Multiple Piecewise Research Articles

A general piecewise droop design method for DC microgrid

ABSTRACT Droop control is an essential component of primary control in hierarchical control paradigm of DC microgrid, which allows for current sharing among power converters without communication, and thus high reliability, plug-and-play (PnP) operation, system expandability and low cost can be achieved. However, the problem with basic droop control with constant coefficient is that higher current sharing accuracy will produce higher bus voltage deviation, and thus degrade power quality and efficiency of DC microgrid. Although secondary control can be applied to restore the bus voltage, the problem with droop control in primary level still exists. In this paper, the general idea of piecewise design of droop curves (GPD) is introduced and three piecewise droop strategies are derived for DC microgrids. Stability and sensitivity analyses of the control system are also carried out based on derived small-signal model of the DC microgrid. Finally, the comparison of the proposed GPD methods, the basic droop control and the nonlinear droop control for both step and ramping load conditions, the impact of multiple piecewise zones, and the influence of the sensing errors are all demonstrated by experimental results.

Time-varying H∞ filtering for discrete-time switched systems with admissible edge-dependent average dwell time

This paper addresses the [Formula: see text] filtering problem for a class of discrete-time switched systems by using an admissible edge-dependent average dwell time (AED-ADT) method. By means of a convex combination of positive definite matrices, a novel multiple piecewise convex Lyapunov function (MPCLF) is constructed, which can loosen the restrictions of Lyapunov function at switching points and interval interior points. Based on the MPCLF approach, sufficient conditions are established such that the filtering error system is globally uniformly exponentially stable (GUES) and a prescribed noise attenuation level in an [Formula: see text] sense is achieved. Moreover, the corresponding time-varying [Formula: see text] filters are given as well. Finally, the results of the simulation illustrate the feasibility and effectiveness of the proposed approaches.

Two Interpolation Methods Using Multiply-Rotated Piecewise Cubic Hermite Interpolating Polynomials

AbstractTwo interpolation methods are presented, both of which use multiple Piecewise Cubic Hermite Interpolating Polynomials (PCHIPs). The first method is based on performing 16 PCHIPs on 8 rotated versions of the plot of the data versus an independent variable (such as pressure or time). These 16 PCHIPs are then used to form 8 interpolations of the original data, and finally, these 8 are averaged. When the original data are unevenly spaced with respect to the independent variable, we show that it is best to perform the Multiply-Rotated PCHIP (MR-PCHIP) method using the “data index” as the independent variable, and then to subsequently perform one last PCHIP of the data index with respect to the original independent variable. This MR-PCHIP method avoids the flat spots that are a feature of the PCHIP method when the data have multiple values approximately equal to a local extreme value. The MR-PCHIP interpolated data have continuous first derivatives at the data points. This method also avoids the unrealistic overshoots that can occur when using the standard cubic spline interpolation procedure. The second interpolation method is designed specifically for hydrographic data with the aim of minimizing the formation of unrealistic water masses by the interpolation procedure. This is achieved by applying a Piecewise Cubic Hermite Interpolating Polynomial to each of 8 rotations of the salinity versus temperature plot (Multiply-Rotated Salinity–Temperature PCHIP, MRST-PCHIP) with bottle number (that is, data index) as the vertical interpolating coordinate, thereby making the MRST-PCHIP method independent of the heave of a water column. This method is equivalent to interpolating in the salinity–temperature diagram, and MRST-PCHIP proves very effective at avoiding the production of anomalous water masses that otherwise occur when interpolating temperature and salinity separately.

Genetic algorithm for solving transportation problems on networks with one source and multiple sinks

In this paper we propose a genetic algorithm for solving the nonlinear transportation problem on a network with multiple sinks and concave piecewise cost functions. We prove that the complexity of one iteration of the algorithm is O(n2) and the algorithm converges to a local optimum solution. We show that the algorithm can be used to solve large-scale problems and present the implementation and several testing examples of the algorithm using Wolfram Language.

New Results on Finite-Time Stability and Stabilization of Switched Positive Linear Time-Delay Systems

In this paper, the problems of finite-time stability and stabilization for switched positive linear time-delay systems under mode-dependent average dwell time (MDADT) are investigated. By proposing a novel multiple piecewise copositive Lyapunov-Krasovskii functional, new results on the sufficient conditions of finite-time stability are obtained. In order to solve the limitation of the multiple piecewise copositive Lyapunov-Krasovskii functional on designing controllers, a novel linear combinatorial copositive Lyapunov-Krasovskii functional is constructed, this provides a possibility for the numerical construction of the controller. Then by using state feedback controller, the finite-time stabilization is achieved. Finally, some simulation results are given to show the advantages of our methods.

