Reliable Convergence Research Articles

On the use of differential evolution for forward kinematics of parallel manipulators

Differential evolution (DE) is a real-valued number encoded evolutionary strategy for global optimization. It has been shown to be an efficient, effective and robust optimization algorithm, especially for problems containing continuous variables. We have applied a DE algorithm to solve forward kinematics problems of parallel manipulators. The forward kinematics of a parallel manipulator is transformed into an optimization problem by making full use of the property that it is easy to obtain its inverse kinematics and then DE is used to obtain a globally optimal solution of forward kinematics. A comparison of numerical simulation results of a pneumatic 6-SPS parallel manipulator with DE, genetic algorithm and particle swarm optimization is given, which shows that the DE-based method performs well in terms of quality of the optimal solution, reliability and speed of convergence. It should be especially noted that the proposed method is also suitable for various other types of parallel manipulators, which provides a new way to solve the forward kinematics of parallel manipulators.

Non-orthogonal joint diagonalization with diagonal constraints

Joint diagonalization has attracted much attention and many algorithms have been presented so far. However, some ambiguities still exist in the objective functions for joint diagonalization. In this paper, some criterions are proposed to eliminate the above ambiguities at first, and then a new objective function which satisfies these criterions is presented. The new objective function introduces diagonal constraints for joint diagonalization, thus the trivial and unbalance solutions are excluded easily. Exactly jointly diagonalizable theorem is built to interpret the reasonableness of the new objective function and the conjugate gradient method is used to provide fast and reliable convergence. Finally, non-orthogonal joint diagonalization algorithm with diagonal constraints (DDiag) is developed. Simulations show that DDiag is efficient and robust.

Exploratory data analysis with artificial immune systems

We use a modified version of the CLONALG algorithm to perform exploratory data analysis. Since we wish to compare results from a number of methods, we only report on linear projections which have unique solutions. We incorporate a type of Gram Schmidt orthogonalisation [15] into the affinity maturation process to capture multiple components. We combine the new algorithm with reinforcement learning [17, 20] and with cross entropy maximization [13, 19]. Finally we combine several different non-standard adaptation methods using bagging and show that we get reliable convergence to accurate filters.

Resilience to churn of a peer-to-peer evolutionary algorithm

In this paper we analyse the resilience of a peer-to-peer (P2P) evolutionary algorithm (EA) subject to the following dynamics: computing nodes acting as peers leave the system independently from each other causing a collective effect known as churn. Since the P2P EA has been designed to tackle large instances of computationally expensive problems, we will assess its behaviour under these conditions, by performing a scalability analysis in five different scenarios using the massively multimodal deceptive problem as a benchmark. In all cases, the P2P EA reaches the success criterion without a penalty on the runtime. We show that the key to the algorithm resilience is to ensure enough peers at the beginning of the experiment; even if some of them leave, those that remain contain enough information to guarantee a reliable convergence.

Instantaneous frequency estimation at low signal-to-noise ratios using time-varying notch filters

This paper is aimed at finding parametric signal models that perform well at modelling noisy tonals at low signal-to-noise ratios (SNRs). We focus on models that are applied to a segment of data at a time, rather than work their way through the data in a sequential manner as typified by the adaptive methods. Inspired by notch filter theory, we extend the well-known time-varying AR (TVAR) models to include the effects of additive noise, and arrive at two types of time-varying notch filter (TVNF). The first one, like the TVAR model, employs a basis expansion of the filter coefficients. For the second one, we utilise the fact that tonal instantaneous frequencies (IFs) are directly proportional to the angles of the roots of the denominator polynomial, and perform a basis expansion of the IFs. Adaptive notch filters are well known and have been successfully applied in several fields. By application to simulated signals and a section of a dolphin whistle recording, it is shown that the TVNFs perform better than the TVAR model, and are useful tools for low SNR IF estimation. TVNF estimation employs a regularised Gauss–Newton type iterative search algorithm, which exhibits rapid and reliable convergence. Model order determination by Akaike's final prediction error (FPE) criterion is also discussed along with the selection of notch filter design and regularisation parameters.

