Computational Efficiency of First and Second Order Sensitivity Analysis Methods for Dynamic Systems

1993 ◽  
Author(s):  
Qiushi Cao ◽  
Prakash Krishnaswami
Keyword(s):  
Sensitivity Analysis ◽  
Finite Difference ◽  
Dynamic Systems ◽  
Computational Efficiency ◽  
Computing Time ◽  
Design Sensitivity ◽  
Second Order ◽  
First Order ◽  
Comparison Results ◽  
Finite Difference Solution

Abstract First and second order design sensitivity information have become very popular in engineering design, due to the recent development of appropriate methodology and computer technology. This paper presents an empirical study of the computing effort required for computing first and second order design sensitivity information for constrained dynamic mechanical systems and compares the relative efficiency of analytical and finite difference method. Four typical examples have been solved, with the computing time being recorded in each case. The time comparison results indicate that it is generally much more efficient to produce first order design sensitivity information by a direct analytical method than by finite differencing. For second order design sensitivity analysis, the results indicate that a purely analytical solution is usually more efficient than a pure finite difference solution. However, a hybrid scheme appears to be very competitive in terms of computational efficiency.

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.

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.

Optimal Capacitors Placement of Distribution Systems Using 2nd Order Power Loss Sensitivity Analysis and Hierarchical Clustering

2014 ◽  
Vol 986-987 ◽  
pp. 377-382 ◽  
Author(s):  
Hui Min Gao ◽  
Jian Min Zhang ◽  
Chen Xi Wu
Keyword(s):  
Sensitivity Analysis ◽  
Hierarchical Clustering ◽  
Distribution System ◽  
Power Flow ◽  
Distribution Systems ◽  
Reactive Power ◽  
Digital Simulation ◽  
Second Order ◽  
First Order ◽  
The Impact

Heuristic methods by first order sensitivity analysis are often used to determine location of capacitors of distribution power system. The selected nodes by first order sensitivity analysis often have virtual high by first order sensitivities, which could not obtain the optimal results. This paper presents an effective method to optimally determine the location and capacities of capacitors of distribution systems, based on an innovative approach by the second order sensitivity analysis and hierarchical clustering. The approach determines the location by the second order sensitivity analysis. Comparing with the traditional method, the new method considers the nonlinear factor of power flow equation and the impact of the latter selected compensation nodes on the previously selected compensation location. This method is tested on a 28-bus distribution system. Digital simulation results show that the reactive power optimization plan with the proposed method is more economic while maintaining the same level of effectiveness.

Higher-Order Multilevel Solvers for the EHL Line and Point Contact Problem

1994 ◽  
Vol 116 (4) ◽  
pp. 741-750 ◽  
Author(s):  
C. H. Venner
Keyword(s):  
Contact Problem ◽  
Computing Time ◽  
Point Contact ◽  
Higher Order ◽  
Second Order ◽  
Point Of View ◽  
First Order ◽  
Fundamental Point ◽  
Numerical Solver ◽  
Circular Contact

This paper addresses the development of efficient numerical solvers for EHL problems from a rather fundamental point of view. A work-accuracy exchange criterion is derived, that can be interpreted as setting a limit to the price paid in terms of computing time for a solution of a given accuracy. The criterion can serve as a guideline when reviewing or selecting a numerical solver and a discretization. Earlier developed multilevel solvers for the EHL line and circular contact problem are tested against this criterion. This test shows that, to satisfy the criterion a second-order accurate solver is needed for the point contact problem whereas the solver developed earlier used a first-order discretization. This situation arises more often in numerical analysis, i.e., a higher order discretization is desired when a lower order solver already exists. It is explained how in such a case the multigrid methodology provides an easy and straightforward way to obtain the desired higher order of approximation. This higher order is obtained at almost negligible extra work and without loss of stability. The approach was tested out by raising an existing first order multilevel solver for the EHL line contact problem to second order. Subsequently, it was used to obtain a second-order solver for the EHL circular contact problem. Results for both the line and circular contact problem are presented.

First- and Second-Order Design Sensitivity Analysis Scheme Based on Trefftz Method

1999 ◽  
Vol 121 (1) ◽  
pp. 84-91 ◽  
Author(s):  
E. Kita ◽  
Y. Kataoka ◽  
N. Kamiya
Keyword(s):  
Sensitivity Analysis ◽  
Design Sensitivity ◽  
Second Order ◽  
Design Sensitivity Analysis ◽  
Design Parameters ◽  
Trefftz Method ◽  
Analysis Scheme ◽  
Complete Functions ◽  
Approximate Expressions ◽  
Physical Quantities

This paper presents a new scheme for the first- and second-order design sensitivity analysis of the two-dimensional elastic problem by using Trefftz method. In the Trefftz method, the physical quantities are approximated by superposition of regular T-complete functions. Therefore, direct differentiation of the approximate expressions with respect to design parameters leads to the regular expressions of the sensitivities. The present schemes are applied to some examples in order to confirm the validity.

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