Capturing aerodynamic characteristics of attas aircraft with evolving intelligent system

Abstract

There are many studies in the literature that have been conducted to obtain an accurate mathematical model. In the early times, modeling studies were done with differential equations, but this approach could not fully express the nonlinear characteristics in some cases. Later, it was seen that nonlinear systems can be modeled successfully with the development of artificial intelligence and fuzzy systems. Especially in the aviation industry, where safety and security are of paramount importance, it is critical to accurately represent aircraft models. Mathematical models that accurately represent aircraft dynamics are critical in many studies such as aircraft control system design development, certification, and flight mechanics analysis. Therefore, aerodynamic modeling of the aircraft is very important. Either a wind tunnel or a parameter estimation method is used for aerodynamic modeling. However, wind tunnel, which is an experimental method, is quite costly since it requires an experimental setup. For this reason, many statistical-based system identification algorithms have been developed in the literature to estimate aerodynamic control and stability derivatives using measured flight tests. The Ordinary Least Squares (OLS) method is the most widely used system identification algorithm. In this method, which belongs to the light gray box model category, an aerodynamic mathematical model is developed that best fits the flight dataset and minimizes the squares of the differences between the estimated value and the actual value. However, this method may not be fully successful in expressing the nonlinear characteristics of the aircraft. In the neural network (NN) algorithm, which is in the black box model category, the weight parameters are trained using the input data and output data of the aerodynamic postulated model. The model obtained as a result of the NN algorithm can successfully represent the nonlinear characteristics of the aircraft. However, it is not possible to interpret NN based model since they lack a rule base in their structure. On the other hand, the models obtained with fuzzy logic algorithms are open to interpretation because they have a rule base structure and these models are in the dark gray box model category. Moreover, fuzzy logic algorithms are very successful in modeling complex and nonlinear systems. Considering these advantages of fuzzy systems, many aerodynamic modeling studies have been conducted in the literature with Adaptive Network Based Fuzzy Inference System (ANFIS). Based on these observations, Evolving Type 1 Quantum Fuzzy Neural Network (eT1QFNN) and Evolving Type 2 Quantum Fuzzy Neural Network (eT2QFNN) structures have been developed in this study. These evolving structures can better capture the nonlinear aerodynamic characteristics of the aircraft. Also, they are open to interpretation and they are robust to model uncertainties. The aerodynamic postulate model obtained from this methodology is compared with the aerodynamic postulate models obtained by OLS, NN, and ANFIS structures and the accuracy of the obtained aerodynamic models is analyzed. Firstly, flight data from the flight test campaign previously conducted with the ATTAS aircraft are used to obtain the aerodynamic model of the ATTAS aircraft. When selecting the suitability of this flight data, attention should be paid to whether the aircraft can trigger the longitudinal, lateral and directional modes. In this study, short period, bank to bank and dutch roll maneuvers were used to trigger the longitudinal, lateral and directional modes of the ATTAS aircraft. With these maneuvers, the responses of the aircraft obtained from the sensor were analyzed and the parameters to be used in system identification were recorded. A low-pass filter was used to remove noise from the recorded flight data. Thus, the noise effect in the parameters to be used in the identification of the aerodynamic model of the ATTAS aircraft was removed and made more appropriate. After the obtained flight data were filtered with a low-pass filter, the flight data was preprocessed. In order to preprocess the data, force and moment equations were generated in MATLAB using the weight, moment of inertia, and thrust values of the ATTAS aircraft. Then, the linear accelerations and angular rates obtained from the measured flight data are written into the previously created equations, and the aerodynamic force and moment coefficients are calculated. Thus, reference aerodynamic coefficients expressing the characteristics of the ATTAS aircraft are calculated with these flight data. After obtaining the reference aerodynamic coefficients, the aerodynamic postulate model of the ATTAS aircraft is derived. While constructing this postulate model, the aerodynamic postulate models available in the literature and the stepwise regression algorithm are utilized. With the stepwise regression algorithm, it was determined which stability and control derivative coefficients can be used in the aerodynamic postulate model and the over-parameterization problem was avoided. As a result of these analyses, the postulate models were obtained for 6 aerodynamic coefficients. In the next step, it is aimed to obtain aerodynamic postulate models that can represent the aerodynamic characteristics of the ATTAS aircraft well