Single-scale Models Research Articles

AN INTEGRATED MODEL USING WAVELET DECOMPOSITION AND LEAST SQUARES SUPPORT VECTOR MACHINES FOR MONTHLY CRUDE OIL PRICES FORECASTING

In this paper, a hybrid model integrating wavelet decomposition and least squares support machines (LSSVM) is proposed for crude oil price forecasting. In this model, the Haar à trous wavelet transform is first selected to decompose an original time series into several sub-series with different scales. Then the LSSVM is used to predict each sub-series. Subsequently, the final oil price forecast is obtained by reconstructing the results of the sub-series forecasts. The experimental results show that the integrated model, based on multi-scale wavelet decomposition, outperforms the traditional single-scale models. Furthermore, the proposed hybrid model is the best among all the models compared in this study. To fully integrate the advantages of several models, a combined forecasting model is presented. The study shows that the combined forecasting model is clearly better than any individual model for crude oil price forecasting.

A Complex Automata approach for in-stent restenosis: Two-dimensional multiscale modelling and simulations

In-stent restenosis, the maladaptive response of a blood vessel to injury caused by the deployment of a stent, is a multiscale system involving a large number of biological and physical processes. We describe a Complex Automata model for in-stent restenosis, coupling bulk flow, drug diffusion, and smooth muscle cell models, all operating on different time scales. Details of the single scale models and of the coupling interfaces are described, together with first simulation results, obtained with a dedicated software environment for Complex Automata simulations. Preliminary results show that the model can reproduce growth trends observed in experimental studies and facilitate testing of hypotheses concerning the interaction of key factors.

Single scale model of SUSY breaking, gauge mediation, and dark matter

Single scale model of SUSY breaking, gauge mediation, and dark matter

Does the scale of our observational window affect our conclusions about correlations between endangered salmon populations and their habitat?

Differences in the strength of species-habitat relationships across scales provide insights into the mechanisms that drive these relationships and guidance for designing in situ monitoring programs, conservation efforts and mechanistic studies. The scale of our observation can also impact the strength of perceived relationships between animals and habitat conditions. We examined the relationship between geographic information system (GIS)-based landscape data and Endangered Species Act-listed anadromous Pacific salmon (Oncorhynchus spp.) populations in three subbasins of the Columbia River basin, USA. We characterized the landscape data and ran our models at three spatial scales: local (stream reach), intermediate (6th field hydrologic units directly in contact with a given reach) and catchment (entire drainage basin). We addressed three questions about the effect of scale on relationships between salmon and GIS representations of landscape conditions: (1) at which scale does each predictor best correlate with salmon redd density, (2) at which scale is overall model fit maximized, and (3) how does a mixed-scale model compare with single scale models (mixed-scale meaning models that contain variables characterized at different spatial scales)? We developed mixed models to identify relationships between redd density and candidate explanatory variables at each of these spatial scales. Predictor variables had the strongest relationships with redd density when they were summarized over the catchment scale. Meanwhile strong models could be developed using landscape variables summarized at only the local scale. Model performance did not improve when we used suites of potential predictors summarized over multiple scales. Relationships between species abundance and land use or intrinsic habitat suitability detected at one scale cannot necessarily be extrapolated to other scales. Therefore, habitat restoration efforts should take place in the context of conditions found in the associated watershed or landscape.

Software components for parallel multiscale simulation: an example with LAMMPS

Multiscale simulation is a promising approach for addressing a variety of real-world engineering problems. Various mathematical approaches have been proposed to link single-scale models of physics into multiscale models. In order to be effective, new multiscale simulation algorithms must be implemented which use partial results provided by single-scale software. This work considers aspects of software design for interfacing to existing single-scale simulation code to perform multiscale simulations on a parallel machine. As a practical example, we extended the large-scale atomistic/molecular massively parallel simulator (LAMMPS) atomistic simulation software to facilitate its efficient use as a component of parallel multiscale-simulation software. This required new library interface functions to LAMMPS that side-stepped its dependence on files for input and output and provided efficient access to LAMMPS’s internal state. As a result, we were able to take advantage of LAMMPS’s single-scale performance without adding any multiscale-specific code to LAMMPS itself. We illustrate the use of LAMMPS as a component in three different modes: as a stand-alone application called by a multiscale code, as a parallel library invoked by a serial multiscale code, and as a parallel library invoked by a parallel multiscale code. We conclude that it is possible to efficiently re-use existing single-scale simulation software as a component in multiscale-simulation software.

