Engine fuel consumption calculation method based on aviation transport carbon emissions

Abstract

The application belongs to the field of aviation technology, and proposes an engine fuel consumption calculation method based on aviation transportation carbon emission, the main scheme is: obtaining interval fuel consumption data and its static and dynamic influence factors; taking the minimum fuel consumption fitting error as the target, selecting the network structure combined with width and depth, and using the wide component in the network structure to obtain the linear relationship between the static influence factors and the interval fuel consumption data, and simultaneously using the deep component in the network structure to determine the nonlinear relationship between the flight profile and the interval fuel consumption data; based on the linear relationship and the nonlinear relationship, the interval fuel consumption function of any flight profile is constructed; in the cruising stage, the interval fuel consumption function is subjected to interpolation approximation processing by using the monotone interpolation method, so that the interval fuel consumption function is continuous and has continuous derivative, and the interval fuel consumption function after the interpolation approximation processing is differentiated to calculate, so as to obtain the instantaneous fuel consumption function of any given point; based on the instantaneous fuel consumption function, the flight attitude of the optimal fuel efficiency in the cruising stage is identified.

Description

Technical Field

[0001] This invention relates to the field of aviation technology, and in particular to a method for calculating engine fuel consumption based on carbon emissions from air transport. Background Technology

[0002] According to the ICAO carbon emission calculation method, there is a combustion coefficient of 3.16 between fuel and carbon emissions, meaning that 3.16 tons of CO2 are produced from 1 ton of fuel consumption. Therefore, estimating fuel consumption is the core of the carbon emission accounting process.

[0003] Accurate calculation of aviation emissions is fundamental to identifying the factors influencing aviation carbon emissions and exploring emission reduction methods. Existing carbon emission accounting methods can be broadly divided into two categories. One type uses macro-statistical activity level data combined with corresponding emission factors, such as aviation kerosene consumption, LTO (takeoff and landing) cycles, and transport turnover. While the calculation process and data collection are relatively simple, there is a time lag in the calculation. Moreover, this macro-statistical data is usually only available at the national level, with a lag of one to two years, making it difficult to grasp the changing trends of aviation CO2 emissions at important points in time. In addition, this method is limited by the uncertainty and applicability of the calculation results. Factors affecting aviation CO2 emissions, such as fuel type, aircraft model, aircraft age, engine model, aircraft load, flight distance, and LTO cycles, are not adequately considered (Lyu et al., 2023).

[0004] Another approach employs a bottom-up (Fan et al., 2011; Yang et al., 2020; Yang et al., 2023) or top-down (Zhou et al., 2016; Yu et al., 2020) method based on fuel consumption. This method estimates carbon emissions by collecting CO2 coefficients for various types of aircraft at different flight phases, considering key factors such as flight, aircraft, mileage, origin, and destination. Although this calculation method is considered more convenient and practical and has been more widely used in existing research, its uncertainties warrant consideration. On the one hand, the actual flight distances between the same pair of cities can vary significantly, and a constant correction coefficient based on route length cannot adequately capture all inconsistencies. Furthermore, fuel consumption for the same aircraft model can vary considerably due to factors such as aircraft age, weight, configuration, and engine (Yang et al., 2020). Therefore, this method can only roughly estimate aviation carbon emissions from different origin-destination (OD) flows, and its accuracy needs further improvement. Summary of the Invention

[0005] The purpose of this invention is to provide an engine fuel consumption calculation method based on carbon emissions from air transport. This method can construct an interval fuel consumption function for any flight profile using existing flight profile data and interval fuel consumption data for different flight phases through a wide-depth combined network structure. Then, based on the interval fuel consumption function, an accurate instantaneous fuel consumption function for any given point can be obtained. Finally, the optimal fuel efficiency flight attitude during the cruise phase can be identified through the accurate instantaneous fuel consumption function, thereby enabling the aircraft to maintain the optimal fuel efficiency flight attitude during the cruise phase and reduce fuel consumption during the cruise phase.

[0006] The technical solution adopted by this invention to solve its technical problem is as follows:

[0007] The method for calculating engine fuel consumption based on carbon emissions from air transport includes the following steps:

[0008] Obtain flight profiles and interval fuel consumption data for different flight phases within the flight profiles;

[0009] Obtain the static and dynamic influencing factors associated with aircraft interval fuel consumption data;

[0010] With the goal of minimizing the fuel consumption fitting error, a wide-depth combined network structure is selected. The wide components in the network structure are used to obtain the linear relationship between static influencing factors and interval fuel consumption data. At the same time, the deep components in the network structure are used to capture the nonlinear characteristics of dynamic influencing factors, and the nonlinear characteristics are used to determine the nonlinear relationship between flight profile and interval fuel consumption data.

