A GENETIC ALGORITHM-BASED BP NEURAL NETWORK METHOD FOR OPERATIONAL PERFORMANCE ASSESSMENT OF ATC SECTOR

To assess operational performance of air traffic control sector, a multivariate detection index system consisting of 5 variables and 17 indicators is presented, which includes operational trafficability, operational complexity, operational safety, operational efficiency, and air traffic controller work-load. An improved comprehensive evaluation method, is designed for the assessment by optimizing initial weights and thresholds of back propagation (BP) neural network using genetic algorithm. By empirical study conducted in one air traffic control sector, 400 sets of sample data are selected and divided into 350 sets for network training and 50 sets for network testing, and the architecture of genetic algorithm-based back propagation (GABP) neural network is established as a three-layer network with 17 nodes in input layer, 5 nodes in hidden layers, and 1 node in output layer. Further testing with both GABP and traditional BP neural network reveals that GABP neural network performs better than BP neural work in terms of mean error, mean square error and error probability, indicating that GABP neural network can assess operational performance of air traffic con-trol sector with high accuracy and stable generalization ability. The multivariate detection index system and GABP neural network method in this paper can provide comprehensive, accurate, reliable and practical operational performance assessment of air traffic control sector, which enable the frontline of air traffic service provider to detect and evaluate operational performance of air traffic control sector in real time, and trigger an alarm when necessary.


INTRODUCTION
A sector is a volume of airspace for air traffic control (ATC), normally positioned with a team of air traffic controllers [1,2].Research on operational performance assessment of ATC sector is meaningful for all the main aspects of air traffic management (ATM), composed of air traffic service, air traffic flow management (ATFM), and airspace management.The effective results of operational performance assessment of ATC sector should be the basis and precondition for the adjustment of ATC operation and ATFM strategies, and also the optimization of ATC airspace structure.
As the primary task of ATM, it has taken a long time to study how to prevent aircraft collision and aircraft-obstacle collision.Before 1990s, the phenomena of traffic congestion and flight delay in ATC

A GENETIC ALGORITHM-BASED BP NEURAL NETWORK METHOD FOR OPERATIONAL PERFORMANCE ASSESSMENT OF ATC SECTOR
Traffic Engineering Original Scientific Paper Submitted: Nov. 19,2015 Accepted: July 14, 2016 airspace were not serious since the air traffic flow was not relatively heavy, and the studies on operational performance assessment of ATC sector focused on aircraft separation and collision risk analysis.Reich proposed possibility distribution functions to estimate aircraft collision risk, and discussed aircraft separation minima to be applied in longitudinal, lateral and vertical dimensions in airspace, respectively.Related analytical techniques were applied in the North Atlantic region [3][4][5].Follow-up studies introduce the improved collision risk models for different categories, such as confliction, air miss, and collision, based on Reich's model [6][7][8][9].On the basis of Reich's model and the improved models, the concept of Target Level of Safety (TLS) in airspace is proposed by International Civil Aviation Organization (ICAO) [10].Besides, the studies on aircraft lateral separation minima in the North Atlantic region [11], aircraft vertical separation minima in Europe [12][13][14], aircraft longitudinal separation minima in the Asia-Pacific region [15], as well as collision risk analysis for Performance-based Navigation (PBN) procedures [16][17][18][19], are all based on Reich's study.The mentioned aircraft separation and collision risk studies contribute greatly to aircraft separation minima determination in the aspects of structured airspace and evolved flight procedure.However, they are not the total efforts to prevent aircraft collision and aircraft-obstacle collision.In the aspect of daily operation, a number of automation systems have been applied to automate air traffic conflict detection and resolution since the early 1990s, taking Traffic Alert and Collision Avoidance System (TCAS) and Ground Proximity Warning System (GPWS) in cockpit and conflict predictors in ATC automation system for examples, considering that human failures or errors are unavoidable and highlighted in the meanwhile [20].
