Optimisation of mine winder: state-constrained minimum-energy problem

In the application of modern control theory to mining processes, the optimal control of winding engines has recently been investigated. This letter sets the problem in a general context, and derives the optimal minimum-energy controller when the system is subject to hard state constraints on the midshaft speed.     

A generalized eigensystem approach to the inverse problem ofelectrocardiography

The authors develop a new approach to the ill-conditioned inverse problem of electrocardiography which employs finite element techniques to generate a truncated eigenvector expansion to stabilize the inversion. Ordinary three-dimensional isoparametric finite elements are used to generate the conductivity matrix for the body. The authors introduce a related eigenproblem, for which a special two-dimensional isoparametric area matrix is used, and solve for the lowest eigenvalues and eigenvectors. The body surface potentials are expanded in terms, of the eigenvectors, and a least squares fit to the measured body surface potentials is used to determine the coefficients of the expansion. This expansion is then used directly to determine the potentials on the surface of the heart. The number of measurement points on the surface of the body can be less than the number of finite element nodes on the body surface, and the number of modes employed in the expansion can be adjusted to reduce errors due to noise     

A finite difference approach to the wire junction problem

An approach to treating the thin-wire junction geometry, which arises in the computer modeling of a great many electromagnetic radiation and scattering problems, is presented. The method is based upon a finite-difference type interpretation of the differential operator in the Pocklington form of the integro-differential equation representing the junction problem. An important advantage of the method is that it is capable of producing accurate results even with relatively simple basis and testing functions, e.g., pulse anddelta-functions. Furthermore, the method does not require the imposition of additional constraints, such as the Kirchhoff current law or the conservation of charge, at the junction points. The method is versatile in that it applies to L-shaped structures as well as to junctions of thin wires of dissimilar radii. Numerical results based on the present finite difference approach have been computed and good agreement with results derived by other independent methods has been observed. An important conclusion of this work is that the conventional interpretation of the differential operator leads to erroneous results since the sampling interval in the conventional finite difference scheme is different from the correct value of the sampling interval found in this paper.     

A probabilistic approach to the single-point, single-dose problem

A general probabilistic approach is applied to the single-point, single-dose method for estimating individual infusion rates and serum drug concentrations. By using transformations of probability density functions, the effects of variations in the elimination rate constant upon pharmacokinetic variables may be studied and optimal sampling times may be chosen. Although this study treats the case of error-free sampling in a single-compartment model with a normal distribution of rate constants, the methods presented can be extended to more general situations.     

A neural network approach to MVDR beamforming problem

A Hopfield-type neural network approach which leads to an analog circuit for implementing the real-time adaptive antenna array is presented. An optimal array pattern can be steered by updating the weights across the array in order to maximize the output signal-to-noise ratio (SNR). The problem of adjusting the array weights can be characterized as a constrained quadratic nonlinear programming. The adjustment of settings is required to respond to a rapid time-varying environment. A Hopfield-type neural net with a number of graded-response neurons designed to perform the constrained quadratic nonlinear programming would lead to a solution in a time determined by RC time constants, not by algorithmic time complexity. The constrained quadratic programming neural net has associated it with an energy function which the net always seeks to minimize. A fourth-order Runge-Kutta simulation shows that the circuit operates at a much higher speed than conventional techniques and the computation time of solving a linear array of 10 elements is about 0.1 ns for RC=5×10 ^-9     

A simple approach to the problem of in-circuit resistance measurement

This letter proposes a simplification to the circuit presented by M. Rehman et al. in "A Self-Balancing Bridge for In-Circuit Resistance Measurement" published in the November 1985 issue of the PROCEEDINGS.     

A new approach to the thin scatterer problem using the hybrid equations

A new set of integral equations for electromagnetic scattering problems, the "hybrid" equations, is presented. The advantages of these equations for thin perfect conductors are discussed in comparison to the magnetic and electric field integral equations. Specific comparisons are made with the solution of the electric field integral equation for a finite hollow cylinder. It is demonstrated that the primary advantage of these equations is obtained by minimizing the coupling between component equations for the two surface currents.     

Frequency-domain approach to model-reduction problem

Model reduction is performed in the frequency domain by matching the first Taylor-series-expansion coefficients of the square magnitude of the original and the approximating transfer functions at suitable frequencies. The method is computationally simple and may lead to a satisfactory approximation while preserving stability and minimum-phase characteristics.     

