Mathematical-heuristic modelling for human performance envelope

Abstract

BACKGROUND:

Using the theory of complex systems, some human functions (thinking, memory, language) and human relationships have been analyzed and explained. In order to study the limits of human performance (in Air Traffic Controllers and pilots) a new concept was created, called the Human Performance Envelope (HPE).

OBJECTIVE:

The aim of this paper is to apply the principles of the complex system to the analysis of the human factors of the HPE concept. Moreover, this paper’s objective is to create a mathematical model that will give the opportunity to study all the physiological ergonomic factors, not only the ones that are most commonly studied. The most studied factors are mental workload, stress and situation awareness (SA). By applying the mathematical model, it is possible to analyze all the physiological factors (stress, mental workload, fatigue, attention, vigilance and SA).

METHODS:

In the present paper the theory of complex systems (hybrid modelling) was applied to the Human Performance Envelope concept. A mathematical model was created, then it was validated and solved based on previous researches.

RESULTS:

Firstly, a literature analysis was performed on the complex systems application by the present researchers concerning pilots’ HPE. The proportional and inverse proportional relationships between the nine human factors were visually illustrated. Finally, a mathematical model was proposed, consisting of a set of equations, which were partially solved and validated by the experiments on pilots done by other researchers.

CONCLUSIONS:

Further research is required to validate the whole mathematical model, including physiological measurements (experiments) for the six ergonomic factors and the applied heuristic psychosocial methods for the others.

Keywords

Complex system human performance envelope pilots

Victoria Rusu, Transilvania University of Brasov, Faculty of Technological Engineering and Industrial Management, Department of Manufacturing Engineering, Romania. Scientific Fields: Ergonomics of workplaces in aerospace research.

Dr. Eng. Gavrila Calefariu, University Professor at Transilvania University of Brasov, Faculty of Technological Engineering and Industrial Management, Department of Engineering and Industrial Management, Romania. Scientific Fields: Manufacturing Systems, Operations Management, Production/Operations Management, Lean Manufacturing.

1 Introduction

The human being has been a focal point for a number of researchers and scientists (A. St. Clair Gibson, T. D. Noakes, Yaneer Bar-Yam, Armin Fuchs, E. V. Lambert), who used the principles of the complex systems. However, the human being is still insufficiently understood from the scientific point of view, as there are still a lot of unexplained functions and behaviors.

From biological and physiological points of view, the human brain is a complex system, as it consists of elements (neurons); which are responsible for brain function and have multiple interactions between each other. Moreover, through these interactions (synapses) chemicals are transferred. Thus, the human brain is affected by substances transported through the bloodstream from different body parts, for example adrenaline. Because of the large number of neurons in the brain (10¹¹) and the multiple variation forms of neurons specific to particular sections of the brain, the complete behavior of neurons represents a complex problem. Once the complex neuronal system is analyzed using mathematical or biological models, a lot of human brain functions can be explained, including sensory processing, language, logic, motor control, planning, creativity and even self-awareness [1].

Once the neuron’s activity is understood, neuron models could be built, which are essential in theory demonstration and in environmental stimulus research [2]. Moreover, EEG studies explain how neural columns and activity patterns of neurons produce EEGs and represent an example of chaotic behavior [3]. Furthermore, the application of complex systems to the human brain has led to the development of mental models. Such models were studied by Pew and Mavor (1998) and were focused on human behavior and performance (memory, attention, multitasking, decision making and situation awareness). In 2008, Zacharias and his colleagues arranged the mental models as following: microlevel formal models (decision theory, cognitive architecture, game theory), mesolevel formal models (social network models, social choice model, voting) and macrolevel formal model (organizational modeling) [4].

The neural dynamic system was further developed by A. St. Clair Gibson and T. D. Noakes, who proposed a new model for physical exhaustion, which is a relative event and is a sensory representation of the neural processes. As stated, the human brain has complex interactions with peripheral physiological systems, which leads to hypothesized fatigue. The interactions between physiological systems are responsible for the activity before, during and even after a bout of exercise, generating a complex, dynamic or non-linear system [5 –7].

Another application of complex systems theory can be represented by the Haken-Kelso-Bunz (HKB) model, which describes the phase dynamics between two oscillating limbs or fingers under a scale of frequency. This model was extended to situations involving different body parts (arm and leg, limb and metronomes) even further to involve two different humans. The HKB model is considered to be the best known model of human movement behavior and the most extensively tested [8].

Furthermore, the theory of complex systems and especially the network organization was applied in medicine, to studies of disease spread and virus propagation in society (epidemy) [9, 10].

Apart from this, social systems are considered complex adaptive systems because the social agents (people) interact with each other through stable, relatively simple or complicated and changing connections. Social agents are capable of change and have to continually make choices, which can be based on direct cognition or on the heuristics stores of their actions. These connections lead to complexity; this is why social agents must learn how to react to the actions of other social agents. As a result, social agents are coupled to one another very closely, the interactions become nonlinear, complexity grows and the system is almost impossible to decompose [11].

As presented above, the theory of complex system was widely used in research concerning the human being. Models were developed which explained physiological phenomena (neuron models, brain models) and social interactions (organization model). This is the reason why the complex systems theory was chosen for modelling the nine ergonomic factors of pilots’ Human Performance Envelope (this concept is further explained).

2 Application-level analysis of the complex system theory in human performance envelope

2.1 Human performance envelope (HPE)

Physiological measurements of air traffic controllers (ATC) have been performed throughout the past decades [12].

The concept of the Human Performance Envelope (HPE) brought the idea of interdependence between multiple ergonomic factors together with their influence on air traffic controllers’ performance and was briefly studied in Edward Tamsyn’s PhD thesis “Human performance in Air Traffic Control”. Throughout the thesis it was demonstrated that all previous research considered one human factor as an independent variable and another human factor as a dependent one, so there was a lack of study on the relationship between multiple human factors. In addition to this, Eurocontrol experts selected nine ergonomic factors (stress, fatigue, mental workload, situation awareness –(SA), attention, vigilance, communication, teamwork and trust) which affect performance and have played an important role in aviation incidents, according to aviation incident reports [13]. In other words, the aim of the HPE concept is to promptly identify the edges of the human behavior (in pilots or air traffic controllers), especially that critical points where human performance is in decline [14].

The EU-funded research project “Future Sky Safety”; applied the HPE concept to pilots and explained in more detail each of the nine ergonomic factors. HPE Factor Cards were created to summarize and organize information about each of the nine human factors. The HPE Factor Cards represent state-of-the-art information on the components of HPE and could be used as tools for updated findings [15].

The concept of HPE has been further applied in other studies. According to the literature analysis for Human Performance Envelope, nine articles were selected (from a total of 34) which contain the application of the HPE concept on pilots or on ATC. After analyzing the articles, the conclusion was drawn that some ergonomic factors (stress, mental workload and SA) are studied more than others (teamwork, fatigue, trust, attention, communication and vigilance). The explanation could be that the less studied human factors are more difficult to quantify, requiring more physiological measurements, sociological methods and much more time for testing. On the other hand, all physiological measurements were done on one pilot, usually the captain. In reality life, aviation incidents and accidents depend on the decisions taken by both crew members (captain and first officer), so the Human Performance Envelope could be extended to the whole team [13].

