Piecewise Linear Technique Research Articles

Prediction of scour at abutments using piecewise regression

Scour is one of the main causes of bridge failure and scour depth prediction is thus a very important issue. Although many studies have been carried out to develop formulas for the prediction of scour depth at abutments, the existing formulas do not yield accurate results, mainly due to the complexity of the scour phenomena around abutments. This paper reports on a study of abutment scour using piecewise multiple linear regression analysis. First, scour depth data were collected from the literature and the existing formulas were evaluated and compared. To develop new formulas, the conventional governing parameters were selected as the independent variables. The piecewise multiple linear regression technique was applied to investigate the relationship between dimensionless scour depth and the governing dimensionless parameters in several subdomains. Errors of the proposed formula and previous models were also compared. Compared with existing formulas, the error measures in the proposed method show a significant improvement in prediction accuracy.

Two‐stage logarithmic converter with reduced memory requirements

This study presents an efficient method for converting a normalised binary number x (1 ≤ x <; 2) into a binary logarithm. The algorithm requires less memory and fewer arithmetic components to achieve 23 bits of fractional precision than other algorithms using uniform and non-uniform piecewise linear or piecewise polynomial techniques and requires less than 20 kbits of ROM and a maximum of three multipliers. It is easily extensible to higher numeric precision and has been implemented on Xilinx Spartan3 and Spartan6 field programmable gate arrays (FPGA) to show the effect of recent architectural enhancements to the reconfigurable fabric on implementation efficiency. Synthesis results confirm that the algorithm operates at a frequency of 42.3 MHz on a Spartan3 device and 127.8 MHz on a Spartan6 with a latency of two clocks. This increases to 71.4 and 160 MHz, respectively, when the latency is increased to eight clocks. On a Spartan6 XC6SLX16 device, the converter uses just 55 logic slices, three multipliers and 11.3kbits of Block RAM configured as ROM.

Pricing traffic in a spanning network

Users need to connect a pair of target nodes in the network. They share the fixed connection costs of the edge. The system manager elicits target pairs from users, builds the cheapest forest meeting all demands, and choose a cost sharing rule satisfying:Routing-proofness: a user cannot lower his cost by reporting as several users along an alternative path connecting his target nodes;Stand Alone core stability: no group of users pay more than the cost of a subnetwork meeting all connection needs of the group.We construct two such rules. When all connecting costs are 0 or 1, one is derived from the random spanning tree weighted by the volume of traffic on each edge; the other is the weighted Shapley value of the Stand Alone cooperative game. Both rules are then extended by the familiar piecewise-linear technique. The former is computable in polynomial time, the latter is not.

CFD evaluation of natural ventilation of indoor environments by the concentration decay method: CO2 gas dispersion from a semi-enclosed stadium

Computational Fluid Dynamics (CFD) simulations can be used to assess indoor natural ventilation by solving the interaction between the urban wind flow and the indoor airflow. The air exchange rate (ACH) can be obtained from the simulated volume flow rates through the ventilation openings or by the concentration decay method that is often used in experimental studies. This paper presents 3D unsteady Reynolds-averaged Navier–Stokes (RANS) CFD simulations to reproduce the decay of CO2 concentration in a large semi-enclosed stadium. The study focuses on the hours after a concert, when the indoor CO2 concentration generated by the attendants has reached a maximum. The wind flow, indoor airflow and dispersion of heat, water vapour and CO2 are modelled on a high-resolution grid based on a grid-sensitivity analysis. The simulations are validated with on-site measurements of wind velocity and CO2 concentration decay. The validated CFD model is used to analyse the significant horizontal and vertical CO2 concentration gradients in the stadium, showing local differences at t=300s up to 700ppm (i.e. 37% of the maximum of 1900ppm). A specific piecewise-linear technique is applied for the concentration decay method to determine the ACH values for smaller time-intervals. This is needed because the plotted semi-logarithmic decay curve itself is not linear because the ventilation rate changes over time, due to the changing buoyancy forces. It shows that the ACH values decrease from about 2h−1 at the beginning of the concentration decay simulations to about 0.3h−1 at the end.

Making Sensor Networks Immortal: An Energy-Renewal Approach With Wireless Power Transfer

Wireless sensor networks are constrained by limited battery energy. Thus, finite network lifetime is widely regarded as a fundamental performance bottleneck. Recent breakthrough in the area of wireless power transfer offers the potential of removing this performance bottleneck, i.e., allowing a sensor network to remain operational forever. In this paper, we investigate the operation of a sensor network under this new enabling energy transfer technology. We consider the scenario of a mobile charging vehicle periodically traveling inside the sensor network and charging each sensor node's battery wirelessly. We introduce the concept of renewable energy cycle and offer both necessary and sufficient conditions. We study an optimization problem, with the objective of maximizing the ratio of the wireless charging vehicle (WCV)'s vacation time over the cycle time. For this problem, we prove that the optimal traveling path for the WCV is the shortest Hamiltonian cycle and provide a number of important properties. Subsequently, we develop a near-optimal solution by a piecewise linear approximation technique and prove its performance guarantee.

