System and method for aircraft takeoff weight estimation

Abstract

Systems and methods for aircraft takeoff weight estimation are disclosed. The method comprises the following steps: receiving input data corresponding to flight trajectory data of an aircraft; generating a set of input parameters based on the trajectory data, wherein the set of input parameters includes a first subset of parameters corresponding to a take-off phase of the flight and a second subset of parameters corresponding to a climb phase of the flight; and processing the set of input parameters using a training model to generate an estimate of the takeoff weight of the aircraft.

Description

Technical Field

[0001] The present disclosure generally relates to systems and methods for estimating the takeoff weight of an aircraft. Background Art

[0002] With the continuous increase in air traffic, effective aircraft management has become increasingly important accordingly. Aspects of aircraft management include the accurate estimation of the takeoff weight of a particular aircraft, as the takeoff weight can be an important parameter for determining flight performance. For example, the takeoff weight affects the takeoff speed and distance, the takeoff and climb thrust requirements, the drag force, and the fuel consumption. Since it is impractical to directly measure the takeoff weight, the accurate estimation of the takeoff weight allows for more fuel-efficient operation of the aircraft, which in turn makes aircraft management more efficient. Summary of the Invention

[0003] In a specific implementation, a method includes: receiving input data corresponding to the trajectory data of an aircraft flight. The method further includes generating a set of input parameters based on the trajectory data, where the set of input parameters includes a first subset of parameters corresponding to the takeoff phase of the flight and a second subset of parameters corresponding to the climb phase of the flight. The method further includes using a trained model to process the set of input parameters to generate an estimated value of the takeoff weight of the aircraft.

[0004] In another specific implementation, a device includes one or more processors configured to receive input data corresponding to the trajectory data of an aircraft flight. The one or more processors are further configured to generate a set of input parameters based on the trajectory data, where the set of input parameters includes a first subset of parameters corresponding to the takeoff phase of the flight and a second subset of parameters corresponding to the climb phase of the flight. The one or more processors are also configured to use a trained model to process the set of input parameters to generate an estimated value of the takeoff weight of the aircraft.

[0005] In another specific implementation, a non-transitory computer-readable medium includes instructions that, when executed by one or more processors, cause the one or more processors to receive input data corresponding to the trajectory data of an aircraft flight. The instructions further cause the one or more processors to generate a set of input parameters based on the trajectory data, where the set of input parameters includes a first subset of parameters corresponding to the takeoff phase of the flight and a second subset of parameters corresponding to the climb phase of the flight. The instructions further cause the one or more processors to use a trained model to process the set of input parameters to generate an estimated value of the takeoff weight of the aircraft.

[0006] In another specific implementation, a device includes a unit for receiving input data corresponding to trajectory data of an aircraft flight. The device further includes a unit for generating a set of input parameters based on the trajectory data, where the set of input parameters includes a first subset of parameters corresponding to the take-off phase of the flight and a second subset of parameters corresponding to the climb phase of the flight. The device further includes a unit for using a trained model to process the set of input parameters to generate an estimated value of the take-off weight of the aircraft.

[0007] The features, functions, and advantages described herein can be implemented independently in various embodiments or can be combined in other embodiments, and further details thereof can be found in the following description and the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Figure 1 An example system for estimating the take-off weight of an aircraft according to some examples of the present disclosure is shown.

[0009] Figure 2 An example architecture for estimating the take-off weight of an aircraft according to some examples of the present disclosure is shown.

[0010] Figure 3 A box plot of z-scores of multiple features according to some examples of the present disclosure is shown.

[0011] Figure 4 An example visualization of the impact of a selected set of features according to some examples of the present disclosure is shown.

[0012] Figure 5 An example curve graph of the estimated take-off weight (“TOW”) value of a Boeing 777 compared to the actual take-off weight value according to some examples of the present disclosure is shown.

[0013] Figure 6 An example is shown according to some examples of the present disclosure regarding Figures 1 - 5 a bar graph of the number of aircraft for each of the absolute error values of the performance of the trained model.

[0014] Figure 7 An example graph of the estimated take-off weight values of three types of aircraft (Boeing 737, Boeing 777, and Boeing 787) compared to the actual take-off weight values according to some examples of the present disclosure is shown.

[0015] Figure 8 An example is shown according to some examples of the present disclosure showing regarding Figures 1 - 4 and Figure 7 a bar graph of the number of aircraft for each of the absolute error values of the performance of the trained model.

[0016] Figure 9It is a flowchart of an example method for estimating the takeoff weight of an aircraft according to some examples of the present disclosure.

[0017] Figure 10 It is a block diagram of a computing environment including aspects of a computing device configured to support computer-implemented methods and computer-executable program instructions (or code) according to some examples of the present disclosure. Detailed implementation

[0018] An accurate estimate of the takeoff weight can make aircraft management more efficient. For example, for a given cruise altitude, speed, and temperature, a heavier aircraft burns more fuel and requires more power. A lighter aircraft can climb with reduced thrust and consume less fuel. Although the empty operating weight of a given aircraft is publicly available, the payload weight and fuel quantity vary with the operation of a particular aircraft.

[0019] Accurately estimating the takeoff weight affects various areas of aircraft management. For example, the takeoff weight directly affects the performance of an aircraft during takeoff, climb, cruise, and landing. The aircraft management system can use this data to calculate performance parameters such as takeoff distance, climb rate, cruise speed, and range. By considering the takeoff weight of each aircraft in the fleet, the system can optimize flight routes, altitudes, and speeds to ensure efficient operation and reduce fuel consumption. As another example, the takeoff weight affects aircraft safety. Exceeding the maximum takeoff weight impairs the aircraft's performance capabilities to climb and maneuver safely. The aircraft management system can monitor the takeoff weight to prevent overloading and ensure that each flight remains within the safe operating limits. As a further example, the takeoff weight affects maintenance planning because heavier aircraft impose increased stress on their components, which can lead to more rapid wear and tear. Tracking the takeoff weight can allow the aircraft management system to assist in planning maintenance schedules, reduce unscheduled downtime, and extend the life of the aircraft.

[0020] Accurately estimating the takeoff weight can enable a more effective aircraft management system because it is impractical to directly measure the actual takeoff weight and / or it is only available for specific aircraft or airlines. Further, some estimates of the takeoff weight rely on data that is only available for specific aircraft or airlines.

