Showing papers on "Mathematical model published in 2004"

Near-fault ground motions, and the response of elastic and inelastic single-degree-of-freedom (SDOF) systems

Abstract: SUMMARY In order to investigate the response of structures to near-fault seismic excitations, the ground motion input should be properly characterized and parameterized in terms of simple, yet accurate and reliable, mathematical models whose input parameters have a clear physical interpretation and scale, to the extent possible, with earthquake magnitude. Such a mathematical model for the representation of the coherent (long-period) ground motion components has been proposed by the authors in a previous study and is being exploited in this article for the investigation of the elastic and inelastic response of the single-degree-of-freedom (SDOF) system to near-fault seismic excitations. A parametric analysis of the dynamic response of the SDOF system as a function of the input parameters of the mathematical model

Mathematical Modelling and Numerical Simulation of the Cardiovascular System

Abstract: Publisher Summary The development of mathematical models, algorithms and numerical simulation tools for the investigation of the human cardiovascular system has received a great impulse in the past years This chapter addresses the problem of developing models for the numerical simulation of the human circulatory system It particularly focuses on the problem of hemodynamics in large human arteries There are several important aspects, which require the use of sophisticated mathematical and numerical tools, such as the reconstruction of geometries from medical data; the transport of biochemicals in blood and vessel wall tissue; the heart dynamics; and blood rheology Besides, the need of validating the models calls for development of accurate in-vivo measurement techniques The number and complexity of the mathematical, numerical and technological problems involved makes the development of tools for accurate, reliable and efficient simulations of the human cardiovascular system one of the challenges of the next decades

Analytical models of water impact

Abstract: Mathematical models for the prediction of the hydrodynamic pressure distribution and the force on a body entering liquid are investigated. Particular attention is paid to analytical models which are based on the velocity potential given by the classical Wagner theory. Formal use of the Wagner theory provides the loads on an entering body, which are higher than the measured ones. To improve the predictions, the higher order terms in the Bernoulli equation are taken into account within the generalized Wagner model and the Logvinovich model. It is shown that the Logvinovich model corresponds better to the experimental data than the generalized Wagner model. A rational derivation of the Logvinovich model is given in the paper for the two-dimensional case. The analytical models are tested against both numerical and experimental results.

A high fidelity traffic simulation model based on cellular automata and car-following concepts

Abstract: A high fidelity cell based traffic simulation model (CELLSIM) has been developed for simulation of high volume of traffic at the regional level. Straightforward algorithms and efficient use of computational resources make the model suitable for real time traffic simulation. The model formulation uses concepts of cellular automata (CA) and car-following (CF) models, but is more detailed than CA models and has realistic acceleration and deceleration models for vehicles. A simple dual-regime constant acceleration model has been used that requires minimal calculation compared to detailed acceleration models used in CF models. CELLSIM is simpler than most CF models; a simplified car-following logic has been developed using preferred time headway. Like CA models, integer values are used to make the model run faster. Space is discretized in small intervals and a new concept of percent space occupancy (SOC) is used to measure traffic congestion. CELLSIM performs well in congested and non-congested traffic conditions. It has been validated comprehensively at the macroscopic and microscopic levels using two sets of field data. Comparison of field data and CELLSIM for trajectories, average speed, density and volume show very close agreement. Statistical comparison of macroscopic parameters with other CF models indicates that CELLSIM performs as good as detailed CF models. Stability analyses conducted using mild and severe disturbances indicate that CELLSIM performs well under both conditions.

Model validation via uncertainty propagation and data transformations

Abstract: Model validation has become a primary means to evaluate accuracy and reliability of computational simulations in engineering design. Because of uncertainties involved in modeling, manufacturing processes, and measurement systems, the assessment of the validity of a modeling approach must be conducted based on stochastic measurements to provide designers with confidence in using a model. A generic model validation methodology via uncertainty propagation and data transformations is presented. The approach reduces the number of physical tests at each design setting to one by shifting the evaluation effort to uncertainty propagation of the computational model. Response surface methodology is used to create metamodels as less costly approximations of simulation models for the uncertainty propagation. Methods for validating models with both normal and nonnormal response distributions are proposed. The methodology is illustrated with the examination of the validity of two finite element analysis models for predicting springback angles in a sample flanging process.

