Showing papers on "Mathematical model published in 2012"
TL;DR: This paper presents mathematical optimization models of residential energy hubs which can be readily incorporated into automated decision making technologies in smart grids, and can be solved efficiently in a real-time frame to optimally control all major residential energy loads, storage and production components while properly considering the customer preferences and comfort level.
Abstract: This paper presents mathematical optimization models of residential energy hubs which can be readily incorporated into automated decision making technologies in smart grids, and can be solved efficiently in a real-time frame to optimally control all major residential energy loads, storage and production components while properly considering the customer preferences and comfort level. Novel mathematical models for major household demand, i.e., fridge, freezer, dishwasher, washer and dryer, stove, water heater, hot tub, and pool pumps are formulated. Also, mathematical models of other components of a residential energy system including lighting, heating, and air-conditioning are developed, and generic models for solar PV panels and energy storage/generation devices are proposed. The developed mathematical models result in Mixed Integer Linear Programming (MILP) optimization problems with the objective functions of minimizing energy consumption, total cost of electricity and gas, emissions, peak load, and/or any combination of these objectives, while considering end-user preferences. Several realistic case studies are carried out to examine the performance of the mathematical model, and experimental tests are carried out to find practical procedures to determine the parameters of the model. The application of the proposed model to a real household in Ontario, Canada is presented for various objective functions. The simulation results show that savings of up to 20% on energy costs and 50% on peak demand can be achieved, while maintaining the household owner's desired comfort levels.
478 citations
TL;DR: This work shows how to systematically construct quantum models that break this classical bound, and that the system of minimal entropy that simulates such processes must necessarily feature quantum dynamics.
Abstract: Mathematical models are an essential component of quantitative science. They generate predictions about the future, based on information available in the present. In the spirit of simpler is better; should two models make identical predictions, the one that requires less input is preferred. Yet, for almost all stochastic processes, even the provably optimal classical models waste information. The amount of input information they demand exceeds the amount of predictive information they output. Here we show how to systematically construct quantum models that break this classical bound, and that the system of minimal entropy that simulates such processes must necessarily feature quantum dynamics. This indicates that many observed phenomena could be significantly simpler than classically possible should quantum effects be involved.
132 citations
TL;DR: In this paper, the authors investigated the possibility of improving the performance of railway vehicle suspensions by incorporating a newly developed mechanical device known as the inerter, which improved the lateral and vertical ride comfort, as well as lateral body movement when curving.
Abstract: This paper investigates the possibility of improving the performance of railway vehicle suspensions by incorporating a newly developed mechanical device known as the inerter A comparative study of several low-complexity passive suspension layouts is made Improved performance for the lateral and vertical ride comfort, as well as lateral body movement when curving are demonstrated in comparison with the conventional suspension layout The constraints imposed are to maintain the same level of other performance metrics The calculations and optimisations are based on linearised plan-view and side-view high-speed train mathematical models
121 citations
TL;DR: Here, some common concerns are addressed and a brief tutorial on the use of logic-based models are provided, which is motivated with biological examples.
Abstract: Highly complex molecular networks, which play fundamental roles in almost all cellular processes, are known to be dysregulated in a number of diseases, most notably in cancer. As a consequence, there is a critical need to develop practical methodologies for constructing and analysing molecular networks at a systems level. Mathematical models built with continuous differential equations are an ideal methodology because they can provide a detailed picture of a network's dynamics. To be predictive, however, differential equation models require that numerous parameters be known a priori and this information is almost never available. An alternative dynamical approach is the use of discrete logic-based models that can provide a good approximation of the qualitative behaviour of a biochemical system without the burden of a large parameter space. Despite their advantages, there remains significant resistance to the use of logic-based models in biology. Here, we address some common concerns and provide a brief tutorial on the use of logic-based models, which we motivate with biological examples.
120 citations
TL;DR: In this paper, a modified Turner's formula is used to model the entrainment between the two fluids, and a two-layer shallow-water model was used to simulate all the runs to test the model validity and compare laboratory results with previous expressions found in the literature.
