Generalized Reference Basis Model Updating in Structural Dynamics

1997 ◽  
Author(s):  
Rachel Kenigsbuch ◽  
Yoram Halevi
Keyword(s):  
Experimental Data ◽  
Closed Form ◽  
Prior Knowledge ◽  
Structural Dynamics ◽  
Optimization Problem ◽  
Model Updating ◽  
Optimization Criterion ◽  
Constrained Optimization Problem ◽  
Closed Form Solutions ◽  
Insight Into

Abstract The paper considers the problem of updating an analytical model from experimental data. The approach that is taken is the reference basis, where some of the parameters are considered to be completely accurate while the others are updated by solving a constrained optimization problem. The main results of this paper are closed form solutions to these problems with general weighting matrices in the optimization criterion. These are generalizations of several model reference updating problems that were solved and reported in the literature. The importance of this generalization is the ability to incorporate prior knowledge regarding the accuracy of the model in specified areas into the method. Another aspect of this work is the investigation of geometrical interpretation of the results which provides insight into the mechanism of the updating process. The advantages of the new updating schemes are demonstrated by means of examples.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

A Benchmark Study on Crushing and Cutting of Plated Structures

1997 ◽  
Vol 41 (02) ◽  
pp. 147-160
Author(s):  
Jeom Kee Paik ◽  
Tomasz Wierzbicki
Keyword(s):  
Experimental Data ◽  
Closed Form ◽  
Dynamic Effects ◽  
Crushing Strength ◽  
Closed Form Solutions ◽  
Cutting Resistance ◽  
Benchmark Study ◽  
Stiffened Structures ◽  
The Mean

A benchmark study on several closed-form solutions for the mean crushing strength and the cutting resistance of plated structures during collision or grounding is carried out by comparing theoretical solutions with experimental data. Based on expressions which have been derived for unstiffened structures, an extension of the methods is proposed for longitudinally and/or transversely stiffened structures. Dynamic effects on the crushing and cutting response are discussed, and applicability of the quasistatic formulations to analyze the crushing and cutting damage of the structure in the dynamic situations is investigated.

MODELING EXPERIMENTAL DATA WITH POLYNOMIALS CHAOS

2018 ◽  
Vol 34 (1) ◽  
pp. 14-26
Author(s):  
Emeline Gayrard ◽  
Cédric Chauvière ◽  
Hacène Djellout ◽  
Pierre Bonnet
Keyword(s):  
Experimental Data ◽  
Constrained Optimization ◽  
Numerical Experiments ◽  
Optimization Problem ◽  
Polynomial Chaos ◽  
Numerical Procedure ◽  
Chaos Expansion ◽  
Constrained Optimization Problem ◽  
Raw Data ◽  
Accurate Representation

Given a raw data sample, the purpose of this paper is to design a numerical procedure to model this sample under the form of polynomial chaos expansion. The coefficients of the polynomial are computed as the solution to a constrained optimization problem. The procedure is first validated on samples coming from a known distribution and it is then applied to raw experimental data of unknown distribution. Numerical experiments show that only five coefficients of the Chaos expansions are required to get an accurate representation of a sample.

Assessment of Aided-INS Performance

2011 ◽  
Vol 65 (1) ◽  
pp. 169-185 ◽  
Author(s):  
Itzik Klein ◽  
Sagi Filin ◽  
Tomer Toledo ◽  
Ilan Rusnak
Keyword(s):  
Closed Form ◽  
Analytical Solutions ◽  
Navigation Systems ◽  
Inertial Navigation Systems ◽  
Closed Form Solutions ◽  
Land Vehicles ◽  
Error Covariance ◽  
Model Dependency ◽  
Error State ◽  
Insight Into

Aided Inertial Navigation Systems (INS) systems are commonly implemented in land vehicles for a variety of applications. Several methods have been reported in the literature for evaluating aided INS performance. Yet, the INS error-state-model dependency on time and trajectory implies that no closed-form solutions exist for such evaluation. In this paper, we derive analytical solutions to evaluate the fusion performance. We show that the derived analytical solutions manage to predict the error covariance behavior of the full aided INS error model. These solutions bring insight into the effect of the various parameters involved in the fusion of the INS and an aiding sensor.

Analytical and Graphical Solutions to the Forward Position Problem of Two Robots Manipulating a Spatial Linkage Payload

1997 ◽  
Vol 119 (3) ◽  
pp. 349-358
Author(s):  
G. R. Pennock ◽  
K. G. Mattson
Keyword(s):  
Closed Form ◽  
Orthogonal Transformation ◽  
Solution Technique ◽  
Closed Form Solutions ◽  
Transformation Matrices ◽  
Kinematic Geometry ◽  
Order Polynomial ◽  
Position Problem ◽  
Four Bar Linkage ◽  
Insight Into

