Otonom sualtı aracının hidrodinamik sönümleme modeli
Hydrodynamic damping model of the autonomous underwater vehicle
Yazar: ERDEM FARUK TOPAL
Danışman: PROF. DR. AFİFE LEYLA GÖREN
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Kontrol ve Otomasyon Mühendisliği Ana Bilim Dalı / Kontrol ve Otomasyon Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2022
Konu: Bilgisayar Mühendisliği Bilimleri-Bilgisayar ve Kontrol = Computer Engineering and Computer Science and Control ; Gemi Mühendisliği = Marine Engineering
Dizin: Hidrodinamik model = Hydrodynamic model ; Otonom araçlar = Autonomous vehicles ; Su altı = Underwater

Özet:
Bu tezin amacı, 3-DOF doğrusal olmayan AUV modelindeki hidrodinamik sönümleme katsayılarını sistem tanıma deneyi ile kestirmektir.
Bu tez çalışmasında, REMUS-100 modeli AUV'nin 3-DOF yatay eksen doğrusal olmayan açık çevrim modeli ele alınmıştır. Yatay eksen modeli, aracın x ve y eksenlerindeki doğrusal hareketlerini ve z ekseni etrafındaki dönme hareketini temsil etmektedir. Modeldeki ana kısıt, aracın herhangi bir yunuslama ya da yuvarlanma hareketi yapmamasıdır. Aracın 3-DOF Kuvvet-Moment denklemleri elde edildikten sonra, ek kütle matrisi ve kontrol yüzeyi katsayıları referans model kullanılarak oluşturulmuştur. Aracın ileri hız modeli deneysel olarak belirlenmiştir. Modelde y eksenindeki doğrusal ve z eksenindeki rotasyonel harekete karşı direnç ifadeleri olan, doğrusal ve açısal hızlara bağlı hidrodinamik sönümleme katsayıları LS yöntemi ile kestirilirmiştir. 
Çalışmada, AUV'nin gerçeğe oldukça yakın bir modeli MATLAB ortamında simüle edilmiş ve bu modelden alınan veriler kullanılarak sistem tanıma deneyi gerçekleştirilmiştir. Simülasyon verilerinin gerçeğe benzerliğini arttırmak için çıkış verilerine beyaz gürültü eklenmiştir. Ayrıca zamanla doğrusal değişim gösterecek şekilde modellenen deniz akıntısı da rotasyonel bir hareket yapmayacak şekilde yalnızca doğrusal olarak çıkış verilerine eklenmiştir. Sistem tanıma deneyi için simülasyonda farklı giriş senaryoları denenmiş ve LS yöntemi ile akıntıdan arındırılan çıkış verileri ile kestirim gerçekleştirilmiştir. Seçilen giriş işaretinin kestirim için yeterli olup olmadığı Kesintisiz Uyarma (PE) Mertebesi yöntemi ile analiz edilmiştir. Parametre kestiriminde kullanılan giriş işaretinden farklı olarak seçilen giriş işaretleriyle model doğrulama testleri yapılmıştır. Doğrulama testleri çıktıları korelasyon analizi yöntemlerinde sıkça kullanılan beyazlık ve bağımsızlık testleri ile analiz edilmiştir. Simülasyon ve test sonuçları grafiklerle sunulmuştur.

Abstract:
This thesis aims to estimate the hydrodynamic damping coefficients in the 3-DOF nonlinear AUV model by system identification.
In this thesis, the 3-DOF horizontal axis nonlinear open-loop model of the REMUS-100 model AUV is examined. The 3-DOF model is derived from the 6-DOF classic Newton&Euler-based model. The horizontal axis maneuver model represents the linear motions of the vehicle in the x and y axes and the rotational motion around the z-axis. The main constraint in the model is that the vehicle does not make any pitch or roll motion. After the 3-DOF Force-Moment equations of the vehicle were obtained, the added mass matrix and control surface coefficients were defined using the reference model. The hydrodynamic damping expressions of the obtained model are modeled to include third order and cross expressions to express the maneuvering characteristics more precisely at high speeds. The forward velocity model of the vehicle was created experimentally. The forward speeds reached by the vehicle in response to different propeller thrusts were observed and a third-degree curve was fitted using the obtained results. In the model, hydrodynamic damping coefficients depending on linear and angular velocities, which are the expressions of resistance to linear motion in the y-axis and rotational motion in the z-axis, are estimated by the LS method.