[0021] The systems and methods disclosed herein utilize publicly available information to provide an accurate estimate of the takeoff weight of a specific aircraft, including by generating a subset of input parameters that at least correspond to the takeoff phase of a flight and the climb phase of a flight, and using a trained model to process the subset of input parameters to generate an estimate of the takeoff weight of the aircraft.

[0022] The technical advantage of the present disclosure is that it can improve an aircraft management system by allowing the system to accurately estimate the takeoff weight of an aircraft based on publicly available information corresponding to multiple flight phases. The takeoff weight estimate can be used by the aircraft management system to, for example, more accurately plan the route, altitude, and speed of the aircraft to reduce fuel consumption; ensure an operating safety margin; monitor maintenance schedules, or some combination thereof.

[0023] The drawings and the following description illustrate specific exemplary embodiments. It should be understood that those skilled in the art will be able to design various arrangements that, although not explicitly described or shown herein, embody the principles described herein and are included within the scope of the claims following this description. Additionally, any examples described herein are intended to assist in understanding the principles of the present disclosure and are to be construed as not limiting. Accordingly, the present disclosure is not limited to the specific implementations or examples described below, but is defined by the claims and their equivalents.

[0024] The detailed description is described herein with reference to the drawings. In the description, throughout the drawings, common features are denoted by common reference numerals. As used herein, different terms are used only for the purpose of describing a particular implementation and are not intended to be restrictive. For example, unless the context clearly indicates otherwise, the singular forms "a", "an", and "the" are intended to also include the plural forms. Further, some features described herein are singular in some implementations and plural in other implementations. For illustration, Figure 1 a system 100 including one or more processors ( Figure 1 "processor" 106 therein) is described, which indicates that in some embodiments the system 100 includes a single processor 106 and in other embodiments, the system 100 includes multiple processors 106. For ease of reference herein, such features are generally introduced as "one or more" features and are subsequently referred to in the singular or optionally plural (denoted by "(s)") unless the aspect being described relates to multiple features.

[0025] The terms "comprise", "comprises", and "comprising" are used interchangeably with "include", "includes", or "including". Additionally, the term "wherein" is used interchangeably with the term "wherein". As used herein, "exemplary" indicates an example, implementation, and / or aspect and should not be construed as limiting or indicating a preference or preferred implementation. As used herein, ordinal terms (e.g., "first", "second", "third", etc.) used to modify elements (such as structures, components, operations, etc.) do not themselves indicate any priority or order of the element relative to another element, but merely distinguish the element from another element having the same name (but for the use of the ordinal term). As used herein, the term "group" refers to a grouping of one or more elements, and the term "plurality" refers to a multiplicity of elements.

[0026] As used herein, "generate", "calculate", "use", "select", "access", and "determine" are interchangeable unless the context indicates otherwise. For example, "generate", "calculate", or "determine" a parameter (or signal) can refer to actively generating, calculating, or determining a parameter (or signal) or can refer to using, selecting, or accessing a parameter (or signal) that has already been generated, such as by another component or device. As used herein, "coupled" can include "communicatively coupled", "electrically coupled", or "physically coupled", and can also (or alternatively) include any combination thereof. Two devices (or components) can be coupled (e.g., communicatively coupled, electrically coupled, or physically coupled) directly or indirectly via one or more other devices, components, wires, buses, networks (e.g., a wired network, a wireless network, or a combination thereof), etc. Two devices (or components) that are electrically coupled can be included in the same device or different devices and can be connected via electronics, one or more connectors, or inductive coupling, as illustrative, non-limiting examples. In some embodiments, two devices (or components) that are communicatively coupled (e.g., electrically communicatively) can send and receive electrical signals (digital or analog signals) directly or indirectly, for example, via one or more wires, buses, networks, etc. As used herein, "directly coupled" is used to describe two devices that are coupled (e.g., communicatively coupled, electrically coupled, or physically coupled) without an intermediate component.

[0027] As used herein, the term "machine learning" shall be understood to have any of its ordinary and customary meanings within the fields of computer science and data science, such meanings including, for example, a process or technique by which one or more computers can learn to perform an operation or function without being explicitly programmed to perform the operation or function. As a typical example, machine learning can be used to enable one or more computers to analyze data to identify patterns in the data and generate results based on that analysis. For some types of machine learning, the results generated include data indicative of the underlying structure or patterns of the data itself. Such techniques include, for example, so-called "clustering" techniques, which identify clusters (e.g., groupings of data elements of the data).

[0028] For some types of machine learning, the results generated include data models (also referred to as "machine learning models" or simply "models"). Generally, a model is generated using a first set of data to facilitate the analysis of a second collection of data. For example, a first portion of a large batch of data can be used to generate a model that can be used to analyze the remaining portion of the large batch of data. As another example, a set of historical data can be used to generate a model that can be used to analyze future data.

[0029] Because a model can be used to evaluate a set of data different from the data used to generate the model, a model can be considered a type of software (e.g., instructions, parameters, or both) that is automatically generated by a computer during the machine learning process. As such, a model can be portable (e.g., can be generated at a first computer and then moved to a second computer for further training, for use, or both). Additionally, a model can be used in combination with one or more other models to perform a desired analysis. By way of illustration, first data can be provided as input to a first model to generate first model output data, and the first model output data can be provided as input to a second model to generate second model output data indicative of the results of the desired analysis. Depending on the analysis and data involved, different combinations of models can be used to generate such results. In some examples, multiple models can provide input to the model output of a single model. In some examples, a single model provides model output as input to multiple models.

[0030] Examples of machine learning models include, but are not limited to, perceptrons, neural networks, support vector machines, regression models, decision trees, Bayesian models, Boltzmann machines, adaptive neuro-fuzzy inference systems, and combinations, ensembles, and variants of these and other types of models. Variants of neural networks include, for example, but are not limited to, prototype networks, autoencoders, transformers, self-attention networks, convolutional neural networks, deep neural networks, deep belief networks, etc. Variants of decision trees include, for example, but are not limited to, random forests, boosted decision trees, etc.

