Reliable Convergence Research Articles

A Sequential Numbering Power Flow Calculation Method for Distribution Network

As distribution network is of radial pattern, the forward and backward substitution algorithm and its variations are widely used for radial distribution network power flow calculation, which needs to form associated admittance matrix and matrix operations. This paper proposes a sequential numbering power flow calculation algorithm for distribution network. Based on the graph theory of nodes, the proposed method can handles multiple branches radiation network.. In the simulation test, our proposed algorithm is applied to a typical radial distribution network in order to verify the efficacy on power flow calculation. The results show that the sequential numbering power flow algorithm has good performance in terms of convergence rate and reliability.

Convergence behaviour of coupled pressure and thermal networks

Purpose – The purpose of this paper is to present a method for thermal computations of power devices based on a coupling between thermal and pressure networks. The concept of the coupling as well as the solution procedure is explained. The included examples demonstrate that the new method can be efficiently used for design of transformers and other power devices. Design/methodology/approach – The bidirectional propagation of temperature signal is introduced to the pressure network, which enables control of the power flow and a close coupling to the thermal network. The solution method is based on automatic splitting of the network definition (netlist) into two separate networks and iteratively solving the model using the Newton-Raphson approach as well as the adaptive relaxation enhanced by the direction change control. Findings – The proposed approach offers reliable convergence behaviour even for models with unknown direction of the fluid flow (bidirectional flows). The accuracy is sufficient for engineering applications and comparable with the computational fluid dynamics method. The computation times in the range of milliseconds and seconds are attractive for using the method in engineering design tools. Originality/value – The new method can be considered as a foundation for a consistent network modelling system of arbitrary thermodynamic problems including fluid flow. Such a modelling system can be used directly by device designers since the complexity of thermodynamic formulations is encapsulated in predefined network elements while the numerical solution is based on a standard network description and solvers (Spice).

Sudoku associative memory

This work presents bipolar neural systems for check-rule embedded pattern restoration, fault-tolerant information encoding and Sudoku memory construction and association. The primitive bipolar neural unit is generalized to have internal fields and activations, which are respectively characterized by exponential growth and logistic differential dynamics, in response to inhibitory and excitatory stimuli. Coupling extended bipolar units induces multi-state artificial Potts neurons which are interconnected with inhibitory synapses for Latin square encoding, K-alphabet Latin square encoding and Sudoku encoding. The proposed neural dynamics can generally restore Sudoku patterns from partial sparse clues. Neural relaxation is based on mean field annealing that well guarantees reliable convergence to ground states. Sudoku associative memory combines inhibitory interconnections of Sudoku encoding with Hebb’s excitatory synapses of encoding conjunctive relations among active units over memorized patterns. Sudoku associative memory is empirically shown reliable and effective for restoring memorized patterns subject to typical sparse clues, fewer partial clues, dense clues and perturbed or damaged clues. On the basis, compound Sudoku patterns are further extended to emulate complex topological information encoding.

Differential evolution and simulated annealing algorithms for mechanical systems design

In this study, nature inspired algorithms – the Differential Evolution (DE) and the Simulated Annealing (SA) – are utilized to seek a global optimum solution for ball bearings link system assembly weight with constraints and mixed design variables. The Genetic Algorithm (GA) and the Evolution Strategy (ES) will be a reference for the examination and validation of the DE and the SA. The main purpose is to minimize the weight of an assembly system composed of a shaft and two ball bearings. Ball bearings link system is used extensively in many machinery applications. Among mechanical systems, designers pay great attention to the ball bearings link system because of its significant industrial importance. The problem is complex and a time consuming process due to mixed design variables and inequality constraints imposed on the objective function. The results showed that the DE and the SA performed and obtained convergence reliability on the global optimum solution. So the contribution of the DE and the SA application to the mechanical system design can be very useful in many real-world mechanical system design problems. Beside, the comparison confirms the effectiveness and the superiority of the DE over the others algorithms – the SA, the GA, and the ES – in terms of solution quality. The ball bearings link system assembly weight of 634,099 gr was obtained using the DE while 671,616 gr, 728213.8 gr, and 729445.5 gr were obtained using the SA, the ES, and the GA respectively.

A new mathematical approach for handling DVH criteria in IMRT planning

The appropriate handling of planning criteria on the cumulative dose-volume histogram (DVH) is a highly problematic issue in intensity-modulated radiation therapy (IMRT) plan optimization. The nonconvexity of DVH criteria and globality of the resulting optimization problems complicate the design of suitable optimization methods, which feature numerical efficiency, reliable convergence and optimality of the results. This work examines the mathematical structure of DVH criteria and proves the valuable properties of isotonicity/antitonicity, connectedness, invexity and sufficiency of the Karush---Kuhn---Tucker condition. These properties facilitate the use of efficient and goal-oriented optimization methods. An exemplary algorithmic realization with feasible direction methods gives rise to a functional framework for interactive IMRT planning on DVH criteria. Numerical examples on real world planning cases prove its practical capability.

