New recursive algorithm for matrix inversion

To reduce the computational complexity of matrix inversion, which is the majority of processing in many practical applications, two numerically efficient recursive algorithms （called algorithms I and II, respectively） are presented. Algorithm I is used to calculate the inverse of such a matrix, whose leading principal minors are all nonzero. Algorithm II, whereby, the inverse of an arbitrary nonsingular matrix can be evaluated is derived via improving the algorithm I. The implementation, for algorithm II or I, involves matrix-vector multiplications and vector outer products. These operations are computationally fast and highly parallelizable. MATLAB simulations show that both recursive algorithms are valid.

Fast recursive algorithm for two-dimensional Tsallis entropy thresholding method

Recently, a two-dimensional （2-D） Tsallis entropy thresholding method has been proposed as a new method for image segmentation. But the computation complexity of 2-D Tsallis entropy is very large and becomes an obstacle to real time image processing systems. A fast recursive algorithm for 2-D Tsallis entropy thresholding is proposed. The key variables involved in calculating 2-D Tsallis entropy are written in recursive form. Thus, many repeating calculations are avoided and the computation complexity reduces to O（L2） from O（L4）. The effectiveness of the proposed algorithm is illustrated by experimental results.

Minimal cut-based recursive decomposition algorithm for seismic reliability evaluation of lifeline networks

In this paper, a new probabilistic analytical approach, the minimal cut-based recursive decomposition algorithm （MCRDA）, is presented to evaluate the seismic reliability of large-scale lifeline systems. Based on the minimal cut searching algorithm, the approach calculates the disjoint minimal cuts one by one using the basic procedure of the recursive decomposition method. At the same time, the process obtains the disjoint minimal paths of the system. In order to improve the computation efficiency, probabilistic inequality is used to calculate a solution that satisfies the prescribed error bound. A series of case studies show that MCRDA converges rapidly when the edges of the systems have low reliabilities. Therefore, the approach can be used to evaluate large-scale lifeline systems subjected to strong seismic wave excitation.

An improved cut-based recursive decomposition algorithm for reliability analysis of networks

In this paper, an improved cut-based recursive decomposition algorithm is proposed for lifeline networks. First, a complementary structural function is established and three theorems are presented as a premise of the proposed algorithm. Taking the minimal cut of a network as decomposition policy, the proposed algorithm constructs a recursive decomposition process. During the decomposition, both the disjoint minimal cut set and the disjoint minimal path set are simultaneously enumerated. Therefore, in addition to obtaining an accurate value after decomposing all disjoint minimal cuts and disjoint minimal paths, the algorithm provides approximate results which satisfy a prescribed error bound using a probabilistic inequality. Two example networks, including a large urban gas system, are analyzed using the proposed algorithm. Meanwhile, a part of the results are compared with the results obtained by a path-based recursive decomposition algorithm. These results show that the proposed algorithm provides a useful probabilistic analysis method for the reliability evaluation of lifeline networks and may be more suitable for networks where the edges have low reliabilities.

A RECURSIVE ALGORITHM AND ITS CONVERGENCE FOR PARAMETER ESTIMATION OF CONVOLUTION MODEL

In this article, the problem on the estimation of the convolution model parameters is considered. The recursive algorithm for estimating model parameters is introduced from the orthogonal procedure of the data, the convergence of this algorithm is theoretically discussed, and a sufficient condition for the convergence criterion of the orthogonal procedure is given. According to this condition, the recursive algorithm is convergent to model wavelet A- = （1, α1,..., αq）.

REESSE Unified Recursive Algorithm for Solving Three Computational Problems

Different from the extended Euclidean algorithm which can compute directly only the multiplicative inverse of an element in Zm^＊ and the greatest common divisor of two integers, a recursive algorithm called REESSE is designed by the authors, which can not only seek directly the multiplicative inverse and the greatest common divisor, but also solve directly a simple congruence for general solutions. This paper presents the definition and the two valuable properties of a simple congruence, analyzes in detail the reduction and recursion process of solving simple congruences, induces the recursive formula for solving simple congruences, and describes formally and implements in C language the recursive algorithm. At last, the paper compares REESSE with the extended Euclidean algorithm in thought, applicability and time complexity.

CONVERGENCE AND STABILITY OF RECURSIVE DAMPED LEAST SQUARE ALGORITHM

The recursive least square is widely used in parameter identification. But if is easy to bring about the phenomena of parameters burst-off. A convergence analysis of a more stable identification algorithm-recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. rt is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.

