Design Sensitivity Analysis: Computational Issues of Sensitivity Equation Methods

Stanley, Lisa G.; Stewart, Dawn L.

doi:10.1115/1.1623756

Cited by 20 publications

(24 citation statements)

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“…Indeed, textbooks have been written on sensitivity analysis of structures [7,8]. To our knowledge, there is only one book on sensitivity analysis of flow problems [5]. It is rather recent and more specialized than structural mechanics books.…”

Section: Introductionmentioning

confidence: 99%

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A continuous second‐order sensitivity equation method for time‐dependent incompressible laminar flows

Ilinca

Pelletier

Borggaard

2007

Numerical Methods in Fluids

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Section: Introductionmentioning

confidence: 99%

“…There are several means of computing flow sensitivities: finite differences of flow solutions, the complex step method [2], automatic differentiation [3],a n dS E M s [4][5][6]. The first option is costly because the problem must be solved for two or more values of each parameter of interest.…”

Section: Introductionmentioning

confidence: 99%

A continuous second‐order sensitivity equation method for time‐dependent incompressible laminar flows

Ilinca

Pelletier

Borggaard

2007

Numerical Methods in Fluids

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“…In this work, we have adopted the continuous sensitivity equation (CSE) method [25][26][27].T h e CSEs are derived formally by implicit differentiation of flow equations with respect to parameter a. The sensitivity equations are then discretized and solved numerically to obtained the desired sensitivities.…”

Section: Introductionmentioning

confidence: 99%

Finite element and sensitivity analysis of thermally induced flow instabilities

Giguère

Ilinca

Pelletier

2010

Numerical Methods in Fluids

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This paper presents a finite element algorithm for the simulation of thermo‐hydrodynamic instabilities causing manufacturing defects in injection molding of plastic and metal powder. Mold‐filling parameters determine the flow pattern during filling, which in turn influences the quality of the final part. Insufficiently, well‐controlled operating conditions may generate inhomogeneities, empty spaces or unusable parts. An understanding of the flow behavior will enable manufacturers to reduce or even eliminate defects and improve their competitiveness. This work presents a rigorous study using numerical simulation and sensitivity analysis. The problem is modeled by the Navier–Stokes equations, the energy equation and a generalized Newtonian viscosity model. The solution algorithm is applied to a simple flow in a symmetrical gate geometry. This problem exhibits both symmetrical and non‐symmetrical solutions depending on the values taken by flow parameters. Under particular combinations of operating conditions, the flow was stable and symmetric, while some other combinations leading to large thermally induced viscosity gradients produce unstable and asymmetric flow. Based on the numerical results, a stability chart of the flow was established, identifying the boundaries between regions of stable and unstable flow in terms of the Graetz number (ratio of thermal conduction time to the convection time scale) and B, a dimensionless ratio indicating the sensitivity of viscosity to temperature changes. Sensitivities with respect to flow parameters are then computed using the continuous sensitivity equations method. We demonstrate that sensitivities are able to detect the transition between the stable and unstable flow regimes and correctly indicate how parameters should change in order to increase the stability of the flow. Copyright © 2009 John Wiley & Sons, Ltd.

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“…However, to the best of our knowledge, thus far there is no literature on sensitivity equations and the related analysis for size-structured population models. Sensitivity analysis of dynamical systems has drawn the attention of numerous researchers [1,6,9,10,11,13,14,15,16,17,20,24,25,27,28,35,38,40] for many years because the resulting sensitivity functions can be used in many areas such as optimization and design [16,26,27,34,38], computation of standard errors [9,10,19,21,36], and information theory [12] related quantities (e.g., the Fisher information matrix) as well as control theory, parameter estimation and inverse problems [5,8,9,10,11,40,41]. One of our motivations for investigating sensitivity for size-structured population models derives from our efforts reported in [7], where a shrimp biomass production system and a…”

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confidence: 99%

Sensitivity equations for a size-structured population model

Banks

Ernstberger

2009

Quart. Appl. Math.

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Abstract. In this paper we consider the classical Sinko-Streifer size-structured population model and derive sensitivity partial differential equations for the sensitivities of solutions with respect to initial conditions, growth rate, mortality rate and fecundity rate. Sample numerical results to illustrate the use of these equations are also presented. [3,4,29,32] have focused on establishing well-posedness and stability analysis of models, formulating schemes for numerical solutions, and parameter estimation of individual rates. However, to the best of our knowledge, thus far there is no literature on sensitivity equations and the related analysis for size-structured population models. Sensitivity analysis of dynamical systems has drawn the attention of numerous researchers [1,6,9,10,11,13,14,15,16,17,20,24,25,27,28,35,38,40] for many years because the resulting sensitivity functions can be used in many areas such as optimization and design [16,26,27,34,38], computation of standard errors [9,10,19,21,36], and information theory [12] related quantities (e.g., the Fisher information matrix) as well as control theory, parameter estimation and inverse problems [5,8,9,10,11,40,41]. One of our motivations for investigating sensitivity for size-structured population models derives from our efforts reported in [7], where a shrimp biomass production system and a

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Design Sensitivity Analysis: Computational Issues of Sensitivity Equation Methods

Cited by 20 publications

References 0 publications

A continuous second‐order sensitivity equation method for time‐dependent incompressible laminar flows

A continuous second‐order sensitivity equation method for time‐dependent incompressible laminar flows

Finite element and sensitivity analysis of thermally induced flow instabilities

Sensitivity equations for a size-structured population model

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