The WIND

A newsletter from //Windward Technologies, Inc.

Q3 99

 

 

INSIDE THIS ISSUE

·            Computer Breezes

·            ConFit Upgraded

·            ConFit Solves Oil Assay Problem

·            RBFpack used in Antenna Design

·            What’s new at WTI

·            Presentations and Publications

·            Products and Services

Computer Breezes

·        BPplans to use Microsoft's Windows CE to power its Internet kiosks. The cyber-ready pumps, which will be able to send e-mail to corporate headquarters when they need servicing, will create savings by helping BP manage its equipment.

·       Microsoft said it doubled the computer processing capability of its Windows 2000 server-operating system, set for release by year end, to compete against powerful systems made by Sun Microsystems Inc. The server system comes in three versions that address varying degrees of computing needs. Windows 2000 Server now will support four processors rather than two; Windows 2000 Advanced Server will support eight processors instead of four; and Windows 2000 Datacenter Server will support 32 processors rather than 16.

·       Compaq and Intel are licensing the Profusion technology for companies that want to produce an eight way parallel intel based machine.  The new systems can run several Operating Systems including Unix, Novel Netware, and Linux, but they are designed primarily for Windows NT. 

 

·        AOL facts: Over 18 million members, 1.1 million simultaneous users, 67 million daily e-mails (double from last year), more than 10 million members shopping on line.

 

Confit Upgraded to Handle Integral Constraints

ConFit, announced by Windward in 1996, is a program designed to produce an approximating function, namely a spline represented as a linear combination of B-spline functions, from data. The program allows the user to impose local shape properties on the approximating function. The original version was able to handle constraints on function values and on derivatives.  For example, the constraint, f'(x) ³ 0, for a £ x £ b, will produce a spline function that is monotone increasing on the interval a £ x £ b.  The new version of ConFit has been enhanced to handle integral constraints, ò_a^b f(x) dx.  The ConFit  DLL interface can be called by a user written interface such as an Excel spreadsheet application.  The DLL has three exported functions: ConFit, bvalue, and bintegral.  The ConFit function computes the spline fit to user-supplied data, bvalue evaluates the spline and its derivatives, and bintegral evaluates the integral of the Spline over an interval.

 

The following three plots show why the approximating functions produced by ConFit are better than fits produced without constraints.  The first plot shows the data.

 

 

Increasing data

 

 

The second plot shows the fit produced without constraints. This illustrates the frustration of getting an approximating fit that wiggles much more than the “true” curve.

 

 

Standard least squares fit

 

The third plot shows the spline fit produced by ConFit with a constraint of the form f'(x) ³ 0 to enforce monotonicity.

 

Shape preserving fit,  f'(x) ³ 0

 

The following article discusses how ConFit is being used to solve problems in the hydrocarbon processing industry.

Using ConFit in the Hydrocarbon Processing Industry

By Ward B. Davis, President of HPI Consultants, Inc.

 

HPI Consultants, Inc. provides consulting and software products for the hydrocarbon processing industry.  Work with Crude Oil Assays constitutes a significant portion of our efforts. Assays are used by the purchasers of crude oil to establish the value of a crude when it is run through a particular refinery.  In addition, the optimization of the refinery uses the crude assays as one of the most important inputs to the process. Assays are expensive to generate, costing between $10,000 and $20,000 each.  An additional process allows the assays of known crudes to be updated based on some simple and inexpensive tests on the whole crude.

 

The raw data for Crude Oil Assays are produced in laboratories around the world by fractionating crude oil into consecutive discrete cuts or fractions.  Properties determined from these cuts are averages over the cuts.  Because each company has different processing options in their refineries, the cut points for the fractionation are not standardized.  To make the results useful, the data must be converted to a common set of cut points for all crudes. This is done with a modeling process.

 

There are several ways to perform this modeling. The simplest way is to assume that the average property is related to the average boiling point of the cut and interpolate to the average boiling point of the new cuts.  This is accurate if the relationships are linear, but they are often very "lumpy".  The more accurate method is to generate an "instantaneous" curve that represents the value of the property at each point over the mass of the cuts.  The integral of this curve gives the average values over the cuts.  

 

ConFit is being used by HPI Consultants to manipulate Crude Oil Assay data in an Excel 97 worksheet.  HPI is using a new version of ConFit (DLL interface) that allows integral constraints, in addition to constraints for values and derivatives.  The ability to specify function constraints, derivative constraints, and integral constraints is what makes ConFit so useful for these Crude Oil Assay problems.

 

A graph and equations of the instantaneous values of the properties can be generated by enforcing the integral (average value * cut range) as a constraint over the range of the cut.  Control over the number of knots, the order, slopes and values are also used to get reasonable results The use of the integral tends to stabilize the curve fit process.

 

ConFit allows integral values to be determined from the curve fit constants.  New cut properties can be determined by getting the integral value over a specified range and then dividing by the interval of the cut. 

