# Phil B BrubakerOptimal Designs Enterprise · Problem-Solving

Phil B Brubaker

BS in Mathematics

Leadership Training

## About

27

Publications

12,613

Reads

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2

Citations

Citations since 2017

Introduction

Phil Brubaker current project is 'Curve fitting: Non-Linear Data using Lorentzian, Sine, Damped Sine, etc.'; Match-n-Freq™, Matched Filter (Pole/Zero) Design; FC-Compiler™, a Calculus-level Compiler for solving Algebra thru ODEs equations, constrained, IVP, BVP, etc.; and other Calculus Based apps.
Also, have a SpectrumSolvers™ app for estimating the Power Spectral Density (PSD) with several numerical methods; 13 spectral estimation algorithms include Akaike, Burg, Durbin, Maximum Likelihood Method, Mayne-Firoozan, Prony, Yule-Walker, and et al.
Guest Speaker ... https://speakerhub.com/speaker/phil-brubaker

Additional affiliations

May 1991 - present

**Optimal Designs Enterprise**

Position

- Owner

Description

- Main objective is to train engineers & scientists to solve their own math problems without real programming. Most modeling, simulation & optimization problems can be solved in a page or two with the aide of a calculus level language/compiler.

Education

September 1962 - June 1967

## Publications

Publications (27)

Calculus-level Problem-Solving class overview: from NASA's Apollo Space program developing the 1st such language, Slang, to today's (Windows) FortranCalculus Compiler App. Think outside-the-box in order to learn the simplicity of solving most math problems in Research & Development to controlling Manufacturing Processes (aka Operations Research)....

Objective-Driven Engineering for Entire Company requires one to develop a nesting level of Optimization of Optimizations. Here is an overview of what this would entail ... Automobile Manufacturing example.

Intro to Calculus-level Problem-Solving: Improve Models while Increase Productivity ... Agenda:
Design Objectives, Language Background, Example Code, Optimization of Optimizations

Improve Math Models while Increasing Productivity for Scientists, Engineers & Management.

Which estimator is best for your job? SpectrumSolvers™ (free) program helps Find best Spectral Estimation Method for a Power Spectral Density plot. A menu of 11+ spectral estimators from Steven Kay's textbook 'Modern Spectral Estimation' 1988 is available to choose from. The results differ dramatically from one estimator to another. Plus, varying i...

The equations for modeling flight and debris floating in the ocean, are in need. If you know the equations for either model, please contact us. An airplane disappears with parts scattered here and there. Little is known about some of the crash parts found and we want to locate the crash point.

We have a dye sensitizer attached to nano-structured Titanium dioxide (TiO2) film. The nano-structured particles are in a dye which transports the electrons from the electrode to the dye sensitizer. Incident light at a certain wavelength excites electrons in the dye sensitizer. So what happens to this electron after the excitation? A very fast proc...

Many new Industry topics need to be taught in Seminars and/or Classes. Where are the teachers with practical experience in solving today's problems and able to teach such topics?

John D Rockefeller was quoted as saying, "If you want to succeed you should strike out on new paths, rather than travel the worn paths of accepted success." Today, this is referred to as “thinking outside-the-box”. Are you willing to try a 'new path' in order to simulate your Business Strategies on a computer before implementing them?
As I have be...

Today's & future CEOs need an Operations Research (OR) team to test Business Strategies via War Games on a computer. 'What if' this or that happens, how will such an event affect their company goal(s)? What if the company buys, sells, or trades some company locations or product lines; how would such an event affect their goal? Why not teach OR stud...

NASA's Apollo Space program that got us into space and back. Slow software solutions to their Fundamental math equations, forced them to find a new way to solve math problems. This lead to the discovery of Automatic Differentiation and Calculus-level languages/compilers. Recommend movie titled "Hidden Figures" for a 'picture' of what NASA folks fac...

Lorentzian and/or Modified Lorentzian series are very much in need in industry. The Lorentz function, y = 1/(1+x*x) is a symmetrical function. And, it is very simple equation even when made into a series. But it is Symmetrical! Most industrial datasets are Asymmetrical, however slight their imperfections are due to manufacturing, processing, or hum...

