Keywords

1 Introduction

Flight safety is one of the most significant issues in aviation. Various factors and the interaction among these factors may affect flight performance and safety [1]. Statistical data in recent years indicate among these factors the impact of human factors on flight safety issues is kept in high proportion. During the design of the aircraft, designer must consider human factors, but people usually find it difficult to predict and describe human behavior affected by human factors accurately. Thus, it is very important to construct practical methods to express and explain the impact of human factors for aircraft design, flight safety and so on.

In the last few decades, a wide range of techniques and approaches has been made by researchers to explain or predict human behavior. A crossover model was created by McRuer and Jex [2] to analyze the control quality of human. An optimal control pilot model was applied for different operator’s performances by Kleinman etc. [3]. Later Hodgkinson [4] improved the optimal control model and add a compensatory pilot model to express adoption, composite application of gain and lag compensations. Recently, five cognitive modeling tools were applied to safety issues associated with pilot’s operation and performance in the National Aeronautics and Space Administration Human Performance Modeling (NASA HPM) Project [5]. These five models contain cognitive model, task network model and so on. All of these models can provide help to the human factors research at different levels. However, most of them can only reflect the impact of human factors on flight performance, while they can not give an answer to the formation mechanism and principle of human factors.

The main objective of this paper is to explore a method that can correctly explain the principles and mechanisms of the human factors such as the problem how the human operational time delay and errors were introduced, and reflect the impact of these human factors on flight performance by computer simulation. It has been proved that modeling is a good solution to this kind of problems [6]. Then, this paper attempts to build an accurate, applicable and computable HPM to simulate the operations and performances of a real human pilot. A human cognitive model [7] which contains three main components: information perception, decision making, and action execution is used as a basic structure of the HPM. Based on the cognitive psychology theory of information processing, a specific decision-making model in the HPM is proposed to express how the human pilot process the information obtained from outside world and make a decision of control rules. In order to improve computing efficiency, the HPM ignores other secondary human factors such as operation habits and mainly consider the human factors that have a greater impact on flight performance. In addition, this paper studies the problem that the variance of information will lead to human errors and the change of human time delay. A series of human time delay models and decision-making model are built to explain the problem. Finally, a simulation experiment is designed to validate the HPM. The simulation experiment is realized by the man–aircraft–environment (MAE) complex systems model [8], which makes it possible to generate a large number of flight data in a short time.

2 Specification of Human Performance Model

2.1 Overview of Human Factors in HPM

Among many human factors, human errors have the greatest impact on flight performance. Human errors has become an important, well-defined discipline and people has realized that human errors induced system failure is much more important and costly than the typical 100–500 ms delay observed in the reaction time study [9]. Such human factors often lead to the loss of the stability of the system. Human time delay and biases have second impact. Such human factors can affect the performance of the system such as the lag of the reaction and the decrease of the operation precision. Human habits such as operation habits, scan patterns have minimal impact on the system. So in this paper, the HPM is mainly concerned with human errors and human time delay while the other less affected human factors are ignored.

Human errors exist in both three components of cognitive process mentioned in the previous. However, in different component, the cause and the impact of human errors are different. About human errors, there are more systematic theory [10], but this paper does not consider too complex human errors, only consider the errors that have great impact and can be quantified accurately such as information missing (or overflow), decision-making mistakes, decision-making biases, the operation errors etc.

Like human errors, human time delay also exists throughout the cognitive process. In addition, human time delay has a coupling relationship with other human factors such as decision-making biases, operation error etc. The paper will explain the causes and effects of human errors and human time delay in different component in detail.

2.2 Structure of HPM

The behavior of pilots in the course of aircraft flight is similar to the process of human cognitive models. That is repeating the cycle process: get aircraft instrument information - determine the state of aircraft and environment – make decision – operation - get information. In the case of an aircraft system, the function of a human being is similar to an automatic control system. Every time a cognitive cycle is updated, the input of the controller is updated and the corresponding control variables are given by human, and then the human neuromuscular system is applied to the specific aircraft operation. However, different from the general controller, in many flight scenarios and flight tasks, two forms of control methods continuous control and discrete control coexist, and for different control objects, the proportion of continuous control and discrete control is different. For example, the control of the rudder and the elevator in the cruise task is continuous during the control period, which is similar to servo control. However, in the process of the task, if the other operations need to be occupied or the change of flight state leads to the change of control rules, the continuous control will be interrupted. The control of flaps and so on is discrete. Only certain conditions such as reaching a certain height are triggered will lead to changes of controlled variable, and once a change occurs, the control variable will remain constant over a long period of time until the next condition triggers. For the above two different situations, the controlled variable and the corresponding models are divided into two categories. One is the continuous control, of which the corresponding controlled variables include the elevator, rudder, throttle, etc. The other is the discrete control, of which the corresponding controlled variables include flaps, spoilers, landing gear etc. Since the rules have been determined, the time delay of the continuous control model in a single cognitive cycle is short. For the discrete control model, because people need to determine the state of aircraft and make complex decisions, the time delay is long. A special case is in continuous control model, the time delay will be longer if the state of the aircraft is changed and the current control rules need to be changed (Fig. 1).