Synthesis of Bias-Scalable CMOS Analog Computational Circuits Using Margin Propagation

Approximation techniques are useful for implementing pattern recognizers, communication decoders and sensory processing algorithms where computational precision is not critical to achieve the desired system level performance. In our previous work, we had proposed margin propagation (MP) as an efficient piecewise linear (PWL) approximation technique to a log-sum-exp function and had demonstrated its advantages for implementing probabilistic decoders. In this paper, we present a systematic and a generalized approach for synthesizing analog piecewise-linear (PWL) computing circuits using the MP principle. MP circuits use only addition, subtraction and threshold operations and hence can be implemented using universal conservation principles like the Kirchoff's current law. Thus, unlike the conventional translinear CMOS current-mode circuits, the operation of the MP circuits are functionally similar in weak, moderate, and strong inversion regimes of the MOS transistor making the design approach bias-scalable. This paper presents measured results from MP circuits prototyped in a 0.5 μm standard CMOS process verifying the bias-scalable property. As an example, we apply the synthesis approach towards designing linear classifiers and we verify its performance using measured results.

Solar irradiance in clear atmosphere: study of parameterisations of change with altitude

Abstract. Parameterisation of changes of the solar irradiance at ground level with a specific variable (e.g. solar zenithal angle, aerosol optical depth, altitude, etc.) is often used in operational processes because it saves computational time. This paper deals with the modelling of the vertical profile of downwelling solar irradiance for the first two kilometres above ground in clear sky conditions. Two analytical parameterisations are evaluated for direct and global irradiance in spectral bands as well as for the total irradiance. These parameterisations reproduce the vertical profile with good accuracy for global spectral irradiance and are less accurate for direct component, especially in turbid atmosphere. A piecewise linear interpolation technique using irradiance values known at surface and 4 altitudes every 500 m performs better in any case.

Piecewise linear regression techniques to analyse the timing of head coach dismissals in Dutch soccer clubs

The key question in research on dismissals of head coaches in sports clubs is not whether they should happen but when they will happen. This paper applies piecewise linear regression to advance our understanding of the timing of head coach dismissals. Essentially, the regression sacrifices degrees of freedom for increased possibilities of interpretation. In the empirical part, we show that badly performing clubs tend to wait for clear evidence before dismissing a head coach. Dutch soccer clubs only dismiss head coaches during the soccer season when a club loses a match it should not have. We also find that once the decision to dismiss the incumbent head coach has been made, clubs quickly tend to appoint a new one, possibly by attracting an interim coach

Perceived Level of Service, Driver, and Traffic Characteristics: Piecewise Linear Model

The objective of this research is the analysis of perceived highway level of service in relation to drivers’ personal characteristics and traffic conditions. A field survey was carried out for that purpose, in which drivers were asked to assess the traffic conditions experienced on a freeway segment, just after having actually driven along this segment. At the same time, traffic counts were taking place. Exploratory analysis revealed a large dispersion in drivers’ assessment of level of service for each volume-to-capacity (v/c) value, especially at moderate traffic conditions. Furthermore, the effect of driver’s age, gender, driving experience, familiarity with the road, vehicle capacity, and v/c on perceived level of service was examined by means of nonparametric statistical tests. It was found that, in this sample, only traffic conditions affected drivers’ assessment of level of service. Perceived level of service was then modeled against v/c by means of a piecewise linear regression technique for three...

Simultaneous Optical-Electrical Measurement of the Delay between formation of the Fusion Pore and Proton Equilibration in Exocytosis of Single Vesicles

Optical detetction of neutralization of pH in granules or vesicles is often used to define exocytotic events. However, combined measurents of ensemble capacitance and pH-dependent vesicular fluorescence changes have suggested that the movement of protons only becomes possible after fusion pore expansion with a mean delay of > 300 ms (1). To enhance the temporal resolution of such measurements, we have combined capacitance recordings of single vesicle fusion in RBL cells transfected with synapthpHluorin as a reporter of vesicular pH. To monitor cell capacitance steps due to exocytosis of single granules in whole cell patch-clamp mode, we used the piecewise linear technique. Internal solution contained 10 μM free Ca2+ and 300 μM GTPγS.View Large Image | View Hi-Res Image | Download PowerPoint Slide Before establishing whole cell recordings, punctate fluorescence signals could be detected with excitation at 460 nm, while during perfusion with internal solution and excitation at 480 nm, punctate fluorescence signals gradually appeared at corresponding sites. Fluorescence increases clearly lagged capacitance steps by several 100 ms- seconds, supporting the idea that pH equilibration through the fusion pore is delayed.(1) Barg et al.: Neuron, 33, 287-299, 2002.

