Adjoint Sensitivity Analysis Method Research Articles

An adjoint variable method for sensitivity analysis of non‐linear elastic systems

AbstractAn adjoint variable method for design sensitivity analysis of non‐linear elastic systems is presented. The method uses domain parameterization and a mutual form of the Hu‐Washizu energy principle, and extends results reported in a recent work for linear elastic systems to non‐linear elasticity. Non‐linearities due to finite deformations and non‐linear, hyperelastic constitutive models are considered. In contrast to other methods for non‐linear sensitivity analysis, the present formulation can be applied with force, displacement or mixed approximate solution methods.The mutual energy expression used in the adjoint sensitivity derivation is developed from a non‐linear extension of the Hu‐Washizu energy functional and yields a linear governing equation for the adjoint system. This has important ramifications for the computational cost of a sensitivity analyses of non‐linear systems: excluding the cost of determining the response of the system, the cost of a sensitivity analysis for a non‐linear system is essentially the same as that for a linear system. Finite element implementation of the resulting sensitivity expressions is discussed, and two numerical examples are presented. The first example involves large deformations of a Mooney‐Rivlin body, while the second involves design sensitivity analysis for mixed solution methods.

Multilevel substructuring sensitivity analysis

Solution techniques for handling large scale engineering optimization problems are reviewed. Potentials for practical applications as well as their limited capabilities are discussed. A new solution algorithm for design sensitivity is proposed. The algorithm is based upon the multilevel substructuring concept to be coupled with the adjoint method of sensitivity analysis. There are no approximations involved in the present algorithm except the usual approximations introduced due to the discretization of the finite element model. It is a well-known fact that substructuring concept can be exploited in order to reduce computer core memory requirement and the total solution time executed. These advantages have been realized not only for statics analysis, but also for design sensitivity analysis. For truly large scale structures, however, it is necessary to use multilevel substructuring. The present paper has formulated a multilevel algorithm for design sensitivity analysis. A two-level substructuring example is used to verify the proposed algorithm. The sensitivity vector obtained by the multilevel algorithm is exactly identical to the one obtained by a more conventional approach.

Sensitivity Analysis of a Radiative-Convective Model by the Adjoint Method

Abstract The adjoint method of sensitivity analysis is demonstrated on a radiative-convective climate model. A single adjoint calculation, which requires about the same computation time as the original model suffices to calculate sensitivities of surface air temperature to all 312 model parameters. The uses of these sensitivities are discussed and illustrated. The sensitivities accurately predict the effect on surface air temperature of small variations in the model parameters. Relative sensitivities are used to rank the importance of all the parameters. Several of the sensitivities to parameters customarily considered in previous works (e.g., solar constant, surface albedo, relative humidity, CO2 concentration) are reproduced, but the largest sensitivities are to constants used to compute the saturation vapor pressure of water. The uncertainties in the model results are expressed formally in terms of all the sensitivities and parameter covariances. For results that cannot readily be compared with observa...

A State Space Method for Kinematic Optimization of Mechanisms and Machines

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.