Abstract: The work is devoted to solving the problem of temperature stresses, caused by the heating point of the round plate. The plate is made of elastoplastic material, so the Prandtl-Reis model is used. A piecewise-linear condition of the Ishlinsky-Ivlev flow is taken as the loading surface, in which the yield stress depends on the temperature. Piecewise-linear conditions (Treska or Ishlinsky-Ivlev), in contrast to the Mises condition, make it possible to obtain solutions of the equilibrium equation in an analytical form. In the problem under consideration, using the conditions of Tresca, it is impossible to obtain a solution. This is due to the fact that the equation of equilibrium ceases to be satisfied when the two Tresca conditions are fulfilled at once. Using the conditions of plastic flow Ishlinsky-Ivlev allows one to solve the problem. At the same time, there are also no solutions on the edge of the Ishlinsky-Ivlev hexagon in the plane-stressed state. Therefore, the authors of the article propose to jump from the edge to the edge of the mine edge, which gives an opportunity to obtain an analytical solution. At the same time, there is also no solution on the edge of the Ishlinsky-Ivlev hexagon in a plane stressed state; therefore, in this paper, the authors of the article propose to jump from the side to the side of the mine edge, which gives an opportunity to receive an analytical solution. The paper compares solutions of the problem of plate thermal deformation. One of the solutions was obtained under the condition that the elastic moduli (Young's modulus, Poisson's ratio) which depend on temperature. The yield point is assumed to be parabolically temperature dependent. The main results of the comparisons are that the region of irreversible deformation is larger in the calculations obtained for solving the problem with constant elastic moduli. There is no repeated plastic flow in the solution of the problem with elastic moduli depending on temperature. The absolute value of the irreversible deformations is higher for the solution of the problem in which the elastic moduli are constant; there are also insignificant differences in the distribution of the residual stresses.
Abstract: One challenge faced by procurement decision-maker during the acquisition process is how to compare similar products from different suppliers and allocate orders among different products or services. This work focuses on allocating orders among multiple suppliers considering rebate. The objective function is to minimize the total acquisition cost including purchasing cost and rebate benefit. Rebate benefit is complex and difficult to estimate at the ordering step. Rebate rules vary for different suppliers and usually change over time. In this work, we developed a system to collect the rebate policies, standardized the rebate policies and developed two-stage optimization models for ordering allocation. Rebate policy with multi-tiers is considered in modeling. The discontinuous cost function of rebate benefit is formulated for different scenarios. A piecewise linear function is used to approximate the discontinuous cost function of rebate benefit. And a Mixed Integer Programing (MIP) model is built for order allocation problem with multi-tier rebate. A case study is presented and it shows that our optimization model can reduce the total acquisition cost by considering rebate rules.
Abstract: The method of moments combined with the method
of symmetrical components is used for the analysis of interstitial
hyperthermia applicators. The basis and testing functions are both
piecewise sinusoids, qualifying our technique as a Galerkin one. The
dielectric coatings are modeled by equivalent volume polarization
currents, which are simply related to the conduction current
distribution, avoiding in that way the introduction of additional
unknowns or numerical integrations. The results of our method
for a four dipole circular array, are in agreement with those
already published in literature for a same hyperthermia configuration.
Apart from being accurate, our approach is more general, more
computationally efficient and takes into account the coupling between
the antennas.
Abstract: In Dynamic Data Envelopment Analysis (DDEA), which is a subfield of Data Envelopment Analysis (DEA), the productivity of Decision Making Units (DMUs) is considered in relation to time. In this case, as it is accepted by the most of the researchers, there are outputs, which are produced by a DMU to be used as inputs in a future time. Those outputs are known as intermediates. The common models, in DDEA, do not take into account the shape of the distribution of those inputs, outputs or intermediates data, assuming that the distribution of the virtual value of them does not deviate from linearity. This weakness causes the limitation of the accuracy of the analytical power of the traditional DDEA models. In this paper, the authors, using the concept of piecewise linear inputs and outputs, propose an extended DDEA model. The proposed model increases the flexibility of the traditional DDEA models and improves the measurement of the dynamic performance of DMUs.