Is bird incidence in Atlantic forest fragments influenced by landscape patterns at multiple scales?

The degree to which habitat fragmentation affects bird incidence is species specific and may depend on varying spatial scales. Selecting the correct scale of measurement is essential to appropriately assess the effects of habitat fragmentation on bird occurrence. Our objective was to determine which spatial scale of landscape measurement best describes the incidence of three bird species (Pyriglena leucoptera, Xiphorhynchus fuscus and Chiroxiphia caudata) in the fragmented Brazilian Atlantic forest and test if multi-scalar models perform better than single-scalar ones. Bird incidence was assessed in 80 forest fragments. The surrounding landscape structure was described with four indices measured at four spatial scales (400-, 600-, 800- and 1,000-m buffers around the sample points). The explanatory power of each scale in predicting bird incidence was assessed using logistic regression, bootstrapped with 1,000 repetitions. The best results varied between species (1,000-m radius for P. leucoptera; 800-m for X. fuscus and 600-m for C. caudata), probably due to their distinct feeding habits and foraging strategies. Multi-scale models always resulted in better predictions than single-scale models, suggesting that different aspects of the landscape structure are related to different ecological processes influencing bird incidence. In particular, our results suggest that local extinction and (re)colonisation processes might simultaneously act at different scales. Thus, single-scale models may not be good enough to properly describe complex pattern–process relationships. Selecting variables at multiple ecologically relevant scales is a reasonable procedure to optimise the accuracy of species incidence models.

Improved hybrid wavelet neural network methodology for time-varying behavior prediction of engineering structures

An improved neuro-wavelet modeling (NWM) methodology is presented, and it aims at improving prediction precision of time-varying behavior of engineering structures. The proposed methodology distinguishes from the existing NWM methodology by featuring the distinctive capabilities of constructing optimally uncoupled dynamic subsystems in light of the redundant Haar wavelet transform (RHWT) and optimizing neural network. In particular, two techniques of imitating wavelet packet transform of RHWT and reconstructing the major crests of power spectrum of analyzed data are developed with the aim of constructing the optimally uncoupled dynamic subsystems from time-varying data. The resulting uncoupled dynamic subsystems make the underlying dynamic law of time-varying behavior more tractable than the raw scale subwaves arose from the RHWT, and they provide a platform for multiscale modeling via individual modeling at the uncoupled dynamic subsystem level. Furthermore, on each uncoupled dynamic subsystem, the technique of optimal brain surgeon in conjunction with a new dynamic mechanism refreshing is employed to optimize the neural network, and the recombination of the modeling outcomes on every subsystem constitutes the overall modeling of time-varying behavior. The improved NMW methodology offers a feasible framework of multiscale modeling due to its flexibility, adaptability and rationality, and it is particularly useful for prediction applications of time-varying behavior of engineering structures. As an illustrative example, the improved NWM methodology is applied to model and forecast dam deformation, and the results show that the methodology possesses positive advantages over the existing multiscale and single scale modeling techniques. The improved NMW methodology is promising and valuable for the safety monitoring and extreme event warning of engineering structures.