by using system identification algorithms. These models are compared with the reference models obtained from the force and moment equations to analyze whether they accurately represent the aerodynamic characteristics of the ATTAS aircraft. In this study, eT1QFNN and eT2QFNN are proposed to model the aerodynamic characteristics of the ATTAS aircraft. These evolving structures, which contain quantum fuzzy sets and neural network structures, have multiple inputs and a single output. In these evolving structures, the learning process starts with an empty rule base and the structure is continuously updated as a new data sample arrives. With each new data sample, these evolving structures generate a hypothetical rule that drives the autonomous evolution of the fuzzy rules. The generated hypothetical rules need to evolve significantly before they are incorporated into the network structure. The significance is evaluated using the Gaussian Mixture Model to predict complex changes in the data. If the generated hypothetical rules provide more contribution and meaning than the existing rules, they are added to this structure as new rules. On the other hand, when the hypothetical rules do not provide more meaning than the existing rules, the parameters of the quantum membership function and the consequent weight parameters in the rule base are updated by a decoupled extended Kalman filter. To do this, a winning rule is developed that depends on the maximum spatial firing power. In other words, the antecedent membership function and consequent weight parameters of the rule with maximum spatial firing power are updated. Thus, the performance of the evolving structures is preserved. These evolving structures are robust to uncertainties and data noise thanks to quantum membership functions as well as automatic rule learning and parameter tuning capabilities. They can also represent the nonlinear aircraft model by creating multiple linear sub-models with a rule-based structure through an incremental learning strategy instead of the traditional batch learning approach. In the next step of the study, the aerodynamic postulate models obtained from the proposed eT1QFNN and eT2QFNN are compared with the aerodynamic postulate models obtained from the OLS, NN, and ANFIS structures. Thus, the proposed methodology can be compared with previously existing methodologies in the literature in terms of modeling performance. In order to examine whether the system identification algorithms can successfully represent the aerodynamic characteristics of the ATTAS aircraft, two different settings were made. In the first one, training was performed with 80% of the flight data and testing with 20% of the flight data, while in the second one, training was performed with 50% of the flight data and testing with 50% of the flight data. Thus, models trained with both large and small data sets were analyzed. Furthermore, it was questioned whether the aerodynamic characteristics of the ATTAS aircraft could be captured with less flight data. In addition, during the training process of ANFIS and NN based aerodynamic models, overfitting was checked using test data. In contrast, no such overfitting check was performed for the OLS, eT1QFNN, and eT2QFNN models. This distinction arises from the fact that ANFIS and NN models are trained through multiple iterations, whereas OLS, eT1QFNN and eT2QFNN models are trained in a single iteration. In the next phase of the study, the Delta method was applied to the aerodynamic models estimated with the eT1QFNN and eT2QFNN with more training data, since more training data included short period, bank to bank, and dutch roll maneuvers. Thus, all longitudinal, lateral, and directional modes of the ATTAS aircraft could be triggered. As a result of the application of this method, the control and stability derivative parameters of the aerodynamic model were obtained. The dynamics, stability and controllability of the aircraft could be analyzed using these parameters. In this study, the control and stability derivative parameters are obtained by perturbing each of the input variables by about 1% in each direction. While one input variable is perturbed, the others should remain constant. The values of the control and stability derivative parameters during the flight time are shown and analyzed in histogram plots. The structure and sensitivity of the evolving structures in the rule bases could be interpreted by looking at the changes of these parameters in the histogram plots. The parameters obtained from this evolving structure with the Delta method were compared with the parameters obtained from the OLS method. Thus, it was analyzed whether the control and stability derivative parameters obtained from the evolving structure consistently represent the aerodynamic characteristics of the ATTAS aircraft. As a result, when the aerodynamic models obtained with the eT1QFNN and eT2QFNN are compared with the aerodynamic models obtained with other system identification algorithms, it is seen that the eT2QFNN better represents the aerodynamic characteristics of the ATTAS aircraft. In making this comparison, the closeness of the obtained aerodynamic postulate model to the reference aerodynamic model obtained in the flight test was considered. In addition, the accuracy of the values of the control and stability derivative parameters of the aerodynamic postulate model was also analyzed.