Enhancing SPH using moving least-squares and radial basis functions

In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using: moving least-squares approximation (MLS); radial basis functions (RBF). Using MLS approximation is appealing because polynomial consistency of the particle approximation can be enforced. RBFs further appeal as they allow one to dispense with the smoothing-length - the parameter in the SPH method which governs the number of particles within the support of the shape function. Currently, only ad hoc methods for choosing the smoothing-length exist. We ensure that any enhancement retains the conservative and meshfree nature of SPH. In doing so, we derive a new set of variationally-consistent hydrodynamic equations. Finally, we demonstrate the performance of the new equations on the Sod shock tube problem.

Efecto determinante de la motivación de viaje sobre la imagen de destino en turistas de ocio a un destino urbano: El caso de Monterrey, México. Una aproximación por medio de mínimos cuadrados parciales (PLS) = Determinant effect of travel motivation on the destination image of leisure tourist in an urban destination: the case of Monterrey, México. An approach through partial least squares (PLS)

Los turistas urbanos se caracterizan por ser uno de los segmentos de mayor crecimiento en los mercados turísticos actuales. Monterrey (México), uno de los principales destinos urbanos del país, ha apostado en la actualidad por mejorar su competitividad. Esta investigación se propuso encontrar evidencia acerca de la relación causal de la motivación de viaje sobre la imagen percibida del destino, dos variables importantes por su influencia en la satisfacción de los visitantes. Una revisión de la literatura permitió proponer constructos teóricos integrados en un instrumento para la recogida de datos vía encuesta a una muestra representativa. Por medio del método de regresión y ecuaciones estructurales por mínimos cuadrados parciales (PLS), se identificaron los componentes principales de ambas variables y se obtuvo un modelo explicativo de la imagen percibida del destino en función de la motivación de viaje. Finalmente, se emiten recomendaciones para la gestión del destino urbano en función de los resultados obtenidos. ABSTRACT: Abstract Urban tourists are recognized as one of the fastest growing segments in today’s tourism markets. Monterrey, Mexico, one of the main urban destinations in the country aims at improving its competitiveness. This research work had the purpose of finding evidence on the causal relationship between travel motivation and destination image, two important variables because of their influence on visitors’ satisfaction. A literature review enabled the proposal of a research instrument with theoretically based constructs to gather data through survey from a representative sample. Using regression and structural equations modelling by partial least squares (pls) a set of main components of both variables were identified thus enabling the obtention of a explanatory model of destination image in terms of travel motivations. Finally based on the results some recommendations of tourism management are given.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of-reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced-assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

A finite-strain solid–shell using local Löwdin frames and least-squares strains

A finite-strain solid–shell element is proposed. It is based on least-squares in-plane assumed strains, assumed natural transverse shear and normal strains. The singular value decomposition (SVD) is used to define local (integration-point) orthogonal frames-of- reference solely from the Jacobian matrix. The complete finite-strain formulation is derived and tested. Assumed strains obtained from least-squares fitting are an alternative to the enhanced-assumed-strain (EAS) formulations and, in contrast with these, the result is an element satisfying the Patch test. There are no additional degrees-of-freedom, as it is the case with the enhanced- assumed-strain case, even by means of static condensation. Least-squares fitting produces invariant finite strain elements which are shear-locking free and amenable to be incorporated in large-scale codes. With that goal, we use automatically generated code produced by AceGen and Mathematica. All benchmarks show excellent results, similar to the best available shell and hybrid solid elements with significantly lower computational cost.