2.2 Literature analysis of the complex systems application in HPE

According to the “Future Sky Safety” studies, Air Traffic Management is considered to be a critical complex system, which generates high cognitive demands on air traffic controllers, pilots and air traffic managers. That is why modern technology and automation are heavily used in control and navigation tasks. However, in unexpected situations, technical systems reach their limits (“automation failures”), so human operators play a very significant role in holding responsibility for flight safety. Therefore, pilots and air traffic controllers are the key actors in a very complex and complicated socio-technical system, being situated at the sharp edge of this system (Air Traffic System) [15, 16].

The studies concerning aviation as a complex system refer to the aviation system as a whole: automation, safety models, airplane as a continuous system [17 –20]. So, the theory of complex system is not applied in the HPE studies, even in research where the HPE concept is applied to pilots or ATC [14 , 21–23].

On the other hand, in aviation studies were used some models, like classic distributed turbulence model, nonlinear flight dynamic model or a multi-loop compensatory pilot model. These models were utilized to examine how terrain roughness affect pilot workload. According to the findings, pilot workload can rise when airspeed increases and flight altitude decreases in response to the terrain roughness [24].

Besides nonlinear dynamics model, there can be utilized linearized model. For example, to demonstrate that the ideal model and the plant need not be identical while not unduly complicating the control work for the pilot [25].

The majority of pilot-focused dedicated experiments based on the HPE concept involve measuring different physiological parameters (heart rate, respiratory rate, pupil size, blink duration, etc.) during the flight period which takes place on a simulator and follows established scenarios [21, 23]. The results collected from the experiments are then statistically analyzed using t-tests or ANOVA and the workload rating tool called NASA Task Load Index (NASA TLX). This index (NASA TLX) provides an overall workload score based on an average rating on physical demand, mental demand, temporal demand, effort, frustration and performance. NASA TLX collects all the data from questionnaires taken from a variety of applications at different moments of a task [21].

According to Tamsyn Edwards’ studies on air traffic controllers’ ergonomic factors, (workload and situation awareness), a nonlinear multiple regression model approach was considered to be unsuitable for analyzing the association between ergonomic factors and performance, because of the low control in the exercise for regression findings and the sample size. That is why a median split analysis method was chosen, as recommended by Miles and Shevlin as a simple way for dichotomous variable creation from the predictor variables [22].

As demonstrated above, the theory of complex systems is not used in the existing HPE studies. Therefore, the aim of this paper is to apply the principles of the complex system to the analysis of the human factors of the HPE concept. Moreover, objective of this paper is to create a mathematical model that will give the opportunity to study all the physiological ergonomic factors, not only the ones that are most commonly studied. The most studied factors are mental workload, stress and situation awareness (SA). By applying the mathematical model it is possible to analyze all the physiological factors (stress, mental workload, fatigue, attention, vigilance and SA).

3 Method: Mathematical-heuristic model

Mathematical-heuristic model is a hybrid model used for complex system simulation, control and risk determination. It is composed of interconnected models, where one is a mathematical model (continuous, discrete, stochastic, network, graph) and the other is a knowledge-based heuristic model (inferential network, logico-linguistic, structured objects). Combining different types of mathematical models with different types of heuristic models can generate more than 15 types of hybrid models which could be applied in the simulation of diverse systems [26].

Furthermore, mathematical-heuristic simulation models are usually applied in the simulation of highly complex systems (economic system, macroeconomic system, electro-energetic, hydro-energetic, environment protection and ecological system). Highly complex systems have a partially known structure, some of them cannot be completely mathematically formalized, but there exists an expert knowledge base which may be convertible in a heuristic model [26].

A mathematical-heuristic model is suitable for Human Performance Envelope (HPE) simulation, as it contains the numerical model which can be applied for ergonomic factors (workload, stress, mental fatigue, situation awareness, attention and vigilance) quantified by psycho-physiological variables (respiratory activity, electroencephalography, electrocardiography, electrooculography, electrodermal activity, eye tracking, etc.), and the heuristic model used for studying psychosocial ergonomic factors (trust, teamwork and communication) determined by direct observations, questionnaires studies and incident report analysis.

The combination of these two different models generates a hybrid model (mathematical –heuristic) used for a better understanding both for the six physiological ergonomic factors and for the three psycho-social factors of HPE.

The methodology represents the application of Stanciulescu’s hybrid macroeconomic model on the Human Performance Envelope concept, by developing a mathematical model for physiological ergonomic parameters and by establishing the baseline for the heuristic model (interdependent relationships).

In order to develop the mathematical model, the output variables and the state variables were established. The output variables represent the six HPE physiological factors chosen by Eurocontrol experts. The state variables were established after the analysis of the HPE Factor Cards created by Future Sky Project. Subsequently, the state equations have been developed together with the coefficients for each state variable and the conditions for output variables. The mathematical model is validated and solved using the data from previous researches done by others. Chapter 3.2 and Fig. 1 provide an illustration of the methodology process.

Fig. 1

Methodology scheme.

The present paper is focused more on mathematical model, by developing, validating and solving it. The heuristic model will be developed during future studies.

3.1 Interactions between human factors

All nine ergonomic factors that influence pilots –performance have strong relationships between each other. Some factors like mental workload, stress, fatigue, have a strong influence on more than one human factor, while some factors like situation awareness, attention, vigilance are dependent on others. Plus, there exists an interdependent relationship between ergonomic factors like attention –vigilance, teamwork –trust, teamwork –communication, stress –mental workload, stress –fatigue. The different relationships between the nine HPE factors, are represented in Fig. 2.

Fig. 2

Relationship between HPE factors. Red lines (grey lines) reflect the inversely proportional relationship, for example: the increased task difficulty, respectively the increase of Mental Workload leads to the decrease of Situation Awareness, Vigilance and Attention. Should be mentioned that the increasing value of one factor may be different from the decreasing value of the other factor. The dark green arrows (dark grey arrows) show the direct proportional relationship, but also the values might differ. For example: if mental workload increases, then the stress and fatigue will also increase and vice versa. The blue lines (light grey lines) show that there exist relationships, but it is not clear what type of relationships, for example: exist mistrust and over-trust which interact differently with Mental Workload, Stress and Communication. Arrows represent the direction of the influence, so the Situation Awareness is influenced by Stress, Mental Workload, Fatigue, Vigilance, Attention and Teamwork, but could influence Communication.

The understanding of interactions between human factors is essential because it helps to determine the influence of ergonomic factors on human performance and contributes to the creation of the hybrid model.

3.2 Mathematical model of HPE

The HPE Factor Cards created by the Future Sky Safety project represent the result of the HPE Concept workshop and HPE components. These cards contain structured and organized information about all nine ergonomic factors (including a short explanation, measuring techniques, observations, and used measuring methods) based on a systematic review of 167 scientific studies [15].

