# Investigating Flight Envelope Variation Predictability of Impaired Aircraft using Least-Squares Regression Analysis

## TL;DR

This study explores the predictability of flight envelope changes in impaired aircraft using linear and nonlinear least-squares models, aiming to enhance in-flight safety by anticipating control loss due to failures.

## Contribution

It introduces polynomial and hyperbolic tangent models to predict flight envelope variations, providing a novel approach to assess aircraft failure impacts.

## Key findings

- Models predict envelope variation with good accuracy
- Polynomial models enable sensitivity analysis of failure parameters
- Hyperbolic tangent models effectively capture nonlinear envelope changes

## Abstract

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's 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.

---
Source: https://tomesphere.com/paper/1905.07875