Linear Approximation Technique Research Articles

Sensor Actor Network Modeling utilizing the Holonic Architectural Framework

Sensor Actor Network Modeling utilizing the Holonic Architectural FrameworkThis paper discusses the results of utilizing advanced EKM modeling techniques to manage Sensor-Actor networks (SANETs) based upon the Holonic Architectural Framework. EKMs allow a quantitative analysis of an algorithmic artificial neural network process by using an indirect-mapping EKM to self-organize from a given input space to administer SANET routing and clustering functions with a control parameter space. Results demonstrate that in comparison to linear approximation techniques, indirect mapping with EKMs provide fluid control and feedback mechanisms by operating in a continuous sensory control space - thus enabling interactive detection and optimization of events in real-time environments.

An Empirical Model for Probability of Packet Reception in Vehicular Ad Hoc Networks

Today's advanced simulators facilitate thorough studies on VANETs but are hampered by the computational effort required to consider all of the important influencing factors. In particular, large-scale simulations involving thousands of communicating vehicles cannot be served in reasonable simulation times with typical network simulation frameworks. A solution to this challenge might be found in hybrid simulations that encapsulate parts of a discrete-event simulation in an analytical model while maintaining the simulation's credibility. In this paper, we introduce a hybrid simulation model that analytically represents the probability of packet reception in an IEEE 802.11p network based on four inputs: the distance between sender and receiver, transmission power, transmission rate, and vehicular traffic density. We also describe the process of building our model which utilizes a large set of simulation traces and is based on general linear least squares approximation techniques. The model is then validated via the comparison of simulation results with the model output. In addition, we present a transmission power control problem in order to show the model's suitability for solving parameter optimization problems, which are of fundamental importance to VANETs.

Approximation Schemes for Functional Optimization Problems

Approximation schemes for functional optimization problems with admissible solutions dependent on a large number d of variables are investigated. Suboptimal solutions are considered, expressed as linear combinations of n-tuples from a basis set of simple computational units with adjustable parameters. Different choices of basis sets are compared, which allow one to obtain suboptimal solutions using a number n of basis functions that does not grow "fast" with the number d of variables in the admissible decision functions for a fixed desired accuracy. In these cases, one mitigates the "curse of dimensionality," which often makes unfeasible traditional linear approximation techniques for functional optimization problems, when admissible solutions depend on a large number d of variables.

Modified piecewise linear current density recursive convolution finite-difference time-domain method for anisotropic magnetised plasmas

A modified piecewise linear current density recursive convolution (PLCDRC) finite-difference time-domain (FDTD) for anisotropic magnetised plasma is proposed. The method is derived using two recursive conclusion. The electric field is time-shifted in the first convolution and the current density is time-shifted in the second convolution. The computation of the current density and the electric field employ the piecewise linear approximation technique. Like PLCDRC FDTD, the method has more accuracy over CDRC FDTD. Moreover, it is faster in computation velocity than PLCDRC FDTD. The high efficiency and accuracy of the method are confirmed by computing the reflection and transmission through a magnetised plasma layer, with the direction of propagation parallel to the direction of the biasing field. The bistatic radar cross-section of conducting sphere covered with magnetised plasma is also calculated. Then, the numerical dispersion relation of the new PLCDRC FDTD scheme is derived. The numerical dispersion error and dissipation error caused by the new PLCDRC-FDTD method are investigated by comparing the real and imaginary parts of the numerical wave number with those of the analytical wave number. Finally, the stability of the new PLCDRC-FDTD method is discussed. This method can also be used in other frequency dispersion electromagnetic problem if it is modified slightly.

Seat Allocation Problem in Multiple Flight-legs Using Linear Approximation Technique

Seat Allocation Problem in Multiple Flight-legs Using Linear Approximation Technique

Local Linear Regression in Proportional Hazards Model with Censored Data

In this article we study the method of nonparametric regression based on a transformation model, under which an unknown transformation of the survival time is nonlinearly, even more, nonparametrically, related to the covariates with various error distributions, which are parametrically specified with unknown parameters. Local linear approximations and locally weighted least squares are applied to obtain estimators for the effects of covariates with censored observations. We show that the estimators are consistent and asymptotically normal. This transformation model, coupled with local linear approximation techniques, provides many alternatives to the more general proportional hazards models with nonparametric covariates.