The HPE Factor Cards present the information for all the nine factors: the section “Psycho-physiological measure” describes the observations, the techniques and the equipment used in scientific studies concerning one of the ergonomic factors [15]. For example, for the mental workload factor the electrocardiography (ECG) technique was used with simulator and cockpit equipment. The observations were that: increasing mental workload leads to an increasing heart rate and blood pressure and a decreasing heart rate variability. In the same key information is presented for the rest ergonomic factors. After analysing the HPE Factor Cards, priority variables common to at least two factors were selected. These variables represent the results of the physiological measurements from different studies which had the aim of measuring ergonomic factors (mental workload, stress, fatigue etc.) using objective tools. The selected variables are used in the mathematical model.

For the psychosocial factors (teamwork, communication and trust) researchers used only three measurement techniques: Targeted Acceptable Responses to Generated Events (TARGET), Behavioral Observation Scale (BOS) and analysis of incidents reports. These have led to some qualitive conclusions; therefore, they will be used in heuristic methods but not mathematical ones.

To establish state equations, abbreviations were used for all the variables, for example: Oxygenated Hemoglobin –(HbO₂), Heart rate –(HR), Heart rate variability –(HRV), Systolic blood pressure –(SBP), Respiratory rate –(RR) and so on. All variables depend on the time of the measurements, that is why they are written as HbO₂(t), HR(t), HRV(t), SBP(t), etc. Ergonomic factors also have abbreviations for the mathematical reason: mental workload –(MW), stress –(S), fatigue –(F), situation awareness –(SA), attention –(A), vigilance –(V), teamwork –(TW), communication –(C), trust –(T). Variables utilized in the mathematical model are presented in Table 1. For each ergonomic factor the variables were selected which have an influence on that ergonomic factor, for example: in stressful conditions respiratory rate increases, heart rate increases, but heart rate variability decreases. Therefore, for the stress (S) ergonomic factor the following variables were chosen: respiratory rate (RR), heart rate (HR), systolic blood pressure (SBP), muscle tension (MT), electrodermal activity (EDA), adrenaline (AD), noradrenaline (NAD) and heart rate variability (HRV), according to the information from the HPE Factor Cards [15].

Table 1
Variables used in the mathematical model

Variables of state (at a specific moment t) Output variables

HbO₂(t) Oxygenated Hemoglobin MW Mental Workload

HR(t) Heart rate S Stress

HRV(t) Heart rate variability F Fatigue

SBP(t) Systolic Blood pressure SA Situation Awareness

RR(t) Respiratory rate A Attention

BR(t) Eye blink rate V Vigilance

BD(t) Eye blink duration

PD(t) Pupil diameter

ABP(t) Alpha band power

BBP(t) Beta band power

TBP(t) Theta band power

DBP(t) Delta band power

MT(t) Muscle tension

EDA(t) Electrodermal activity

AD(t) Adrenaline

NAD(t) Noradrenaline

SEM(t) Saccadic eye movement

MA(t) Mental activity

BOB(t) Blood oxygenation in the brain

CABFV(t) Right cerebral arterial blood flow velocities

Variables of state (at a specific moment t)	Output variables
HbO₂(t)	Oxygenated Hemoglobin	MW	Mental Workload
HR(t)	Heart rate	S	Stress
HRV(t)	Heart rate variability	F	Fatigue
SBP(t)	Systolic Blood pressure	SA	Situation Awareness
RR(t)	Respiratory rate	A	Attention
BR(t)	Eye blink rate	V	Vigilance
BD(t)	Eye blink duration
PD(t)	Pupil diameter
ABP(t)	Alpha band power
BBP(t)	Beta band power
TBP(t)	Theta band power
DBP(t)	Delta band power
MT(t)	Muscle tension
EDA(t)	Electrodermal activity
AD(t)	Adrenaline
NAD(t)	Noradrenaline
SEM(t)	Saccadic eye movement
MA(t)	Mental activity
BOB(t)	Blood oxygenation in the brain
CABFV(t)	Right cerebral arterial blood flow velocities

Based on the same information from the HPE cards, the increasing and the decreasing of physiological measured parameters was assigned a sign (+ or -) for each state variable [15].

Based on Stanciulescu’s mathematical heuristic model for macroeconomic system, the state equation for each ergonomic factor was elaborated [26]. The proposed state equations for the mathematical model are the following:

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} HR (t) + β_{1} SBP (t) + γ_{1} RR (t) \\ + δ_{1} PD (t) + ω_{1} BBP (t) + φ_{1} TBP (t) \\ + η_{1} MT (t) + θ_{1} EDA (t) - κ_{1} HRV (t) \\ - λ_{1} BR (t) - μ_{1} BD (t) - τ_{1} ABP (t) \end{matrix}$ (1)

$\begin{matrix} \frac{d}{dt} S (t) = & ν_{2} HbO 2 (t) + γ_{2} RR (t) + α_{2} HR (t) \\ + β_{2} SBP (t) + η_{2} MT (t) + θ_{2} EDA (t) \\ + ξ_{2} AD (t) + ρ_{2} NAD (t) - κ_{2} HRV (t) \end{matrix}$ (2)

$\begin{matrix} \frac{d}{dt} F (t) = & μ_{3} BD (t) + σ_{3} DBP (t) + φ_{3} TBP (t) \\ + τ_{3} ABP (t) + κ_{3} HRV (t) - δ_{3} PD (t) \\ - χ_{3} SEM (t) - ω_{3} BBP (t) - α_{3} HR (t) \\ - η_{3} MT (t) - γ_{3} RR (t) - θ_{3} EDA (t) \end{matrix}$ (3)

$\begin{matrix} \frac{d}{dt} SA (t) = & υ_{4} MA (t) + α_{4} HR (t) - κ_{4} HRV (t) \\ - λ_{4} BR (t) - μ_{4} BD (t) \end{matrix}$ (4)

$\begin{matrix} \frac{d}{dt} A (t) = & α_{5} HR (t) - κ_{5} HRV (t) - λ_{5} BR (t) \\ - μ_{5} BD (t) - τ_{5} ABP (t) - ρ_{5} CABFV (t) \end{matrix}$ (5)

$\begin{matrix} \frac{d}{dt} V (t) = & α_{6} HR (t) - κ_{6} HRV (t) - λ_{6} BR (t) \\ - μ_{6} BD (t) - τ_{6} ABP (t) - ρ_{6} CABFV (t) \end{matrix}$ (6)

${MW}_{0} < MW (t), S_{0} < S (t), F_{0} < F (t)$ (7)

${SA}_{0} > SA (t), A_{0} > A (t), V_{0} > V (t)$ (8)

In addition, the conditions (7) and (8) were established. In order to evaluate human performance, researchers create special stressful conditions (complex tasks, multiple tasks) in simulated flights or work environment [14 , 21–23]. These stressful conditions lead to the increase in cognitive workload (W₀ < W (t)), stress (S₀ < S (t)) and fatigue (F₀ < F (t)), while situation awareness, attention and vigilance decrease (SA₀ > SA (t), A₀ > A (t), V₀ > V (t)).