Least-squares finite strain hexahedral element/constitutive coupling based on parametrized configurations and the Löwdin frame

Two novelties are introduced: (i) a finite-strain semi-implicit integration algorithm compatible with current element technologies and (ii) the application to assumed-strain hexahedra. The Löwdin algo- rithm is adopted to obtain evolving frames applicable to finite strain anisotropy and a weighted least- squares algorithm is used to determine the mixed strain. Löwdin frames are very convenient to model anisotropic materials. Weighted least-squares circumvent the use of internal degrees-of-freedom. Het- erogeneity of element technologies introduce apparently incompatible constitutive requirements. Assumed-strain and enhanced strain elements can be either formulated in terms of the deformation gradient or the Green–Lagrange strain, many of the high-performance shell formulations are corotational and constitutive constraints (such as incompressibility, plane stress and zero normal stress in shells) also depend on specific element formulations. We propose a unified integration algorithm compatible with possibly all element technologies. To assess its validity, a least-squares based hexahedral element is implemented and tested in depth. Basic linear problems as well as 5 finite-strain examples are inspected for correctness and competitive accuracy.

A Comparative Analysis Between Genetic Algorithms and Complex Nonlinear Least Squares on Electrical Impedance Characterization

This paper compares the performance of the complex nonlinear least squares algorithm implemented in the LEVM/LEVMW software with the performance of a genetic algorithm in the characterization of an electrical impedance of known topology. The effect of the number of measured frequency points and of measurement uncertainty on the estimation of circuit parameters is presented. The analysis is performed on the equivalent circuit impedance of a humidity sensor.

Forecasting with serially correlated regression models

In this article we investigate the asymptotic and finite-sample properties of predictors of regression models with autocorrelated errors. We prove new theorems associated with the predictive efficiency of generalized least squares (GLS) and incorrectly structured GLS predictors. We also establish the form associated with their predictive mean squared errors as well as the magnitude of these errors relative to each other and to those generated from the ordinary least squares (OLS) predictor. A large simulation study is used to evaluate the finite-sample performance of forecasts generated from models using different corrections for the serial correlation.

Combination of altimetry data from different satellite missions

Substantial altimetry datasets collected by different satellites have only become available during the past five years, but the future will bring a variety of new altimetry missions, both parallel and consecutive in time. The characteristics of each produced dataset vary with the different orbital heights and inclinations of the spacecraft, as well as with the technical properties of the radar instrument. An integral analysis of datasets with different properties offers advantages both in terms of data quantity and data quality. This thesis is concerned with the development of the means for such integral analysis, in particular for dynamic solutions in which precise orbits for the satellites are computed simultaneously. The first half of the thesis discusses the theory and numerical implementation of dynamic multi-satellite altimetry analysis. The most important aspect of this analysis is the application of dual satellite altimetry crossover points as a bi-directional tracking data type in simultaneous orbit solutions. The central problem is that the spatial and temporal distributions of the crossovers are in conflict with the time-organised nature of traditional solution methods. Their application to the adjustment of the orbits of both satellites involved in a dual crossover therefore requires several fundamental changes of the classical least-squares prediction/correction methods. The second part of the thesis applies the developed numerical techniques to the problems of precise orbit computation and gravity field adjustment, using the altimetry datasets of ERS-1 and TOPEX/Poseidon. Although the two datasets can be considered less compatible that those of planned future satellite missions, the obtained results adequately illustrate the merits of a simultaneous solution technique. In particular, the geographically correlated orbit error is partially observable from a dataset consisting of crossover differences between two sufficiently different altimetry datasets, while being unobservable from the analysis of altimetry data of both satellites individually. This error signal, which has a substantial gravity-induced component, can be employed advantageously in simultaneous solutions for the two satellites in which also the harmonic coefficients of the gravity field model are estimated.

Statistical model based 3D shape prediction of postoperative trunks for non-invasive scoliosis surgery planning

One of the major concerns of scoliosis patients undergoing surgical treatment is the aesthetic aspect of the surgery outcome. It would be useful to predict the postoperative appearance of the patient trunk in the course of a surgery planning process in order to take into account the expectations of the patient. In this paper, we propose to use least squares support vector regression for the prediction of the postoperative trunk 3D shape after spine surgery for adolescent idiopathic scoliosis. Five dimensionality reduction techniques used in conjunction with the support vector machine are compared. The methods are evaluated in terms of their accuracy, based on the leave-one-out cross-validation performed on a database of 141 cases. The results indicate that the 3D shape predictions using a dimensionality reduction obtained by simultaneous decomposition of the predictors and response variables have the best accuracy.