Piecewise linear second moment statistical simulation of ICs affected by non‐linear statistical effects

AbstractThis paper presents a methodology for statistical simulation of non‐linear integrated circuits affected by device mismatch. This simulation technique is aimed at helping designers maximize yield, since it can be orders of magnitude faster than other readily available methods, e.g. Monte Carlo. Statistical analysis is performed by modeling the electrical effects of tolerances by means of stochastic current or voltage sources, which depend on both device geometry and position across the die. They alter the behavior of both linear and non‐linear components according to stochastic device models, which reflect the statistical properties of circuit devices up to the second order (i.e. covariance functions). DC, AC, and transient analyses are performed by means of the stochastic modified nodal analysis, using a piecewise linear stochastic technique with respect to the stochastic sources, around a few automatically selected points. Several experimental results on significant circuits, encompassing both the analog and the digital domains, prove the effectiveness of the proposed method. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Comparison of piece‐wise linear, linear, and nonlinear atlas‐to‐patient warping techniques: Analysis of the labeling of subcortical nuclei for functional neurosurgical applications

Digital atlases are commonly used in pre-operative planning in functional neurosurgical procedures performed to minimize the symptoms of Parkinson's disease. These atlases can be customized to fit an individual patient's anatomy through atlas-to-patient warping procedures. Once fitted to pre-operative magnetic resonance imaging (MRI) data, the customized atlas can be used to plan and navigate surgical procedures. Linear, piece-wise linear and nonlinear registration methods have been used to customize different digital atlases with varying accuracies. Our goal was to evaluate eight different registration methods for atlas-to-patient customization of a new digital atlas of the basal ganglia and thalamus to demonstrate the value of nonlinear registration for automated atlas-based subcortical target identification in functional neurosurgery. In this work, we evaluate the accuracy of two automated linear techniques, two piece-wise linear techniques (requiring the identification of manually placed anatomical landmarks), and four different automated nonlinear atlas-to-patient warping techniques (where two of the four nonlinear techniques are variants of the ANIMAL algorithm). Since a gold standard of the subcortical anatomy is not available, manual segmentations of the striatum, globus pallidus, and thalamus are used to derive a silver standard for evaluation. Four different metrics, including the kappa statistic, the mean distance between the surfaces, the maximum distance between surfaces, and the total structure volume are used to compare the warping techniques. The results show that nonlinear techniques perform statistically better than linear and piece-wise linear techniques. In addition, the results demonstrate statistically significant differences between the nonlinear techniques, with the ANIMAL algorithm yielding better results.

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.

Nonlinear solar cycle forecasting: theory and perspectives

Abstract. In this paper we develop a modern approach to solar cycle forecasting, based on the mathematical theory of nonlinear dynamics. We start from the design of a static curve fitting model for the experimental yearly sunspot number series, over a time scale of 306 years, starting from year 1700 and we establish a least-squares optimal pulse shape of a solar cycle. The cycle-to-cycle evolution of the parameters of the cycle shape displays different patterns, such as a Gleissberg cycle and a strong anomaly in the cycle evolution during the Dalton minimum. In a second step, we extract a chaotic mapping for the successive values of one of the key model parameters – the rate of the exponential growth-decrease of the solar activity during the n-th cycle. We examine piece-wise linear techniques for the approximation of the derived mapping and we provide its probabilistic analysis: calculation of the invariant distribution and autocorrelation function. We find analytical relationships for the sunspot maxima and minima, as well as their occurrence times, as functions of chaotic values of the above parameter. Based on a Lyapunov spectrum analysis of the embedded mapping, we finally establish a horizon of predictability for the method, which allows us to give the most probable forecasting of the upcoming solar cycle 24, with an expected peak height of 93±21 occurring in 2011/2012.