CurvFit Intro.: http://goal-driven.net/videos/CurvFit Class.MP4 8 min.
Seminar Speaker: https://speakerhub.com/speaker/phil-brubaker

John D Rockefeller was quoted as saying, "If you want to succeed you should strike out on new paths, rather than travel the worn paths of accepted success." Are you willing to try a 'new path' for verifying your Business Strategies?
As I have been writing a request for proposals on Oil Production, it became obvious that there are not company leade...

We are seeking High School & College math teachers that may be interested in the following problem: "Detection of an Irregular (Human) Heart Beat" by Curve Fitting data sets to some math models (see attached file). This type problem would be of great help for many future Engineering & Science students in industry. Do you know of any HS teachers tha...

[Purpose: get Engineers & Scientists thinking outside-the-box ... think -large- problems. What's possible today vs. needs for tomorrow?]
Oil production dependends on many factors; e.g. Supply, Demand, present inventory, etc. A oil company may have many refineries with many distillation units. How can a company simulate extracting products 'a', 'b'...

PROSE language was the mathematical 4GL virtual machine which established the holistic modeling paradigm known as Synthetic Calculus (AKA MetaCalculus). A successor to the SLANG/CUE simulation and optimization language developed at TRW Systems, it was introduced in 1974 on Control Data supercomputers. It was the first commercial language to employ...

Recommend viewing https://www.researchgate.net/publication/330655098_NASA's_Apollo_Space_Program_Solving_it's_Fundamental_Equations web page after this page in order to get a better understanding of NASA's problems and developments.

For CEOs of Technical Firms
---------------------------------------------
We will introduce Calculus-based software for Engineers and Scientists to use in their Problem-Solving efforts. Such software has been shown to increase productivity by as much as 20 times. At the same time, we will try to increase the problem size from one unit to many units...

Engineers in industry wanted to ‘tweak’ their parameters. So this textbook was written to show the simplicity of ‘tweaking’ parameters in algebraic through differential equation problems when using a Calculus-level language like PROSE or FortranCalculus. FortranCalculus (FC) is available on the web.
Automatic Differentiation (AD) and Operator over...

With the Lorentz (function) where y = 1/(1+x*x), one can fit data to a wide variety of data. There is a Windows App called 'CurvFit' that has an option of a Lorentzian or Modified Lorentzian series; Sine & Damped Sine; and other series. Visit fortranCalculus.info/apps/curvfit.html. Please download, install, and run some of its demo files. It's free...

Ask a dozen engineers what their objective is for their present project and you'll get dozen+ objectives.
Projects need Team players to solve their tasks. A team must have -one- main objective and All members must know it.

Main objective is to train engineers & scientists to solve their own math problems without real programming. Most modeling, simulation & optimization problems can be solved in a page or two with the aide of a calculus level language/compiler.

The Fast Fourier Transform (FFT) algorithm was a favorite computer method during the 1970's and 1980's for approximating Yi(w). The FFT assumes yi(t) is one period of data from the periodic function y(t) and that Yi(w) is band-limited. Discontinuities at the beginning and ending of the data window will cause Yi(w) to be convolved with a Sinc functi...

Automated modeling is not a new concept, but rather a neglected one. Contemporary with the invention of FORTRAN, while the analog computer was still the mainstay of scientific computing, Jay W. Forrester was moving from the intense mathematical world of electrical engineering to the Sloan School of Management at MIT, where he began translating the...

Recommend viewing https://www.researchgate.net/publication/330655098_NASA's_Apollo_Space_Program_Solving_it's_Fundamental_Equations web page before this page in order to get a better understanding of NASA's problems and developments.

Equalization for magnetic recording with LC filters was reported in 1963 [1], and since then many other approaches have been used to alter the readback signal to reduce error. These ideas have been extended to arbitrary input-arbitrary output fillers which are realized as LC structures without mutual inductance. An asymmetrical signal from an isola...

## Questions

Questions (19)

Brief intro to my STEM presentation on "

**Why Optimization over Simulation?**"For more slides on this presentation, go to https://goal-driven.net/download/Why%20Optimization%20over%20Simulation.pdf

I'm having numerical problems with a nested solver. Any ideas how to solve this?

**JOVE**solver is a sequential unconstrained optimization technique applying Newton's second-order gradient search;

FIND Yzero, Zimag, Zreal;

1 in flatDlay; by

**Jove**( contrl2); 2 with lower zeroLow;

3 TO MINIMIZE errDlay

This 'Find' stmt. eventually calls following (nested) 'Find' stmt.