[0011] Construct an interval fuel consumption function for arbitrary flight profiles based on linear and nonlinear relationships;

[0012] During the cruise phase, the interval fuel consumption function is approximated by monotonic interpolation, making the interval fuel consumption function continuous and having continuous derivatives. The derivative of the interval fuel consumption function after interpolation is calculated to obtain the instantaneous fuel consumption function at any given point.

[0013] The flight attitude with optimal fuel efficiency during the cruise phase is identified based on the instantaneous fuel consumption function.

[0014] As a further optimization, ADS-B data was used to obtain flight profiles and interval fuel consumption data for different flight phases within the flight profiles.

[0015] As a further optimization, the static influencing factors associated with the aircraft's interval fuel consumption data include: aircraft type, aircraft age, wingspan empty weight, and maximum takeoff weight;

[0016] The dynamic influencing factors associated with the aircraft's inter-regional fuel consumption data include: flight altitude and flight speed.

[0017] As a further optimization, the method of using wide components in the network structure to obtain the linear relationship between static influencing factors and interval fuel consumption data refers to:

[0018] By using a wide component to perform linear combination calculations on static influencing factors and adding a bias, the linear relationship between static influencing factors and interval fuel consumption data is obtained, expressed as: , The calculation formula is:

[0019] ,

[0020] in, This represents the end time corresponding to the start time being 0 in the interval fuel consumption. This represents the set of static influencing factors. include One static influencing parameter, , This represents the first static influence parameter. This indicates the second static influencing factor. Indicates the first One static influencing factor, This represents the input vector of the wide component. Include dimensional features, Represents the model parameters of the wide component. , This represents the first model parameter of the wide component. This represents the second model parameter of the wide component. The wide component represents the first Each model parameter This indicates the bias term.

[0021] As a further optimization, the flight altitude is represented as a time series of flight altitudes, i.e.: The flight speed is represented as a flight speed time series, i.e.: ;

[0022] Obtain the Fourier coefficients of the flight altitude time series Fourier coefficients of flight speed time series .

[0023] As a further optimization, before using deep components in the network structure to capture the nonlinear characteristics of dynamic influencing factors and using these nonlinear characteristics to determine the nonlinear relationship between the flight profile and interval fuel consumption data, the method further includes:

[0024] Fourier coefficients of the flight altitude time series Fourier coefficients of flight speed time series All dimensions are set to 100, corresponding to the truncation and expansion of the flight altitude time series and flight speed time series.

[0025] As a further optimization, when the flight altitude time series and flight speed time series are truncated and expanded, the truncation radius of the flight altitude time series is expressed as: The cutoff radius of the flight velocity time series is expressed as: ;

[0026] For those with For a specific aircraft, assuming a flight's altitude and speed are respectively... and The other flight's altitude and speed were respectively and And since the fuel consumption function for these two flights is continuous, then: in any interval In the function space on, such that and exist The above approximation is used here. At this point, the flight altitude time series and flight speed time series are respectively expressed as:

[0027] ,

[0028] in, For the purpose of estimation and The basis functions satisfy , and These are the coefficients obtained during the approximation process. This represents an approximate function for flight altitude. This represents an approximate function of flight speed, where the Fourier coefficients of the flight altitude time series are... Using vectors express, Fourier coefficients of flight speed time series Using vectors express, .

[0029] As a further optimization, the Fourier coefficients of the flight altitude time series were obtained. vector Fourier coefficients representing the time series of flight speed vector Following the indication, it also includes:

[0030] Fourier series were used to evaluate the Fourier coefficients of the flight altitude time series. Fourier coefficients of flight speed time series Approximation processing is performed, through express All information, through express All the information in it.