With continuous growth of air traffic flow and expansion of air routes since the 1990s, traffic congestion and flight delay have happened frequently and seriously with more complex air traffic distribution, while air traffic controller (ATCO) workload increased under the circumstance.Thus, studies about the operational performance assessment of ATC sector expanded to airspace capacity and the related fields, including airspace utilization, complexity of air traffic flow, and ATCO workload as well.Most studies proposed that ATCO workload threshold can be used to access ATC sector capacity, in terms of either the number of simultaneously present aircraft or the number of aircraft traversing the sector per unit of time [1,[21][22][23][24].The literature in this field is mostly related to the analysis of the factors affecting the complexity of the controller's task and workload [22].Moreover, the capacity of a sector presents variability and unpredictability, which are also explained by those factors, summarized as three categories, airspace physical structure, air traffic situation, and operational constraints [1].Airspace utilization reveals the relationship between airspace capacity and traffic flow distribution, and it can be reflected in space-based or time-based utilization [25][26], traffic congestion status [27][28], and statistics of flight delays [29][30][31].Furthermore, the complexity of air traffic flow is proposed for the recognition of air traffic situation in airspace, which is more accurate, comprehensive and dynamic than airspace capacity and its utilization.As the most representative assessment technique for the complexity of air traffic flow, dynamic density concept has been measured by detecting aircraft altitude, speed and heading changing times [32][33][34][35][36][37].Even though ATCO workload is not directly related to operational performance of ATC sector, it is a kind of essential investment to implement ATC operation, and has great influence on the operational performance.ATCO workload is mainly measured by time consuming of visible task and converted time consuming of invisible task, to be evaluated in quantitative way [38][39].Based on previous studies, the concept of operational performance of ATC sector could be defined as the operational quality and related level from different angles such as aircraft separation and collision risk, airspace capacity and its utilization, air traffic complexity and ATCO workload.
It is worth noting that recent studies have highlighted that the operational performance assessment of ATC sector has been involved in a multivariate problem, and affected by many factors which interfere with each other [40][41][42].To improve operational performance of ATC sector, a multi-objective decision strategy should be considered.In [2], to ensure safety and efficiency of the aircraft, the desirable objectives of ATC are listed as follows: maximizing the runway throughput, minimizing the approach time of aircraft before landing, minimizing air traffic controllers' workload, maximizing fairness among the aircraft, minimizing the aircraft taxi-in/taxi-out time, minimizing the arrival/departure delay, minimizing deviations from an appropriate balance between arrivals and departures [2].In [21], the analysis shows that congestion and delay reduction by significant capacity increase may be not applicable in a short term, while better traffic demand management and available capacity allocation could be more effective from both strategic and tactical perspectives [21].Most of the existing studies, however, as far as we can see, are limited in only one aspect, or based on a single side.It is clear that one-factor-only studies cannot detect and evaluate operational performance of ATC sector systematically.On the other hand, most studies aim at theoretical, not empirical research.A novel method is needed to assess the operational performance of ATC sector at the frontline of air traffic service provider as empirical use.
Thus, to support multi-objective decision making for the improvement of operational performance of ATC sector for empirical and practical purpose, the The method mentioned is suitable for theoretical or experimental research.But for empirical and practical purpose in the paper, the selected indicators are supposed to be easily measured based on the feasibility of real-time operation data acquisition, and validated with numerous on-site investigations from senior AT-COs besides theoretical or experimental references.Based on that, this paper puts forward an integrated and universal multivariate detection index system systematically for operational performance of ATC sector, including 5 variables and 17 indicators.
In detail, the studies on aircraft collision prevention could trigger a variable named operational safety, under which the indicators of Short-Term Conflict Alert (STCA) and Minimum Safe Altitude Warning (MSAW) can be detected and recorded from conflict predictors in ATC automation system in the operation site of air traffic service provider.The studies on airspace capacity and its utilization could involve two variables named operational trafficability and operational efficiency.The variable operational trafficability could include the indicator of air traffic flow reflecting airspace capacity, and the indicators of flight miles for space-based airspace utilization and flight time for time-based airspace utilization, while the variable operational efficiency could include the indicators of sector saturation and sector queue length for traffic congestion status, and the indicators of delay percentage, delay time and average delay time as the statistics of flight delays.The studies on complexity of air traffic flow could connect a new variable named operational complexity with the indicators of aircraft climbing frequency, aircraft descending frequency, aircraft speed changing frequency, and aircraft heading changing frequency, and the variable operational trafficability again with the indicator of air traffic flow density as well.Meanwhile, the studies on ATCO workload as a variable could be indicated by occupation percentage of air-ground communication radio and call times of air-ground communication radio.For each variable as mentioned, the indicator definitions and notations are listed in Table 1.