Stabilization and L₂– Gain Performance of Periodic Piecewise Impulsive Linear Systems

This paper deals with the stability, stabilization and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - gain problem of periodic piecewise impulsive linear system. Firstly, by developing a new Lyapunov function called multiple piecewise time-varying Lyapunov function, a sufficient condition that guarantee the system λ* - exponentially stable is established. Moreover, a state-feedback controller is designed to stabilize the system. Then L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - gain analysis is investigated to obtain a result that guarantee the system λ* - exponentially stable and with L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> - gain performance. Finally, numerical simulation examples are provided to verify the effectiveness of the results proposed in this paper.

Research on the American Call Options on the Stocks Paying Multiple Dividends

Cassimon et al. (2007) propose a pricing formula of American call options under the multiple dividends by extending Roll (1977). However, because these studies investigate the option pricing formula under the escrow model, there is inconsistency for the assumption of the stock prices. This paper proposes pricing formulas of American call options under the multiple dividends and piecewise geometric Brownian motion. For the formulas, I approximate the log prices of ex-dividend dates to follow a multivariate normal distribution, and decompose the option price as a function of payoffs and exercise boundaries. Then, I obtain an upper bound of the American call options by substituting approximated log prices into the both of the payoffs and the exercise boundaries. Besides, I obtain a lower bound of the price by substituting approximated price only into the exercise boundaries. These upper and lower bounds are exact prices when the amounts of dividends are linear to the stock prices. According to the numerical study, the lower bound produces relatively small errors. Especially, it produces small errors when the dividends are more sensitive to the stock price changes.

Time-varying H∞ Control for Discrete-time Switched Systems with Admissible Edge-dependent Average Dwell Time

The problem of H∞ control for discrete-time switched systems is investigated via admissible edge-dependent average dwell time (AED-ADT) method in this paper. By virtue of a convex combination of positive definite matrices, a novel multiple piecewise convex Lyapunov function (MPCLF) is designed, which can relax the restricted conditions of Lyapunov functions at switching points and interval interior points. Based on the MPCLF approach, the time-varying H∞ state feedback controllers, guaranteeing that the corresponding closed-loop system is globally uniformly exponentially stable (GUES) with a prescribed H∞ performance, are established for the considered switched system. Finally, three numerical examples are provided to illustrate the effectiveness of the proposed approaches.

Association between hemoglobin levels and diabetic retinopathy risk in type 2 diabetes mellitus

Objective To investigate the independent association of the body mass index(BMI) with serum uric acid among shorter children and adolescent. Methods A cross-sectional study was conducted to collect general clinical data of 922 subjects with shorter statures. In each case, their information about height, weight, insulin-like growth factor-Ⅰ(IGF-Ⅰ), growth hormone peak, uric acid, and blood lipids were collected, and their BMI and BMI standard deviations score(SDS) were calculated. Smooth curve fitting and multiple piecewise linear regression were used to analyze the relationship between BMI SDS and uric acid. Results Univariate analysis found that serum uric acid was positively correlated with age, height standard deviation score, body weight standard deviation score, BMI SDS, IGF-Ⅰ standard deviation score, growth hormone peak, triglyceride, and creatinine(P<0.05), while negatively correlated with high-density lipoprotein-cholesterol(P<0.01). Female had significantly lower serum uric acid levels than male(P=0.003). The serum uric acid level was significantly increased after puberty(P<0.01). After adjusting for potential confounders, the smooth curve fitting revealed a U-shaped relationship between BMI SDS and uric acid, with a BMI SDS inflection point of -0.7. In the population of BMI SDS<-0.7, for every unit increase of BMI SDS, serum uric acid decreased by 11.78 μmol/L(P=0.030). In the population of BMI SDS≥-0.7, uric acid increased by 11.79 μmol/L(P<0.01) for every unit increase of BMI SDS. Conclusion Serum uric acid levels seem to be affected by BMI, and increased in population with thin or obesity. We should pay attention to the measurement of serum uric acid in both thin and obese children. Key words: Body mass index; Uric acid; Children and adolescents; Cross-sectional study

Improved stability results for discrete-time switched systems: A multiple piecewise convex Lyapunov function approach

In this paper, the stability problem is investigated for a class of discrete-time switched systems with unstable subsystems under the mode-dependent average dwell time (MDADT) switching. A multiple convex Lyapunov function (MCLF) and a multiple piecewise convex Lyapunov function (MPCLF) are firstly proposed, which are formulated in a convex combination form of positive definite matrices with quasi-time-dependent coefficients. It is pointed out in the paper that the multiple Lyapunov function (MLF) and the multiple discontinuous Lyapunov function (MDLF) can be regarded as special cases of the proposed MCLF and MPCLF, respectively. Then, the exponential stability conditions are derived by the new Lyapunov functions. Both slow switching and fast switching are exerted on stable modes and unstable modes, respectively. Finally, two numerical examples are given to demonstrate that larger stability regions and tighter MDADT bounds can be obtained by using our developed techniques compared with some recent results.

