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Power flow is an extensively used tool in various operations and planning of power systems. In this paper, we propose an efficient hybrid method for solving the power flow problems in ill-conditioned power systems. This method is implemented in a framework of two-part alternating iteration. In Part I of this method, PV bus voltages are regarded as constant and PQ bus voltages are updated by the Z-bus Gauss method. In Part II of this method, PQ bus loads are equivalent to dynamic admittances, and PV bus voltage angles are updated by Newton’s method. The values of PQ bus voltage magnitudes and PV bus voltage angles are passed between Part I and Part II. The proposed method is validated in well- and ill-conditioned systems and compared with several well-known power flow methods. Results show that the proposed method is robust and efficient to address the issues related with large-scale ill-conditioned power systems and it is not significantly affected by the considered initial guess.

Besides censoring, multicollinearity and outliers are two common problem in regression analysis. In this paper we propose a family of robust ridge estimators for the censored semiparametric regression models. The proposed robust estimators is based on least trimmed squares (LTS) method. This method is insensitive to corruption due to outliers, provided that the outliers constitute less than 50 % of the set, in other words, LTS is a robust estimator with a 50 % breakdown point. The FAST-LTS algorithm is developed for the computation of the estimators. Furthermore, a robust method for the estimate of shrinkage parameters is suggested. Monté-Carlo simulation study demonstrates the merit of the new method in the aspect of solving the multicollinearity and sensitivity to outliers over the ordinary least squares estimation. Finally, an example of real data is given for illustration. [ABSTRACT FROM AUTHOR]

• The purpose of this article is to study a power flow algorithm with strong convergence, initial value adaptability, and efficiency. • This paper proposes a two-part alternating iterative framework based on dynamic equivalent admittance. • The proposed algorithm has universality for well-and ill-conditioned systems. • The proposed method combines the convergence characteristics of the Z-bus Gauss method and Newton's method, so it is easy to implement based on existing program codes. Power flow is an extensively used tool in various operations and planning of power systems. In this paper, we propose an efficient hybrid method for solving the power flow problems in ill-conditioned power systems. This method is implemented in a framework of two-part alternating iteration. In Part I of this method, PV bus voltages are regarded as constant and PQ bus voltages are updated by the Z-bus Gauss method. In Part II of this method, PQ bus loads are equivalent to dynamic admittances, and PV bus voltage angles are updated by Newton's method. The values of PQ bus voltage magnitudes and PV bus voltage angles are passed between Part I and Part II. The proposed method is validated in well- and ill-conditioned systems and compared with several well-known power flow methods. Results show that the proposed method is robust and efficient to address the issues related with large-scale ill-conditioned power systems and it is not significantly affected by the considered initial guess. [ABSTRACT FROM AUTHOR]

It is not unusual to have outliers and multicollinearity simultaneously in censored semiparametric linear models. In this paper for dealing with multicollinearity and outliers we introduce a family of robust censored Liu and non-Liu type of estimates for the regression parameter when some non-stochastic linear restrictions are imposed. The proposed robust estimators is based on least trimmed squares (LTS) method. The efficiency of LTS estimator statistically is more than the well-known least median squares (LMS) estimator. Unfortunately the computational complexity of LTS is less well understood than that of LMS in which the objective is to minimize the median squared residual. Here, we provide the robust estimators for linear and non-linear parts of the censored model based on robust shrinkage Liu estimators. The performance of proposed estimators compared to ordinary estimators numerically is evaluated by Monte Carlo simulation studies. We further illustrate the our procedures by an application. [ABSTRACT FROM AUTHOR]

