Civil Engineering Reference
In-Depth Information
It should be noted here that uncertainty analysis is different from decision analy-
sis that demands its own lengthy attention, which its complete discussion is out of
our scope here. As it was described earlier, at the end of an uncertainty analysis we
get a probability distribution of the outcome in question. Different people with dif-
ferent attitudes may make different and still all correct decisions based on a per-
formed uncertainty analysis. In different literatures, there are many different
proposed methods of decision making under uncertainty, each using their own deci-
sion criteria. Decision criteria such as maximin expected utility, reliability weighted
expected utility, optimism-pessimism index, etc. Each of these methods rely on
some kind of utility value that is used to help the decision maker makes his decision
in selecting the proper option (in our case the system with the lowest energy con-
sumption value). A utility function is a function that relates the level of risk taking
of a decision maker with his possible gain.
Let's try to see how a typical decision could be made after a probabilistic energy
modeling has been done by utilizing decision trees and utility functions. A decision
tree starts with a problem or question as the beginning node or starting point and
depending on the number and complexity of the decision possibilities develops to a
multi branch tree. First group of these branches out of the original point represent
the possible different decisions that could be made and carry the percentages show-
ing the possibility of each decision compared to the rest of the decisions. Therefore
if there are only two possible options to choose and each option has equal probabil-
ity there will be only two lines at the starting point that each will carry a 50 % pos-
sibility tag and the possible values at the end of each line. Other tree branches will
be added to the end of each primary branch to show the percentage possibility and
the value represented by that percentage, and so on.
Let's assume the original question is the cost of an offi ce building (133,600 ft
2
in
Atlanta) HVAC system and its next 5 years energy consumption, and we have made
two sets of probabilistic energy modeling for this building based on two different
HVAC systems. First system a traditional variable air volume system and the second
system a ground source heat pump system. Also let's assume the results of the
probabilistic energy modeling for energy consumption of two systems are shown in
bell shape distributions that can be simplifi ed in three simple outputs with 16 %,
68 %, and 16 % chance for 0.83 $/ft
2
/year, 0.93 $/ft
2
/year, and 1.03 $/ft
2
/year and
0.63 $/ft
2
/year, 0.73 $/ft
2
/year, and 0.83 $/ft
2
/year respectively. Additionally assume
based on the previous project experiences the fi rst cost for HVAC system installa-
tion for these systems can be defi ned simply as 40 % and 60 % chance for 26 $/ft
2
and 29 $/ft
2
and 34 $/ft
2
and 37 $/ft
2
respectively. Furthermore assume a yearly
increase in energy cost for both systems to be identical in 80 and 20 % chance for
8.5 and 7 %. Using the above information and the following utility function
(
)
/
Utility Function
=
Maximum Attribute
-
Selected Attribute
(
)
( 13.1 )
Maxim
um Attribute
-
Minimum Attribute