The indicators and related measurement methods are compared with other options as a form of selection and validation based on the following principles through expert investigation method by an expert team including related scientific researchers, senior ATCOs, and experienced engineers.

Principle 1: Engineering feasibility
The feasibility of real-time operation data acquisition is positioned to lay the base of indicator selection.All those 17 indicators in total within the multivariate detection index system are measured based on hourly statistical real-time operation data, collected from ATC automation system, automatic message switching system, and very high frequency (VHF) voice contributions of this paper with respect to the related state-of-the-art could be listed as follows.An integrated and universal multivariate detection index system is established for operational performance of ATC sector, introducing 5 variables including operational trafficability (traffic throughput and containing ability), operational complexity, operational safety, operational efficiency, and ATCO workload, and 17 indicators calculated with real-time operation data which can be acquired with high engineering feasibility.A novel method to comprehensively evaluate operational performance of ATC sector in more reliable and accurate way is provided with Back Propagation (BP) neural network, in which the initial weights and thresholds are optimized by Genetic Algorithm (GA).Both the index system and the method are validated to have the availability to be integrated into application system for the frontline of air traffic service provider, to assist the operation personnel in the judgment and decision making about operation strategies from both strategic and tactical perspectives.
The remainder of this paper is as follows: Section 2 presents an integrated and universal multivariate detection index system, in which both the indicators under each variable and the definition for each indicator are listed.A comprehensive evaluation method based on GABP neural network is provided in Section 3, in which detailed method progress is discussed.Next, Section 4 presents an empirical study which is conducted in one ATC sector in China, and results analysis and discussion are carried out.Last but not least, Section 5 contains the conclusions and future research expectations.

MULTIVARIATE DETECTION INDEX SYSTEM
The operational performance of ATC sector is affected by various factors which have been investigated by the existing studies from single sides, i.e. aircraft collision prevention, airspace capacity and its utilization, complexity of air traffic flow, and ATCO workload.
Each study focus has connected some variables and the related indicators.Since there is a number of indicators related to operational performance assessment of ATC sector showing up in previous works, the question is how to select and validate the indicators in the paper.In [35] a systematic method is presented, based on data mining to figure it out [35].On the one hand, it is considered to extract the meaningful principal components as the selected indicators from a large scope of metrics based on linear correlation finding through Principal Component Analysis (PCA).On the other hand, it could be to select the most relevant indicators investigating the link between the indicator set and ATC sector configurations using neural networks, assuming there are non-linear interactions.communication system.The ATC automation system combines and then processes the data of surveyed flight tracks exported from surveillance facilities such as primary and secondary radar, and output integrated flight track information.The automatic message switching system is used to send and receive air traffic service messages via Aeronautical Fixed Telecommunication Network (AFTN).By connecting to this system, air traffic service message contents can be reformatted and analysed for flight plan data.The VHF voice communication system connects ATCO and pilots by wireless communication, and both duration and time of the radio calls can be acquired for ATCO workload assessment after decoding.The integrated flight track information, flight plan information, and voice communication information between ATCO and pilots compose source data for the calculation of all the 17 indicators above.Since the ATC automation system with intrinsic conflict predictors results in STCA and MSAW outputs, the indicators of STCA and MSAW are selected for their high weight in engineering feasibility [20].Similarly, the indicators of occupation percentage of air-ground communication radio and call times of air-ground communication radio are selected because the results are acquired easily from the VHF voice communication system.

Principle 2: Scientific typicality
The variables are designed after the previous scientific studies have been sorted out.Some indicators and related measurement methods are selected if they have strong scientific identifications in prior studies, which are suitable for operational performance assessment.For example, the indicators of air traffic flow density, aircraft climbing frequency, aircraft descending frequency, aircraft speed changing frequency, and aircraft heading changing frequency have high typicality since they are the focus in the studies on complexity of air traffic flow [32][33][34][35][36][37], while the indicators of sector saturation and sector queue length are also very typical in the studies on traffic congestion status in air traffic flow management [27-28, 40, 42].

