A non-iterative shooting method for a non-linear diffusion problem using automatic differentiation

We present a non-iterative shooting method for the solution of a non-linear two-point boundary value problem that models the steady-state temperature distribution in a cylinder of unit radius. By non-iterative it is meant that there is no need to solve one or more initial value problems repeatedly. The method of this article avoids the need for such repetition by numerically obtaining a single algebraic non-linear equation involving only the initial condition. Thus, the appropriate initial condition for the final solution is available just after one solution of the initial value problem corresponding to an arbitrary initial value. In addition, the solution of the initial value problem is obtained as a Taylor series expansion of arbitrary order, using a technique known as automatic differentiation, which is the process of obtaining the coefficients in the Taylor series expansion using recursive formulas. Thus, the method does not face the need to deal with step size issues or the need to carry out lengthy algebraic manipulations. The method successfully reproduces the solutions obtained previously by other researchers.     

Micromechanics-based progressive failure analysis of fibre-reinforced composites with non-iterative element-failure method

This paper proposes a micromechanics-based progressive failure analysis strategy for fibre-reinforced composites. A non-iterative element-failure method (NEFM) is developed and integrated with a micromechanics-based failure criterion. The micromechanics of failure (MMF) is further investigated and modified to improve predictions. The NEFM is focused on implementation of damaged elements with direct solution and implicit nodal forces. Progressive failure of fibre-reinforced laminates is analysed with the micromechanics-based NEFM and the results are compared with those from the traditional finite element method or experiments. The comparison demonstrates computational efficiency and validity of the micromechanics-based NEFM in progressive failure analysis of composites.     

Choosing a track association method

This paper examines the problem of selecting a track association method. This is the first stage of the track fusion process and the performance of such a method is essential to the overall success of this process. It is shown that more issues must be considered than just examining the probability of correct association when judging the performance of an association technique. A method that provides a high probability of correct association may well have poor performance in other areas. This paper examines several additional features that should be considered as they also have a significant effect on the quality of the combined tracks that are the final outcome of the fusion process. The problem is illustrated by examining several track-to-track association techniques for the problem of correlating radar tracks with electronic support measures (ESM) tracks for airborne sensors.     

Construction of a parallel computational model by composition of computational facilities

We consider a general algorithm for constructing a parallel numerical model by composition of several computational objects. The only requirement for the applicability of the proposed algorithm is for the disturbance propagation speed to be finite. We present one possible approach to map a numerical model onto an object-oriented program model. Some results of numerical experiments on solving the heat conduction equation in linear and nonlinear cases are discussed.     

On One method for constructing a family of approximations of zeta constants by rational fractions

We present a new method for fast approximation of zeta constants, i.e., values ζ(n) of the Riemann zeta function, n ≥ 2, n is an integer, by rational fractions. The method makes it possible to fast approximate zeta constants and certain combinations of successive values of zeta constants by rational fractions. By choosing values of coefficients involved in the combinations, one can control the convergence rate of the approximations and the computation complexity for the zeta constants.     

A computational method for the solution of time-optimal control problems by Newton's method

In this paper we apply Newton's method for the solution of time-optimal control problems. The free-terminal time problem is converted into a fixed-terminal time problem, and the inequality constraints on the control variables are suitably approximated. It is an integral part of the algorithm to determine the minimum time. Several algorithms are proposed. Two examples are given to illustrate the method.     