Abstract: This paper presents the investigation of gravity currents by both laboratory experiments and a mathematical model. Eleven lock-exchange experiments, in which lock position, the initial current height, and density varied, were carried out to test the model validity and to compare laboratory results with previous expressions found in the literature. A two-layer shallow-water model was used to simulate all the runs. This model is new if compared with previous shallow-water models used to simulate gravity currents, because it accounts for both the entrainment and the free surface. A modified Turner's formula is used to model the entrainment between the two fluids. The developed shallow-water models with and without entrainment are also compared, showing a better agreement when mixing is accounted for. Also, the effect of the free surface is shown by comparing the developed two-layer shallow-water model with a free surface and two different single-layer models with a rigid-lid approximation. Laboratory experiments and model simulations, accounting for both the entrainment and the free surface, are in good agreement. Front velocities, measured during the slumping phase, were compared with both predicted ones and previous expressions found in the literature, showing in most of the cases better result when the developed model is used. DOI: 10.1061/(ASCE)HY.1943-7900.0000484. © 2012 American Society of Civil Engineers.
119 citations
Book•
26 Apr 2012
TL;DR: An Introduction to MATLAB and Optimal Harvesting for Age-Structured Population andOptimal Control of Diffusive Models are presented.
Abstract: An Introduction to MATLAB. Elementary Models with Applications.- Optimal Control of Ordinary Differential Systems. Optimality Conditions.- Optimal Control of Ordinary Differential Systems. Gradient Methods.- Optimal Harvesting for Age-Structured Population.- Optimal Control of Diffusive Models.- Appendices.- References.- Index.
114 citations
14 Nov 2012
TL;DR: Christian Soize presents the main concepts, formulations, and recent advances in the use of a mathematical-mechanical modeling process to predict the responses of a real structural system in its environment.
Abstract: Christian Soize presents the main concepts, formulations, and recent advances in the use of a mathematical-mechanical modeling process to predict the responses of a real structural system in its environment.
109 citations
TL;DR: In this article, a simple model derived from a self-consisted random walk is proposed to simulate ion transport through biological and synthetic channels (nanopores) and conductance as a function of bath concentrations is investigated.
Abstract: The mathematical modelling and simulation of ion transport through biological and synthetic channels (nanopores) is a challenging problem, with direct application in biophysics, physiology and chemistry. At least two major effects have to be taken into account when creating such models: the electrostatic interaction of ions and the effects due to size exclusion in narrow regions. While mathematical models and methods for electrostatic interactions are well-developed and can be transferred from other flow problems with charged particles, e.g. semiconductor devices, less is known about the appropriate macroscopic modelling of size exclusion effects.Recently several papers proposed simple or sophisticated approaches for including size exclusion effects into entropies, in equilibrium as well as off equilibrium. The aim of this paper is to investigate a second potentially important modification due to size exclusion, which often seems to be ignored and is not implemented in currently used models, namely the modification of mobilities due to size exclusion effects. We discuss a simple model derived from a self-consisted random walk and investigate the stationary solutions as well as the computation of conductance. The need of incorporating nonlinear mobilities in high density situations is demonstrated in an investigation of conductance as a function of bath concentrations, which does not lead to obvious saturation effects in the case of linear mobility.
108 citations
TL;DR: The proposed dynamic model and module can be combined with the human-machine interface to help the driver easily identify safe lane-change trajectories and area and efficiently obtain the percentage of safe trajectories by computing the minimum gap and time to collision.
Abstract: This paper introduces a dynamic model of the driver control strategy of lane-change behavior and applies it to trajectory planning in driver-assistance systems. The proposed model reflects the driver control strategies of adjusting longitudinal and latitudinal acceleration during the lane-change process and can represent different driving styles (such as slow and careful, as well as sudden and aggressive) by using different model parameters. We also analyze the features of the dynamic model and present the methods for computing the maximum latitudinal position and arrival time. Furthermore, we put forward an extended dynamic model to represent evasive lane-change behavior. Compared with the fifth-order polynomial lane-change model, the dynamic models fit actual lane-change trajectories better and can generate more accurate lane-change trajectories. We apply the dynamic models in emulating different lane-change strategies and planning lane-change trajectories for collision prediction. In the simulation, we use the models to compute the percentage of safe trajectories in different scenarios. The simulation shows that the maximum latitudinal position and arrival time of the generated lane-change trajectories can be good indicators of safe lane-change trajectories. In the field test, the dynamic models can generate the feasible lane-change trajectories and efficiently obtain the percentage of safe trajectories by computing the minimum gap and time to collision. The proposed dynamic model and module can be combined with the human-machine interface to help the driver easily identify safe lane-change trajectories and area.
