Piecewise Linear Description Research Articles

Модели бетона и арматуры при взрывных нагрузках

In this article, the mathematical models of structural materials describing their dynamic properties are considered for calculating building structures for the action of dynamic loads. Physical and mechanical properties are described related to reinforcing steel and concrete under the action of explosive loads, as well as the influence of the loading rate and other factors on the deformation diagram of steel and concrete. The analysis is carried out concerning the reasons for the increase in the resistance of concrete and reinforcement under rapidly increasing loads. The relevance of the topic is determined by its compliance with the main goals and objectives of the Russian state policy in the field of improving the safety of buildings and structures when exposed to explosive loads. The article describes the methods of mathematical description of the structural materials behavior under the action of explosive loads. A simplified method for modeling the dynamic properties of reinforcing steel and concrete by multiplying the calculated resistance by the dynamic strengthening factor, as well as a more time-consuming method based on the equations of gas-hydrodynamics and implemented in the LS-DYNA software package, are considered. The authors used the method of taking into account the dynamic strengthening of reinforcing steel and concrete based on the nonlinear behavior of materials using diagrams with a piecewise linear description. Dynamic hardening was considered using hardening factors. The purpose of the study is to compare the results of numerical calculation according to the method proposed by the authors with the data obtained during the experimental program Blind Blast Test. The calculation was carried out by the finite element method using the Lira 10.12 calculation complex. The DYNAMICS+ system was used to simulate the load from the action of an external explosion. The experimental model is a reinforced concrete slab reinforced with ASTM Grade 60#3 rods. The results of numerical calculation showed high convergence with the experimental program. The use of the method of accounting for the dynamic hardening of reinforcing steel and concrete, based on the nonlinear behavior of materials using diagrams with a piecewise linear description, is the most optimal model that allows to get a fairly accurate solution and at the same time is acceptable from the point of view of labor intensity. This article is of interest to design engineers engaged in the calculation of structures for explosive loads.

Crystallographic descriptions of regular 2-periodic weavings of threads, loops and nets.

Piecewise linear descriptions are presented of weavings of threads, loops and 2-periodic nets. Crystallographic data are provided for regular structures, defined as those with one kind (symmetry-related) of vertex (corner) and edge (stick). These include infinite families of biaxial thread weaves, interwoven square lattices (sql), honeycomb (hcb) nets, and tetragonal and hexagonal polycatenanes.

Model predictive control of pH neutralization processes: A review

The paper provides a review of the different approaches of Model Predictive Control (MPC) to deal with the nonlinearities and transient behavior associated with pH and its control.Firstly a description of the pH system and what makes it difficult to control is presented, followed by the general description of the structure of MPC. The different applications of MPC vary mostly in the way the model is described and how the optimization is carried out to obtain the desired control action. The different modeling techniques applied to the MPC, which is used to describe the behavior of the pH are ranging from simple linear models, multiple linear models like piecewise linear descriptions and fuzzy models, to nonlinear descriptions like Wiener models and the use of artificial neural networks. The models and their respective ways of application are reviewed. Finally, the areas where more research is needed are addressed.

Target tracking with binary proximity sensors

We explore fundamental performance limits of tracking a target in a two-dimensional field of binary proximity sensors, and design algorithms that attain those limits while providing minimal descriptions of the estimated target trajectory. Using geometric and probabilistic analysis of an idealized model, we prove that the achievable spatial resolution in localizing a target's trajectory is of the order of 1/ρ R , where R is the sensing radius and ρ is the sensor density per unit area. We provide a geometric algorithm for computing an economical (in descriptive complexity) piecewise linear path that approximates the trajectory within this fundamental limit of accuracy. We employ analogies between binary sensing and sampling theory to contend that only a “lowpass” approximation of the trajectory is attainable, and explore the implications of this observation for estimating the target's velocity. We also consider nonideal sensing, employing particle filters to average over noisy sensor observations, and geometric geometric postprocessing of the particle filter output to provide an economical piecewise linear description of the trajectory. In addition to simulation results validating our approaches for both idealized and nonideal sensing, we report on lab-scale experiments using motes with acoustic sensors.

Controlled onset of low-velocity collisions in a vibro-impacting system with friction

This paper investigates the onset of low-velocity, near-grazing collisions in an example vibro-impacting system with dry friction with particular emphasis on feedback control strategies that regulate the grazing-induced bifurcation behaviour. The example system is characterized by a twofold degeneracy of grazing contact along an extremal stick solution that is shown to result in a locally one-dimensional and piecewise-linear description of the near-grazing dynamics. Explicit control strategies are derived that ensure a persistent, low-impact-velocity, steady-state response across the critical parameter value corresponding to grazing contact even in instances where the dynamics in the absence of control exhibit a sudden transition to a high-impact-velocity response.

Continuous and discontinuous grazing bifurcations in impacting oscillators

This paper seeks to formulate conditions for the persistence of a local attractor in the immediate vicinity of periodic and quasiperiodic grazing trajectories in an impacting mechanical system. A local analysis based on the discontinuity-mapping approach is employed to derive a normal-form description of the dynamics near the grazing trajectory. In agreement with previous studies of grazing periodic trajectories, it is found that the catastrophic loss of a local attractor and strong instability characteristic of grazing bifurcations is directly associated with the repeated application of a square-root term that appears to lowest order in the normal-form expansion. Specifically, it is found that the square-root term is absent in the description of the dynamics normal to a quasiperiodic trajectory covering a co-dimension-one invariant torus resulting in a piecewise linear description of the normal dynamics and, at most, a weak instability. In contrast, for co-dimension-two or higher, the square-root term is generically present in the normal dynamics. Here, however, the quasiperiodicity of the grazing motion implies that there is no upper limit to the time between impacts on nearby trajectories suggesting the persistence of a local attractor for some interval about the parameter value corresponding to grazing. The results of the analysis are illustrated through a series of model examples.

