You Are Cleared to Fly
How optimization-based methodologies are improving the flight control systems’ safety
Since the introduction of the first non-experimental digital fly-by-wire system in the F-8 Crusader, the exponential growth of the embedded control systems computing power has enabled the military aerospace industry to develop more efficient and agile aircraft.
Generally, modern fighters are designed to be naturally unstable for the sake of maneuverability and agility, requiring the use of Flight Control Laws (FCL) to artificially stabilize the aircraft dynamics and to provide diverse safety-critical flight envelope protection functions, along with automatic or semiautonomous flight modes.
To ensure the safe operation of the aircraft and the correct functioning of the FCL, a clearance assessment must be performed.
The FCL clearance encompasses a set of activities on which the controller robustness against plant un-modeled dynamics and sensors measurement errors is assessed for every flight condition and pilot/operator commands that lie within the target operating envelopes, and for every aircraft system performance status, including all possible detected and undetected failures that might occur during the aircraft’s operational life.
The Flight Control Laws Clearance Assessment
The FCL clearance can be defined as a model-based non-linear robustness assessment problem, composed of a large number of parameters defining the aircraft systems’ status and the flight conditions, with hundreds of “unknowns” and un-modeled dynamics terms that must be covered in the assessment work via model-tolerances.
The main objective of a flight control laws clearance assessment is to define the conditions and the flight envelope areas where the aircraft can be operated within the safety levels required by the airworthiness regulations.
FCL clearance activities can be categorized into three major groups:
- Generalized stability assessments
- Nonlinear off-line simulations
- Manned simulations
The first group is composed of all the clearance tasks aimed at evaluating the controller’s robustness in terms of stability margins using linearized models, describing functions methods and more generalized nonlinear stability assessment methodologies.
The other two major tasks rely mainly on complex nonlinear simulation models to assess the air vehicle handling qualities, and to check the correct functioning and performance of the FCL’s flight envelope automatic protection functions.
In modern airliners and high-performance military aircraft, these protection functions reduce the required pilot workload in complex scenarios with high-demanding tasks and provide Full-Carefree Handling (FCH) capabilities to the aircraft, allowing the pilot to perform aggressive maneuvers with fast variations on the stick, throttle, and pedal inputs, without the need to observe and care for the aircraft structural and flight envelope limits.
The main objective of the offline nonlinear simulation assessments is to check the aircraft’s risk to depart from controlled flight for every condition within the operational flight envelope.
To meet this goal, all the flight mechanics parameters that describe the aircraft dynamics and the embedded systems states are monitored in the nonlinear simulations to ensure that the exceedances of the flight protections limits remain bounded within the carefree limits, granting a low risk to encounter unrecoverable departures from controlled flight and not to over-stress the airframe.
In other words, if your brain’s control functions were to be redesigned by a bioengineering team, prior to letting you live with your brand new superpower capabilities, they would have to check they have connected every neuron the right way so they perform as per design. They would then simulate your entire life in a computer, from your birth to your death, checking that you make it without any major issue up to your “design day”. In short, that would be the clearance assessment of your bioengineered brain’s control functions.
A Hard Mathematical Problem
The vast amount of variables and parameters defining the aircraft systems status, flight conditions, model tolerances, and pilot inputs, makes the FCL clearance a challenging task that requires a large number of super-computing resources to cope with the tight time constraints of the FCL verification and validation process (typically weeks). Some of these variables or degrees of freedom are:
- Flight condition
- Pilot’s control stick inputs
- Pilot’s throttle inputs
- Pilot’s pedal inputs
- Aerodynamic model tolerances
- Air Data System tolerances
- Undetected/detected system’s failures
- Atmospheric perturbations
- Centre of Gravity (CG) translation derived from aircraft’s fuel sloshing phenomenon
- Mass-CG envelope
- External and internal payloads
- Missiles and bombs firing
Moreover, the complexity of the FCL clearance further increases in the particular case of FCL designed to provide Full Carefree Handling capabilities, as the number of degrees of freedom (DoF) related to the pilot’s control inputs increases dramatically.