[0031] As a further optimization, the deep components in the network structure include an input layer, a hidden layer, and an output layer;

[0032] Fourier coefficients of the flight altitude time series Fourier coefficients of flight speed time series Represented as uniform Fourier coefficients At this point, the input layer of the deep component is represented as The hidden layer is represented as The stacking of hidden layers is represented as Each hidden layer introduces non-linearity through the ReLU activation function. The number of hidden layers is 3-5. The output layer is a linear output layer, represented as follows: ;

[0033] in:

[0034] ,

[0035] ,

[0036] ,

[0037] in, Indicates the first Hidden layers It is the first The node values ​​in the hidden layer, It is all hidden layer tables The node value, It is the first Model weights in hidden layers It is the first Deviation of hidden layers It is all hidden layer tables Deviation;

[0038] At this point, the interval fuel consumption function for any flight profile constructed based on linear and nonlinear relationships is expressed as follows: ,in:

[0039] ,

[0040] in, It is an S-shaped function. This indicates that a linear relationship is calculated using wide components. This indicates the use of deep components to calculate nonlinear relationships. Corresponding bias term.

[0041] As a further optimization, after constructing the interval fuel consumption function for any flight profile, the step of using monotonic interpolation to approximate the interval fuel consumption function refers to:

[0042] The time interval corresponding to the interval fuel consumption function is divided into three equally divided sub-intervals, and each sub-interval is approximated by a three-segment interpolation polynomial, so that the interval fuel consumption function satisfies the function value, the first stage, and the second stage of the six boundary conditions.

[0043] The beneficial effects of this invention are as follows: First, it acquires flight profiles and interval fuel consumption data for different flight stages within the flight profiles. Second, it acquires static and dynamic influencing factors associated with the interval fuel consumption data. Then, with the goal of minimizing fuel consumption fitting error, it selects a wide-depth combined network structure and uses the wide components in the network structure to acquire the linear relationship between static influencing factors and interval fuel consumption data. Simultaneously, it uses the deep components in the network structure to capture the nonlinear characteristics of dynamic influencing factors and uses the nonlinear characteristics to determine the nonlinear relationship between the flight profile and interval fuel consumption data. Thus, based on the linear and nonlinear relationships, it constructs an interval fuel consumption function for any flight profile. Then, during the cruise phase, it uses monotonic interpolation to approximate the interval fuel consumption function, making the interval fuel consumption function continuous and having a continuous derivative. It then calculates the derivative of the interval fuel consumption function after interpolation approximation to obtain the instantaneous fuel consumption function at any given point. Finally, it identifies the flight attitude with optimal fuel efficiency during the cruise phase based on the instantaneous fuel consumption function.

[0044] Therefore, this invention can accurately calculate instantaneous fuel consumption at any given point, thereby enabling the aircraft to cruise in the attitude corresponding to the optimal fuel efficiency during the cruise phase, which greatly reduces the aircraft's fuel consumption during the cruise phase. Attached Figure Description

[0045] Figure 1 This is a flowchart of the engine fuel consumption calculation method based on carbon emissions from air transport in Embodiment 1 of the present invention. Detailed Implementation

[0046] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0047] Example 1

[0048] This embodiment provides a method for calculating engine fuel consumption based on carbon emissions from air transport; its flowchart is shown below. Figure 1 The method may include the following steps:

[0049] S1. Obtain the flight profile and the interval fuel consumption data for different flight stages in the flight profile;

[0050] S2. Obtain the static and dynamic influencing factors associated with aircraft interval fuel consumption data;

[0051] S3. With the goal of minimizing the fuel consumption fitting error, a wide-depth combined network structure is selected. The wide components in the network structure are used to obtain the linear relationship between static influencing factors and interval fuel consumption data. At the same time, the deep components in the network structure are used to capture the nonlinear characteristics of dynamic influencing factors. The nonlinear characteristics are used to determine the nonlinear relationship between the flight profile and interval fuel consumption data.

[0052] S4. Construct an interval fuel consumption function for arbitrary flight profiles based on linear and nonlinear relationships;

[0053] S5. During the cruise phase, the interval fuel consumption function is approximated by monotonic interpolation to make the interval fuel consumption function continuous and have continuous derivatives. The derivative of the interval fuel consumption function after interpolation is calculated to obtain the instantaneous fuel consumption function at any given point.

[0054] S6. Identify the flight attitude with optimal fuel efficiency during the cruise phase based on the instantaneous fuel consumption function.

[0055] It should be noted that, since this embodiment needs to identify the flight attitude with optimal fuel efficiency so that the aircraft can always maintain energy-saving cruise flight during the cruise phase, and the aircraft flight attitude corresponds to instantaneous fuel consumption, this embodiment needs to accurately calculate the instantaneous fuel consumption data of the aircraft during the cruise phase.

