scholarly journals Effects of higher order Taylor series terms on the solution accuracy of NI-RPIM for 3D elastostatic problems

2014 ◽  
Vol 38 ◽  
pp. 411-433
Author(s):  
Mustafa Murat YAVUZ ◽  
Bahattin KANBER
Keyword(s):  
Taylor Series ◽  
Higher Order ◽  
Solution Accuracy

scholarly journals An EKF-Based Fixed-Point Iterative Filter for Nonlinear Systems

Sensors ◽  
2019 ◽  
Vol 19 (8) ◽  
pp. 1893
Author(s):  
Feng ◽  
Feng ◽  
Wen
Keyword(s):  
Fixed Point ◽  
Kalman Filter ◽  
Nonlinear Systems ◽  
Iterative Method ◽  
Taylor Series ◽  
Nonlinear Filtering ◽  
Higher Order ◽  
Point Function ◽  
State Estimate ◽  
Linearized System

In this paper, a fixed-point iterative filter developed from the classical extended Kalman filter (EKF) was proposed for general nonlinear systems. As a nonlinear filter developed from EKF, the state estimate was obtained by applying the Kalman filter to the linearized system by discarding the higher-order Taylor series items of the original nonlinear system. In order to reduce the influence of the discarded higher-order Taylor series items and improve the filtering accuracy of the obtained state estimate of the steady-state EKF, a fixed-point function was solved though a nested iterative method, which resulted in a fixed-point iterative filter. The convergence of the fixed-point function is also discussed, which provided the existing conditions of the fixed-point iterative filter. Then, Steffensen’s iterative method is presented to accelerate the solution of the fixed-point function. The final simulation is provided to illustrate the feasibility and the effectiveness of the proposed nonlinear filtering method.

scholarly journals The Attractors of the Common Differential Operator Are Determined by Hyperbolic and Lacunary Functions

2008 ◽  
Vol 2008 ◽  
pp. 1-19
Author(s):  
Wolf Bayer
Keyword(s):  
Differential Operator ◽  
Taylor Series ◽  
Analytic Functions ◽  
Chaotic Behavior ◽  
Higher Order ◽  
Limit Behavior ◽  
Hyperbolic Functions ◽  
Limit Sets ◽  
The Common

For analytic functions, we investigate the limit behavior of the sequence of their derivatives by means of Taylor series, the attractors are characterized by -limit sets. We describe four different classes of functions, with empty, finite, countable, and uncountable attractors. The paper reveals that Erdelyiéshyperbolic functions of higher orderandlacunary functionsplay an important role for orderly or chaotic behavior. Examples are given for the sake of confirmation.

scholarly journals Generalized Quadratic Linearization of Machine Models

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Parvathy Ayalur Krishnamoorthy ◽  
Kamaraj Vijayarajan ◽  
Devanathan Rajagopalan
Keyword(s):  
Nonlinear System ◽  
Taylor Series ◽  
State Feedback ◽  
Taylor Series Expansion ◽  
Higher Order ◽  
Exact Linearization ◽  
Linearization Technique ◽  
Practical Applications ◽  
Higher Order Terms ◽  
Approximate Linearization

In the exact linearization of involutive nonlinear system models, the issue of singularity needs to be addressed in practical applications. The approximate linearization technique due to Krener, based on Taylor series expansion, apart from being applicable to noninvolutive systems, allows the singularity issue to be circumvented. But approximate linearization, while removing terms up to certain order, also introduces terms of higher order than those removed into the system. To overcome this problem, in the case of quadratic linearization, a new concept called “generalized quadratic linearization” is introduced in this paper, which seeks to remove quadratic terms without introducing third- and higher-order terms into the system. Also, solution of generalized quadratic linearization of a class of control affine systems is derived. Two machine models are shown to belong to this class and are reduced to only linear terms through coordinate and state feedback. The result is applicable to other machine models as well.

HIGHER-ORDER GEODESIC DEVIATIONS AND THE CALCULUS OF RELATIVISTIC ORBITS

2002 ◽  
Vol 17 (20) ◽  
pp. 2756-2756 ◽  
Author(s):  
R. COLISTETE
Keyword(s):  
Harmonic Oscillator ◽  
Taylor Series ◽  
Gravitational Radiation ◽  
Circular Orbit ◽  
Linear Equations ◽  
Higher Order ◽  
Test Particles ◽  
Oscillator Type ◽  
Constant Coefficients ◽  
Systems Of Linear Equations

Starting with an exact and simple geodesic, we generate approximate geodesics1,2 by summing up higher-order geodesic deviations in a fully relativistic scheme. We apply this method to the problem of orbit motion of test particles in Schwarzschild3 and Kerr metrics; from a simple circular orbit as the initial geodesic we obtain finite eccentricity orbits as a Taylor series with respect to the eccentricity. The explicit expressions of these higher-order geodesic deviations are derived using successive systems of linear equations with constant coefficients, whose solutions are of harmonic oscillator type. This scheme is best adapted for small eccentricities, but arbitrary values of M/R. We also analyse the possible application to the calculation of the emission of gravitational radiation from non-circular orbits around a very massive body3.

Propagating Skewness and Kurtosis Through Engineering Models for Low-Cost, Meaningful, Nondeterministic Design

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Travis V. Anderson ◽  
Christopher A. Mattson
Keyword(s):  
Order Statistics ◽  
Taylor Series ◽  
Computational Cost ◽  
Higher Order ◽  
Second Order ◽  
System Model ◽  
Higher Order Statistics ◽  
Actual System ◽  
System Output ◽  
Skewness And Kurtosis

System models help designers predict actual system output. Generally, variation in system inputs creates variation in system outputs. Designers often propagate variance through a system model by taking a derivative-based weighted sum of each input’s variance. This method is based on a Taylor-series expansion. Having an output mean and variance, designers typically assume the outputs are Gaussian. This paper demonstrates that outputs are rarely Gaussian for nonlinear functions, even with Gaussian inputs. This paper also presents a solution for system designers to more meaningfully describe the system output distribution. This solution consists of using equations derived from a second-order Taylor series that propagate skewness and kurtosis through a system model. If a second-order Taylor series is used to propagate variance, these higher-order statistics can also be propagated with minimal additional computational cost. These higher-order statistics allow the system designer to more accurately describe the distribution of possible outputs. The benefits of including higher-order statistics in error propagation are clearly illustrated in the example of a flat-rolling metalworking process used to manufacture metal plates.

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