The fact that both the Lorenz 1963 and 1969 models suggest finite predictability is well known. However, less well known is the fact that the mechanisms (i.e., sensitivities) within both models, which lead to finite predictability, are different. Additionally, the mathematical and physical relationship between these two models has not been fully documented. New analyses, along with a literature review, are performed here to provide insights regarding similarities and differences for these two models. The models represent different physical systems, one for convection and the other for barotropic vorticity. From the perspective of mathematical complexities, the Lorenz 1963 (L63) model is limited-scale and nonlinear; and the Lorenz 1969 (L69) model is closure-based, physically multiscale, mathematically linear, and numerically ill-conditioned. The former possesses a sensitive dependence of solutions on initial conditions, known as the butterfly effect, and the latter contains numerical sensitivities due to an ill-conditioned matrix with a large condition number (i.e., a large variance of growth rates). Here, we illustrate that the existence of a saddle point at the origin is a common feature that produces instability in both systems. Within the chaotic regime of the L63 nonlinear model, unstable growth is constrained by nonlinearity, as well as dissipation, yielding time varying growth rates along an orbit, and, thus, a dependence of (finite) predictability on initial conditions. Within the L69 linear model, multiple unstable modes at various growth rates appear, and the growth of a specific unstable mode (i.e., the most unstable mode during a finite time interval) is constrained by imposing a saturation assumption, thereby yielding a time varying system growth rate. Both models were interchangeably applied for qualitatively revealing the nature of finite predictability in weather and climate. However, only single type solutions were examined (i.e., chaotic and linearly unstable solutions for the L63 and L69 models, respectively), and the L69 system is ill-conditioned and easily captures numerical instability. Thus, an estimate of the predictability limit using either of the above models, with or without additional assumptions (e.g., saturation), should be interpreted with caution and should not be generalized as an upper limit for atmospheric predictability. [ABSTRACT FROM AUTHOR]

To satisfy the robust and real-time requirements of power flow calculation for large-scale power systems, a globally convergent method is proposed with trust-region techniques, which shows satisfying robustness and convergence. Then, this method is combined with Newton's method to achieve a two-stage algorithm, benefiting from their different advantages. In the first stage, the proposed globally convergent method is used for searching power flow solution. When the values of state variables in a certain iteration are close enough to the real operational point, the algorithm enters the second stage to use Newton's method to achieve the solution. This two-stage algorithm can achieve an accurate solution for solvable cases, and can also achieve a least-square solution, which is an approximate solution for unsolvable cases. Numerical experiments show that the proposed globally convergent method and two-stage algorithm have better robustness and efficiency than the existing methods in previous research. They have universality for well- and ill-conditioned systems as well as the cases under ill-conditioned operational modes, heavy loads and inappropriate initial values. They can also handle different limit violations, such as reactive power limit in PV buses and voltage limit with tap changers action, which could significantly benefit real practice. [ABSTRACT FROM AUTHOR]

Abstract The g -function model is nowadays the most popular approach for the modeling of the thermal response of geothermal heat exchangers. By assuming the mean azimuthal borehole wall temperature to be uniform along the boreholes, it achieves a convenient uncoupling of the heat transfer problem in the borehole and its surroundings from the heat conduction problem in the ground, which significantly reduces the computational cost. This assumption, however, renders the g -function model ill-posed when the buried depth D of the boreholes is zero. This issue has passed unreported for the last 30 years, most probably due to the need of numerical discretizations with extremely fine meshes to observe the divergent behavior of the problem. In the present work a mathematical explanation for this ill-posedness is given. Also the well-posedness for all values of D of the alternative definition for the g -function model found in the literature is shown. [ABSTRACT FROM AUTHOR]

We consider the ridge and restricted ridge estimation in semiparametric linear models when the covariates are measured with errors and the covariance matrix of the parameters is ill conditioned. The estimators are compared and the dominance conditions as well as the regions of optimality of the proposed estimators are determined based on quadratic risks. A simulation studies are conducted to illustrate the finite sample performance of the proposed procedures. [ABSTRACT FROM AUTHOR]