[0056] For a specific aircraft, the engine's fuel consumption is mainly used for the following purposes: maintaining altitude, climbing or descending, maintaining airspeed, accelerating or decelerating. Therefore, the instantaneous fuel consumption of an aircraft is not only related to inherent physical parameters (static influencing factors) such as aircraft type and age, but also directly related to the aircraft's altitude, speed, rate of change of altitude, and rate of change of speed (dynamic influencing factors).

[0057] Since the instantaneous fuel consumption of an aircraft is related to the aforementioned static and dynamic influencing factors, and the flight profile is composed of several flight phases, including takeoff, climb, cruise, maneuvering, attack, descent, and landing, with the takeoff base as the origin, it is difficult to accurately calculate the instantaneous fuel consumption at any point in time during the cruise phase. Therefore, in this embodiment, the flight profile is first obtained to acquire interval fuel consumption data. Then, with the goal of minimizing the fuel consumption fitting error, a wide-depth combined network structure is used to determine the linear and nonlinear relationships between the flight profile and the interval fuel consumption data, thereby constructing an interval fuel consumption function for any flight profile. Finally, during the cruise phase, the interval fuel consumption function is approximated using monotonic interpolation to make it continuous and have a continuous derivative. The derivative of the interval fuel consumption function after interpolation is calculated to obtain the instantaneous fuel consumption function at any given point. Thus, the flight attitude with optimal fuel efficiency during the cruise phase can be identified based on the instantaneous fuel consumption function.

[0058] Example 2

[0059] Building upon Example 1, this example first requires acquiring interval fuel consumption data. Since ADS-B data acquisition is relatively inexpensive and contains detailed aircraft flight parameter information, ADS-B data can be used to acquire the flight profile and interval fuel consumption data for different flight phases within the flight profile, thus reducing the cost of acquiring aircraft flight data. It should be noted that, without considering data acquisition costs, the aforementioned interval fuel consumption data can also be obtained by recording fuel quantity changes at certain intervals in the ACRARS data.

[0060] After obtaining the interval fuel consumption data, since the interval fuel consumption data is also affected by the above-mentioned static and dynamic influencing factors, the accuracy of the instantaneous fuel consumption data cannot be guaranteed when directly calculating the instantaneous fuel consumption data. Therefore, it is necessary to process the static and dynamic influencing factors.

[0061] In this embodiment, the static influencing factors associated with the aircraft interval fuel consumption data may include: aircraft type, aircraft age, wingspan empty weight, and maximum takeoff weight, etc.; the dynamic influencing factors associated with the aircraft interval fuel consumption data mainly include: flight altitude and flight speed.

[0062] Since the aforementioned interval fuel consumption data is also affected by the aforementioned static and dynamic influencing factors, the flight attitude also exhibits a complex nonlinear relationship with these factors. Therefore, it is necessary to process the aforementioned static and dynamic influencing factors separately. Thus, in this embodiment, a wide-depth combined network structure is selected. The wide component in the network structure is used to obtain the linear relationship between the static influencing factors and the interval fuel consumption data, while the deep component in the network structure is used to capture the nonlinear characteristics of the dynamic influencing factors. The nonlinear characteristics are then used to determine the nonlinear relationship between the flight profile and the interval fuel consumption data.

[0063] Therefore, in this embodiment, using wide components in the network structure to obtain the linear relationship between static influencing factors and interval fuel consumption data can mean:

[0064] By using a wide component to perform linear combination calculations on static influencing factors and adding a bias, the linear relationship between static influencing factors and interval fuel consumption data is obtained, expressed as: , The calculation formula is:

[0065] ,

[0066] in, This represents the end time corresponding to the start time being 0 in the interval fuel consumption. This represents the set of static influencing factors. include One static influencing parameter, , This represents the first static influence parameter. This indicates the second static influencing factor. Indicates the first One static influencing factor, This represents the input vector of the wide component. Include dimensional features, Represents the model parameters of the wide component. , This represents the first model parameter of the wide component. This represents the second model parameter of the wide component. The wide component represents the first Each model parameter This indicates the bias term.