Multiaxial Behaviors of Laminated Rubber Bearings and Their Modeling. II: Modeling

Abstract: Mathematical models of laminated rubber bearings under multiaxial loads are proposed on the basis of the experimental data in a companion paper. First, a 1-D model of the bearings is proposed. In this model, an elastoplastic model is extended by adding the displacement-dependent isotropic hardening rule and the parallel nonlinear elastic spring. The equivalent stiffness and damping ratio of the model are derived in the analytical forms, which are useful for the design. Second, the 3-D constitutive law is simplified by considering the biaxial simple shear deformation to derive the 2-D elastoplastic model. Then, this model is extended by a similar way as in the 1-D case to obtain the 2-D model of the bearings. The proposed models are shown to well reproduce the experimental results. Third, to confirm the ability of the proposed models to predict the seismic response, a triaxial hybrid seismic response experiment is conducted. In comparison with experimental results, the simulations by the proposed model are found to accurately predict the response of the experiment.

Hydrodynamic models of human stability in a flood

Abstract: Major loss of life can occur in a flood when people are toppled by floodwater currents. Three approximate mechanical models and two empirical models of the hydrodynamics of toppling are presented and calibrated to align with available experimental observations to assist the analysis of the risk of life loss. The mechanical models consider circular cylindrical, square cylindrical and cylindrical composite, heavy bodies assembled to represent a human immersed in a flow field and subject to drag and buoyancy forces. The models can account for the height and weight of the exposed persons, and the velocity and depth of the flow. The models are in good mutual agreement and, when calibrated, yield failure functions that can be used to calculate the probability of loss of stability.

Two-stepped evolutionary algorithm and its application to stability analysis of slopes

Abstract: Based on genetic algorithm and genetic programming, a new evolutionary algorithm is developed to evolve mathematical models for predicting the behavior of complex systems. The input variables of the models are the property parameters of the systems, which include the geometry, the deformation, the strength parameters, etc. On the other hand, the output variables are the system responses, such as displacement, stress, factor of safety, etc. To improve the efficiency of the evolution process, a two-stepped approach is adopted; the two steps are the structure evolution and parameter optimization steps. In the structure evolution step, a family of model structures is generated by genetic programming. Each model structure is a polynomial function of the input variables. An interpreter is then used to construct the mathematical expression for the model through simplification, regularization, and rationalization. Furthermore, necessary internal model parameters are added to the model structures automatically. For each model structure, a genetic algorithm is then used to search for the best values of the internal model parameters in the parameter optimization step. The two steps are repeated until the best model is evolved. The slope stability problem is used to demonstrate that the present method can efficiently generate mathematical models for predicting the behavior of complex engineering systems.

Representation of equilibrium solutions to the table problem of growing sandpiles

Abstract: In the dynamical theory of granular matter the so-called table problem consists in study- ing the evolution of a heap of matter poured continuously onto a bounded domainR 2 . The mathematical description of the table problem, at an equilibrium configuration, can be reduced to a boundary value problem for a system of partial differential equations. The analysis of such a sys- tem, also connected with other mathematical models such as the Monge-Kantorovich problem, is the object of this paper. Our main result is an integral representation formula for the solution, in terms of the boundary curvature and of the normal distance to the cut locus of .

State variable and parameter estimator comprising several partial models for an electrical energy storage device

Abstract: The invention relates to a state variable and parameter estimator (1) for determining state variables and parameters of a mathematical energy storage model, especially a battery model. Said estimator (1) calculates the state variables (Z) and parameters (P) of the mathematical energy storage model from operating parameters (UBatt, IBatt, TBatt) of an energy storage device (3). The state variables and parameters can be estimated in a particularly simple manner if the state variable and parameter estimator (1) comprises several partial mathematical models (4, 5) that are valid for different operating ranges and/or frequency ranges of the energy storage device (3).

Overview of satellite thermal analytical model

Abstract: Thermal analysis is the major engineering work throughout the entire satellite development process, with some crucial stages such as design, test, and ground operations simulation. In the formal design and verification (by test) phases, a general thermal mathematical model for the entire satellite is constructed from a combined conduction and radiation heat transfer equation with environmental heating and cooling as boundary conditions. Some representative numerical schemes with constraints used in satellite thermal analysis, as well as an introduction to the thermal model for the thermal balance test, are presented. However, the general thermal model may be too complicated or inefficient for conceptual design, test monitoring, and ground-operation simulation while developing a satellite. Therefore, simpler governing equations for pure radiation heating and cooling with exact mathematical solutions are developed to fulfill this objective at the expense of analysis accuracy. The linear approximation and exact formulation for solving this simplified problem, as well as the corresponding results shown in graphical form, are also discussed.

