İç nokta algoritması kullanılarak muharebe tankı süspansiyonunun çok amaç fonksiyonlu pareto optimizasyonu
Suspansion system optimization of a battle tank using multiobjective interior point algorithm
Yazar: EMRE ERTÜRK
Danışman: PROF. DR. ATA MUGAN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Katı Cisimlerin Mekaniği Bilim Dalı
Derece: Yüksek Lisans, 2015
Konu: Makine Mühendisliği = Mechanical Engineering

Özet:
Optimizasyon çalışmaları insanoğlunun en iyiye ulaşma içgüdüsü için çok önemli bir araç olması bakımından geçmişten günümüze oldukça önem verilen konular arasında yer almıştır. Optimizasyon çalışmalarının gelişim süreci içerisinde özellikle doğada gerçekleşen ve sonucunda optimuma ulaşılan birçok olaydan faydalanılmış, doğadaki bu davranışlar matematik olarak modellenerek benzer biçimde en iyiyi elde etme çalışmalarında kullanılabilecek algoritmalar haline getirilmiştir. Sonuç olarak bilgisayar teknolojisinin de bu gelişime dahil olması ile birçok farklı tipte optimizasyon probleminin çözümü için birçok farklı algoritma geliştirilmiş, bu algoritmalar bilimin arzu edilen her dalında en iyiyi elde etme çalışmalarda kullanılır hale gelmiştir. 
Otomotiv endüstrisi optimizasyon çalışmalarına oldukça ihtiyaç duyulan alanlardan biridir. Özellikle araçların sayı olarak yüksek adetlerde üretilmeleri herhangi bir optimizasyon sonucunda elde edilecek düşük miktarda bir iyileşmenin dahi ekonomik anlamda çok büyük fayda elde edilmesine olanak sağlamaktadır. Ekonomik getirilerin dışında optimizasyon çalışmaları bu araçların içerisinde bulunan canlıların huzuru ve sağlığı açısından da önem arz etmektedir. Araç süspansiyon sisteminin optimizasyonu huzur ve sağlığı ilgilendiren en önemli konulardandır.
Bu tez çalışmasında muharebe tankı süspansiyon sisteminin optimizasyonu gerçekleştirilmiştir. Çalışmanın ilk aşamasında üzerinde optimizasyon çalışması gerçekleştirilmiş olan, Manuel F.R. Afonso'nun "ride dynamic analysis of tracked vehicles" adlı çalışmasında M113 zırhlı personel taşıyıcı araç için  geliştirmiş olduğu, aynı zamanda çok tekerlekli zırhlı araçlar ve muharebe tankları için de kullanılabilecek olan matematik modeller sunulmuştur. 
İkinci aşamada optimizasyon metoduna giriş, günümüzde yaygın olarak kullanılmakta olan bazı optimizasyon algoritmaları hakkında temel kavramlar, bilgiler ile çalışmada kullanılan algoritma hakkında kısa bilgi verilmiştir.
Üçüncü aşamada zırhlı aracın matematik modellerine ait olan diferansiyel denklemlerin çözümü hali hazırda araç üzerinde kullanılan parametreler kullanılarak gerçekleştirilmiş, aracın dinamik davranışları elde edilmiştir. Elde edilen diferansiyel denklem çözümü tasarım değişkenleri içeren hedef fonksiyonları olacak şekilde çok hedef fonksiyonu kullanılarak iç nokta algoritması içine gömülüp araç dinamik davranışının sürüş konforu açısından optimize edilmesi sağlanmıştır. Sonuçta hem başlangıç parametreleri ile hem de optimize edilmiş parametrelerle elde edilen araç dinamik davranışı, gövde kütle merkezi düşey deplasmanı, düşey ivme ve açısal ivme yönünden karşılaştırılmıştır.
Hem diferansiyel denklemlerin çözümünde hem de optimizasyon işleminin gerçekleştirilmesinde Matlab yazılımı kullanılmıştır.

Abstract:
Optimization studies be one of the most important subjects due to its role as a tool for humanity's instinct to reach the optimum from past. In optimization tool development process, scientists have benefited from many natural events trying to achieve the optimum result. This behavior of nature is mathematically modeled and has been turned into algortihms  that can be used by optimization studies in a smilar manner. As a result, by involving the computer technologies  to this development stage, many different algorithms for the solution of many different types of optimization problems  were developed and these algorithms has come to be used in many branches of science and technology.