Principle 3: Operational practicability
Some indicators and related measurement methods are selected if they have been authorized to play an important role in operational performance metrics.Both the Federal Aviation Administration of the United States (FAA) and the European Organization for the Safety of Air Navigation (EUROCONTROL) have identified the key performance indicators (KPIs) for ATM-related operational performance [25].Among those KPIs, the indicators of air traffic flow, delay percentage, delay time, average delay time, flight miles, flight time are selected and shaped with appropriate measurement methods based on the applicability of ATC sector [25,29].In practice, the total delay can be divided into unavoidable delay which has already existed at the entrance of the sector and cannot be recovered any more, and consecutive delay which represents the delay required to solve potential aircraft conflicts or sequencing problem computed from the entrance to the exit of the sector [30][31].Since there is nothing the ATCOs can do to shorten the unavoidable delay, the delay-related indicators of operational performance are defined as consecutive delay, and measured by comparing the real flight time with the normal flight time.
It should be noted that the index system of Table 1 is designed for ATC sector mainly in en-route control and terminal control phases.In aerodrome ground control phase, neither the sector concept nor the index system is applicable.In this phase, the focus should be on: (1) occupancy status of runway, taxiway and parking position, i.e., operational trafficability, which could be measured with the occupying aircraft number, occupancy duration or distance; (2) hotspot status in the whole layout of aerodrome, i.e., operational complexity and safety, which could be measured with conflict detection tool, saturation degree of runway, taxiway and parking position; (3) delay status, i.e., operational efficiency, which could be measured with detailed capacity utilization ratio, detailed delay percentage or time, in terms of gate traffic delay, taxi delay and runway delay; and (4) ATCO workload, which is involved with more complex task analysis and measurement.For a special part of en-route control and terminal control phases, it is also necessary to tailor the index system for applicability purpose.Taking a part of final approach as example, some indicators and related measurements on separation between the leading and trailing aircraft should be involved and play an important role in the balance analysis between operational safety and efficiency [40].

METHOD DESIGN 3.1 BP Neural Network
BP neural network has been widely applied in decision-making system since it was introduced in 1986.Zhang et al. put forward a comprehensive evaluation method on ATC operation performance based on BP neural network, proving that BP neural network could be used in ATC operation performance classification [42].The structure of BP neural network based on the introduced multivariate detection index system for operational performance assessment of ATC sector can be shown as in Figure 1.
Input layer Hidden layer Output layer

Figure 1 -Structure of BP neural network for operational performance assessment of ATC sector
There are three layers in the BP neural network, i.e., input layer, hidden layer and output layer.In Figure 1, X i (i=1,..,n) is the input as detection indicator, and Y is the output as the ranking result of the operational performance of ATC sector through comprehensive evaluation.α k and β are the thresholds of the k-th(k=1,…,H) node in the hidden layer and the single node in output layer, respectively.ω i,k and ' k ~ are the weights for input-to-hidden, and hidden-to-output, respectively.The BP neural network could be modelled as follows [43]: where f h and f o are the activation functions of the hidden layer and output layer.
With initial weights and thresholds, the BP neural network will be trained with training input data, to update weights and thresholds until the training errors (difference between trained output and expected output) are small enough to be accepted.Thus, it can be seen that initial weights and thresholds will decide whether or not the training process can result in acceptable training errors within suitable time.

GABP Neural Network Method
It is clear that BP neural network is built on multinode architecture which can structurally support comprehensive evaluation on operational performance of ATC sector with multivariate detection index system.Besides, both weights and thresholds are two important criteria for the final evaluation results, since they are the basis for network training.However, initial weights and thresholds are normally assigned randomly in BP network, resulting in the training convergence process being slow, and the BP network easily stuck in local optimum [44][45].
GABP neural network is proposed by the idea that the Genetic Algorithm is capable of global optimization of initial weights and thresholds through selection, crossover and mutation operation.Besides, GA could speed the convergence process of traditional BP neural network, and make it easier to find the global optimum and avoid the local optimum.The idea of using GA to optimize BP neural network has been testified in previous studies [46].Furthermore, as pointed by one referee, there could be other optional metaheuristics to optimize the BP neural network.To select the proper algorithm, we have compared the performance of BP neural network optimized by Simulated Annealing (SA) algorithm and GA in a primary test, respectively.Results show that GA is better in terms of convergence process and CPU time.So, GA is adopted in our case to optimize the traditional BP neural network (more detailed and thorough comparison among more metaheuristics would be done in our future studies).
To optimize the BP neural network with GA, the initial weights and thresholds will be coded as the chromosome in GA, by selection, crossover and mutation operation, and a group of those chromosomes will be imported into a BP neural network, then the network will be iterated with training input data.In return, the training errors will be used to construct the fitness function in GA, and the chromosome with the best fitness value will be the optimized initial weight and threshold for further BP neural network training.