Moisture Transport in Wood: A Study of Physical-Mathematical Models and their Numerical Implementation

Abstract: The ability to predict the moisture variations in wood is important in a number of cases. The applications are extremely wide, ranging from the conditions in the living tree to moisture induced deformations in timber structures. In between, in the course of transformation from living tree to structural timber, a number of processes such as drying and preservative treatment involve the transport and heat and mass. In this report three particular scenarios are dealt with, and in addition, some general numerical procedures for the solution of the transport models have been developed. The main contributions of the thesis are summarized in Chapters 4 to 7. In Chapter 2 the structure and basic features of wood as related to moisture transport are briefly discussed. Both hardwoods and softwoods are treated with particular emphasis on the different liquid and gas pathways resulting from the microscopic structure of the woods. In Chapter 3 the general theory of moisture transport in porous media is reviewed. The relevant conservation equations are stated and the constitutive relations governing the transport of the different water phases are discussed. The application of this theory to wood is then considered and a number of apparent discrepancies pointed out. These relate particularly to the common assumption of thermodynamic equilibrium as well as to the transport of vapour and air within the wooden cellular structure. Further, the mechanisms governing the transport of free water at moisture contents slightly above the fiber saturation point are discussed, and it is demonstrated that some care must be taken when applying the conventional generalized Darcy’s law. In Chapter 4 the problem of moisture transport below the fiber saturation point is treated. Here the conventional models often fail to describe the transport of moisture, both qualitatively as well as quantitatively, and one often speaks of the behaviour being ‘non–Fickian’. A new model capable of describing this behaviour is presented. As in previous attempts of modeling the transfer of water below the fiber saturation point, the transport of bound water and water vapour are described separately from one another such that a state of non–equilibrium exists. The gradual approach to equilibrium is accounted for by linking the water phases via a mass transfer term whose principal functional variation is discussed in some detail. It is found that in order to accommodate the experimental facts a measure of the proximity to equilibrium has to be introduced such that the rate of conversion of water vapour to bound water and vice versa depends on two parameters: the absolute

Relative Permeabilities for Strictly Hyperbolic Models of Three-Phase Flow in Porous Media

Abstract: Traditional mathematical models of multiphase flow in porous media use a straightforward extension of Darcy’s equation. The key element of these models is the appropriate formulation of the relative permeability functions. It is well known that for one-dimensional flow of three immiscible incompressible fluids, when capillarity is neglected, most relative permeability models used today give rise to regions in the saturation space with elliptic behavior (the so-called elliptic regions). We believe that this behavior is not physical, but rather the result of an incomplete mathematical model. In this paper we identify necessary conditions that must be satisfied by the relative permeability functions, so that the system of equations describing three-phase flow is strictly hyperbolic everywhere in the saturation triangle. These conditions seem to be in good agreement with pore-scale physics and experimental data.

Models and the History of Modeling

Abstract: After a very fast tour through 30,000 years of modeling history, we describe the basic ingredients to models in general, and to mathematical models in particular.

Nonlinear and stochastic aspects of parametric rolling modeling

Abstract: This paper addresses, starting from an extensive series of tests in longitudinal regular waves (already done) and irregular waves (in progress), the problems connected with the threshold formulation for parametric rolling and its amplitude modeling above threshold. Both head and following waves have been considered, also in view of the greater attention to head sea conditions called for during International Maritime Organisation Subcommittee on Stability and Load Lines, and on Fishing Vessels Safety (IMO/ SLF) discussion on the revision of the Intact Stability Code. Particular attention is given in the regular wave case to the nonlinear damping, nonlinear restoring, and nonlinear parametric excitation terms. The mathematical models so developed are compared with experimental results by means of an ad hoc parameter estimation technique. It is, on the other hand, well known that several different thresholds can be proposed in the case of irregular waves and that the nonlinear modeling of roll motion variance above threshold is at present not properly addressed. Here, too, a series of experiments will be conducted in the presence of narrow band irregular waves having the bandwidth as parameter. A mathematical description of the nonlinear parametric rolling can be obtained with the use of approximate analytical techniques.

Mathematical models of martensitic microstructure

Abstract: Martensitic microstructures are studied using variational models based on nonlinear elasticity Some relevant mathematical tools from nonlinear analysis are described, and applications given to austenite-martensite interfaces and related topics

A LuGre tire friction model with exact aggregate dynamics

Abstract: The LuGre dynamic point contact friction model for the two-dimensional translation of a body on a surface has been used in the past to derive a model for the friction forces and moments at the contact patch of a tire. The resulting tire friction model is distributed, described by a set of partial differential equations. Several approximations have been used in the literature to approximate this distributed model using a set of ordinary differential equations, making the model appropriate for control design and on-line estimation. In this paper, the method of moments is used to derive a set of ordinary differential equations to describe the exact average dynamics of the distributed model. Three cases of normal load distribution are considered and compared: uniform, trapezoidal and cubic load distribution. Simulations are also presented to compare with existing approximate steady-state lumped models.