 

One much used feature of Confit is the ability to define the position of the knots to be the same as the X-values.  There are times when this gives much smoother results than will be generated from the default method of setting knots at equal intervals over X.

 

For this work, Confit is run entirely from VBA in Excel through its DLL interface.  A few range names are defined to specify X and Y input, weighting factors, number of knots and output locations.  This approach makes it easy to build an Excel worksheet that cycles through all the properties.  A table of available constraints is marked to show which ones are active for a particular problems. Some additional code allows a selection of crudes to be processed

unattended, with potential errors (including constraint violations) to be logged for later evaluations.

 

For more information, contact HPI Consultants by e-mail at HPI@flash.net or visit the Web site: www.hpiconsultants.com

 

A free trial version of ConFit can be downloaded from our Web site.  

Northrop Grumman uses RBFpack in Antenna Design

Northrop Grumman in conjunction with Alpha Omega Electromagnetics reported* a novel use of RBFpack.  This package was used to extrapolate computationally expensive Finite Element solutions modeling the Antenna.   Without this capability it would have been impossible to produce the optimal configurations of the antenna.  At issue were several physical dimensions and parameters describing the geometry of the antenna.

 

The Northrop Grumman engineers found that RBFpack was the most useful tool for erecting surfaces over two and three-dimensional domains.  One interesting feature of these surfaces is that they are complex valued.  RBFpack supports this concept quite well since the dependent result can have any dimension (in the case of complex data that dimension is two).  In fact as the problems become more complex the Northrop Grumman engineers are beginning to experiment with even higher dimensional data sets. 

 

*A Ridge-Guide Travelling Wave Slot Design Antenna Methodology Using FEM and Generalized S-Parameters by Eric Lucas, David Sall, Thomas P. Fontana, and William B. Yablon)

What’s New at WTI

We have a new domain name.  The WTIweb site can be found at www.maxthis.com. 

WTI or its products can be found at the following Internet Web sites:

Research Systems Inc. (CONSTRAINED_MIN / GRG2) www.rsinc.com

Visual Solutions (VisSim/OptimizePRO)
www.vissim.com, click on Products, then Professional VisSim, then OptimizePRO.  Note that VisSim 3.0 is now available.

Mathworks (GRG2, BCLS, LP_QP_Solve, and RBFpack) www.mathworks.com/connections, search for Constrained Optimization and Data Fitting.   

 

 

 

Presentations and Publications

 

Phil Smith attended the Purdue University Mathematics Advisory Council meeting held at Purdue University, in West Lafayette, Indiana, April 9-10.  He plans to attend the next meeting in West Lafayette on September 24-25.

 

Tom Aird attended the Spring meeting of the Dean’s Advisory Council, School of Science, Purdue University, in West Lafayette, Indiana, May 7-9. 

Tom also attend the IFIP WG 2.5 business meeting at Purdue University, in West Lafayette, Indiana, on May 19-20 and gave a talk on "Software for Portfolio Optimization".  The WG 2.5 meeting was followed by the International Symposium on Computational Sciences, celebrating the contributions of John R. Rice on the occasion of his 65th birthday.   

 

The Wind is a quarterly newsletter written and edited by Tom Aird and Phil Smith.  Please let us know what your interests are and what type of articles you would like to see.  If you would like to contribute an article to the newsletter, please contact us at Wti@maxthis.com.

 

You can keep up with the latest information from WTI  by visiting our Web site: www.maxthis.com 

Products and Services

• GRG2 Nonlinear optimization with bounds on variables and nonlinear constraints.
• LSGRG2 Large-scale nonlinear optimization with bounds on variables and nonlinear constraints.
• LP_QP_Solve Large-scale LP and QP problems.
• CURVI Nonlinear optimization with bounds on variables.
• BCLS Linear least squares with bounds on variables and linear constraints.
• RBFpack Multidimensional data fitting by radial basis functions.
• ConFit Shape preserving curve fitting.
• VisSim/OptimizePRO An add-on to VisSim a drag and drop simulation language.
• MATLAB interfaces for GRG2, BCLS, and RBFpack.

Consulting and Program Development Services We offer services in the following areas: Parallel computing, MPI, DSP, C, C++, Visual Basic, Fortran, Assembler, Applied Math, Visualization, Optimization, and Training. If your organization would benefit by having access to a part-time mathematical software development team, contact us!

GUARANTEE We are so convinced in the quality of this service and our products in general that if you are not completely satisfied, we offer a 90 day money-back guarantee.

Let us hear from you!

This is a quarterly newsletter of Windward Technologies, Inc. Please let us know what your interests are and what sort of articles you would like to see. Please contact us if you would like to have your name added to our newsletter mailing list or if you would like to contribute an article to the newsletter!

 

 

The Wind is a quarterly newsletter written and edited by Tom Aird and Phil Smith. Please let us know what your interests are and what type of articles you would like to see. If you would like to contribute an article to the newsletter, please contact us at info@maxthis.com.

Regards,

Tom Aird
TomAird@maxthis.com

and

Phil Smith
PWSmith@aol.com