Here are the steps for GABP neural network method:

Step 1: Establish the training sample set
The training sample set contains training input data and related expected output data.The training input data are from historical database including all 17 detection indicators of operational performance of an ATC sector in a period of time (one hour) as a sample, denoted as X 1 ,…,X 17 ; while expected output data are based on ATC expert panel's ranking for those historical samples, from 1 to 5, indicating that the operational performance is at an excellent, very good, good, average, or bad level, respectively.The panel is made up of 5 senior ATCOs, who are qualified through skill assessment and have more than 10 years of relevant working experience.The ATCOs' ranking for the operational performance is made by their subjective judgments facing the 5 variables (operational trafficability, complexity, safety, efficiency, and ATCO workload) based on observed clues from the historical video and audio records of the operation process of each sample.Normally, it is extremely difficult for each expert to make the same ranking for every sample.If there are 4 ATCOs in the panel or more, giving the same ranking for a sample, namely consistent ranking, the sample is selected as a typical sample.Those typical samples with 17 detection indicators and consistent ranking will compose the training sample set.Besides, on the premise of sufficient number of typical samples, the proportion of training samples with different rank, i.e., 1,2,3,4,5, could be allocated as 10%, 20%, 40%, 20%, and 10%, respectively.

Step 2: Normalize the training sample data
The training sample data should be normalized to eliminate the dimension differences among indicators before further training.Let x j,i and x , ' j i be the j-th(j=1,2,…,N) original and normalized training sample data for the i-th(i=1,2,…,17) indicator.The normalization formula is the mapminmax function in MATLAB which allows the normalized x , ' j i ranging from -1 to 1 [47].
( ,..., , ..., ) / ( ,..., , ..., ) ( , ..., , ..., ) ( ) min max m in Step 3: Initialize BP neural network BP neural network, in the case, is shaped as 17-input and single-output architecture.While the number of nodes in the hidden layer, H, is normally decided by rule-of-thumb, which is: H A B C < + + (in the case, A=17 and B=1 are the number of nodes in input and output layers, respectively.C is an integer from 1 to 10 [42].Besides, for the p-th time of network training, let L j,k,p be the output value of the k-th(k=1,2,…,H) node in the hidden layer with regard to the j-th(j=1,2,…,N) training sample data, and Y j,p be the output value in output layer.Then, both L j,k,p and Y j,p can be derived with the tansig activation functions.The tansig is a hyperbolic tangent sigmoid transfer function in neural network, tansig(net)=2/(1+exp(-2 • net))-1, where net is the linear activation of the neuron [47].,…,H) node in the hidden layer and the node in output layer, respectively.
Step 4: Encode the population of GA The population of GA consists of certain chromosomes which contain initial weights and thresholds of BP neural network.i.e. the chromosome can be coded in the real number as follows: ...

~~~~~~a a ~~b
The length of GA chromosome is thus limited by the total number of weights and thresholds, and the number of chromosomes in GA is denoted as Q. Step

5: Define fitness function
The fitness function of chromosome l(l=1,…,Q) after the d-th iteration is the reciprocal of absolute error between trained output Y , j d l and expected output E , j d l [48]: Step 6: Select Rolette is used to select individuals from the population to produce new offspring.For each chromosome l, the probability of being selected is Step 7: Cross Since the chromosomes are coded as real numbers in the case, so the crossover is done by the socalled real number crossover.Let g l,m,d and g l',m,d be the genes to be crossed, and they are located in the mth position of chromosomes l and l ' .Then after crossover the new genes are [48]: ; r is a random number from 0 to 1.
Step 8: Mutate By mutation, ' g , , l m p in chromosome l will be mutated to '' g , , l m d in certain probability determined by formulas 10 and 11 [48] Both a and b are random numbers from 0 to 1; g max and g min are the values of upper bound and lower bound for ' g , , l m d , respectively.And d and D max are current and maximum iterations, respectively.
Step 9: Find the best chromosome If the maximum iteration D max is reached, then stop running and find the best chromosome with the biggest fitness value to identify the best initial weights and thresholds for GABP neural network training.If not, go back to Step 6 for further iteration.