AN IMPROVED POPULATION BASED OPTIMIZATION SOLUTION METHOD BY COMBINING LOCAL AND GLOBAL SEARCHING

Optimization Solution Task is a typical and important task in many applications. Many optimization problems have been proved to be NP-hard problems, which cannot be solved by some predefined mathematic formulae. In this case, computer aided method is very helpful. While some local search algorithms are easily to fall into a local optimum solution. On contrast, the population based methods, such as Genetic Algorithms, Artificial Immune System, Autonomy Oriented Computing, are global search algorithms. However, they are not good at the local search. In this paper, an improved method is proposed by combining the local and global search ability, so as to improve the performance in terms of the convergence speed and the convergence reliability. We construct a generic form to deal with the common objective function space or the objective function with the partial derivative. In addition, we present an n-hold method in population based evolution method. The experiments indicate that our approach can effectively improve the convergence reliability, which is much concerned in some applications with the expensive executing expense.

Computer Code for Passivity Enforcement of Rational Macromodels by Residue Perturbation

Passivity of rational macromodels is a necessary requirement for guaranteeing a stable time-domain simulation. This paper describes a freely available routine for passivity enforcement of multiport models (y parameters) using residue perturbation. The procedure calculates a correction to the original model by adjusting its residues and constant term as a postprocessing step while minimizing the model perturbation in the least squares (LS) sense. Control parameters are available for limiting the number of free variables and for specifying different LS weighting schemes. Two different constraint types can be specified, which helps to ensure reliable convergence when applied in an iterative scheme. Usage of a sparse solver is shown to greatly reduce the computation time. The software is demonstrated by several numerical examples

Least-squares variational treatment of positron (electron)–diatomic molecule scattering

A computer code based on the least-squares variational method (LSVM) is developed for the treatment of the collisions of positrons and electrons with diatomic molecules. The code was tested and employed for the investigation of the elastic scattering of positrons and electrons by hydrogen molecules within the framework of the adiabatic approximation. The system is described by a set of prolate spheroidal coordinates which is the most suitable representation of diatomic molecules. Reliable convergence of the scattering phaseshifts has been achieved by optimizing the nonlinear parameters and increasing the number of L2 components of the trial wavefunctions. The cross section of the lowest partial wave is calculated at energies varying from 0.136 eV to 13.6 eV, under the assumption that positronium formation, exchange interactions, and all excitation channels are closed. A comparison is presented between our results and those determined by other authors.

Mathematical modeling and analysis of a unified power flow controller: A comparison of two approaches in power flow studies and effects of UPFC location

This paper is focused on the mathematical modeling of unified power flow controller (UPFC), which is an advanced and versatile member of flexible ac transmission systems (FACTS). The proposed model is for the implementation of the device in conventional Newton–Raphson (NR) power flow algorithm and in power system analysis software package (PSASP). The model, derived from two-voltage source representation, is presented and analyzed in detail. The model represents a more robust and feasible alternative to others, because it is able to take operational losses of UPFC into account. A program in Fortran-77 language has been written in order to extend conventional NR algorithm based on proposed model. The model has also been adapted into PSASP by means of user-defined modeling technique. Different computer simulation studies performed on IEEE 14-bus and IEEE 30-bus test systems are presented in the paper to test and compare the two approaches. A robust and reliable convergence of the power flow studies is guaranteed by implementing the two approaches with high convergence speeds. UPFC can be theoretically located anywhere along a transmission line. In this respect, also the effects of UPFC allocation on power system operation have been investigated in detail.

AN IMPROVED NEWTON METHOD FOR RADIAL DISTRIBUTION SYSTEM LOAD ANALYSIS

This paper presents a modified Newton method of load flow analysis for radial distributionsystems. It is derived with the Jacobian matrix is in UDUT form, where U is a constantupper triangular matrix depending solely on system topology and D is a block diagonalmatrix. With this formulation, the conventional steps of forming the Jacobian matrix,LU factorization and forward/back substitution are replaced by back/forward sweeps on radialfeeders with equivalent impedances. The method has advantages over Newton’ s method interms of speed of solution (no. of iterations), and reliability of convergence by inserting a minimization technique (Cubic Interpolation Technique). The algorithm exhibits a control of the convergence. As such the method converges for cases when conventional Newton’ s method and some other popular methods diverge. Two large distribution systems of 490 nodes and 722 nodes with different r/x ratio in line impedance are used to examine the performance of the method. These tests have shown that the proposed method is as robust and efficient as the forward/back sweep method. The proposed method can be extended to the solution of three phase unbalanced representation.

