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Simplification of the Kalman filter for meteorological data assimilation

The paper proposes a new statistical method of data assimilation that is based on a simplification of the Kalman filter equations. The forecast error covariance evolution is approximated simply by advecting the mass-error covariance field, deriving the remaining covariances geostrophically, and accounting for external model-error forcing only at the end of each forecast cycle. This greatly reduces the cost of computation of the forecast error covariance. In simulations with a linear, one-dimensional shallow-water model and data generated artificially, the performance of the simplified filter is compared with that of the Kalman filter and the optimal interpolation (OI) method. The simplified filter produces analyses that are nearly optimal, and represents a significant improvement over OI.

Dee, Dick P.

Modeling and model simplification of aeroelastic vehicles: An overview

The rigid-body degrees of freedom and elastic degrees of freedom of aeroelastic vehicles are typically treated separately in dynamic analysis. Such a decoupling, however, is not always justified and modeling assumptions that imply decoupling must be used with caution. The frequency separation between the rigid-body and elastic degrees of freedom for advanced aircraft may no longer be sufficient to permit the typical treatment of the vehicle dynamics. Integrated, elastic vehicle models must be developed initially and simplified in a manner appropriate to and consistent with the intended application. This paper summarizes key results from past research aimed at developing and implementing integrated aeroelastic vehicle models for flight controls analysis and design. Three major areas will be addressed: (1) the accurate representation of the dynamics of aeroelastic vehicles, (2) properties of several model simplification methods, and (3) the importance of understanding the physics of the system being modeled and of having a model which exposes the underlying physical causes for critical dynamic characteristics.

Waszak, Martin R.

Automated Simplification of Full Chemical Mechanisms

A code has been developed to automatically simplify full chemical mechanisms. The method employed is based on the Intrinsic Low Dimensional Manifold (ILDM) method of Maas and Pope. The ILDM method is a dynamical systems approach to the simplification of large chemical kinetic mechanisms. By identifying low-dimensional attracting manifolds, the method allows complex full mechanisms to be parameterized by just a few variables; in effect, generating reduced chemical mechanisms by an automatic procedure. These resulting mechanisms however, still retain all the species used in the full mechanism. Full and skeletal mechanisms for various fuels are simplified to a two dimensional manifold, and the resulting mechanisms are found to compare well with the full mechanisms, and show significant improvement over global one step mechanisms, such as those by Westbrook and Dryer. In addition, by using an ILDM reaction mechanism in a CID code, a considerable improvement in turn-around time can be achieved.

Norris, A. T.

Strategy-Enhanced Interactive Proving and Arithmetic Simplification for PVS

We describe an approach to strategy-based proving for improved interactive deduction in specialized domains. An experimental package of strategies (tactics) and support functions called Manip has been developed for PVS to reduce the tedium of arithmetic manipulation. Included are strategies aimed at algebraic simplification of real-valued expressions. A general deduction architecture is described in which domain-specific strategies, such as those for algebraic manipulation, are supported by more generic features, such as term-access techniques applicable in arbitrary settings. An extended expression language provides access to subterms within a sequent.

diVito, Ben L.

Strategy-Enhanced Interactive Proving and Arithmetic Simplification for PVS

We describe an approach to strategy-based proving for improved interactive deduction in specialized domains. An experimental package of strategies (tactics) and support functions called Manip has been developed for PVS to reduce the tedium of arithmetic manipulation. Included are strategies aimed at algebraic simplification of real-valued expressions. A general deduction architecture is described in which domain-specific strategies, such as those for algebraic manipulation, are supported by more generic features, such as term-access techniques applicable in arbitrary settings. An extended expression language provides access to subterms within a sequent.

DiVito, Ben L.

Simplification of the Grid Model and its Impact on the Analysis of Electrical Power Systems

Here, this paper analyzes the impact of the use of Kron reduction on the state variables of a three-phase electrical system, even when it does not meet the necessary conditions for its application. Reduction is applied to a power line model to eliminate the equation corresponding to the neutral conductor of the line. The ATP program is used to model and simulate the behavior of an electrical system considering different degrees of disequilibrium as a reference for the comparison of results. The results show that under certain conditions of disequilibrium the Kron reduction can lead to significant errors in the state variables of the system.

Electric Power Systems