Kalman filtresi ve yapay sinir ağları yardımı ile kuvvet tahmini
Force estimation by using kalman filter and artificial neural networks
Yazar: ÇAĞDAŞ MIDIKLI
Danışman: PROF. DR. ATA MUĞAN
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Katı Cisimlerin Mekaniği Bilim Dalı
Derece: Yüksek Lisans, 2023
Konu: Makine Mühendisliği = Mechanical Engineering

Özet:
Geçmişten günümüze yapıların incelenmesi ve değerlendirilmesi insanlığın işlevsel ve güvenilir yapılar üretmesinin kilit adımı olmuştur. Bir sistem, makine yada yapı hayata geçirilirken en optimum yaklaşım ile üretilmek ve ortaya konmak istenmektedir. Bir yapı hayata geçirilirken işlevselliğini uzun süreler boyunca koruması, dayanım ihtiyaçlarını karşılaması, üretilebilirliğinin, kütlesinin ihtiyaçlar doğrultusunda şekillenmesi ve ekonomik olması gibi en optimum tasarımı ortaya koymak için sistemler sonradan karşılaşabilecekleri durumlara karşın hazırlanmak istenmiştir. Bu yolculukta sistemin maruz kalacağı etkileri bilmek doğru incelemenin ve hedeflere ulaşabilmenin kilit adımı olmuştur. 
Dışarıdan gelen hesaplanamaz etkiler sistemleri karşılaşabilecekleri zorlanma durumlarına maruz bırakılmış ve etkiler öngörülmeye çalışılmıştı. Dış etkiler dışardan gelen raslantısal uyaranlar sebebi ile kolaylıkla hesaplanamadığından dolayı bu yol tercih edilmiştir. Bir aracı ele aldığımızda karşılaşabileceği yol yükleri, rüzgar sürtünmesi, içinde ki ağırlık bileşeni gibi etkiler ve bunların pozisyonları dolayısı ile yol ile temasını sağlayan aracın bütün bu etkilerin izdüşümü olarak şaftında, aksında vb. birçok bölgesinde zorlanmalar meydana gelir. Bu zorlanmalar ele alındığında hesaplanmak yerine kullanılması planlana ortamlarda test edilir. Bu test esnasında üzerine gelen etkilerin öğrenilmeye çalışılan komponentin üzerine ivme ölçerler ve straingaugeler konularak en kilit bölgelerinden yapı hakkında bilgiler toplanır. Bu toplanılan bilgiler doğrultusunda sistemin bütünü için önem taşıyan bu komponentlerin üzerine gelen yükler hesaplanılmaya çalışır. Bu sayede en doğru şekilde validasyon girdilerine sahip olunup sanala validasyon metodları ile lokal etkilerden aracın bütünün analizi yapılabilir. Bu gelişme daha az test sayısı ile güvenli bir yapıya ulaşmayı sağlar  ve aracın tümü incelenir. Daha az maliyet ve zamanla ortaya bir ürünün çıkması süreci özünde sistemin üzerine gelen etkileri bilmekten geçer. Bu etkiler özellikle uçak, rüzgar türbini gibi akışkanlar vasıtası ile zorlanma durumuna maruz kalan komponentlerde etkiyen yükler, zor hesaplanabilmesinden öte hesaplanması mümkün olmayan durumları oluşturur. Bu gibi durumlarda benzer bir yol izlenerek yapının üzerine ivme ölçer, straingauge, basınç ve hız ölçerler yerleştirilerek elde edilen veriler yardımı ile kuvvet tahmin edilmeye çalışılır. 
Bu veriler birçok metod yardımı ile kuvvete tahmini yapmakta kullanılınır. Bu çalışmada kuvvet kestirim metodları incelenmiş. Başlıca kullanılanlar anlatılmıştır. Literatürden farklı kuvvete kestirim metodlarının etkinlikleri araştırılmıştır. Kalman filtresi tabanlı olan, doğrudan bir metod olarak değerlendirilen, frekans yanıt fonksiyonu tabanlı metot ve ağırlıklandırılmış ivmeler metodu karşılaştırılmış ve en doğru kuvvet kestirim sonucun kalman filtresi tabanlı metod yardımı ile ulaşılabileceği değerlendirilerek devam edilmiştir.  Bunlar yapılırken kalman filtresi sadece sistemin dinamik durumunu öngörmeye yaradığı ve çıktıyı elde edebilmek için elde edilen durum vektörleri vasıtası ile en küçük kareler metodu kullanılarak kuvvet öngörüsü yapmaktadır. 
