A comparative analysis of evaluation methods for amplitude—phase distribution of weak signals with a spread-spectrum

Methods for processing signals with a spread-spectrum in multielement antenna arrays are considered. A singular decomposition method for evaluating the amplitude-phase distribution of the field at array elements is designed. The comparative analysis of the proposed method and the coherent averaging method is given. The possibility of detecting weak signals with a spread-spectrum is considered in the framework of the proposed approach. A numerical experiment is performed for comparatively analyzing the methods. The advantages and prospects of the proposed approach are uncovered.     

Boundedness conditions for relative error in fast simulation of reliability of non-Markovian systems

A general model is considered that describes the functioning of non-Markovian systems. A new method is proposed for fast simulation of failure probability. The method allows obtaining estimates with a bounded relative error under some weak conditions. This method is used to evaluate the reliability of a specific class of systems. Numerical examples are considered. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 63–80, July–August 2006.     

Robust/H∞ filtering for nonlinear systems

A robust (or H_∞) approach to filtering for nonlinear systems is considered. A bound on the estimate error as a function of the disturbance energy is obtained. The corresponding dynamic programming equation is a first-order PDE. This has computational ramifications. The case where the measurements are discrete time is considered also. A numerical method is discussed.     

Synthesis of decoupling laws for attitude stabilization of a spacecraft

The problem of attitude stabilization of a spacecraft is considered. A method for solving the problem of accurate pole placement is proposed. The decoupling control laws for attitude stabilization of a spacecraft are synthesized using the proposed method.     

Robust/H∞ filtering for nonlinear systems

A robust (or H_∞) approach to filtering for nonlinear systems is considered. A bound on the estimate error as a function of the disturbance energy is obtained. The corresponding dynamic programming equation is a first-order PDE. This has computational ramifications. The case where the measurements are discrete time is considered also. A numerical method is discussed.     

Joint application of the incomplete Galerkin method and scattering matrix method for modeling multilayer diffraction gratings

A mathematical model of wave diffraction from a one-dimensional multilayer periodic grating is considered. A rigorous mathematical statement is given for the problem where partial radiation conditions are used for domain confinement. A complete formulation of the numerical algorithm based on a combination of the incomplete Galerkin method and the scattering-matrix method is presented. The algorithm’s convergence rate and computational complexity are analyzed and the optimal values of the computational parameters are recommended.     

Interactive garment design

A method for the design of garments at a workstation is proposed. An underlying body form analogous to a trade mannequin is first represented in the computer. Garment panels are considered to be surfaces of complex shape, whose fit with respect to body form may vary over the surface. A method of easy entry of data for representing panels is proposed, whereby fit around panel edges can be defined. The problems of controlling fit in the interior of panels is considered and a scheme is proposed which accomplishes design with economy of effort from the designer.     

Near Time-Optimal Control of Redundant Manipulators along a Specified Path with Jerks Constraint

A time-optimal control scheme for a general type of closed-chain manipulator is proposed. The considered manipulator is composed of multiple serial manipulators that are connected to each other and single manipulators may be kinematically redundant. Also, the limit on the actuator torques and actuator jerks are considered. The jerk constraints create a smooth trajectory for reducing strain on robot actuators and satisfy torque limitations of industrial actuators. Inclusion of the jerk constraints increases the traversal time, hence, a method is introduced to optimize this time. To this end, a simple method to find switching points is investigated.     

Fictitiousness analysis of states of a finite-state machine synthesized from its specification transformed from the language L* to the language L

A method for synthesizing an FSM from its specification in the logical language L* is considered. The method is based on translating such a specification into the less expressive language L and applying an available method for synthesizing the sought-for FSM from the specification in this language. The resulting FSM may contain redundant states that are called fictitious and must be eliminated. A simple method for checking states for fictitiousness is proposed.     

Derivation of operational matrices of differentiation for orthogonal polynomials

A direct method for deriving an operational matrix of differentiation for Legendre polynomials is presented. The general case is also considered. The presented formulas are formally proved. Results are compared with the other known method. The new method is accurate for all matrix dimensions, while the other method may fail for higher dimensions.     

Joint Matrix Universal Coding of Sequences of Independent Symbols

Coding divergences of probability distributions are introduced. A method of joint matrix universal coding for a set of sequences of independent symbols with different statistics is proposed and studied. Two methods of multialphabet matrix coding are considered. The method proposed is compared with the PPM algorithm, and ways for integrating them are discussed.     