Calculation and Analysis of the Strands Short-Circuit in Stator Transposition Bar for Large Generators

The transposition of the stator bar is an important technique in the large generator design. Under the excitation of vibration and thermal effect, the insulation of strand is easily damaged, which leads to short-circuiting fault, and adversely impacts the generator’s secure operation. To better protect the generator, there is a need for detailed research of the characteristics of stator transposition bar under the strands short-circuit condition. In this paper, we proposed a 3D finite numerical method (FEM) for calculating the strand short-circuit current. In the proposed method, the whole model of stator transposition bar is divided into multiple piecewise segments, and each segment is coupled together by the circuit. Based on this method, the electromagnetic properties of the 308° stator transposition bar under the strands short-circuit fault condition are analyzed. Then, the properties of the strand short-circuit current is studied. Finally, the calculated results are compared with the measured data. The results show that the calculation of the strand short-circuit current with high precision and the strand short-circuit current jump is one of the characteristics of strands short-circuit fault in stator transposition bar.

Compander Design for OFDM PAPR Reduction Using Optimal Perturbation of Piecewise Linear Segments

In this paper, we develop an optimal perturbation approach to design companders to mitigate the peak-to-average power ratio problem experienced by orthogonal frequency division multiplexing (OFDM) signals. Specifically, we generalize single-linear component design approaches, which modify the Rayleigh-distributed OFDM signal amplitude tail, to use of multiple contiguous piecewise linear components. The new compander design approach defines and solves a constrained optimization problem to optimally perturb a given proposed multicomponent piecewise linear segment set to meet the power and probability density function constraints. The use of multiple piecewise linear components provides greater design flexibility to meet the constraints, thus providing solutions for pairs of inflection points and cutoff values where more rigidly designed companders fail to exist. We present examples of compander design, and demonstrate compander performance through numerical simulation. The new compander design approach can generate companders that offer performance improvements over current companders.

Student Mobility in Multilevel Growth Modeling: A Multiple Membership Piecewise Growth Model

ABSTRACT This study proposes a new model, termed the multiple membership piecewise growth model (MM-PGM), to handle individual mobility across clusters frequently encountered in longitudinal studies, especially in educational research wherein some students could attend multiple schools during the course of the study. A real data set containing some students who switched elementary schools was used to demonstrate and explain the MM-PGM. Parameter and model fit differences were compared between the MM-PGM and two other techniques for handling student mobility: the first school-PGM, which only used school membership at the first measurement occasion, and the delete-PGM, which removed mobile students from the analysis. Results indicated that the three approaches of handling mobile students led to different conclusions about the impact of school-level predictors of growth parameters and the school-level variability in the growth rates. Furthermore, deleting mobile students altered the impact of student-level predictors compared to the other two approaches.

Adaptive Compensation for Nonlinear Time-Varying Multiagent Systems With Actuator Failures and Unknown Control Directions.

This paper investigates a problem of designing an adaptive asymptotic cooperative control scheme for nonlinear time-varying multiagent systems, which can simultaneously tolerate unknown actuator failures and unknown control directions. To address such the problem, we propose a conditional inequality, which allows multiple piecewise Nussbaum functions to acquire the control robustness. Benefiting from this robustness, a part of failure uncertainties and system errors are compensated for, while the remaining parts are handled by adaptive control technique. Moreover, structural properties of the proposed adaptive laws are utilized so that Barbalat's lemma is applicable to make all the followers asymptotically converge to the leader based on the neighborhood information.

Iterative image segmentation with feature driven heuristic four-color labeling

Multilabel segmentation is an important research branch in image segmentation field. In our previous work, Multiphase Multiple Piecewise Constant and Geodesic Active Contour (MMPC-GAC) model was proposed, which can effectively describe multiple objects and background with intensity inhomogeneity. It can be approximately solved with Multiple Layer Graph (MLG) methods. To make the optimization more efficient and limit the approximate error, four-color labeling theorem was further introduced which can limit the MLG within three layers (representing four phases). However, the adopted random four-color labeling method usually provides chaotic color maps with obvious inhomogeneity for those semantic consistent regions. For this case, a new and alternative method named heuristic four-color labeling is proposed in this paper, which aims to generate more reasonable color maps with a global view of the whole image. And compared with the random four-color labeling strategy, the whole iterative algorithm based on our method usually produces better segmentations with faster convergence, particularly for images with clutters and complicated structures. This strategy is a good substitute for random coloring method when the latter produces unsatisfactory messy segmentation. Experiments conducted on public dataset demonstrate the effectiveness of the proposed method.

