One of the challenging problems in the case of aircraft failure is to determine the new altered dynamics of the impaired aircraft. Among various methods, neural networks and neuro-fuzzy systems can be used for high-fidelity modeling of the aircraft nonlinear dynamics with the aim of onboard applications in real time. However, the method with better generalization capability is more preferred specifically in the case of unpredicted aircraft failures. Generalization of a network is mainly dependent on the network's parameters, the employed training algorithm, and the amount of training data. In this paper, several neural networks and local model networks are trained using different training algorithms and different amounts of training data to model the nonlinear dynamics of an impaired aircraft with the damaged rudder. These networks are compared based on their generalizations to the new cases of rudder failure. The effect of using different amounts of training data on the generalization capability and performance of the networks has also been investigated. The results of this paper show that both network types have good performance but neural networks generalize better to the new failure cases than local model networks. Also based on the obtained results, a significant reduction in the number of training samples could be accomplished without a considerable decrease in the network's performance and generalization. Finally, a neural network-based sensitivity analysis method is proposed which utilizes the network's regression equation as an emulator for fast model evaluations and can be used as an advisory tool for choosing safer path planning strategies.

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Aircraft failures alter the aircraft dynamics and cause maneuvering flight envelope to change. Such envelope variations are nonlinear and generally unpredictable by the pilot as they are governed by the aircraft complex dynamics. Hence, in order to prevent in-flight Loss of Control it is crucial to practically predict the impaired aircraft's flight envelope variation due to any a-priori unknown failure degree. This paper investigates the predictability of the number of trim points within the maneuvering flight envelope and its centroid using both linear and nonlinear least-squares estimation methods. To do so, various polynomial models and nonlinear models based on hyperbolic tangent function are developed and compared which incorporate the influencing factors on the envelope variations as the inputs and estimate the centroid and the number of trim points of the maneuvering flight envelope at any intended failure degree. Results indicate that both the polynomial and hyperbolic tangent function-based models are capable of predicting the impaired fight envelope variation with good precision. Furthermore, it is shown that the regression equation of the best polynomial fit enables direct assessment of the impaired aircraft's flight envelope contraction and displacement sensitivity to the specific parameters characterizing aircraft failure and flight condition.Nomenclature V = total airspeed, knot ,  = angle of attack, sideslip angle, respectively, deg p, q, r = angular velocity components (roll rate, pitch rate, yaw rate, respectively), deg/s 1 Ph.D. Candidate, Faculty of New Sciences and Technologies; ramin.norouzi@ut.ac.ir. Student Member AIAA. 2 Associate Professor, Faculty of New Sciences and Technologies; kosari_a@ut.ac.ir. 3 Assistant Professor, Faculty of New Sciences and Technologies; sabourmh@ut.ac.ir. , , ,  = Euler angles (roll, pitch, yaw, respectively), flight path angle, deg , = state vector, control vector, respectively , , , ℎ = deflection angles (elevator, aileron, rudder, respectively), deg, throttle setting (%) ∈ [0, 1] , �, = fitted model's residual, outcome, parameters (coefficients) vectors, respectively , = predictor vector, model parameters (coefficients) vector, respectively = total degree of polynomial , ℍ, , = gradient, Hessian, Jacobian of the objective function , identity matrix, respectively = Newton's method search direction = Marquardt parameter = hyperbolic tangent function 1 , 2 = total number of neurons in the first (hidden) layer, second (last) layer, respectively = backpropagation training iteration ℒ , ℒ , ℒ , ℒ, = (net output, net input, bias) of ℒ ℎ neuron in layer , respectively ℒ,= weight's element of ℒ ℎ neuron in layer due to ℎ neuron of the previous layer .̂ = standard backpropagation sensitivity, Marquardt sensitivity, respectively ℰ, = contribution of the ℰ ℎ neuron of the last (second) layer to the error of the ℎ training sample = statistical expected value of the ℎ input factor Subscripts , = total number of training samples, total number of model parameters, res...

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