Showing papers on "Mathematical model published in 1994"

A review of techniques for parameter sensitivity analysis of environmental models

Abstract: Mathematical models are utilized to approximate various highly complex engineering, physical, environmental, social, and economic phenomena. Model parameters exerting the most influence on model results are identified through a ‘sensitivity analysis’. A comprehensive review is presented of more than a dozen sensitivity analysis methods. This review is intended for those not intimately familiar with statistics or the techniques utilized for sensitivity analysis of computer models. The most fundamental of sensitivity techniques utilizes partial differentiation whereas the simplest approach requires varying parameter values one-at-a-time. Correlation analysis is used to determine relationships between independent and dependent variables. Regression analysis provides the most comprehensive sensitivity measure and is commonly utilized to build response surfaces that approximate complex models.

Modeling of dynamic systems

Abstract: I. MODELS. 1. Systems and Models. 2. Examples of Models. 3. Models for Systems and Signals. II. PHYSICAL MODELLING. 4. Basic Principles for Physical Modelling. 5. Some Basic Physical Analogies. 6. Bond-graphs. 7. Computer Support for Physical Modelling. III. SYSTEM IDENTIFICATION. 8. Estimation of Transient Response, Spectra and Frequency Functions. 9. Parameter Estimation of Dynamical Models. 10. System Identification as Tool for Modeling. IV. SIMULATION AND MODEL APPLICATIONS. 11. Simulation. 12. Simulators. 13. Model Validation and Model Use. Appendix A: Linear Systems - Description and Properties. Appendix B: Linearization. Appendix C: Signal Spectra.

Modelling and identification of nonlinear dynamic loads in power systems

Abstract: This paper describes an approach for experimental determination of aggregate dynamic loads in power systems. The work is motivated by the importance of accurate load modeling in voltage stability analysis. The models can be expressed in general as nonlinear differential equations or equivalently realised in block diagram form as interconnections of nonlinear (memoryless) functions and linear dynamic blocks. These components are parameterized by load indexes and time constants. Experimental results from tests in Southern Sweden on the identification of these parameters are described. >

State-Space Representation of Aerodynamic Characteristics of an Aircraft at High Angles of Attack

Abstract: Mathematical modeling of unsteady aerodynamic forces and moments plays an important role in aircraft dynamics investigation and stability analysis at high angles of attack. In this article the state-space representation of aerodynamic forces and moments for unsteady aircraft motion is proposed. Consideration of separated flow about an airfoil and flow with vortex breakdown about a slender delta wing gives the base for mathematical modeling using internal variables describing the flow state. Coordinates of separation points or vortex breakdown can be taken, e.g., as internal state-space variables. These variables are governed by some differential equations. Within the framework of the proposed mathematical model it is possible to achieve good agreement with different experimental data obtained in water and wind tunnels. These high angle-of-attack experimental results demonstrate considerable dependence of aerodynamic loads on motion time history.

Comparison of numerical models for computing underwater light fields

Abstract: Seven models for computing underwater radiances and irradiances by numerical solution of the radiative transfer equation are compared. The models are applied to the solution of several problems drawn from optical oceanography. The problems include highly absorbing and highly scattering waters, scattering by molecules and by particulates, stratified water, atmospheric effects, surface-wave effects, bottom effects, and Raman scattering. The models provide consistent output, with errors (resulting from Monte Carlo statistical fluctuations) in computed irradiances that are seldom larger, and are usually smaller, than the experimental errors made in measuring irradiances when using current oceanographic instrumentation. Computed radiances display somewhat larger errors.

A Simple but Realistic Model for Laser Cladding

Abstract: A model which takes into account the main phenomena occurring during the laser-cladding process is proposed. For a given laser power, beam radius, powder jet geometry, and clad height, this model evaluates two other processing parameters, namely, the laser-beam velocity and the powder feed rate. It considers the interactions between the powder particles, the laser beam, and the molten pool. The laser power reaching the surface of the workpiece is estimated and, assuming this power is used to remelt the substrate with the clad having been predeposited, the melt-pool shape is computed using a three-dimensional (3-D) analytical model, which produces mmediate results, even on personal computers. The predictions obtained with this numerical model are in good agreement with experimental results. Processing engineers may therefore use this model to choose the correct processing parameters and to establish cladding maps.