To solve this robustness assessment problem, it’s customary in the aerospace industry to apply a deterministic grid-based analysis approach, discretizing the problem space and simplifying the number of combinations of cases to be analyzed using engineering judgment and lessons learned from previous FCL clearance assessments.
The bad news is that this approach does not ensure engineers find all the clearance problems, because worst cases are not always obtained with the extreme combination of the inputs due to the high nonlinear FCL’s functions, and also due to nonlinearities present in the aircraft’s simulation models.
This deterministic grid-based analysis approach is suitable only to provide an overview of the general clearance problems, but it does not guarantee finding the worst combination of the inputs, because not all the inputs and tolerance combinations are explored because of supercomputing resources and time frame limitations.
The Optimization-based Approach
The solution to cope with all of the grid-based analysis drawbacks is to incorporate global optimization methodologies into the mainstream FCL clearance process, in order to search quickly for the worst-case scenarios.
Special global optimization algorithms have been developed by the aerospace industry for such purpose, increasing the probability of successfully finding FCL issues and saving a considerable amount of computation time. This is the case of the Multi-strategy Adaptive Global Optimization (MAGO) algorithm recently developed by Airbus Defence and Space.
The MAGO Algorithm for Optimization-based FCL Clearance Assessment
The MAGO algorithm is a population-based meta-heuristic single-objective global optimization algorithm developed as a versatile optimization tool for the FCL clearance assessment, with the main objective of detecting the conditions, tolerances combinations, and pilot inputs that leads to the worst-case breach of the different safety and clearance requirements in a shorter time.
As with all population-based optimization algorithms, MAGO uses a population of individuals to search for the global minimum of a cost function. The population of candidate solutions evolves in each optimization generation until reaching an exit criterion, usually the maximum number of function evaluations, a critical parameter due to the limited time and available supercomputing resources to perform an FCL clearance.
One of the most challenging problems for the end-user of any global optimization algorithms is the selection of the optimization algorithm’s configuration parameters that maximize the opportunities to find the global minimum of a cost function. In black-box optimization problems, there is little or no previous information about the cost function topology, so the proper selection of the optimizer configuration parameters becomes a complex task, and usually requires multiple trial and error tests.
To overcome this handicap, the optimization algorithm should be able to adapt itself throughout the optimization process by using information about the obtained improvements in the population cost as the algorithm progresses with the optimization.
Finding the best optimization algorithm parameters has been considered to be part of the algorithm design and not part of its application. The aim is to have a robust well-performing algorithm with the minimum number of parameters to be selected by the end-user.
This basic idea has been incorporated at the core of MAGO to elaborate a novel concept of smart adaptive behavior using notions and theories from cooperative games.
As an example, you can see the superior performance of the MAGO algorithm compared to other top-notch global optimization algorithms (like the Particle Swarm Optimization and the SPS-LSHADE-EIG algorithms) in the figure below, where the flight envelope of a highly maneuverable aircraft is shown (speed of sound / Mach vs flight altitude) with the violations of a certain clearance requirement is highlighted in a colormap (the darker the worst).
You can find more insights about how the MAGO algorithm works in this technical paper.
The aerospace industry and the airworthiness authorities take flight safety very seriously, both in the civil environment and in the military world, that’s why the flight control system’s software is proved, tested, and validated thoroughly in the FCL clearance process.
The next time you travel by plane, remember why this is the safest mode of transportation in the world…
“You Have Been Cleared to Fly”
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Rodney Rodríguez Robles is an aerospace engineer, cyclist, blogger, and cutting edge technology advocate, living a dream in the aerospace industry he only dreamed of as a kid. He talks about coding, the history of aeronautics, rocket science, and all the technology that is making your day by day easier.