A generalized-exponential decomposition method for the analysis of inhomogeneous assembly/disassembly systems with unreliable machines and finite buffers

This paper presents a new approximate analytical method for the performance evaluation of inhomogeneous assembly/disassembly (A/D) systems with machines subject to failures and finite buffers. Processing times of machines in these systems are deterministic but not identical. Times between failures and times to repair are both assumed to be exponentially distributed. The method developed in this paper provides a generalized approach for analyzing A/D systems. Unlike the previous work on this subject, generalized exponential distributions are adopted instead of exponential distributions to approximate the repair time distributions of the fictitious machines. As a result the proposed method can handle the situation where the orders of magnitude of machines' reliability parameters (mean times between failures and mean times to repair) are not at the same level. A new algorithm is also developed to improve the convergence reliability and efficiency of the method. Extensive numerical experiments and simulation have been carried out to illustrate that the method proposed for A/D systems is quite accurate and efficient.

Recent developments in expectation‐maximization methods for analyzing complex data

The expectation–maximization (EM) algorithm is highly popular in computational statistics because it possesses a number of desirable properties such as reliable global convergence, numerical stability, and simplicity of implementation. More complex data are now increasingly prevalent across many application areas in a wide scope of scientific fields. These data could exhibit a hierarchical or longitudinal structure and involve atypical and/or asymmetric observations. The application of the EM algorithm in the analysis of these complex data presents significant challenges to existing EM methods. It is because the models developed often lead to intractable expectation‐steps or complicated maximization‐steps in order to model the correlation between hierarchical data and/or the skewness of asymmetric observations. This paper discusses recent advanced developments in EM methods to overcome these barriers in handling complex problems. WIREs Comput Stat 2013, 5:415–431. doi: 10.1002/wics.1277This article is categorized under: Statistical and Graphical Methods of Data Analysis > EM Algorithm Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods

Modelling and Design of Closed-Loop Manufacturing Systems

This paper introduces an analytical method for evaluating the performance of closed loop manufacturing systems with unreliable machines and finite buffers. The method involves transforming an arbitrary loop into one without thresholds and then evaluating the transformed loop using a new set of decomposition equations. It is more accurate than existing methods and is effective for a wider range of cases. The convergence reliability, and speed of the method are also discussed. In addition, observations are made on the behavior of closed loop production systems under various conditions. Finally, the method is used in a case study to design a flexible manufacturing system for production of aerospace parts.

Helical swimming in Stokes flow using a novel boundary-element method

We apply the boundary-element method to Stokes flows with helical symmetry, such as the flow driven by an immersed rotating helical flagellum. We show that the two-dimensional boundary integral method can be reduced to one dimension using the helical symmetry. The computational cost is thus much reduced while spatial resolution is maintained. We review the robustness of this method by comparing the simulation results with the experimental measurement of the motility of model helical flagella of various ratios of pitch to radius, along with predictions from resistive-force theory and slender-body theory. We also show that the modified boundary integral method provides reliable convergence if the singularities in the kernel of the integral are treated appropriately.

Min-Max Univariate Dynamic Encoding Algorithm for Searches (uDEAS) and Its Application to Optimal Design of Electric Machines

Optimal design of Interior Permanent Magnet Synchronous Machines (IPMSM) is to obtain the global design optimum in association with the characteristic analysis investigating nonlinear magnetic saturation based on Finite Element Analysis (FEA). Since characteristic analysis occupies most part of the convergence time, the number of objective function must be called minimally. Hence, in this paper, MuDEAS is newly implemented in order to compensate the excessive computation time and the reliability of convergence to the global optimum. MuDEAS has been verified through a benchmark function and applied to the optimal design of IPMSM for maximizing Maximum Torque Per Ampere (MTPA) indentified with FEA.

HYDROTHERMAL COORDINATION FOR SHORT RANGE FIXED HEAD STATIONS USING FAST GENETIC ALGORITHM

This paper presents a Fast genetic algorithm for solving Hydrothermal coordination (HTC) problem. Genetic Algorithms (GAs) perform powerful global searches, but their long computation times, put a limitation when solving large scale optimization problems. The present paper describes a Fast GA (FGA) to overcome this limitation, by starting with random solutions within the search space and narrowing down the search space byconsidering the minimum and maximum errors of the population members. Since the search space is restricted to a small region within the available search space the algorithm works very fast. This algorithm reduces the computational burden and number of generations to converge. The proposed algorithm has been demonstrated for HTC of various combinations of Hydro thermal systems. In all the cases Fast GA shows reliable convergence. The final results obtained using Fast GA are compared with simple (conventional) GA and found to be encouraging.

