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.

Topology Designs of Slider Air Bearings

2004 ◽  
Vol 126 (2) ◽  
pp. 342-346 ◽  
Author(s):  
Sang-Joon Yoon ◽  
Dong-Hoon Choi
Keyword(s):  
Sensitivity Analysis ◽  
Design Methodology ◽  
Large Scale ◽  
Unconstrained Minimization ◽  
Design Sensitivity ◽  
Computational Effort ◽  
Optimization Techniques ◽  
Topology Design ◽  
Air Bearings ◽  
Design Variables

A new approach for topology designs of slider air bearings in magnetic recording disk drives is suggested by using large-scale discrete variable optimization techniques. Conventional optimization techniques are restricted to the original topology of the slider by modifying the initial designs. To overcome the restriction, a new topology design approach is presented with enhanced mathematical techniques. Topology optimization of slider air bearings typically has a large number of design variables because the finite mesh must be fine enough to represent the shape of the air bearing surface (ABS). To handle a large number of design variables, an efficient strategy for the optimization including the sensitivity analysis must be established. As a gradient-based local optimization algorithm, the sequential unconstrained minimization technique (SUMT) using an exterior penalty function is used, which requires little computational effort and computer memory. For the gradient calculation, the analytical design sensitivity analysis method introducing an adjoint variable is employed. A topology design problem is formulated as a function of the residuals which is calculated by solving the generalized Reynolds equation. A very large number of discrete design variables (=9409) are dealt with, which denote the rail heights at grid cells. To validate the suggested design methodology, a developed program is applied to two slider models with one and three trailing rails. The simulation results demonstrated the effectiveness of the proposed design methodology by showing that the optimized topologies have reasonable shapes without any initial designs.

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.

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.

A State Space Method for Kinematic Optimization of Mechanisms and Machines

1982 ◽  
Vol 104 (1) ◽  
pp. 101-107 ◽  
Author(s):  
V. Sohoni ◽  
E. J. Haug
Keyword(s):  
Sensitivity Analysis ◽  
State Space ◽  
Kinematic Analysis ◽  
Large Scale ◽  
Design Sensitivity ◽  
Design Sensitivity Analysis ◽  
Large Scale Systems ◽  
Synthesis Of Mechanisms ◽  
Derivatives Of ◽  
Kinematic Optimization

Problems of optimal kinematic synthesis of mechanisms and machines are formulated in a state space setting that allows for treatment of large scale systems with general design objectives and constraints. An iterative kinematic analysis method is presented. An adjoint variable method of design sensitivity analysis is presented that uses the same matrices generated in kinematic analysis to efficiently calculate derivatives of cost and constraint functions with respect to design. A gradient projection optimization algorithm is presented, based on the state space kinematic and design sensitivity analysis formulation. Two mechanism synthesis problems are solved to illustrate the method and to evaluate its effectiveness.

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