Adaptive processing of a set of weak signals against a background of intense interference

Methods for processing weak signals in a complex interference situation are considered. A new class of adaptive methods of direction finding with supression of power interfering signals, which generalizes the Capon method and the thermal noise method, is proposed. The method of adaptive filtration of a set of signals is developed. The results of numerical modeling are given. The advantages and the prospects of the proposed approach are determined.     

Application of gradient-based optimization methods for a rotor system with static stress, natural frequency,and harmonic response constraints

This paper demonstrates the application of gradient-based optimization methods to the minimal weight design optimization of rotor systems. A nonlinear constrained optimization problem is considered. Design variables are inner radii and wall thicknesses of shaft sections. Constraints are imposed on torsional and equivalent stresses, natural frequencies, and unbalance response amplitudes. The sizing optimization problem is solved using a gradient projection method and a sequential quadratic programming technique. A typical turbine rotor system is considered. An in-house beam-based finite element method code is used for the prediction of static and dynamic characteristics of the rotor system. Analytical sensitivity analysis is performed for the static and harmonic equations using the adjoint method. Sensitivity coefficients for the natural frequencies are obtained directly from the quadratic eigenvalue problem. Results of several optimization runs with different constraint sets show a significant shaft weight reduction in comparison with the baseline configuration with all constraints being satisfied. The two optimization methods are compared and discussed in regard to their performance.     

Identification of Constant Parameters of Dynamic Systems by a Time-Frequency Method

A time-frequency method for identifying linear dynamic systems of a general form with constant parameters and delays in their observable variables is considered. The identification problem is found to be decomposable into the problem of estimating unknown parameters and the problem of estimating the initial conditions. Applying the time-frequency method to identify the differential equation of the Van der Pol oscillator, which is nonlinear by both its state and parameters, is considered. Examples are used to show that the time-frequency method solves the identification problem both for stable and unstable dynamic systems.     

A fourth-order-accurate direct and inverse cauchy integral solver

A numerical procedure is presented for solving Cauchy integrals with fourth-order accuracy. The method, based on Spline Collocation Polynomials, is shown to be superior, by far, to a second-order-accurate finite difference approach. The evaluation of the integral (direct problem) and of the integrand as well (inverse problem) is considered. Several approaches are considered and some unexpected results for the case of the inverse problem are pointed out.     

3D SLAM from stereoimages

A method of visual navigation by stereoimages for autonomous underwater vehicles is suggested. Two modifications of the method are considered. The first one is based on integration of measurement data of onboard navigation system with visual data. The second modification relies on the use of a six-cloud computation scheme. Results of computational experiments with model data are presented.     

Mathematical modelling of 2D electromagnetic scattering

The singular integral equation method is used for solving the problem of diffraction by infinite nonhomogeneous cylinder. A numerical method is developed, and certain aspects of its practical application are considered. Some numerical results are described.     

Decomposition Method for Solving Three-Index Transportation Problems

A decomposition method based on the sequential modification of the optimality criterion is used for solving the classical three-index transportation problem. The method consists of a sequence of solutions of local problems with three constraints. A monotonic (in the optimality criterion) process that converges to the solution of the original problem is constructed. The solutions of the transportation problem with a linear and quadratic objective function are considered and the numerical results are presented.     

An Inspection Policy for Deteriorating Processes Using Delay-Time Concept

A method for determining the discrete time points of inspection for a deteriorating single-unit system under condition-based maintenance is developed. The system is in a normal state, a symptom state or a failed state. A delay-time model is utilized to describe the transition of the states. The transition time from a normal state to a symptom state and that from a symptom state to a failed state are derived assuming continuous deteriorating processes based on a reaction rate model which is categorized as a failure physics model. Failed-dangerous and failed-safe probabilities of an imperfect inspection are considered. A method for minimizing the long-run average cost per unit time is formulated. The characteristics and sensitivity of the proposed method are investigated.     

Variational method for hexahedral grid generation with control metric

A variational method of generating spatial structured (or regular) grids composed of hexahedral cells is considered. In the method it is minimized the functional, whose integrand is a dimensionless ratio of metric invariants. The functional depends on the metric elements of two metrics. One metric is induced by a curvilinear grid generated in the physical domain, while the other control metric given in a special way provides additional control of the cell shape such as condensing the coordinate surfaces and orthogonalizing the coordinate lines of the grid towards the domain boundary. Nondegeneracy conditions for the grid and the hexahedral cell are discussed. The method for redistributing nodes over the domain boundary is considered. Grid generation examples are given.