Proposed Approximation Technique Research Articles

Linear Phase Two-Dimensional FIR Digital Filter Functions Generated by applying Christoffel-Darboux Formula for Orthonormal Polynomials

Global Christoffel-Darboux formula for four orthonormal polynomials on two equal finite segments for generating linear phase two-dimensional finite impulse response (FIR) digital filter functions in a compact explicit representative form is proposed in this paper. The formula can be most directly applied for solving mathematically the approximation problem of a filter function of even and odd order. An example of a new class extremely economic linear phase two-dimensional FIR digital filter without multipliers obtained by the proposed approximation technique is presented. The generated linear phase two-dimensional FIR filter functions have two symmetries, that is, the following relations are valid: H(z1,z2)=H(z2,z1) and H(z1,z2)=H(-z1,-z2) and . Ill. 3, bibl. 15 (in English; abstracts in English and Lithuanian).DOI: http://dx.doi.org/10.5755/j01.eee.120.4.1449

Application of Passive Techniques for Three Dimensional Cameras

Depth estimation is an active area of research for 3-dimensional (3D) shape recovery. In this paper, we present a passive depth estimation method. Since the 3-dimensional (3D) cameras currently available are quite expensive, we propose the passive method as a means to decrease the high cost associated with 3D cameras. Our algorithm is based on the fuzzy-neuro approach. A fuzzy inference system (FIS) is designed and trained using the neural network for the calculation of the depth map. The proposed approximation technique yields good results when it is tested with several 3D objects.

A multi-objective lead time control problem in multistage assembly systems using an interactive method

In this paper, we develop a multi-objective model to optimally control the lead time of a multistage assembly system, using an interactive method. The multistage assembly system is modelled as an open queueing network, whose service stations represent manufacturing or assembly operations. It is assumed that the product order arrives according to a Poisson process. In each service station, there is either one or infinite number of servers (machines) with exponentially distributed processing time, in which the service rate (capacity) is controllable. The transport times between the service stations are independent random variables with generalized Erlang distributions. The problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. The objective functions are the total operating costs of the system per period (to be minimized), the average lead time (min), the variance of the lead time (min) and the probability that the manufacturing lead time does not exceed a certain threshold (max). Finally, the STEM method is used to solve a discrete-time approximation of the original problem. We also investigate the trade-off between the accuracy (correctness) and the computational time of the proposed approximation technique.

First-order estimation of stochastic parameters of a sediment transport model

First-order approximation techniques for estimating stochastic parameters of a sediment transport model are presented. The non-homogeneous compound Poisson model of Shen-Todorovic eliminating certain idealized assumptions to describe the movement of sediment in natural streams is a revision of the earlier homogeneous model of Einstein-Hubbell-Sayre. However, the complexity of the non-homogeneous model and the difficulty in determining the model parameters has limited its application. The proposed approximation techniques employ the first-order Taylor expansions, with respect to a selected temporal or spatial point by a finite difference, of the cumulative probability distribution function (CDF) of particle displacements. The first-order expansions are divided by the original CDF for further simplification. The simplified forward- and backwardexpansions are numerically solved as a system to evaluate the parameter at the specified point. The non-homogeneous parameters are pursued with successive applications of this procedure to various points. An example of sediment infiltration into the gravel column is provided showing the procedures of parameter estimation and the verification of results. Temporal and spatial variations of the parameters are also discussed.

Approximate similarity retrieval with M-trees

Motivated by the urgent need to improve the efficiency of similarity queries, approximate similarity retrieval is investigated in the environment of a metric tree index called the M-tree. Three different approximation techniques are proposed, which show how to forsake query precision for improved performance. Measures are defined that can quantify the improvements in performance efficiency and the quality of approximations. The proposed approximation techniques are then tested on various synthetic and real-life files. The evidence obtained from the experiments confirms our hypothesis that a high-quality approximated similarity search can be performed at a much lower cost than that needed to obtain the exact results. The proposed approximation techniques are scalable and appear to be independent of the metric used. Extensions of these techniques to the environments of other similarity search indexes are also discussed.

An efficient method for approximating submesh reliability of two dimensional-meshes

An analytical model for submesh reliability of mesh-connected systems is proposed in this paper. A mesh is considered operational as long as a functional submesh of the required size is available. We use the principle of inclusion and exclusion to find the exact probability of having a functional submesh within a partition of the mesh. The partitions are taken along either dimension of the mesh. The partitions along the rows are called row partitions (RPs) and along the columns are called column partitions (CPs). The reliability of a partition is then used to approximate the submesh reliability of the system and, thus, this model is called partitioned mesh (PM) model. Instead of using a computationally intensive recursive algorithm as done in the previous work, a closed form approximation of the submesh reliability is derived in this paper. The PM model is validated through simulation and compared with the earlier proposed approximation techniques. It is shown that the PM model provides better approximations for submesh reliability with constant computational complexity.

On methods for bounding the overall properties of periodic piezoelectric fibrous composites

The homogenization problem of linearly piezoelectric fibrous composites with a periodic microstructure is formulated by adopting the free- and complementary-energy minimum principles, as well as the Hashin Shtrikman principles. The auxiliary electroelastic problems involved in the Hashin-Shtrikman principles are solved by a transformation from the space domain to the Fourier domain. Approximations of those variational principles, suitable for numerical computations, are built up by adopting the Fourier-series method and the finite-element method. In this way, rigorous upper and lower bounds on the overall material moduli are obtained. An example is presented, in order to show the effectiveness of the proposed approximation techniques and to compare them.

Optimization of mechanical systems: On strategy of non‐linear first‐order approximation

AbstractThe paper presents an extended approach to non‐linear first‐order approximation of non‐linear programming problems and it explains how to transform an approximate problem into a strictly convex one. The essence of the proposed approximation technique is to rewrite each given function hj as a composite gj o Ψj. The function Ψj has to be chosen—the paper explains how to do this—while gj is linear approximated with gj. The approximation of hj is then obtained as gj o Ψj.This approach enables one to obtain approximate functions with variable conservativeness, which implies an adjustable approximate problem. A solution procedure, which replaces the original problem with a sequence of approximate problems, can therefore adjust each succeeding approximate problem to improve the convergence properties.The theory is illustrated with a three parameters controlled approximation. This technique represents, together with an optimality criteria based solution procedure, a powerful and economic tool for solving nonlinear programming problems. The three parameters, which influence to a great extent the conservativeness of the approximate functions, are under full control of the optimizer. They are varied automatically during the process of optimization to speed‐up the convergence or to prevent oscillations.The benefits gained from the proposed approach are demonstrated on several numerical examples involving structures and a dynamic multibody system.

On approximation of low-pass type band-limited waves by interpolation

An approximation method is proposed for a class of band-limited waveforms whose Fourier spectra F(ω) are confined in the interval -ω1 ≦ ω ≦ ω1. The side lobes of such waveforms are also small in the range of 0 < ω0 < ∥ω∥ < ω1. First, the approximation waveform is obtained from summation of the product of an interpolating function and the sampling value f(tk) at the sampling point tk (k = 0 ∼ K). One objective of the proposed method is to find an interpolating function that will minimize the envelope of a family of approximation waveforms, which is used as a measure of error associated with the approximation. The optimum interpolating function, also satisfies the condition of discrete orthogonality. The proposed approximation technique also piovides convergence to the actual waveform with respect to a set of sampling points determined by the conventional sampling theorem. The approximation error is evaluated and weighted in the frequency domain using Fourier series expansion. The lower and upper bounds of approximation error in the frequency domain are derived and their relationships to the original waveform are established.