CN114022212A - Civil aircraft direct operation cost prediction method based on flight time and seat number - Google Patents
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Abstract
The invention discloses a civil aircraft direct operation cost prediction method based on flight time and seat number, which comprises the following steps of S1: collecting flight schedule data of an airline company, and calculating a direct operation cost value of each airplane type flying on the airline by using a NASA05 method; s2: respectively taking the maximum value and the minimum value of the direct operation cost of the airplane calculated in the step S1 as the upper limit and the lower limit of an interval value of the direct operation cost of the airplane, and respectively taking the corresponding flight time as the upper limit and the lower limit of the interval value of the flight time; establishing a local regression prediction model of the direct operation cost interval of the civil aircraft by taking the direct operation cost of the aircraft as a dependent variable and the flight time and the seat number of the corresponding aircraft type as independent variables; s3: and solving model parameters in the regression prediction model of the civil aircraft direct operation cost interval. The method can predict the direct operation cost of the airplane, can be well adapted to different operating environments, and has relatively stable and reliable prediction results.
Description
Technical Field
The invention relates to the technical field of direct operation cost of civil airliners, in particular to a method for predicting the direct operation cost of a civil airliner based on flight time and seat number.
Background
The aviation industry is one of the high cost, low profit industries typical of the world. Therefore, starting from the design of the model, most aircraft manufacturers place a great deal on the operating costs of the various models. By accurately estimating the operation cost, an aircraft manufacturer can optimize the design of aircraft models, perform competition comparison among the aircraft models, determine the aircraft model suitable for a specific airline in the future, and also can select a suitable accessory for the aircraft model to provide economic analysis. Therefore, accurate calculation of the operating costs of civil aircraft is of great importance both for the aircraft manufacturer and for the airline companies that operate these aircraft models in the future. In order to accurately estimate the operating cost of a civil aircraft, aircraft manufacturers must simulate the operating environment in which the aircraft will operate in the future, including economic, financial, aircraft performance factors, and the like. And then estimating the operation cost of the civil aircraft by using the related cost item model. Since this operating cost is closely related to the aircraft type, it is defined by both the aircraft engineer and the economic analyst as a direct operating cost, with the major cost items including flight crew cost, fuel/oil cost, insurance cost, rental cost, maintenance cost, depreciation/amortization cost, and passenger service cost.
The key to estimating the Direct Operating Cost (DOC) of a civil aircraft is determining how to build a DOC model. The American Air Transport Association (Air Transport Association of America) and the European airline Association (Association of European Airlines) defined cost projects for direct operating costs in 1967 and 1988, respectively. A model of several typical cost items is then constructed based on the type of aircraft in operation. However, the models of these typical cost items are mainly constructed on the basis of the models of the old models, and with the emergence of new-generation models, the technical performance of these new models is significantly improved, and the DOC estimation model based on the old models becomes inaccurate. Furthermore, the estimation models of the associated cost items typically have a complex mathematical structure, requiring a large number of input parameters. Therefore, it is difficult to apply the method to the economic analysis of civil aircraft models in the design stage.
In order to improve the estimation model, more recent researches are carried out to find out relevant factors influencing the DOC value of the airplane when the civil airplane flies. Research typically attempts to relate the number of seats of a civil aircraft model to the flight distance of that type of aircraft on the flight line, and then build a regression model. The model is mainly used for estimating the DOC value of the airplane model in the design stage and determining the DOC average value of the airplane model in the future under the given operation environment.
The innovative models significantly simplify the input parameters for estimating the DOC value, making the estimation process simpler and more flexible. However, the DOC model is difficult to reflect the influence of uncertainty and fluctuation characteristics existing in actual operation on the DOC of the airplane, such as (1) the influence of external conditions of the operation environment, such as wind speed and wind direction, on fuel/oil consumption in flight; (2) the pilot's ability to operate the aircraft being piloted, such as because the pilot's ability to operate is low and requires additional fuel/oil. This uncertainty and volatility makes the DOC value impossible to express with a real number, i.e. this pattern leads to inaccuracies in the estimation and to a high risk of aircraft-related decisions.