[0031] Since a machine learning model is generated by a computer (or computers) based on input data, the machine learning model can be discussed in terms of at least two different time windows - the creation / training phase and the runtime phase. During the creation / training phase, the model is created, trained, adapted, validated, or otherwise configured by a computer based on input data (which is typically referred to as "training data" during the creation / training phase). Note that training a model corresponds to software that has been generated and / or refined during the creation / training phase to perform a specific operation such as classification, prediction, encoding, or other data analysis or data synthesis operations. During the runtime phase (or "inference" phase), the model is used to analyze input data to generate a model output. The content of the model output depends on the type of model. For example, a model can be trained to perform a classification task or a regression task, by way of non-limiting example. In some implementations, the model can be updated continuously, periodically, or occasionally, in which case the training time and runtime can be interleaved, or one version of the model can be used for inference while a copy is updated, and thereafter the updated copy can be deployed for inference.

[0032] In some implementations, machine learning techniques are used to train (or retrain) a previously generated model. In this context, "training" refers to adapting a model or the parameters of a model to a specific data set. Unless otherwise clear from the specific context, the term "training" as used herein includes "retraining" or refining a model to a specific data set. For example, training can include so-called "transfer learning". In transfer learning, a general or typical data set can be used to train a base model, and subsequently a more specific data set can be used to refine (e.g., retrain or further train) the base model.

[0033] The data set used during training is referred to as the "training data set" or simply "training data". The data set can be labeled or unlabeled. "Labeled data" refers to data that has been assigned a category label that indicates the group or class associated with the data, and "unlabeled data" refers to data that has not been labeled. Generally, "supervised machine learning processes" use labeled data to train a machine learning model, while "unsupervised machine learning processes" use unlabeled data to train a machine learning model; however, it should be understood that the label associated with the data is itself just another data element that can be used in any suitable machine learning process. By way of illustration, many clustering operations can operate on unlabeled data; however, this clustering operation can use labeled data by ignoring the label assigned to the data or by treating the label as the same as other data elements.

[0034] Training a model based on a training data set generally involves changing the parameters of the model based on the data input into the model, with the goal of making the output of the model have specific characteristics. To distinguish it from model generation operations, model training may be referred to as optimization or optimization training in this document. In this context, "optimization" refers to improving a metric and does not mean finding the ideal (e.g., global maximum or global minimum) value of the metric. Examples of optimization trainers include, but are not limited to, backpropagation trainers, derivative-free optimizers (DFO), and extreme learning machines (ELM). As an example of training a model, during supervised training of a neural network, input data samples are associated with labels. When an input data sample is provided to the model, the model generates output data, which is compared with the label associated with the input data sample to generate an error value. The parameters of the model are modified to attempt to reduce (e.g., optimize) the error value. As another example of training a model, during unsupervised training of an autoencoder, data samples are provided to the autoencoder as input, and the autoencoder reduces the dimensionality of the data samples (which is a lossy operation) and attempts to reconstruct the data samples as output data. In this example, the output data is compared with the input data samples to generate a reconstruction loss, and the parameters of the autoencoder are modified to attempt to reduce (e.g., optimize) the reconstruction loss.

[0035] Figure 1 An example system 100 for estimating the takeoff weight of an aircraft in accordance with some examples of the present disclosure is shown. In some implementations, system 100 includes a computing device 102 configured to communicate with one or more devices 104. Computing device 102 may be configured to generate an estimate of takeoff weight 138 based on input data 130 received from device 104.

[0036] In some implementations, the device(s) 104 may include, correspond to, or be included within an electronic device that includes one or more processors 132, and the one or more processors 132 are coupled to a memory 134 that stores monitoring data 140. In some aspects, the monitoring data 140 may include publicly available monitoring data associated with the flight of the aircraft. For example, the monitoring data 140 may include the aircraft's automatic dependent surveillance-broadcast ("ADS-B") data. As another example, the monitoring data 140 may include the aircraft's quick access recorder ("QAR") data.

[0037] The device 104 can be configured to transfer the input data 130 to the computing device 102. In some implementations, the input data 130 corresponds to or is otherwise associated with the surveillance data 140. For example, the input data 130 may include a subset of the surveillance data 140 related to a particular aircraft, a group of aircraft, an airline, etc. The input data 130 may also include data from one or more mathematical models of the aircraft. For example, the input data 130 may include data underlying the aircraft data ("BADA") model of the aircraft.

[0038] The computing device 102 can be configured to receive the input data 130 corresponding to the trajectory data of the aircraft flight. In some implementations, the computing device 102 may include one or more processors 106 coupled to the memory 108. The processor 106 may include an input parameter generator 110 configured to generate a set of input parameters 118 based on the trajectory data. In some aspects, the set of input parameters 118 may include one or more parameters associated with one or more aspects of the trajectory data. For example, the set of input parameters 118 may include data such as approach speed, flight range, cruise time, climb flight path angle, etc.

[0039] In some implementations, the set of input parameters 118 may include multiple subsets, where each parameter subset is associated with a particular flight phase. As an illustrative example, a flight can be divided into five phases: ground roll, takeoff, climb, cruise, and landing. In some aspects, the set of input parameters 118 may include a first subset 120 of parameters corresponding to the takeoff phase of the flight and a second subset 122 of parameters corresponding to the climb phase of the flight. In some aspects, the set of input parameters 118 may include a third subset of parameters corresponding to the ground roll phase of the flight, the cruise phase of the flight, or the landing phase of the flight. In the same or alternative aspects, the set of input parameters 118 may include parameter subsets corresponding to each of the ground roll phase of the flight, the cruise phase of the flight, and the landing phase of the flight. Although a flight is described by the above five phases, more, fewer, and / or different phases may be used without departing from the scope of the present disclosure. For example, the landing phase can be subdivided into further phases. As another example, the takeoff and climb phases can be combined into a single phase.

[0040] In some implementations, the processor 106 may include an input parameter processor 112 configured to process the set of input parameters 118 using the training model 124 to generate an estimated value 138 of the aircraft takeoff weight. As described in more detail below and with reference to Figures 2 - 10, a training model 124 can be trained with respect to a data set including data representing multiple phases of flight of a large number of aircraft. The training data set 142 for training the training model 124 can include data from actual flights, synthetic data from mathematical models of flights, or some combination thereof. In some aspects, the computing device 102 can be configured to train the training model 124 with the training data set 142, which includes a collection of QAR data 144, synthetic data 146, or a combination thereof. In a particular aspect, at least a portion of the synthetic data 146 is generated from the BADA model of the aircraft.

