A time-harmonic target-field method for designing unshielded RF coils in MRI

Time-harmonic methods are required in the accurate design of RF coils as operating frequency increases. This paper presents such a method to find a current density solution on the coil that will induce some desired magnetic field upon an asymmetrically located target region within. This inverse method appropriately considers the geometry of the coil via a Fourier series expansion, and incorporates some new regularization penalty functions in the solution process. A new technique is introduced by which the complex, time-dependent current density solution is approximated by a static coil winding pattern. Several winding pattern solutions are given, with more complex winding patterns corresponding to more desirable induced magnetic fields.

Light alloy castings for automotive applications: The case of Al vs Mg

The economical and environmental effects of mass reduction through Al and Mg primary alloys substitutions for cast iron and steel in automotive components are discussed using MF. Ashby's penalty functions method The viability of Mg alloy substitutions for existing Al alloy cast components is also considered. The cost analysis shows that direct, equal-volume, Al alloy substitutions for cast iron and steel are the most feasible in terms of the CAFE liability, followed by substitutions involving flat panels of prescribed stiffness. When the creation of CO2 associated to the production of Al and Mg is considered, the potential gasoline savings over the lifespan of the car compensate for the intrinsic environmental burden of Al in all applications, while electrolytic Mg substitutions for cast iron and steel are feasible for equal volume and panels only. Magnesium produced by the Pidgeon thermal process appears to be too primary energy intensive to be competitive in structural applications. Magnesium substitutions for existing Al alloy beams and panels are generally unviable. The current higher recycling efficiency of Al casting alloys confers Al a significant advantage over Mg alloys.

Powertrain optimisation in a hybrid electric bus

This paper describes the use of a formal optimisation procedure to optimise a plug-in hybrid electric bus using two different case studies to meet two different performance criteria; minimum journey cost and maximum battery life. The approach is to choose a commercially available vehicle and seek to improve its performance by varying key design parameters. Central to this approach is the ability to develop a representative backward facing model of the vehicle in MATLAB/Simulink along with appropriate optimisation objective and penalty functions. The penalty functions being the margin by which a particular design fails to meet the performance specification. The model is validated against data collected from an actual vehicle and is used to estimate the vehicle performance parameters in a model-in-the-loop process within an optimisation routine. For the purposes of this paper, the journey cost/battery life over a drive cycle is optimised whilst other performance indices are met (or exceeded). Among the available optimisation methods, Powell's method and Simulated Annealing are adopted. The results show this method as a valid alternative modelling approach to vehicle powertrain optimisation. © 2012 IEEE.

Classificação de atividade eletromiográfia facial de indivíduos saudáveis e com hanseníese por meio de máquina de vetores de suporte

A number of studies in the areas of Biomedical Engineering and Health Sciences have employed machine learning tools to develop methods capable of identifying patterns in different sets of data. Despite its extinction in many countries of the developed world, Hansen’s disease is still a disease that affects a huge part of the population in countries such as India and Brazil. In this context, this research proposes to develop a method that makes it possible to understand in the future how Hansen’s disease affects facial muscles. By using surface electromyography, a system was adapted so as to capture the signals from the largest possible number of facial muscles. We have first looked upon the literature to learn about the way researchers around the globe have been working with diseases that affect the peripheral neural system and how electromyography has acted to contribute to the understanding of these diseases. From these data, a protocol was proposed to collect facial surface electromyographic (sEMG) signals so that these signals presented a high signal to noise ratio. After collecting the signals, we looked for a method that would enable the visualization of this information in a way to make it possible to guarantee that the method used presented satisfactory results. After identifying the method's efficiency, we tried to understand which information could be extracted from the electromyographic signal representing the collected data. Once studies demonstrating which information could contribute to a better understanding of this pathology were not to be found in literature, parameters of amplitude, frequency and entropy were extracted from the signal and a feature selection was made in order to look for the features that better distinguish a healthy individual from a pathological one. After, we tried to identify the classifier that best discriminates distinct individuals from different groups, and also the set of parameters of this classifier that would bring the best outcome. It was identified that the protocol proposed in this study and the adaptation with disposable electrodes available in market proved their effectiveness and capability of being used in different studies whose intention is to collect data from facial electromyography. The feature selection algorithm also showed that not all of the features extracted from the signal are significant for data classification, with some more relevant than others. The classifier Support Vector Machine (SVM) proved itself efficient when the adequate Kernel function was used with the muscle from which information was to be extracted. Each investigated muscle presented different results when the classifier used linear, radial and polynomial kernel functions. Even though we have focused on Hansen’s disease, the method applied here can be used to study facial electromyography in other pathologies.