Disclosure of Invention
Aiming at the existing problems, the invention aims to provide a civil aircraft direct operation cost prediction method based on flight time and seat number, which can be well adapted to different operating environments and has relatively stable and reliable prediction results.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the civil aircraft direct operation cost prediction method based on flight time and seat number is characterized by comprising the following steps,
s1: collecting flight schedule data of an airline company, and calculating a direct operation cost value of each airplane type flying on the airline by using a NASA05 method;
s2: respectively taking the maximum value and the minimum value of the direct operation cost of the airplane calculated in the step S1 as the upper limit and the lower limit of an interval value of the direct operation cost of the airplane, and respectively taking the corresponding flight time as the upper limit and the lower limit of the interval value of the flight time; establishing a local regression prediction model of the direct operation cost interval of the civil aircraft by taking the direct operation cost of the aircraft as a dependent variable and the flight time and the seat number of the corresponding aircraft type as independent variables;
s3: and solving model parameters in the regression prediction model of the civil aircraft direct operation cost interval.
Further, the model used by the NASA05 method in step S1 in calculating the direct operation cost of the aircraft includes the cost of flight crew, the cost of fuel and oil, the cost of insurance premium, the cost of rent, the cost of maintenance, the cost of depreciation and distribution, the cost of service of passengers, and the cost of take-off and landing; the finally obtained direct operation cost of the airplane is the sum of the costs solved by the eight models;
the calculation method of each cost respectively comprises the following steps:
aircraft unit cost FCC ═ AF X K × (MTOGW)0.4×BH；
Fuel and lubricant costs FC ═ FP × (BF)N-C+BFC) X DEP; wherein:
TOGW＝OEW+225×AS×LF+1.5×6.5×FPD，
the premium cost IC is 0.0056 × AP;
the rent cost RC is 0.0835 multiplied by AP;
the maintenance cost MC ═ AMC + EMC, where,
AMC＝L[(WREF)0.72118(FH)0.46050(DEP)0.32062(NAC)0.20700(1+Rin)-0.43177]，
EMC＝L[(T)0.89650(NE)0.92340(FH)0.15344(DEP)0.37535(NAC)0.4429(1+Rout)-0.34704]，
L＝ST×1.73×(CF)(MF)(ET)：
depreciation amortization cost
Passenger service cost PSC 1.6 × 55500 × (N)FA) Wherein
Cost of take-off and landing LF 0.00147 × (ST) (RF) (MLW) (DEP);
wherein K is a course factor, AF is an airline factor, MTOGW is the maximum gross takeoff weight, and BH is the annual gear hours; FP is fuel price, BFN－CFor fuel consumption in the non-cruise phase, BFCFor cruise section fuel consumption, DEP is the number of take-offs and landings per year; SFC is the pound hour Thrust of the airplane during takeoff, Thrust is the total Thrust of the airplane during takeoff, TOGW is the total weight of the airplane during takeoff, OEW is the empty weight of the airplane during use, AS is the number LF of seats available to the airplane AS the seating rate, FPD is the fuel/lubricating oil consumption of the airplane in the flight segment, W is the weight of the airplane in the beginning stage of cruising, R is the flight segment distance of the airplane, SFC is the pound hour Thrust of the airplane during cruising, V is the average cruising speed of the airplane, and L/D is the lift-drag ratio of the airplane; AP is the purchase price of the airline company when purchasing the airplane; rinIs the ratio of maintenance in the company, RoutFor off-company maintenance ratio, ST is service type, ET is engine type, MF is airplane type factor, CF is airline cost factor, T is thrust of a power plant under standard atmospheric conditions at sea level, NE is number of engines per airplane, AMC is airframe maintenance cost, EMC is engine maintenance cost, L is a constant, W is engine maintenance costREFFor reference weight, equal to the minimum used empty weight minus the dry weight of the engine, FH is the number of flight hours for the fleet over the year, and NAC is the yearNumber of airplanes of the airplane share team; RV is residual value, and DP is depreciation age limit; n is a radical ofFAIs a null multiplier; RF is the course factor and MLW is the maximum landing weight.