Step10: Calculate training errors
With the best initial weights and thresholds from GA, BP neural network will be trained with the training sample set.The training errors will be the differences between trained output and expected output.

Step 12: Find the best-trained GABP neural network
By training GABP neural network with different available number of nodes in the hidden layer, find the most suitable number of nodes in the hidden layer which minimizes the total training errors for the besttrained GABP neural network.

Step 14: Alarm
It is feasible to integrate software module implementing the best-trained GABP neural network into application system for real-time usage in the operation site.When the rank result of operational performance of ATC sector is 5, indicating that the performance is at a bad level, an alarm could be a trigger to alert the operation personnel to adjust the operation strategies before it is too late.
Figure 2 presents the flow chart of GABP neural network training process.

EMPIRICAL STUDY
To validate the GABP method, an empirical study is conducted in one ATC sector.There are 948 sets of sample data collected in total.A panel of 5 senior AT-COs gives their sample ranks facing the 5 variables (operational trafficability, complexity, safety, efficiency, and ATCO workload) based on observed clues from the historical video and audio records, including the time and space distribution of air traffic flow, the available sector airspace status impacted by meteorological hazards and military operation, the situation of vectoring and holding flights, the aircraft separation biases, the outputs of MSAW and STCA, the duration and frequency of air-ground communication radio calls, and etc., which consumes quite a long time (a huge workload in other words).Finally, 400 sets of sample data remain for further analysis as typical samples, in which 350 sets of sample data are randomly selected for network training, and the other 50 sets of sample data are for network testing.Both the training sample set and the testing sample set have the designed proportion of Step 1. Table 2 presents an example of the selected sample data.
As mentioned earlier, the number of nodes in the hidden layer is determined by H A B C < + + , which limits the value of H to be [5,14].By choosing different values of H with BP neural network, the most suitable number of nodes in the hidden layer which minimizes the total training errors is 5. So, there are 17 nodes in input layers, 5 nodes in the hidden layer, and 1 node in the output layer within the architecture of GABP neural network.
According to the method process, the GABP method is programmed with MATLAB 2014a.The initial value of BP neural network learning rate is 0.05, which is moderate considering that smaller learning rates will slow down the learning process and make it hard to be converged, and larger rates will speed up the learning process and make it unstable.The target on convergence accuracy of training errors is 0.00001, to acquire the better iteration results with higher accuracy.The target on training epochs is 500, and the number of validation checks is 6, which are large enough to get a stable, reliable result with reasonable training and validation process.Besides, the number of chromosomes in GA is 10, and the maximum iteration number is 50.Too many chromosomes and iteration steps will increase the optimization burden and calculation time.The crossover rate and mutation rate are 0.4 and 0.1, at a moderate level, respectively.Small crossover rates will lead the iteration into local optimum, while a large crossover rate will update the individuals with a high frequency and lose the advantages in existing chromosomes.Large mutation rates will update the chromosomes in a very random way, and small mutation rate will generate new individuals with low possibility.So both too small or large crossover rate and mutation rate will weaken the optimization process.
Meanwhile, since the ranks of operational performance of ATC sector are all integers from 1 to 5, the final results by GABP will be rounded before being exported.
On the other hand, to compare the accuracy of GABP with BP neural network, we process with traditional BP neural network training again with the same training sample set and find the best-trained BP neural network; then import the 50 sets of typical sample data normalized with Formula 12 into both the besttrained GABP and BP neural networks and export ranking results for testing.The testing errors, i.e., mean error, mean square error, maximum error, minimum error, and error probability, are all presented in Table 3.It is clear that the testing errors of GABP neural network are better than those of BP neural network in total.The mean error and mean square error of GABP neural network decrease by 44% and 32% with respect to BP neural network.There are 16 errors among all 50 sets of testing data by BP neural network, while there are only 9 errors out of 50 sets detected in GBAP neural network, so the error probability of BP neural network is 1.78 times of GABP neural network.This indicates that GABP neural network performs better than BP neural network and can assess operational performance of ATC sector with high accuracy.Besides, the evaluation result by GABP neural network is steadier than BP neural network, since the initial weights and thresholds are optimized by GA in GABP neural network, while in BP neural network, both the weights and thresholds are randomly assigned.Thus, GABP neural network can be further generalized for unknown data, which will qualify GABP neural network method with better reliability.Figure 3 and Figure 4 present the testing results and testing errors of GABP neural network.With the best-trained GABP neural network, the operational performance assessment of ATC sector can be made by importing the normalized real-time detected data.Alarms could be triggered when the evaluation results reach the value of 5.