The most difficult expressions to calculate in an AUV model are the hydrodynamic damping coefficients. The most critical information to know for the estimation of these coefficients is the water speed of the AUV. There are sensors in AUVs that can measure water speeds, but the measurements are not sufficient for estimation. While the EM-log can only measure forward water speed, the DVL measures less reliable and is a problem in deep waters. The most reliable velocity measurements that can be used for estimation in AUVs are the ground velocities measured from the INS. For INS measurements to be used in estimation, the sea current acting on the AUV must be known. If the sea current is known, the water speed of AUV is obtained. Since it is not possible to directly measure the sea current, in this thesis, the sea current was estimated by the LS method using AUV ground velocity measurements and heading. A first-order Markov-type sea current model is used. The sea current was modeled irrotationally to affect the AUV in the north and east directions in the NED plane. In addition, the sea currents are formed to behave almost linearly. In the sea current estimation simulation, the AUV made 4 maneuvers at constant forward water speed and the data to be used in the estimation were collected just before the maneuvers. Sea currents were estimated in 4 regions with the collected data and a linear interpolation process was applied to the estimation results. The estimated sea current velocity and the real sea current velocity were recorded in the NED plane and were also used in the parameter estimation simulation. The parameter estimation was carried out with AUV's water speeds purged from the estimated sea current velocities.
In the study, a very close model of the AUV was simulated in MATLAB. By using the data collected from this model in simulation, sea current estimation and system identification experiments were completed. Standard normal distribution white noises were added to the output data to increase the simulation data's similarity to reality. 
The most critical step in AUV nonlinear 3-DOF model estimation is the selection of the input signal used in estimation. Input signal design has a dominant role in the development of the dynamic model of an AUV with system identification. To estimate the hydrodynamic parameters of the nonlinear dynamic model of the AUV, the amplitude-modulated pseudo-random binary signal (APRBS) was chosen. APRBS is a non-periodic signal at random amplitudes. Considering the vehicle dynamics, the APRBS has been applied according to the speed and maneuver capacity of the vehicle. The goal is to get a rich input signal that stimulates the vehicle in as many different regions as possible. In system identification, it is necessary to analyze whether the selected input signal is suitable for estimation. Whether the input signal selected for parameter estimation is sufficient for estimation was analyzed by calculating the persistent excitation order of the input signal. If the spectral density function of a selected u(t) input signal remains positive for n different values in the range [−π,π], then u(t) signal has a persistent excitation of the nth order.
At the end of the simulation which was performed using the selected input signal for estimation, the ground velocities, rudder, and acceleration data were recorded to be used in parameter estimation. The estimated sea current velocities were converted to the body plane and subtracted from the ground velocities, and thus the water speeds of AUV to be used in parameter estimation were obtained. The hydrodynamic coefficients of the AUV were estimated using the least-squares method. Parameter estimation was also performed with an input signal that stimulated the AUV in a more linear region, and the results were found to be unsuccessful. The last step of system identification is verification. In these tests, also known as model validation, the quality of the estimated model was evaluated. It has been tested how well the model defines the independent behaviors of the AUV with 9 input signals selected to be different from the input signal used during parameter estimation. Different sea currents were used in all 9 validation scenarios. These scenarios consist of circular, zig-zag, square, rectangular, sinus, and APRBS maneuvers. Two very important and widely used tests were used for model validation. These tests are the whiteness and independence tests, respectively. For a successful estimated model, whiteness and independence tests must be provided. These tests are correlation tests and measurement quantities were created based on the correlation analyzes of the signals. The difference between the estimation based on past observations and the real value is called the prediction error. In system identification, if the model is selected correctly and the parameter estimation is completed correctly under noise, the prediction error will be a white noise with zero expected value. This is also called the whiteness hypothesis. Within the scope of the whiteness test, the variation of the prediction error over time for each scenario was analyzed.
Another critical requirement in the estimation model is the independence of the input and output signals. There are two independent tests. One of them is applied for open-loop experiments and the other for closed-loop experiments. In this thesis, since all experiments were conducted in an open loop, the independence test was applied for open-loop experiments. In the test of independence, the ratio of the cross covariances of the prediction error and the input signal to the product of their variance at time zero is the measurement quantity. The conditions required by this ratio were analyzed separately for each scenario. Sea current estimation, parameter estimation, validation tests, and correlation analysis results are presented in graphics. The results are discussed separately.