DEVELOPING FOURIER-BASED MODEL USING FEW VARIABLES OBTAINED BY PRINCIPAL COMPONENT ANALYSIS IN RUNNING AT DIFFERENT SPEEDS

Öz

Most of the recent studies focus on human walking and running movements which we often use in daily life and many athletics events. Aim of the study is to reduce dimension of kinematics data by using Principal Component Analysis method and describing human motion at different velocities by low dimensional Fourier model. In order to collect kinematics data of running movement a short distance runner (age:26, height:1.82m, kilo:76kg) was asked to run on treadmill at 8km/h, 12km/h and 16km/h running speed and 6 strides were captured. Principal Components of data including instantaneous postures which were described 3D position values of 16 anatomical markers attached on subject. It was observed that first four Principal Components can cover over 98% of original data and Running at different velocities can be effectively defined by using low-dimensional Fourier series. It was observed that the original spatial locations of the anatomical points which constitute the postures in each instant are coherent with the locations derived from the constructed running model (8km/h, R=0.97, 12km/h, R=0.94 and 16km/h, R=0.93). In this study, it has been determined that human running at varying speeds can be defined with lower dimensional data by modeling the behaviors of the first 4 components derived by using PCA method. Although components derived from PCA do not correspond to a parameter in reality, it can be seen that the second component represents the motion of the feet, the third component represents the motion of the arms and fourth component represents bouncing structure in the running process. The PCs identified in the data belonging to larger amounts of individuals and various positions, can make it possible to classify, analyze, diagnose, compare and collate between movement positions depending on different situations such as gender, running velocity, fatigue, physical structure, injury and well arrangement of technique.

Anahtar Kelimeler

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TEMEL BİLEŞENLER ANALİZİ YARDIMI İLE ELDE EDİLEN DAHA AZ SAYIDA DEĞİŞKEN KULLANILARAK FARKLI HIZLARDA İNSAN KOŞUSUNUN FOURİER TABANLI MODELİNİN OLUŞTURULMASI.

Öz

Günümüzde gerçekleştirilen çalışmaların bir çoğu günlük yaşantımızda ve birçok spor branşında en sık kullandığımız yürüme ve koşu hareketleri üzerine yoğunlaşmaktadır. Bu çalışmada hareket analizi sistemlerinden elde edilen yüksek boyutlardaki kinematik veri setinin boyutlarının Temel Bileşenler Analizi (TBA) yöntemi kullanılarak indirgenmesi ve daha az sayıdaki yeni değişkenler ile farklı koşu hızları için Fourier tabanlı koşu modeli oluşturularak modelde yer alan parametrelerin koşu yapısı üzerindeki etkilerinin incelenmesi amaçlanmıştır. Farklı hızlardaki (8km/s, 12km/s ve 16km/s) koşu hareketine ait kinematik verilerin elde edilmesi amacıyla kısa mesafe koşucusu olan bir atlet (yaş:26, boy:1.82m, kilo:76kg) koşu bandında koşturularak ardışık 6 adımına ait veriler kullanılmıştır. Denek üzerinde işaretlenen 16 anatomik işarete ait 3 Boyutlu (3B) konum değerleri yardımı ile tanımlanan anlık duruşlardan oluşan veri setlerinin temel bileşenleri hesaplanmıştır. İlk dört temel biaçıklaleşenin veri setlerinin %98'inden fazlasını temsil edebildiği gözlenmiştir. Ortalama duruş olarak adlandırılan ilk bileşen ve izleyen ilk 3 bileşenin doğrusal kombinasyonu olarak ifade edilen düşük boyutlardaki Fourier tabanlı koşu modelinin, farklı hızlardaki koşu hareketinin tümü hakkında önemli bilgileri kapsadığı gözlenmiştir. Her bir andaki duruşları oluşturan anatomik noktaların gerçek uzaysal konumları ile ilk 4 bileşen kullanılarak oluşturulan koşu modelinden elde edilen konumların birbirleriyle uyumlu oldukları (8km/s için R=0.97, 12km/s için R=0.94 ve 16km/s için R=0.93) gözlenmiştir. Bu çalışmada insan koşusunun TBA yöntemi ile elde edilen ilk dört bileşenin davranışları modellenerek daha düşük boyutlarda veri setleri ile ifade edilebileceği gözlenmiştir. Her ne kadar TBA'dan elde edilen bileşenler gerçekte bir değişkene karşılık gelmesede, birinci bileşenin ortalama duruş bilgisini ikinci bileşenin ayakların salınımını, üçüncü bileşenin kolların salınımını ve dördüncü bileşenin ise koşunun sıçrama özelliğini temsil edebildikleri düşünülmektedir. Daha fazla sayıdaki birey ve cinsiyet, koşu hızı, yorgunluk, fiziksel yapı, sakatlık, tekniğin düzgünlüğü gibi farklı durumlara ait koşu verileri kullanılarak oluşturulan düşük boyutlardaki koşu modellerinin, sınıflama, analiz, teşhis, karşılaştırma ya da hareket durumları arasında harmanlama yapılabilmesine olanak sağlayacağı düşünülmektedir.

Anahtar Kelimeler

• İnsan koşusu, Temel bileşenler analizi, Fourier analizi

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