Scaling - Revision history

Jpye at 07:20, 5 July 2011

2011-07-05T07:20:38Z

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	'''For more information,''' see the 'Equation-based Modeling' document by Piela and Westerberg.		'''For more information,''' see the 'Equation-based Modeling' document by Piela and Westerberg.

			See also [[nominal]].

	[[Category:Documentation]]		[[Category:Documentation]]

Jpye at 07:20, 5 July 2011

2011-07-05T07:20:22Z

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	Most nonlinear (and many linear) models cannot be solved without proper scaling of the variables.		Most nonlinear (and many linear) models cannot be solved without proper scaling of the variables.
	<tt>scale_self</tt> should reset the <tt>.nominal</tt> value on every real variable in need of scaling. It should then		<tt>scale_self</tt> should reset the <tt>.[[nominal]]</tt> value on every real variable in need of scaling. It should then
	call the <tt>scale_self</tt> method on all the locally-defined ([[IS_A]]) parts of the [[MODEL]]. A proper nominal		call the <tt>scale_self</tt> method on all the locally-defined ([[IS_A]]) parts of the [[MODEL]]. A proper nominal
	is one such that you expect at the solution		is one such that you expect at the solution

Jpye at 07:16, 5 July 2011

2011-07-05T07:16:47Z

← Older revision		Revision as of 07:16, 5 July 2011
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	is one such that you expect at the solution		is one such that you expect at the solution

	<math> 0 \le \left\| \frac {x} {x_\mathrm{nominal}} \right\| \le 10</math>		:<math> 0 \le \left\| \frac {x} {x_\mathrm{nominal}} \right\| \le 10</math>

	As one is dividing by the nominal value for the variable to establish its scaled value, zero is about		As one is dividing by the nominal value for the variable to establish its scaled value, zero is about

Jpye at 07:15, 5 July 2011

2011-07-05T07:15:48Z

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	''This text is an extract of the PDF [[Category:Documentation\|documentation]].''		''This text is an extract of the PDF [[:Category:Documentation\|documentation]].''

	Most nonlinear (and many linear) models cannot be solved without proper scaling of the variables.		Most nonlinear (and many linear) models cannot be solved without proper scaling of the variables.

Jpye at 03:48, 1 June 2010

2010-06-01T03:48:33Z

← Older revision		Revision as of 03:48, 1 June 2010
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	call the <tt>scale_self</tt> method on all the locally-defined ([[IS_A]]) parts of the [[MODEL]]. A proper nominal		call the <tt>scale_self</tt> method on all the locally-defined ([[IS_A]]) parts of the [[MODEL]]. A proper nominal
	is one such that you expect at the solution		is one such that you expect at the solution


	<math> 0 \le \left\| \frac {x} {x_\mathrm{nominal}} \right\| \le 10</math>		<math> 0 \le \left\| \frac {x} {x_\mathrm{nominal}} \right\| \le 10</math>
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	Historically, and still today, dimensionless engineering quantities are frequently used in dimensionless equations. The primary benefits of this are		Historically, and still today, dimensionless engineering quantities are frequently used in dimensionless equations. The primary benefits of this are


	* the solution can be tabulated for a huge range of physical systems that have the same single dimensionless description.		* the solution can be tabulated for a huge range of physical systems that have the same single dimensionless description.
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	'''For more information,''' see the 'Equation-based Modeling' document by Piela and Westerberg.		'''For more information,''' see the 'Equation-based Modeling' document by Piela and Westerberg.

			[[Category:Documentation]]



	[[Category:Documentation]]

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2010-05-13T13:54:54Z

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''This text is an extract of the PDF [[Category:Documentation|documentation]].''

Most nonlinear (and many linear) models cannot be solved without proper scaling of the variables.
<tt>scale_self</tt> should reset the <tt>.nominal</tt> value on every real variable in need of scaling. It should then
call the <tt>scale_self</tt> method on all the locally-defined ([[IS_A]]) parts of the [[MODEL]]. A proper nominal
is one such that you expect at the solution

<math> 0 \le \left| \frac {x} {x_\mathrm{nominal}} \right| \le 10</math>

As one is dividing by the nominal value for the variable to establish its scaled value, zero is about
the worst value you could choose for a nominal value.

This method should not change the .nominal values for models and variables that are received
through the parameter list of the model.

Variables (like fractions), when bounded such that they cannot be too far away from 1.0 in magni-
tude, probably don’t need scaling most of the time, so long as they they are also bounded away from
0.0.

Some solvers, but not all, will attempt to scale the equations and variables by heuristic matrix-based methods. This works, but inconsistently; '''manual user-defined scaling is generally superior'''. ASCEND makes scaling equations easy to do. You scale the variables, which can only be done well by knowing something about where the solution is going to be found (by being an engineer, for example).

Then ASCEND can calculate an appropriate equation-scaling by efficient symbolic methods, if relation nominal calculations are enabled in the solver. The nominal value for scaling a relation is the value of its largest additive term. There is some difference of opinion whether the largest additive term should be calculated using initial (unconverged) values of the variables in the equation or using the .nominals of the variables in the equation.

Historically, and still today, dimensionless engineering quantities are frequently used in dimensionless equations. The primary benefits of this are

* the solution can be tabulated for a huge range of physical systems that have the same single dimensionless description.
* the solution via computation is largely self-scaling and the user can assume nominals of 1.0.

Beware, however, that dimensionless quantities are also used in many dimensional equations and thus the user is ultimately responsible for handling the issue.

'''For more information,''' see the 'Equation-based Modeling' document by Piela and Westerberg.

[[Category:Documentation]]