Advanced Building Simulation

70 Degelman
Dry-bulb temperature (°F)
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Using the random number generator function is similar to “rolling the dice,” and
is where we finally embrace the concepts on the Monte Carlo method. We start the
process by entering a totally meaningless, 8-digit seed value somewhere between
0 and 1 (e.g. 0.29845718). In our software we call the random number generator
function by the equation, B�RANDOM(B). The number, B, returned is always an
8-digit number between 0.00001 and 1. Next, we multiply this value by 31 and round
up to the next higher integer, creating numbers from 1 to 31. Then, we enter the
y-axis of the CDF curve and read the temperature value from the x-axis, the result
being the temperature value for that day.
Following this procedure generated the results shown in Figure 3.5 for a selection
of the first 20 days. If one were to select a second set of 20 days, a different sequence
would result. Every time a series of numbers is selected, a different sequence of days
will occur, only repeating the exact sequence after about 100 million trials.
3.4.4 Practical computational methodology
For simplicity in computation of daily temperatures, the means and standard
deviations are “normalized” to a Normal Distribution curve with mean (�)�0, and
standard deviation (�)�1. The 31 possible choices for daily values are shown in
Table 3.1. These values range from a low of �2.11 to a high of 2.11 standard deviations,
with the center point being 0.
For practical software applications, the CDF values f(x) are stored into a dimensioned
array, and the x-value from Table 3.1 is a random variable that only takes on
values from 1 to 31. We’ll call the dimensioned array FNORMAL(31). The computational
sequence is as follows:
(a) Establish X by calling the random number generator and multiplying by 31.
X�31 * RANDOM(rn) (3.7)
where rn is the random number between 0 and 1.
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2 4 6 8 10 12 14 16 18 20
Day of the month (January)
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Ave. max. = 37.1°F
Monthly ave.= 30.8°F
Figure 3.5 Monte Carlo generated daily maximum and average temperatures for 20 consecutive days
in January.
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