Non-parametric estimation of a multiscale CHARN model using SVR

The present paper studies the non-parametric estimation of volatility in financial time series. Support Vector Regression (SVR) is applied and compared with alternative techniques for estimating a Conditional Heteroskedastic AutoRegressive Nonlinear (CHARN) model. A multiscale decomposition analysis decomposes a time series into several scales, and then several separated SVRs, equal to the number of scales, are fed for running the CHARN model by scaled decomposed series. A multiscale CHARN model, which is an incorporation of wavelet decomposition analysis with a CHARN model estimated by SVR, is proposed and investigated using real-world data sets. To exploit the locality advantage of wavelets, we use wavelet analysis and combine it with SVR. Wavelets are able to economically describe phenomena that are heterogeneous. Recent studies on heterogeneous agents in financial markets theoretically support advocated scale-based analysis of markets, and, of course, the multiscale CHARN model proposition, since it is believed that each scale corresponds to each heterogeneous agent who acts differently in the market. Our objective is to improve the accuracy of estimation by applying multiscale decomposition. The results of applying SVR to estimate the CHARN model in a single resolution on real-world time series indicate that it outperforms the technical benchmarks. Also, the multiscale CHARN model estimated by SVR is more accurate than a single scale model.

Multiscale Coupling through Locally Enriched Finite Elements

AbstractMultiscale modeling helps us to focus our limited computational power into those special places where traditional models based on continuum mechanics will fail while not losing the big picture of the macro scale behavior. An hourglass shaped development can be observed in today's simulation technologies. Simulation tools in the macroscale category and that for the micro phenomenons are both relatively well developed. Many algorithms and methods have been proposed in recent years to fill the gap between them. However, rather than trying to bridging different techniques, many tend to replace them completely and become independent simulation tools. Since many single–scale models have already been widely adopted by both the industry and the academy, it would be more beneficial to concentrate just on coupling techniques which can be applied without significant modifications of the original simulation framework. In this work, we present a multiscale idea of coupling the fine–scale model with the coarse–scale model through local enrichment within the elements at the coupling boundary. Higher order shape functions have been used to ‘enrich’ the coarse–scale model, allowing softer transition of the displacement field from the fine–scale model to the coarse–scale model. A least–square process has been used to fit the displacement gradients of different models at the coupling region. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Homogenization of the nonlinear Maxwell model of viscoelasticity and of the Prandtl—Reuss model of elastoplasticity

This paper deals with processes in nonlinear inelastic materials whose constitutive behaviour is represented by the inclusionhere we denote by σ the stress tensor, by ε the linearized strain tensor, by B(x) the compliance tensor and by ∂ϕ(·, x) the subdifferential of a convex function ϕ(·, x). This relation accounts for elasto-viscoplasticity, including a nonlinear version of the classical Maxwell model of viscoelasticity and the Prandtl—Reuss model of elastoplasticity.The constitutive law is coupled with the equation of continuum dynamics, and well-posedness is proved for an initial- and boundary-value problem. The function ϕ and the tensor B are then assumed to oscillate periodically with respect to x and, as this period vanishes, a two-scale model of the asymptotic behaviour is derived via Nguetseng's notion of two-scale convergence. A fully homogenized single-scale model is also retrieved, and its equivalence with the two-scale problem is proved. This formulation is non-local in time and is at variance with that based on so-called analogical models that rest on a mean-field-type hypothesis.

Low-Rank Variance Approximation in GMRF Models: Single and Multiscale Approaches

We present a versatile framework for tractable computation of approximate variances in large-scale Gaussian Markov random field estimation problems. In addition to its efficiency and simplicity, it also provides accuracy guarantees. Our approach relies on the construction of a certain low-rank aliasing matrix with respect to the Markov graph of the model. We first construct this matrix for single-scale models with short-range correlations and then introduce spliced wavelets and propose a construction for the long-range correlation case, and also for multiscale models. We describe the accuracy guarantees that the approach provides and apply the method to a large interpolation problem from oceanography with sparse, irregular, and noisy measurements, and to a gravity inversion problem.