**JUPITER**solver is a moving exterior truncations penalty-function method applying a Davidon-Fletcher-Powell (DFP) variable-metric search;

FIND gain, pReal, pImag;

1 in transfer; by

**Jupiter**( contrl1); 2 with lower poleLow; and uppers poleHi;

3 TO MINIMIZE errTran

This 'find' stmt. calls 'transfer' routine until 'errTran' parameter is minimized.

Then execution returns to the first 'find' stmt. where it changes it's parameters

(Yzero, Zimag, Zreal) in order to achieve its objective of minimizing 'errDlay'.

This loop may continue for 20+ iteration, but I'm getting an error msg. saying

"*** THE OBJECTIVE FUNCTION BEING OPTIMIZED IS NEITHER AN EXPLICIT NOR

AN IMPLICIT FUNCTION OF THE INDEPENDENT VARIABLES."

But it just finished the 2nd 'find' stmt. summary #1 having tweaked parameters

gain, pReal, pImag on its 1st loop. Here is part of the summay ..

LOOP NUMBER ......... [INITIAL] 7 8

UNKNOWNS

GAIN 2.293703E-03 2.293707E-03 2.293697E-03

PREAL ( 1) 6.259960E-02 6.259913E-02 6.259846E-02

PREAL ( 2) 4.406212E-02 4.406053E-02 4.405971E-02

PREAL ( 3) 5.736741E-02 5.753962E-02 5.743653E-02

PIMAG ( 1) 2.148273E-01 2.148198E-01 2.148219E-01

PIMAG ( 2) 3.752846E-01 3.752705E-01 3.752753E-01

PIMAG ( 3) 9.999969E-01 9.999994E-01 9.999997E-01

OBJECTIVE

ERRTRAN 2.881500E-03 2.881502E-03 2.881502E-03

---

Another time with different initial values ...

LOOP NUMBER ......... [INITIAL] 1

UNKNOWNS

GAIN 2.141501E-05 2.199075E-03

PREAL ( 1) 2.000000E-01 2.241059E-02

PREAL ( 2) 2.000000E-01 5.400497E-02

PREAL ( 3) 2.000000E-01 6.942999E-02

PIMAG ( 1) 1.000000E-01 4.238228E-01

PIMAG ( 2) 2.000000E-01 3.050316E-01

PIMAG ( 3) 3.000000E-01 1.751917E-01

OBJECTIVE

ERRTRAN 1.840880E-01 1.657471E-03

---END OF LOOP SUMMARY

"*** IMPROPER RANK IN REFERENCE TO A DYNAMIC ARRAY" at a different place

in my code ... hmmm :(

Same problem just different initial conditions ... better objective :)

I'm trying to fit to a dataset that has the shape of a mountain (right side of peak only). So after a few iterations it should be settling in on the 5th, 6th, 7th, etc. digits of accuracy; kind of a stiff equation at this point. I’ve done this before with sequential find stmt. in a loop and it works. But I learned why an engineer will want it in a nested find stmt.

I have tried multiplying the error function by 10,000 in order to magnify the last few digits. It help some but still ends with such error msg.s.

Ideas or comments?

A

*Calculus-level computer language*, e.g. FortranCalculus, can solve most math problems in minutes. Their libraries have varies numerical methods available for use. A user adds a '**By xxx**' clause to invoke their 'xxx' numerical method. States their math equations in a routine and initial conditions in another routine. Compiles the problem and executes it. The solution will be Optimal. In minutes, Job done! Amount of coding is normally on the order of 20 lines plus number of lines for ones equations. Nice and short.*Automatic Differentiation*is used by solvers to calculate the necessary Jacobian or Hessian matrix. Derivatives of equations must exist for most problems to converge to an optimal solution.

If interested in a free

**seminar or webinar**, please reply.Some say that the

**Group Delay**equals the negative of derivative of H(j w) with respect to w, GD = - d [ H(j w)] / dw. Other ideas and why?I'm a retired applied mathematician seeking a volunteer job using my (math/EE) education and experience in (disc drive/airplane/space) industries. A calculus-level compiler provides a quick way to solve most continuous equations. Know where such a job may be found?