3.2.1 Mathematical model validation

The above proposed state equations must be validated before they could be widely used. Based on existing HPE experiments, the equations can be only partly validated because the equipment used for physiological measurements (CSEM smart vest, Biopac MP 160, Tobii Pro Glasses 2) is able to measure only some of the state variables for a specific human factor and not all the variables at the same time. In addition, the researchers select only some human factors for their studies and so they measure only a part of the state variables.

The literature review completed by Gianluca Borghini and others confirms that an increase in HR results from an increase in mental workload. Moreover, according to the same paper, there is a strong link between behavioral activities and both HR and HRV [27].

Another literature review on heart rate and respiratory rate in relation to pilot mental workload was done by A.H. Roscoe. The author used a variety of evidence to support his claim that an increase in mental workload causes an increase in heart rate; one example is the heart rate record from two helicopter pilots during a transatlantic flight. The handling pilot’s average heart rate was 102 bpm and the co-pilot’s heart rate was 85 bpm during a normal flight. In the case of a demanding task like flight refueling, the pilot’s heart rate was 118 bpm. Another example is heart rate monitoring during the NASA C-141 Kuiper Airborne Observatory flights, which demonstrated that the heart rate changed throughout the flight segments and that heart rate had higher values for the flying pilot than for co-pilot (not flying) [28].

In research performed by Hidalgo-Munoz A.R. and colleagues, 21 private pilots participated in an examination of heart rate (HR) and heart rate variability (HRV) during two realistic flying scenarios. The findings demonstrated that HR is sensitive to cognitive strain, with HR rising as the complexity of the secondary task increased (Fig. 3) [29].

Fig. 3

Heart rate for three time-on-task levels for High and Low Cognitive Workload [29].

The pilot’s heart rate variability case study, during a real flight at 8000 ft altitude, demonstrated that HRV parameters decrease as the mental workload burden increases. The results for the rMSSD (root mean square of successive differences in interbeat intervals), an HRV parameter that describes the function of the parasympathetic system, show that for pilots 1 and 3 (5.17 ms and 5.81 ms), the parameter’s value is less than the standard range (27–57 ms), whereas it is higher for pilot 2. (23.23 ms). Thus, pilot 2 had a moderate task to perform (Fig. 4) [30].

Fig. 4

Obtained results for rMSSD parameters compared to normative HRV scores [30].

Further research conducted by Grassmann M. and colleagues, analyzes physiological and self-reported measurements of 115 pilots, who executed multiple tasks (spatial orientation, working memory, perceptual speed) and rested. The repeated-measures ANOVA revealed the HR increment (77.37^b) while task performing and HR decrease (70.58^c) during the rest period. Moreover, the HRV parameters (rMSSD, pNN50, HF and LF) had a reduced value during the task execution and a higher value during the recovery period. Also, the respiratory rate (RR) increased to 18.96^b and decreased to 14.64^c during the rest time (Table 2) [31].

Table 2

ANOVA results for cardiorespiratory study variables

Variables	Base Line		Multiple task		Recovery
	Mean	Standard Deviation	Mean	Standard Deviation	Mean	Standard Deviation
HR	71.32^a	11.12	77.37^b	12.02	70.58^c	10.89
rMSSD	46.15^a	25.65	37.74^b	23.87	45.16^a	23.89
pNN50	23.56^a	20.76	16.51^b	18.06	22.73^a	20.18
HF	1009.33^a	1052.45	687.43^b	1221.17	938.26^a	1118.61
LF	2275.38^a	3236.53	1289.84^b	1239.32	1796.70^a	1585.80
RR	13.24^a	3.95	18.96^b	3.15	14.64^c	4.00

Note. ^a,b,c Identify notable variations between the experimental periods (p < 0.05) [31].

The purpose of HPE pilot-based experiments was to find out how mental workload, stress, and situation awareness interact with one another and how this impacts the performance of the pilots. Both experiments used the HR and HRV variables for mental workload and stress appreciation [21, 23].

Additionally, the respiration rate (ECG) for stress and mental workload determination was assessed in one of the two experiments. Beginning with normal breathing, the participant held their breath for one minute, after which normal breathing resumed. This experiment was graphically represented and was further used to illustrate the respiration during the whole flight (Fig. 5). Additionally, the HR variable (Fig. 6) and the HRV variable (Fig. 7) were graphically represented for the whole flight, demonstrating that when faced with increased mental workload and stress (engine failure), the respiratory rate (RR) and heart rate (HR) both increase, while heart rate variability (HRV) declines significantly [21].

Fig. 5

Respiratory rate (RR) obtained from ECG during a whole flight [21].

Fig. 6

Average heart rate (HR) during a whole flight [21].

Fig. 7

Heart rate variability (HRV) during a whole flight [21].

In this way equation (1) could be considered partially validated (+ RR(t) + HR(t) –HRV(t)), but in order to validate the whole equation is important to find or to realize experiments which will measure the rest of the variables (SBP, PD, TBP, MT, EDA, BR, BD). As a result, a deeper literature analysis is required to validate the proposed equations.

3.2.2 Mathematical model solving

In order to solve the equations, each variable has a coefficient (α, γ, ρ, υ, β, σ etc.), which is helpful because each variable has a unique unit of measurement. Greek letters were chosen to signify each variable (HR, SBP, RR, PD, BD, BR) and coefficient.

Table 3 was created based on the results of the other studies. The unit of measurement and a mean value were assigned to each variable linked to mental workload (heart rate, systolic blood pressure, respiration rate, pupil diameter, eye blink rate, eye blink duration, etc.). The mean value represents the arithmetic mean of the values from three different sources. The studies were searched for in scientific databases (Science Direct Freedom Collection Elsevier, IEEE, Web of Science) and the scientific research service Google Scholar. The key words used in searches were: “heart rate mental workload”, “EDA mental workload”, “blood pressure mental workload”, “eye tracking mental workload”, “EEG mental workload” and so on. The research studies that addressed calculating the mental workload for pilots or air traffic controllers using physiological measures were chosen from the resulting list of articles. The articles with the highest number of participants and those that are more heavily cited received priority during the reading of the chosen articles and the data extraction for physiological measures. Usually were selected the mean values for variables, from the result section, after the author’s application of the statistical analysis (ANOVA or MANOVA). In some cases, were selected the absolute values from the graphics (alpha power band, beta power band and theta power band), because authors are focused on them more than on mean values. This is due to the idee of showing the difference between low workload and high workload. In cases where the article contained more results for the same physiological measure (variable), an arithmetic mean was calculated.