Further, the civil aircraft direct operation cost section regression prediction model described in step S2 is specifically Y ═ β0+β1X1+β2X2Wherein Y represents the number of intervals of direct running cost, X1Denotes the number of seats, X2Number of intervals, beta, representing time of flight0，β1，β2Are regression coefficients, i.e. model parameters.
Further, the specific operation of step S3 includes the following steps,
s301: solving a midpoint sequence and a radius sequence of an interval value of the direct operation cost of the airplane and an interval value of the flight time by using an interval midpoint regression method based on a midpoint radius method;
s302: obtaining regression parameters of the midpoint sequence by adopting a least square method, obtaining a midpoint regression equation, and calculating a midpoint predicted value;
s303: establishing a relation between a dependent variable and an independent variable of a radius sequence based on error transmission, and calculating a predicted value of the radius;
s304: and adding or subtracting the predicted value of the radius from the predicted value of the midpoint to obtain the upper and lower boundaries of the interval, and obtaining the predicted value of the interval.
Further, the specific operation of step S301 includes the steps of,
s3011: if E ═ E1，e2，...，enIs a p +1 dimensional dataset of samples n, for any eiE, which can be expressed as Ei＝(xi1，xi2，...，xip，yi)，
Wherein the content of the first and second substances,
is the jth interval independent variable XiAnd has an observation of
yiIs an observation of the dependent variable Y of the interval, and has
S3012: let jth interval independent variable observe xijRespectively has a midpoint and a radius of
And
then
S3013: making interval dependent variable observe yiRespectively has a midpoint and a radius of
And
then
Further, the specific operation of step S302 includes the following steps,
s3021: let beta be0，β1，...，βpEstablishing an interval dependent variable Y for the regression coefficient of the midpoint sequence and epsilon as an error termcAnd interval independent variable
Common linear regression model in between
S3022: converting the ordinary linear regression model in step S3021 into a regression equation by the least square method
Further, the specific operation of step S303 includes the following steps,
s3031: dividing the error term in the ordinary linear regression model in step S3021 into several random terms corresponding to the observed error of each independent variable, the ordinary linear regression model in step S3021 may be expressed as Y ═ f (X)c+Xr) In the formula (I), wherein,
representing observed random errors and obeying
S3032: obtaining Y ═ f (X) using a second order taylor expansionc+Xr) Is expressed as a second order Taylor expansion
The expected value and variance of the function, which can be obtained from the second-order taylor expansion, are denoted as e (y) ═ f (X), respectivelyc)，
In the formula (I), the compound is shown in the specification,
to represent
And
a correlation coefficient therebetween, and
and
are independent of each other;
s3033: rewriting the variance formula in step S3032 to
S3034: according to the principle of error propagation, the variance of the dependent variable Y, i.e. YrThus, for each observation of the sequence of radii
Using in conjunction with the regression equation in step S3022
Calculating the variance of the dependent variable;
s3035: the section dependent variable which can be predicted from the calculation result of step S3034
Wherein
The invention has the beneficial effects that:
the DOC value and the corresponding flight time of the civil aircraft flying on the airline are represented by the interval number, the seat number of the passenger plane is combined, the DOC of the civil aircraft on the airline is used as a dependent variable, and the seat number and the flight time on the airline are used as independent variables to construct a civil aircraft direct operation cost interval regression prediction model; corresponding DOC interval values of flight of several specific airplane types on an air route are calculated by collecting real operation data of an airline company and using a model (NASA 05) published by the National Aeronautics and Space Administration (NASA) in 2005, and then a method based on error propagation is provided for calculating parameters of a regression model. The model is tested for many times by using three different data sets, so that the result of the proposed model is close to that of the NASA05 method in the aspect of evaluation indexes of regression in the use interval, and the prediction result is relatively stable and reliable; sensitivity analysis shows that the method provided by the invention can be well adapted to different economic environments.
Drawings
FIG. 1 shows regression relationships between time of flight and DOC for different samples in simulation experiments.