MULTISCALE MODELLING: APPLICATION OF THE COMPLEX AUTOMATA SIMULATION TECHNIQUE (COAST)

Computer simulations and rule-based modelling can be effective methodologies to describe complex systems and understand or control their behaviour. As many complex biological systems encompass several spatial and temporal scales, as well as several elementary components they cannot be described by a single homogenous model. COAST is developing a multi-scale, multi-science framework coined ‘Complex Automata’ for modelling and simulation of complex systems. The key tenet of COAST is that a multi-scale system can be decomposed into a number of single-scale Cellular Automata or agent-based models that mutually interact across the scales. Decomposition is facilitated by building a Scale Separation Map (SSM) on which each single-scale system is represented according to its spatial and temporal characteristics. Processes having well-separated scales are thus easily identified as the fundamental components of the multi-scale model.

Materials integrity in microsystems: a framework for a petascale predictive-science-based multiscale modeling and simulation system

Microsystems have become an integral part of our lives and can be found in homeland security, medical science, aerospace applications and beyond. Many critical microsystem applications are in harsh environments, in which long-term reliability needs to be guaranteed and repair is not feasible. For example, gyroscope microsystems on satellites need to function for over 20 years under severe radiation, thermal cycling, and shock loading. Hence a predictive-science-based, verified and validated computational models and algorithms to predict the performance and materials integrity of microsystems in these situations is needed. Confidence in these predictions is improved by quantifying uncertainties and approximation errors. With no full system testing and limited sub-system testings, petascale computing is certainly necessary to span both time and space scales and to reduce the uncertainty in the prediction of long-term reliability. This paper presents the necessary steps to develop predictive-science-based multiscale modeling and simulation system. The development of this system will be focused on the prediction of the long-term performance of a gyroscope microsystem. The environmental effects to be considered include radiation, thermo-mechanical cycling and shock. Since there will be many material performance issues, attention is restricted to creep resulting from thermal aging and radiation-enhanced mass diffusion, material instability due to radiation and thermo-mechanical cycling and damage and fracture due to shock. To meet these challenges, we aim to develop an integrated multiscale software analysis system that spans the length scales from the atomistic scale to the scale of the device. The proposed software system will include molecular mechanics, phase field evolution, micromechanics and continuum mechanics software, and the state-of-the-art model identification strategies where atomistic properties are calibrated by quantum calculations. We aim to predict the long-term (in excess of 20 years) integrity of the resonator, electrode base, multilayer metallic bonding pads, and vacuum seals in a prescribed mission. Although multiscale simulations are efficient in the sense that they focus the most computationally intensive models and methods on only the portions of the space–time domain needed, the execution of the multiscale simulations associated with evaluating materials and device integrity for aerospace microsystems will require the application of petascale computing. A component-based software strategy will be used in the development of our massively parallel multiscale simulation system. This approach will allow us to take full advantage of existing single scale modeling components. An extensive, pervasive thrust in the software system development is verification, validation, and uncertainty quantification (UQ). Each component and the integrated software system need to be carefully verified. An UQ methodology that determines the quality of predictive information available from experimental measurements and packages the information in a form suitable for UQ at various scales needs to be developed. Experiments to validate the model at the nanoscale, microscale, and macroscale are proposed. The development of a petascale predictive-science-based multiscale modeling and simulation system will advance the field of predictive multiscale science so that it can be used to reliably analyze problems of unprecedented complexity, where limited testing resources can be adequately replaced by petascale computational power, advanced verification, validation, and UQ methodologies.