The trust-region subproblem (TRS) minimizes a quadratic f(s) = sTHs=2 + sTg over the ellipsoidal constraint ||s||M ≤ Δ for a symmetric and positive definite matrix M. For a large scale TRS, a Lanczos-type approach, namely, the generalized Lanczos trust-region (GLTR) method was introduced by Gould, Lucidi, Roma, and Toint [SIAM J. Optim., 9 (1999), pp. 504{525], and extends nicely the classical Lanczos method for the eigenvalue problem to TRS. Basically, GLTR attempts to obtain a feasible approximation in the Krylov subspace Kk(M-1H,M-1g) is usually modest for a well-conditioned TRS, but can be large for ill-conditioned problems. This causes numerical difficulties in the computational costs, memory requirements, and numerical stability. This paper introduces an efficient nested restarting strategy for GLTR and resolves these numerical troubles. Convergence analysis and numerical testings are carried out to support our improvements upon GLTR. [ABSTRACT FROM AUTHOR]

The saddle-point system is considered, where A is an m × n matrix with full column rank, B is an m × m symmetric and positive definite matrix, and b is an mvector. When the perturbed systems are still saddle-point systems, perturbation theory is presented under three cases, such as the case of A and b perturbed, the case of B and b perturbed, and the case of A, B and b perturbed.We find that the bounds for the errors of the solution depend on A and B. To remove their influence, some conditions are disposed. To improve the accuracy of the solution, a scaling is given. When the perturbed systems are generalized saddle-point systems, the block LDLT factorization is applied. Thus the sensitivity of the block LDLT factorization should be discussed, then perturbation theorems for this case are presented. [ABSTRACT FROM AUTHOR]

An accurate numerical method is established for matrix inversion. It is shown theoretically that the scheme possesses the high order of convergence of seven. Subsequently, the method is taken into account for solving linear systems of equations. The accuracy of the contributed iterative method is clarified on solving numerical examples when the coefficient matrices are ill-conditioned. All of the computations are performed on a PC using several programs written in Mathematica 7.

Kalman filter is one of the most common ways to deal with dynamic data and has been widely used in project fields. However, the accuracy of Kalman filter for discrete dynamic system is poor when the observation matrix is ill-conditioned. Therefore, the method for overcoming the harmful effect caused by ill-conditioned observation matrix in discrete dynamic system is studied in this paper.The causes of the ill-conditioned observation matrix and its effect on Kalman filter are analyzed. Biased Kalman filter and its algorithm are proposed by combining the biased estimation and Kalman filter in the sense of mean square error (MSE). The methods of choosing biased parameter in the new algorithm is proposed. By separately exerting some disturbance on the observation matrix and observation vector, two simulations are carried out. The experimental results show that the traditional Kalman filter is inaccurate when the observation matrix is ill-conditioned, and the biased Kalman filter is more accurate than the traditional one in terms of MSE. [ABSTRACT FROM AUTHOR]

Distance-related errors complicate the resolution of real-time ambiguity in medium–long baseline marine surveys. Therefore, detection and recovery of cycle slips in real time is required to ensure high accuracy of global navigation satellite system positioning and navigation in marine surveys. To resolve this, an improved method was presented, where linear combinations of the triple-differenced (TD) between carriers L1and L2were formed for a wide lane and free ionosphere. To overcome severe ill-conditioned problems of the normal equation, the Tikhonov regularization method was used. The construction of a regularized matrix by combining a priori information of known coordinates of reference stations, followed by the determination of the corresponding regularized parameter are suggested. A float solution was calculated for the TD ambiguity. The search cycle slip (TD integer ambiguity) was obtained using the least-squares ambiguity decorrelation adjustment (LAMBDA) method. Using our method, cycle slips of several reference station baselines with lengths of a few hundred to one thousand kilometers were detected in real time. The results were consistent with professional software, with a success rate of 100%. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inverse problem of determining the unknown temperature at x = 0 and section of initial condition at t = 0 in an inverse heat conduction problem (IHCP). Two new numerical methods are developed by using the solution of an auxiliary problem and heat polynomials as basis functions in presence of noisy data. Due to ill-posed IHCP, we use the Tikhonov regularization technique with the GCV scheme to solve the resulting matrix system of the basis function methods (BFM). Some numerical examples are presented to illustrate the strength of the methods. [ABSTRACT FROM AUTHOR]