Table 3
Mean value for mental workload variables

Variables Unit Mean value ref. I Mean value ref. II Mean value ref. III Mean

Mental Workload

Heart rate - HR Beats per minute: bpm 86 [29] 77,37 [31] 80 [21] 81,12

Systolic blood pressure - SBP Millimeters of mercury: mmHg 121,7 [33] 161,4 [34] 140 [35] 211,55

Respiratory rate - RR Breaths per minute: breaths/min 15,22 [21] 18,55 [36] 15,6 [37] 16,45

Pupil diameter - PD Millimeters - mm 4,2 [38] 3,76 [39] 3,42 [40] 3,79

Eye blink duration - BD Milliseconds - ms 918,75 [36] 448,75 [41] 334,8 [42] 567,43

Eye blink rate - BR Blinks/min 10,2 [37] 6,74 [43] 6,78 [44] 7,90

α band power - ABP Frequency (8–14) Hz 0,85 [45] 0,31 [36] 0,589 [46] 0,58

β band power - BBP Frequency (14–30) Hz 1,04 [45] 0,34 [36] 0,788 [46] 0,72

Θ band power - TBP Frequency (4-8) Hz 0,96 [45] 0,36 [36] 0,424 [46] 0,58

Muscle tension - MT Microvolt - μv 26,65 [47] 14,92 [48] 23,095 [49] 21,55

Electrodermal activity - EDA Micro seconds - μs 5,44 [50] 6,38 [51] 18,6 [52] 10,14

Heart rate variability - HRV rMSSD (ms) –square root of the mean of the sum of the squares of the differences between adjacent NN intervals, characterizes the work of the parasympathetic nervous system 29 [29] 37,74 [31] 26,5 [21] 31,08

Variables	Unit	Mean value ref. I	Mean value ref. II	Mean value ref. III	Mean
Heart rate - HR	Beats per minute: bpm	86 [29]	77,37 [31]	80 [21]	81,12
Systolic blood pressure - SBP	Millimeters of mercury: mmHg	121,7 [33]	161,4 [34]	140 [35]	211,55
Respiratory rate - RR	Breaths per minute: breaths/min	15,22 [21]	18,55 [36]	15,6 [37]	16,45
Pupil diameter - PD	Millimeters - mm	4,2 [38]	3,76 [39]	3,42 [40]	3,79
Eye blink duration - BD	Milliseconds - ms	918,75 [36]	448,75 [41]	334,8 [42]	567,43
Eye blink rate - BR	Blinks/min	10,2 [37]	6,74 [43]	6,78 [44]	7,90
α band power - ABP	Frequency (8–14) Hz	0,85 [45]	0,31 [36]	0,589 [46]	0,58
β band power - BBP	Frequency (14–30) Hz	1,04 [45]	0,34 [36]	0,788 [46]	0,72
Θ band power - TBP	Frequency (4-8) Hz	0,96 [45]	0,36 [36]	0,424 [46]	0,58
Muscle tension - MT	Microvolt - μv	26,65 [47]	14,92 [48]	23,095 [49]	21,55
Electrodermal activity - EDA	Micro seconds - μs	5,44 [50]	6,38 [51]	18,6 [52]	10,14
Heart rate variability - HRV	rMSSD (ms) –square root of the mean of the sum of the squares of the differences between adjacent NN intervals, characterizes the work of the parasympathetic nervous system	29 [29]	37,74 [31]	26,5 [21]	31,08

In addition, two systematic review articles were studied in order to choose essential authors [27, 32].

When the table was complete, the mean value replaced the unknown variables from the mental workload equation, so the result is the Equation (9):

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} 81, 12 + β_{1} 211, 55 + γ_{1} 16, 45 \\ + δ_{1} 3, 79 + ω_{1} 0, 72 + φ_{1} 0, 58 \\ + η_{1} 21, 55 + θ_{1} 10, 14 - κ_{1} 31, 08 \\ - λ_{1} 7, 90 - μ_{1} 567, 43 - τ_{1} 0, 58 \end{matrix}$ (9)

In order to solve the Equation (9), using Cramer’s system 11 more equations were established, so that in total to be 12 equations as the number of variables. For this reason, the studies mentioned in Table 3 were revised again and values for each variable were selected from graphs or from tables. Some studies offer just the mean value which is obtained after the application of statistical methods (ANOVA or MANOVA). This is why from three different references (ref I, ref II, ref III), was chosen the one that has graphs or tables with more variables, not just the mean one. One exception represents the values for the systolic blood pressure, as the chosen reference ([33]) has only eight values, so the other three values were selected from the reference ([34]), which offered only three values. The list of chosen references is the following:

Heart rate –[21]

Systolic blood pressure –[33] and [34]

Respiratory rate –[21]

Pupil diameter –[38]

Eye blink duration –[41]

Eye blink duration –[43]

Alpha band power –[45]

Beta band power –[45]

Theta band power –[45]

Muscle tension –[47]

EDA –[51]

HRV (rMSSD) –[21]

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} 73 + β_{1} 110, 8 + γ_{1} 13 + δ_{1} 3, 85 \\ + ω_{1} 0, 92 + φ_{1} 0, 85 + η_{1} 19 + θ_{1} 2, 7 \\ - κ_{1} 27 - - λ_{1} 4, 5 - μ_{1} 420 - τ_{1} 0, 78 \end{matrix}$ (10)

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} 73, 5 + β_{1} 112, 3 + γ_{1} 13, 5 \\ + δ_{1} 3, 93 + ω_{1} 0, 93 + φ_{1} 0, 86 + η_{1} 20 \\ + θ_{1} 2, 97 - κ_{1} 28 - λ_{1} 5, 0 \\ - μ_{1} 425 - τ_{1} 0, 79 \end{matrix}$ (11)

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} 74 + β_{1} 114, 2 + γ_{1} 14 + δ_{1} 3, 94 \\ + ω_{1} 0, 94 + φ_{1} 0, 87 + η_{1} 21 + θ_{1} 3, 94 \\ - κ_{1} 29 - λ_{1} 5, 2 - μ_{1} 430 - τ_{1} 0, 80 \end{matrix}$ (12)

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} 74, 5 + β_{1} 120, 8 + γ_{1} 14, 5 \\ + δ_{1} 3, 95 + ω_{1} 0, 95 + φ_{1} 0, 88 \\ + η_{1} 22 + θ_{1} 4, 98 - - κ_{1} 30 - λ_{1} 5, 5 \\ - μ_{1} 435 - τ_{1} 0, 81 \end{matrix}$ (13)

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} 75 + β_{1} 121, 7 + γ_{1} 15 + δ_{1} 3, 96 \\ + ω_{1} 0, 96 + φ_{1} 0, 89 + η_{1} 23 + θ_{1} 7, 64 \\ - κ_{1} 31 - λ_{1} 6 - μ_{1} 440 - τ_{1} 0, 82 \end{matrix}$ (14)

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} 75, 5 + β_{1} 123, 7 + γ_{1} 15, 5 \\ + δ_{1} 4, 05 + ω_{1} 0, 97 + φ_{1} 0, 90 \\ + η_{1} 24 + θ_{1} 7, 81 - - κ_{1} 32 - λ_{1} 6, 5 \\ - μ_{1} 445 - τ_{1} 0, 83 \end{matrix}$ (15)

