Piecewise Linear Technique Research Articles

Surface parametrization and curvature measurement of arbitrary 3-D objects: five practical methods

Curvature sampling of arbitrary, fully described 3-D objects (e.g. tomographic medical images) is difficult because of surface patch parameterization problems. Five practical solutions are presented and characterized-the Sander-Zucker approach, two novel methods based on direct surface mapping, a piecewise linear manifold technique, and a turtle geometry method. One of the new methods, called the cross patch (CP) method, is shown to be very fast, robust in the presence of noise, and is always based on a proper surface parameterization, provided the perturbations of the surface over the patch neighborhood are isotropically distributed. >

Halothane Alters the Oxygen Consumption-Oxygen Delivery Relationship Compared with Conscious State

The authors' objectives were as follows: 1) to characterize for the first time the relationship between whole body O2 delivery (DO2) and O2 consumption (VO2) in adult conscious dogs; and 2) to asses the effects of the inhalational anesthetic, halothane, on that relationship. DO2 was varied over a wide range in chronically instrumented dogs by gradual inflation and deflation of a hydraulic occluder implanted around the thoracic inferior vena cava to alter venous return and cardiac output. VO2 was measured at different values of DO2 in dogs in the fully conscious state and again during halothane anesthesia. A "binning" technique indicated that halothane decreased VO2 (P less than 0.01) at any given value of DO2 over a broad range of VO2. A two-line piecewise linear regression analysis technique indicated that halothane decreased (P less than 0.01) the critical O2 delivery (COD) from 20 +/- 3 to 10 +/- 1 ml.kg-1.min-1 and increased (P less than 0.01) O2 extraction at COD from 31 +/- 3 to 40 +/- 2%. However, the DO2-VO2 plots measured in both conscious and halothane-anesthetized dogs did not exhibit a discrete discontinuity but rather were closely fit (correlation coefficient = 0.98) by an exponential equation of the following form: O2 extraction = B1.(1 - exp (-DO2/B2))/DO2, where B1 is the delivery-independent estimate of VO2 and B2 is the "delivery constant," i.e., the DO2 associated with a VO2 equal to 63% of B1. Halothane decreased B1 (P less than 0.01) from 5.3 +/- 0.1 to 3.9 +/- 0.1 ml.kg-1.min-1 and decreased B2 (P less than 0.01) from 5.6 +/- 0.3 to 3.6 +/- 0.3 ml.kg-1.min-1 compared with that measured in conscious dogs. Thus, compared with the conscious state, halothane anesthesia alters the fundamental relationship between DO2 and VO2 and may have a beneficial effect on tissue oxygenation at low values of DO2.

A DSS oriented method for multiobjective linear programming problems

Most of practical linear programming problems involve multiple and conflicting objectives. The paper presents an interactive method to approach this kind of problems. The main original aspect of this method lies in the fact that it combines the advantageous features of both the paradigms of Satisfactory Goals and Multiattribute Utility Assesment. It is a DSS oriented approach providing a ‘two level’ interaction: 1. (1) interactive assessment of the decision maker's utility function using the UTA ordinal regression model; 2. (2) interactive modification of the satisfaction levels. Piecewise linear optimazation techniques are used to determine, at each iteration, a new compromise solution over the set of efficient solutions.

Analysis and Prediction of Consolidation Settlement of Normally Consolidated Clay Foundation Under Embankment Loading

Piecewise linear approximation technique is newly applied for describing multi-dimensional elasto-plastic consolidation deformation behaviour of a normally consolidated clay foundation. The stiffness factor of clay foundation in terms of effective stresses can be determined from time to time by applying the linearization technique to observations of non-linear consolidation deformation behaviour of the foundation. When gradual load application such as an execution stage of embanking with finite width is considered, although shear deformation of the clay should proceed under partially drained condition, the stiffness factor of the clay foundation is still found to deteriorate. On the other hand, when consolidation becomes more predominant than shear deformation, the stiffness factor will recover its value from the deteriorated state. This is typically found just after the finish of embanking, although consolidation never proceeds without the occurrence of a considerable amount of shear deformation even in the halt of external loading. Thus, it is found that the partially drained behaviour of clay deformation in which consolidation proceeds with shear deformation is well described by monitoring the process of deterioration and recovery of the stiffness factor of a clay foundation. The piecewise linear approximation technique gives this monitoring procedure. The developed procedure is applied to the observational method of predicting consolidation settlement.

Recent work using volterra series as a methodology to analyze nonlinear aircraft dynamic properties

Preliminary results are discussed which demonstrate the accuracy of the Volterra series approach and its potential for defining nonlinear flying quality parameters. Simulations are presented which show that two-term Volterra submodels predict nonlinear responses, such as limit cycles, that are not predicted using piecewise linear techniques. Incorporating higher order terms in the approximation is shown to result in more accurate predictions.

Capacitance coefficients for VLSI multilevel metallization lines

The problem of reducing the complexity of parasitic capacitance evaluation of interconnection lines in a multilevel stratified dielectric medium (a good approximation for VLSI) is considered. We start out with a review of the Green's function method for the Si-SiO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> composite and its derivation via the Fourier integral approach. Next, a piecewise linear finite-element technique is proposed to solve the integral equations that relate charges to potentials and lead to the desired capacitance matrix. We show by example that the proposed method is both less complex than methods based on piecewise constant surface charge distributions and equally accurate. This supports the accuracy and usefulness of the technique for IC design.

Transient responses of combined regenerative and rheostatic braking for DC chopper-fed motors

The possible modes of operation are explained and the dynamic equations for the combined regenerative and rheostatic braking of dc chopper controlled series motor are derived. A computer-based piecewise linear technique is used to analyze the transient responses, taking the full account of nonlinearities such as the magnetic saturation and the product of variable terms. The responses in the transient conditions, which occur in practical situations, are predicted by a computer model and are compared with the practical measurement.

