On this page you can learn more about Simulation, Parameter Identification and Flight Safety:

## Parameter Identification

System Identification is a method for modeling physical system dynamics. The approach is based on measured input- and output data of the real system. Flight vehicle system identification focuses on the aircraft dynamics and on modeling the forces and moments that act on it. The result is a validated model with known uncertainty bounds that is reliable in a known region of the flight envelope.

System identification techniques allow to compare and combine dynamic models from very different sources, e.g. from flight test data, wind-tunnel tests or computational fluid dynamics (CFD), leading to very accurate results. As it is very laborious to achieve similar results purely from traditional modeling techniques, flight vehicle system identification is an integral part of common flight test programs / aircraft development programs.

### The Basic Idea of System Identification

Flight Vehicle System Identification describes the process of deriving a mathematical model and the governing parameters from experimental flight test data. It can roughly be split into three steps: Flight test planning & execution, System Identification & Parameter Estimation and Model Validation.

In the first step, a flight test program is designed and performed, which aims at exciting the motion of the aircraft in such a way, that the measured outputs contain a maximum of information about the aircraft characteristics.

In the second step a suitable model structure is postulated and the recorded flight data is used to estimate the governing parameters, i.e. to maximize the match between measured and model outputs according to a cost criterion. The model can be implemented with different levels of fidelity, ranging from simple linear state-space models to high fidelity six degree-of-freedom non-linear simulations.

Finally, the estimated model of the foregoing step is analyzed and validated, concerning two main aspects. On the one hand, the statistical properties of the estimated parameters have to be investigated. On the other hand, the model predictive capability has to be checked, i.e. the ability of the model to predict outputs that were not included in the original estimation process.

### Applications

The system identification group focuses on unmanned aerial systems and general aviation aircraft, both equipped with low cost sensors, that constitute a field of special interest at FSD. In doing so the group is contributing to many projects. This includes the modeling of fixed wing aircraft, helicopter and multicopter systems. The identified models were used as the basis for e.g. the model based design of flight control systems and as flight dynamics model in high fidelity flight simulators.

### Methods & Research Areas

The methods that are used by the system identification research group at the institute of flight system dynamics incorporate both time and frequency domain approaches.

The workflow of the former contains up to four steps. In a preprocessing step the actual flight data has to be checked for consistency and measurement errors. This first step is usually called flight path reconstruction. Then the data is transformed to the frequency domain, where empirical transfer function estimates can be generated. If so desired, those empirical estimates are then parameterized to be applicable in simulations. Research in the frequency domain is mainly focused on different ways to achieve the transformation and several ways of obtaining empirical transfer function estimates, as well as the applicability to online, in-flight identification.

The time domain identification at FSD is mainly based on maximum likelihood methods, such as the equation error, output error and filter error method. When obtaining raw flight data, the same flight path reconstruction step is taken to obtain kinematically consistent data. The parameters in a model are adjusted such that the model outputs resemble the measured data as closely as possible, which is done using well established optimization strategies. The models can range from simple algebraic or linear dynamic systems to complex, high-fidelity, non-linear simulations. The main research areas under investigation are the applicability of collocation methods in system identification and input optimization in order to maximize information content in the recorded data.

Furthermore, online identification methods can be used for monitoring tasks. In order to detect a fault, online estimates of governing parameters or stability measures are compared to their nominal values. If too large a difference is detected, measures can be taken to counteract the fault.

### Contact

For further information on our work or if you are interested in any kind of cooperation, please feel free to contact us!

Barzin Hosseini, Christian Merkl, Xiaolong Wang

## Flight Safety

### Background

Today, airlines are required by law to implement a safety management system for their flight operation as described by the ICAO document, *Safety Management Manual* (ICAO DOC 9589, 3^{rd} Edition, 2013). As part of the safety management system, each airline is required to commit itself to a so-called Acceptable Level of Safety Performance (ALoSP). The *Safety Management Manual* defines the ALoSP as follows:

*“The minimum level of safety performance […] of a service provider, as defined in its safety management system expressed in terms of safety performance targets and safety performance indicators.”*

This definition implies that the ALoSP should be defined in numerical terms, i.e. as a target safety value. Such a numerical value also requires corresponding safety performance indicators (SPIs) for measuring the current level of safety. By comparing these SPIs with the ALoSP, it is possible to judge whether the safety objectives have been achieved.

A potential definition of an ALoSP can also be found in Europe’s vision for aviation in the year 2050, *Flightpath 2050*. This report defines a safety target for the whole of Europe in terms of accident rates, specifically, an accident rate of less than one accident for ten million flights. This is equivalent to an accident probability of 10^{-7} per flight, and can serve as a starting point for defining a specific ALoSP for an individual airline.

However, before an airline is able to consider the actions necessary to achieve such a target accident probability, it must be able to measure its safety level. In addition, if an airline wants to manage its safety, it will need specific values that account, for example, for the safety culture, route network, fleet, operations, and training *specific to* that airline.