Early arrival waveform tomography on near-surface refraction data

We develop a waveform-tomography method for estimating the velocity distribution that minimizes the waveform misfit between the predicted and observed early arrivals in space-time seismograms. By fitting the waveforms of early arrivals, early arrival waveform tomography (EWT) naturally takes into account more general wave-propagation effects compared to the high-frequency method of traveltime tomography, meaning that EWT can estimate a wider range of slowness wavenumbers. Another benefit of EWT is more reliable convergence compared to full-waveform tomography, because an early-arrival misfit function contains fewer local minima. Synthetic test results verify that the waveform tomogram is much more accurate than the traveltime tomogram and that this algorithm has good convergence properties. For marine data from the Gulf of Mexico, the statics problem caused by shallow, gassy muds was attacked by using EWT to obtain a more accurate velocity model. Using the waveform tomogram to correct for statics, the stacked section was significantly improved compared to using the normal move-out (NMO) velocity, and moderately improved compared to using the traveltime tomogram. Inverting high-resolution land data from Mapleton, Utah, showed an EWT velocity tomogram that was more consistent with the ground truth (trench log) than the traveltime tomogram. Our results suggest that EWT can provide supplemental, shorter-wavelength information compared to the traveltime tomogram for both shallow and moderately deep seismic data.

Modelling and Simulation of Universal Digital AC Bridge Using Ann Technique

Bridges are the measuring devices used for accurate measurement of impedance. As such, there is no universal bridge circuit that measures impedance of all types of passive components. Moreover, the bridges available cannot be used for high-frequency impedance measurements. This paper proposes an automatic digital AC bridge model, which is considered to be universal and suitable for high-frequency impedance measurement up to 1MHz. In this adaptive digital AC Bridge, balancing is achieved by means of Artificial Neural Network based on stochastic gradient search algorithm. Among the various gradient search techniques, the Widrow-Hoff's Least Mean Square (LMS) technique has been chosen as it involves less computational burden. The digital AC bridge operations have been verified by simulation. The simulated system was tested for measuring impedances of pure and impure inductors, capacitors, resistors, and a series combination of an inductance and a capacitance. The effects of various parameters like supply voltage, reference resistance, learning rate, and sampling rate were considered to investigate the performance of universal high-precision AC Bridge, and the results are reported. This model is advantageous over the traditional heuristic methods in terms of higher accuracy, faster convergence, and greater reproducibility and reliability.

Backward-Smoothing Extended Kalman Filter

The principle of the iterated extended Kalman filter has been generalized to create a new filter that has superior performance when the estimation problem contains severe nonlinearities. The new filter is useful when nonlinearities might significantly degrade the accuracy or convergence reliability of other filters. The new filter solves a nonlinear smoothing problem for the current and past sample intervals using iterative numerical techniques. This approach retains the nonlinearities of a fixed number of stages that precede the stage of interest, and it processes information from earlier stages in an approximate manner. The algorithm has been simulation tested on a difficult spacecraft attitude estimation problem that includes sensing of fewer than three axes and significant dynamic model uncertainty. The filter compensates for this uncertainty via simultaneous estimation of moment of inertia parameters. The new filter exhibits markedly better convergence reliability and accuracy than an extended Kalman filter and an unscented Kalman filter for estimation problems that start with large initial attitude or attitude rate errors.