[0041] In some aspects, training the training model 124 can include training multiple trial models and selecting one of the trained multiple trial models by the processor 106 based on performance criteria. For example, the (one or more) processors 106 can train multiple trial models according to multiple regression model types (e.g., extreme tree regression, linear regression, gradient boosting regressor, Gaussian process regressor, etc.), and select one of the trained multiple trial models based on the mean absolute percentage error of the estimated takeoff weight 138 relative to the actual known takeoff weight value. In a specific aspect, the processor 106 can be configured to divide the training data into a training data subset and a test data subset. In such an aspect, the performance criteria can be based on the test data subset. For example, the performance criteria can be based on which of the multiple training models generates the most accurate estimated takeoff weight 138 based on the test data subset. In a further specific aspect, the training data subset can include synthetic data and the test data subset can include real data. Such a configuration can, for example, select one of the multiple training models (trained based on synthetic data) based on which one generates the best estimated takeoff weight 138 when using real data.

[0042] In some implementations, the processor 106 can further include a feature extractor 114 and a feature selector 116. The feature extractor 114 can be configured to extract a plurality of features 126 from the input data 130. The processor 106 can also be configured to determine a feature importance value 136 for each of the plurality of features 126. In some aspects, the feature importance value 136 can be stored at the memory 108. The feature selector 116 can be configured to select a set of the plurality of features 128 based at least on the feature importance value 136. In a particular aspect, the set of input parameters 118 corresponds to the selected set of features 128.

[0043] For example, the feature extractor 114 can be configured to extract multiple features 126 from the input data 130. This can include identifying one or more data points, data types, etc. from the input data 130 that are particularly relevant to a specific phase of flight, a specific aircraft type, etc. Extracting the multiple features 126 can also include performing mathematical, statistical, or other operations, calculations, derivations, etc. on one or more data points, data types, etc. of the input data 130 to generate one or more features 126, as described in more detail below with reference to Figure 2 For example, the feature extractor 114 can be configured according to the following formula to calculate the specific energy gradient where V is the airspeed of the aircraft, g 0 is the gravitational constant at the Earth's surface, and h is the altitude. The feature selector 116 can be configured to select the maximum value of the specific energy gradient to be used as an input parameter associated with the takeoff phase of flight.

[0044] As described above, the feature selector 116 can be configured to select a set of features 128 based at least on the feature importance values 136. The feature importance value 136 for a particular feature can be one or more data values indicating the importance of the particular feature to a specific phase of flight, a specific aircraft type, a specific aircraft tail number, a specific set of conditions, or some other appropriate variable. For example, a particular set of features 128 may be more important in determining an estimated value 138 of the accurate takeoff weight of one type of aircraft (e.g., 737), but less important in determining an estimated value 138 of the accurate takeoff weight of another type of aircraft (e.g., 777). Boeing is a registered trademark of The Boeing Company in Delaware.

[0045] As another example, the above-mentioned specific energy gradient may be relatively more important in determining the estimated value 138 of the takeoff weight when applied to data associated with the takeoff flight phase than when applied to data associated with the climb takeoff flight phase. The selection of the set of features 128 and the feature importance values 136 are described in more detail below with reference to Figures 2 - 8 more detail.

[0046] In some implementations, the processor 106 may also be configured to adjust parameters of a planned flight of the aircraft, where the planned flight follows an analysis flight of the aircraft. For example, the processor 106 may be configured to adjust a planned takeoff speed parameter for a subsequent flight of the aircraft. In a particular aspect, the processor 106 may be configured to provide a verification indication of the initial weight of the aircraft prior to the planned flight. For example, the processor(s) 106 may provide a verification indication to the pilot prior to the planned flight to indicate that one or more parameters of the planned flight are inconsistent with an estimated takeoff weight 138. As a specific example, the processor 106 may provide a warning to the user that the estimated takeoff weight 138 is 5% lighter than the industry average, 5% lighter than the takeoff weight for a similar route for this type of aircraft, etc.

[0047] In operation, the computing device 102 may receive input data 130 from the device 104, where the input data 130 corresponds to trajectory data of an aircraft flight. For example, the input data 130 may include ADS-B surveillance data from a flight of a particular aircraft. The ADS-B surveillance data may include a large number of data fields over a time frame associated with the flight, including data related to airframe position, surface position, aircraft identification, airframe speed, aircraft status, aircraft operating status, etc. Based on the trajectory data, the computing device 102 may generate a set of input parameters 118 according to the ADS-B surveillance data, according to synthetic data based on the aircraft's BADA model, or some combination thereof. The training model 124 may then use the set of input parameters 118 to generate an estimated takeoff weight 138.

[0048] To perform this accurately and efficiently, the set of input parameters 118 may include a first subset 120 of parameters corresponding to the takeoff phase of the flight and a second subset 122 of parameters corresponding to the climb phase of the flight. For example, the computing device 102 may use the training model 124 to process the first subset 120 of parameters - including (1) an average specific energy parameter and a maximum specific energy gradient parameter obtained from the BADA model, and (2) a time span parameter and a maximum acceleration parameter obtained from the surveillance data, and the second subset 122 of parameters includes (1) a climb thrust parameter and a specific energy gradient obtained from the BADA model, and (2) a maximum gamma parameter and parameters associated with the maximum, minimum, and average values of the climb rate of the aircraft obtained from the surveillance data. In some configurations, the computing device 102 may process additional parameters in the set of input parameters 118 using the training model 124. The training model 124 may be configured to generate an estimated takeoff weight 138 of the aircraft.

[0049] In some implementations, computing device 102 may be associated with, integrated into, or otherwise included in an aircraft, an aircraft management system, or other larger system. System 100 may also include Figure 1 components not shown in Figure 1 . For example, computing device 102 may also include a receiver configured to receive input data 130 from device 104. The receiver may be configured to receive data, for example, via a computer bus. As an additional example, system 100 may also include one or more input / output interfaces, one or more network interfaces, etc. Additionally, although Figure 1 memory 108 of system 100 is shown as storing certain data, more, less, and / or different data may be present within memory 108 without departing from the scope of the present disclosure.

[0050] Additionally, although Figure 1 some operations are shown as occurring within computing device 102, these operations may be performed by other components of system 100 without departing from the scope of the present disclosure. For example, one or more components external to computing device 102 may be configured to host or otherwise incorporate some or all of the components of device 104, training data set 142, or some combination thereof. Such components may be located remotely from computing device 102 and accessed via a modem of computing device 102.

