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A FILTER COMBINIG GA AND MCF
GA-MCF
A study to investigate the relationships between the Genetic Algorithm and the Monte Cairo Filter has been
conducted. Both the MCF and the GA is the algorithm to reconstruct a set of realizations representing the state
variables from an initial set of random numbers.
In the MCF, the particles representing the state vector are always generated obeying the conditional probability
density function that is influenced by past-information of the structural response. The MCF has, therefore, a
function to decrease the influence of past observation noises. On the contrary, it can not perform high tracking
ability for an abrupt change of dynamic characteristics of structural systems.
We developed an algorithm introducing the mutation procedure of Genetic Algorithm into the MCF to speed up
convergence for identifying non-stationary structural parameters and called GA-MCF. The proposed method is
defined by the following steps:
1. Generate a initial set (j=l^/77)of the state vector f^1
function p Q (\)
obeying an arbitrary probability density
2. Repeat the following steps until the end of time steps.
(a) Generate a set of random number wj/ 1 obeying probability density function q(w,,)
(b) Compute prediction partcles using the state transfer eaution
bJ/UFff^X/') (32)
(c) Compute the likelihood value of each particles by
m (^, , 11 K ^ 5G
(33)
(d) Choose k particles from a set of particles obtained by Eq.(32) and construct a new set of the
prediction particles B = (b! 7 ' J --b^} in which each particles has a large likelihood value.
(e) Generate new filter particles by mutating the filter particles which generate a set of the
prediction particles B and compute again prediction particles B' using Eq.(32)
(f) Comparing the likelihood value of each component of B' with that of B When the
likelihood value of a component in B' is larger than that of a component in B, the particle
in B is replaced by the particle in B'.
(g) Generate f,| ;)
by the resampling of b (y)
(h) Return to (a) until the end of observation data.
Numerical examples
To demonstrate the efficiency of the proposed GA-MCF filter to identify the non-stationary structural
parameters. We simulate a set of observed structural responses of which dynamic parameters varies at ten
seconds(1000 steps) after the earthquake motion input to the structure. The number of particles is 5000.In