Classificação de atividade eletromiográfia facial de indivíduos saudáveis e com hanseníase por meio de máquina de vetores de suporte

A number of studies in the areas of Biomedical Engineering and Health Sciences have employed machine learning tools to develop methods capable of identifying patterns in different sets of data. Despite its extinction in many countries of the developed world, Hansen’s disease is still a disease that affects a huge part of the population in countries such as India and Brazil. In this context, this research proposes to develop a method that makes it possible to understand in the future how Hansen’s disease affects facial muscles. By using surface electromyography, a system was adapted so as to capture the signals from the largest possible number of facial muscles. We have first looked upon the literature to learn about the way researchers around the globe have been working with diseases that affect the peripheral neural system and how electromyography has acted to contribute to the understanding of these diseases. From these data, a protocol was proposed to collect facial surface electromyographic (sEMG) signals so that these signals presented a high signal to noise ratio. After collecting the signals, we looked for a method that would enable the visualization of this information in a way to make it possible to guarantee that the method used presented satisfactory results. After identifying the method's efficiency, we tried to understand which information could be extracted from the electromyographic signal representing the collected data. Once studies demonstrating which information could contribute to a better understanding of this pathology were not to be found in literature, parameters of amplitude, frequency and entropy were extracted from the signal and a feature selection was made in order to look for the features that better distinguish a healthy individual from a pathological one. After, we tried to identify the classifier that best discriminates distinct individuals from different groups, and also the set of parameters of this classifier that would bring the best outcome. It was identified that the protocol proposed in this study and the adaptation with disposable electrodes available in market proved their effectiveness and capability of being used in different studies whose intention is to collect data from facial electromyography. The feature selection algorithm also showed that not all of the features extracted from the signal are significant for data classification, with some more relevant than others. The classifier Support Vector Machine (SVM) proved itself efficient when the adequate Kernel function was used with the muscle from which information was to be extracted. Each investigated muscle presented different results when the classifier used linear, radial and polynomial kernel functions. Even though we have focused on Hansen’s disease, the method applied here can be used to study facial electromyography in other pathologies.

Krein's strings whose spectral functions are of polynomial growth

In case Krein's strings with spectral functions of polynomial growth a necessary and su fficient condition for the Krein's correspondence to be continuous is given.

Genetic parameters for growth traits in pigs estimated using third degree polynomial functions

Selostus: Sian kasvuominaisuuksien perinnölliset tunnusluvut arvioituna kolmannen asteen polynomifunktion avulla

Neurofuzzy network model construction using Bézier-Bernstein polynomial functions

Neurofuzzy modelling systems combine fuzzy logic with quantitative artificial neural networks via a concept of fuzzification by using a fuzzy membership function usually based on B-splines and algebraic operators for inference, etc. The paper introduces a neurofuzzy model construction algorithm using Bezier-Bernstein polynomial functions as basis functions. The new network maintains most of the properties of the B-spline expansion based neurofuzzy system, such as the non-negativity of the basis functions, and unity of support but with the additional advantages of structural parsimony and Delaunay input space partitioning, avoiding the inherent computational problems of lattice networks. This new modelling network is based on the idea that an input vector can be mapped into barycentric co-ordinates with respect to a set of predetermined knots as vertices of a polygon (a set of tiled Delaunay triangles) over the input space. The network is expressed as the Bezier-Bernstein polynomial function of barycentric co-ordinates of the input vector. An inverse de Casteljau procedure using backpropagation is developed to obtain the input vector's barycentric co-ordinates that form the basis functions. Extension of the Bezier-Bernstein neurofuzzy algorithm to n-dimensional inputs is discussed followed by numerical examples to demonstrate the effectiveness of this new data based modelling approach.