Picture fuzzy clustering: a new computational intelligence method

Fuzzy clustering especially fuzzy \(C\)-means (FCM) is considered as a useful tool in the processes of pattern recognition and knowledge discovery from a database; thus being applied to various crucial, socioeconomic applications. Nevertheless, the clustering quality of FCM is not high since this algorithm is deployed on the basis of the traditional fuzzy sets, which have some limitations in the membership representation, the determination of hesitancy and the vagueness of prototype parameters. Various improvement versions of FCM on some extensions of the traditional fuzzy sets have been proposed to tackle with those limitations. In this paper, we consider another improvement of FCM on the picture fuzzy sets, which is a generalization of the traditional fuzzy sets and the intuitionistic fuzzy sets, and present a novel picture fuzzy clustering algorithm, the so-called FC-PFS. A numerical example on the IRIS dataset is conducted to illustrate the activities of the proposed algorithm. The experimental results on various benchmark datasets of UCI Machine Learning Repository under different scenarios of parameters of the algorithm reveal that FC-PFS has better clustering quality than some relevant clustering algorithms such as FCM, IFCM, KFCM and KIFCM.     

Stability preservation and computational aspects of a newlyproposed reduction method

The stability of the reduced-order models obtained using the method suggested by A. Lepschy et al. (Syst. Contr. Lett., vol.8, pp.405-10, May 1987) is analyzed. The relation between this method and the Routh approximation is pointed out. Some interesting properties related to the construction of the reduced-order transfer functions and to the evaluation of certain quadratic integrals are derived. An examples shows the practicality of the procedures     

Determination of a vocal source by the spectral ratio method

The inverse problem with respect to functions proportional to a voice source and volume velocity of the air flow through the glottis is solved as follows: we compute the inverse Fourier transform of the regularized fraction of short-term speech-signal spectra at intervals with an opened (closed) glottis, minimizing the optimality criterion with respect to the regularization parameter and the glottis opening (closing) time. The optimality criterion for solutions includes the values of the volume velocity and its time derivative at the ends of the interval with an opened glottis and the total value of the negative volume velocity. To obtain an empirical error estimate for the solution, experiments using synthesized signals with various parameters, direct measurements of the glottis, and signals synchronously recorded through pairs of microphones of different types are performed. The most probable determination error for the volume velocity is less than 5% for synthetic sources; if the area of the glottis of the source is measured experimentally, then the said error is about 10%. The discrepancy of solutions for the same signal synchronously recorded through a pair of microphones of different types is less than 10%.     

On one method for fast approximation of zeta constants by rational fractions

We present a new method for deriving both known and new fast approximations of zeta constants ζ(n), n ≥ 2, n is an integer, by rational fractions.     

Convergence analysis of a computational method for time-lag optimal control problems

We consider a class of non-linear time-lag optimal control problems. The class of admissible controls are taken to be the class of piecewise smooth functions. A control parameterization technique is used to approximate the optimal control problem by a sequence of optimal parameter selection problems. The solution of each of these approximate problems gives rise to a sub-optimal solution to the true optimal control problem in an obvious way. The error bound is derived for the sub-optimal costs and the true optimal cost.     

Design optimization for a compliant mechanism based on computational intelligence method

Neural Computing and Applications - Modeling and optimization for compliant mechanisms are challenging tasks thanks to an unclear kinematic merging among rigid and flexible links. Hence, this paper...     

Determination of vibration characteristics of multiple-load-path blades by a modified Galerkin's method

A modified Galerkin's method is developed to determine the natural vibration characteristics of multiple-load-path rotor blades. The development follows parallel to the CAMRAD program procedure for a single load-path-blade. Two types of finite series expansion functions are utilized: exact transcendental solutions to nonrotating uniform beam problems, and polynomial functions. A computer program based on this method is developed to determine the free vibration characteristics of multiple-load-path blades undergoing coupled flapwise bending, chordwise bending, twisting and extensional motions. Numerical results are obtained for two rotors. The first has constant properties along the span and the second is modelled from a nonuniform experimental rotor with discontinuous properties. Natural frequencies compare well with those predicted using a finite element approach, and with the experimental results for the second rotor.     

A computational intelligence method for solving a class of portfolio optimization problems

In this paper, we revisit the mean-variance model of Markowitz and the construction of the risk-return efficient frontier. A few other models, such as the mean absolute deviation, the minimax and maximin, and models with diagonal quadratic form as objectives, which use alternative metrics for risk are also introduced. Then we present a neurodynamic model for solving these kinds of problems. By employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original problem. The validity and transient behavior of the neural network are demonstrated by using several examples of portfolio selection.     