En küçük kareler yöntemi ile yapılan kuvvet tahminlerinin literatür araştırması yapıldığında sapmaları olduğu ve kalman filtresi yardımı ile iyi bir durum tahmini yapılsa da kuvvet kestirimi için kullanılan en küçük kareler metodunun yetersizlikleri olduğu gözlemlenmiştir. Bununla birlikte günümüzde çokça yaygın olarak kullanılan ve bir çok fonksiyon yakınsaması problemine doğru şekilde cevap verebilen yapay sinir ağları modeli kullanılması değerlendirilmiştir. Fonksiyon yakınsaması ve regression problemleri için kullanılan üç farklı yapay sinir ağı modelinin karşılaştırılması literatürde bulunanlar yardımı ile yapılmış ve optimum sonucun ileri beslemeli ve geri yayılımlı yapay sinir ağı vasıtası ile gerçekleştirileceği değerlendirilmiştir. 
Yapılan araştırmanın sonuçlarını uygulayabilmek için Euler Bernolli kiriş modeli kullanılarak her bir düğüm noktası 2 serbestlik derecesine sahip olan 30 elemandan oluşan 1 boyutlu ankastre kiriş modelinin sonlu elemanlar modeli oluşturulmuş. Bu modele bilinen bir kuvvet verilmiştir. Ardından sistemin ivme çıktısı ölçüm değeri olarak kullanılarak sistem üzerinden yer değiştirmeler öngörülmüştür. Burada elde edilen durum tahmini ve ivme değerleri verileri kullanılarak bilinen kuvvet değerleri ile birlikte 2 gizli katmana sahip olan çok girdi ve çok çıktısı olan Bayesian düzeltmesine sahip olan bir ileri beslemeli yapay sinir ağı modeli oluşturulmuş ve bilinen kuvvetler yardımı ile eğitilmiştir. Girdi olarak ivme ve durum tahminlerini kullanan bu yapay sinir ağı vasıtası ile yüksek doğrulukta kuvvet tahmini gerçekleştirilebilmiştir.

Abstract:
The examination and evaluation of structures from past to present have been the key step in producing functional and reliable structural systems of humanity. A system is desired to be produced and revealed with the most optimum approach while implementing a machine, machine, or structure. In order to reveal the most optimum design such as protecting its functionality for a long time, meeting its strength needs, and shaping its mass in line with the needs and economics, the systems have been wanted to be prepared despite the subsequent situations. Knowing the effects of the system on this journey has been the key step in the correct examination and achieving goals. When the structural requirements of a system are inspected in terms of strength and safety, the correct inspection can only be performed by correctly detecting the loads on it. The methods and approaches to be determined during the static, dynamic, and fatigue analyses of the system are based on the inputs of the system. One of the most important of these inputs is force. Knowing the force constitutes the main component of virtual verification and test verification processes and it is necessary to make strength, weight, and economic evaluations of the system.
System parameters such as displacement, acceleration, speed, and strain can be measured from thesystem with the help of various methods, while the force is a component that cannot be directly measured through the system. In order to obtain the force that affects the system, the force is estimated by using the parameters that can be measured over the system directly or with the help of iterative methods. Within the scope of this study, the methods used for force estimation were examined and the advantages and disadvantages were evaluated according to each other the most appropriate method was created and the force estimate was made.
Since external effects cannot be easily calculated due to external random stimuli, these external effects are tried to be estimated by using the measurable components of the system. Consider a tool to describe such random factors and the irreversibility of the force and to illustrate the situation that may face. The road loads that a vehicle may encounter affect the wind friction,  contact with the roa, the weight component in it, and due to their positions, as the projection of all these effects of the vehicle that provides the excitation on he shaft of the vehicle.Because of these complex inputs, exact load on the structural components of vehicle cant be calculated. When these challenges are taken into consideration, it is tested in environments that are planned to be used instead of being calculated. During this test, acceleration meters and strain gauges are placed on the component that tried to learn the effects on it, and information about the structure is collected from the most key regions. In accordance with the information collected, the loads on these components, which are important for the whole of the system, try to calculate. In this way, the most accurate Validation inputs can be analyzed by virtual validation methods and local influences. This development provides a safe structure with fewer tests and the entire vehicle is examined. The process of the emergence of a product in less cost and time is to know the effects of the system in essence. These effects, especially in the components exposed to components such as aircraft, and wind turbines, constitute situations that cannot be calculated beyond difficult calculation. In such cases, a similar path is followed by the acceleration meter, strain gauge, pressure, and velocity meters by placing a similar path and trying to estimate the force with the help of the data obtained.