FIG. 2 is a comparison graph of three regression prediction results and observed values in a simulation experiment of the present invention.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the following further describes the technical solution of the present invention with reference to the drawings and the embodiments.
The civil aircraft direct operation cost prediction method based on flight time and seat number comprises the following steps,
s1: collecting flight schedule data of an airline company, and calculating a direct operation cost value of each airplane type flying on the airline by using a NASA05 method;
specifically, the model adopted by the NASA05 method when calculating the direct operation cost of the airplane comprises the cost of flight units, the cost of fuel oil and lubricating oil, the cost of insurance fee, the cost of rent, the cost of maintenance, the cost of depreciation and allocation, the cost of service of passengers and the cost of taking off and landing; the computational model for each cost term in the NASA05 method is based on Form 41 files published by the Department of Transportation (DOT), and the model was proposed by Harris in 2005 using nearly all U.S. 1999 civil aviation operating data. Thus, it may represent an average level of industry operational costs. The relevant parameters for all models are shown in table 1 below.
TABLE 1 NASA05 model-related parameters
The calculation formulas of the eight models in NASA05 are shown in table 2 below.
TABLE 2 calculation formulas of eight estimation models
Further, S2: respectively taking the maximum value and the minimum value of the direct operation cost of the airplane calculated in the step S1 as the upper limit and the lower limit of an interval value of the direct operation cost of the airplane, and respectively taking the corresponding flight time as the upper limit and the lower limit of the interval value of the flight time; establishing a local regression prediction model of the direct operation cost interval of the civil aircraft by taking the direct operation cost of the aircraft as a dependent variable and the flight time and the seat number of the corresponding aircraft type as independent variables; the regression prediction model of the civil aircraft direct operation cost interval is specifically Y ═ beta0+β1X1+β2X2Wherein Y represents the number of intervals of direct running cost, X1Denotes the number of seats, X2Number of intervals, beta, representing time of flight0，β1，β2Are regression coefficients, i.e. model parameters.
Further, S3: and solving model parameters in the regression prediction model of the civil aircraft direct operation cost interval.
Specifically, S301: solving a midpoint sequence and a radius sequence of an interval value of the direct operation cost of the airplane and an interval value of the flight time by using an interval midpoint regression method based on a midpoint radius method;
s302: obtaining regression parameters of the midpoint sequence by adopting a least square method, obtaining a midpoint regression equation, and calculating a midpoint predicted value;
s303: establishing a relation between a dependent variable and an independent variable of a radius sequence based on error transmission, and calculating a predicted value of the radius;
s304: and adding or subtracting the predicted value of the radius from the predicted value of the midpoint to obtain the upper and lower boundaries of the interval, and obtaining the predicted value of the interval.
More specifically, the specific operation of step S301 includes the following steps:
s3011: if E ═ E1，e2，...，enIs a p +1 dimensional dataset of samples n, for any eiE, which can be expressed as Ei＝(xi1，xi2，...，xip，yi)，
Wherein the content of the first and second substances,
is the jth interval independent variable XjAnd has an observation of
yiIs an observation of the dependent variable Y of the interval, and has
S3012: let jth interval independent variable observe xijRespectively has a midpoint and a radius of
And
then
S3013: making interval dependent variable observe yiRespectively has a midpoint and a radius of
And
then
The specific operation of step S302 includes the following steps:
s3021: let beta be0，β1，...，βpEstablishing an interval dependent variable Y for the regression coefficient of the midpoint sequence and epsilon as an error termcAnd interval independent variable
Common linear regression betweenModel (model)
S3022: converting the ordinary linear regression model in step S3021 into a regression equation by the least square method
The specific operation of step S303 includes the following steps:
s3031: the earliest interval analysis was proposed from an error propagation perspective, with the radius values actually reflecting the errors of the intervals. Thus, based on equation (17), the regression error term is divided into several random terms, and equation (17) may be re-expressed as the observed error for each independent variable
Y＝f(Xc+Xr) (19)
In the formula (I), the compound is shown in the specification,
representing observed random errors and obeying
S3032: obtaining Y ═ f (X) using a second order taylor expansionc+Xr) Is expressed as a second order Taylor expansion
The expected value and variance of the function can be obtained from equation (20), in particular
E(Y)＝f(Xc) (21)
In the formula (I), the compound is shown in the specification,
to represent
And
a correlation coefficient therebetween, and
and
are independent of each other;
s3033: the variance formula in the formula (22) is rewritten as
S3034: according to the principle of error propagation, the variance of the dependent variable Y, i.e. YrThus, for each observation of the sequence of radii
Combining formula (18), calculating the variance of the dependent variable using formula (24)
S3035 estimating the predicted section dependent variable according to the calculation result of the step S3034
Wherein
Simulation experiment:
in the invention, three indexes, namely an interval mean square error Root (RMSE), average Accuracy (AR) and an observation interval average ratio (PCO) containing a prediction interval are selected to evaluate the prediction result of the prediction method.