In this paper, the numerical solutions for groundwater flow in unsaturated layered soil using the Richards equation are presented. A linearisation process for the nonlinear Richards equation to deal with groundwater flow in unsaturated layered soil is derived. To solve one-dimensional flow in the unsaturated zone of layered soil profiles, flux conservation and the continuity of pressure potential at the interface between two consecutive layers are considered in the numerical model. In addition, a novel method, named the dynamical Jacobian-inverse free method, incorporated with a two-side equilibration algorithm for solving ill-conditioned systems with extreme contrasts in hydraulic conductivity is proposed. The validity of the model is established in numerous test problems by comparing the numerical results with the analytical solutions. The results show that the proposed method can improve convergence and numerical stability for solving groundwater flow in unsaturated layered soil with extreme contrasts in hydraulic conductivity. [ABSTRACT FROM AUTHOR]

• Different variations of the Gauss Seidel and the Implicit Z load flow algorithms are presented. • The proposed methods are applicable to radial, weakly and fully meshed distribution networks. • A linearized (non-iterative) of the method is also presented. • A variation of the convergence criteria is also analysed and proposed. The primary and secondary distribution grids are typically designed separately and operated with a radial configuration; therefore, specialized load flow methods only applicable to radial or weakly meshed networks are normally used. However, projections indicate that the distribution grids will be more interconnected in the future, mainly because of the inclusion of distributed generation, voltage and reliability optimization, as well as an efficiency improvement when the primary and secondary networks are considered in an integrated way. For this new meshed grids scenario, the efficient and precise typically used load flow methods for distribution networks are no longer applicable and it becomes necessary using load flow algorithms that are also applicable for meshed configurations, such as the ones classically used for transmission networks like the Newton-Raphson, Gauss-Seidel and Gauss Implicit Z-bus methods, while also procuring to avoid potential singularity problems which may arise when dealing with long radial grids. In this work, variations of the Gauss-Seidel and Gauss Implicit Z-bus methods are presented, that are adequate for low and medium voltage grids regardless of the network configuration. Additionally, a linear, direct, and non-iterative load flow variation is presented as well as a comparison between different possible convergence criteria for the classical methods. [ABSTRACT FROM AUTHOR]

In order to avoid the bad effect provided by the biases of the biased estimation, bias-corrected regularization is presented. But how to choose the bias-corrected term is a key link. In this paper,based on the key information from the multicollinearity diagnosis, measurement and test, parameters seriously harmed by the multicollinearity are estimated. Then based on the bias-corrected theory,the analytical condition of the bias-corrected regularization is derived. Truncation ridge estimation based on the bias-corrected theory by multicollinearity diagnosis is proposed. The numerical results demonstrate that the new method can improve the numerical stability and accuracy of parameter estimation. [ABSTRACT FROM AUTHOR]

The occurring mechanism of the ill-conditioned system due to degenerate scale in the direct boundary element method (BEM) and the indirect BEM is analytically examined by using degenerate kernels. Five regularization techniques to ensure the unique solution, namely hypersingular formulation, method of adding a rigid body mode, rank promotion by adding the boundary flux equilibrium (direct BEM), CHEEF method and the Fichera's method (indirect BEM), are analytically studied and numerically implemented. In this paper, we examine the sufficient and necessary condition of boundary integral formulation for the uniqueness solution of 2D Laplace problem subject to the Dirichlet boundary condition. Both analytical study and BEM implementation are addressed. For the analytical study, we employ the degenerate kernel in the polar and elliptic coordinates to derive the unique solution by using five regularization techniques for any size of circle and ellipse, respectively. Full rank of the influence matrix in the BEM using Fichera's method for both ordinary scale and degenerate scale is also analytically proved. In numerical implementation, the BEM programme developed by NTOU/MSV group is employed to see the validity of the above formulation. Finally, the circular and elliptic cases are numerically demonstrated by using five regularization techniques. Besides, a general shape of a regular triangle is numerically implemented to check the uniqueness solution of BEM. [ABSTRACT FROM AUTHOR]