Modelling microscopic flow in woven fabric reinforcements and its application in dual-scale resin infusion modelling

Abstract A physical unit cell impregnation model is proposed for the micro-scale flow in plain woven reinforcements. The modelling results show a characteristic relationship between tow impregnation speed, the surrounding local macro-scale resin pressure and the tow saturation within the unit cell. This relationship has been formulated into a mathematical algorithm which can be directly incorporated into a continuum dual-scale model to predict the ‘sink’ term. The results using the dual-scale model show a sharp resin front in inter-tow-pore spaces and a partially saturated front region in intra-tow-pore spaces. This demonstrates that the impregnation of fibre tows lags behind the resin front in the macro pore spaces. The modelling results are in agreement with two reported experimental observations. It has been shown that the unsaturated region at the flow front could increase or have a fixed length under different circumstances. These differences are due to the variation in tow impregnation speed (or the time required for the tow to become fully impregnated), the weave architecture and the nesting and packing of plies. The modelling results have also demonstrated the drooping of the inlet pressure when flow is carried out under constant injection rates. The implementation of the algorithm into a dual-scale model shows coherence with a single-scale unsaturated model, but demonstrates an advantage in flexibility, precision and convenience in application.

Generalized Model of Polypeptide Chain with two-scale interactions

On the basis of the Generalized Model of Polypeptide Chain (GMPC) introduced earlier, which describes the helix-coil transition in both polypeptides and polynucleotides, a Hamiltonian is proposed consisting of two different-scale GMPC Hamiltonians. Within the framework of the transfer-matrix approach the degree of helicity and the correlation length are calculated. It is shown that the two-scale-interaction model may be reduced to a single-scale model with redefined parameter of the hydrogen bond closure.

Effect of Multi-Scale Porosity in Local Permeability Modelling of Non-Crimp Fabrics

The influence of multi-scale porosity of fibre reinforcements on local permeability is investigated, in order to determine the possibility of simplifying permeability models for more efficient permeability calculations. Unit cell models of a biaxial Non-Crimp Fabric are developed and used to investigate, whether or not the porous bundles can be excluded, when modelling the local permeability. Numerical accuracy of calculations is controlled to guarantee the quality of the results and the conclusions drawn from them. It is found that fibre bundles with high fibre density can be excluded from permeability models, while bundles with low fibre volume fractions need to be included. A new method to model the local permeability of multi-scale reinforcements is developed and verified for low fibre density in the bundles. In this method, the effects of the flow inside the fibre bundles are included through modifications of the boundary conditions of a single-scale model representing the interbundle regions. The local permeability of multi-scale reinforcements can, therefore, be calculated by models with simplified fluid domains for all fibre bundle porosities, instead of being calculated by models consisting of the entire multi-scale geometry.

Homogenization of some models of hysteresis

This paper deals with the behaviour of the classical Prandtl–Reuss model of elasto-plasticity in the limit of rapidly oscillating parameters. Two- and single-scale effective models are illustrated.

Numerical simulation of sudden-expansion two-phase flows with two-scale second-order moment particle turbulence model

A two-scale second-order moment particle turbulence model is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The model is employed to simulate gas-particle flows in a sudden-expansion chamber. Simulation results are compared with the experimental results and with those obtained by the single-scale second-order moment two-phase turbulence model. It is shown that the two-scale model is with higher calculating accuracy than the single-scale model.

Parameter Estimation for Multiscale Diffusions

We study the problem of parameter estimation for time-series possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a homogenized single-scale model to such multiscale data. We demonstrate, numerically and analytically, that if the data is sampled too finely then the parameter fit will fail, in that the correct parameters in the homogenized model are not identified. We also show, numerically and analytically, that if the data is subsampled at an appropriate rate then it is possible to estimate the coefficients of the homogenized model correctly.The ideas are studied in the context of thermally activated motion in a two-scale potential. However the ideas may be expected to transfer to other situations where it is desirable to fit an averaged or homogenized equation to multiscale data.

A two-scale second-order moment particle turbulence model for gas-particle flow

A two-scale second-order moment two-phase turbulence model was developed and used to simulate gas-particle flow in a sudden-expansion chamber and a channel. The simulation results were in agreement with the experimental results, and the results were compared with those of the single-scale second-order moment two-phase turbulence model. Several improved features show that the two-scale model is to a certain extent better than the single-scale model, which may be attributed to the fact that particle turbulence is well characterized by the two-scale turbulence model.