Hardware Implementation of Single Iterated Multiplicative Inverse Square Root

Inverse square root has played an important role in Cholesky decomposition, which devoted to hardware efficient compressed sensing. However, the performance is usually limited by the trade-off between throughput and precision. This paper presents hardware implementation of fixed-point single iterated multiplicative inverse square root. Multiple piecewise linear approximation in softly nonlinear range is used to compute the initial value. Single iterated Newton-Raphson method is employed to obtain high precision. Multiple constants multiplication technique is proposed to achieve high throughput. The combination of these techniques yields high performance in terms of throughput and precision. It obtains more than 70 % of throughput improvement and almost 100 × higher precision over the inverse square root Intellectual Property (IP) from Altera. In addition, Cholesky decomposition has been presented to validate the proposed architecture, which shows that 42 % of throughput improvement is achieved compared with the IP.DOI: http://dx.doi.org/10.5755/j01.eie.23.4.18717

Optimal illusion and invisibility of multilayered anisotropic cylinders and spheres.

In this paper, full-wave electromagnetic scattering theory is employed to investigate illusion and invisibility of inhomogeneous anisotropic cylinders and spheres. With the use of a shell designed according to Mie series theory for multiple piecewise anisotropic layers, radar cross section (RCS) of the coated inhomogeneous anisotropic object can be dramatically reduced or disguised as another object in the long-wavelength limit. With the suitable adjustment of the anisotropy parameters of the shell, optimal illusion and invisibility characteristics of the coated inhomogeneous anisotropic object can be achieved. Details of theoretical analysis and numerical examples are presented to validate the proposed methodology.

Robust sensor fault detection and isolation of gas turbine engines subjected to time-varying parameter uncertainties

In this paper, a novel robust sensor fault detection and isolation (FDI) strategy using the multiple model-based (MM) approach is proposed that remains robust with respect to both time-varying parameter uncertainties and process and measurement noise in all the channels. The scheme is composed of robust Kalman filters (RKF) that are constructed for multiple piecewise linear (PWL) models that are constructed at various operating points of an uncertain nonlinear system. The parameter uncertainty is modeled by using a time-varying norm bounded admissible structure that affects all the PWL state space matrices. The robust Kalman filter gain matrices are designed by solving two algebraic Riccati equations (AREs) that are expressed as two linear matrix inequality (LMI) feasibility conditions. The proposed multiple RKF-based FDI scheme is simulated for a single spool gas turbine engine to diagnose various sensor faults despite the presence of parameter uncertainties, process and measurement noise. Our comparative studies confirm the superiority of our proposed FDI method when compared to the methods that are available in the literature.

Adaptive extended piecewise histogram equalisation for dark image enhancement

Histogram equalisation has been widely used for image enhancement because of its simple implementation and satisfactory performance. However, traditional histogram equalisation uniformly redistributes an entire histogram or multiple piecewise histograms with the same equalisation strategy, which may produce unnatural artefacts, over-enhancement or under-enhancement in wide dynamic range dark image enhancement. This study proposes an adaptive extended piecewise histogram equalisation algorithm (AEPHE) for dark image enhancement. First, an original histogram is divided into a group of extended piecewise histograms. Then, an adaptive histogram equalisation, which balances intensity preservation and contrast boosting, is further developed and respectively applied to these extended piecewise histograms. The final histogram for image enhancement is produced by a weighted fusion of these equalised histograms. The experimental results indicate that AEPHE is superior to multiple state-of-the-art algorithms.

Reduction of dissipation in Lagrange cell-centered hydrodynamics (CCH) through corner gradient reconstruction (CGR)

This work presents an extension of a second order cell-centered hydrodynamics scheme on unstructured polyhedral cells [13] toward higher order. The goal is to reduce dissipation, especially for smooth flows. This is accomplished by multiple piecewise linear reconstructions of conserved quantities within the cell. The reconstruction is based upon gradients that are calculated at the nodes, a procedure that avoids the least-square solution of a large equation set for polynomial coefficients. Conservation and monotonicity are guaranteed by adjusting the gradients within each cell corner. Results are presented for a wide variety of test problems involving smooth and shock-dominated flows, fluids and solids, 2D and 3D configurations, as well as Lagrange, Eulerian, and ALE methods.