Assuming a total of n observation samples, yiIs the sample interval of the ith observation sample,
the prediction interval of the ith observation sample is
Is provided with
The width of the interval formed by the elements contained in common in the sample interval and the prediction interval of the ith observation sample,
width of a section formed by all elements included in the sample section and the prediction section of the i-th observation sample, ω (y)i)、
The width of the sample interval and the width of the prediction interval of the ith observation sample respectively are
Based on actual operation data of a certain domestic airline company for two months, the DOC value of each record is calculated by adopting the existing NASA05 method. 780 data samples of different airlines operated by the 10 airlines are collected, from which three test data sets are formed. Finally, the prediction method of the invention is used for calculation and result verification.
The model numbers of the airplanes used in the collected flight schedule are counted according to the symbols and symbolic descriptions listed in table 1, and the performance parameters of 10 models of airplanes obtained by referring to the airplane manual are shown in table 3 below.
TABLE 3 sample model data
The economic environment is set according to the current economic status and the collected flight schedule as shown in table 4 below.
Table 4 table for taking value of operating environment condition
To verify the validity of the model proposed by the present invention, six data sets were constructed as follows.
(1) Data set I consisted of 130 pieces of data generated by run B738, 90 were randomly chosen for model training and the remaining 40 (data set IV) were used for predictive testing.
(2) Data set II consists of 613 pieces of data generated by operating all narrow body models (a319, a320, a321, B733, B738, and B752). Of these 430 were randomly selected for training the model and the remaining 183 (dataset V) were used for the prediction test.
(3) Data set III consists of 852 data generated by operating all models, where 596 were randomly selected for training the model and the remaining 256 (data set VI) were used for predictive testing.
For simplicity of illustration, the corresponding regression based on the three datasets described above may be referred to as regression models I, II and III, respectively.
According to the calculation methods of the formula (22) and the formula (23), the midpoint sequence of the flight time and the direct operation cost is subjected to regression analysis, and the linear relation of the samples is shown in the attached figure 1, wherein (a) is the regression relation between the flight time of the regression model I and the DOC, (b) is the regression relation between the flight time of the model regression model II and the DOC, and (c) is the regression relation between the flight time of the model regression model III and the DOC.
As can be seen from fig. 1, the flight times of the three types of sample points and the direct operation cost have strong linear relationships, and therefore, the linear regression models are respectively established as follows:
when the regression model I carries out regression prediction, the sample seat numbers are the same value and have no linear relation with the direct running cost, and the sample seat numbers are removed when the regression model I is established. In the formula
A midpoint value representing the time of flight,
the median value of the seat number is represented, and the coefficients of the independent variables in the two intervals are positive numbers as can be seen from the three regression models, namely, the seat number and the flight time are positively correlated with the direct operation cost and are consistent with the reality.
With reference to equation (24), three interval regression models were calculated, and evaluation indexes of the three models were calculated using equations (25) to (27). The results are shown in Table 5 below. All RMSE in the three models remained at a low level. Furthermore, as the data capacity expands as the airplane model class increases in the sample, both AR and PCO decrease. The reason is that the larger number of interval data broadens a certain number of regression intervals, so that the prediction intervals intersect with the corresponding observation intervals, or reduces the intersection degree of the certain number of prediction intervals and the observation intervals thereof, so as to ensure that more data sample observation intervals intersect with the prediction intervals. But the index values generally remained at a relatively good level, indicating that the constructed model had a good fitting effect.