Fig. 1.
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The structure of HPM

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2.3 Three Components of Human Performance Models

Information Perception

The component of information perception refers to the process of selective access to potentially useful information from the outside world. In the flight, the pilot can obtain visual, auditory, somatosensory and other information from the outside world, but only some of the information is potentially useful for pilots. The information is potentially useful is based on a subjective judgment of the pilot. The pilot has a conscious selective access to information to reduce unnecessary time consumption. For pilots, potentially useful information include aircraft instrument information (aircraft status), window visual information, voice indication information, somatosensory information (including spatial location, acceleration, etc.). In the subsequent experimental verification process, because it is difficult to quantify the later information in the program, only aircraft instrument information is taken into account.

The time required to obtain the instrument information is calculated by the empirical formula obtained by the serial self-terminating search (SSTS) model [11]. The SSTS model considers that the search time ST required to search for N instruments is proportional to N:

$$ ST = a_{p} + bN $$
(1)

Where \( a_{p} \) is a constant used to describe the inherent time of the search, including head movement time, attention shift time and so on, b is search and dwell time of a single instrument and the different instruments have different b. The values of these two constants are empirical values obtained by experiments. \( ST \) is equal to the time delay of the information perception in single cycle. For all discrete controlled variables, this time delay is present throughout the flight, because pilot need to obtain enough useful information to determine the status of aircraft and environment. For the continuous controlled variables, because of the small number of instruments to be observed, the information acquisition and the operation can be carried out simultaneously. In this case time delay is a relatively small value. No matter what kind of control, the number of instruments required to search N is determined by the current flight mission and flight phase. The main human errors in the information acquisition is the omission of information and the false recognition of information content. This part of the error will have an impact on the subsequent decision making process, so it will be described later in detail.

Decision-Making

Information Process.

Decision-making contains the front information processing section. Information processing is to get some useful information from the part of information perception then select and fuse the information in order to get a complete description of the aircraft states. The selection of information is to select the information that is required for the operation to be performed from all the useful information. For example, the pilot may repeatedly check the airspeed indicator, altimeter, flight attitude indicator etc. However, in the implementation of the left turn 90 degrees flight mission, the operation requires only a small amount of information such as yaw angle, speed, etc. For information fusion, it is difficult to describe exactly how people integrate information into a whole concept, but the process of information fusion does exist and work. This paper does not consider the specific mechanism of information fusion, but in the process of decision-making, the multi information is combined into the judgment condition as the form of information fusion. Through the experiment, it is difficult to distinguish the time delay of information processing and the time delay of decision-making, and only their common time delay can be obtained. Because the information processing does not need to carry on the complex logical inference, and has the subconscious participation, the actual process is quite rapid. A very small constant is used to express the time delay.

Decision-making.

The decision-making process includes two meanings: the generation of decision rules and the choice of decision rules. The generation of decision rules is a complex process. There is still no universal theory in the fields of biomedicine, psychology and so on to explain how the human produce ideas. Therefore, the HPM model does not show how these control rules are generated. The HPM use a method similar to expert control, which write the standard control rules for different flight scenes according to the experience of experts. The flight check list, flight crew operating manual (FCOM), and so on, are use this method to give an answer to the pilot’s handling of the aircraft in the standard or some emergency situations. These rules that have been written in advance belong to the normative decision making. In fact, the decision made by pilots in most of the time during flight belongs to this type. In the remaining situation that has not been considered in advance, pilots need to determine the situation and generate the decision rules. This type of decision belongs to heuristic decision making [12]. Although this decision, especially in the face of unexpected situations will be more important (this is the main reason that the current computer can not completely replace the pilots), as mentioned earlier, it is impossible to accurately describe the process. Therefore, heuristics is not considered in this paper. The core problem of normative decision making is how to make decision or choice according to the best reference frame. In this paper, a task network model [13] is used to simulate human decision making. The whole flight can be divided into takeoff, cruise and other stages, and each stage can be divided into many specific flight tasks. The process of the choice of decision rules is to determine which task needs to be executed by the aircraft status and the overall flight plan, then in each task, it is necessary to determine which control rules need to be selected to control the aircraft in accordance with the more specific aircraft status information. The entire process is similar to borrowing from the library, the control rules written in advance are classified by the actions, tasks, stages, etc. The decision making process of pilots is to determine which rule applies to the current state of the aircraft through a series of If… Else… conditions.

