Kalman filtresi temelli sensör arıza tespit, teşhis ve ayrıştırma algoritmalarının helikopter dinamik modeline uygulanması
Application of helicopter dynamic modeling of Kalman filter based sensor fault detection, isolation and accommodation algorithms
Yazar: ÖZLEM DÖKME
Danışman: PROF. DR. CENGİZ HACIZADE
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Uçak ve Uzay Mühendisliği Ana Bilim Dalı / Uçak ve Uzay Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2018
Konu: Uçak Mühendisliği = Aircraft Engineering
Dizin: Aerodinamik = Aerodynamics ; Arıza tespiti = Fault diagnosis ; Kalman filtre = Kalman filter ; Uçuş dinamiği = Flight dynamics

Özet:
Bu çalışmada, algılayıcılardan en uygun verinin türetilmesi amacıyla helikopter modelinde algılayıcı arıza tespiti, ayıklaması ve düzeltilmesi konuları ele alınmıştır. Hava araçlarının görevlerinin başarılı bir şekilde yapabilmeleri için oldukça önemli bir konu olan algılayıcıda meydana gelen ve helikopter dinamiğine etkileyen arızaları tespit etmek üzere Kalman filtresinin innovasyon sürecine dayanan arıza tespit yöntemi kullanılmıştır.  Bu yöntem doğrultusunda Kalman filtresi tekniği temelinde algoritmalar geliştirilmiştir. Geliştirilen algoritmalarda, algılayıcı arızalarının tespit ve teşhisi için farklı algılayıcı bozulma durumlarında  testler uygulanmıştır. Algoritmaları test etmek amacıyla, sürekli sapma durumu, ani sensor gürültüsü artışı ve "0" sensor çıkış değeri verecek şekilde üç farklı algılayıcı hatası durumu incelenmiştir. Arızalı algılayıcı olması durumunda helikopter modeline uygulanmış Kalman filtresinin innovasyon sürecinde oluşan değişikliklere bağlı olarak arıza tespiti yapılmaktadır. Algılayıcı arıza teşhisi için ise normalleştirilmiş innovasyon sürecin örneklem beklenen değerinin ve örneklem varyansının   değişimine dayanan iki farklı yöntem kullanılmıştır.  Bu yöntemler arızanın tespit edildiği durumlarda hangi algılayıcının arızalı olduğu bilgisini elde etmemizi sağlamaktadır.  Bu ayrışma, her bir ölçüm kanalına ait normalleştirilmiş innovasyon süreci temelinde elde edilen  istatistiklerin hesaplanmasına dayanan iki farklı algoritmalarıyla elde edilen değerlerin  teorik olarak hesaplanmış güven aralığında bulunmasının kontrolü ile sağlanmaktadır. Modellenen veriler Optimal Kalman filtresi, gürbüz Kalman filtresi ve yeniden yapılandırılır Kalman filtresi  temelinde arıza tespit, teşhis ve ayrıştırılması yapılmıştır. Algoritmalar öncelikle optimal Kalman filtre ile test edilmiştir.  Optimal Kalman filtresi ile elde edilen sonuçları kıyaslamak ve etkinliğini göstermek amacıyla gürbüz Kalman filtresi ve yeniden yapılandırılır Kalman filtresi kullanılmıştır. Gürbüz Kalman filtresi, sistemin ölçme kanallarının birinde bozulma olduğu durumları göz önüne almak ve ona karşı gelebilmek için kullanılmıştır. Optimal Kalman filtre algoritmasında arıza tespit edildiğine normalleştirilmiş innovasyon sürecinin, güven aralığınta tutulmasını sağlamak amacıyla gürbüz Kalman filtre algoritması kullanılmıştır. yeniden yapılandırılır Kalman filtre algoritması ise algılayıcılarda arıza tespit ve teşhis edildikten sonra, arızalı kanalı izole ederek filtrenin çalışmaya devam etmesini sağlamak amacıyla kullanılmıştır. Helikopter matematiksel modeline ait 12 durum değişkeni uçuşun 20 saniyelik bölümünü ifade eden simülasyon sonuçları ile elde edilmiştir.  Arıza tespiti ve teşhisi, Kalman filtresi temelli sonuçlar aracılığıyla yunuslama açısal hızı için sunulmuştur. Simülasyon sonuçları her üç Kalman filtresi algoritmasının helikopter durum parametrelerinin yüksek doğrulukta kestirimini yaptığını göstermektedir. Ancak yeniden yapılandırılır Kalman filtresinde hata değerinin, daha az ölçüm değeri kullanılması nedeniyle daha fazla olduğu görülmüştür. Ayrıca, algılayıcılarda oluşan arızaların innovasyon süreci analiziyle belirlenebildiği gösterilmiştir. Algılayıcı arıza senaryolarının farklı karakteristik özellik gösterdiği tespit edilerek arıza teşhisi için kullanılan algoritmalarda iyileştirmeler yapılmıştır. Farklı Kalman filtresi yöntemleri temelinde simülasyonlar yapılarak arızalı algılayıcı durumunda durum koordinatlarının kestirimi incelenmiş ve öneriler verilmiştir.  Çalışmada simülasyon ortamı algılayıcı arızaları tespiti için kullanılmış olup incelenen üç değişik arıza durumunun tamamının tespit edildiği gösterilmiş ve basitçe uygulanabildiğinden tasarlanan algoritmaların kullanılmasının yararlı olacağı belirtilmiştir.  Sonuçlar, sensör arızası tespiti, izolasyonu ve düzeltilmesi ile ilgili önceki çalışmaları desteklemekte ve gelecekteki çalışmalara ışık tutmaktadır.