A novel optimal scale polynomial interpolation method (OSPIM) is proposed to attack the Duffing oscillator. This method is based on the ideas of multi-scaling and equilibrated matrix, such that the condition number of the coefficient matrix of the polynomial interpolation is minimized. The OSPIM can eliminate the Runge phenomenon, which occurs in the conventional polynomial interpolation, and is well suited for solving nonlinear oscillatory systems. In addition, we further alleviate the ill-posedness of polynomial interpolation by proposing a half-order technique, with which one can use a $$m$$ -order polynomial to interpolate as many as $$2m+1$$ points. We then employ the half-order OSPIM, i.e., OSPIM(H), as a trial function in conjunction with the simple point-collocation method, to solve the nonlinear Duffing equation. Moreover, the differential transformation method is used for the first time to solve a forced Duffing oscillator to compare with the present method. Finally, illustrative examples verify the accuracy and efficiency of the present method. [ABSTRACT FROM AUTHOR]

An accurate numerical method is established for matrix inversion. It is shown theoretically that the scheme possesses the high order of convergence of seven. Subsequently, the method is taken into account for solving linear systems of equations. The accuracy of the contributed iterative method is clarified on solving numerical examples when the coefficient matrices are ill-conditioned. All of the computations are performed on a PC using several programs written in. Mathematica 7 [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a boundary-type meshfree algorithm is proposed to accurately and stably deal with the two-dimensional inverse Stokes problems, which are highly ill-conditioned. Based on the Laplacian decomposition, the Stokes equations are recast as three Laplace equations. Then the modified collocation Trefftz method (MCTM), one of the most promising boundary-type meshless methods, is adopted to solve these three Laplace equations. The MCTM can stabilize the numerical scheme and obtain highly accurate results by utilizing the characteristic length. Accordingly, the numerical solutions of these three Laplace equations are expressed by linear combination of the modified T-complete functions. The unknown coefficients in the solution expressions are found by enforcing the satisfactions of the boundary conditions at the boundary collocation points. Three numerical examples are provided to show the efficacy and stability of the proposed meshless method. Besides, noises are added into the boundary conditions to demonstrate the stability of the proposed scheme for dealing with the inverse Stokes problems. [Copyright &y& Elsevier]

Ionospheric tomography inverse algorithms are usually an ill-conditioned problem because the geometric distribution of continuously operating reference GPS stations is not ideal for this task. In order to cope with such ill-conditioning, a new tomographic algorithm, termed two-step algorithm (TSA), is presented. The electron density is estimated in two steps: Phillips smoothing method (PSM) is first used to resolve the ill-conditioned problem in the ionospheric tomography system, and then, the PSM solution is input as an initial value to the multiplicative algebraic reconstruction technique (MART) and iteratively improved. Numerical simulations using the International Reference Ionosphere 2007 model demonstrate that the TSA is applicable to GPS-based ionospheric tomography reconstruction and is superior to PSM and MART when these techniques are used alone. The new algorithm is applied to reconstruct the ionospheric electron density distribution over China using GPS observations, and a comparison with ionosonde observations is made. [ABSTRACT FROM AUTHOR]

Abstract: The output of many instruments can be modeled as a convolution of an impulse response and a series of sharp spikes. Deconvolution considers the inverse problem: estimate the input spike train from an observed (noisy) output signal. We approach this task as a linear inverse problem, solved using penalized regression. We propose the use of an L 0 penalty and compare it with the more common L 2 and L 1 penalties. In all cases a simple and iterative weighted regression procedure can be used. The model is extended with a smooth component to handle drifting baselines. Application to three different data sets shows excellent results. [Copyright &y& Elsevier]

In this paper, a new iterative refinement of the solution of an ill-conditioned linear system of equations are given. The convergence properties of the method are studied. Some numerical experiments of the method are given and compared with that of two of the available methods. [ABSTRACT FROM AUTHOR]