A binary model of textile composites—I. Formulation

Abstract: This paper presents a finite element model of polymer composites with three-dimensional (3D) reinforcement. The model performs Monte Carlo simulations of failure under monotonic and fatigue loading. The formulation of the model is guided by extensive prior experimental observations of 3D woven composites. Special emphasis is placed on realistic representation of the pattern of reinforcing tows, random irregularity in tow positioning, randomness of the strengths of constituent elements, and the mechanics of stress redistribution around sites of local failure. The constitutive properties of model elements (or their distributions) are based on micromechanical models of observed failure events. Material properties that are appropriately analyzed by the model are contrasted with those amenable to much simpler models. Some illustrative model simulations are presented. Prescriptions for the calibration of the model for design and reliability applications and details of its performance in simulating the elastic and damaged regimes of 3D woven composites will appear in subsequent papers.

Low-dimensional description of free-shear-flow coherent structures and their dynamical behaviour

Abstract: The snapshot form of the Karhunen-Loeve (K–L) expansion has been applied to twodimensional, two-component hot-wire data from the region of a weakly pertubed free shear layer that includes the first pairing process. Low-level external perturbation was provided by a loudspeaker driven by a computer-generated signal composed of two sine waves of equal amplitude at the frequencies of the naturally developing fundamental instability wave and its first subharmonic, separated by a controllable initial phase angle difference. It was found that a large fraction of the fluctuation energy is carried by the first few modes. A low-dimensional empirical eigenfunction space is obtained which describes the shear-flow coherent structures well. Galerkin projection of the Navier-Stokes equations onto this basis set of principal eigenfunction modes results in a low-order system of dynamical equations, and solution of this system of equations describes the dynamics of the coherent structures associated with eigenfunctions. Finally the simulation, as obtained from the system of dynamical equations, is shown to compare reasonably well with the experiments.

Strain-rate effect on brittle failure in compression

Abstract: A simple model of an array of interacting, dynamically growing wing cracks is used to simulate the rate-dependent dynamic damage evolution and subsequent brittle failure of solids under compression. The validity of the model is discussed. Parameters which identify the overall failure by the coalescence of compression-induced, interacting, tensile microcracks are calculated in closed form, and relations between microstructure and the corresponding rate dependency of the overall response are examined in some detail. It is shown that the experimentally observed change in the compressive failure stress with increasing strain rate, may be considered to be a consequence of the generation and dynamic growth of interacting, compression-induced, tensile microcracks. Examples of brittle failure in uniaxial stress and uniaxial strain conditions, respectively, produced in the Hopkinson compression bar and normal plate-impact experiments, are discussed in terms of this model.

Semi-Markov Random Evolutions

Abstract: A mathematical model of the random medium in the form of a Markov renewal process, which was introduced in Chapter 1, forms a basis for constructing various mathematical models of the evolution of stochastic systems in the random medium.

Order reduction of large-scale linear oscillatory system models

Abstract: Eigenanalysis and signal analysis techniques of deriving representations of power system oscillatory dynamics result in very high-order linear models. In order to apply many modern control design methods, the models must be reduced to a more manageable order while preserving essential characteristics. Presented in this paper is a model reduction method well suited for large-scale power systems. The method searches for the optimal subset of the high-order model that best represents the system. An Akaike information criterion is used to define the optimal reduced model. The method is first presented, and then examples of applying it to Prony analysis and eigenanalysis models of power systems are given. >

A new aperture admittance model for open-ended waveguides

Abstract: A new model for the aperture admittance of open-ended waveguide structures radiating into a homogeneous, lossy dielectric is presented. The model is based on the physical and mathematical properties of the driving point admittance of passive, stable one-port networks. The model parameters, which depend upon the geometry of the waveguide and aperture, are determined from a relatively small number of computed admittances. This computed data is obtained by a full-wave moment method solution and, hence, includes the effects of radiation and energy storage in the near field and the evanescent waveguide modes. The accuracy of the numerical method is demonstrated by comparison with measured values. As an example, the model parameters are determined for the coaxial-line geometry. The accuracy of the model, for both the direct and inverse problem, is verified and a rigorous sensitivity and uncertainty analysis is performed. The new model has important applications in the field of dielectric spectroscopy. >

Spatial averaging of unsaturated flow equations under infiltration conditions over areally heterogeneous fields 2. Numerical simulations

