# Statistical Evaluation of Pilot’s Behavior Models Parameters Connected to Military Flight Training

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## Abstract

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## 1. Introduction

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- Finding common features in the pilots’ behavior during flight control,
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- Finding the behavioral changes during military flight training and under different influencing factors,
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- Comparing the control quality of young, less trained pilots with pilots who have completed 400, 500, or more flying hours on real airplanes, not just simulators.

## 2. Mathematical Background to Pilot Modeling

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- Control level (compensatory feedback control),
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- Coordination level (control based on rules),
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- Organization or cognitive level (control based on knowledge).

_{L}, T

_{I}, ω, and ξ are also very important. These parameters—the parameter ratio, in particular—define, specifically, the resulting control action. For example, the ratio of the time constants T

_{L}and T

_{I}describes, primarily, the method and approach to control. For the derivative, the lead time constant, T

_{L}, reflects the pilot’s ability to predict the given situation, whereas the T

_{I}constant, conversely, reflects a certain inertia or lag. The values of the frequency (ω) and damping (ξ) indicate the presence of an oscillating component.

## 3. Assessing Pilots’ Training Phase and Experience

_{I}, T

_{L}, ω, ξ, or τ. This assessment involves the measurement and analysis of the pilot’s responses by using a flight simulator.

^{−1}). At a certain time, the altitude was step-changed to 2600 ft., and the task of the pilot was to correct the altitude back to the original 2900 ft., where the current altitude was indicated by the altimeter.

_{L}, T

_{I}, and τ, described in the previous chapter, and can be utilized in a wide range of controlling or piloting activities; its properties and application possibilities are discussed and analyzed in References [17,21].

_{N}, is a parameter describing the dynamic properties of a human-pilot neuromuscular system, and its value tends to be relatively small (0.05–0.2 s). The T

_{L}parameter relates to the prediction ability, while T

_{I}expresses a certain inertia or lag and dampening of rapid control actions. The ratio of these constants describes the character of the control action—slow and damped if T

_{I}> T

_{L}, or vice versa, and fast with derivative features if T

_{I}< T

_{L}. The values of these parameters are most often in the order of seconds. The remaining parameters, i.e., the gain, K, and the reaction delay, τ, were, together with their properties, discussed in the previous section.

_{L}), and reaction delay (τ) of Model (3) is similar to the previous model, Model (2). Frequency (ω) and damping (ξ) characterize the oscillating component of pilot’s control action.

## 4. Evaluation and Results

_{I}, T

_{L}, ω, ξ, or τ, describe the dynamic properties of pilot’s behavior and provide information about a pilot’s attitude to control. The applied approach is based on measuring the pilots’ responses to a step change of an altitude using flight simulator(s), as described in the previous section.

#### 4.1. Statistical Evaluation of the Selected Parameters of the Behavioral Model

_{L}(with the most probable, and relatively high, value of about 6 s), define the character of the pilots’ control action as a derivative—fast and more aggressive.

#### 4.2. Assessing the Pilot Training Based on the Evaluation of Behavioral Model Parameters

_{L}, T

_{I}, T

_{N}, and τ (see (2)) for each pilot and flight task can be viewed as statistical datasets, and their basic characteristics can be specified. As mentioned above, seven pilots participated in each measurement set, with each of the participants subjected to 10 repetitive flight tasks; in total, 70 cycles were thus carried out for each set. Although the entire group is not large in terms of statistical significance, the results show that the repeatability of the measurements with respect to the variance of the parameters is satisfactory.

_{L}and T

_{I}, it defines the resulting response dynamics. The graph—Figure 7 clearly indicates that, in the second set of measurements, the interval of values in which this parameter may be present was extended. At the same time, however, the median was shifted upward, to increase the gain value from 0.19 to 0.21. This fact reflects a rise in the control process speed, meaning that the pilots generally achieved the desired value more quickly.

_{I}and T

_{L}, whose ratio is related to the way the pilot adapts to the controlled dynamics and determines (together with the gain K) the basic dynamic properties of the human controller. At the same time, these parameters account for the prediction ability (T

_{L}) and a certain inertia or lag (T

_{I}).

_{I}values. In terms of the controlled dynamics, this effect relates to a certain degree of suppression (or damping) of fast and sudden control interventions, causing reduced oscillation in the resulting transient process.

_{N}. The parameter characterizes the dynamics of the human neuromuscular system, which, in the case of Model (2), is approximated by the inertia formula (T

_{N}s + 1). It is a parameter whose values range from tenths to hundredths of a second, and its value should be—together with the time, namely the training stage—virtually invariable. This effect was also confirmed in the individual tests, as shown in Table 2.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Single-loop compensatory tracking tasks (based on Reference [1]).

**Figure 2.**The flight simulators in use—(

**a**) the fixed-base flight simulator and (

**b**) the moving-base flight simulator.

**Figure 3.**Data representing pilot’s control action (stick deflection) (

**a**) and as a response to the initial step change of altitude (perceived input signal) (

**b**).

**Figure 4.**Data representing altitude, H—perceived input signal (

**upper**) and control action (

**bottom**) of Pilot No. 1 (10 repeated measurements).

**Figure 5.**Histogram depicting the distribution of reaction delay parameter for the group of 10 military pilots.

**Figure 6.**Histograms depicting the distribution of parameters of Model (3) for the group of 10 military pilots.

**Table 1.**Mean values of pilots’ reaction delay τ (A—the first testing set; B—the second testing set).

Pilot No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

τ (s)-A | 0.64 | 0.71 | 0.66 | 0.59 | 0.83 | 0.63 | 0.67 |

τ (s)-B | 0.53 | 0.65 | 0.63 | 0.69 | 0.65 | 0.61 | 0.60 |

**Table 2.**Mean values of pilots’ neuromuscular time constant T

_{N}(A—the first testing set; B—the second testing set).

Pilot No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

T_{N} (s)-A | 0.13 | 0.13 | 0.06 | 0.07 | 0.17 | 0.12 | 0.09 |

T_{N} (s)-B | 0.13 | 0.14 | 0.08 | 0.07 | 0.18 | 0.12 | 0.07 |

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**MDPI and ACS Style**

Jirgl, M.; Boril, J.; Jalovecky, R.
Statistical Evaluation of Pilot’s Behavior Models Parameters Connected to Military Flight Training. *Energies* **2020**, *13*, 4452.
https://doi.org/10.3390/en13174452

**AMA Style**

Jirgl M, Boril J, Jalovecky R.
Statistical Evaluation of Pilot’s Behavior Models Parameters Connected to Military Flight Training. *Energies*. 2020; 13(17):4452.
https://doi.org/10.3390/en13174452

**Chicago/Turabian Style**

Jirgl, Miroslav, Jan Boril, and Rudolf Jalovecky.
2020. "Statistical Evaluation of Pilot’s Behavior Models Parameters Connected to Military Flight Training" *Energies* 13, no. 17: 4452.
https://doi.org/10.3390/en13174452