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} 76 + β_{1} 131, 2 + γ_{1} 15, 7 + δ_{1} 4, 06 \\ + ω_{1} 0, 98 + φ_{1} 0, 91 + η_{1} 25 + θ_{1} 11, 92 \\ - κ_{1} 33 - λ_{1} 6, 7 - μ_{1} 450 - τ_{1} 0, 84 \end{matrix}$ (16)

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} 76, 5 + β_{1} 139, 2 + γ_{1} 16 + δ_{1} 4, 10 \\ + ω_{1} 0, 99 + φ_{1} 0, 92 + η_{1} 26 + θ_{1} 12, 90 \\ - κ_{1} 34 - λ_{1} 7 - μ_{1} 455 - τ_{1} 0, 85 \end{matrix}$ (17)

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} 77 + β_{1} 157, 5 + γ_{1} 16, 5 + δ_{1} 4, 14 \\ + ω_{1} 1 + φ_{1} 0, 93 + η_{1} 27 + θ_{1} 13, 77 \\ - κ_{1} 35 - λ_{1} 7, 5 - μ_{1} 460 - τ_{1} 0, 86 \end{matrix}$ (18)

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} 77, 5 + β_{1} 162, 9 + γ_{1} 16, 7 + δ_{1} 4, 15 \\ + ω_{1} 1, 01 + φ_{1} 0, 94 + η_{1} 28 + θ_{1} 22, 63 \\ - κ_{1} 36 - λ_{1} 8 - μ_{1} 465 - τ_{1} 0, 87 \end{matrix}$ (19)

$\begin{matrix} \frac{d}{dt} MW (t) = & α_{1} 78 + β_{1} 163, 9 + γ_{1} 17 + δ_{1} 4, 16 \\ + ω_{1} 1, 02 + φ_{1} 0, 95 + η_{1} 29 + θ_{1} 35, 7 \\ - κ_{1} 37 - λ_{1} 8, 5 - μ_{1} 468 - τ_{1} 0, 88 \end{matrix}$ (20)

The Cramer’s system is the following:

${\begin{matrix} α_{1} 81, 12 + β_{1} 211, 55 + γ_{1} 16, 45 + δ_{1} 3, 79 + ω_{1} 0, 72 + φ_{1} 0, 58 + η_{1} 21, 55 + θ_{1} 10, 14 - κ_{1} 31, 08 - λ_{1} 7, 90 - μ_{1} 567, 43 - τ_{1} 0, 58 = MW \\ α_{1} 73 + β_{1} 110, 8 + γ_{1} 13 + δ_{1} 3, 85 + ω_{1} 0, 92 + φ_{1} 0, 85 + η_{1} 19 + θ_{1} 2, 7 - κ_{1} 27 - λ_{1} 4, 5 - μ_{1} 420 - τ_{1} 0, 78 = MW \\ α_{1} 73, 5 + β_{1} 112, 3 + γ_{1} 13, 5 + δ_{1} 3, 93 + ω_{1} 0, 93 + φ_{1} 0, 86 + η_{1} 20 + θ_{1} 2, 97 - κ_{1} 28 - λ_{1} 5, 0 - μ_{1} 425 - τ_{1} 0, 79 = MW \\ α_{1} 74 + β_{1} 114, 2 + γ_{1} 14 + δ_{1} 3, 94 + ω_{1} 0, 94 + φ_{1} 0, 87 + η_{1} 21 + θ_{1} 3, 94 - κ_{1} 29 - λ_{1} 5, 2 - μ_{1} 430 - τ_{1} 0, 80 = MW \\ α_{1} 74, 5 + β_{1} 120, 8 + γ_{1} 14, 5 + δ_{1} 3, 95 + ω_{1} 0, 95 + φ_{1} 0, 88 + η_{1} 22 + θ_{1} 4, 98 - κ_{1} 30 - λ_{1} 5, 5 - μ_{1} 435 - τ_{1} 0, 81 = MW \\ α_{1} 75 + β_{1} 121, 7 + γ_{1} 15 + δ_{1} 3, 96 + ω_{1} 0, 96 + φ_{1} 0, 89 + η_{1} 23 + θ_{1} 7, 64 - κ_{1} 31 - λ_{1} 6 - μ_{1} 440 - τ_{1} 0, 82 = MW \\ α_{1} 75, 5 + β_{1} 123, 7 + γ_{1} 15, 5 + δ_{1} 4, 05 + ω_{1} 0, 97 + φ_{1} 0, 90 + η_{1} 24 + θ_{1} 7, 81 - κ_{1} 32 - λ_{1} 6, 5 - μ_{1} 445 - τ_{1} 0, 83 = MW \\ \begin{matrix} α_{1} 76 + β_{1} 131, 2 + γ_{1} 15, 7 + δ_{1} 4, 06 + ω_{1} 0, 98 + φ_{1} 0, 91 + η_{1} 25 + θ_{1} 11, 92 - κ_{1} 33 - λ_{1} 6, 7 - μ_{1} 450 - τ_{1} 0, 84 = MW \\ α_{1} 76, 5 + β_{1} 139, 2 + γ_{1} 16 + δ_{1} 4, 10 + ω_{1} 0, 99 + φ_{1} 0, 92 + η_{1} 26 + θ_{1} 12, 90 - κ_{1} 34 - λ_{1} 7 - μ_{1} 455 - τ_{1} 0, 85 = MW \\ α_{1} 77 + β_{1} 157, 5 + γ_{1} 16, 5 + δ_{1} 4, 14 + ω_{1} 1 + φ_{1} 0, 93 + η_{1} 27 + θ_{1} 13, 77 - κ_{1} 35 - λ_{1} 7, 5 - μ_{1} 460 - τ_{1} 0, 86 = MW \\ α_{1} 77, 5 + β_{1} 162, 9 + γ_{1} 16, 7 + δ_{1} 4, 15 + ω_{1} 1, 01 + φ_{1} 0, 94 + η_{1} 28 + θ_{1} 22, 63 - κ_{1} 36 - λ_{1} 8 - μ_{1} 465 - τ_{1} 0, 87 = MW \\ α_{1} 78 + β_{1} 163, 9 + γ_{1} 17 + δ_{1} 4, 16 + ω_{1} 1, 02 + φ_{1} 0, 95 + η_{1} 29 + θ_{1} 35, 7 - κ_{1} 37 - λ_{1} 8, 5 - μ_{1} 468 - τ_{1} 0, 88 = MW \end{matrix} \end{matrix}$ (21)

To solve Cramer’s system is necessary to find the derivate of MW function, so further researches are needed. Moreover, additional mathematic programs (MatLab) could be used for solving Cramer’s system.

