A non-uniform or nonstationary atmosphere can create a momentary disturbance to an aircraft which is in steady flight condition. The longitudinal stability of an aircraft plays a vital role in keeping the aircraft in equilibrium condition. In the current investigation a novel approach Bayesian Regularization neural network (BRNN) has been proposed to find stability control derivatives for the short-period longitudinal dynamic mode and compared with Levenberg–Marquardt algorithm (LM). The proposed approach has been accomplished by using a reliable software i.e. MATLAB®R2020a. In this lieu, the combination of artificial neural networks (ANN) with optimized trained algorithm provides a transformative, promising and unparallel prediction rate of flight derivatives. In BRNN method, Angle of Attack (AOA), elevator input and pitch rate used as input parameters whereas, lift coefficient and pitching moment coefficient have been as output parameters to increase the robustness of the mathematical model and train the BRNN model. With the proposed approach the mean square error (MSE), regression analysis, coefficient of lift (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">${C}_{L}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>L</mi> </msub> </math></EquationSource> </InlineEquation>), and coefficient of moment (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">${C}_{m}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mi>m</mi> </msub> </math></EquationSource> </InlineEquation>) for estimated and simulated data have been carried out. The MSE value of coefficient of lift (BRNN 2.2016^10−9 for epoch 51 and LM 9.8424^10−9 for epoch 351) and for coefficient of moment (BRNN 9.8844^10−9 for epoch 62 and LM 9.9281^10−9 for epoch 87) have been noticed. Hence, it has been revealed that Bayesian Regularization neural network training showed far better performance as compared to existing Levenberg–Marquardt algorithm. From the above analysis it has been confirmed that BRNN has greater potential for predicting flight control derivatives. Further work can be studied for lateral and directional mode using the above approach.

A Bayesian regulation framework for robust estimation of aircraft stability and control derivatives

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发表日期：

2026年3月16日

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Challa Parvathi Rudesh,
Sanjay Singh,
P. Srinivasa Rao

摘要

A non-uniform or nonstationary atmosphere can create a momentary disturbance to an aircraft which is in steady flight condition. The longitudinal stability of an aircraft plays a vital role in keeping the aircraft in equilibrium condition. In the current investigation a novel approach Bayesian Regularization neural network (BRNN) has been proposed to find stability control derivatives for the short-period longitudinal dynamic mode and compared with Levenberg–Marquardt algorithm (LM). The proposed approach has been accomplished by using a reliable software i.e. MATLAB®R2020a. In this lieu, the combination of artificial neural networks (ANN) with optimized trained algorithm provides a transformative, promising and unparallel prediction rate of flight derivatives. In BRNN method, Angle of Attack (AOA), elevator input and pitch rate used as input parameters whereas, lift coefficient and pitching moment coefficient have been as output parameters to increase the robustness of the mathematical model and train the BRNN model. With the proposed approach the mean square error (MSE), regression analysis, coefficient of lift ( ${C}_{L}$ $C_{L}$ ), and coefficient of moment ( ${C}_{m}$ $C_{m}$ ) for estimated and simulated data have been carried out. The MSE value of coefficient of lift (BRNN 2.2016^10⁻⁹ for epoch 51 and LM 9.8424^10⁻⁹ for epoch 351) and for coefficient of moment (BRNN 9.8844^10⁻⁹ for epoch 62 and LM 9.9281^10⁻⁹ for epoch 87) have been noticed. Hence, it has been revealed that Bayesian Regularization neural network training showed far better performance as compared to existing Levenberg–Marquardt algorithm. From the above analysis it has been confirmed that BRNN has greater potential for predicting flight control derivatives. Further work can be studied for lateral and directional mode using the above approach.