An improved recursive decomposition algorithm for reliability evaluation of lifeline networks

The seismic reliability evaluation of lifeline networks has received considerable attention and been widely studied. In this paper, on the basis of an original recursive decomposition algorithm, an improved analytical approach to evaluate the seismic reliability of large lifeline systems is presented. The proposed algorithm takes the shortest path from the source to the sink of a network as decomposition policy. Using the Boolean laws of set operation and the probabilistic operation principal, a recursive decomposition process is constructed in which the disjoint minimal path set and the disjoint minimal cut set are simultaneously enumerated. As the result, a probabilistic inequality can be used to provide results that satisfy a prescribed error bound. During the decomposition process, different from the original recursive decomposition algorithm which only removes edges to simplify the network, the proposed algorithm simplifies the network by merging nodes into sources and removing edges. As a result, the proposed algorithm can obtain simpler networks. Moreover, for a network owning s-independent components in its component set, two network reduction techniques are introduced to speed up the proposed algorithm. A series of case studies, including an actual water distribution network and a large urban gas system, are calculated using the proposed algorithm. The results indicate that the proposed algorithm provides a useful probabilistic analysis method for the seismic reliability evaluation of lifeline networks.

A Kind of Second-Order Learning Algorithm Based on Generalized Cost Criteria in Multi-Layer Feed-Forward Neural Networks

A kind of second order algorithm--recursive approximate Newton algorithm was given by Karayiannis. The algorithm was simplified when it was formulated. Especially, the simplification to matrix Hessian was very reluctant, which led to the loss of valuable information and affected performance of the algorithm to certain extent. For multi layer feed forward neural networks, the second order back propagation recursive algorithm based generalized cost criteria was proposed. It is proved that it is equivalent to Newton recursive algorithm and has a second order convergent rate. The performance and application prospect are analyzed. Lots of simulation experiments indicate that the calculation of the new algorithm is almost equivalent to the recursive least square multiple algorithm. The algorithm and selection of networks parameters are significant and the performance is more excellent than BP algorithm and the second order learning algorithm that was given by Karayiannis.

Recursive Algorithm Based Reliability Analysis of Multiphase Satellite Systems with Propagated Failures

Modern satellite systems are generally designed to fulfill multiphase-missions. Component /subsystem redundancies are commonly used to achieve high reliability and long life of modern satellite systems. These characteristics have leaded to a critical issue of reliability analysis of satellites that is how to deal with the reliability analysis with multiphase-missions and propagated failures of redundant components. Traditional methods based on the binary decision diagram( BDD) can hardly cope with these issues efficiently. Accordingly, a recursive algorithm method was introduced to facilitate the reliability analysis of satellites. This method was specified for the analysis of static fault tree and it was implemented by generating combination of component failures and carrying out a backward recursive algorithm. The effectiveness of the proposed method was demonstrated through the reliability analysis of a multiphase satellite system with propagated failures.The major advantage of the proposed method is that it does not need composition of BDD and its computational process is automated.

Prediction of Time Series Empowered with a Novel SREKRLS Algorithm

For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.

A Recursive Algorithm on Rational Interpolation

In this paper we introduce a so called C-Matrix w.r.t a rational interpolation problem and study the relationship between the unattainable points and C-Matrix. Finally, we present a recursive algorithm on rational interpolation.

Nonlinear Modeling and Identification of the Electro-hydraulic Control System of an Excavator Arm Using BONL Model

Electro-hydraulic control systems are nonlinear in nature and their mathematic models have unknown parameters. Existing research of modeling and identification of the electro-hydraulic control system is mainly based on theoretical state space model, and the parameters identification is hard due to its demand on internal states measurement. Moreover, there are also some hard-to-model nonlinearities in theoretical model, which needs to be overcome. Modeling and identification of the electro-hydraulic control system of an excavator arm based on block-oriented nonlinear（BONL） models is investigated. The nonlinear state space model of the system is built first, and field tests are carried out to reveal the nonlinear characteristics of the system. Based on the physic insight into the system, three BONL models are adopted to describe the highly nonlinear system. The Hammerstein model is composed of a two-segment polynomial nonlinearity followed by a linear dynamic subsystem. The Hammerstein-Wiener（H-W） model is represented by the Hammerstein model in cascade with another single polynomial nonlinearity. A novel Pseudo-Hammerstein-Wiener（P-H-W） model is developed by replacing the single polynomial of the H-W model by a non-smooth backlash function. The key term separation principle is applied to simplify the BONL models into linear-in-parameters struc^tres. Then, a modified recursive least square algorithm（MRLSA） with iterative estimation of internal variables is developed to identify the all the parameters simultaneously. The identification results demonstrate that the BONL models with two-segment polynomial nonlinearities are able to capture the system behavior, and the P-H-W model has the best prediction accuracy. Comparison experiments show that the velocity prediction error of the P-H-W model is reduced by 14%, 30% and 75% to the H-W model, Hammerstein model, and extended auto-regressive （ARX） model, respectively. This research is helpful in controller design, system monitoring and diagnosis.