Crucial properties of the moment closure model FENE-QE

We investigate four crucial properties for testing and evaluating a moment closure approximation of the FENE dumbbell model for dilute polymer solutions: non-negative configuration distribution function, energy dissipation, accuracy of approximation and computational expense. Through mathematical analysis, numerical experiments and comparisons with closure model FENE-P and FENE-YDL, we prove that the FENE-QE approximation has non-negative configuration distribution function, approximates the energy dissipation behavior of original kinetic theory and provides good accuracy. To improve the efficiency of this closure approximation, we introduce a piecewise linear approximation technique that greatly reduces the computational cost. This extension of FENE-QE, FENE-QE-PLA, is the closure model we recommend for simulating dilute polymer solutions.

Computing Aviation Sparing Policies: Solving a Large Nonlinear Integer Program

Deployed US Navy aircraft carriers must stock a large number of spare parts to support the various types of aircraft embarked on the ship. The sparing policy determines the spares that will be stocked on the ship to keep the embarked aircraft ready to fly. Given a fleet of ten or more aircraft carriers and a cost of approximately 50 million dollars per carrier plus the cost of spares maintained in warehouses in the United States, the sparing problem constitutes a significant portion of the Navy's resources. The objective of this work is to find a minimum-cost sparing policy that meets the readiness requirements of the embarked aircraft. This is a very large, nonlinear, integer optimization problem. The cost function is piecewise linear and convex while the constraint mapping is highly nonlinear. The distinguishing characteristics of this problem from an optimization viewpoint are that a large number of decision variables are required to be integer and that the nonlinear constraint functions are essentially "black box" functions; that is, they are very difficult (and expensive) to evaluate and their derivatives are not available. Moreover, they are not convex. Integer programming problems with a large number of variables are difficult to solve in general and most successful approaches to solving nonlinear integer problems have involved linear approximation and relaxation techniques that, because of the complexity of the constraint functions, are inappropriate for attacking this problem. We instead employ a pattern search method to each iteration of an interior point-type algorithm to solve the relaxed version of the problem. From the solution found by the pattern search on each interior point iteration, we begin another pattern search on the integer lattice to find a good integer solution. The best integer solution found across all interations is returned as the optimal solution. The pattern searches are distributed across a local area network of non-dedicated, heterogeneous computers in an office environment, thus, drastically reducing the time required to find the solution.

Visualization and Quantification of the Medial Surface Dynamics of an Excised Human Vocal Fold During Phonation

The purpose of this investigation was to investigate physical mechanisms of vocal fold vibration during normal phonation through quantification of the medial surface dynamics of the fold. An excised hemilarynx setup was used. The dynamics of 30 microsutures mounted on the medial surface of a human vocal fold were analyzed across 18 phonatory conditions. The vibrations were recorded with a digital high-speed camera at a frequency of 4,000 Hz. The positions of the sutures were extracted and converted to three-dimensional coordinates using a linear approximation technique. The data were reduced to principal eigenfuctions, which captured over 90% of the variance of the data, and suggested mechanisms of sustained vocal fold oscillation. The vibrations were imaged as the following phonatory conditions were manipulated: glottal airflow, an adductory force applied to the muscular process, and an elongation force applied to the thyroid cartilage. Over the range of variables studied, only the variation in glottal airflow yielded significant changes in subglottal pressure and fundamental frequency. All recordings showed high correlation for the distribution of the dynamics across the medial surface of the vocal fold. The distribution of the different displacement directions and velocities showed the highest variations around the superior region of the medial surface. Although the computed vibration patterns of the two largest empirical eigenfunctions were consistent with previous experimental observations, the relative prominence of the two eigenfunctions changed as a function of glottal airflow, impacting theories of vocal efficiency and vocal economy.

Turbo-Coded OFDM Transmission Over a Nonlinear Channel

In this paper, deliberate level clipping and turbo coding are combined to achieve an orthogonal frequency division multiplexing (OFDM) transmission system with a low peak-to-average power ratio (PAR) and a good performance. Using the linear approximation technique based on the minimum mean square error (MMSE) criterion, we first modify the metric computation for the turbo decoding in order to consider the distortion effects of the nonlinearity, caused by the Cartesian clipper. Also, this paper introduces a modified turbo decoder which simultaneously performs the data estimation and signal reconstruction. In other words, the turbo decoder iteratively recovers the clipped signal by using the estimated data, and then improves the data estimation by using the newly recovered signal. Numerical results are presented showing an improvement in the performance of the OFDM transmission system over the nonlinear channel, an increase in the efficiency of the high power amplifier (HPA), and/or an expansion of the transmitter coverage area.