TABLE 5 evaluation index values of regression training samples under different samples
To verify the prediction accuracy of the proposed model, the prediction effects produced by the three regression models are compared to the corresponding observations using data sets IV, V and VI. Table 6 below lists the correlation indices between all prediction intervals and observation intervals, including the average relative error and the single maximum error for the left and right endpoints and the maximum error for the interval length.
TABLE 6 comparison of regression results in different cases
As can be seen from table 6, all relevant indices remained at a low level. This indicates that the predictive model of the present invention is suitable for predicting DOC values for a given seat number and its time of flight. However, the results in model III were reduced compared to using both model I and model II. The reason is that the wide model on the long haul route is added to the data sample, so that both DOC and time of flight are higher than the narrow model. This results in more discrete data relationships in the sample and results in relatively poor regression performance. This is also demonstrated by the single maximum error indicator and the interval length maximum error indicator.
In order to facilitate comparative analysis, the observation values and the prediction results of the three regression models are further drawn and analyzed. The flight time is used as an abscissa, the DOC value is used as an ordinate to draw a rectangular chart, the prediction results of the three regression models on the observed value are shown in the attached figure 2, wherein the graphs (a), (b) and (c) respectively correspond to the comparison of the regression model I, the regression model II, the regression model III and the observed value. As can be seen from FIG. 2, the prediction results of the three regression models are very close to the observed values, and the coincidence degree has no obvious deviation.
The evaluation index values of the prediction samples were calculated, and the results are shown in table 7 below. There is no apparent regularity in RMSE due to the different sample volumes of the three data sets. The RMSE values remained low, indicating a good fit. However, as the model considers more airplane types, the values of both AR and PCO decrease as the number of airplane types increases and the sample capacity of the three regression problems increases. The reason is similar to table 5.
TABLE 7 evaluation index values of regression training samples under different samples
In summary, the predictive model of the present invention is validated and feasible in a given operating environment.
Further, the change of the operating environment is simulated to verify the adaptability of the model provided by the invention. The DOC values were calculated using the NASA05 model by adjusting the operating environment parameter values 20% down and 20% up, respectively, and 3 regression analyses were performed again. The relevant indices are shown in tables 8 and 9 below.
TABLE 8 training sample index value after 20% market environmental parameter adjustment
TABLE 9 training sample index value with 20% upregulated market environmental parameters
The index result is similar to the index calculation result in the table 5, the correlation rule is verified, and the fitting effect of the model in the invention under different operating environments is similar, which also shows that the model can adapt to the change of the operating environment.
Data sets IV, V, VI were also used for predictive analysis. The index value of the operating environment is respectively adjusted down by 20 percent and up by 20 percent. The predicted results are shown in tables 10 and 11 below.
TABLE 10 predicted results after a 20% reduction in market environmental parameters
TABLE 11 predicted results of 20% increase in market environmental parameters
The result of regression prediction is closer to the observed value. The prediction results of different models have the same change rule as the above, and the prediction effect of the models under different conditions is relatively stable.
Table 10 shows the results of comparisons between all prediction interval and observation interval data, including the average relative error and the single maximum error for the left and right endpoints and the maximum error for the interval length; the result shows that the prediction results of the three regression models are close to the observed value, and the prediction results of the regression models are still relatively accurate after the market environment parameters are reduced by 20%.
Table 11 shows the comparative effect between all prediction intervals and observation intervals, including the average relative error and the single maximum error of the left and right endpoints and the maximum error of the interval length; the result shows that the prediction results of the three regression models are close to the observed value, and the prediction results of the regression models are still relatively accurate after the market environment parameters are increased by 20%.
Comparing the analysis results of tables 10 and 11 with the analysis results of table 6, no significant difference in mean relative error was found, indicating that the model is generally relatively stable under this market condition. However, the single maximum error and the maximum interval length error fluctuate, which indicates that different routes are influenced by different market environments to different degrees, and the predicted values slightly change under different market conditions. Thus, changes in aircraft type and course cause these two indicators to change.