Generalized neurofuzzy network modeling algorithms using Bezier-Bernstein polynomial functions and additive decomposition

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bezier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bezier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bezier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bezier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.

Direct Computation of Operational Matrices for Polynomial Bases

Several numerical methods for boundary value problems use integral and differential operational matrices, expressed in polynomial bases in a Hilbert space of functions. This work presents a sequence of matrix operations allowing a direct computation of operational matrices for polynomial bases, orthogonal or not, starting with any previously known reference matrix. Furthermore, it shows how to obtain the reference matrix for a chosen polynomial base. The results presented here can be applied not only for integration and differentiation, but also for any linear operation.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact-impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact-impact. The smoothed signed distance functions are constructed by a moving least-squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright (C) 2002 John Wiley Sons, Ltd.

Classification of some penalty methods

Optimization problems arise in science, engineering, economy, etc. and we need to find the best solutions for each reality. The methods used to solve these problems depend on several factors, including the amount and type of accessible information, the available algorithms for solving them, and, obviously, the intrinsic characteristics of the problem. There are many kinds of optimization problems and, consequently, many kinds of methods to solve them. When the involved functions are nonlinear and their derivatives are not known or are very difficult to calculate, these methods are more rare. These kinds of functions are frequently called black box functions. To solve such problems without constraints (unconstrained optimization), we can use direct search methods. These methods do not require any derivatives or approximations of them. But when the problem has constraints (nonlinear programming problems) and, additionally, the constraint functions are black box functions, it is much more difficult to find the most appropriate method. Penalty methods can then be used. They transform the original problem into a sequence of other problems, derived from the initial, all without constraints. Then this sequence of problems (without constraints) can be solved using the methods available for unconstrained optimization. In this chapter, we present a classification of some of the existing penalty methods and describe some of their assumptions and limitations. These methods allow the solving of optimization problems with continuous, discrete, and mixing constraints, without requiring continuity, differentiability, or convexity. Thus, penalty methods can be used as the first step in the resolution of constrained problems, by means of methods that typically are used by unconstrained problems. We also discuss a new class of penalty methods for nonlinear optimization, which adjust the penalty parameter dynamically.

Penalty fuzzy function for derivative-free optimization

Penalty and Barrier methods are normally used to solve Nonlinear Optimization Problems constrained problems. The problems appear in areas such as engineering and are often characterised by the fact that involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. This means that optimization methods based on derivatives cannot net used. A Java based API was implemented, including only derivative-free optimizationmethods, to solve both constrained and unconstrained problems, which includes Penalty and Barriers methods. In this work a new penalty function, based on Fuzzy Logic, is presented. This function imposes a progressive penalization to solutions that violate the constraints. This means that the function imposes a low penalization when the violation of the constraints is low and a heavy penalisation when the violation is high. The value of the penalization is not known in beforehand, it is the outcome of a fuzzy inference engine. Numerical results comparing the proposed function with two of the classic penalty/barrier functions are presented. Regarding the presented results one can conclude that the prosed penalty function besides being very robust also exhibits a very good performance.

Direct-search penalty/barrier methods

In Nonlinear Optimization Penalty and Barrier Methods are normally used to solve Constrained Problems. There are several Penalty/Barrier Methods and they are used in several areas from Engineering to Economy, through Biology, Chemistry, Physics among others. In these areas it often appears Optimization Problems in which the involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. In this work some Penalty/Barrier functions are tested and compared, using in the internal process, Derivative-free, namely Direct Search, methods. This work is a part of a bigger project involving the development of an Application Programming Interface, that implements several Optimization Methods, to be used in applications that need to solve constrained and/or unconstrained Nonlinear Optimization Problems. Besides the use of it in applied mathematics research it is also to be used in engineering software packages.