[0067] In this embodiment, the main dynamic influencing factors are flight altitude and flight speed, both of which can be represented as time-dependent sequences, i.e., the flight altitude is represented as a flight altitude time series. The flight speed is represented as a flight speed time series. ;because and It is non-linear, therefore, it is necessary to obtain and The Fourier coefficients are used to fully express the... and Therefore, in this embodiment, it is also necessary to obtain the Fourier coefficients of the flight altitude time series, in addition to all the information in the data. Fourier coefficients of flight speed time series .

[0068] It should be noted that before using the deep components in the wide-depth combined network structure to process the nonlinear relationship between flight profiles and interval fuel consumption data, it is necessary to ensure the continuity of flight altitude and flight speed at the two points, given the specific static influencing factors. The continuous flight altitude and flight speed should be approximated using Fourier series before being processed by the deep components. Therefore, in this embodiment, before using the deep components in the network structure to capture the nonlinear characteristics of dynamic influencing factors and using these nonlinear characteristics to determine the nonlinear relationship between flight profiles and interval fuel consumption data, it is also necessary to include: processing the Fourier coefficients of the flight altitude time series... Fourier coefficients of flight speed time series All dimensions are set to 100, corresponding to the truncation and expansion of the flight altitude time series and flight speed time series.

[0069] Furthermore, when the flight altitude time series and flight speed time series are truncated and expanded, the truncation radius of the flight altitude time series is expressed as: The cutoff radius of the flight velocity time series is expressed as: ;

[0070] For those with For a specific aircraft, assuming a flight's altitude and speed are respectively... and The other flight's altitude and speed were respectively and And since the fuel consumption function for these two flights is continuous, then: in any interval In the function space on, such that and exist The above approximation is used here. At this point, the flight altitude time series and flight speed time series are respectively expressed as:

[0071] ,

[0072] in, For the purpose of estimation and The basis functions satisfy , and These are the coefficients obtained during the approximation process. This represents an approximate function for flight altitude. This represents an approximate function of flight speed, where the Fourier coefficients of the flight altitude time series are... Using vectors express, Fourier coefficients of flight speed time series Using vectors express, .

[0073] Specifically, after obtaining the Fourier coefficients of the flight altitude time series vector Fourier coefficients representing the time series of flight speed vector After indicating, it also needs to include:

[0074] Fourier series were used to evaluate the Fourier coefficients of the flight altitude time series. Fourier coefficients of flight speed time series Approximation processing is performed, through express All information, through express All the information in it.

[0075] At this point, deep components can be used to process the data after the above-mentioned truncation, expansion, and approximation processes. and .

[0076] It should be noted that the deep components in the network structure of this embodiment may include an input layer, a hidden layer, and an output layer; here, the Fourier coefficients of the flight altitude time series are... Fourier coefficients of flight speed time series Represented as uniform Fourier coefficients At this point, the input layer of the deep component is represented as The hidden layer is represented as The stacking of hidden layers is represented as Each hidden layer introduces non-linearity through the ReLU activation function. To ensure training efficiency and accuracy, the number of hidden layers can be determined by cross-validation. Ultimately, the optimal number of hidden layers is 3-5. The output layer is a linear output layer, represented as follows: ;

[0077] in:

[0078] ,

[0079] ,

[0080] ,

[0081] in, Indicates the first Hidden layers It is the first The node values ​​in the hidden layer, It is all hidden layer tables The node value, It is the first Model weights in hidden layers It is the first Deviation of hidden layers All hidden layers Deviation;

[0082] At this point, the interval fuel consumption function for any flight profile constructed based on linear and nonlinear relationships is expressed as follows: ,in:

[0083] ,

[0084] in, It is an S-shaped function. This indicates that a linear relationship is calculated using wide components. This indicates the use of deep components to calculate nonlinear relationships. Corresponding bias term.

[0085] It should be noted that after constructing the interval fuel consumption function for arbitrary flight profiles, in order to accurately construct the instantaneous fuel consumption function from the interval fuel consumption, it is necessary to ensure the monotonicity and smoothness of the interpolation function. Therefore, this embodiment adopts a piecewise second-order Hermite interpolation method to ensure that the constructed interval fuel consumption function is continuous and has continuous derivatives, avoiding non-physical oscillations caused by conventional interpolation. At the same time, each time interval in the interval fuel consumption function is divided into three equal parts, and each is approximated by a three-segment interpolation polynomial, satisfying six boundary conditions for the function value, first derivative, and second derivative.

