Simple Algebraic Algorithm Research Articles

Two-Phase Flow Measuring with Ultrasonic Tomography

The exact measurement of multiphase flow is an important and essential task in the oil and petrochemical related industries. Several methods have already been proposed in this field. In the existing methods, flow rate measurement depends on the fluid flow pattern. Flow pattern recognition requiring calibration has created instability in such systems. In this paper, a imple and reliable method is proposed which is based on ultrasonic tomography. It is free from calibration and instability problems that existing methods have. The obtained data from a 32-digit array of ultrasonic sensors have been used and the two-phase flow rate including liquid and gas phases have been calculated through a simple algebraic algorithm. Simulation results show that while applying this method the measurement technique is independent from the fluid flow pattern and the system error is decreased. For the proposed algorithm, the average amount of the spatial imaging error (SIE) for a bubble at different positions inside the pipe is about 5%.

New control strategy for DSTATCOM without current sensors and its engineering application

This paper analyses the negative sequence equivalent circuit of DSTATCOM in unbalanced distribution networks. A new control model of negative sequence voltage without current sensors based on instantaneous power balancing algorithm is deduced. To compensate for balanced and unbalanced voltages, a new cascade voltage loop control strategy, in which the negative sequence voltage control loop is parallel to the positive sequence voltage loop, is proposed. Then the mathematical model of the new cascade loop voltage control method is discussed. The DSTATCOM output voltage command is directly obtained from the bus voltage at the Point of Common Coupling (PCC) and the DC-side voltage via a simple algebraic algorithm based on power balance equation. In addition, the implementation costs can be reduced since current sensors are not required in the proposed control strategy. Simulation and industrial application results are presented to verify the validity of the proposed control strategy. It is successfully implemented in the DSTATCOM installed in the Lianyuan Iron and Steel Corporation in Hunan province of China.

On algebraic soft-decision decoding algorithms for BCH codes

Three algebraic soft-decision decoding algorithms are presented for binary Bose-Chaudhuri-Hocquengham (BCH) codes. Two of these algorithms are based on the bounded distance (BD)+1 generalized minimum-distance (GMD) decoding presented by Berlekamp (1984), and the other is based on Chase (1972) decoding. A simple algebraic algorithm is first introduced, and it forms a common basis for the decoding algorithms presented. Next, efficient BD+1 GMD and BD+2 GMD decoding algorithms are presented. It is shown that, for binary BCH codes with odd designed-minimum-distance d and length n, both the BD+1 GMD and the BD+2 GMD decoding algorithms can be performed with complexity O(nd). The error performance of these decoding algorithms is shown to be significantly superior to that of conventional GMD decoding by computer simulation. Finally, an efficient algorithm is presented for Chase decoding of binary BCH codes. Like a one-pass GMD decoding algorithm, this algorithm produces all necessary error-locator polynomials for Chase decoding in one run.

Method of solving a triplet comprising a singlet and a cemented doublet with given primary aberrations

A simple algebraic algorithm is proposed as a computational tool for the thin-lens design of a triplet which consists of a singlet and a cemented doublet. The triplet is required to yield specified amounts of lens power, primary spherical aberration, central coma, longitudinal chromatic aberration and secondary spectrum. The three element powers of the triplet are first obtained by solving the simultaneous linear equations of the total lens power, longitudinal chromatic aberration and secondary spectrum. A quadratic equation is obtained by combining the equations of spherical aberration and central coma, and the lens shapes are then obtained by solving this quadratic equation. The solving process is purely algebraic and is therefore easy to calculate and guarantees that all the solutions can be found.

Simple algebraic algorithm for determination of the generic-rank of structured systems

Within the framework of structural controllability, a new simple algebraic algorithm for determining the generic-rank of a structured pair (A, B) is presented.