The inverse problem of the initial condition about the boundary value of the chord vibration equation is ill-posed. First, we transform it into a Fredholm integral equation. Second, we discretize it by the trapezoidal formula method, and then obtain a severely ill-conditioned linear equation, which is sensitive to the disturbance of the data. In addition, the tiny error of right data causes the huge concussion of the solution. We cannot obtain good results by the traditional method. In this paper, we solve this problem by the Tikhonov regularization method, and the numerical simulations demonstrate that this method is feasible and effective. [ABSTRACT FROM AUTHOR]

Volokh and Vilnay [Appl. Math. Lett. 13 (2000), pp. 119-124] proposed a method for computing an accurate solution of nearly singular linear systems of equations. The method is processed in two stages. Their method uses the truncated singular value decomposition of the initial coefficient matrix at the first stage and the Gaussian elimination procedure for well-conditioned reduced system of linear equations at the second stage. In this note, we propose a multistage approach based on the Volokh and Vilnay's method. Some numerical results are given to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A model is developed using a thermal network analysis approach. An experimental setup is designed and built to validate the model. The model is based on an inverse thermal network analysis using a singular value decomposition algorithm. The data from the experiments are used to determine the thermal conductances using inverse model's unsteady- and steady-state forms. The model development and experimental results are presented together with possible sources of error and how to avoid or decrease their influence. Good agreement between the thermal network model predictions and experiments was found. [ABSTRACT FROM AUTHOR]

Abstract: A method based on modal superposition and regularisation technique is developed to identify moving loads on an elastically supported multi-span continuous bridge deck. The effects of different influencing parameters, such as the measuring noise, sampling rate, vertical and rotational stiffness and the travelling velocity of the moving loads, are studied. Numerical simulations show that the method can identify accurately the moving loads on the bridge supported by elastic bearings using different types of measured responses. The stiffness of the bearing should be large relative to the stiffness of the bridge deck. Measured acceleration gives better results than those from strains, and the number of vibration modes used in the identification should exceed the highest frequency of the excitation forces for an accurate identification. [Copyright &y& Elsevier]

Abstract: The three-dimensional location of a body-fixed axis system is described by position and orientation parameters that can be calculated knowing local and global coordinates of three or more body-fixed markers. However, marker distribution can become ill-conditioned when marker placement is symmetrical with respect to the mean of the markers. As symmetry and ill-conditioning increases, random errors in marker locations can affect the stability of orientation parameters as a result of the mathematical approach adopted. The present study investigates the methods of Veldpaus et al. [1988; Journal of Biomechanics 21, 45], Challis [1995; Biomechanics 28, 733] and Andriacchi et al. [1998; Journal of Biomedical Engineering 120, 743] for obtaining segment orientation parameters when segment markers ranged from well-defined to highly ill-conditioned depending on the symmetry of segment markers. A novel fourth approach is also presented that enabled comparisons of the root mean square error of reconstructed marker coordinates to verify that an optimal solution was obtained. No single method produced optimal results for all axis orientation parameters when reconstructing movement trials. The best performed was the method of Veldpaus et al. [1988; Journal of Biomechanics 21, 45] based on consistent results and ease of implementation. The fourth approach presented provided a reliable method in all but the highly ill-conditioned markers, however implementation was computationally difficult. The method of Challis [1995; Biomechanics 28, 733] was only suited to well-conditioned marker sets which avoided markers lying in a single plane with symmetries in marker distribution relative to the mean. The method of Andriacchi et al. [1998; Journal of Biomedical Engineering 120, 743] produced, at best, orientation parameters that approximated the results obtained by least squares methods. [Copyright &y& Elsevier]

Abstract: The ill-conditioned subproblems appeared in constrained optimization can often impede the preformance of optimization algorithms. In this paper we introduce a class of efficient iterative semi-refinement technique to solve the ill-conditioned trust-region subproblems. The nonmonotone technique is also used to increase the efficiency of the algorithm. The numerical results show that the presented method is competitive. [Copyright &y& Elsevier]