Data assimilation for marine monitoring and prediction: The MERCATOR operational assimilation systems and the MERSEA developments

During the past 15 years, a number of initiatives have been undertaken at national level to develop ocean forecasting systems operating at regional and/or global scales. The co-ordination between these efforts has been organized internationally through the Global Ocean Data Assimilation Experiment (GODAE). The French MERCATOR project is one of the leading participants in GODAE. The MERCATOR systems routinely assimilate a variety of observations such as multi-satellite altimeter data, sea-surface temperature and in situ temperature and salinity profiles, focusing on high-resolution scales of the ocean dynamics. The assimilation strategy in MERCATOR is based on a hierarchy of methods of increasing sophistication including optimal interpolation, Kalman filtering and variational methods, which are progressively deployed through the Syst`eme d’Assimilation MERCATOR (SAM) series. SAM-1 is based on a reduced-order optimal interpolation which can be operated using ‘altimetry-only’ or ‘multi-data’ set-ups; it relies on the concept of separability, assuming that the correlations can be separated into a product of horizontal and vertical contributions. The second release, SAM-2, is being developed to include new features from the singular evolutive extended Kalman (SEEK) filter, such as three-dimensional, multivariate error modes and adaptivity schemes. The third one, SAM-3, considers variational methods such as the incremental four-dimensional variational algorithm. Most operational forecasting systems evaluated during GODAE are based on least-squares statistical estimation assuming Gaussian errors. In the framework of the EU MERSEA (Marine EnviRonment and Security for the European Area) project, research is being conducted to prepare the next-generation operational ocean monitoring and forecasting systems. The research effort will explore nonlinear assimilation formulations to overcome limitations of the current systems. This paper provides an overview of the developments conducted in MERSEA with the SEEK filter, the Ensemble Kalman filter and the sequential importance re-sampling filter.

Dual-orthogonal radial basis function networks for nonlinear time series prediction

A new structure of Radial Basis Function (RBF) neural network called the Dual-orthogonal RBF Network (DRBF) is introduced for nonlinear time series prediction. The hidden nodes of a conventional RBF network compare the Euclidean distance between the network input vector and the centres, and the node responses are radially symmetrical. But in time series prediction where the system input vectors are lagged system outputs, which are usually highly correlated, the Euclidean distance measure may not be appropriate. The DRBF network modifies the distance metric by introducing a classification function which is based on the estimation data set. Training the DRBF networks consists of two stages. Learning the classification related basis functions and the important input nodes, followed by selecting the regressors and learning the weights of the hidden nodes. In both cases, a forward Orthogonal Least Squares (OLS) selection procedure is applied, initially to select the important input nodes and then to select the important centres. Simulation results of single-step and multi-step ahead predictions over a test data set are included to demonstrate the effectiveness of the new approach.

Prediction of coagulation properties, titratable acidity and pH of bovine milk using mid-infrared spectroscopy

This study investigated the potential application of mid-infrared spectroscopy (MIR 4,000–900 cm−1) for the determination of milk coagulation properties (MCP), titratable acidity (TA), and pH in Brown Swiss milk samples (n = 1,064). Because MCP directly influence the efficiency of the cheese-making process, there is strong industrial interest in developing a rapid method for their assessment. Currently, the determination of MCP involves time-consuming laboratory-based measurements, and it is not feasible to carry out these measurements on the large numbers of milk samples associated with milk recording programs. Mid-infrared spectroscopy is an objective and nondestructive technique providing rapid real-time analysis of food compositional and quality parameters. Analysis of milk rennet coagulation time (RCT, min), curd firmness (a30, mm), TA (SH°/50 mL; SH° = Soxhlet-Henkel degree), and pH was carried out, and MIR data were recorded over the spectral range of 4,000 to 900 cm−1. Models were developed by partial least squares regression using untreated and pretreated spectra. The MCP, TA, and pH prediction models were improved by using the combined spectral ranges of 1,600 to 900 cm−1, 3,040 to 1,700 cm−1, and 4,000 to 3,470 cm−1. The root mean square errors of cross-validation for the developed models were 2.36 min (RCT, range 24.9 min), 6.86 mm (a30, range 58 mm), 0.25 SH°/50 mL (TA, range 3.58 SH°/50 mL), and 0.07 (pH, range 1.15). The most successfully predicted attributes were TA, RCT, and pH. The model for the prediction of TA provided approximate prediction (R2 = 0.66), whereas the predictive models developed for RCT and pH could discriminate between high and low values (R2 = 0.59 to 0.62). It was concluded that, although the models require further development to improve their accuracy before their application in industry, MIR spectroscopy has potential application for the assessment of RCT, TA, and pH during routine milk analysis in the dairy industry. The implementation of such models could be a means of improving MCP through phenotypic-based selection programs and to amend milk payment systems to incorporate MCP into their payment criteria.