Regenerative characteristics of DC chopper controlled series motors

Simple equations to determine the steady-state characteristics of dc series motors in regenerative braking are derived. These characteristics include the braking current, speed and power against the duty cycle of the chopper controller. The dynamic equations are also derived and a computer based piecewise linear technique is used to analyze the transient responses. The responses in the transient conditions, which occur in practical situations, are predicted by a computer model and are compared with the practical measurements.

Modeling and analysis of several classes of self-oscillating inverters: Part I- State-plane representations

An overview is provided concerning the analysis of a selfoscillating dc-to-square-wave transistor parallel inverter. The inverter is characterized by an equivalent nonlinear RLC network consisting of a voltage-controlled resistor in parallel with a square-loop saturable reactor and a linear capacitor. Piecewise-linear techniques in conjunction with state-plane interpretations are employed to describe in detail the behavior of the inverter including: the complex switching interactions of semiconductor devices and magnetics, the stability nature of limit cycles, conditions for oscillation, and starting characteristics. The model provides significant insights into the inverter design and is verified experimentally.

Temporal variation in the V t-T i relationship in humans

The variation with time of the relationship between tidal volume (V t) and inspiratory duration (T i) was assessed by analysis of 34 breathing sequences, nominally of 300 breath duration, during eupnea and hypercapnic hypernea in 6 human subjects. Two approaches were used: (1) each sequence was delivered into consecutive 50-breath and standard regression techniques used to characterize V t as a function of T i; and (2) a piecewise linear regression technique was applied to cluster consecutive breaths into regression regimes. Analysis of covariance was used with the results of both approaches to determine the likelihood that a single regression line was adequate to describe the entire data set. Similar results obtained regardless of the approach used. In only 4 of the 34 experiments would the hypothesis of regression slope homogeneity be accepted ( p > 0.05) using the clustering approach; in 27 experiments, it was indicated that the regression slope estimates of V t and T i should not be considered homogeneous. Changes in the V t-T i slope were not correlated with changes in mean levels of V t, T i, minute ventilation (V̇, mean inspiratory flow (V t/T i), nor alveolar P CO 2 (P a CO 2 ). Thus it is apparent that the V t-T i relation cannot be considered temporally invariant, but changes with time over periods ranging from less than 20 to more than 100 breaths.

Dynamic Responses of DC Chopper-Controlled Series Motor

This paper uses a computer-based piece-wise linear technique to analyze the dynamic performances of an armature voltage-controlled chopper circuit with a low-pass input filter taking the account of nonlinearities such as the magnetic saturation and the product of variable terms. The performances in the transient conditions which occur in practical situations are predicted by a computer model and are compared with the practical measurements.

Rotational Vibration With Backlash—Part 2

This paper is a continuation of a paper [1] previously published. In this paper, the experimental results for the 3-mass system as defined in Part I are presented. Physical simulation very close to an ideal limiting case where the driven pinion is linked to the output pulley with a very low stiffness shaft was performed. The nonlinear responses of a system with backlash and subject to impact and/or displacement excitation were obtained. The presence of multiple critical speeds for a single degree of freedom system under impact and/or displacement excitation has been analytically explained and experimentally confirmed. Computer solutions based on the piecewise linear iteration technique as outlined in Part 1 have achieved a considerable degree of success. Computer predictions agree well with actual responses in various speed ranges despite a series of bold assumptions that were made to simplify the numerical process.

Analysis of d.c. chopper circuits by computer-based piecewise-linear technique: Mellitt, B. and Rashid, M. H.Proc. Inst. Elect. Eng. Vol 121, No 3 (March 1974) pp 173–178

Analysis of d.c. chopper circuits by computer-based piecewise-linear technique: Mellitt, B. and Rashid, M. H.Proc. Inst. Elect. Eng. Vol 121, No 3 (March 1974) pp 173–178

Analysis of d.c. chopper circuits by computer-based piecewise-linear technique

A computer-based method for analysing the performance of d.c. chopper circuits is proposed. In the paper, a piecewise-linear description is established by considering sequential circuit modes, defined by the switching action of thyristors and diodes. The method is quite general, and could be applied to any particular chopper circuit to provide both transient and steady-state performance data. As an illustration, the method is used to describe the performance of a d.c. series motor controlled by a chopper circuit that provides both armature and field control. Control characteristics of this circuit are established, and these are compared with practical results obtained by measurement on a 220 V, 8 A series motor.

Discussion on “Analysis of d.c. chopper circuits by computer-based piecewise-linear technique”

Discussion on “Analysis of d.c. chopper circuits by computer-based piecewise-linear technique”

Analysis of Limit Cycles in a Two-Transistor Saturable-Core Parallel Inverter

A familiar two-transistor saturable-core parallel inverter is modeled as a nonlinear negative resistance in parallel with energy-storage elements. The techniques of singular-point analysis are combined with piecewise linear techniques to permit determination of solution trajectories on the phase plane. Clear insight is provided, not only into steady-state oscillation, but also into transient behavior of the circuit. Experimental results confirming the analytical model are included.

The response of an automatic phase control system to FM signals and noise

An Automatic Phase Control (APC) System is analyzed in order to determine its response to frequency modulated signals, and narrow-band Gaussian noise. Emphasis is placed on the system's response to signals having "ramp" type FM. The response of the APC System to an FM signal is obtained using a perturbation and a piecewise linear technique. The response of the system to noise is obtained using an iteration technique. The complete response to an FM signal and noise is then discussed using an iteration technique and extending the results previously obtained.