Abstract: Two models for horizontally averaged unsaturated flow have been developed from two different approaches in the first (Chen et al., this issue) of these companion papers. In this paper the results from both the spatially horizontally averaged Richards equation (SHARE) model and the averaged Green-Ampt model are compared with the results from a three-dimensional finite difference model of unsaturated flow which is perceived as the reference solution. The results of the averaged Green-Ampt model show very good agreement with the averaged results from the three-dimensional model, while SHARE model results are applicable only when fluctuations in soil parameters are small with respect to their mean values. It is also shown that methods of simple parameter averaging (arithmetic or geometric averages) with the local Richards equation does not yield meaningful results in heterogeneous soils. This study suggests that spatially horizontally averaged simplified models (such as the averaged Green-Ampt model) are attractive alternatives to perturbation models (such as the SHARE model) in heterogeneous fields. Due to their simplicity in formulation, accuracy in predicting average behaviors, and minimal requirement of computer effort, the spatially horizontally averaged simplified models can be easily implemented in large-scale models, such as atmospheric mesoscale models. boundary and initial conditions. The average saturation at each depth was obtained by areal integration of the local scale water saturation over the specified area under the assumption of independent vertical soil columns at field scales. Relative occurrence frequency curves of the spatially varying parameters were required for the solution of the average quantities. The second model developed was the spatially horizontally averaged Richards equation (SHARE) model. This model was developed by using spatial averaging and regular perturbation techniques under the assumption of no source or sink in the study area. The SHARE model was expressed as a system of two coupled one-dimensional partial differential equations in terms of the mean saturation and the cross-covariance of saturation and saturated hydrau-

Laterally loaded piles in elastic media

Abstract: A numerical approach and parametric study for the calculation of the soil and pile interaction under lateral loading are presented. The method uses variational calculus to obtain the governing differential equations of the soil and pile system. A principal parameter (γ) is used in this model to present the elastic foundation. The properties and the significance of the primary model parameters, such as γ, Poisson's ratio υ, slenderness ratio Ψ, and flexibility factor Kr, are carefully investigated in order to have a better understanding of the relationships between those parameters. A number of important features, including linear relationships between the coefficients and simple analytical equations, are presented here. On the basis of the new aspect and related mathematical expressions, an improved predictive capability is obtained. This general analytical perspective allows the further improvement and simplification of the proposed model and suggests a way to predict the response of laterally loaded pil...

An Analytical and Experimental Investigation of the Driver-Seat-Suspension System

Abstract: SUMMARY Vertical seat-suspension systems are characterized by a generalized two- degree-of-freedom model incorporating nonlinearities due to shock absorber damping, linkage friction and bump stops. The analytical model is validated using the results obtained from laboratory tests performed under sinusoidal excitations in the 0.5-8.0 Hz frequency range. Human body models of varying complexities, derived from the mechanical impedance data, are discussed and integrated to the nonlinear seat-suspension model to derive a coupled driver- seat-suspension model. Nonlinear analytical models are expressed by their linear equivalent models using a local equivalent linearization technique based on energy similarity. The vibration attenuation performance characteristics of the seat-suspension and driver-seat-suspension models are investigated for deterministic and random cab floor excitations. The results of the study revealed that the seated human body contributes considerably to the overall ride performance.

Updating of finite element models using vibration tests

Abstract: Today the adjustment of structural models is an essential step in the modeling of complex structures. In this paper, we are interested in the improvement of finite element models. Our approach is a parametric updating using modal test results, which supply eigenvalues and associated eigenvectors. It is based on the computation of the error measure on the constitutive relation and allows us to correct both the stiffness and the mass matrices. In particular, this paper shows how this tuning strategy can improve a given finite element model when the measures are noisy. Several simulation examples illustrate the behavior of this method. A E e

Energy Models for One-Carrier Transport in Semiconductor Devices

Abstract: Moment models of carrier transport, derived from the Boltzmann equation, have made possible the simulation of certain key effects through such realistic assumptions as energy dependent mobility functions. This type of global dependence permits the observation of velocity overshoot in the vicinity of device junctions, not discerned via classical drift-diffusion models, which are primarily local in nature. It has been found that a critical role is played in the hydrodynamic model by the heat conduction term. When ignored, the overshoot is inappropriately damped. When the standard choice of the Wiedemann-Franz law is made for the conductivity, spurious overshoot is observed. Agreement with Monte-Carlo simulation in this regime has required empirical modification of this law, as observed by IBM researchers, or nonstandard choices. In this paper, simulations of the hydrodynamic model in one and two dimensions, as well as simulations of a newly developed energy model, the RT model, will be presented. The RT model, intermediate between the hydrodynamic and drift-diffusion model, was developed at the University of Illinois to eliminate the parabolic energy band and Maxwellian distribution assumptions, and to reduce the spurious overshoot with physically consistent assumptions. The algorithms employed for both models are the essentially non-oscillatory shock capturing algorithms, developed at UCLA during the last decade. Some mathematical results will be presented, and contrasted with the highly developed state of the drift-diffusion model.

