Uçak modal parametrelerinin uçuş esnasında takibi için operasyonel modal analiz kullanılması
Operational modal analysis for tracking aircraft modal parameters in flight
Yazar: METİN KÖKEN
Danışman: PROF. DR. ERDİNÇ ALTUĞ
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Makine Dinamiği, Titreşimi ve Akustiği Bilim Dalı
Derece: Yüksek Lisans, 2024
Konu: Havacılık ve Uzay Mühendisliği = Aeronautical Engineering ; Makine Mühendisliği = Mechanical Engineering
Dizin: Mekanik titreşim = Mechanical vibration ; Titreşim sinyal analizi = Vibration signal analysis

Özet:
Yapıların dinamik karakterleri bir çok endüstride olduğu gibi hava araçları için de çok önemli olmuştur. Yapının dinamik karakteri; aeroelastisite, yapı kararlılığı, uçuş dinamiği ve yapıların yorulma dayanımları gibi farklı yönlerden etkilere sahip olması sebebiyle, hava aracı tasarım ve üretimi yapan mühendisler tarafından incelenmektedir. Bu amaçla, nümerik ve deneysel modal analiz yöntemleri kullanılarak hava aracının doğal frekans, mod şekilleri ve modal sönüm oranları gibi modal parametreleri hesaplanmakta ve doğrulanmaktadır. Ancak, nümerik modeldeki belirsizlikler ve yer testleri imkanlarının kısıtlı oluşu sebebiyle doğrudan uçuş esnasında modal analiz yapılması da gereklilik haline gelmiştir. Model doğrulamanın yanında, yapı sağlığı izleme, çırpınma testi ve gerçek zamanlı yapı kararlılığı takibi açısından da operasyonel modal analiz yöntemlerinin geliştirilmesi önem kazanmaktadır. Telemetri ve günümüz bilgisayar teknolojisi ile birlikte veri işlemenin kolaylaşması ile operasyonel modal analiz yöntemleri de doğru orantılı olarak ilerleme kaydetmektedir. Genellikle, yapı mühendisliği alanında kullanılan operasyonel modal analiz yöntemlerinin havacılık alanında kullanımı da test edilmektedir. Ancak, zamana bağlı olarak değişmeyen sistemlerden farklı olarak, hava aracı yapıları hem kütle durumu hem aerodinamik açısından zamanla değişmeyen sistem kabulü yapılmasından oldukça uzaktır. Özellikle geniş uçuş zarfına sahip uçaklarda modal parametreler farklı uçuş koşullarından farklı modal karakteristik göstermektedir. Dolayısıyla, yapılan operasyonel modal analiz çalışmaları da bu bağlamda zamanla değişen sistemler için uyarlanmaktadır. Bu tez çalışmasında operasyonel modal analiz yöntemleri hem nümerik sistemde hem uçuş test verisiyle test edilerek performansları farklı açılardan kıyaslanmıştır. Gerçek zamanlı operasyonel modal analizin gerekliliği olarak otonomlaştırılan algoritmaların belirli zaman aralıklarıyla modal parametreleri tespit etmeleri ve zamanla değişen modal parametreleri izlemesi sağlanmıştır. Hem frekans bölgesi hem zaman bölgesi yöntemleri test edilerek her yöntemin kendine göre belli koşullardaki avantajlarını kullanma amacıyla, algoritmalar arası oylama yöntemiyle hataya daha dayanıklı bir gerçek zamanlı operasyonel modal analiz algoritması elde edilmesi amaçlanmıştır. Frekans-Uzamsal Bölge Ayrıştırması (FSDD), Ibrahim Zaman Bölgesi (ITD), Özsistem Gerçekleme Algoritması (ERA), Özbağlanımlı ve Çoklu Referans (AR/PR) ve Olasılıksal Alt Uzay Tanımlama (SSI) yöntemleri gerçeklenerek nümerik sistem üzerinde test edildikten sonra uçuş verisiyle operasyonel modal analiz yapılıp, hava aracının deneysel modal analiz sonuçlarıyla kıyaslandığındaki peformansları ele alınmıştır. Nihai olarak ise, otonom şekilde gerçek zamanlı modal parametre takibi yapılarak modal parametrelerin değişimi izlenmiştir. Oylama algoritmasıyla birlikte, her yöntemin katılım gösterdiği modal parametre takibinin çeşitli uçuş koşullarında hataya daha dayanıklı olduğu görülmüştür. Elde edilen sonuçların, çırpınma testleri, gerçek zamanlı sönüm oranı ve doğal frekans takibi, yapı sağlığı izleme çalışmalarına katkı sağlaması öngörülmüştür.