Intrinsic inversion charge in the mobility region of fully depleted SOI-MOSFETs

In this paper we propose a new method to calculate the inversion channel charge in the mobility region of fully depleted (FD) SOI-MOSFETs. The proposed calculation is based on our DC model [Technische Fakultät der CAU Kiel, Ph.D. Thesis, 1999 [1]], which includes both the partially depleted (PD) and the FD operation modes as well as the FD–PD transition. A new approach for the description of integrated minority concentration relying on piece-wise linear dependencies on the quasi-Fermi potential of electrons is used. This approach allows a very accurate description of the total intrinsic inversion channel charge of FD double gate devices, accounting for all possible conditions at both silicon film surfaces. We introduce the piece-wise linear description of the integrated concentration first. Then we explain the proposed calculation in detail and give a comparison between the gained analytical expressions and results of numerical simulations using MEDICI [MEDICI. Avant! Corporation, Freemont, CA 94538, 1996–2000 [2]].

Small signal frequency domain model of an HVDC converter

A small-signal analytic frequency domain model of a 6-pulse HVDC converter is presented. The model consists of a set of explicit algebraic equations which relate the transfer of distortion from AC voltage, DC current and firing angle modulation, to AC current and DC voltage. The equations represent the linearisation of the transfers around a base operating point, and are derived from a piecewise linear description of the AC current and DC voltage waveforms. The model provides an understanding of the transfer of distortion by the converter and is in excellent agreement with time domain simulations.

The simplified model of the Class E inverter with the PWL model of the MOSFET turn off

The paper presents the simplified model of the Class E inverter in which the MOSFET transistor is based on the piecewise‐linear (PWL) model. The model does not contain inductances. The PWL description makes it possible to obtain the model in the form of general closed formulae. The general formulae have been obtained by means of MATHCAD and verified with the IsSPICE® simulator. The analysis of MOSFET switching performance in the active region at the constant load current is delivered. The work is a successive step in the systematic research of the Class E inverter as a supplying source in high frequency levitation heating/melting systems. The equivalent RL parameters of the load in such systems vary across a relatively wide range.

Further extensions to Chua's explicit piecewise linear function descriptions

In this paper we will further extend the class of explicit piecewise linear descriptions expressed with the absolute-value operator. Previously it was shown that each piecewise linear mapping with a lower triangular matrix of the linear complementary problem (LCP) could be modelled into an explicit function description. Now we will show that this is even true for each piecewise linear mapping with the LCP matrix of class P. It turns out that the explicit model is composed of the same set of base functions as proposed earlier in the literature.

Extensions to Chua's explicit piecewise-linear function descriptions

In this paper, we extend the class of explicit piecewise linear descriptions in the modulus form that was recently introduced by Chua cum suis. This is achieved by transforming a special form of a more general implicit description given by Van Bokhoven (1981) using the modulus transformation. This results in a set of base functions that can be used to compose the more general explicit description. It is shown that with this set all previously presented explicit PL descriptions can be covered. Furthermore, we pose some problems that occur when trying to construct an even more general description. >

Unified Modeling of Rectifier-Controlled DC-Power Supplies

The known analysis of dc-dc converters in discontinuous operation mode and with voltage commutation based on a piecewise-linear description is extended to the analysis of line-commutated converters. With the latter as system-dependent pulsewidths the overlap angles appear, which can be computed in a manner analogous to the current-flow duration and the reloading time, respectively. This leads to a unified state-space modeling of dc-dc and ac-dc converters by which the steady-state and the dynamic small-signal behavior can be evaluated directly. If the piecewise-defined system equations are integrated numerically, a rather generalized analysis of power converters is found if the structure of switched systems is taken into account. As an illustrative example, a voltage-commutated dc-dc converter with a nonlinear dc inductance is studied.

The consolidation problem treated by a consistent (static) finite element approach

AbstractThe consolidation problem in a plane strain porous elastic medium is treated by adopting a consistent formulation of the finite element model. To this purpose, the fluid‐phase behaviour is modelled in static terms through a piecewise linear description of the pore pressure field and the behaviour of the two‐phase medium is consistently modelled through rigorously equilibrated piec̀ewise linear stress distribution.Incompressibility of the pore fluid and of the skeleton grains is assumed, as is linear elastic behaviour of the solid phase.After a compact description of the model, the governing equations for the continuum problem are recalled and the solution system for the discretized problem is obtained following Galerkin's method of weighted residuals. Some examples are finally illustrated, in order to assess the reliability of the approach and to introduce possible comparisons with other methods.

Modeling the influence of carrier profiles on MESFET characteristics

Continuing development of materials methods and the need to improve MESFET device performance calls for accurate modeling of the effect of free-carrier profiles upon MESFET performance. A computer program known as SATVO is described which provides, by means of a numerical solution, saturation characteristics and gate-electrode capacitances for devices of specified geometry fabricated from layers of any profile which may be specified by either Gaussian expressions (as for ion-implanted layers) or by piecewise-linear descriptions. Examples of the use of this program are also provided.

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.