Towards Flight Stability Verification Using Statistical Techniques

Flight dynamics is the study of aircraft response to its control inputs, gravitational forces, and perturbations. This science plays a key role in aircraft models, which have to adhere to strict design and safety requirements.... [ view full abstract ]

Flight dynamics is the study of aircraft response to its control inputs, gravitational forces, and perturbations. This science plays a key role in aircraft models, which have to adhere to strict design and safety requirements. One such safety requirement is the stability (static/dynamic) criteria, defined as the ability of an aircraft to support a uniform flight and to recover to an equilibrium condition from the effects of perturbation such as vertical gusts, center of gravity, or deflection of the controls by the pilot. Against the backdrop of aggressive time-to-market schedules and Federal Aviation Administration guidelines, modeling and verification of the stability property still remains a priority across the aviation industry.

Traditionally, simulation methods are used to verify the stability criteria of an aircraft. Aerodynamic mathematical models in the form of ordinary differential equations (ODE) are constructed and simulated for understanding of functional behavior in the absence of perturbation. However, growing complexity of requirements and the stochastic nature of the flight dynamics require a robust modeling and verification environment. To gain high confidence in the system, the aerodynamic model should be statistically simulated for different initial, environment and manufacturing conditions. We, therefore propose a modeling and estimation method that allows us to capture the perturbation in the form of Stochastic Differential Equations (SDE) for the statistical monitoring of the stability property. We test our approach analytically and numerically on a HL20 and F4 aircraft systems.

Figure 1 shows the proposed aerodynamic system modeling and verification framework. Given an aircraft system, the first step is to describe the aerodynamic behavior as a system of ODEs. We use state space equations to describe the stability property.The next step is to include perturbation as a set of stochastic processes that adhere to certain probability distributions as shown in Figure 1. This is done through the use of SDEs. To find an analytical solution for the SDEs, special mathematical interpretation in the form of stochastic calculus is required. However, as most aerodynamic models do not have a closed-form solution, the behavioral validation has to rely on well-established numerical approximation methods for the SDEs. Thereafter, the SDE numerical approximation, manufacturing constraints, and the initial condition of the system are evaluated in a statistical environment as shown in Figure 1.

The statistical technique relies on MonteCarlo simulation with statistical monitors in the front- end and hypothesis testing in the back-end to verify the aerodynamic model. Hypothesis testing is the use of statistics to make decision about acceptance or rejection of some statements based on the data from a random sample, meaning, to determine the probability that a given hypothesis is true. Hypothesis testing in general, has two parts: Null hypothesis, denoted by H0, which is what we want to test and Alternative hypothesis, denoted by H1, which is what we want to test against the null hypothesis. If we reject H0, then the decision to accept H1 is made. The conclusion is drawn with certain probability of error (α and β) along with specific confidence level.