Belirsiz beyin korteks modelinin durum ve parametre kestirimi

Year 2018, Volume: 24 Issue: 8, 1425 - 1434, 29.12.2018

Meriç Çetin Selami Beyhan

Abstract

Beyin korteksinin yaklaşık modeli, günümüzde başta
epilepsi, Parkinson gibi hastalıklar olmak üzere birçok hastalığın tedavisinde
kullanılmaktadır. Korteks matematiksel modeli kesin olduğu kabul edilmektedir.
Fakat zamanla değişen parametreler, gürültü ve diğer bozucu etkilerden dolayı
bu model her zaman geçerli değildir. Ayrıca bazı durumların ölçülmesi zor ve
pahalı olmasından dolayı yazılım temelli yapılması hedeflenmiştir. Dolayısıyla,
bu çalışmada, belirsizlik içeren beyin korteks modelinin durum ve parametre
kestirimi farklı karakteristiklere sahip doğrusal-olmayan gözetleyiciler ile
beraber yapılmaktadır. Sadece durum kestirimi [1] çalışmasında yapılmıştır.
Doğrusal-olmayan gözetleyici genişletilmiş Kalman filtre (EKF), kayan kip
gözetleyici (SMO) ve ayrıklaştırma temelli gradyan gözetleyici (DBGO)
yaklaşımları tasarlanmıştır. Ölçülemeyen durum ve belirsizlik parametresi
kestirimleri normal çalışma ve epileptik durumları için yapılmaktadır. Çünkü
korteks model doğrusal-olmayan dinamiklere sahiptir fakat epilepsi esnasında
kaotik bir davranışa sahiptir. Bu yüzden önce normal durum çalışma sonra nöbet
durumu için tahminler yapılmaktadır. Sayısal benzetimlerde tasarlanan
gözetleyicilerin başarılı şekilde ölçülemeyen durum ve parametre tahminlerini
yaptığı gözlenmiştir. Tahmin sonuçları ve tahmin başarım performansları
tasarlanan gözetleyicileri gürültülü ve gürültüsüz durumlarda karşılaştırmak
için verilmiştir.

Keywords

Korteks model, Doğrusal-olmayan gözetleyici, Durum ve parametre kestirimi, EKF, SMO, DBGO

State and parameter estimation of uncertain brain cortex model

Abstract

Nowadays, an approximate mathematical model of the
brain cortex has been used for the treatment of the first epilepsy and
Parkinson, and several diseases. It is assumed that the mathematical model of
the cortex is an exact model. However, due to the time-varying parameters,
noise and other disturbances, this model is not always valid. Moreover, since
it is difficult and expensive to measure some states, software based solution
is aimed here.  Consequently, in this
paper, state and parameter estimation of the brain cortex model are jointly
achieved using nonlinear observers of different characteristics. The state
estimation of the model was merely performed in [1]. As the nonlinear
observers, extended-Kalman filter (EKF), sliding-mode observer (SMO) and
discretization based gradient observer (DBGO) approaches are designed. The
estimation of unmeasurable states and parameters are performed both for the
epileptic and normal state of the mathematical model since the cortex model has
normally nonlinear dynamics but it exhibits chaotic behavior in epileptic
state. Therefore, the estimations are provided for first normal state, then
epileptic state. In computational results, it is observed that the designed
nonlinear observers resulted successful estimations for unmearuable states and
parameters. The estimation results and estimation performances are given to compare
the nonlinear observers for noisy and noiseless cases.

Keywords

Cortex model, Nonlinear observer, State and parameter estimation, EKF, SMO, DBGO

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