Prediction of moisture, calorific value, ash and carbon content of two dedicated bioenergy crops using near-infrared spectroscopy

The potential of near infrared spectroscopy in conjunction with partial least squares regression to predict Miscanthus xgiganteus and short rotation coppice willow quality indices was examined. Moisture, calorific value, ash and carbon content were predicted with a root mean square error of cross validation of 0.90% (R2 = 0.99), 0.13 MJ/kg (R2 = 0.99), 0.42% (R2 = 0.58), and 0.57% (R2 = 0.88), respectively. The moisture and calorific value prediction models had excellent accuracy while the carbon and ash models were fair and poor, respectively. The results indicate that near infrared spectroscopy has the potential to predict quality indices of dedicated energy crops, however the models must be further validated on a wider range of samples prior to implementation. The utilization of such models would assist in the optimal use of the feedstock based on its biomass properties.

Prediction of processed cheese instrumental texture and meltability by mid-infrared spectroscopy coupled with chemometric tools

The objective of this study was to determine the potential of mid-infrared spectroscopy coupled with multidimensional statistical analysis for the prediction of processed cheese instrumental texture and meltability attributes. Processed cheeses (n = 32) of varying composition were manufactured in a pilot plant. Following two and four weeks storage at 4 degrees C samples were analysed using texture profile analysis, two meltability tests (computer vision, Olson and Price) and mid-infrared spectroscopy (4000-640 cm(-1)). Partial least squares regression was used to develop predictive models for all measured attributes. Five attributes were successfully modelled with varying degrees of accuracy. The computer vision meltability model allowed for discrimination between high and low melt values (R-2 = 0.64). The hardness and springiness models gave approximate quantitative results (R-2 = 0.77) and the cohesiveness (R-2 = 0.81) and Olson and Price meltability (R-2 = 0.88) models gave good prediction results. (c) 2006 Elsevier Ltd. All rights reserved..

Application of mid-infrared spectroscopy to the prediction of maturity and sensory texture attributes of cheddar cheese

The objective of this study was to determine the potential of mid-infrared spectroscopy in conjunction with partial least squares (PLS) regression to predict various quality parameters in cheddar cheese. Cheddar cheeses (n = 24) were manufactured and stored at 8 degrees C for 12 mo. Mid-infrared spectra (640 to 4000/cm) were recorded after 4, 6, 9, and 12 mo storage. At 4, 6, and 9 mo, the water-soluble nitrogen (WSN) content of the samples was determined and the samples were also evaluated for 11 sensory texture attributes using descriptive sensory analysis. The mid-infrared spectra were subjected to a number of pretreatments, and predictive models were developed for all parameters. Age was predicted using scatter-corrected, 1st derivative spectra with a root mean square error of cross-validation (RMSECV) of 1 mo, while WSN was predicted using 1st derivative spectra (RMSECV = 2.6%). The sensory texture attributes most successfully predicted were rubbery, crumbly, chewy, and massforming. These attributes were modeled using 2nd derivative spectra and had, corresponding RMSECV values in the range of 2.5 to 4.2 on a scale of 0 to 100. It was concluded that mid-infrared spectroscopy has the potential to predict age, WSN, and several sensory texture attributes of cheddar cheese..