[0086] Example 3

[0087] Based on Example 2, this example verifies the method of Example 2, as follows:

[0088] First, assume the aircraft's instantaneous fuel consumption is... A fixed parameter Represented as , where parameters This can refer to the aircraft's intrinsic attributes, such as model, wingspan, age, empty weight, and maximum takeoff weight. Therefore, the aircraft's instantaneous fuel consumption can be written as:

[0089] ,

[0090] in, and , are functions of aircraft altitude and speed with respect to time, respectively. First and second derivatives. , and , This represents the rate of change of altitude and speed. Applying the above formula to... By integrating the above data, we can obtain the fuel consumption for the specified range, denoted as:

[0091] ,

[0092] It is a function and The function, with parameters as and Given a set and There exists a corresponding range of fuel consumption. .

[0093] Then, verify the flight altitude of the aircraft during the two flights. and flight speed The continuity.

[0094] In this embodiment, for having For a specific aircraft, if the altitude of the two flights is... and speed If the flight profiles are exactly the same, then the fuel consumption of the two flights will also be exactly the same. However, if the altitude and speed profiles of the two different flights are slightly different—for example, if the altitude and speed of the first flight are... and The altitude and speed of the second flight were respectively and ,but

[0095] ,

[0096] Representative function The change is represented as:

[0097] ,

[0098] This indicates the function about and It is continuous.

[0099] Then, to and We perform function approximation. Assume we have a set of basis functions. In the interval In the function space on, consider the function and exist A good approximation on is:

[0100] ,

[0101] in, and That is the cutoff radius. If this formula can approximate the function well... and Then there is and .

[0102] and These are the coefficients obtained during the estimation process. It is used to estimate and The basis functions. If these approximations are accurate, then the function This can be represented as:

[0103] ,

[0104] when and When large enough, the function and This will become small enough. Considering the continuity assumptions and conditions, we can obtain the function... The approximate values ​​are as follows:

[0105] ,

[0106] Thus, with The relevant derivatives ultimately lie on the basis functions. Above. Due to It is a known function, and the instantaneous fuel consumption The expression does not explicitly depend on time. Therefore, its right side can be integraled in the following form:

[0107] ,

[0108] Here, vector and These are vectors. Therefore, the interval fuel consumption function... It has been simplified to involve Parameters Multivariable real-valued functions, and Therefore, the calculation of interval fuel consumption is transformed into a problem of fitting a multivariable real-valued function.

[0109] Currently, many deep learning techniques are available for solving this type of fitting problem for multivariate real-valued functions with parameters, including DNN (Deep Neural Networks), Wide and Deep Methods, and DeepFM. If the interval fuel consumption for any given segment in an ADS-B sequence can be determined using the above results, then the instantaneous fuel consumption can be calculated. Here, it is assumed that the interval fuel consumption between any two segments can be calculated. Therefore, there are the following N interval fuel consumption sequences:

[0110] ,

[0111] For those with specific parameters Given a sequence, taking into account fuel consumption The positive aspect, Therefore, construct a definition in monotonically increasing function on , making .if exist If the previous two consecutive values ​​are differentiable, then the instantaneous fuel consumption is: This ensures It has a clear definition and can be precisely calculated at any point within the interval.

[0112] Therefore, it is now possible to accurately calculate section fuel consumption and instantaneous fuel consumption based on the ADS-B data of flights.

[0113] In this embodiment, Fourier series is used for approximation. Therefore, Fourier series is used as an example to introduce a method for approximating time series data and to evaluate its performance.

[0114] This section focuses primarily on two sequences of ADS-B: velocity. and height Time series Assuming It is large enough that the sequence has enough points available for computation. (Regarding the data...) Standardization Mapping time series to the interval , , is a large constant.

[0115] Using linear interpolation in the interval Inner Fit Function as follows:

[0116] ,

[0117] Function Mapping to symmetric intervals Make it a symmetrical interval an even function on, if ,but .

[0118] The Fourier series approximation is:

[0119] ,

[0120] here It is the number of terms in the Fourier series. Note that... exist If the number above is even, we have and :

[0121] ,

[0122] According to Riemann's theorem, respectively ,

[0123] definition:

[0124] ,

[0125] but for:

[0126] ,

[0127] when Then:

[0128] ,

[0129] The coefficients of the fitted ADS-B velocity sequence can be easily obtained using the same method. Now, regarding We now have a good Fourier series approximation. Here, as long as... and Large enough, the Fourier series and and The error will be small enough. In other words, and All the information can be represented by a sequence. and Complete expression.