[0051] As an additional example, in some implementations, one or more components external to computing device 102 may be configured to train training model 124. Training model 124 may then be included in computing device 102 or otherwise associated with computing device 102 such that computing device 102 may be configured to use training model 124 to process a set of input parameters 118 to generate an estimate 138 of takeoff weight. In some aspects, training model 124 may be trained by a first set of components separate from computing device 102 and hosted by another set of components separate from computing device 102.

[0052] Further, although Figure 1 computing device 102 and device(s) 104 are shown as separate, other configurations are possible without departing from the scope of the present disclosure. For example, computing device 102 and device(s) 104 may be integrated into an aircraft service provider. As an additional example, one or more components of computing device 102 may be distributed across multiple computing devices (e.g., a set of processor cores).

[0053] Even further, although Figure 1The computing device 102, the device(s) 104, and the training data set 142 are shown as separate, but other configurations are possible without departing from the scope of the subject disclosure. For example, the components of the computing device 102 and the components of the device(s) 104 may be integrated into one or more electronic devices different from the computing device 102, integrated with the computing device 102, or some combination thereof.

[0054] Figure 2 An example architecture 200 for aircraft takeoff weight estimation according to some examples of the present disclosure is shown. The example architecture 200 includes a set of inputs 202 communicatively coupled to a data preprocessing system 206, a feature extractor 114, a feature selector 116, a regression method system 232, and one or more outputs 242.

[0055] Generally, the exemplary architecture 200 corresponds to Figure 1 the structure and functionality of the system 100. For example, the inputs 202 generally correspond to the device(s) 104; and the data preprocessing system 206, the feature extractor 114, and the feature selector 116 generally correspond to one or more components of the processor(s) 106 and / or functions performed by the processor(s) 106.

[0056] As described above with reference to Figure 1 the device(s) 104 and the training data set 142 may be configured to store the monitoring data 140, the QAR data 144, the synthetic data 146, or some combination thereof for communication to the computing device 102. Referring to Figure 2 the monitoring data 140, the QAR data 144, or some combination thereof may be stored as the monitoring data 203. The inputs 202 may be configured to transmit some or all of the monitoring data 203 and the synthetic data 146 as input data 238 to the data preprocessing system 206. In a particular aspect, the inputs 202 may include any suitable one or more electronic devices configured to store the monitoring data 203, the synthetic data 146, or some combination thereof, including network storage devices, servers, personal computers, laptop computers, smart phones, etc.; various input / output devices such as keyboards, mice, touchscreens, etc.; data transmissions from another electronic device; other suitable devices for storing the input data, or some combination thereof.

[0057] The inputs 202 may transmit the input data 238 to the data preprocessing system 206. The data preprocessing system 206 may be any suitable electronic device configured to process the input data 238 to generate processed data 212. For example, the data preprocessing system 206 may be included in Figure 1 the computing device 102 of Figure 1The computing device 102 shares functions or is otherwise associated with Figure 1 the computing device 102. In some aspects, the data preprocessing system 206 may include a data cleaning and filtering system 208 configured to, for example, ensure the data integrity of the input data 238, filter the input data 238 for specific operations, etc. In the same or alternative aspects, the data preprocessing system 206 may include a flight phase data partitioning system 210 configured to partition some or all of the input data 238 into trajectory data associated with one or more flight phases, as described above with reference to Figure 1 .

[0058] In some implementations, the data preprocessing system 206 may be configured to generate processed data 212, which may include cleaned, filtered, and / or flight phase partitioned data. The data preprocessing system 206 may then transmit the processed data 212 to the feature extractor 114.

[0059] As described above with reference to Figure 1 in more detail, the feature extractor 114 may be configured to extract a plurality of features 126 from the processed data 212, including identifying one or more data points, data types, etc. that are particularly relevant to a specific phase of flight, a specific aircraft type, etc. from the processed data 212. In the Figure 2 example architecture, the feature extractor 114 is configured to identify a plurality of data types associated with each of five flight phases.

[0060] For example, in Figure 2 , the feature extractor 114 is configured to determine a plurality of subsets of a set of a plurality of features 126, including a subset 214 of features corresponding to the ground roll phase of flight, and the subset 214 of features includes maximum ground speed, average flap angle, weight estimate, ground roll distance, or some combination thereof. In a particular configuration, the maximum ground speed, average flap angle, and ground roll distance may be generated, calculated, retrieved, or otherwise obtained from the surveillance data 203, while the weight estimate is marked with an asterisk (*) to identify it as a feature that may be generated, calculated, retrieved, or otherwise obtained from the synthetic data 146 (e.g., based on the BADA model of a specific aircraft).

[0061] The maximum ground speed may be obtained from the surveillance data 203 by using the speed of the aircraft at the first takeoff. The ground roll distance may also be obtained from the surveillance data 203. The average flap angle may be obtained from the surveillance data and the aerodynamic lift formula using the lift coefficient (CL) during ground roll.

[0062] As another example, in Figure 2 ,Figure 1 The set of multiple features 126 may include a subset 216 of features corresponding to the takeoff phase of flight, and the subset 216 of features includes the average specific energy of a particular aircraft, the takeoff time span, the maximum acceleration, the maximum specific energy gradient, or some combination thereof. In a particular configuration, the takeoff time span and the maximum acceleration may be generated, calculated, retrieved, or otherwise obtained from the surveillance data 203, while the average specific energy of a particular aircraft may be generated, calculated, retrieved, or otherwise obtained from the synthetic data 146. The maximum specific energy gradient may be obtained from a combination of the surveillance data 203 and the synthetic data 146 using the formulas described in more detail above Figure 1 The average specific energy (E specific ) may be obtained from a combination of the surveillance data 203 and the synthetic data 146 according to the following formula E specific = 0.5(V 2 )+(g 0 *h): where V is the airspeed of the aircraft, g 0 is the gravitational constant at the Earth's surface, and h is the altitude.