Abstract:
In this study, the detection, identification and correction of sensor faults were discussed in order to derive the most appropriate data from the sensors in the helicopter model. To increase the reliability of helicopters with appropriate flight data and reduce the costs associated with hardware redundancy, fault detection, isolation and accommodation algorithms are applied in the design of flight systems. The main mission of diagnosis is to compensate by activating the backup systems, adjusting the gain value or taking other corrective measures with the ability to detect abnormal changes. To estimate the state variables is important to analyze the helicopter faults that affect the dynamics. The problem of deriving the most acceptable flight data for the helicopter is discussed in the study. Detection and isolation of sensor data; determination of the most suitable sensor data, estimation using other data; the derivation of the most appropriate data has been examined on the basis of the Kalman filter technique. The failure process based on the innovation squence of the Kalman filter has been used to detect faults affecting the helicopter's dynamics, which is a crucial issue for aircraft to perform their tasks successfully.  When the Kalman filter algorithm is built for helicopter state estimation, it is used for the combined longitudinal and lateral dynamics of aircraft. Hence, the state vector to be estimated is formed of 12 states. In the developed algorithms, different sensor failure tests have been applied for the detection and isolation of sensor faults. To test the algorithms, three different sensor fault conditions have been investigated in terms of continuous bias, noise increment and "0" sensor output. The continuous bias term is formed by adding a constant term of the measurement of pitch and roll angular rates, q and p, between the 2nd and 4th seconds. In the second measurement malfunction scenario, measurement fault is characterized by multtiplying the variance of the noise of the angular rate component measurements with the constant term between the 2nd and 4th seconds. In the last measurement malfunction scenario, it is assumed that state variable cannot be measured and the related sensor gives "0" as the output. This sort of fault is easily simulated by taking the state variable measurements as "0" for the filter algorithm in between the  2nd and 4th seconds. The results of these algorithms are compared for different types of measurement malfunctions and recomendations about their utilization are given. In the case of a faulty sensor, the Kalman filter applied to the helicopter model is diagnosed according to the changes in the innovation sequence. In the proposed study, this important sensor failure issue has been examined in detail. Two important approaches have been used to diagnose faults in sensors. These are fault detection and isolation. Fault detection is the determination of the presence of an error in the sensor which is based on a comparison of a statistical function and a threshold value. Fault detection has been performed depending on the changes in the innovation sequence of the Kalman filter. After the fault is detected, faulty sensor information is provided in the fault isolation step. Two different methods based on the expected value of the normalized innovation sequence sample and change of sample variance have been used for fault isolation of sensors. These methods enable us to acquire knowledge of which sensor is faulty in the event that an anomaly is detected. This fault isolation is obtained by two different algorithms that calculated by the statistics obtained on the basis of the normalized innovation process for each measurement channel are ensured by checking whether they are within the theoretically calculated confidence interval. Fault detection, isolation and accommodation of the modeled data are based on the basis of optimal Kalman filter(OKF), robust Kalman filter(RKF) and reconfigurable Kalman filter. The optimal Kalman filter, is an algorithm that uses a series of measurements observed over time, containing random noise and other inaccuracies, and produces estimates of unknown variables that tend to more precise than those based on a single measurement alone. Generally, the filtering process of Kalman filters is examined in two distinct phases. The first phase is time update where the estimations of the preceding step is used for producing the estimations of the present step. The second phase is measurement update that the estimation of the present step is realized by using prediction  phase outputs and, also, measurements information operation, where the predictions are improved. Hence, the optimal Kalman filter works on the principle of correction of the prediction. Algorithms were first tested with optimal Kalman filter. Under normal operation conditions, where any kind of measurement malfunction is not observed, the optimal Kalman filter gives sufficiently good estimation result. However, when the measurements are faulty due to malfunctions is the estimation system filter estimation outputs become inaccurate. Therefore, an RKF algorithm, which brings fault tolerance to the filter and secures accurate estimation results in case of faulty measurements without affecting the remaining good estimation characteristics, should be introduced. The base of the robust Kalman filter is the comparison of real and theoretical values of the covariance of the innovation sequence. When the operational condition of the measurement system mismatches with the models used in the synthesis of the filter, then Kalman filter gain changes according to the differentiation in the covariance matrix