Abstract: We study the problem of synthesis of lumped sources
control for the objects with distributed parameters on the basis of
continuous observation of phase state at given points of object. In the
proposed approach the phase state space (phase space) is beforehand
somehow partitioned at observable points into given subsets (zones).
The synthesizing control actions therewith are taken from the class of
piecewise constant functions. The current values of control actions
are determined by the subset of phase space that contains the
aggregate of current states of object at the observable points (in these
states control actions take constant values). In the paper such
synthesized control actions are called zone control actions. A
technique to obtain optimal values of zone control actions with the
use of smooth optimization methods is given. With this aim, the
formulas of objective functional gradient in the space of zone control
actions are obtained.
Abstract: The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.
Abstract: The total mass attenuation coefficients m/r, of some halides such as, NaCl, KCl, CuCl, NaBr, KBr, RbCl, AgCl, NaI, KI, AgBr, CsI, HgCl2, CdI2 and HgI2 were determined at photon energies 279.2, 320.07, 514.0, 661.6, 1115.5, 1173.2 and 1332.5 keV in a well-collimated narrow beam good geometry set-up using a high resolution, hyper pure germanium detector. The mass attenuation coefficients and the effective atomic cross sections are found to be in good agreement with the XCOM values. From these mass attenuation coefficients, the effective atomic cross sections sa, of the compounds were determined. These effective atomic cross section sa data so obtained are then used to compute the effective atomic numbers Zeff. For this, the interpolation of total attenuation cross-sections of photons of energy E in elements of atomic number Z was performed by using the logarithmic regression analysis of the data measured by the authors and reported earlier for the above said energies along with XCOM data for standard energies. The best-fit coefficients in the photon energy range of 250 to 350 keV, 350 to 500 keV, 500 to 700 keV, 700 to 1000 keV and 1000 to 1500 keV by a piecewise interpolation method were then used to find the Zeff of the compounds with respect to the effective atomic cross section sa from the relation obtained by piece wise interpolation method. Using these Zeff values, the electron densities Nel of halides were also determined. The present Zeff and Nel values of halides are found to be in good agreement with the values calculated from XCOM data and other available published values.
Abstract: The design and implementation of the hybrid control method for a three-pole active magnetic bearing (AMB) is proposed in this paper. The system is inherently nonlinear and conventional nonlinear controllers are a little complicated, while the proposed hybrid controller has a piecewise linear form, i.e. linear in each sub-region. A state-feedback hybrid controller is designed in this study, and the unmeasurable states are estimated by an observer. The gains of the hybrid controller are obtained by the Linear Quadratic Regulator (LQR) method in each sub-region. To evaluate the performance, the designed controller is implemented on an experimental setup in static mode. The experimental results show that the proposed method can efficiently stabilize the three-pole AMB system. The simplicity of design, domain of attraction, uncomplicated control law, and computational time are advantages of this method over other nonlinear control strategies in AMB systems.
Abstract: Piecewise polynomial regression model is very flexible model for modeling the data. If the piecewise polynomial regression model is matched against the data, its parameters are not generally known. This paper studies the parameter estimation problem of piecewise polynomial regression model. The method which is used to estimate the parameters of the piecewise polynomial regression model is Bayesian method. Unfortunately, the Bayes estimator cannot be found analytically. Reversible jump MCMC algorithm is proposed to solve this problem. Reversible jump MCMC algorithm generates the Markov chain that converges to the limit distribution of the posterior distribution of piecewise polynomial regression model parameter. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of piecewise polynomial regression model.