Local linear approximation for tracking frequency in power systems

In this paper, we present an application of the local linear approximation technique in tracking power system frequency. Samples of the voltage phase angle are fitted using linear function. This approximation is valid locally on the left-sided window with variable length. The window slides with each new sample. The linear coefficient of the locally fitted function is the point estimate of the frequency deviation from the nominal value. For each new sample this technique automatically selects optimal window length in order to maximize estimation accuracy. A long window is selected if the frequency is slow varying, to increase efficiency in filtering noise and harmonics. For a fast varying frequency the window length automatically reduces in order to make frequency tracking more accurate but sacrificing on filtering efficiency. Automatic selection of the optimal window length that balances between tracking and filtering performance makes this technique very powerful in tracking frequency in a wider range, as required in generator control and protection applications. The paper concludes with the presentation of the representative simulation results.

Nonlinear Set Membership prediction of river flow

In the present paper, a Nonlinear Set Membership prediction method previously proposed by the authors is applied to a river flow prediction problem. The method does not require the choice of the functional form of the model used for prediction, but assumes a bound on the gradient norm of the regression function defining the model. The method is used for the univariate prediction of the time series consisting of the mean daily discharges of the Dora Baltea river in northern Italy, taken from year 1941 to 1979. The obtained prediction performances are compared with those obtained by means of neural networks and of local linear approximation techniques used by other authors for this time series.

Estimating the aging trend of dry‐type current transformer

Owing to the need for a reliable power supply to prevent unexpected power faults, developing on‐line surveillance and diagnosis technology is crucial. This investigation employs an aging experiment to accelerate insulation aging in a 12.5kV dry‐type current transformer. Three aging indices are investigated, namely maximum discharge, discharge sum and average discharge, and are incorporated using a linear approximation technique to forecast trends in insulation aging. An on‐line simulation is conducted using the measured data to study the feasibility of the proposed linear approximation technique. The results reveal that the average discharge is the most suitable of the three aging indices, and that when the window size is 6, the inaccuracy of the positive half cycle is 12.32 %, while that of negative half cycle is 8.09%. Besides verifying its suitability, the proposed aging index combined with the linear approximation technique will also be proven to be an invaluable reference for the subsequent study of insulation aging.

A shape-based approach to change detection of lakes using time series remote sensing images

Shape analysis has not been considered in remote sensing as extensively as in other pattern recognition applications. However, shapes such as those of geometric patterns in agriculture and irregular boundaries of lakes can be extracted from the remotely sensed imagery even at relatively coarse spatial resolutions. This paper presents a procedure for efficiently retrieving and representing shapes of interesting features in remotely sensed imagery using supervised classification, object recognition, parametric contour tracing, and proposed piecewise linear polygonal approximation techniques. In addition, shape similarity can be measured by means of a computationally efficient metric. The study was conducted on a time series of radiometric and geometric rectified Landsat Multispectral Scanner (MSS) images and Thematic Mapper (TM) images, covering the scenes containing lakes in the Nebraska Sand Hills region. The results validate the effectiveness of the proposed processing chain in change detection of lake shapes and show that shape similarity is an important parameter in quantitatively measuring the spatial variations of objects.

Simulation of Distributed Parameter Systems Using a Matlab-Based Method of Lines Toolbox: Chemical Engineering Applications

Computational modeling is now generally accepted as an essential procedure for the dynamic analysis of chemical processes. Many of these processes are distributed parameter systems, i.e., systems in which state variables depend on several independent variables (such as time and space) and which are described by sets of nonlinear partial differential equations (PDEs). The method of lines (MOL) is probably the most widely used approach to the solution of evolutionary PDEs, and the objective of this paper is to report on the development of a Matlab-based MOL toolbox. The toolbox contains a set of linear spatial approximation techniques, e.g., finite-difference methods, implemented using the concept of differentiation matrices, as well as a set of nonlinear spatial approximations, e.g., flux limiters. In addition, several time integrators, including basic explicit methods and some advanced linearly implicit methods, are included. The underlying philosophy of these developments is to provide the user with a va...

A fuzzy goal programming procedure for solving quadratic bilevel programming problems

This article presents a fuzzy goal programming (FGP) procedure for solving quadratic bilevel programming problems (QBLPP). In the proposed approach, the membership functions for the defined fuzzy objective goals of the decision makers (DM) at both the levels are developed first. Then, a quadratic programming model is formulated by using the notion of distance function minimizing the degree of regret to satisfaction of both DMs. At the first phase of the solution process, the quadratic programming model is transformed into an equivalent nonlinear goal programming (NLGP) model to maximize the membership value of each of the fuzzy objective goals on the extent possible on the basis of their priorities in the decision context. Then, at the second phase, the concept of linear approximation technique in goal programming is introduced for measuring the degree of satisfaction of the DMs at both the levels by arriving at a compromised decision regarding the optimality of two different sets of decision variables controlled separately by each of them. A numerical example is provided to illustrate the proposed approach. © 2003 Wiley Periodicals, Inc.