The algorithm of Mathias and Stewart is examined as a tool for constructing regularized solutions to rank-deficient and ill-posed linear equations. The algorithm is based on a sequence of QR factorizations. If it is stopped after the first step, it produces the same solution as the complete orthogonal decomposition used in LAPACK's xGELSY. However, we show that for low-rank problems a careful implementation can lead to an order of magnitude improvement in speed over xGELSY as implemented in LAPACK. We prove, under assumptions similar to assumptions used by others, that if the numerical rank is chosen at a gap in the singular value spectrum and if the initial factorization is rank-revealing, then, even if the algorithm is stopped after the first step, approximately half the time its solutions are closer to the desired solution than are the singular value decomposition (SVD) solutions. Conversely, the SVD will be closer approximately half the time, and in this case overall the two algorithms are very similar in accuracy. We confirm this with numerical experiments. Although the algorithm works best for problems with a gap in the singular value spectrum, numerical experiments suggest that it may work well for problems with no gap. [ABSTRACT FROM AUTHOR]

Estimation of the frequency and spatial dependent boundary traction vector from measured vibration responses in a vibrating structure is addressed. This problem, also referred to as the inverse problem, may in some circumstances be ill-conditioned. Here a technique to overcome the ill-conditioning is proposed. A subset of a set of available eigenmodes is chosen such that the problem becomes well-conditioned enough. It is shown that the ill-conditioning originates from the fact that not all eigenmodes are orthogonal over the surface where the traction vector is sought. Consequently, by choosing a set of eigenmodes orthogonal over the surface of interest, the problem becomes well-conditioned. The calculated traction vector is shown to converge to the true one in the sense of a L2-norm on the boundary of the body. The proposed technique is verified, using numerical simulation of measured responses, with good agreement. [ABSTRACT FROM AUTHOR]

A minimization theory, which is based on the Hilbert space theory, is proposed and applied to two-dimensional cavity flow past a strut with the assumption of potential flow. That is, the minimization of the cavity drag of the strut on the cavity flow is studied with the help of the optimization theory proposed. To accelerate the optimization process, the Euler beam theory is introduced to generate a small variation in the strut. The introduction of the Euler beam theory makes the mathematical formulation for the present theory ill-conditioned. To overcome this condition, the Tikhonov regularization and the Morozov's discrepancy principle are used to regularize the present optimal theory. From the numerical study, it is shown that the proposed minimization theory is able to find an optimized shape for the given strut and corresponding optimized cavity drag. [ABSTRACT FROM AUTHOR]

We derive a stable technique, based upon matrix pencils, for the reconstruction of (or approximation by) polygonal shapes from moments. We point out that this problem can be considered the dual of 2 — D numerical quadrature over polygonal domains. An analysis of the sensitivity of the problem is presented along with some numerical examples illustrating the relevant points. Finally, an application to the problem of gravimetry is explored where the shape of a gravitationally anomalous region is to be recovered from measurements of its exterior gravitational field. [ABSTRACT FROM AUTHOR]

The paper discusses, from a process control perspective, different approaches to performance weight selection when using H-infinity objectives. Approach A considers direct bounds on important transfer functions such as sensitivity and complementary sensitivity. Approach B considers the output response to sinusoidal disturbances, setpoints and noise. We also give some insight into the practical use of H-infinity and μ methods. μ is the structured singular value (SSV) introduced by Doyle (1982). μ-synthesis is generally not a convex optimisation problem and is presently not straightforward. We will discuss some of the problems we have encountered. [ABSTRACT FROM PUBLISHER]

Summary: In this paper, several methods are proposed to find the load flow (LF) solution of large‐scale ill‐conditioned systems. These methods are based on the Adams‐Bashforth formulation. With the use of the proposed methods, the convergence problems of the most popular LF methods are addressed especially when the flat initial guess point is considered. The proposed methods are validated using three ill‐conditioned systems: the modified IEEE 300‐bus system, the 3375‐bus Polish system, and a 13 659‐bus portion of the European transmission system. The obtained results prove that the proposed methods constitute a family of robust and efficient methods for the LF problem. [ABSTRACT FROM AUTHOR]