In fact, an application system named Air Traffic Control Operational Performance Monitoring System (ATCOPMS), which has been developed and deployed at the Air Traffic Control Center of the Southwest Regional Air Traffic Management Bureau of Civil Aviation of China in Chengdu, could ensure the usability of the GABP neural network method by software update importing the best-trained GABP neural network for respective ATC sector.Data pools could be built up to collect real-time operation data, including integrated flight track information from ATC automation system, air traffic service message from automatic message switching system, and sky-talk records between ATCO and pilot from VHF voice communication system.With these data as input, ATCOPMS can output ATC operational performance indicator detection results within seconds, based on the real-time operation situation of all 17 indicators.Moreover, the comprehensive evaluation results on ATC operational performance could be output within minutes by some artificial intelligence methods including traditional BP neural network, according to the real-time operation situation [42].The mechanism is validated in Chengdu to be effective in the optimization of ATC operation strategies, taking on-duty roster for example, and airspace planning and utilization, taking flexible airspace usage with military side for example [40].Also, more positive contributions of the system could be predictable after the software updating for the application of the GABP neural network method.

CONCLUSIONS
Most of the existing studies on operational performance assessment of ATC sector are limited to a single side and cannot apply to real-time assessment at the frontline of air traffic service provider.To solve these issues, this paper constructs a quantitative detection index system with 5 variables and 17 indicators through expert investigation method based on the principles of engineering feasibility, scientific typicality, and operational practicability, which covers most of the related factors influencing operational performance of ATC sector, and provides an improved comprehensive evaluation method based on BP neural network optimizing the initial weights and thresholds by GA.On the one hand, by sorting out the existing studies, the multivariate detection index system accommodates operational trafficability, operational complexity, operational safety, operational efficiency, and ATCO workload, which has the characteristics of integration.Meanwhile, all indicators are settled by senior ATC experts, so that this index system can be applied to any ATC system with the characteristics of universality.
On the other hand, the GABP neural network method has higher accuracy and more stable generalization ability, which can be better suitable to operational performance assessment of ATC sector than the traditional BP neural network in terms of comparison of testing errors.
Another important feature is that, taking ATCOPMS in Chengdu for validation, since all the 17 indicators of the multivariate detection index system can be accessed in the operation site, the GABP neural network method could be realized by importing the best-trained neural network for respective ATC sector into application system for the frontline, which will improve the operation management efficiency by presenting real-time assessment result and essential alarm to air traffic service provider, avoiding fatigue and poor timeliness caused by traditional experience-based assessment.
To sum up, the proposed GABP method for operational performance assessment of ATC sector is improved in comprehensiveness by establishing an integrated and quantifiable detection index system, accuracy and reliability by optimizing BP neural network method with Genetic Algorithm, and practicability by updating related software module in application system for the frontline.Last but not least, it should be noted that the assessment results based on the proposed method are relevant only to the sectors from which the initial data have been gathered because of the limitation of the generalization ability of the neural network, which indicates the guidance of future studies.and suggestions on our draft paper.The research was partly financially supported by the National Science Foundation jointly with the Civil Aviation Administration of China (No. U1333202) and the Fundamental Research Funds for the Central Universities (No. NJ20140018).

~
are the weights for input-to-hidden and hidden-to-output during the p-th network training process.α k,p and β p are the thresholds of the k-th(k=1

Step 11 :
Terminate training Update weights and thresholds according to the training errors.When any of the targets on training errors' convergence accuracy, training epochs, and other validation check is reached, terminate training.

Figure 5
presents the network topology layout of the system.Triggered by the data mining based on ATCOPMS, the Air Traffic Control Center in Chengdu works out an operation management decision-making mechanism, probing the weaknesses objectively based on the operational performance indicator detection results and related comprehensive evaluation results.It then finds the reasons (solving problems in other words) based on the playback of related video and audio records from various angles, such as operation model, airspace status and sector configuration, military restriction, meteorological hazard, expertise level of ATCO.

Table 1 -
Multivariate detection index system for operational performance of ATC sector assessment .

Table 3 -
Testing errors of the best-trained GABP and BP neural network