Abstract: Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.
Abstract: The Com-Poisson (CMP) model is one of the most
popular discrete generalized linear models (GLMS) that handles
both equi-, over- and under-dispersed data. In longitudinal context,
an integer-valued autoregressive (INAR(1)) process that incorporates
covariate specification has been developed to model longitudinal
CMP counts. However, the joint likelihood CMP function is
difficult to specify and thus restricts the likelihood-based estimating
methodology. The joint generalized quasi-likelihood approach
(GQL-I) was instead considered but is rather computationally
intensive and may not even estimate the regression effects due
to a complex and frequently ill-conditioned covariance structure.
This paper proposes a new GQL approach for estimating the
regression parameters (GQL-III) that is based on a single score vector
representation. The performance of GQL-III is compared with GQL-I
and separate marginal GQLs (GQL-II) through some simulation
experiments and is proved to yield equally efficient estimates as
GQL-I and is far more computationally stable.
Abstract: A scheme integrated with deterministic–stochastic subspace system identification and the method of damage localization vector is proposed in this study for damage detection of structures based on seismic response data. A series of shaking table tests using a five-storey steel frame has been conducted in National Center for Research on Earthquake Engineering (NCREE), Taiwan. Damage condition is simulated by reducing the cross-sectional area of some of the columns at the bottom. Both single and combinations of multiple damage conditions at various locations have been considered. In the system identification analysis, either full or partial observation conditions have been taken into account. It has been shown that the damaged stories can be identified from global responses of the structure to earthquakes if sufficiently observed. In addition to detecting damage(s) with respect to the intact structure, identification of new or extended damages of the as-damaged (ill-conditioned) counterpart has also been studied. The proposed scheme proves to be effective.
Abstract: The concept of adaptive shape parameters (ASP) has been presented for solution of incompressible Navier Strokes equations using mesh-free local Radial Basis Functions (RBF). The aim is to avoid ill-conditioning of coefficient matrices of RBF weights and inaccuracies in RBF interpolation resulting from non-optimized shape of basis functions for the cases where data points (or nodes) are not distributed uniformly throughout the domain. Unlike conventional approaches which assume globally similar values of RBF shape parameters, the presented ASP technique suggests that shape parameter be calculated exclusively for each data point (or node) based on the distribution of data points within its own influence domain. This will ensure interpolation accuracy while still maintaining well conditioned system of equations for RBF weights. Performance and accuracy of ASP technique has been tested by evaluating derivatives and laplacian of a known function using RBF in Finite difference mode (RBFFD), with and without the use of adaptivity in shape parameters. Application of adaptive shape parameters (ASP) for solution of incompressible Navier Strokes equations has been presented by solving lid driven cavity flow problem on mesh-free domain using RBF-FD. The results have been compared for fixed and adaptive shape parameters. Improved accuracy has been achieved with the use of ASP in RBF-FD especially at regions where larger gradients of field variables exist.
Abstract: This paper examines the problem of designing a robust H∞ filter for a class of uncertain fuzzy descriptor systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain nonlinear descriptor systems to have an H∞ performance are derived. To alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities which are independent of the singular perturbation ε, when ε is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard uncertain nonlinear descriptor systems. A numerical example is provided to illustrate the design developed in this paper.
Abstract: The problem of incompressible steady flow simulation around an airfoil is discussed. For some simplest airfoils (circular, elliptical, Zhukovsky airfoils) the exact solution is known from complex analysis. It allows to compute the intensity of vortex layer which simulates the airfoil. Some modifications of the vortex element method are proposed and test computations are carried out. It-s shown that the these approaches are much more effective in comparison with the classical numerical scheme.
Abstract: Power system state estimation is the process of
calculating a reliable estimate of the power system state vector
composed of bus voltages' angles and magnitudes from telemetered
measurements on the system. This estimate of the state vector
provides the description of the system necessary for the operation
and security monitoring. Many methods are described in the
literature for solving the state estimation problem, the most important
of which are the classical weighted least squares method and the nondeterministic
genetic based method; however both showed
drawbacks. In this paper a modified version of the genetic
algorithm power system state estimation is introduced, Sensitivity of
the proposed algorithm to genetic operators is discussed, the
algorithm is applied to case studies and finally it is compared with
the classical weighted least squares method formulation.
Abstract: This paper presents a forgetting factor scheme for variable step-size affine projection algorithms (APA). The proposed scheme uses a forgetting processed input matrix as the projection matrix of pseudo-inverse to estimate system deviation. This method introduces temporal weights into the projection matrix, which is typically a better model of the real error's behavior than homogeneous temporal weights. The regularization overcomes the ill-conditioning introduced by both the forgetting process and the increasing size of the input matrix. This algorithm is tested by independent trials with coloured input signals and various parameter combinations. Results show that the proposed algorithm is superior in terms of convergence rate and misadjustment compared to existing algorithms. As a special case, a variable step size NLMS with forgetting factor is also presented in this paper.
Abstract: Particle Swarm Optimization (PSO) with elite PSO
parameters has been developed for power flow analysis under
practical constrained situations. Multiple solutions of the power flow
problem are useful in voltage stability assessment of power system.
A method of determination of multiple power flow solutions is
presented using a hybrid of Particle Swarm Optimization (PSO) and
local search technique. The unique and innovative learning factors of
the PSO algorithm are formulated depending upon the node power
mismatch values to be highly adaptive with the power flow problems.
The local search is applied on the pbest solution obtained by the PSO
algorithm in each iteration. The proposed algorithm performs reliably
and provides multiple solutions when applied on standard and illconditioned
systems. The test results show that the performances of
the proposed algorithm under critical conditions are better than the
conventional methods.
Abstract: Installation of power compensation equipment in
some cases places additional buses into the system. Therefore, a total
number of power flow equations and voltage unknowns increase due
to additional locations of installed devices. In this circumstance, power flow calculation is more complicated. It may result in a
computational convergence problem. This paper presents a power flow calculation by using Newton-Raphson iterative method together
with the proposed load transfer technique. This concept is to eliminate additional buses by transferring installed loads at the new buses to existing two adjacent buses. Thus, the total number of power
flow equations is not changed. The overall computational speed is
expectedly shorter than that of solving the problem without applying the load transfer technique. A 15-bus test system is employed for test
to evaluate the effectiveness of the proposed load transfer technique. As a result, the total number of iteration required and execution time
is significantly reduced.