A genetic algorithm approach to a general category projectscheduling problem

A genetic algorithm (GA) approach is proposed for the general resource-constrained project scheduling model, in which activities may be executed in more than one operating mode, and renewable as well as nonrenewable resource constraints exist. Each activity's operation mode has a different duration and requires different amounts of renewable and nonrenewable resources. The objective is the minimization of the project duration or makespan. The problem under consideration is known to be one of the most difficult scheduling problems, and it is hard to find a feasible solution for such a problem, let alone the optimal one. The GA approach described in this paper incorporates problem-specific scheduling knowledge by an indirect chromosome encoding that consists of selected activity operating modes and an ordered set of scheduling rules. The scheduling rules in the chromosome are used in an iterative scheduling algorithm that constructs the schedule resulting from the chromosome. The proposed GA is denoted a hybrid GA (HGA) approach, since it is integrated with traditional scheduling tools and expertise specifically developed for the general resource-constrained project scheduling problem. The results demonstrate that HGA approach produces near-optimal solutions within a reasonable amount of computation time     

An analytical approach to the dynamic topology problem

Currently, it is possible to modify (say, hourly) the topology of a data communications network by adding or deleting network links and/or by increasing or decreasing bandwidth on existing links in response to changing traffic loads and/or projected network conditions. The intent of this paper is to study a Markov decision process (MDP) model of the dynamic topology problem (DTP), the problem of activating and/or deleting links, as a function of the current traffic in the network and of the most recent network topology design. We present a decomposition of this model and structural results for the decomposition. The decomposition and structural results enhance the tractability of procedures for determining optimal link control policies. A numerical example is used to illustrate these results.Research supported by ARO Contract No. DAAG-29-85-K0089, NSF Grant No. ECS-8708183, and DCA Contract No. DCA 100-89-C-0031.     

An analytical approach to the partial scan problem

The scan design is the most widely used technique used to ensure the testability of sequential circuits. In this article it is shown that testability is still guaranteed, even if only a small part of the flipflops is integrated into a scan path. An algorithm is presented for selecting a minimal number of flipflops, which must be directly accessible. The direct accessibility ensures that, for each fault, the necessary test sequence is bounded linearly in the circuit size. Since the underlying problem is NP-complete, efficient heuristics are implemented to compute suboptimal solutions. Moreover, a new algorithm is presented to map a sequential circuit into a minimal combinational one, such that test pattern generation for both circuit representations is equivalent and the fast combinational ATPG methods can be applied. For all benchmark circuits investigated, this approach results in a significant reduction of the hardware overhead, and additionally a complete fault coverage is still obtained. Amazingly the overall test application time decreases in comparison with a complete scan path, since the width of the shifted patterns is shorter, and the number of patterns increase only to a small extent.     

A neural network approach to the traffic control problem in reverse baseline networks

A neural network for the traffic control problem applied to reverse baseline networks has been proposed in this paper. This problem has been first represented by an energy function. A neural network is applied for maximizing the energy of the function under the constraints of the reverse baseline network. The number of iteration steps in our neural network is limited by a performed upper bound O(n), wheren is the size of ann ×n network. The throughputs of our neural network have been shown by the empirical results to be better than the conventional algorithm (modified Bipartite Matching Algorithm) when the packet densities rise higher than 50%.     

A novel approach to the 2-D blind deconvolution problem in medical ultrasound

The finite frequency bandwidth of ultrasound transducers and the nonnegligible width of transmitted acoustic beams are the most significant factors that limit the resolution of medical ultrasound imaging. Consequently, in order to recover diagnostically important image details, obscured due to the resolution limitations, an image restoration procedure should be applied. The present study addresses the problem of ultrasound image restoration by means of the blind-deconvolution techniques. Given an acquired ultrasound image, algorithms of this kind perform either concurrent or successive estimation of the point-spread function (PSF) of the imaging system and the original image. In this paper, a blind-deconvolution algorithm is proposed, in which the PSF is recovered as a preliminary stage of the restoration problem. As the accuracy of this estimation affects all the following stages of the image restoration, it is considered as the most fundamental and important problem. The contribution of the present study is twofold. First, it introduces a novel approach to the problem of estimating the PSF, which is based on a generalization of several fundamental concepts of the homomorphic deconvolution. It is shown that a useful estimate of the spectrum of the PSF can be obtained by applying a proper smoothing operator to both log-magnitude and phase of the spectra of acquired radio-frequency (RF) images. It is demonstrated that the proposed approach performs considerably better than the existing homomorphic (cepstrum-based) deconvolution methods. Second, the study shows that given a reliable estimate of the PSF, it is possible to deconvolve it out of the RF-image and obtain an estimate of the true tissue reflectivity function, which is relatively independent of the properties of the imaging system. The deconvolution was performed using the maximum a-posteriori (MAP) estimation framework for a number of statistical priors assumed for the reflectivity function. It is shown in a series of in vivo experiments that reconstructions based on the priors, which tend to emphasize the "sparseness" of the tissue structure, result in solutions of higher resolution and contrast.     