RMSE, AR and PCO also remained at relatively good levels compared to table 7. From the AR and PCO perspectives, the results of tables 12 and 13 show an overall descending pattern, consistent with the results of table 7. From the perspective of RMSE, the three values changed slightly after recalculating the market parameters. The change is that the recalculated data set deviates closer to or further from the regression line. The three RMSE values generated by the three models decreased overall after a 20% reduction in the parameters as the relationship between these recalculated data became closer to the linear regression line.
TABLE 12 index values for predicted samples with 20% parameter reduction
TABLE 13 index values for predicted samples with 20% increase in parameter
According to the analysis, the conclusion can be drawn that the proposed model has good prediction effect under different operation environments, and the prediction result is relatively stable and reliable. The model can adapt to various environmental conditions.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (7)
1. The civil aircraft direct operation cost prediction method based on flight time and seat number is characterized by comprising the following steps,
s1: collecting flight schedule data of an airline company, and calculating a direct operation cost value of each airplane type flying on the airline by using a NASA05 method;
s2: respectively taking the maximum value and the minimum value of the direct operation cost of the airplane calculated in the step S1 as the upper limit and the lower limit of an interval value of the direct operation cost of the airplane, and respectively taking the corresponding flight time as the upper limit and the lower limit of the interval value of the flight time; establishing a local regression prediction model of the direct operation cost interval of the civil aircraft by taking the direct operation cost of the aircraft as a dependent variable and the flight time and the seat number of the corresponding aircraft type as independent variables;
s3: and solving model parameters in the regression prediction model of the civil aircraft direct operation cost interval.
2. The method for predicting civil aircraft direct operation cost based on flight time and seat number as claimed in claim 1, wherein the NASA05 method in step S1 adopts the model for calculating the direct operation cost of the aircraft, which comprises the cost of flight crew, the cost of fuel and oil, the cost of insurance fee, the cost of rent deposit, the cost of maintenance, the cost of depreciation and contribution, the cost of service of passengers and the cost of taking off and landing; the finally obtained direct operation cost of the airplane is the sum of the costs solved by the eight models;
the calculation method of each cost respectively comprises the following steps:
aircraft unit cost FCC ═ AF X K × (MTOGW)0.4×BH；
Fuel and lubricant costs FC ═ FP × (BF)N-C+BFC) X DEP; wherein:
TOGW＝OEW+225×AS×LF+1.5×6.5×FPD，
the premium cost IC is 0.0056 × AP;
the rent cost RC is 0.0835 multiplied by AP;
the maintenance cost MC ═ AMC + EMC, where,
L＝ST×1.73×(CF)(MF)(ET)；
depreciation amortization cost
Passenger service cost PSC 1.6 × 55500 × (N)FA) Wherein
Cost of take-off and landing LF 0.00147 × (ST) (RF) (MLW) (DEP);
wherein K is a course factor, AF is an airline factor, MTOGW is the maximum gross takeoff weight, and BH is the annual gear hours; FP is fuel price, BFN-CFor fuel consumption in the non-cruise phase, BFCFor cruise section fuel consumption, DEP is the number of take-offs and landings per year; SFC is the pounds hour Thrust of the airplane during takeoff, Thrust is the total Thrust of the airplane during takeoff, TOGW is the total weight of the airplane during takeoff, OEW is the empty weight of the airplane, AS is the number of seats available for the airplane LF is the seating rate, FPD is the fuel/lubricating oil consumption of the airplane in the flight segment, and W is the cruise switchThe weight of the airplane in the initial stage, R is the flight distance of the airplane, SFC is the pound hour thrust of the airplane during cruising, V is the average cruising speed of the airplane, and L/D is the lift-drag ratio of the airplane; AP is the purchase price of the airline company when purchasing the airplane; rinIs the ratio of maintenance in the company, RoutFor off-company maintenance ratio, ST is service type, ET is engine type, MF is airplane type factor, CF is airline cost factor, T is thrust of a power plant under standard atmospheric conditions at sea level, NE is number of engines per airplane, AMC is airframe maintenance cost, EMC is engine maintenance cost, L is a constant, W is engine maintenance costREFFor reference weight, equal to the minimum used empty weight minus the dry weight of the engine, FH is the number of flight hours of the fleet for the year, and NAC is the number of aircraft in the fleet for that year; RV is residual value, and DP is depreciation age limit; n is a radical ofFAIs a null multiplier; RF is the course factor and MLW is the maximum landing weight.