[0063] As an additional example, in Figure 2 , Figure 1 the set of multiple features 126 may include a subset 218 of features corresponding to the climb phase of flight, and the subset 218 of features includes the climb thrust; the maximum, minimum, and average values of the climb rate; and the maximum flight path angle ("γ"). In a particular configuration, the climb rate and the maximum γ may be generated, calculated, retrieved, or otherwise obtained from the surveillance data 203, while the climb thrust may be generated, calculated, retrieved, or otherwise obtained from a combination of the surveillance data 203 and the synthetic data 146. For example, the climb thrust may be calculated according to one or more BADA equations that take altitude and Mach number (from the surveillance data 203) as inputs and generate a set of climb thrust values for each point on the climb trajectory. The set of values may be averaged (or other statistical analysis applied) to generate a climb thrust value.

[0064] As a further example, in Figure 2 , Figure 1 the set of multiple features 126 may include a subset 220 of features corresponding to the cruise phase of flight, and the subset 220 of features includes the maximum specific energy, the travel duration, the maximum altitude, the maximum Mach, the maximum calibrated airspeed ("CAS"), or some combination thereof. In a particular configuration, the travel duration, the maximum altitude, and the maximum Mach may be generated, calculated, retrieved, or otherwise obtained from the surveillance data 203, while the maximum specific energy may be generated, calculated, retrieved, or otherwise obtained from the synthetic data 146 (e.g., based on the BADA model of a particular aircraft).

[0065] As yet another example, in Figure 2 , Figure 1 a set of multiple features 126 of

[0066] may include a subset 222 of features corresponding to the landing phase of a flight, where the subset 222 of features includes a landing weight estimate, an approach speed, an average flap angle, or some combination thereof. In a particular configuration, the approach speed and the average flap angle may be generated, calculated, retrieved, or otherwise obtained from the surveillance data 203, while the landing weight estimate may be generated, calculated, retrieved, or otherwise obtained from the synthetic data 146. Figure 2 In an example of S , the landing phase may include trajectory data from zero to two nautical miles before landing. The landing weight estimate may be calculated based on the aerodynamic lift formula and the stall speed of a particular aircraft. The stall speed (V ) may be calculated using the formula W , where S is an approximation of the relationship between the stall speed and the nominal speed at which the aircraft lands (e.g., 1.23), V app is an approximation of the wind conditions at landing (e.g., 7 knots), and V

[0067] is the approach speed of the aircraft, which may be obtained from the surveillance data. Figure 2 In some embodiments, the features extracted by the feature extractor 114 may include more, fewer, and / or different features compared to the features shown in Figure 1 . As described in more detail below with reference to the feature selector 116, the set of features selected to correspond to the input parameters 118 of

[0068] may vary depending on the particular aircraft, aircraft type, selected flight phase, etc. The feature extractor 114 may be configured to extract only those features selected by the feature selector 116 (e.g., after training the training model 124), a superset of the features considered by the feature selector 116 (e.g., for training multiple trial models and selecting one of the multiple training models based on performance criteria), or some combination thereof. Figure 2 The feature extractor 114 may be configured to transmit data associated with the extracted features 126 to the feature selector 116. In an example of Figure 1 , the feature selector 116 may be configured to select a set of the extracted features 126 based at least on one or more feature importance values (e.g., the feature importance values 136 of

[0069] ). The feature importance values may be associated with a particular aircraft, particular aircraft type, particular flight phase, etc. Figure 2In the example of, the feature selector 116 is configured to evaluate multiple features based on the "z-score" of each feature, as described in more detail below with reference to Figure 3 For complex models, it may be difficult to relate the accuracy and interpretability of specific features; analyzing the z-score of each feature can mitigate this difficulty. The z-score is determined by the deviation of an individual feature from the mean of the set of features being analyzed.

[0070] Figure 3 A box plot 300 of the z-scores 302 of multiple features 304 according to some examples of the present disclosure is shown. In some aspects, the multiple features 304 include the extracted features 126 and multiple shadow features introduced for the purpose of evaluating the extracted features 126. In Figure 3 the example of, the shadow features include "Max_Shadow", "Mean_Shadow", "Median_Shadow", and "Min_Shadow". The extracted features 126 include the average thrust during the climb phase ("cl_MeanThurst"), the weight estimate during the landing phase ("lnd_weight"), the flight range ("Flight_Range"), the cruise phase time ("cr_Time"), the maximum Mach during the cruise phase ("cr_MaxMach"), the average flap angle during the landing phase ("lnd_Mean_Flap"), the average climb rate during the climb phase ("cl_meanROC"), the minimum climb rate during the climb phase ("cl_minROC"), the ground roll weight estimate ("gr_Weight"), the average specific energy during the takeoff phase ("pt_MSE"), the maximum altitude during the cruise phase ("cr_MaxAlt"), the average specific energy during the cruise phase ("cr_MSE"), the maximum CAS during the cruise phase ("cr_MaxCAS"), the takeoff phase time ("pt_Time"), the approach speed during the landing phase ("ldn_Vapp"), the average flap angle during the ground roll phase ("gr_MeanFlap"), the maximum γ during the climb phase ("cl_Maxγ"), the maximum climb rate during the climb phase ("cl_MaxROC"), the maximum ground speed during the ground roll phase ("gr_MaxGS"), the maximum specific energy gradient during the takeoff phase ("pt_MaxSEG"), and the ground roll phase distance ("gr_Distance"). The multiple features 304 may include features associated with a specific flight phase (e.g., the takeoff phase time, etc.) and features associated with the flight in general and are not limited to a specific flight phase (e.g., the flight range).

[0071] In Figure 3In the example, since the z-score of the ground roll distance is approximately equal to the z-score of the shadow feature, the ground roll distance feature is identified as unimportant. Similarly, the maximum specific energy gradient during the takeoff phase and the maximum ground speed feature during the ground roll phase are identified as temporarily important because their z-scores are slightly higher than the z-scores of the three shadow features but generally equal to the score of the fourth shadow feature, Max_Shadow. The remaining nineteen features are identified as features that will be selected as part of the selected features 128 that will be used as inputs for training the model 124.

[0072] The z-scores of individual features can vary depending on the specific training model. Referring again to Figure 2 , at 227, the feature selector 116 applies the Shapley Additive Explanation ("SHAP") algorithm for different models, and at 228, selects the most relevant features. The feature selector 116 can be configured to transmit data associated with the selected features 128 to the regression method system 232. The regression method system 232 can include one or more components configured to create one or more machine learning models, train models, evaluate models, apply models, or some combination thereof. For example, the regression method system 232 can include one or more components configured to create the (multiple) machine learning models 234. In a particular configuration, creating the machine learning model 234 can include creating multiple regression models, such as extreme tree regressors, linear regression models, gradient boosting regressors, Gaussian process regressors, etc.