106 citations
TL;DR: In this article, a comparative study of three different mathematical models for the packed bed latent heat storage system, comprised of a cylindrical storage tank filled with paraffin encapsulated spherical containers, is presented.
92 citations
TL;DR: In this paper, the applicability of a vertically-integrated modeling approach to CO2 sequestration depends on the time scale of the vertical brine drainage within the plume, relative to the time-scale of the simulation.
TL;DR: Novel tensor product (TP) models for the control of two complex components of the vehicle automatic transmission systems, namely the drive line without clutch and, the valve-clutch are discussed.
Abstract: This paper discusses novel tensor product (TP) models for the control of two complex components of the vehicle automatic transmission systems, namely the drive line without clutch and, the valve-clutch. The TP models are obtained by a transformation of the linear parameter-varying models derived from the first principle nonlinear mathematical models of the controlled processes. Experimental results validate the performance of the proposed TP models.
TL;DR: The mathematical models of the Kalman filters used in this study are presented, and the results of the identification procedure are described, showing the effectiveness of the proposed high-performance control structure.
Abstract: In this paper, issues related to parameter identification and high-performance control of the drive system with an elastic joint are discussed. After a brief introduction, the mathematical model of the drive and the proposed high-performance control structure are presented. The effect of the location of closed-loop poles and cancellation of zeros of the structure is examined. Then, the mathematical models of the Kalman filters used in this study are presented, and the results of the identification procedure are described. The effectiveness of the proposed structure has been examined under simulation and experimental study.
TL;DR: In this paper, the effects of process parameters on the temperature field and weld bead dimensions were investigated via process modeling, using an FEM and RSM combined approach, and the effect of parameters and their interactions on the responses were studied using the developed response surface models.
Abstract: In this paper, simultaneous laser transmission welding process is systematically investigated via process modeling, using an FEM and RSM combined approach. The objective of the present research is to study the effects of process parameters on the temperature field and weld bead dimensions. The thermal field is simulated by solving a three dimensional transient heat diffusion equation with temperature dependent material properties using the ANSYS ® multi-physics. Response surface methodology is then applied for developing mathematical models based on simulation results. The second order equations developed by RSM can predict the values of the responses with significant accuracy. The effect of parameters and their interactions on the responses are studied using the developed response surface models. The mathematical models are further used in search of the optimal process window for obtaining an acceptable weld. The graphical optimization results into a couple of overlay contours plots, which allow quick visual inspection of the area of feasible response values in the factor space to choose the favorable welding parameter combination.
TL;DR: This review surveys kinetic models coupled with time-reversible deterministic thermostats for the modeling of large systems composed both by inert matter particles and living entities and a variety of thermostatted mathematical models in physics and life sciences.
TL;DR: Three types of probabilistic models are distinguished for time headway (TH) distribution in this paper: the single model, the combined model and the mixed model, and the two mixed models are shown to be statistically equivalent and provide the best fits in a wide range of TH samples.
Abstract: Three types of probabilistic models are distinguished for time headway (TH) distribution in this paper: the single model, the combined model and the mixed model. To challenge the flexibility of the models, a sample set is established based on different sampling methods according to different data bases from the roadways in France. Particularly, the data from the RN118 national roadway are aggregated over 6 min and classified according to traffic flow and traffic occupancy. An estimation process is proposed for the existing estimation methods when calibrating combined and mixed models. As a result, the two mixed models, the gamma based Semi-Poisson Model and the gamma based Generalized Queuing Model (gamma-GQM) are shown to be statistically equivalent, provide the best fits in a wide range of TH samples. The gamma-GQM without location parameter is recommended to use in TH modeling. Besides, the Shifted Hyper Log-normal Model (HyperLNM) is examined for the first time and fits to TH data very well in many cases. The statistical role of the location parameter in TH models is also discussed. Moreover, it is found that the Ratio between time Headway and Instantaneous Speed (RHIS) can be modeled well using the gamma-GQM.
TL;DR: This study applied a downscaling methodology based on commonly available spatial parameters to model on-road CO(2) emissions at the 1 × 1 km scale for the Boston, MA region and tested the approach with surface-level CO( 2) observations.