Bacterial regrowth model for water distribution systems incorporating alternating split-operator solution technique

Abstract: This paper presents a new mathematical model of bacterial regrowth in distribution systems, which combines hydraulic calculations, inclusive of dispersion, with a description of the following microbial processes: free and attached growth, detachment, endogenous respiration, and inactivation by chlorine. The microbial process description has been simplified from previous models based on a sensitivity analysis. The alternating split-operator algorithm is used to solve this model. This method differs from previous approaches by decoupling the transport and reaction processes, allowing a choice among numerical algorithms that is best suited for each part of the model. The proposed solution resolves sharp fronts of a concentration profile more accurately than traditional finite difference methods. The results of the model are also compared against EPANET to show the importance of accounting for dispersion, as would occur during low water demand conditions when velocity is low. Use of the model to understand the interaction among key parameters affecting bacterial regrowth is illustrated for a simple hypothetical network.

Several related models for multilayer sandwich plates

Abstract: Mathematical models for multilayer sandwich plates consisting of alternating stiff and compliant layers are derived. Two main types of models are described. First an initial model (analogous to the three-layer Rao–Nakra model) is derived under Kirchhoff plate assumptions for the stiff layers and Mindlin shear-deformable displacement assumptions for the compliant layers. The second type of model can be obtained from the original model by dropping the in-plane and rotational inertia. The resulting model is a generalization of the well-known model of Mead and Markus. Well-posedness and continuous parameter dependence results are described. Some variations of the initial model corresponding to thin compliant layers are described and shown to be regular perturbations of the initial model.

Models quantify the total maximum daily load process

Abstract: Mathematical models have been used for many years to assist in the management of water quality. The total maximum daily load ~TMDL! process is no exception; models represent the means by which the assimilative capacity of a water body can be quantified and a waste load allocation can be determined such that the assimilative capacity is not exceeded. Unfortunately, in many TMDLs, the use of models has not always adhered to the best modeling practices that have been developed over the past half-century. This paper presents what are felt to be the most important principles of good modeling practice relative to all of the steps in developing and applying a model for computing a TMDL. These steps include: Problem definition and setting management objectives; data synthesis for use in modeling; model selection; model calibration and, if possible confirmation; model application; iterative modeling; and model postaudit. Since mathematical modeling of aquatic systems is not an exact science, it is essential that these steps be fully transparent to all TMDL stakeholders through comprehensive documentation of the entire process, including specification of all inputs and assumptions. The overriding consideration is that data richness and quality govern the level of model complexity that can be applied to a given system. The model should never be more complex than the data allow. Also, in applying a model, one should always attempt to quantify the uncertainty in predictions. In general, quantifying uncertainty is easier with simple models, which is another reason to begin with a simple framework.

Evaluation of the Use of Artificial Neural Networks for the Simulation of Hybrid Solar Collectors

Abstract: In the last decade, Artificial Neural Networks (ANNs) have been receiving an increasing attention for simulating engineering systems due to some interesting characteristics such as learning capability, fault tolerance, speed and nonlinearity. This article describes an alternative approach to assess two types of hybrid solar collector/heat pipe systems (plate heat pipe type and tube heat pipe type) using ANNs. Multiple Layer Perceptrons (MLPs) and Radial Basis Networks (RBFs) were considered. The networks were trained using results from mathematical models generated by Monte Carlo simulation. The mathematical models were based on energy balances and resulted in a system of nonlinear equations. The solution of the models was very sensitive to initial estimates, and convergence was not obtained under certain conditions. Between the two neural models, MLPs performed slightly better than RBFs. It can be concluded that similar configurations were adequate for both collector systems. It was found that A...

Identification and verification of a longitudinal human driving model for collision warning and avoidance systems

Abstract: The main contribution of this paper is the identification of a human driving model based on field measured car-following data, and the verification of the model's performance in a microscopic traffic simulator We first examined the SAVME database and obtained a well-defined set of data under closing-in and decelerating lead-vehicle scenarios, ie the transient manoeuvre starts with a large range and negative range rate toward the equilibrium point with proper range and zero range rate Subsequently, the ICC FOT database is used to extract model parameters under normal highway driving conditions These well-defined data sets are then used to test the flexibility of several existing driving models, ie the model parameters are tuned to fit these data The Gipps model was found to be able to fit the highest number of manoeuvres, and the identified parameters are used to represent human-controlled vehicles, which are deterministic but have different attributes (aggressiveness, target speed, etc) The Gipps model and the parameter sets are then implemented in a microscopic traffic simulator Macroscopic and microscopic behaviours of these simulated human-controlled vehicles are presented