Geology Reference
In-Depth Information
about FLC and definitions of important terms
related to FLC the readers are directed to Ali and
Ramaswamy (2007, 2009a) and the references
therein. The inference engine has a dual role in
fuzzy control theory. It maps the input fuzzified
variables to the output variables based on user-
defined rules known as knowledge base. It also
provides a decision based on the results obtained
from implementation of these rules. Usually, the
rule base of the fuzzy controller is formed from
operator experience and expert knowledge (Cas-
ciati et al., 1995). The more the control rules, the
more the efficiency of the control system. Control
rules are usually in the form of if-then rules to
link input to the output variables. Fuzzy 'if' is
called antecedent; 'then' is called consequence.
For example rule R
i
: if relative velocity is positive
large; and acceleration is positive large; then the
control current is positive large; where, i = 1,...,
n; where n represents the total number of control
rules. The initial FLC rule base adopted in this
study (which is modified based on evolutionary
optimization) is shown in the Table 2. This rule
base pattern is based on first mode of vibration
of structures (Ahlawat and Ramaswamy, 2004).
technique (Ishibuchi et al., 1997), the iterative rule
techniques, the Pittsburgh approach (Driankov
et al., 1992; Ishibuchi et al., 1997), etc. In this
study, a geometric interpretation to the rule-base
structure is given and based on that a relatively
simple optimization scheme is adopted, which
requires very few optimization variables.
The FLC considered in this chapter has two
input variables, namely, acceleration and relative
velocity, at the damper location and provides MR
damper voltage as an output. The input/output
variables are normalized over the UOD (universe
of discourse) of [ −1, 1]. The input variables range
their respective UODs using five equally spaced
'gbell' shaped membership functions (MFs) (NL
= negative large, NS = negative small, ZE = zero,
PS = positive small, PL = positive large). Seven
equally spaced 'gbell' shaped MFs have been
used to define the output voltage (v(t) ∈ [0, 1]),
(PO = positive; NE = negative MFs are extra).
The extreme MFs for input variables are kept
unbounded in the respective positive (s-shaped)
and negative (z-shaped) UOD. This is done to
consider the values of input that are outside the
range of the UOD. It is to be noted that the output
contains negative values, which is done to keep
symmetry about zero in UOD.
Optimization of the FLC is attempted with a
priori information in relation to the number of rules
and the number of MFs that give meaning to those
rules as noted earlier. Fuzzy input scaling gains,
membership function parameters and the fuzzy
rule base are optimized. The method proposed in
this study considers only ten variables to obtain an
optimal FLC structure. The MF properties altered
by optimization are MF shape, MF centre shift, and
MF slope at 0.5 membership grade. The adaptive
rule base design will be elaborated in this section,
for adaptive membership function design and more
detail study the readers are requested to follow
Ali and Ramaswamy (2009a). The application of
adaptive FLC to benchmark nonlinear building is
reported in Ali and Ramaswamy (2008).
Optimal Fuzzy Logic Control
The selection of fuzzy parameters, especially
the rule base structure is based on trial and error
approach. A number of optimization schemes
are studied and reported in the literature to select
optimal rule base structure, like, the Michigan
Table 2. Initial inference rules for FLC used in
the study
Acceleration
NL
NL
NE
ZE
PO
PL
NE
NL
NE
NS
NS
ZE
Velocity
ZE
NE
NS
ZE
ZE
ZE
PO
NS
ZE
ZE
ZE
PS
PL
ZE
ZE
ZE
PS
PO
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