The automotive industry is one of the sectors that utilize optimization studies in product design and development stages. Especially as the number of vehicles to be produced is in large quantities, even a small improvement obtained by using optimization results in great economic benefits. Optimization studies have more important benefits  than economic ones in terms of comfort and health of people transported in these vehicles. Vehicle suspension system optimization is one of the most important topics concerning the tranquility and health. The vibrations occured by existing irregularities on the way be sometimes not felt while it can sometimes reach to annoying or even unbearable levels and may expose a health treat. When the subject is road cruise condition of military vehicles, it is much more severe and service periods of these vehicles may be much longer. Also in the majority of these vehicles, there are weapon systems which need to hit the target while the vehicle passing from obstacles that makes a suspension optimization problem inevitable to be studied. Therefore, the suspension system which has to fulfill the vibration damping function must have optimum suspension components.
When the vehicle suspension system is discussed, both driving comfort and road holding performance are important. Damping the vibrations occuring in the vehicle body, the displacement occuring in the body-wheel interface etc. contribute to road handling and driving comfort. This is why the acceleration of the sprung – unsprung mass, velocity and displacement values play a critical role in selection of the optimum parameters for the suspension system design. 
In this thesis, a battle tank which plays a critical role among military vehicles is considered and its suspension system optimization is carried out. The mathematical model to be optimized is taken from Manuel F.R. Afonso's study titled "Ride dynamic analysis of tracked vehicles" in which four different mathematical models that belong to the M113 armoured personel carrier are examined. These mathematical models were useful for both multi wheeled armored vehicles and for battle tanks also.
In the study of Manuel F.R. Afonso, four different mathematical models of armored vehicles of different complexity are presented. In this thesis, three of these four mathematical models were optimized using the interior point algorihtm. In model I, the trailing arm road wheel suspension is idealized by a parallel combination of linear spring and viscous damper. The kinematics due to the suspension linkage and dynamic due to the track are neglected. The ride dynamic performance of a multi-wheeled vehicle can be investigated  using this model. In model II, the kinematic and dynamic due to the suspension linkage are neglected; however, the dynamics of the track is incorporated via restoring force generated by coupling springs between the sprocket and first road wheel, adjacent road wheels, and idler and last road wheel. The elastic properties of the track are represented by point contact springs in series with road wheel tire springs. In model III, kinematics of the trailing road arm linkage suspension are taken into consideration involving torsional stiffness due to the torsion bars and damping force due to inclined shock absorber. The dynamics due to the track are neglected.
While in the first stage of our study, the content was about Manuel F.R. Afonso's  mathematical models which belongs to a M113 armoured personel carrier, in the second stage an introduction to optimization methods, some basic concepts about gradient based algorithms which are also suitable for use in this thesis and the method called interior point algorithm used in this study are given.
In the third stage, the solution of differential equations of amoured vehicle's mathematical model is carried out using preoptimization parameters which are already used in the vehicle and the vehicle's dynamic behavior is obtained. Solutions of the differential equations of the three models are obtained by reducing the equations to the state space form and using the Matlab function called 'lsim'. After obtaining the solution of seven degrees of freedom differential equations, numerical displacement and velocity solutions that belong to each degree of freedom are obtained. By using the numerical velocity results, acceleration values are then calculated by forward difference method. The solutions of differential equations which belong to preoptimized vehicle parameters are then used to create infrastructure of the objective function with unknown stiffness and damping variables. By using a weighting technique among the multiobjective functions, the interior point algorithm in Matlab program converted the three objective functionals into  a single objective function to get a more realistic and true result despite of more difficulty. Due to the nature of the weighting technique, each of the three objective functions are multiplied by a weighting factor and thus a new composite single objective function is obtained. Optimal point for all loops (Pareto optimal solutions) are obtained. Then, selection of the Pareto optimal solution is done by considering a relative importance of the objective functions in relation to each other. RMS values of vertical directional displacement of the vehicle hull COG, vertical directional and angular acceleration of the hull COG are chosen as the objective functions. Here, RMS values of each of the three objective functions are used not to minimize the local picks but to minimize the system vibrational oscillations.
Finally, dynamic responses obtained using preoptimized parameters as well as those of optimized parameters are compared in terms of vertical, angular acceleration and vertical displacement. When Model I results are examined, it is concluded that while the hull COG vertical displacement RMS value is increased by 2.76%, the RMS values of vertical and angular accelerations of the body COG are decreased by 18.1% and 0.48%, respectively. In Model II, the hull COG vertical displacement RMS value, hull COG vertical acceleration and hull COG angular acceleration values are decreased by 2.68%, 0,23% and 6,05%, respectively. Model III RMS value of the vertical displacement of the hull COG remaied stable, while the hull COG vertical and angular acceleration RMS values are reduced by 29.77% and 1.85%, respectively.
The codes employed in this study for obtaining both the solutions of differential equations as well as implement the optimization procedure are written in Matlab software.