A fast and fully automatic registration approach based on point features for multi-source remote-sensing images

Automatic registration of multi-source remote-sensing images is a difficult task as it must deal with the varying illuminations and resolutions of the images, different perspectives and the local deformations within the images. This paper proposes a fully automatic and fast non-rigid image registration technique that addresses those issues. The proposed technique performs a pre-registration process that coarsely aligns the input image to the reference image by automatically detecting their matching points by using the scale invariant feature transform (SIFT) method and an affine transformation model. Once the coarse registration is completed, it performs a fine-scale registration process based on a piecewise linear transformation technique using feature points that are detected by the Harris corner detector. The registration process firstly finds in succession, tie point pairs between the input and the reference image by detecting Harris corners and applying a cross-matching strategy based on a wavelet pyramid for a fast search speed. Tie point pairs with large errors are pruned by an error-checking step. The input image is then rectified by using triangulated irregular networks (TINs) to deal with irregular local deformations caused by the fluctuation of the terrain. For each triangular facet of the TIN, affine transformations are estimated and applied for rectification. Experiments with Quickbird, SPOT5, SPOT4, TM remote-sensing images of the Hangzhou area in China demonstrate the efficiency and the accuracy of the proposed technique for multi-source remote-sensing image registration.

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.

Numerical study for the impact of liquid droplets on solid surfaces

The impinging behaviour of liquid droplets on solid surfaces is studied using a computational approach. The analysis comprises the unsteady three-dimensional conservation equations of mass and momentum, with the surface tension effect treated by the continuous surface force model. Gas-liquid interfacial motions are simulated by the volume-of-fluid method in conjunction with the piecewise linear interface construction technique. In the computer code validation for a water droplet impacting on a polished stainless steel surface, computer-generated images of the time evolution of the droplet impingement dispersal shape are compared with magnified photographs by Pasandideh-Fard et al. The flow and transport phenomena in the impingement flowfield are further examined in detail. In order to respond to the need for its use in practical applications, the study is extended to explore the spreading progression to achieve a better understanding of the interaction of a 30 μm diameter polyethylenedioxy thiophene liquid droplet with a 50 × 50 μm indium tin oxide-coating square cavity at an impact velocity of 6 m/s.

A novel DDS using nonlinear ROM addressing with improved compression ratio and quantization noise

This paper presents a novel direct digital frequency synthesis (DDFS) ROM compression technique based on two properties of a sine function: (a) piecewise linear technique to approximate a sinusoid, and (b) variation in the slope of the sinusoid at different phase angles. In the proposed DDFS architecture the ROM stores a few of the sinusoidal values, and the interpolation points between the successive stored values are calculated using linear and nonlinear addressing schemes. The nonlinear addressing scheme is used to adaptively vary the number of interpolation points as the slope of the sinusoid changes, leading to a greatly reduced ROM size. The proposed architecture achieves a high compression ratio with a spurious response comparable to that of recent ROM compression techniques. To validate the proposed DDS architecture, the linear, nonlinear, and conventional DDS ROM architectures were implemented in a Xilinx Spartan II FPGA and their spurious performances were compared.

Ejection Process Simulation for a Piezoelectric Microdroplet Generator

The purpose of this work is to investigate the liquid ejection process of a novel microdroplet generator applying a computational approach. In simulations, the theoretical model is based on the unsteady three-dimensional conservation equations of mass and momentum with the treatment of surface tension effect at the gas-liquid boundary by the continuous surface force scheme. The volume-of-fluid method along with the piecewise linear interface construction technique is implemented to describe the interfacial movements. The time evolution of droplet meniscus shape is predicted and compared to Shield’s microphotographed images for the computer code validation. To explore the practicability of the proposed new microdroplet generator, the flow behavior during the stages of liquid ejection and droplet formation are examined with water as the baseline test fluid for a full ejection cycle of 50μs. In addition, 12 numerical experiments were conducted to determine droplet ejection characteristics by systematically varying the ejection time period as well as surface tension and viscosity of liquids. Simulations reveal that a liquid strand with a shorter breakup time and a longer breakup length could be achieved by reducing the ejection time and decreasing the liquid surface tension and viscosity. For the ejection time greater than 4.0μs, the ejection velocity is too low to render a sufficient momentum for droplet breakup. The feasibility studies have demonstrated the potential of this proposed microdroplet generator in dispensing diverse liquids with the surface tension and the viscosity up to 0.08N∕m and 3.0cps.

A two-grids/projection algorithm for obstacle problems

In order to emphasize the possible relation between discontinuous and continuous approximations on different meshes, a two-grids method for the resolution of parabolic variational inequality problems is presented. The numerical methodology combines a time splitting algorithm to decouple a diffusion phenomenon from an obstacle problem. The diffusion problem is solved by using finite-differences, while piecewise linear finite-element techniques are used together with a Newton method for the obstacle problem. Projections are used to interpolate the solution from one grid to the other. Numerical experiments show that the resulting method has good accuracy properties.