For the machine, it is possible to check all the necessary information in each cycle (the machine refresh clock) and then give the value of all the controlled variables. Because of the limited resources and capabilities, it is impossible for human to do a large amount of information processing and decision-making behavior in a short period of time (the order of the machine refresh clock). Human make decision in a similar way to Time Division Multiplexing. For two pilots, tasks of continuous control and discrete control can be assigned to the main pilot and the copilot respectively. For one pilot, if the continuous control has confirmed the rules and maintained this rule for a longer period of time (for example, manual control of aircraft Cruise), it will only take up fewer resources. The pilot can execute other controls at the same time. On the contrary, because of the complexity of the state determining and decision making, only one discrete control can be carried out at the same time. If every time to obtain all useful information and make decision, the time delay will be too large. In the real situation, the pilot will not do so. This paper presents a form of regular and trigger to simulate the real process. The pilots mainly execute continuous control during the flight. The main concern of pilots is the information that is closely related to the continuous control such as speed, height, etc. In this case, the cycle time of each HPM is very short. Every once in a while (This time can be modified according to the actual operation of the pilot, in this paper it is set to 10 times the period of the continuous control in HPM) the pilot checks all the useful information to determine if any other minor continuous or discrete control is needed. This cycle corresponds to a longer time delay. In addition, at any time, once other control rules is triggered by a certain information, all operations are interrupted. If a new operation (other controls) is added, which leads to the amount of control reaches the upper limit of the pilot’s control, one of the previous operations will be suspended until the new operation is returned (Fig. 2).

Fig. 2.
figure 2

The process of decision-making

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The Human Time Delay of Decision-Making.

The human time delay of decision making is approximately calculated by hick-hyman-law [14, 15]. Hick-hyman-law is a formula used to calculate the choice reaction time (RT). The choice reaction time can be regarded as the time required for human decision making (here is the choice of decision rules). The Law points out that the choice reaction time is proportional to the amount of information contained in the choice:

$$ RT = a + bH $$
(2)

Where a and b are both constant obtained by experiment. \( a \) describes the sum of processing latencies that are independent of uncertainty reduction, such as the amount of time spent on stimulus encoding and response execution, \( H \) is the average amount of information for a certain rule calculated by the formula:

$$ H_{avg} = \mathop \sum \limits_{i = 1}^{n} P_{i} [log_{2} \left( {\frac{1}{{P_{i} }}} \right)] $$
(3)

Where \( P_{i} \) is the probability of the occurrence of a certain information in the rule. The sum of the probabilities of all information used to determine this rule is 1. The time delay of continuous control and discrete control in decision-making can be calculated by Hick-hyman-law. Specially in the continuous control, due to the existence of a certain period of time the control rules remain unchanged, then the corresponding decision-making time delay is 0.

The Human Errors of Decision Making.

Although most of the time people are expected to be able to make accurate decisions in accordance with the best reference frame, people can not correctly perform the operation due to some subjective or objective reasons, which means the human errors and biases. This paper mainly studies the human errors induced by the change of information. Where the change of information is refer to the change of the amount of information (missing or overflow). When the information is missing, it will lead to the failure to select the right rules which will cause decision-making biases or errors. This is simulated in HPM as follows: If at a certain moment, the combination of the condition of the rules that should be used is A&B&C (A, B, C are conditions containing different information, & refers to a certain logical operation) but the information that has been obtained is only A&B. Then a rule will be randomly selected from all the rules of the A&B condition. If the information overflow, although it will not lead to the choice of wrong rules, the extra time cost of information perception will also have an impact on the performance.

Action Execution

Action execution mainly involves continuous control. Because the discrete controlled variables such as flaps, landing gear are generally switch control, only the time delay of which has to be considered. In the paper, it is an empirical value. For continuous control, different control methods and different control precision etc. will affect the results. In this paper, the control rules are not written for the whole flight but for the stage final approach and landing. During the final approach and landing, the continuous controlled variables mainly includes the three control objects, the elevator, rudder and throttle. The PI control methods is used for a simple simulation of human’s control methods. For example, the control rules of the elevator \( \updelta{\text{e }} \) in the approaching process is:

$$ {\updelta }{\text{e}} = (K_{pv} + K_{iv} *T_{delay} ) *{\updelta }V + (K_{pp} + K_{ip} *T_{delay} ) *{\updelta }P $$
(4)

Where \( K_{pv} \) is the proportional coefficient of velocity deviation, \( K_{iv} \) is the integral coefficient of velocity deviation, \( T_{delay} \) is the time delay of single cycle. \( \delta V \) is the deviation between the expected speed and the instrument speed. Similarly, the latter part of the formula is the coefficient of the position and position deviation.