### Predictive Analysis – The Challenge of Small Numbers

One possible solution to the problems described above is based on predictive analysis. Predictive analysis refers to making a quantitative statement about a future state or condition based on previous experience or knowledge. Predictive analysis focuses on quantifying the probabilities of serious incidents for an individual airline, which are small, yet not equal to zero.

Before incident probabilities can be quantified, incident metrics must to be developed. Incident metrics are used to describe the closeness of a single flight to ending in a specific incident. Put another way, the incident metric describes a safety margin of a particular flight with respect to a particular incident.

Incident metrics have two main characteristics: Firstly, incident metrics can be compared to a limit in order to exactly determine whether an incident has occurred. Secondly, the closer the calculated incident metric is to the limit, the more critical the flight regarding that particular incident. These kinds of incident metrics can be calculated after each flight based on its flight operational data. An example of such an incident metric is the stop margin, with respect to a runway overrun, or the tail clearance, with respect to a tailstrike.

### Incident Model

The hypothesis in this method is that a given incident can be described as a sum of its constituent parts, so-called contributing factors. When considered individually, an excessive value for a contributing factor is often benign. For example, aircraft landings are often conducted with an approach speed that is slightly higher than normal, with a slightly longer flare than normal, or a little higher tailwind than usual. While any of these deviations itself is harmless, an overrun is usually a result of a combination of a too-high approach speed, a slightly higher tailwind, etc.

Incident models include the functional relationships between the contributing factors. Some of these relationships are based on aircraft dynamics, which apply to all airlines, while other relationships result from airline-specific procedures and other information. Once the model has been developed, the airline-specific statistical distributions for each of the contributing factors are propagated through the incident model to obtain a probability for the incident. That resulting probability is no longer equal to zero, even if the airline has never experienced the incident.

### Parameter Estimation

There are also contributing factors that are major physical drivers for incidents but cannot easily be obtained by any current FDM system. Parameter estimation techniques can be applied in order to quantify these types of contributing factors.

The methods of parameter estimation can be described as a backward computation technique for obtaining parameters that are not recorded during flight operation. The methods that are applied during parameter estimation to analyze the data gathered in routine flight operation are similar to those typically used for flight-testing. The scientific challenge is to still observe the relevant contributing factors without the availability of dedicated sensors and excitation maneuvers. After applying a tailored parameter estimation technique to the available flight data, the unrecorded parameters are obtained as if they had been recorded all along during the flight.

### Distribution Fitting: Making Data Talk

The frequently used bell curve (i.e. the Normal or Gaussian distribution) is often unsuitable for describing contributing factor data. This is because the bell curve underestimates the occurrence of values that are far away of the mean value. For this reason, it must be ensured that the probabilistic description of each factor, i.e. the fitted probability distribution, fits the collected data particularly closely at the tail ends of the distributions.

### Identifying the Unknown

So far, contributing factors have been combined into models to predict incident probabilities. The next natural step would then be to look for and quantify previously unknown contributing factors, as well as their impact on incidents.

In general, a typical measure for quantifying the dependence between two factors is the correlation coefficient, which is already used in many flight data monitoring tools. However, these correlation coefficients are only capable of correctly capturing a certain type of dependence between two factors, the so-called linear dependence. This means that many other types of dependences cannot be captured at all. However, in aviation, multiple factors influence the incident metric simultaneously. Additionally, different incident metrics can even have an impact on each other, and the aim is to describe the dependence structure beyond only linear dependencies between more than two parameters.

To overcome these drawbacks for correlation coefficients, a more advanced statistical tool based on the concept of copulas can be used. Copulas make it possible to simultaneously describe the dependencies between many parameters.

The judgment by experts, pilots and aviation professionals will always remain the primary source for reviewing flight safety. However, adding statistically valid numbers gained from the recorded truth of the own airline and based on an undisputable foundation such as the laws of physics will add insight, credibility and objectivity.

Predictive analysis will be an integral part of the box of tools that will keep the skies of tomorrow safe!

## Contact us

More information or any kind of cooperation please feel free to contact us!

Phillip Koppitz, Stefan Schiele, Florian Schwaiger

## Selected Publications:

[5] | Bayesian Approach Implementation on Quick Access Recorder Data for Estimating Parameters and Model Validation", in Probabilistic Safety Assessment and Management PSAM, 2014.
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[4] | Copulas applied to Flight Data Analysis", in Probabilistic Safety Assessment and Management PSAM, 2014.
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[3] | Extracting Unmeasured Parameters Based on Quick Access Recorder Data Using Parameter-Estimation Method", in AIAA Atmospheric Flight Mechanics Conference, 2013.
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[2] | Determining and Quantifying Hazard Chains and their Contribution to Incident Probabilities in Fight Operation", in AIAA Modeling and Simulation Technologies Conference, 2012.
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[1] | Predicting the Occurrence of Incidents Based on Flight Operation Data", in AIAA Modeling and Simulation Technologies Conference, 2011.
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