16-QAM 신호에 대한 CCA 적응 등화 알고리즘 성능 분석

Abstract This paper deals with the performance anlysis of CCA adaptive equalization algorithm, that is used for reduction of intersymbol interference at the receiving side which occurs in the time dispersive communication channel. Basically, this algorithm is borned for the solving phase unrecovery problem in the CMA equalizer, and the comines the concept of DDA (Decision Directed Algorithm) and RCA (Reduce Constellation Algorithm). The DDA has a stable convergence characteristics in unilevel signal, but not in the number of levels in multilevel signal such as QAM, so it has unstable problem. The RCA does not provide reliable initial convergence. And even after convergence, the equalization noise due to the steady state misadjustment exhibited by it is very high as compared to DDA. For the solving the abovemensioned point, the CCA adaptive eualization alogorithm has borned. In order to performance analysis of CCA algorithm, the recovered signal constellation that is the output of the equalizer, the convergence characteristic by the residual isi and MD (maximum distortion), the SER characteristic are used by computer simulation and it was compared with the DDA, RCA respectively. As a result of simulation, the DDA has superior performance than other algoithm, but it has a convergence unguarantee and unstability in the multilevel signal. In order to solving this problem, the CCA has more good performance than RCA in every performance index.

Cross-Entropy Optimization for the Design of Triangular FBG Filter With Asymmetrical Spectrum

This letter reports the use of optimization methods to design triangular fiber Bragg grating (TFBG) filter with asymmetrical spectrum. In the optimization methods, TFBG synthesis problems are formulated as nonlinear objective functions, and stochastic optimization techniques are applied to search for index modulation profiles that minimize the difference between the synthesized and targeted spectra. However, the performances of traditional stochastic optimization techniques are affected by the initial guess. A poor initial guess may result in low-efficiency optimizations and easily get trapped into local solutions; in some cases, it may even lead to a false result. Accordingly, we introduce the use of cross-entropy optimization (CEO) in searching for the optimal index modulation profiles. CEO is an effective algorithm that solves various continuous multiextremal optimization problems and demonstrates robustness with respect to starting conditions. Computer simulation results show that the index modulation profiles obtained using the proposed method performed better compared with those obtained using the conventional covariance matrix adaptation evolution strategy (CMAES). In addition, CEO also provides a reliable convergence to the near-optimum solution. These findings indicate the CEO is more suitable than CMAES for the design of TFBG filters with asymmetrical spectrum for sensor applications.

Study on a Uniform Algorithm for Single-Phase and Three-Phase Load Flow Calculation

This paper presents a uniform algorithm for single-phase and three-phase load flow calculation. Firstly, two iterative equations with static factors are studied for single-phase power flow calculation based on Gauss power flow algorithm. One is used for all PQ nodes iteration similar to the traditional Gauss power flow algorithm, and the other one is exploited for all PV nodes and the slack node, which is a new algorithm studied in this paper. Then, the three-phase power flow iterative equations are studied. Virtual generator nodes are generated so that it is enough to built equations to solve the unknown parameters and each equation has a unique solution. Two iterative equations are studied for three-phase power flow calculation based on the single-phase formulation studied in this paper. The calculation result shows that the algorithm has the advantage of fast calculation speed, reliable convergence and powerful applicability. It has been shown that the algorithm is suitable for online calculation of single-phase and three-phase power system.

Experiments with the interior-point method for solving large scale Optimal Power Flow problems

This paper reports extensive results obtained with the interior-point method (IPM) for nonlinear programmes (NLPs) stemming from large-scale and severely constrained classical Optimal Power Flow (OPF) and Security-Constrained Optimal Power Flow (SCOPF) problems. The paper discusses transparently the problems encountered such as convergence reliability and speed issues of the method.