DPA: a deterministic approach to the MAP problem

Deterministic pseudo-annealing (DPA) is a new deterministic optimization method for finding the maximum a posteriori (MAP) labeling in a Markov random field, in which the probability of a tentative labeling is extended to a merit function on continuous labelings. This function is made convex by changing its definition domain. This unambiguous maximization problem is solved, and the solution is followed down to the original domain, yielding a good, if suboptimal, solution to the original labeling assignment problem. The performance of DPA is analyzed on randomly weighted graphs.     

A new approach to the general minimum distance decoding problem: The zero-neighbors algorithm

Minimum distance decoding (MDD) for a general error-correcting linear code is a hard computational problem that recently has been shown to beNP-hard. The complexity of known decoding algorithms is determined bymin (2^{k},2^{n-k}), wherenis the code length andkis the number of information digits. Two new algorithms are suggested that reduce substantially the complexity of MDD. The algorithms use a new concept of zero neighbors--a special set of codewords. Only these codewords (which can be computed in advance) should be stored and used in the decoding procedure. The number of zero neighbors is shown to be very small compared withmin (2^{k},2^{n-k})forn gg 1and a wide range of code ratesR = k/n. For example, forR approx 0.5this number grows approximately as a square root of the number of codewords.     

A new approach to the problem of wave fluctuations in localized smoothly varying turbulence

In the past, smoothly varying turbulence has been studied by changing the structure constant to the functionC_{n}^{2}(bar{r}). The purpose of this paper is to show that this approach is insufficient, and that a random process developed by Silverman can be used to describe the wave fluctuations in localized smoothly varying turbulence. The localized turbulence is characterized by a correlation function which is a product of a function of the average coordinate and a function of the difference coordinate. The corresponding spectrum is also given by a product of a function of the difference wavenumber and a function of the average wavenumber. They are related to each other through two Fourier transform pairs. Making use of the preceding representations, the fluctuations of a wave propagating through such a turbulence can be given either by the integrals with respect to the two wavenumbers or by a convolution integral of the structure constantC_{n}^{2}(bar{r}) and a function involving the outer scale of the turbulenceL_{0}. It is shown that for a plane wave case, if the distanceLis within (L_{0}^{2}/lambda), then the usual formula given by Tatarski is valid. But if the distance is betweenL_{0}^{2}/lambdaand(bL_{0})/lambdawherebis the total transverse size of the turbulence, the variance of the wave is nearly constant, and ifL gg (bL_{0})/lambda, the variance decays asL^{-2}. Similar conclusions are shown for a spherical wave case. Some examples are shown illustrating the effectiveness of this method.     

A new approach to the electromagnetic diffraction problem of a perfectly conducting half-plane screen

It is well known that the magnetic vector potential of an electromagnetic (EM) field incident upon a perfectly conducting thin plate satisfies, on the plate, an inhomogeneous Helmholtz equation. Rahmat-Samii, Mittra et al., and also Wilton and Dunaway applied this fact to the numerical solution of the thin-plate EM diffraction problem, using a modified version of the electric field integral equation. They pointed out that the Helmholtz equation alone determines the vector potential on the plate only up to an unknown term which expresses the coupling of the current-density components, which is due to the influence of the edge of the plate. It is demonstrated that their method is applicable in the theoretical analysis of some EM plate diffraction problems as well. The method will be applied, in combination with the Wiener-Hopf method, to reproduce the well-known solution of the classical problem of diffraction of plane electromagnetic waves by perfectly conducting half-plane screens. This approach can be done directly in vector form for general, three-dimensional incident waves. The result is applied to the discussion of grazing incidence.     

New modeling approach to the frequency assignment problem in broadcasting

This paper presents an original algorithm that uses a new modeling approach of the interference constraints and uses a probabilistic taboo search algorithm to solve the frequency assignment problem in the field of broadcasting. The results obtained by our algorithm are compared to the operating solutions in the field of FM broadcasting in France and the best known results obtained by hybrid genetic algorithm (Idoumghar et al. 2002) that uses a classical modeling of the interference constraints. By analyzing the results obtained by our approach we can observe that we efficiently enhance the quality of the solutions.     

Rendezvous point based approach to the multi-constrained multicast routing problem

The Quality of Service (QoS) routing requires a special approach to graph algorithms modeling. One of the mathematical concepts that reflects this class of problems is the multi-constrained minimum Steiner tree problem (MCMST). In this article, the RDP (named after the concept of the RenDezvouz Point), a novel algorithm for solving the MCMST problem is presented.