4 Conclusion

The theory of complex systems is widely applied in research concerning human beings and especially in ergonomic studies. This gives the opportunity to apply the theory in the aerospace activity to understand the Human Performance Envelope (HPE). This paper has demonstrated that the existing literature on HPE does not use the complex system as a method of researching the relationships between the nine ergonomic factors. This may be due to the challenges in theoretically applying complex systems, as it is much simpler to conduct tests and draw findings afterward. However, a mathematical model was proposed, which contains state equations for six ergonomic factors (mental workload, stress, fatigue, attention, vigilance, and situation awareness) which are quantified by several physiological variables (heart rate, heart rate variability, respiratory rate, blood pressure, etc.). The mental workload equation was partially validated by the experiments done by other researchers in the field of Human Performance Envelope on pilots. This represents a starting point for future mathematical validations using experiments. Furthermore, the first equation was almost solved using Cramer’s system of equations. Much more time and research is needed to solve the remaining state equations.

In addition, the hybrid model (mathematical - heuristic) is the right instrument in HPE studies, because some ergonomic factors (trust, communication, and teamwork) cannot be measured quantitatively. This is why there is a need of heuristic methods (logico-linguistic, inferential network, structured objects). However, in order to choose the right heuristic method, it is necessary to understand the connections and the levels of influence between ergonomic factors. This is why the graph for direct proportional and inversely proportional relationships between the nine ergonomic factors was created. Heuristic modeling still requires more research, especially in the psychosocial domain.

5 Future research

To validate the proposed equations, more studies are needed. This means that there is a need of experiments either on flight simulators or on real aircrafts. In future experiments, six pilots will participate from the National Institute for Aerospace Research “Elie Carafoli” –INCAS. During their flights, physiological measurements will be taken. It is important to mention that after reviewing the findings of the experiments, the mathematical model will be revised and improved.

The psychological studies concerning psychosocial ergonomic factors like trust, communication and teamwork will use questionnaires, interviews and other social science research methods for data collection. The correct method for the quantification of the collected data will be chosen, which will lead to the heuristic model.

6 Limitations

The study limitations are related to the heuristic part of the model, as the psychosocial ergonomic factors mean deeper psychological analysis is required as well as finding the measurement methods which will lead to quantified results. A psychologist’s help is a must in data interpretation. As a result, the heuristic part of the model is unfinished due to these limitations.

Another limitation could be associated to the impossibility to validate the whole mathematical model without doing real experiments and observations for each variable or maybe for one or two entire equations.

Footnotes

Acknowledgments

The authors have no acknowledgments.

Author contributions

CONCEPTION: Victoria Rusu

METHODOLOGY: Victoria Rusu

DATA COLLECTION: Victoria Rusu

INTERPRETATION OR ANALYSIS OF DATA: Victoria Rusu and Gavrila Calefariu

PREPARATION OF THE MANUSCRIPT: Victoria Rusu

REVISION FOR IMPORTANT INTELLECTUAL CONTENT: Victoria Rusu and Gavrila Calefariu

SUPERVISION: Gavrila Calefariu

References

Yaneer

Dynamics of complex systems. Massachusetts: Addison-Wesley; 1997;0-201-55748-7. pp. 296.

Waldrop

Complexity: The emerging science at the edge of order and chaos. New York: Simon and Schuster Paperbacks. 1993;978-0-671-76789-1. pp. 20.

Guastello

Chaos as a Construct in Psychology. Chaos and Nonlinear Psychology: Keys to Creativity in Mind and Life. New York: Oxford University Press: 2022;9780190465025. pp. 112.

Rouse

Modeling and visualization of complex systems and enterprises: exploration of physical, human, economic, and social phenomena. New Jersey: John Wiley & Sons. 2015;978-1-118-95413-3. pp. 96.

Lambert

, St Clair Gibson

, Noakes

, Complex systems model of fatigue: integrative homeostatic control of peripheral physiological systems during exercise in humans, British Journal Sports Medicine2005;39:52–62. doi: 10.1136/bjsm.2003.011247.

Noakes

, St Clair Gibson

, Lambert

, From catastrophe to complexity: a novel model of integrative central neural regulation of effort and fatigue during exercise in humans, British Journal of Sports Medicine2004;38:511–4. doi:10.1136/bjsm.2003.009860.

St Clair Gibson

, Noakes

, Evidence for complex system integration and dynamic neural regulation of skeletal muscle recruitment during exercise in humans, British Journal Sports Medicine2004;38:797–806. doi: 10.1136/bjsm.2003.009852.

Fuchs

Nonlinear dynamics in complex systems. Theory and applications for the life-, neuro- and natural sciences. Florida: Springer. 2013;978-3-642-33552-5. DOI 10.1007/978-3-642-33552-5. pp. 133..

Anderson

. Perspective: Complexity Theory and Organization Science, Organization Science1999;10(3):216–32. doi: 10.1287/orsc.10.3.216.

10.

Macau

EEN

A mathematical modeling approach from nonlinear dynamics to complex systems. Vol. 22. Illinois: Springer. 2019;978-3-319-78511-0. DOI: 10.1007/978-3-319-78512-7. pp. 177.

11.

Miller

, Scott

, Complex adaptive system. New Jersey: Princeton University Press. 2007;978-0-691-13096-5.

12.

Melton

, Smith

, McKenzie

, Wicks

, Saldivar

Stress in air traffic personnel: low-density towers and flight service stations. Federal Aviation Administration Washington Dc Office of Aviation Medicine. 1977;DOT F 1700.7.

13.

Rusu

, Calefariu

. Definition and literature review on Human Performance Envelope Concept in aerospace activity, Recent Journal2021;63:041–9. doi: 10.31926/RECENT.2021.63.041.

14.

Marcus

, Matthias

, What the pilots see is what I get: how the pilot’s gaze can increase the Human Performance Envelope to improve safety. Los Angeles: AHFE | Human Factors in Transportation. International Conference on Applied Human Factors and Ergonomics. 2017.

15.

Silvagni

, Napoletano

, Graziani

, Le Blaye

, Rognin

Concept for Human Performance Envelope. Internet. Available from: https://www.futureskysafety.eu/download/. [Accessed 22 April 2021].

16.

Jungst

Technological complexity and employee silence: The buffering role of social support. Human Systems Management. (Pre-press). 2022:1-13. DOI: 10.3233/HSM-220006.

17.

Chialastri

Automation in aviation. INTECH Open Access Publisher. 2012.

18.

Chialastri

, Pozzi

Resilience in the aviation system. In international conference on computer safety, reliability, and security. In International Conference on Computer Safety, Reliability, and Security, pp. 86-98. Berlin: Springer; 2008. DOI: 10.1007/978-3-540-87698-4_10.

19.

Law

, Kelton

Simulation modeling and analysis. Vol. 3. McGraw-Hill Book Co. New York. 2007;0-07-036698-5.

20.

Burton

, McDermid

, Garnett

, Weaver

Safer Complex Systems: An Initial Framework. University of York Hesling, Royal Academy of Engineering. 2021;978- 1-909327-49-8.

21.