Design Optimization of Magnetic Gears Using Mesh Adjustable Finite-Element Algorithm for Improved Torque

Magnetic gears (MGs) are devices which operate through the interaction of magnetic fields produced by multipole magnets to transmit torque with high efficiency. Compared with mechanical gears, it requires no moving contact for the force transmission, hence there are no mechanical fatigue and no mechanical loss and less acoustic noise. There is no need for lubrication and hence MG requires minimal maintenance. However, the heavy use of permanent magnetic (PM) materials leads to a high production cost. In this paper, a novel mesh adjustable finite-element algorithm is proposed to optimize the magnetic gear dimensions in order to maximize the torque output for a given amount of PMs. With the proposed mesh adjustable finite-element algorithm, the coordinates of mesh nodes are moved according to dimensional changes, without compromising the mesh quality. The merit is that no re-mesh is required during the process of optimization, which can significantly reduce the computing time while retaining the robustness of the algorithm. By combining the proposed approach with particle swarm optimization (PSO) algorithm, a reliable convergence to the finding of global optimum is achieved. This proposed method is applied to optimize the dimensions of a coaxial magnetic gear with surface mounted PMs. Optimal results confirm the validity and effectiveness of the proposed algorithm.

Cross-Entropy Optimization for the Design of Fiber Bragg Gratings

This paper considers the synthesis problem of a low-dispersion fiber Bragg grating (FBG) filter. This problem can be formulated as a nonlinear objective problem in practice. However, solving this problem with traditional methods is difficult because of its multimodal and ill-conditioned character. Inspired by the efficient ability of cross-entropy optimization (CEO) method to find near-optimal solutions in large search spaces, we propose the application of CEO method to search for design variables to satisfy the target design criteria. Computer simulation results show that the proposed CEO method can successfully achieve the target values of the design specifications. It also provides a reliable convergence to the near-optimum solution. These findings indicate that the CEO algorithm is more appropriate for the FBG filter design compared with conventional particle swarm optimization method.

An enhanced RCGA for a rapid and reliable load flow solution of electrical power systems

The paper presents a reliable and fast load flow solution by using a real-coded genetic algorithm (RCGA), bus reduction technique and sparsity technique. The proposed load flow solution firstly used reduction technique to eliminate the load buses. Then, the power flow problem is solved for the generator buses only using real-coded GA to calculate the phase angles. Thus, the load flow problem becomes a single objective function, where the voltage magnitudes are specified resulted in reduced computation time for the solution. Once the phase angle has been calculated, the system is restored by calculating the voltages of the load buses in terms of the calculated voltages of the generator buses. A sparsity technique is used to reduce the computation time further as well as the storage requirements. The proposed load flow solution also can efficiently solve the load flow problems for ill-conditioned power systems whereas the conventional RCGA alone fails to solve these systems. The proposed method was demonstrated on 14-bus IEEE, 30-bus IEEE and 300-bus IEEE, and a practical system 362-busbar Iraqi National Grid. The proposed solution has reliable convergence, a highly accurate solution and much less computing time for on-line applications. The method can conveniently be applied for on-line analysis and planning studies of large power systems.

Q-learning and policy iteration algorithms for stochastic shortest path problems

We consider the stochastic shortest path problem, a classical finite-state Markovian decision problem with a termination state, and we propose new convergent Q-learning algorithms that combine elements of policy iteration and classical Q-learning/value iteration. These algorithms are related to the ones introduced by the authors for discounted problems in Bertsekas and Yu (Math. Oper. Res. 37(1):66-94, 2012). The main difference from the standard policy iteration approach is in the policy evaluation phase: instead of solving a linear system of equations, our algorithm solves an optimal stopping problem inexactly with a finite number of value iterations. The main advantage over the standard Q-learning approach is lower overhead: most iterations do not require a minimization over all controls, in the spirit of modified policy iteration. We prove the convergence of asynchronous deterministic and stochastic lookup table implementations of our method for undiscounted, total cost stochastic shortest path problems. These implementations overcome some of the traditional convergence difficulties of asynchronous modified policy iteration, and provide policy iteration-like alternative Q-learning schemes with as reliable convergence as classical Q-learning. We also discuss methods that use basis function approximations of Q-factors and we give an associated error bound.

Q-Learning and Enhanced Policy Iteration in Discounted Dynamic Programming

We consider the classical finite-state discounted Markovian decision problem, and we introduce a new policy iteration-like algorithm for finding the optimal state costs or Q-factors. The main difference is in the policy evaluation phase: instead of solving a linear system of equations, our algorithm requires solving an optimal stopping problem. The solution of this problem may be inexact, with a finite number of value iterations, in the spirit of modified policy iteration. The stopping problem structure is incorporated into the standard Q-learning algorithm to obtain a new method that is intermediate between policy iteration and Q-learning/value iteration. Thanks to its special contraction properties, our method overcomes some of the traditional convergence difficulties of modified policy iteration and admits asynchronous deterministic and stochastic iterative implementations, with lower overhead and/or more reliable convergence over existing Q-learning schemes. Furthermore, for large-scale problems, where linear basis function approximations and simulation-based temporal difference implementations are used, our algorithm addresses effectively the inherent difficulties of approximate policy iteration due to inadequate exploration of the state and control spaces.