Transient temperature fields with general nonlinear boundary conditions in electronic systems

Green's function representations of the solution of the heat conduction equation for general boundary conditions are generalized for the nonlinear, i.e., temperature dependent case. Temperature dependent heat transfer coefficients lead to additional terms in the Green's function representation of the temperature field. For a rectangular structure with averaged homogeneous material parameters several types of Green's functions can be chosen especially simple, because of the new representation with the possibility of differing types of boundary conditions for the temperature field and the Green's function. Exact finite closed form expressions for three-dimensional-Green's functions in the time domain using elliptic theta functions are presented. The temperature field is a solution of a nonlinear integral equation which is solved numerically by iteration. The resulting algorithm is very robust, stable and accurate with reliable convergence properties and avoids matrix inversions completely. The algorithm can deal with all sizes of volume heat sources without additional grid generation. Large and small size volume heat sources are treated simultaneously in the calculations that will be presented. Heat transfer coefficients are chosen representing radiative and convective boundary conditions. An extension of the solution algorithm to composed multilayer systems of arbitrary geometry is outlined.

05/00490 Thermodynamic analyses of refrigerant mixtures using artificial neural networks: Arcaklioglu, E. et al. Applied Energy, 2004, 78, (2), 219–230

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.

Reliable and Efficient Approximation of Polyconvex Envelopes

An iterative algorithm that approximates the polyconvex envelope fpc of a given function $f:{\mathbb{R}}^{n\times m} \to {\mathbb{R}}$, i.e., the largest function below f which is convex in all minors, is established. Also presented are a rigorous error analysis with a focus on reliability and optimal orders of convergence, an efficient strategy that reduces the large number of unknowns, as well as numerical experiments.

Algorithm for Convergence Criteria Simulation on LMS Adaptive Filters

A standard algorithm for LMS-filter simulation, tested with several convergence criteria under system identification configuration is presented in this paper. Establishing a reliable convergence criterion is mandatory in order to properly design an LMS filter and so avoid instability problems that may arise if both quantization effects and interdependency relationship among learning curve behaviors are not taken into account. Simulations performed under Matlab show remarkable differences between convergence criteria proposed by several authors and one presented in a previous work derived from a complete learning curve analysis.

Identification of Structural Systems Using an Evolutionary Strategy

The problem of system identification is an inverse problem of difficult solution. Currently, difficulties lie in the development of algorithms that use measured data from the system to characterize it without significant a priori knowledge of the system. In this paper, a parameter estimation technique based on an evolution strategy (an optimization algorithm inspired by natural evolution) is presented to overcome some of the difficulties encountered in the field. Using this method, a set of direct problems is solved instead of directly tackling the inverse problem. If the uniqueness of the identification solution is guaranteed for the assumed model and the available data, this heuristic method is able to find a solution without incurring restrictions of other classical optimization methods, like the need for reliable initial estimates and convergence to local optima. Some results obtained with this algorithm are presented for the identification of 3 degrees of freedom (DOF) and a 10 DOF structural system under conditions including limited input/output data, noise polluted signals, and no prior knowledge of mass, damping, or stiffness of the system.

Numerical computation of constant mean curvature surfaces using finite elements

This paper presents a method for computing two-dimensional constant mean curvature surfaces. The method in question uses the variational aspect of the problem to implement an efficient algorithm. In principle, it is a flow-like method in that it is linked to the gradient flow for the area functional, which gives reliable convergence properties. In the background, a preconditioned conjugate gradient method works, which gives the speed of a direct elliptic multigrid method.

Distributed Mitigation of Voltage Sag by Optimal Placement of Series Compensation Devices Based on Stochastic Assessment

Central mitigation does not necessarily provide the most economical solution to voltage-sag problems. Distributed mitigation with strategically placed compensation devices should provide a better alternative. Placement studies of this nature usually involve extensive evaluations of candidate compensation schemes, which can become unmanageable for large systems with stochastic voltage-sag data. A probability-based technique known as the weighted sampling method is proposed to simplify the problem. The technique is applied to a distribution system to optimize the cost of placing series compensation. The cost has two components: device cost and cost reduction to consumers due to implementation of the device(s). Series compensation devices being optimized are the two distinctly different dynamic voltage restorer and thyristor voltage regulator. These devices are placed and optimized to best complement each other. To achieve reliable and fast convergence, a genetic algorithm with innovative coding is proposed. A 34-node distribution system is studied with a wide range of voltage-sag data and consumer tolerance characteristics.