The time delay of action execution is related to the operation precision. According to speed-accuracy operating characteristic (SAOC) [16], there is a linear relationship between the logarithm of operation time and operation accuracy:

$$ \log \left[ {\frac{{P\left( {true} \right)}}{{P\left( {false} \right)}}} \right] \propto T $$
(5)

Where \( P\left( {true} \right) \) is the probability of true operation and \( P\left( {false} \right) \) is the probability of false. They meet \( P\left( {false} \right) + P\left( {true} \right) = 1. \) The operation accuracy is expressed by a random number. For example, if the elevator operation accuracy is 95%, the relationship between output \( \updelta{\text{e}}_{actual} \) and expected output \( \updelta{\text{e}}_{expect} \) is:

$$ \updelta{\text{e}}_{actual} =\updelta{\text{e}}_{expect} *random(0.95,1.05) $$
(6)

Where \( random\left( {0.95,1.05} \right) \) is a random number of 0.95 to 1.05.

3 Simulation Results and Discussion

3.1 Simulation Experiment Configuration

Simulation experiment is based on the MAE complex systems model. The model includes a human model, an environment model and an aircraft model. Human model is realized by previously mentioned HPM. The specification of HPM time delay parameters is listed in Table 1:

Table 1. HPM time delay parameters
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Where N(0.2,0.04) refers to a random number according to the standard normal distribution, whose expectation is 0.2, variance is 0.04.

The environment model includes an atmosphere model and a wind speed model. They are based on the international standard atmosphere (ISA). The aircraft model is implemented by a six-degree-of freedom (6-DOF) aircraft flight dynamics model [17]. The parameters of aircraft is based on the dynamic model of Boeing 747-400 [18], the specification is listed in Table 2:

Table 2. The parameters of Boeing 747-400
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The scenario of simulation experiment is set to a final approach and landing mission. In this mission, aircraft is expected to track the flight path with down slope equals to −1:29. The initial status of aircraft are listed in Table 3 and the expected final status of aircraft are listed in Table 4:

Table 3. Initial status of aircraft
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Table 4. Expected final status of aircraft
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Final velocity and touchdown offset (final location) are selected to reflect the flight performance. If the final vertical velocity is greater than 3 m/s, it is considered to be hard landing. If the final airspeed is less than 120 Knot, it is considered to be stalled. The smaller touchdown offset means that the better flight performance.

Four types of experiments are designed as Table 5:

Table 5. Types of experiments
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In type 1, pilot is concerned with position and velocity information for continuous control. And only the rules of position and velocity have been written in the continuous control rules. In type 2, pilot is concerned with acceleration information in addition to position and velocity information. The continuous control rules of type 2 is the same as type 1, which is equivalent to completely ignoring acceleration information. In type 3, pilot is concerned with position, velocity and acceleration information. The continuous control rules of type 3 include the rules of position, velocity and acceleration (The acceleration rule is added on the original rule, and the logic structure of the original rule will not be changed). In type 4, pilot is concerned with position and velocity information. But sometimes the pilot omits the velocity information (a random probability function). The continuous control rules of type 4 is the same as type 1.

3.2 Results and Discussion

Because the time delay, decision rules choice and operation precision all contain uncertainty, each simulation result is different from the other. Each type of experiment was carried out 500 times. The Table 6 show the results of four types of experiments:

Table 6. The results of experiment
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The results show that the final velocity of all the experiments except type 4 is satisfied. The average human time delay of type 1, type 4 are the same and that of type 2, type 3 are the same. The average time delay of type 1 is less than that of type 2. It is obvious that the increase in the amount of information will lead to an increase in time delay. Type 2 contrasts with type 1, the touchdown offset has increased due to the increase of the amount of information. The experimental results of type 2 and type 3 are similar. It can be seen that the control rules corresponding to the acceleration information have little impact on the flight performance. Type 4 contrasts with type 1, the touchdown offset has increased obviously, which shows that velocity information has larger impact on flight performance than the acceleration information.

4 Conclusions

Based on cognitive psychology, this paper constructs a human performance model containing human time delay, human decision biases, operation deviation etc. The impact of human factors and the interactions between them on flight performance is explained by the HPM. The HPM shows that there is a close relationship between human time delay and the complexity of decision-making and there is a coupling between human time delay and operation precision. The pilot controls the aircraft by continuous and discrete control. The decision-making bias occurs mainly in continuous control and it is mainly caused by the change of information. A serious information omission will lead to decision-making errors, which has a great impact on flight safety.