TL;DR: In this paper, a nonlinear modeling and identification of spark ignition engine torque from input-output measurement is presented for identification purposes, and the results are numerically and graphically presented.
09 Nov 2012
TL;DR: In this article, a study on and identifies the different process parameters that affect the cutting speed and surface roughness in wire electric discharge machining of titanium 6-2-4-2.
Abstract: The present article is the first study on and identifies the different process parameters that affect the cutting speed and surface roughness in wire electric discharge machining of titanium 6-2-4-2. Box–Behnken designs are used to plan and analyse the experiments. Mathematical models are developed for cutting speed and surface roughness using regression technique and are utilized for simultaneous optimization of cutting speed and surface roughness. As the influence of process parameters on cutting speed and surface roughness is opposite, the problem is formulated as a multi-objective optimization problem. Non-dominated sorting genetic algorithm-II is then applied to obtain Pareto optimal set of solutions. Confirmatory experiments indicate that the model is suitable for predicting the response parameters. These Pareto optimal sets of solutions can be used as guidelines by manufacturing engineers to select optimal combination of parameters depending upon the job requirements.
TL;DR: In this paper, a semi-empirical model is proposed to simulate the cyclic densification and degradation of coarse granular material under a railway environment where the number of loading cycles is very large.
Abstract: A number of constitutive models exist to model behavior of granular material under cyclic loading. Most of these models are useful to model soil behavior where the number of cycles is very small. Therefore, a semiempirical model is proposed to simulate the cyclic densification and degradation of coarse granular material under a railway environment where the number of loading cycles is very large. A kinematically expanding elastic surface is introduced to separate elastic and elastoplastic deformation of the material with the number of cycles. The reversible response is represented by the pressure-dependent elastoplastic rule. Empirical model parameters are introduced to consider the effect of stress history, stress ratio, number of cycles, and breakage. Model parameters are evaluated based on cyclic triaxial test results. Predicted results are compared with the laboratory data in order to demonstrate the model validity. The proposed model captures the realistic deformation and degradation of ballast at various frequencies and confining pressures for a large number of cycles.
Posted Content•
TL;DR: In this paper, a recently introduced computational methodology is used to work with finite, infinite, and infinitesimal numbers numerically on a new kind of a computer—the Infinity Computer—able toWork with all these types of numbers.
Abstract: Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this paper, a recently introduced computational methodology (that is not related to the non-standard analysis) is used to work with finite, infinite, and infinitesimal numbers \textit{numerically}. This can be done on a new kind of a computer - the Infinity Computer - able to work with all these types of numbers. The new computational tools both give possibilities to execute computations of a new type and open new horizons for creating new mathematical models where a computational usage of infinite and/or infinitesimal numbers can be useful. A number of numerical examples showing the potential of the new approach and dealing with divergent series, limits, probability theory, linear algebra, and calculation of volumes of objects consisting of parts of different dimensions are given.
01 Jul 2012
TL;DR: In this article, the authors examined the value of adding specific nonlinear terms to hydrodynamic models for wave energy devices, to improve the validity of such models across the full operational spectrum.
Abstract: To date, mathematical models for wave energy devices typically follow Cummins equation, with hydrodynamic parameters determined using boundary element methods. The resulting models are, for the vast majority of cases, linear, which has advantages for ease of computation and a basis for control design to maximise energy capture. While these linear models have attractive properties, the assumptions under which linearity is valid are restrictive. In particular, the assumption of small movements about an equilibrium point, so that higher order terms are not significant, needs some scrutiny. While this assumption is reasonable in many applications, in wave energy the main objective is to exaggerate the movement of the device through resonance, so that energy capture can be maximised. This paper examines the value of adding specific nonlinear terms to hydrodynamic models for wave energy devices, to improve the validity of such models across the full operational spectrum.
TL;DR: In this article, mathematical models based on set of nonlinear equations have been developed for the synthesis of multiple effect evaporator (MEE) systems and a model for predicting fouling resistance is also developed using the experimental data.
TL;DR: In this paper, a correct discrete-continual finite element method (DCFEM) of structural analysis based on precise analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients is presented.