[0073] The regression method system 232 can also include dividing the data into a training set and a test set at 236. In a particular configuration, the data can include the monitoring data 203, the synthetic data 146, or some combination thereof. For example, the QAR data of three different aircraft types can be divided into an 80% training set of QAR data and a 20% test set of QAR data, randomly divided. In another example, the training data can include a portion of the synthetic data 146, and the test data can include a portion of the monitoring data 203.

[0074] The regression method system 232 can also include one or more components configured to use the training data to train the model created at 234 to generate the training model 124. The regression method system 232 can also include one or more components configured to use the test data to evaluate the training model 124. Testing the training model 124 can include evaluating the training model 124 to predict the takeoff weight of the aircraft based on the selected features 128.

[0075] The regression method system 232 can also include one or more components configured to calculate the impact of the selected features 128 on the training model 124 at 240. The following Figure 4An exemplary visualization showing the impact of the selected feature 128 on the specific training model 124. The SHAP algorithm assigns a SHAP value associated with the importance of the feature to each selected feature 128.

[0076] Figure 4 An example visualization 400 showing the impact of a set of selected features 128 according to some examples of the present disclosure. In Figure 4 the example visualization 400, the SHAP values 404 of each selected feature 128 are plotted in descending order, showing the importance of each feature. For example, the SHAP value 404 of the average thrust in the climb phase ("cl_MeanThrust") 128A indicates that if the thrust in the climb phase is generally high, then the takeoff weight of the aircraft is also high, and vice versa. As another example, the average rate of climb in the climb phase ("cl_MeanROC") 128B is inversely correlated with the takeoff weight - the heavier the aircraft, the slower it climbs. Figure 4 Showing the SHAP values 404 of the selected features 128 described above with reference to Figures 2 - 3 .

[0077] Referring again to Figure 2 , the regression method system 232 may also include one or more components configured to use the training model 124 to process Figure 1 a selected set of features 128 to generate an estimated value 138 of the aircraft takeoff weight. The regression method system 232 may also be configured to transmit the estimated value 138 of the takeoff weight to one or more outputs 242. The (multiple) outputs 242 may be, include, be integrated with, or otherwise associated with components of an electronic device component configured to output data to a user, another electronic device, an electronic device component, or any combination thereof. For example, the output 242 may include a display component, such as a screen of a computing device for displaying the estimated value 138 of the takeoff weight.

[0078] As described above, the regression method system 232 may include one or more components configured to evaluate one or more machine learning models. In a specific configuration, creating the machine learning model 234 may include creating multiple regression models. Each of these models may be evaluated based on one or more performance criteria. For example, one of the performance criteria may be based on a subset of test data including real data (e.g., Figure 2 some or all of the monitoring data 203).

[0079] Figure 5FIG. 500 shows an example graph of the estimated takeoff weight (“TOW”) value 502 of a Boeing 777 compared to the actual takeoff weight value 504, according to some examples of the present disclosure. Graph 500 shows the performance of the trained model 124 trained with an extreme tree regressor for over 1,000 flights of a Boeing 777 (with an average actual takeoff weight of 365 tons and a range between 215 and 351 tons). Figures 1 - 4 of the trained model 124. Figure 6 FIG. 600 shows, according to some examples of the present disclosure, the number of aircraft 604 for each of the absolute error values 602 of the performance of the trained model 124 with respect to Figures 1 - 5 . Figure 6 The example also shows that the standard deviation of the data set presented in graph 500 is approximately 1.79 percent of the takeoff weight. Table 1 below shows a comparison of the performance of multiple trained models performing the functions described above with reference to Figures 5 - 6 .

[0080] Table 1

[0081] Model regression type Mean absolute percentage error Standard deviation Extreme tree regressor 1.32% TOW 1.79% TOW Linear regression 1.17% TOW 1.63% TOW Gradient boosting regressor 1.44% TOW 1.84% TOW Gaussian process regressor 1.84% TOW 2.45% TOW

[0082] In some implementations, the trained model 124 can be trained with respect to a training data set for a particular aircraft and / or aircraft type. In the same or alternative embodiments, the trained model 124 can be trained with respect to a training data set for multiple aircraft and / or multiple aircraft types in order to prevent the trained model 124 from overfitting to a particular aircraft and / or aircraft type. Figures 1 - 6

[0083] Figure 7 FIG. 700 shows an example graph of the estimated takeoff weight values 702 of three types of aircraft - Boeing 737, Boeing 777, and Boeing 787 - relative to the actual takeoff weight values 704. Graph 700 shows the performance of the trained model 124 trained with respect to over 2,800 flights of aircraft having a range of takeoff weights. For example, the average takeoff weight range of the aircraft for this training data set is 65 - 351 tons. Figure 8 FIG. 800 shows an example bar chart showing, according to some examples of the present disclosure, the number of aircraft 804 for each of the absolute error values 802 of the performance of the trained model 124 with respect to Figures 1 - 4 and Figure 7 . Figure 8 The example indicates that the performance of a more complex trained model 124 can result in a higher mean absolute error (e.g., 1.80%) and standard deviation (e.g., 2.56%) compared to training on a particular aircraft type, while maintaining accuracy within 2% of the actual takeoff weight.

[0084] ​Table 2 below shows the execution of the above reference Figures 7 - 8 a comparison of the performance of multiple training models that perform the functions described.

[0085] Table 2

[0086] Model regression type Mean absolute percentage error Standard deviation Extreme tree regressor 1.80% TOW 2.56% TOW Linear regression 6.13% TOW 10.60% TOW Gradient boosting regressor 2.26% TOW 3.20% TOW Gaussian process regressor 6.30% TOW 7.87% TOW

[0087] Table 2 shows that the type of training model 124 for a particular implementation can vary depending on the design constraints of the particular implementation. For example, according to Table 1 above, when the linear regression model is trained with training data for a particular aircraft type, the linear regression model performs best for that particular aircraft type. However, Table 2 shows that the linear regression model suffers from performance limitations for multiple aircraft types. Comparing Tables 1-2 illustrates that the extreme tree regressor model performs well in both configurations.