3. The civil aircraft direct operation cost prediction method based on flight time and seat number according to claim 2, wherein the civil aircraft direct operation cost interval regression prediction model in step S2 is specifically Y ═ β0+β1X1+β2X2Wherein Y represents the number of intervals of direct running cost, X1Denotes the number of seats, X2Number of intervals, beta, representing time of flight0，β1，β2Are regression coefficients, i.e. model parameters.
4. The civil aircraft direct operation cost prediction method based on time-of-flight and seat number according to claim 3, characterized in that the concrete operation of step S3 includes the following steps,
s301: solving a midpoint sequence and a radius sequence of an interval value of the direct operation cost of the airplane and an interval value of the flight time by using an interval midpoint regression method based on a midpoint radius method;
s302: obtaining regression parameters of the midpoint sequence by adopting a least square method, obtaining a midpoint regression equation, and calculating a midpoint predicted value;
s303: establishing a relation between a dependent variable and an independent variable of a radius sequence based on error transmission, and calculating a predicted value of the radius;
s304: and adding or subtracting the predicted value of the radius from the predicted value of the midpoint to obtain the upper and lower boundaries of the interval, and obtaining the predicted value of the interval.
5. The civil aircraft direct operation cost prediction method based on time of flight and seat number according to claim 4, characterized in that the specific operation of step S301 comprises the following steps,
s3011: if E ═ E1，e2，...，enIs a p +1 dimensional dataset of samples n, for any eiE, which can be expressed as Ei＝(xi1，xi2，...，xip，yi)，
Wherein the content of the first and second substances,
is the jth interval independent variable XjAnd has an observation of
yiIs an observation of the dependent variable Y of the interval, and has
S3012: let jth interval independent variable observe xijRespectively has a midpoint and a radius of
And
then
S3013: making interval dependent variable observe yiRespectively has a midpoint and a radius of
And
then
6. The civil aircraft direct operation cost prediction method based on time-of-flight and seat number according to claim 5, characterized in that the concrete operation of the step S302 comprises the following steps,
s3021: let beta be0，β1，...，βpEstablishing an interval dependent variable Y for the regression coefficient of the midpoint sequence and epsilon as an error termcAnd interval independent variable
Common linear regression model in between
S3022: converting the ordinary linear regression model in step S3021 into a regression equation by the least square method
7. The civil aircraft direct operation cost prediction method based on time-of-flight and seat number according to claim 6, characterized in that the specific operation of step S303 comprises the following steps,
s3031: dividing the error term in the ordinary linear regression model in step S3021 into several random terms corresponding to the observed error of each independent variable, the ordinary linear regression model in step S3021 may be tabulatedUp to Y ═ f (X)c+Xr) In the formula (I), wherein,
representing observed random errors and obeying
S3032: obtaining Y ═ f (X) using a second order taylor expansionc+Xr) Is expressed as a second order Taylor expansion
The expected value and variance of the function, which can be obtained from the second-order taylor expansion, are denoted as e (y) ═ f (X), respectivelyc)，
In the formula (I), the compound is shown in the specification,
to represent
And
a correlation coefficient therebetween, and
and
are independent of each other;
s3033: rewriting the variance formula in step S3032 to
S3034: according to the principle of error propagation, the variance of the dependent variable Y, i.e. YrThus, for each observation of the sequence of radii
Using in conjunction with the regression equation in step S3022
Calculating the variance of the dependent variable;
s3035: the section dependent variable which can be predicted from the calculation result of step S3034
Wherein
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