Engineering topics

Nachtsheim, Philip R.

Publications and source records attributed to Nachtsheim, Philip R..

7 records

NASA NTRS1999

Method of Conjugate Radii for Solving Linear and Nonlinear Systems

This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.

Nachtsheim, Philip R.↗

NASA NTRS1997

Detecting Tooth Damage in Geared Drive Trains

This paper describes a method that was developed to detect gear tooth damage that does not require a priori knowledge of the frequency characteristic of the fault. The basic idea of the method is that a few damaged teeth will cause transient load fluctuations unlike the normal tooth load fluctuations. The method attempts to measure the energy in the lower side bands of the modulated signal caused by the transient load fluctuations. The method monitors the energy in the frequency interval which excludes the frequency of the lowest dominant normal tooth load fluctuation and all frequencies above it. The method reacted significantly to the tooth fracture damage results documented in the Lewis data sets which were obtained from tests of the OH-58A transmission and tests of high contact ratio spiral bevel gears. The method detected gear tooth fractures in all four of the high contact ratio spiral bevel gear runs. Published results indicate other detection methods were only able to detect faults for three out of four runs.

Nachtsheim, Philip R.↗

NASA NTRS1995

A General Method for Solving Systems of Non-Linear Equations

The method of steepest descent is modified so that accelerated convergence is achieved near a root. It is assumed that the function of interest can be approximated near a root by a quadratic form. An eigenvector of the quadratic form is found by evaluating the function and its gradient at an arbitrary point and another suitably selected point. The terminal point of the eigenvector is chosen to lie on the line segment joining the two points. The terminal point found lies on an axis of the quadratic form. The selection of a suitable step size at this point leads directly to the root in the direction of steepest descent in a single step. Newton's root finding method not infrequently diverges if the starting point is far from the root. However, the current method in these regions merely reverts to the method of steepest descent with an adaptive step size. The current method's performance should match that of the Levenberg-Marquardt root finding method since they both share the ability to converge from a starting point far from the root and both exhibit quadratic convergence near a root. The Levenberg-Marquardt method requires storage for coefficients of linear equations. The current method which does not require the solution of linear equations requires more time for additional function and gradient evaluations. The classic trade off of time for space separates the two methods.

Nachtsheim, Philip R.↗

NASA NTRS1993

A stable second order method for training back propagation networks

A simple method for improving the learning rate of the back-propagation algorithm is described. The basis of the method is that approximate second order corrections can be incorporated in the output units. The extended method leads to significant improvements in the convergence rate.

Nachtsheim, Philip R.↗

NASA NTRS1991

Solving Constraint-Satisfaction Problems In Prolog Language

Technique for solution of constraint-satisfaction problems uses definite-clause grammars of Prolog computer language. Exploits fact that grammar-rule notation viewed as "state-change notation". Facilitates development of dynamic representation performing informed as well as blind searches. Applicable to design, scheduling, and planning problems.

Nachtsheim, Philip R.↗

NASA NTRS1988

A technique for solving constraint satisfaction problems using Prolog's definite clause grammars

A new technique for solving constraint satisfaction problems using Prolog's definite clause grammars is presented. It exploits the fact that the grammar rule notation can be viewed as a state exchange notation. The novel feature of the technique is that it can perform informed as well as blind search. It provides the Prolog programmer with a new technique for application to a wide range of design, scheduling, and planning problems.

Nachtsheim, Philip R.↗

NASA NTRS1988

Simulating futures in extended common LISP

Stack-groups comprise the mechanism underlying implementation of multiprocessing in Extended Common LISP, i.e., running multiple quasi-simultaneous processes within a single LISP address space. On the other hand, the future construct of MULTILISP, an extension of the LISP dialect scheme, deals with parallel execution. The source of concurrency that future exploits is the overlap between computation of a value and use of the value. Described is a simulation of the future construct by an interpreter utilizing stack-group extensions to common LISP.

Nachtsheim, Philip R.↗