Determination of space imagery contrast by a multi-spectral optimized method with AVHRR

Abstract

Satellite data from the Arctic present extensive shaded zones arising from the combination of low Sun elevation and mountainous topography. Field radiometry measurements from training zones on two glaciers in Arctic north-west Svalbard discriminate the different surface states of the glaciers. The SPOT reflectance values have been corrected using the slope orientation and dip parameters from the digital terrain model combined with the corresponding Sun elevation and azimuth. The reflectances of the shaded and illuminated zones have been restored to a new image based on the XS3 versus XS1 bimensional histogram. The pixel values of the new image can distinguish between firn and superimposed ice surface states on the glaciers defined and controlled by field measurements. From the new image a map of the different surface states of the glacier can be produced which is homogeneous in both the shaded and illuminated zones. The boundary between the firn and the superimposed ice can be located on the median and longitudinal profile of the glacier by combining the new image and the digital terrain model. With this method it is possible to locate the boundary between the firn and the superimposed ice and, consequently, the equilibrium line to within 40 m of altitude.     

Convergence analysis of a computational method for optimal control of non-linear differential-algebraic systems

The convergence analysis of a computational method for optimal control problems of non-linear differential-algebraic systems is considered. The class of admissible controls is taken to be the class of piecewise smooth functions. A control parametrizution technique is used to approximate the optimal control problem into a sequence of optimal parameter selection problems. The solution of each of these approximate problems gives rise to a suboptimal solution to the original optimal control problem in an obvious way. The gradients of the cost functional with respect to parameters are derived. Furthermore, the error bounds between the suboptimal costs and the true optimal cost are derived.     

Modeling uncertainties in sodium spatial dispersion using a computational intelligence-based kriging method

Classical and geostatistical methods have been used to create continuous surfaces from sampled data. A common geostatistical method is kriging, which provides an accurate estimation based on the existing spatial structure of sample points. However, kriging is sensitive to errors in the input data, the dispersion of the sample points, and the fit of the model to the variogram. The purpose of this research is to develop a new method to address the uncertainties resulting from the input data and choice of model in the kriging method. In our approach, the existing uncertainties in the input data are modeled by fuzzy computations, and the variogram variables are optimized by a genetic algorithm. To test this new hybrid method, sodium contamination values in the Zanjan aquifer were used. The results show a general improvement in accuracy compared with the ordinary kriging method. Consideration of all equations and values in fuzzy computations highlights the complexity of the computation. Herein, the integration problems experienced by other researchers when trying to use fuzzy kriging are resolved.     

Determination of macroscopic thermodynamic ionization constants under conditions of variable ionic strength by an optimization algorithm

The thermodynamic macroscopic ionization constants of cysteine, penicillamine, 6-amino penicillanic acid and 7-amino cephalosporanic acid were determined at different temperatures by a dynamic method employing potentiometric data obtained at ionic strengths that vary continuously throughout the titration. This method gives thermodynamic pK-values in a single experiment. A computer program has been developed for the titrations. It makes use of an algorithm based on controlled descent.     

Least square method for the calculation of elastic constants

In this paper, a feasible formula is derived and simplified from least square method to calculate the elastic constants of materials. The simplified equation is identical to the stress and strain fluctuation formula obtained from statistical thermodynamics when the expression of the stress is redefined. It endues the formula with the theoretical validity. On the other hand, the convergence of the formula could be investigated via the theory of numerical analysis. Compared to the traditional fluctuation formula, the new technique shows better universality in the elastic bath method. Results obtained with a nearest-neighbor Lennard-Jones fcc crystal indicate that at low temperature the convergence of the formula is the same as the previous stress and strain fluctuation formula but the symmetry of the elastic constants is improved.