of innovation sequence. As a result, more accurate estimation results can be obtain. Indeed, the proposed robust Kalman filter is not so different from optimal Kalman filter from the point of view of structure; it may be assumed to be a modification. Therefore, in case of any kind of malfunctions, related elements of the scale matrix, which correspond to the faulty component of the measurement vector, increase, and that bring about a smaller Kalman gain which reduce the effect of innovation on the state update process. As a result, more accurate estimation is obtained. It must be noted that due to the scale factor $S_k$, the covariance of estimation error of the RKF increases in comparison with the OKF. Therefore, the robust algorithm is used only when the measurements are faulty and, in all other case, the procedure is run optimally with the regular Kalman filter. The process is controlled by use of a kind of statistical information. In addition to, with a reconfigurable Kalman filter, when a sensor fault occurs in  the system, the reconfigurable Kalman filter is used for fault accomodation. In this case, the faulty measurement is ignored, which means it is necessary to reconfigure the filter algorithm because of the changed number of incoming measurements, but the estimation accuracy in comparison with the sensor fault free OKF decrease. Doing that, the system model changes and is less reliable because the error of the estimations increases, but as long as the system fulfills the initial requirements it still can be used. The algorithms investigated have been applied to the helicopter's dynamic model, and the estimated values fit the theory. Robust Kalman filter and reconfigurable Kalman filter were used to compare the results obtained with OKF and to demonstrate its effectiveness. In the optimal Kalman filter algorithm, the robust Kalman filter algorithm is used to ensure that the normalized of innovation sequence to the fault is kept in the confidence interval. The reconfigurable Kalman filter algorithm is used to isolate the faulty channel in the sensors after the fault is detected to the filter continue to operate. It has been proved that the simulations detect three different fault conditions by using the mentioned tests for sensor fault detection. However, it is determined that the sensor failure scenarios show different characteristics and improvements are made in algorithms used for diagnosis. It has also been shown that faults can be determined by the residues found. This is one of the most notable features of the study. The 12 states of the helicopter model that were obtained with simulations express the flight time of 20 seconds. Simulations are realized in 2000 steps for period of 20 s with 0.01 s of sampling time, $\Delta t$. Fault detection, isolation and accommodation are presented for angular rate of pitch "q" and  angular rate of roll 'p' through Kalman filter based results. In this thesis, figures gives the optimal Kalman filter, robust Kalman and reconfigurable Kalman filter state estimation results and the actual values, the error of the estimation process based on the actual values of the helicopter and the variance of the estimation that corresponds to related diagonal element of the covariance matrix of estimation errors are compared. Simulation results show that all three Kalman filter algorithms estimate the helicopter state parameters with high accuracy. Also, in case of measurement faults, simulations are also perform for the optimal Kalman filter to compare the results with robust Kalman filter and reconfigurable Kalman filter algorithm and efficiency of the robust Kalman in more detail. Nonetheless, $\chi^2_{\alpha,s}$ is taken $  276.974$ and this value comes from a Chi-square distribution when the number of degrees of freedom is 12 and reliability level is $99.73\% $. However, the error value of the robust Kalman filter was found to be higher due to the use of less measurement value. Results have also been shown that faults can be determined by an analysis of the innovation sequence of sensors. Since the sensor fault scenarios show different characteristics, the algorithms used for fault diagnosis have been improved. Simulations based on different Kalman filter methods have been applied and the estimation of the state coordinates in case of a faulty sensor has been examined and suggested. Fault detection and isolation are presented for pitch and roll angular rates through Kalman filter based results. In the study, the simulations were used to detect and isolate sensor faults and it has been shown that all three fault conditions examined were detected. The results obtained show the effectiveness of the proposed fault diagnosis methods. As a result, simulations have shown that all three different fault conditions are detected in the sensors and it would be designed simply that is useful for algorithms. Comparison of the performance of the optimal Kalman filter, robust Kalman filter and reconfigurable Kalman filter in case of measurement malfunctions is proposed in the study. Moreover, the simulation results indicated higher the absolute values of error and RMS values of reconfigurable Kalman filter compared to robust Kalman filter. As a result, ıt shows that more accurate estimation is obtained. The results obtained show the effectiveness of the proposed fault diagnosis methods. In accordance to the main motivation behind the study, supplying reliable parameter estimation to system of the helicopter and ensuring that it completes its mission successfully is the objectives of this thesis. The results support previous work on sensor fault detection, isolation and accommodation and shed light on future work.