Design Sensitivity Analysis of Multibody Dynamic Systems for Parallel Processing

1989 ◽  
Author(s):  
T. Tak ◽  
S. S. Kim
Keyword(s):  
Sensitivity Analysis ◽  
Parallel Processing ◽  
Dynamic Systems ◽  
Large Scale ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Parallel Computer ◽  
Sensitivity Equations ◽  
Multibody Dynamic ◽  
High Level

Abstract Design sensitivity analysis of large scale multibody systems is a computationally intensive process, which is well suited for implementation on a parallel computer. This paper presents a parallel processing oriented generalized design sensitivity analysis method for multibody dynamic systems. A direct differentiation method, which is more efficient than an adjoint variable method in a parallel processing environment due to the inherent parallelism, is applied to a recursive formulation for multibody dynamics to set up dynamic sensitivity equations. A high level of parallelism is achieved, exploiting the independence of each set of design sensitivity equations. To verify the formulation for design sensitivity analysis and to demonstrate the speedup on a parallel computer, an example is presented.

Supercomputer-Based Sensitivity Analysis of Constrained Dynamic Systems

1987 ◽  
Author(s):  
P. Krishnaswami ◽  
S. Ramaswamy
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Large Scale ◽  
Computing Time ◽  
Computer Code ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Dramatic Reduction ◽  
Computational Performance ◽  
Computationally Intensive

Abstract Generalized design sensitivity analysis of constrained dynamic systems is a computationally intensive process that is well-suited for implementation on a modern supercomputer. A matrix oriented method for design sensitivity analysis, based on direct differentiation, is developed. An algorithm based on this development was implemented in a computer code which was then run on a Cray X-MP supercomputer. The implementation attempts to make full use of the vectorization capabilities of this machine. The numerical examples that were run on this implementation were compared with results presented in the literature in order to verify the program and to assess its computational performance. The results show that the use of supercomputers for performing design sensitivity analysis of dynamic systems using this method produces a dramatic reduction in the computing time; it is anticipated that this will make the optimization of very large-scale dynamic systems computationally viable.

Direct Differentiation Methods for the Design Sensitivity of Multibody Dynamic Systems

1996 ◽  
Author(s):  
Radu Serban ◽  
Jeffrey S. Freeman
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Mechanism Analysis ◽  
Algebraic Equations ◽  
First Order ◽  
Direct Differentiation ◽  
Multibody Dynamic ◽  
Standard Techniques

Abstract Methods for formulating the first-order design sensitivity of multibody systems by direct differentiation are presented. These types of systems, when formulated by Euler-Lagrange techniques, are representable using differential-algebraic equations (DAE). The sensitivity analysis methods presented also result in systems of DAE’s which can be solved using standard techniques. Problems with previous direct differentiation sensitivity analysis derivations are highlighted, since they do not result in valid systems of DAE’s. This is shown using the simple pendulum example, which can be analyzed in both ODE and DAE form. Finally, a slider-crank example is used to show application of the method to mechanism analysis.

Dynamic Response Optimization of Mechanical Systems With Multiplier Methods

1989 ◽  
Vol 111 (1) ◽  
pp. 73-80 ◽  
Author(s):  
J. K. Paeng ◽  
J. S. Arora
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Response ◽  
Large Scale ◽  
Unconstrained Minimization ◽  
Design Sensitivity ◽  
Computational Effort ◽  
Design Sensitivity Analysis ◽  
Multiplier Methods ◽  
Dynamic Response Optimization ◽  
Response Optimization

A basic hypothesis of this paper is that the multiplier methods can be effective and efficient for dynamic response optimization of large scale systems. The methods have been previously shown to be inefficient compared to the primal methods for static response applications. However, they can be more efficient for dynamic response applications because they collapse all time-dependent constraints and the cost function to one functional. This can result in substantial savings in the computational effort during design sensitivity analysis. To investigate this hypothesis, an augmented functional for the dynamic response optimization problem is defined. Design sensitivity analysis for the functional is developed and three example problems are solved to investigate computational aspects of the multiplier methods. It is concluded that multiplier methods can be effective for dynamic response problems but need numerical refinements to avoid convergence difficulties in unconstrained minimization.

Shape Optimization of a Large-Scale BLDC Motor Using an Adaptive RSM Utilizing Design Sensitivity Analysis

2007 ◽  
Vol 43 (4) ◽  
pp. 1653-1656 ◽  
Author(s):  
Pan Seok Shin ◽  
Han-Deul Kim ◽  
Gyo-Bum Chung ◽  
Hee Sung Yoon ◽  
Gwan-Soo Park ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Shape Optimization ◽  
Large Scale ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Bldc Motor

Design Sensitivity Analysis of Large-Scale Constrained Dynamic Mechanical Systems

1984 ◽  
Vol 106 (2) ◽  
pp. 156-162 ◽  
Author(s):  
E. J. Haug ◽  
R. A. Wehage ◽  
N. K. Mani
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Equations Of Motion ◽  
Design Sensitivity ◽  
Differential Algebraic Equations ◽  
Adjoint Equations ◽  
Design Sensitivity Analysis ◽  
Integration Algorithm ◽  
Coordinate Partitioning ◽  
Generalized Coordinate

A method for computer-aided design sensitivity analysis of large-scale constrained dynamic systems is presented. A generalized coordinate partitioning method is used for assembling and solving sets of mixed differential-algebraic equations of motion and adjoint equations required for calculation of derivatives of dynamic response measures with respect to design variables. The reduction in dimension of the equations of motion and associated adjoint equations obtained through use of generalized coordinate partitioning significantly reduces the computational burden, as compared to methods previously employed. Use of predictor-corrector numerical integration algorithms, rather than an implicit integration algorithm used in the past is shown to greatly simplify the equations that must be formulated and solved. Two examples are presented to illustrate accuracy of the design sensitivity analysis method developed.

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