scholarly journals Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaowang Li ◽  
Zhongmin Deng
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Time History ◽  
Taylor Series Expansion ◽  
Second Order ◽  
New Method ◽  
Dynamic Loads ◽  
Discrete Equation ◽  
System Response ◽  
Structural Dynamic

A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO) numerical simulation study, sinusoidal excitation and white noise excitation are applied on a cantilever beam, respectively, to illustrate the effectiveness of this algorithm. One also makes a comparison between the new method and conventional state space method. The results show that the proposed method can obtain a more accurate identified force time history whether the responses are polluted by noise or not.

An Improved Algorithm of Linearization Localization Based on RSSI Ranging

2013 ◽  
Vol 299 ◽  
pp. 113-116 ◽  
Author(s):  
Lei Li ◽  
Hao Zhu
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Good Accuracy ◽  
Taylor Series Expansion ◽  
New Method ◽  
Iteration Algorithm ◽  
Localization Algorithm ◽  
The Real ◽  
Acceptable Accuracy ◽  
Improved Algorithm

The positioning technology has become one of the most popular studied objects since it has been implemented in many fields. With five reference nodes at least, linearization localization algorithm get an acceptable accuracy. With Taylor Series Expansion, we can overcome this shortcoming. First, we give the blind node an initial coordinate, then we expand the group of binary quadratic based on RSSI with Taylor Series at the point of initial coordinate, remove quadratic and higher, at last ,we apply iteration algorithm to estimate the real coordinate of blind node. Compared to the original, this new method can get a very good accuracy with only three reference nodes.

The second-order theory of conformal solutions

1957 ◽  
Vol 240 (1223) ◽  
pp. 561-580 ◽  
Keyword(s):  
Thermodynamic Properties ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Order Theory ◽  
Second Order ◽  
Intermolecular Potential ◽  
Cell Theory ◽  
Reference Solution ◽  
Random Mixing

This paper describes a theoretical contribution to the statistical thermodynamics of mixtures of spherical molecules. The second-order perturbation free energy of a conformal solution is obtained by a rigorous Taylor-series expansion of the configuration integral in powers of the differences between intermolecular energy and size parameters, about an ideal unperturbed reference solution. Unlike the first-order terms, those of the second order contain statistical functions of the reference solution which cannot, in general, be related to its thermodynamic properties. All but one of these functions are concerned with departures from a random molecular distribution, and have been called molecular fluctuation integrals ; the remaining function can be related exactly to thermodynamic properties for the Lennard-Jones form of the intermolecular potential. The expressions for the molecular fluctuation integrals implied by the full random mixing approximation and by the semi-random mixing approximation of the cell theory, are derived and compared with the correct expressions given by the cell theory. The role of the Taylor series expansion as a critique of solution theories is discussed.

A Taylor Series Integration Method with Coupling in Structural Dynamics

2012 ◽  
Vol 166-169 ◽  
pp. 9-13
Author(s):  
Ze Ying Guo
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Integration Method ◽  
Damping Ratio ◽  
Time Integration ◽  
Taylor Series Expansion ◽  
Time Step ◽  
Structural Dynamic ◽  
Precise Time Integration ◽  
Stability And Accuracy

Based on the coupled precise time integration method and basic assumptions of constant average acceleration method in Newmark family, implicit series solution of structural dynamic equation is put forward by introducing the Taylor series expansion. Relevant time step integration formulas were designed. Stability and accuracy of the method were analyzed. Stability analyses show that the coupling implicit method is stable when damping ratio is equal to 0, and is conditionally stable when damping ratio are other values. The results show that the accuracy of the algorithm can be controlled by choosing the number of truncation order of Taylor series expansion and is better than that of traditional scheme with the increase of time step. Number examples are given to demonstrate the validity of the proposed method.

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