of link functions considered here improves substantially the fit to process variances. This conclusion is reached with a suggested method of comparing ‘empirical variances’ with the ‘theoretical variances’ based on the assumed model. Copyright © 2003 John Wiley & Sons, Ltd.     

Analysing and modelling the performance of the HemeLB lattice-Boltzmann simulation environment

We investigate the performance of the HemeLB lattice-Boltzmann simulator for cerebrovascular blood flow, aimed at providing timely and clinically relevant assistance to neurosurgeons. HemeLB is optimised for sparse geometries, supports interactive use, and scales well to 32,768 cores for problems with ∼81 million lattice sites. We obtain a maximum performance of 29.5 billion site updates per second, with only an 11% slowdown for highly sparse problems (5% fluid fraction). We present steering and visualisation performance measurements and provide a model which allows users to predict the performance, thereby determining how to run simulations with maximum accuracy within time constraints.     

A new formalism for the dynamic modelling of cables

This article proposes a new formalism for the dynamic modelling of cables that can even be applied when they are submitted to cross flow of water or air. An important application is the case of umbilical cables used in remotely operated vehicles. The primary basis for the formulation is to assume that the continuous flexibility is represented by a discrete approach, consisting of rigid links connected by elastic joints, allowing movement in three dimensions. Each elastic joint allows three independent movements, called elevation, azimuth and torsion (twist). A significant contribution of the proposed formalism is the development of a compact equation that allows obtaining the Lagrangian of the system directly and automatically, regardless of the number of links chosen to form a chain of rigid bodies connected by flexible joints to represent the continuous flexibility of the cable. This formulation allows the construction of an algorithm for obtaining the equations of the dynamic model of flexible cables.     

Fuzzy modelling of a moving grate biomass furnace for simulation and control purposes

Takagi–Sugeno (TS) fuzzy models are developed for a moving grate biomass furnace for the purpose of simulating and predicting the main process output variables, which are heat output, oxygen concentration of flue gas, and temperature of flue gas. Numerous approaches to modelling biomass furnaces have been proposed in the literature. Usually their objective is to simulate the furnace as accurately as possible. Hence, very complex model architectures are utilized which are not suited for applications like model predictive control. TS fuzzy models are able to approximate the global non-linear behaviour of a moving grate biomass furnace by interpolating between local linear, time-invariant models. The fuzzy partitions of the individual TS fuzzy models are constructed by an axis-orthogonal, incremental partitioning scheme. Validation results with measured process data demonstrate the excellent performance of the developed fuzzy models.     

Mathematical modelling of a diesel common-rail system

In diesel common-rail systems, the exact knowledge of the injection pressure is important to accurately control the injected diesel mass and thus the combustion process. This paper focuses on the mathematical modelling of the hydraulic and mechanical components of a common-rail system in order to describe the dynamics of the diesel rail pressure. Based on this model, an average model is derived to reduce the model complexity and to allow for a fast calculation of the mass flow into the rail for different crank shaft revolution speeds and openings of the fuel metering unit. The main purpose of this average model is to serve as a basis for a model-based (non-linear) controller design. The stationary accuracy of the models is validated by means of measurement data.     

New mathematical modelling and simulation of an industrial accumulator for elastic webs

This paper concerns the modelling of an accumulator used in industrial elastic web processing plant such as paper mills, fabric, rolling mills etc. Accumulators are used to allow rewind or unwind core changes while the process continues at a constant web velocity. A new nonlinear model of a pneumatic actuated industrial accumulator including pneumatic jack model, static friction representation and web weight is first detailed which enables to deduce a linear model. These models are derived from physical laws that describe web tension and velocity dynamics in each web span. In a second part, the effects of time-varying mechanical parameters, such as web Young modulus, web length and rollers inertia on accumulator dynamics are presented. The performances of the modeled accumulator are illustrated by simulations in Matlab/Simulink software environment.     

System dynamic modelling and simulation of hydrodynamic machines

A graph-theoretic framework for the dynamic simulation of hydrodynamic (both axial and radial flow) machines is presented in this article. The physics based analytical models are developed by considering the dynamics of the hydraulic fluid flow and its interaction with the mechanical components. A linear graph is used to capture the topology of the system and the interconnection of the constituent components. Using the graph-theoretic framework, a dynamic model of an automotive hydrodynamic torque converter is developed to simulate its behaviour under different flow conditions. The ability of the model to capture different features of the torque converter will also be demonstrated by simulation. The simulation results are compared with and validated by experimental results in the literature.     

Uses and abuses of statistical simulation

More and more problems are being tackled by simulation as large computing costs per hour approach those of mathematicians' time. Abuses of simulation arise from ignorance or careless use of little understood procedures, and some of the fundamental tools of the subject are much less well understood than commonly supposed. This is illustrated here by the saga of pseudorandom number generators, normal variate generators and the analysis of queueing system simulations. On the positive side, genuinely new uses of simulation are appearing, particularly in statistical inference. These are exemplified by recursive algorithms for simulating complex systems and simulation-based likelihood inference for point processes.     

Modelling and simulation of heat exchange and moisture content in a cereal storage silo

ABSTRACT

In this paper, a mathematical model is developed based on the heat transfer of stored grains aerated in a cylindrical silo. This work is a part of study that aims to model the whole process of cereal storage system including a dehumidifier. The use of dehumidifier is intended to remove excess moisture from the airflow injected by the ventilator system in the silo filled with wheat, and to keep hygroscopic properties of grain in safe level during the storage period. Temperature and humidity are the two important variables coupled to control the process and to preserve grain quality. The laboratory device permitted us to achieve several tests for different conditions of grain stored in silo without aeration. A simulation of the airflow through the thermal space of the silo and grain parameters has been carried out. The results are reasonably in agreement with experiments and other published data. The system performance is evaluated at critical conditions of storage boundaries.     

Dynamic modelling of life table data

In this paper we formulate a dynamic model expressing the human life table data by using the first-passage-time theory for a stochastic process. The model is derived analytically and then is applied to the mortality data in Belgium and France. A stochastic simulation is also performed for the ‘health state function’ proposed and the related stochastic paths. Furthermore the implications of the proposed model and the results derived for pension funds and option theory are discussed.