Unifying representation of Bézier curve and two kinds of generalized ball curves

This paper presents a new basis, the WSB basis, which unifies the Bemstein basis, Wang-Ball basis and Said-Ball basis, and therefore the Bézier curve, Wang-Ball curve and Said-Ball curve are the special cases of the WSB curve based on the WSB basis In addition, the relative degree elevation formula, recursive algorithm and conversion formula between the WSB basis and the Bern- stein basis are given.

Three-Dimensional Generalized Inverse Matrix Rational Interpolation

In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable.

Optimal distribution of reliability for a large network based on connectivity

It is a non-polynomial complexity problem to calculate connectivity of the complex network. When the system reliability cannot be expressed as a function of element reliability, we have to apply some heuristic methods for optimization based on connectivity of the network. The calculation structure of connectivity of complex network is analyzed in the paper. The coefficient matrixes of Taylor second order expansion of the system connectivity is generated based on the calculation structure of connectivity of complex network. An optimal schedule is achieved based on genetic algorithms （GA）. Fitness of seeds is calculated using the Taylor expansion function of system connectivity. Precise connectivity of the optimal schedule and the Taylor expansion function of system connectivity can be achieved by the approved Minty method or the recursive decomposition algorithm. When error between approximate connectivity and the precise value exceeds the assigned value, the optimization process is continued using GA, and the Taylor function of system connectivity needs to be renewed. The optimization process is called iterative GA. Iterative GA can be used in the large network for optimal reliability attribution. One temporary optimal result will be generated every time in the iteration process. These temporary optimal results approach the real optimal results. They can be regarded as a group of approximate optimal results useful in the real project.

Generating routes for autonomous driving in vehicle-to-infrastructure communications

The study of vehicular networks has attracted considerable interest in academia and the industry.In the broad area,connected vehicles and autonomous driving are technologies based on wireless data communication between vehicles or between vehicles and infrastructures.A Vehicle-to-Infrastructure(V2I)system consists of communications and computing over vehicles and related infrastructures.In such a system,wireless sensors are installed in some selected points along roads or driving areas.In autonomous driving,it is crucial for a vehicle to figure out the ideal routes by the communications between its equipped sensors and infrastructures then the vehicle is automatically moving along the routes.In this paper,we propose a Bezier curve based recursive algorithm,which effectively creates routes for vehicles through the communication between the On-Board Unit(OBU)and the Road-Side Units(RSUs).In addition,this approach generates a very low overhead.We conduct simulations to test the proposed algorithm in various situations.The experiment results demonstrate that our algorithm creates almost ideal routes.

An Effective Method of Threshold Selection for Small Object Image

The image segmentation difficulties of small objects which are much smaller than their background often occur in target detection and recognition. The existing threshold segmentation methods almost fail under the circumstances. Thus, a threshold selection method is proposed on the basis of area difference between background and object and intra-class variance. The threshold selection formulae based on one-dimensional (1-D) histogram, two-dimensional (2-D) histogram vertical segmentation and 2-D histogram oblique segmentation are given. A fast recursive algorithm of threshold selection in 2-D histogram oblique segmentation is derived. The segmented images and processing time of the proposed method are given in experiments. It is compared with some fast algorithms, such as Otsu, maximum entropy and Fisher threshold selection methods. The experimental results show that the proposed method can effectively segment the small object images and has better anti-noise property.

NONLINEAR MODELING AND CONTROLLING OF ARTIFICIAL MUSCLE SYSTEM USING NEURAL NETWORKS

The pneumatic artificial muscles are widely used in the fields of medicalrobots, etc. Neural networks are applied to modeling and controlling of artificial muscle system. Asingle-joint artificial muscle test system is designed. The recursive prediction error (RPE)algorithm which yields faster convergence than back propagation (BP) algorithm is applied to trainthe neural networks. The realization of RPE algorithm is given. The difference of modeling ofartificial muscles using neural networks with different input nodes and different hidden layer nodesis discussed. On this basis the nonlinear control scheme using neural networks for artificialmuscle system has been introduced. The experimental results show that the nonlinear control schemeyields faster response and higher control accuracy than the traditional linear control scheme.

UNIFYING REPRESENTATION OF BZIER CURVE AND GENERALIZED BALL CURVES

This paper presents two new families of the generalized Ball curves which include the Be ′zier curve, the generalized Ball curves defined by Wang and Said independently and some intermediate curves. The relative degree elevation and reduction schemes, recursive algorithms and the Bernstein\|Be ′zier representation are also given.