This paper presents a solution to the forward position problem of two PUMA-type robots manipulating a spatial four-bar linkage payload. To simplify the kinematic analysis, the Bennett linkage, which is a special geometry spatial four-bar, will be regarded as the payload. The orientation of a specified payload link is described by a sixth-order polynomial and a specified joint displacement in the wrist subassembly of one of the robots is described by a second-order polynomial. A solution technique, based on orthogonal transformation matrices with dual number elements, is used to obtain closed-form solutions for the remaining unknown joint displacements in the wrist subassembly of each robot. An important result is that, for a given set of robot input angles, twenty-four assembly configurations of the robot-payload system are possible. Repeated roots of the polynomials are shown to correspond to the stationary configurations of the system. The paper emphasizes that an understanding of the kinematic geometry of the system is essential to verify the number of possible solutions to the forward position problem. Graphical methods are also presented to provide insight into the assembly and stationary configurations. A numerical example of the two robots manipulating the Bennett linkage is included to demonstrate the importance of the polynomial and closed-form solutions.

scholarly journals A novel-iterative simulation method for performance analysis of non-coherent FSK/ASK systems over Rice/Rayleigh channels using the wolfram language

2016 ◽  
Vol 13 (2) ◽  
pp. 157-174 ◽  
Author(s):  
Vladimir Mladenovic ◽  
Danijela Milosevic
Keyword(s):  
Closed Form ◽  
Communication Systems ◽  
Rayleigh Fading ◽  
Simulation Method ◽  
Rician Fading ◽  
New Approach ◽  
Closed Form Solutions ◽  
Numerical Tools ◽  
The Impact ◽  
Insight Into

In this paper, a new approach in solving and analysing the performances of the digital telecommunication non-coherent FSK/ASK system in the presence of noise is derived, by using a computer algebra system. So far, most previous solutions cannot be obtained in closed form, which can be a problem for detailed analysis of complex communication systems. In this case, there is no insight into the influence of certain parameters on the performance of the system. The analysis, modelling and design can be time-consuming. One of the main reasons is that these solutions are obtained by utilising traditional numerical tools in the shape of closed-form expressions. Our results were obtained in closed-form solutions. They are resolved by the introduction of an iteration-based simulation method. The Wolfram language is used for describing applied symbolic tools, and SchematicSolver application package has been used for designing. In a new way, the probability density function and the impact of the newly introduced parameter of iteration are performed when errors are calculated. Analyses of the new method are applied to several scenarios: without fading, in the presence of Rayleigh fading, Rician fading, and in cases when the signals are correlated and uncorrelated.

Combined Expansion and Orthogonalization of Experimental Modeshapes

2004 ◽  
Vol 127 (2) ◽  
pp. 188-196 ◽  
Author(s):  
Y. Halevi ◽  
C. A. Morales ◽  
D. J. Inman
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Model Updating ◽  
Mass Matrix ◽  
Closed Form Solution ◽  
Form Solution ◽  
Entire Structure ◽  
Error Localization ◽  
Procrustes Problem

The paper describes a method of combined expansion and orthogonalization (CEO) of experimental modeshapes. Most model updating and error localization methods require a set of full length, orthogonal with respect to the mass matrix, eigenvectors. In practically every modal experiment, the number of measurements is less than the order of the model, and hence modeshape expansion, i.e., adding the unmeasured degrees of freedom, is required. This step is then followed by orthogonalization with respect to the mass matrix. Most current methods use two separate steps for expansion and orthogonalization, each one optimal by itself, but their combination is not optimal. The suggested method combines the two steps into one optimization problem for both steps, and minimizes a quadratic criterion. In the case of an equal number of analytical and experimental modeshapes, the problem coincides with the Procrustes problem and has a closed form solution. Otherwise the solution involves nonlinear equations. Several examples show the advantage of CEO, especially in cases where the measurements are limited either in number or in space, i.e., not spanned through the entire structure.

The Forward Position Problem of Two Puma-Type Robots Manipulating a Bennett Linkage Payload

1996 ◽  
Author(s):  
Gordon R. Pennock ◽  
Keith G. Mattson
Keyword(s):  
Closed Form ◽  
Orthogonal Transformation ◽  
Solution Technique ◽  
Closed Form Solutions ◽  
Transformation Matrices ◽  
Kinematic Geometry ◽  
Order Polynomial ◽  
Position Solution ◽  
Position Problem ◽  
Insight Into

Abstract This paper presents a solution to the forward position problem of two PUMA-type robots manipulating a Bennett linkage payload. The orientation of a specified payload link is described by a sixth-order polynomial and a specified angular joint displacement in the wrist subassembly of one of the robots is described by a second-order polynomial. A solution technique, based on orthogonal transformation matrices with dual number elements, is used to obtain closed-form solutions for the remaining unknown angular joint displacements in the wrist subassembly of each robot. The paper shows that, for a given set of robot input angles, twenty-four assembly configurations of the robot-payload system are possible. The polynomials provide insight into these configurations, and also reveal stationary configurations of the system. The paper emphasizes that insight into the kinematic geometry of the system is essential in developing the forward position solution. Graphical methods are presented which provide insight into the geometry, and a check of the analytical approach. For illustrative purposes, a numerical example of the two robots manipulating a Bennett linkage is included in this paper to demonstrate the importance of the polynomials and the closed-form solutions.

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