[0130] Based on the above analysis, the fuel consumption range It can be simplified to having A multivariate real-valued function with several parameters. In this case, the interval fuel consumption function for any flight profile constructed based on linear and nonlinear relationships is expressed as: ,in:

[0131] ,

[0132] in, It is an S-shaped function. This indicates that a linear relationship is calculated using wide components. This indicates the use of deep components to calculate nonlinear relationships. Corresponding bias term.

[0133] Finally, monotonic interpolation is used to ensure that the instantaneous fuel consumption function can be accurately constructed from the interval fuel consumption function. Here, the monotonicity and quadratic differentiability of fuel quantity are considered; the former guarantees the positiveness of instantaneous fuel consumption, and the latter guarantees the existence and boundedness of the derivative.

[0134] Here, for interval fuel consumption, information about the amount of fuel is obtained. Satisfying the monotonic condition , , Here we need to obtain a smooth and monotonic function. .

[0135] Since the above time series is non-uniform, therefore, we define... ,and The length is Therefore, the interval derivative is:

[0136] ,

[0137] Considering The derivative at the endpoints of the interval should not be approximated using the interval derivative described above. Therefore, a second-order approximation is given here:

[0138] ,

[0139] here , The approximation error is ,and The error is Therefore, this discussion This is an interpolation approximation problem, therefore, the boundary condition readings are:

[0140] ,

[0141] Here, if we directly use polynomial functions in the interval Performing interpolation approximation on the above will reveal that satisfying so many boundary conditions is challenging. Therefore, to satisfy the above boundary conditions, we can... It is divided into three sub-intervals, namely:

[0142] ,

[0143] here .

[0144] definition In the interval Within, flight time Corresponding fuel consumption It can be calculated using the following formula:

[0145] ,

[0146] in, Defined in superior, Defined in superior, , definition interval, Therefore, the model parameters can be calculated as follows:

[0147] ,

[0148] Hermit polynomial , , and The pronunciation of :

[0149] ,

[0150] The equation can be directly verified by utilizing the properties of Hermitian polynomials. Therefore, this embodiment ensures that while satisfying the boundary conditions, it also guarantees that... The monotonicity and quadratic differentiability of the [aspect]. Finally, through [the study of]... By taking the derivative, we can obtain an expression for the instantaneous fuel consumption at any given point.

[0151] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for calculating engine fuel consumption based on carbon emissions from air transport, characterized in that, Includes the following steps: Obtain flight profiles and interval fuel consumption data for different flight phases within the flight profiles; Obtain the static and dynamic influencing factors associated with aircraft interval fuel consumption data; With the goal of minimizing the fuel consumption fitting error, a wide-depth combined network structure is selected. The wide components in the network structure are used to obtain the linear relationship between static influencing factors and interval fuel consumption data. At the same time, the deep components in the network structure are used to capture the nonlinear characteristics of dynamic influencing factors, and the nonlinear characteristics are used to determine the nonlinear relationship between flight profile and interval fuel consumption data. Construct an interval fuel consumption function for arbitrary flight profiles based on linear and nonlinear relationships; During the cruise phase, the interval fuel consumption function is approximated by monotonic interpolation, making the interval fuel consumption function continuous and having continuous derivatives. The derivative of the interval fuel consumption function after interpolation is calculated to obtain the instantaneous fuel consumption function at any given point. The flight attitude with optimal fuel efficiency during the cruise phase is identified based on the instantaneous fuel consumption function.

2. The method for calculating engine fuel consumption based on carbon emissions from air transport according to claim 1, characterized in that, ADS-B data was used to obtain flight profiles and interval fuel consumption data for different flight phases within the flight profiles.

3. The method for calculating engine fuel consumption based on carbon emissions from air transport according to claim 1, characterized in that, The static influencing factors associated with the aircraft's inter-aircraft fuel consumption data include: aircraft type, aircraft age, wingspan empty weight, and maximum takeoff weight; The dynamic influencing factors associated with the aircraft's inter-regional fuel consumption data include: flight altitude and flight speed.