A unified approach to form error evaluation

Evaluation of form error is a critical aspect of many manufacturing processes. Machines such as the coordinate measuring machine (CMM) often employ the technique of the least squares form fitting algorithms. While based on sound mathematical principles, it is well known that the method of least squares often overestimates the tolerance zone, causing good parts to be rejected. Many methods have been proposed in efforts to improve upon results obtained via least squares, including those, which result in the minimum zone tolerance value. However, these methods are mathematically complex and often computationally slow for cases where a large number of data points are to be evaluated. Extensive amount of data is generated where measurement equipment such as laser scanners are used for inspection, as well as in reverse engineering applications. In this report, a unified linear approximation technique is introduced for use in evaluating the forms of straightness, flatness, circularity, and cylindricity. Non-linear equation for each form is linearized using Taylor expansion, then solved as a linear program using software written in C++ language. Examples are taken from the literature as well as from data collected on a coordinate measuring machine for comparison with least squares and minimum zone results. For all examples, the new formulations are found to equal or better than the least squares results and provide a good approximation to the minimum zone tolerance.

The Analytics of Credible Exchange-Rate-Based Disinflation When Money Facilitates Firms' Transactions

This paper makes three contributions to the supply-side theory of the real effects of exchange-rate-based disinflation: First, the empirical relevance of the supply-side hypothesis has been questioned on the grounds of its reliance on the assumption that purchases of investment goods are subject to a cash-in-advance constraint. This paper replaces this assumption with a more realistic one that assigns money the role of facilitating firms' transactions (such as sales and payments to factor inputs). A formal correspondence is shown to exist between the model proposed in this paper and the one in which investment is a cash good. Second, the implications of the supply-side hypothesis are derived under much weaker restrictions on preferences, technologies, and initial conditions than in existing studies. Third, equilibrium dynamics are characterized without resorting to linear approximation techniques, which are invalid in the context of the theoretical framework used in the literature on exchange-rate-based stabilization, namely, small open economy models with a constant subjective rate of discount and an exogenous world real interest rate.

Hypoxic Ventilatory Responses and Gas Exchange in Patients with Parkinson’s Disease

Ventilatory responses to isocapnic, progressive hypoxic rebreathing (HVR), in supine and sitting positions, lung ventilation and gas exchange while breathing air and during 5 min of breathing 11% O₂ in N₂ were studied in 12 healthy young (20–28 years), 5 old (57–73 years) male subjects, and in 7 male patients with Parkinson’s disease (PD) aged 55–67 years. The piecewise linear approximation technique was used for evaluation of the ventilatory response curves, which allowed a separate analysis of slopes during minor and severe hypoxia. It has been shown that body position affected HVR. In the range of P_ETO₂ from 60 to 35 mm Hg, the ventilatory response in the sitting position was higher than supine: in young persons by 43%, in healthy old persons by 76%, and in the PD patients by 211%. No significant differences in HVR to minor hypoxia (P_ETO₂ from 100 to 60 mm Hg) were found in the 3 groups. During severe hypoxia (P_ETO₂ from 60 to 35 mm Hg) the slope of minute ventilation versus O₂ was 4.6 (supine) and 2.6 (sitting) times greater in healthy old men than PD patients’ slopes. PD patients compared to old controls had 32% lower alveolar ventilation, 10% lower P_ETO₂ and 15% elevation of P_ETCO₂ while breathing air; similar differences were found while the patients were breathing 11% O₂. The reduced alveolar ventilation under severe hypoxia in patients with PD could not be attributed to mechanical restriction of lung function. We suggest that the discrepancy in HVR under minor and severe hypoxia results from dysfunction in chemoreception associated with Parkinsonism.

Comparative study of four adaptive frequency trackers

We study and compare four algorithms for adaptive retrieval of slowly time-varying multiple cisoids in noise: the adaptive notch filter, the multiple frequency tracker, the adaptive estimation scheme, and the hyperstable adaptive line enhancer. The local behavior of the algorithms in a neighborhood of their equilibrium state [assuming high signal-to-noise ratio (SNR) and large data sample] for a two-cisoid signal is treated in a similar way to the linear filter approximation technique used for a single-cisoid case. The validity of the results is confirmed by computer simulations.