Abstract: Wireless Sensor Networks (WSNs), which sense
environmental data with battery-powered nodes, require multi-hop
communication. This power-demanding task adds an extra workload
that is unfairly distributed across the network. As a result, nodes run
out of battery at different times: this requires an impractical
individual node maintenance scheme. Therefore we investigate a new
Cooperative Sensing approach that extends the WSN operational life
and allows a more practical network maintenance scheme (where all
nodes deplete their batteries almost at the same time). We propose a
novel cooperative algorithm that derives a piecewise representation
of the sensed signal while controlling approximation accuracy.
Simulations show that our algorithm increases WSN operational life
and spreads communication workload evenly. Results convey a
counterintuitive conclusion: distributing workload fairly amongst
nodes may not decrease the network power consumption and yet
extend the WSN operational life. This is achieved as our cooperative
approach decreases the workload of the most burdened cluster in the
network.
Abstract: Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.
Abstract: This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.
Abstract: This study is concerned with the visualization of monotone data using a piecewise C1 rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and othertwo are leftfree. Figures are used widely to exhibit that the proposed scheme produces graphically smooth monotone curves.
Abstract: Due to uncertainty of wind velocity, wind power generators don’t have deterministic output power. Utilizing wind power generation and thermal power plants together create new concerns for operation engineers of power systems. In this paper, a model is presented to implement the uncertainty of load and generated wind power which can be utilized in power system operation planning. Stochastic behavior of parameters is simulated by generating scenarios that can be solved by deterministic method. A mixed-integer linear programming method is used for solving deterministic generation scheduling problem. The proposed approach is applied to a 12-unit test system including 10 thermal units and 2 wind farms. The results show affectivity of piecewise linear model in unit commitment problems. Also using linear programming causes a considerable reduction in calculation times and guarantees convergence to the global optimum. Neglecting the uncertainty of wind velocity causes higher cost assessment of generation scheduling.
Abstract: In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhin,s continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained.
Abstract: In this paper we apply one of approaches in category of heuristic methods as Genetic Algorithms for obtaining approximate solution of optimal control problems. The firs we convert optimal control problem to a quasi Assignment Problem by defining some usual characters as defined in Genetic algorithm applications. Then we obtain approximate optimal control function as an piecewise constant function. Finally the numerical examples are given.
Abstract: This paper deals with modeling and parameter
identification of nonlinear systems described by Hammerstein model
having Piecewise nonlinear characteristics such as Dead-zone
nonlinearity characteristic. The simultaneous use of both an easy
decomposition technique and the triangular basis functions leads to a
particular form of Hammerstein model. The approximation by using
Triangular basis functions for the description of the static nonlinear
block conducts to a linear regressor model, so that least squares
techniques can be used for the parameter estimation. Singular Values
Decomposition (SVD) technique has been applied to separate the
coupled parameters. The proposed approach has been efficiently
tested on academic examples of simulation.
Abstract: In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.
Abstract: Linear two-point boundary value problems of order
two are solved using cubic trigonometric B-spline interpolation
method (CTBIM). Cubic trigonometric B-spline is a piecewise
function consisting of trigonometric equations. This method is tested
on some problems and the results are compared with cubic B-spline
interpolation method (CBIM) from the literature. CTBIM is found to
approximate the solution slightly more accurately than CBIM if the
problems are trigonometric.
Abstract: This article is dedicated to development of
mathematical models for determining the dynamics of
concentration of hazardous substances in urban turbulent
atmosphere. Development of the mathematical models implied
taking into account the time-space variability of the fields of
meteorological items and such turbulent atmosphere data as vortex
nature, nonlinear nature, dissipativity and diffusivity. Knowing the
turbulent airflow velocity is not assumed when developing the
model. However, a simplified model implies that the turbulent and
molecular diffusion ratio is a piecewise constant function that
changes depending on vertical distance from the earth surface.
Thereby an important assumption of vertical stratification of urban
air due to atmospheric accumulation of hazardous substances
emitted by motor vehicles is introduced into the mathematical
model. The suggested simplified non-linear mathematical model of
determining the sought exhaust concentration at a priori unknown
turbulent flow velocity through non-degenerate transformation is
reduced to the model which is subsequently solved analytically.