Monitoring of the friction coefficient between tyre and road surface

Abstract: The knowledge of the friction coefficient between tyre and road surface is the central part of vehicle longitudinal and lateral control. For this purpose a friction monitoring system is developed using nonlinear and linear mathematical models to describe the /spl mu/-slip characteristics and to compute the dynamic wheel loads and longitudinal tyre forces. A recursive least squares estimator calculates the parameters of the /spl mu/-slip characteristics online and on-board for use in control systems. >

What good are numerical simulations of chaotic dynamical systems

Abstract: Numerical simulations of mathematical models can suggest that the models are chaotic. For example, one can compute an orbit and its associated finite-time Lyapunov exponents, and these computed exponents can be positive. It is not clear how far these suggestions can be trusted, because, as is well known, numerical methods can introduce spurious chaos or even suppress actual chaos. This focused review examines the fidelity of numerical methods. We look at the didactic example of the Gauss map from the theory of continued fractions, which allows a simple examination of backward error analysis for discrete dynamical systems and gives a clear picture of the effects of floating-point arithmetic. A similar use of backward error analysis, in the form of defect control , gives a useful understanding in the case of continuous dynamical systems. Finally, we discuss limitations of this ‘backward’ point of view.

Numerical modelling of induction heating of long workpieces

Abstract: We consider in this paper an induction heating process. A mathematical model is presented, together with numerical methods used in order to describe the magnetic field, as well as the temperature field evolution. Experimental measurements were performed in order to validate the numerical simulation results. A comparison is presented for both ferromagnetic and non-ferromagnetic materials. An error discussion is provided. >

Nonlinear two-dimensional finite element modeling of permanent magnet eddy current couplings and brakes

Abstract: A two-dimensional finite element model is developed to model the electromagnetic behavior of permanent magnet type eddy current couplers under constant speed operation. The model accounts for the nonlinearity of the steel flux paths and is verified using test measurements from a prototype eddy current coupler. The proposed solution differs from conventional magnetostatic finite element models in that an unknown current-density distribution must be determined through an iterative process. The model is used to study the influence of certain design parameters on the torque-speed characteristics of such devices. >

Advanced statistical energy analysis

Abstract: A high-frequency theory (advanced statistical energy analysis (ASEA)) is developed which takes account of the mechanism of tunnelling and uses a ray theory approach to track the power flowing around a plate or a beam network and then uses statistical energy analysis (SEA) to take care of any residual power. ASEA divides the energy of each sub-system into energy that is freely available for transfer to other sub-systems and energy that is fixed within the sub-system. The theory allows for coupling between sub-systems that are physically separate and can be interpreted as a series of mathematical models, the first of which is identical to standard SEA and subsequent higher order models are convergent on an accurate prediction. Using a structural assembly of six rods as an example, ASEA is shown to converge onto the exact results, whereas SEA is shown to overpredict by up to 60 dB.

Critical behavior for correlated strongly coupled boson systems in 1+1 dimensions.

Abstract: The natural integrable correlated strongly coupled boson system in 1 + 1 dimensions is the $q$-boson hopping model; we calculate its critical exponent $\ensuremath{\theta}$ and determine its correlation functions. For small couplings the $q$-boson model has natural connections with the Bose gas and the $\mathrm{XY}$ models of very large spin for which $\ensuremath{\theta}'\mathrm{s}$ and correlators are reported. For large couplings the hopping model is a new phase of interacting bosons substantially different from the impenetrable Bose gas.

Quench in superconducting magnets. I. Model and numerical implementation

Abstract: A new simple, self‐consistent theoretical model is presented that describes the phenomena of quench propagation in Cable‐in‐Conduit superconducting magnets. The model circumvents many of the difficulties associated with obtaining numerical solutions in more general existing models. Specifically, a factor of 30–50 is gained in CPU time over the general, explicit time‐dependent codes used to study typical quench events. The corresponding numerical implementation of the new model is described and the numerical results are shown to agree very well with those of the more general models, as well as with experimental data.

Comparison of Coupled Radiative Navier-Stokes Flow Solutions with the Project Fire II Flight Data

Abstract: A nonequilibrium, axisymmetric, Navier-Stokes flow solver with coupled radiation has been developed to use in the design of thermal protection systems for vehicles where radiation effects are important The present method has been compared with an existing flow and radiation solver and with the Project Fire II experimental data Very good agreement has been obtained over the entire Fire II trajectory with the experimentally determined values of the stagnation radiation intensity in the 2 to 62 eV range and with the total stagnation heating The agreement was significantly better than previous numerical predictions The effects of a number of flow models are examined to determine which combination of physical models produces the best agreement with the experimental data These models include radiation coupling, multi-temperature thermal models, finite-rate chemistry, and a quasi-steady-state or Boltzmann assumption for the calculation of the excited electronic states Finally, the computational efficiency of the present model is evaluated The radiation properties model developed for this study is shown to offer significant computational savings compared to existing codes