Chira

, Dumitrescu

, Moisoiu

, Tanase

, Human Performance Envelope Model Study Using Pilot’s Measured Parameters, INCAS Bulletin2020;12(4):49–61. doi: 10.13111/2066-8201.2020.12.4.5.

22.

Edwards

, Homola

, Mercer

, Claudatos

, Multifactor interactions and the air traffic controller: the interaction of situation awareness and workload in association with automation, Cognition, Technology & Work2017;19:687–98. doi: 10.1007/s10111-017-0445-z.

23.

Kirwan

, Wies

, Charles

, Dormoy

, Letouze

, Lemkadden

, Maille

, Nixon

, Ruscio

, Schmidt-Moll

Charting the edges of human performance. In MATEC Web of Conferences (Vol. 304).EDPSciences; 2019;eISSN: 2261-236X pp. 06007.

24.

, Chen

, Lu

, White

, Pilot workload investigation for rotorcraft operation in low-altitude atmospheric turbulence, Aerospace Science and Technology2021;111:106567.

25.

Takase

, Entzinger

, Suzuki

Pilot-in-the-loop simulation of simple adaptive fault-tolerant controller. Aerospace Science and Technology. 2020;106;106125.

26.

Stanciulescu

, Modelarea sistemelor de mare complexitate. Bucuresti: Editura Tehnica. 2003;973-31-2155-X. pp. 77-92.

27.

Borghini

, Astolfi

, Vecchiato

, Mattia

, Babiloni

Measuring neurophysiological signals in aircraft pilots and car drivers for the assessment of mental workload, fatigue and drowsiness. Neuroscience & Biobehavioral Reviews, Volume 44. 2014;0149-7634, pp. 58-75, https://doi.org/10.1016/j.neubiorev.2012.10.003. (https://www-sciencedirect-com-443.web.bisu.edu.cn/science/article/pii/S0149763412001704).

28.

Roscoe

, Assessing pilot workload. Why measure heart rate, HRV and respiration? Biological Psychology. Elsevier Science Publisher B.V. 1992;34.2-3:259-87.

29.

Hidalgo-Munoz

, Mouratille

, Matton

, Causse

, Rouillard , El-Yagoubi

Cardiovascular correlates of emotional state, cognitive workload and time-on-task effect during a realistic flight simulation, International Journal of Psychophysiology2018;128:62–9.

30.

Maciejewska

, Galant-Golebiewska

, Case study of pilot’s Heart Rate Variability (HRV) during flight operation, Transportation Research Procedia2021;59:244–52.

31.

Grassmann

, Vlemincx

, von Leupoldt

, Van den Bergh

, Individual differences in cardiorespiratory measures of mental workload: An investigation of negative affectivity and cognitive avoidant coping in pilot candidates, Applied Ergonomics2017;59:274–82.

32.

Charles

, Nixon

, Measuring mental workload using physiological measures: A systematic review, Applied Ergonomics2019;74:221–32.

33.

Bernardi

, Wdowczyk-Szulc

, Valenti

, Castoldi

, Passino

, Spadacini

, Sleight

. Effects of controlled breathing, mental activity and mental stress with or without verbalization on heart rate variability, Journal of the American College of Cardiology2000;35(6):1462–9.

34.

Hjortskov

, Rissén

, Blangsted

, Fallentin

, Lundberg

, Søgaard

, The effect of mental stress on heart rate variability and blood pressure during computer work, European Journal of Applied Physiology2004;92(1):84–9.

35.

Finsen

, Søgaard

, Jensen

, Borg

, Christensen

, Muscle activity and cardiovascular response during computer-mouse work with and without memory demands, Ergonomics2001;44(14):1312–29.

36.

Fairclough

, Venables

, Prediction of subjective states from psychophysiology: A multivariate approach, Biological Psychology2006;71(1):100–10.

37.

Wang

, Zheng

, Lu

, Fu

, Physiological indices of pilots’ abilities under varying task demands, Aerospace Medicine and Human Performance2016;87(4):375–81.

38.

Beatty

, Task-evoked pupillary responses, processing load, and the structure of processing resources, Psychological Bulletin1982;91(2):276.

39.

Causse

, Peysakhovich

, Fabre

, High working memory load impairs language processing during a simulated piloting task: an ERP and pupillometry study, Frontiers in Human Neuroscience2016;10:240.

40.

Van Acker

, Bombeke

, Durnez

, Parmentier

, Mateus

, Biondi

, Saldien

, Vlerick

Mobile pupillometry in manual assembly: A pilot study exploring the wearability and external validity of a renowned mental workload lab measure, International Journal of Industrial Ergonomics2020;75:102891.

41.

De Rivecourt

, Kuperus

, Post

, Mulder

LJM

, Cardiovascular and eye activity measures as indices for momentary changes in mental effort during simulated flight, Ergonomics2008;51(9):1295–319.

42.

Greef

, Lafeber

, Oostendorp

, Lindenberg

Eye movement as indicators of mental workload to trigger adaptive automation. In International Conference on Foundations of Augmented Cognition. Springer, Berlin, Heidelberg. 2009; pp. 219-28.

43.

Fournier

, Wilson

, Swain

, Electrophysiological, behavioral, and subjective indexes of workload when performing multiple tasks: manipulations of task difficulty and training, International Journal of Psychophysiology1999;31(2):129–45.

44.

Sirevaag

, Kramer

, Reisweber

CDWM

, Strayer

, Grenell

, Assessment of pilot performance and mental workload in rotary wing aircraft, Ergonomics1993;36(9):1121–40.

45.

Fairclough

, Venables

, Tattersall

, The influence of task demand and learning on the psychophysiological response, International Journal of Psychophysiology2005;56(2):171–84.

46.

, Wong

, Mak

, Chan

, An evaluation of mental workload with frontal EEG, PloS one2017;12(4):e0174949.

47.

Fallahi

, Motamedzade

, Heidarimoghadam

, Soltanian

, Miyake

, Effects of mental workload on physiological and subjective responses during traffic density monitoring: A field study, Applied Ergonomics2016;52:95–103.

48.

Alhaag

, Ramadan

, Al-harkan

, Alessa

, Alkhalefah

, Abidi

, Sayed

, Determining the fatigue associated with different task complexity during maintenance operations in males using electromyography features, International Journal of Industrial Ergonomics2022;88:103273.

49.

Hoogendoorn

, Hoogendoorn

, Brookhuis

, Daamen

, Psychological elements in car-following models: mental workload in case of incidents in the other driving lane, Procedia Engineering2010;3:87–99.

50.

Ghaderyan

, Abbasi

, An efficient automatic workload estimation method based on electrodermal activity using pattern classifier combinations, International Journal of Psychophysiology2016;110:91–101.

51.

Haarmann

, Boucsein

, Schaefer

, Combining electrodermal responses and cardiovascular measures for probing adaptive automation during simulated flight, Applied Ergonomics2009;40(6):1026–40.

52.

Collet

, Averty

, Dittmar

, Autonomic nervous system and subjective ratings of strain in air-traffic control, Applied Ergonomics2009;40(1):23–32.