Abstract:
Dynamic behaviour of structures is crucial for aircrafts as well as other industries. In different aspects of aerospace engineering, including aeroelasticity, structural stability and fatigue life, dynamic behaviour of the structure has significant influence on design of air vehicles. Therefore, modal parameters are always a concern for engineers who design and manufacture this type of structure. Finite element method, analytical methods and experimental modal analysis are the well-used ways to obtain modal parameters. In general, finite element method and analytical solutions are used in design phase to obtain the dynamic and aeroelastic behaviour of the air vehicle. When the air vehicle is manufactured, numerical analyses are validated by experimental analysis. In ground vibration test, natural frequencies, modal damping and mode shapes of the structure can be obtained. However, ground vibration test can be performed under spesific conditions. These conditions are generally selected depending on different mass states such as empty fuel configuration. Furthermore, ground tests does not cover aeroelastic influence on the structure, aerodynamic-structure coupling cannot be obtained through these tests. Hence, aeroelastic characteristic is examined with flight flutter test. Uncertainities in numerical approaches and limitations during ground vibration test raises the need for operational modal analysis. In addition to model validation, real-time health monitoring, flutter test and stability tracking of structures are in the scope of operational modal analysis, as well. Therefore, operational modal analysis is a useful tool in aerospace applications.
Operational modal analysis is further developed to be enhanced. Telemetry systems and current improvements in computer science allow easier data processing which accelerates development of operational modal analysis. Operational modal analysis methods used in structural engineering is tested in aerospace applications, as well. However, structures in structural engineering are time-invariant where air vehicle structures are time-variant. Different mass states, flight conditions and aeroelastic effects make the aircraft structure highly time-variant that cannot be assumed as a time-invariant system. Especially for the aircraft which has broad flight envelope, natural frequencies and modal damping ratios significantly change in different flight conditions. Therefore, operational modal analysis in aerospace industry is being improved to be able to track modal parameters real time. By windowing the flight data, modal parameters can be assumed to be time-invariant for each window. However, real time operational modal analysis requires autonomous pole selection, physical mode decomposition and ability to distinguish non-physical modes. 
In this study, different operational modal analysis methods are examined with flight data. Both frequency domain and time domain methods are included in the study. Frequency-Spatial Domain Decomposition, Ibrahim Time Domain, Autoregressive Poly Reference, Eigensystem Realization Algorithm and Stochastic Subspace Algorithm are implemented for the study and their performances are compared for both numerical and physical flight data. In addition to operational modal analysis algorithms itself, their autonomous versions are also considered and parameters in the algorithms are evaluated to be optimized. For instance, stabilization diagrams in SSI and ERA are made autonomous by traditional stabilization diagram method and clustering by mode shape, damping and natural frequency criterias, after clustering is made, clusters which have more members are selected as the most confident clusters and their member which has the lowest model degree is selected as a physical mode. In ITD and AR/PR model degree parameters and delayed measurement addition options are optimized. For the algorithms which process impulse responses, correlation function methodology is implemented. Furthermore, effect of bandpass filter is evaluated in operational modal analysis point of view. To obtain the optimized algorithm, different methods for both operational modal analysis and subroutines are reviewed. With the implementation and optimization of autonomous operational modal analysis algorithms, their performance under noise have been evaluated. All of the operational modal analysis algorithms performed succesfully for numerical model.
After validation by the numerical model, autonomous operational modal analysis algorithms have been tested with physical flight data for both offline and online versions of analyses. Also, experimental modal analysis results are referenced for modal parameter results such as natural frequency, modal damping ratio and mode shapes. However, due to the aforementioned limited capacity of experimental modal analysis, experimental modal analysis is not referenced exactly. Firstly, experimental test has been performed under empty fuel mass state and it does not include aeroelastic influence on modal parameters. For offline operational modal analysis, full flight data has been analysed for FSDD, ITD, ERA and AR/PR. In SSI algorithm, spesific window has been selected due to the computational problems for large matrices. Offline analysis results have been evaluated by comparing the algorithms with each other and experimental modal analysis results. Operational modal analysis results are found very similar to each other and experimental modal analysis except the slightly change for natural frequencies which are influenced by fuel state. Modal damping ratios are calculated higher than the experimental modal analysis as expected because of the aeroelastic effect for that flight condition. Also, mode shapes are visualized for a substitute geometry and compared with experimental modal analysis mode shapes. All of the mode shapes in frequency band of interest have been calculated by different operational modal analysis methods. 
In real time analysis, flight data has been seperated into two minutes length segments by 0.95 overlap ratio. For each segment, operational modal analysis has been performed by autonomous FSDD, ITD, AR/PR, ERA and SSI algorithms. By this way, time-variant aeroelastic characteristic of the aircraft has been tracked window by window. In spite of time-variant characteristic, each segment of the flight data is evaluated as time-invariant for that time period. As a result, natural frequencies and modal damping ratios as a function of time have been calculated for the first mode of the air vehicle. It has been observed that modal parameters of some of the algorithms are influenced  by instantaneous flight conditions and the influenced algorithm is changing over different manuever and physical world conditions. To overcome this problem, a voting algorithm has been proposed for enhancing real time modal parameter tracking. Voting algorithm proposes, picking the median modal parameters between calculations for each operational modal analysis method. By this way, more robust and fault tolerant algorithm has been developed. Improvement on the real time natural frequency and modal damping ratio tracking has been observed by voting algorithm on the results. Proposed method for fault tolerant real time operational modal analysis is predicted to contribute to flutter tracking, health monitoring and aeroelastic model validation in different fields, including aerospace industry.