Within the scope of this thesis, different methods were examined first and their activities were compared with each other. The methods commonly used in the literature were identified. These methods are frequency response function-based methods, weighted coefficients methods, and Kalman filter-based methods. Frequency response function-based methods are a direct method used for estimating. Frequency response function-based methods PseudoInverse method were examined within the scope of the study. In the Frequency Response Function-based methods, the transfer function defining the relationship between input and output is determined and using it as a force output by using acceleration and displacement input. The transfer function is multiplied by inputs and the output is obtained and the force estimation is performed with this approach. When the results of the frequency response function method were examined, it was observed to respond to these needs with high accuracy.
In addition, when the weighted coefficient method is examined, acceleration and displacement in some methods are expressed in terms of force. Acceleration and displacement are multiplied by certain coefficients and try to find force. These coefficients are derived from the coefficients that establish the relationship between the input force and acceleration and displacement outputs. Known inputs and outputs relationship is determined with the help of iterative cycles and a function is created that can be used as long as the model of the system remains constant and established the necessary relationship. When the outputs of the weighted coefficient method were examined, it was observed that the error of the estimation was more than other methods.
In addition to these methods, another method used is the Kalman filter-based method. It is the method in which the strength is integrated as a system status within the filter and the system is obtained in its strength as a result of the estimation. The Kalman filter, which is used for the estimation of the system status, is used for the estimation of many situations, not only for force. This method, which is widely used, provides high-accuracy status estimates and has been observed to make high-righteous estimates in the estimation of strength. These three methods in the literature were compared and the highest accuracy results were obtained by Kalman filter-based methods.
When the Kalman filter-based methods were examined, the Kalman filter was asked to be used within the scope of the method, which was estimated to have the system status and the least square method. When the trials were made using the method, it was considered that the Kalman filter made a good system status, but the recursive least squares method was insufficient to make a strength estimate. In this study, it was decided to use artificial neural networks and the Kalman filter for the estimation of this system's status and measurement value. The main methods used in function convergence problems were examined. The Feed Forward Neural Network, Radial Basis Function, and Generalized Regression Neural Network have been examined as three artificial neural networks. Feed-forward neural network, Radial Basis Function, and Generalized Regression Neural Network methods were compared with errors for function convergence problems, and it was decided to use the Feed Forward Neural Network within the scope of this study.
A built-in beam model was created to test the method. The built-in beam was expressed in the finite element model as 30 elements. Euler Bernoulli's beam matrix was used as the element matrix. The finite element model of the system was created. Global matrices were identified and the dynamic equation of the system was created. The dynamic equation of the system was transformed from physical coordinates to modal coordinates to make the account power and ease of transaction effective. After the system equation was obtained in modal coordinates, the system was converted into a state space form. The system was expressed in the state space form and converted into a form that can be used effectively in the Kalman filter. First, the situation of the system was estimated with the help of the Kalman filter. In line with these outputs, Feed Forward Back Propagated Neural Network training was performed using the measurement matrix of the system and the estimated system status as input and as force output. Forces were applied to the model of the system created on the 2nd Node and their outputs were collected. Neural Network was trained using these obtained outputs and inputs as training data. 5 Node Input Layer 1 Node output layer and 2 hidden layers were created and the desired neural network structure was established. Many activation functions were evaluated when creating a neural network, and the TANH activation function was used due to the fact that the outputs were nonlinear and negatively received negative values. In the first trials, the Neural Network was not stuck in the desired convergence in the results of the training. With the help of the results of these steps and the essays, the correction coefficient and the number of training cycles were determined. With the optimum coefficients and training cycle, the artificial neural network was created to perform the desired convergence.
After the desired force was estimated for the situation where the force was applied over a single node, the same method was tried for the situation where the force was applied over 2 nodes. Complex forces over the 2nd and 20th nodes of the system were applied in different periods and amplitude. With the same method, the necessary corrections were made and the force was estimated with an error less than 0.001 in the multiple force input. As a result of this study, the Kalman filter and the artificial neural network were shown to be able to make high-peculiar force estimations.