Tolerance Testing

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When a tolerance calculation is required in SysCAD, it is performed by taking the difference between two values (for example between the current and previous values) and dividing it by a combination of the applicable absolute and relative tolerances.

The difference, D, is defined as:

D = absolute value of (current value - previous value) (Note: Uses SI units for all values.)

The tolerance, T, is defined as:

T = D / (AT + (MV * RT))
where
T = tolerance
D = difference
AT = absolute tolerance
MV = maximum value = maximum of the absolute values of the current value and the previous value. (Note: Uses SI units for all values.)
RT = relative tolerance

The tolerance must be less than or equal to 1.0 for the variable to be converged. Changing the relative tolerance from 0.01 to 0.1 would increase the error margin by an order of magnitude.

Typically the relative tolerance would be greater than or equal to the absolute tolerance used.

Note: Many individual units use the Brent solver to determine convergence. Please see Solver Setting - Tolerances for a description of the Brent convergence routine.

Examples

1. If the relative tolerance was set to 0.1, and the variable of interest was a mass flowrate with a previous value of 1000 kg/s, then for this variable to be converged the current value would have to be in the range of 900 to 1111 kg/s, ie. about 10% either side of the previous value.

2. If the relative tolerance was set to 0.01, and the variable of interest was a mass flowrate with a previous value of 1000 kg/s, then for this variable to be converged the current value would have to be in the range of 990 to 1010 kg/s, ie. about 1% either side of the previous value.

3. The absolute tolerance becomes important when the value of a variable is close to zero. If the relative tolerance was set to 0.1, the absolute tolerance was set to 0.01, and the variable of interest was a mass flowrate with a previous value of 0 kg/s, then for this variable to be converged the current value would have to be less than 0.011 kg/s, ie. a difference of about 0.01 (=the absolute tolerance) from the previous value.