4. The method for calculating engine fuel consumption based on carbon emissions from air transport according to claim 3, characterized in that, The use of wide components in the network structure to obtain the linear relationship between static influencing factors and interval fuel consumption data refers to: By using a wide component to perform linear combination calculations on static influencing factors and adding a bias, the linear relationship between static influencing factors and interval fuel consumption data is obtained, expressed as: , The calculation formula is: ， in, This represents the end time corresponding to the start time being 0 in the interval fuel consumption. This represents the set of static influencing factors. include One static influencing parameter, , This represents the first static influence parameter. This indicates the second static influencing factor. Indicates the first One static influencing factor, This represents the input vector of the wide component. Include dimensional features, Represents the model parameters of the wide component. , This represents the first model parameter of the wide component. This represents the second model parameter of the wide component. The wide component represents the first Each model parameter This indicates the bias term.

5. The method for calculating engine fuel consumption based on carbon emissions from air transport according to claim 3, characterized in that, The flight altitude is represented as a time series of flight altitudes, i.e.: The flight speed is represented as a flight speed time series, i.e.: ; Obtain the Fourier coefficients of the flight altitude time series Fourier coefficients of flight speed time series .

6. The method for calculating engine fuel consumption based on carbon emissions from air transport according to claim 5, characterized in that, Before using deep components in the network structure to capture the nonlinear characteristics of dynamic influencing factors and using these nonlinear characteristics to determine the nonlinear relationship between the flight profile and interval fuel consumption data, the method further includes: Fourier coefficients of the flight altitude time series Fourier coefficients of flight speed time series All dimensions are set to 100, corresponding to the truncation and expansion of the flight altitude time series and flight speed time series.

7. The method for calculating engine fuel consumption based on carbon emissions from air transport according to claim 6, characterized in that, When the flight altitude time series and flight speed time series are truncated and expanded, the truncation radius of the flight altitude time series is expressed as: The cutoff radius of the flight velocity time series is expressed as: ; For those with For a specific aircraft, assuming a flight's altitude and speed are respectively... and The other flight's altitude and speed were respectively and And since the fuel consumption function for these two flights is continuous, then: in any interval In the function space on, such that and exist The above approximation is used here. At this point, the flight altitude time series and flight speed time series are respectively expressed as: ， in, For the purpose of estimation and The basis functions satisfy , and These are the coefficients obtained during the approximation process. This represents an approximate function for flight altitude. This represents an approximate function of flight speed, where the Fourier coefficients of the flight altitude time series are... Using vectors express, Fourier coefficients of flight speed time series Using vectors express, .

8. The method for calculating engine fuel consumption based on carbon emissions from air transport according to claim 7, characterized in that, Fourier coefficients of the obtained flight altitude time series vector Fourier coefficients representing the time series of flight speed vector Following the indication, it also includes: Fourier series were used to evaluate the Fourier coefficients of the flight altitude time series. Fourier coefficients of flight speed time series Approximation processing is performed, through express All information, through express All the information in it.

9. The method for calculating engine fuel consumption based on carbon emissions from air transport according to claim 8, characterized in that, The deep components in the network structure include an input layer, a hidden layer, and an output layer; Fourier coefficients of the flight altitude time series Fourier coefficients of flight speed time series Represented as uniform Fourier coefficients At this point, the input layer of the deep component is represented as The hidden layer is represented as The stacking of hidden layers is represented as Each hidden layer introduces non-linearity through the ReLU activation function. The number of hidden layers is 3-5. The output layer is a linear output layer, represented as follows: ; in: ， ， ， in, Indicates the first Hidden layers It is the first The node values ​​in the hidden layer, It is all hidden layer tables The node value, It is the first Model weights in hidden layers It is the first Deviation of hidden layers It is all hidden layer tables Deviation; At this point, the interval fuel consumption function for any flight profile constructed based on linear and nonlinear relationships is expressed as follows: ,in: ， in, yes Shape functions, This indicates that a linear relationship is calculated using wide components. This indicates the use of deep components to calculate nonlinear relationships. Corresponding bias term.

10. The method for calculating engine fuel consumption based on carbon emissions from air transport according to any one of claims 1-9, characterized in that, After constructing the interval fuel consumption function for any flight profile, the step of using monotonic interpolation to approximate the interval fuel consumption function refers to: The time interval corresponding to the interval fuel consumption function is divided into three equally divided sub-intervals, and each sub-interval is approximated by a three-segment interpolation polynomial, so that the interval fuel consumption function satisfies the function value, the first stage, and the second stage of the six boundary conditions.

Images