Abstract: The distinctive paper is devoted to correct discrete-continual finite element method (DCFEM) of structural analysis based on precise analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients. Corresponding semianalytical (discrete-continual) formulations are contemporary mathematical models which currently becoming available for computer realization. Major peculiarities of DCFEM include uni-versality, computer-oriented algorithm involving theory of distributions, computational stability, optimal conditionality of resulting systems and partial Jordan decompositions of matrices of coeffi-cients, eliminating necessity of calculation of root vectors.
TL;DR: In this article, the authors show how to mathematically describe lift coefficients so as to eliminate the lack of description for centrifugal pumping for wind turbines and compare their simulated numerical code data with experimental data taken from scientific literature.
TL;DR: In this paper, a dual toll pricing method was proposed to mitigate risk of hazardous materials (hazmat) transportation, which simultaneously controls both regular and hazmat vehicles to reduce the risk.
Abstract: In this paper, we propose a dual toll pricing method to mitigate risk of hazardous materials (hazmat) transportation. We aim to simultaneously control both regular and hazmat vehicles to reduce the risk. In our model, we incorporate a new risk measure to consider duration-population-frequency of hazmat exposure. We first formulate the model as a Mathematical Program with Equilibrium Constraints (MPEC). Then we decompose the MPEC formulation into first-stage and second-stage problems. Separate methods are developed to solve each stage. A numerical example is provided and possible extensions are discussed.
TL;DR: In this article, the max-min approach is applied to mathematical models of some nonlinear oscillations and the results indicate that the approach has a good agreement with other well-known methods.
Abstract: The max-min approach is applied to mathematical models of some nonlinear oscillations. The models are regarding to three different forms that are governed by nonlinear ordinary differential equations. In this context, the strongly nonlinear Duffing oscillator with third, fifth, and seventh powers of the amplitude, the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration. The obtained results via the approach are compared with ones achieved utilizing other techniques. The results indicate that the approach has a good agreement with other well-known methods. He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.
TL;DR: In this article, the authors discuss model combination approaches for Boolean models and propose modelling standards for combining Boolean models as a prerequisite for smooth model integration, and demonstrate the coupling of two logical models on two different examples concerning cellular interactions in the liver.
Abstract: The number of mathematical models for biological pathways is rapidly growing. In particular, Boolean modelling proved to be suited to describe large cellular signalling networks. Systems biology is at the threshold to holistic understanding of comprehensive networks. In order to reach this goal, connection and integration of existing models of parts of cellular networks into more comprehensive network models is necessary. We discuss model combination approaches for Boolean models. Boolean modelling is qualitative rather than quantitative and does not require detailed kinetic information. We show that these models are useful precursors for large-scale quantitative models and that they are comparatively easy to combine. We propose modelling standards for Boolean models as a prerequisite for smooth model integration. Using these standards, we demonstrate the coupling of two logical models on two different examples concerning cellular interactions in the liver. In the first example, we show the integration of two Boolean models of two cell types in order to describe their interaction. In the second example, we demonstrate the combination of two models describing different parts of the network of a single cell type. Combination of partial models into comprehensive network models will take systems biology to the next level of understanding. The combination of logical models facilitated by modelling standards is a valuable example for the next step towards this goal.
TL;DR: In this article, a combination of uncertainty and sensitivity analysis was applied to a heat and mass transfer model of a contact baking process, where the Monte Carlo procedure was applied for propagating uncertainty in the input parameters to uncertainty in model predictions.
TL;DR: In this paper, the authors present a complete model aimed at the evaluation of the wheel wear and the wheel profile evolution by means of dynamic simulations, organized in two parts which interact with each other mutually: a vehicle's dynamic model and a model for the wear estimation.
Abstract: The numerical wheel wear prediction in railway applications is of great importance for different aspects, such as the safety against vehicle instability and derailment, the planning of wheelset maintenance interventions and the design of an optimal wheel profile from the wear point of view. For these reasons, this paper presents a complete model aimed at the evaluation of the wheel wear and the wheel profile evolution by means of dynamic simulations, organised in two parts which interact with each other mutually: a vehicle's dynamic model and a model for the wear estimation. The first is a 3D multibody model of a railway vehicle implemented in SIMPACK™, a commercial software for the analysis of mechanical systems, where the wheel–rail interaction is entrusted to a C/C++user routine external to SIMPACK, in which the global contact model is implemented. In this regard, the research on the contact points between the wheel and the rail is based on an innovative algorithm developed by the authors in previous w...