[0088] Referring again to Figure 2 , the various components of the regression method system 232 can be performed by Figure 1 one or more components of the computing device 102. For example, the (one or more) processors 106 can be configured to include one or more components (e.g., the input parameter processor 112) to create a machine learning model, divide data into training and test sets, calculate the impact of the features of the model, or some combination thereof.

[0089] Figure 9 is a flowchart of an example method 900 for estimating the takeoff weight of an aircraft according to some examples of the present disclosure. The method 900 can be initiated, executed, or controlled by one or more processors that execute instructions, such as, by the Figure 1 processor 106 that executes instructions from the memory 108.

[0090] In some implementations, the method 900 includes: at 902, receiving input data corresponding to trajectory data of an aircraft flight. For example, Figure 1 the processor 106 can be configured to receive input data 130 corresponding to the trajectory data of the aircraft flight from the device 104.

[0091] In Figure 9 an example, the method 900 may further include generating a set of input parameters at 904 based on the trajectory data, where the set of input parameters includes a first subset of parameters corresponding to the takeoff phase of the flight and a second subset of parameters corresponding to the climb phase of the flight. For example, Figure 1 the processor 106 can be configured to generate a set of input parameters 118 based on the trajectory data, where the set of input parameters 118 includes a first subset 120 of parameters corresponding to the takeoff phase of the flight and a second subset 122 of parameters corresponding to the climb phase of the flight.

[0092] In Figure 9 the example of, method 900 may further include: at 906, using a trained model to process a set of input parameters to generate an estimate of the takeoff weight of the aircraft. For example, processor 106 may be configured to utilize a trained model to process a set of input parameters 118 to generate an estimate 138 of the takeoff weight of the aircraft.

[0093] Although method 900 is illustrated as including a certain number of steps, more, fewer, and / or different steps may be included in method 900 without departing from the scope of the subject disclosure. For example, method 900 may optionally include additional steps, as described in more detail below.

[0094] In Figure 9 the example of, method 900 may also optionally include: at 908, training the trained model using a set of training data including a set of QAR data, synthetic data, or a combination thereof. For example, Figure 1 processor 106 of may be configured to train trained model 124 using a set of training data 142, the set of training data 142 including a set of QAR data 144, synthetic data 146, or a combination thereof.

[0095] In Figure 9 the example of, method 900 may also optionally include: at 910, extracting a plurality of features. For example, Figure 1 processor 106 of may be configured to extract a plurality of features 126.

[0096] In Figure 9 the example of, method 900 may also optionally include determining a feature importance value for each of the plurality of features at 912. For example, Figure 1 processor 106 of may be configured to determine a feature importance value 136 for each of the plurality of features 126.

[0097] In Figure 9 the example of, method 900 may also optionally include: at 914, selecting a set of the plurality of features based at least on the feature importance values, wherein the set of input parameters corresponds to the selected set of the plurality of features. For example, Figure 1 processor 106 of may be configured to select a set of a plurality of features 128 based at least on the feature importance value 136, wherein the set of input parameters 118 corresponds to the selected set of the plurality of features 128.

[0098] As described above, more, fewer, and / or different steps may be included in method 900 without departing from the scope of the present disclosure. For example, method 900 may vary according to the count and type of input data received. In a particular configuration,Figure 1 The system 100 can be configured to sequentially process a set of input parameters 118 using multiple training models 124 and evaluate each of the multiple training models 124 before proceeding to process the set of input parameters 118 with the next one of the multiple training models 124.

[0099] Figure 10 is a block diagram of a computing environment 1000 that includes a computing device 1010 according to some examples of the present disclosure and aspects that support computer-implemented methods and computer-executable program instructions (or code). For example, the computing device 1010 or portions thereof are configured to execute instructions to initiate, execute, or control one or more operations described in more detail above with reference to Figures 1 - 9 In a particular aspect, the computing device 1010 can include, correspond to, or be included in the computing device 102, the device(s) 104, Figure 1 the training data set 142; Figure 2 the input 202, the data preprocessing system 206, the regression method system 232; one or more servers, one or more virtual devices, or a combination thereof.

[0100] The computing device 1010 includes one or more processors 1020. In a specific aspect, the processor 1020 corresponds to Figure 1 the processor 106. The processor 1020 is configured to communicate with the system memory 1030, one or more storage devices 1050, one or more input / output interfaces 1040, one or more communication interfaces 1060, or any combination thereof. The system memory 1030 includes volatile memory devices (e.g., random access memory (RAM) devices), non-volatile memory devices (e.g., read-only memory (ROM) devices, programmable read-only memory, and flash memory), or both. The system memory 1030 stores an operating system 1032, which may include a basic input / output system for booting the computing device 1010 and a complete operating system that enables the computing device 1010 to interact with users, other programs, and other devices. The system memory 1030 stores system (program) data 1038, such as Figure 1 the input parameters 118, the training models 124, the estimated takeoff weight 138, or a combination thereof.

[0101] The system memory 1030 includes one or more applications 1034 (e.g., instruction sets) executable by the processor 1020. For example, the one or more applications 1034 include instructions 1036 executable by the processor 1020 to initiate, control, or execute with reference to Figures 1 - 9One or more of the described operations. By way of illustration, one or more applications 1034 include instructions 1036 that may be executed by a processor 1020 to initiate, control, or perform one or more of the operations described with reference to receiving input data 130, generating a set of input parameters 118, and processing the set of input parameters 118 using a trained model 124 to generate an estimate 138 of the takeoff weight.

[0102] In a particular implementation, the system memory 1030 includes a non-transitory computer-readable medium (e.g., a computer-readable storage device) storing instructions 1036 that, when executed by the processor 1020, cause the processor 1020 to initiate, perform, or control operations for estimating the takeoff weight of an aircraft. The operations include receiving input data corresponding to trajectory data of the aircraft's flight. The operations also include generating a set of input parameters based on the trajectory data, where the set of input parameters includes a first subset of parameters corresponding to the takeoff phase of the flight and a second subset of parameters corresponding to the climb phase of the flight. The operations further include processing the set of input parameters using a trained model to generate an estimate of the takeoff weight of the aircraft.

[0103] One or more storage devices 1050 include non-volatile storage devices such as magnetic disks, optical disks, or flash memory devices. In a specific example, the storage device 1050 includes both removable and non-removable memory devices. The storage device 1050 is configured to store an operating system, an image of the operating system, applications (e.g., one or more of the applications 1034), and program data (e.g., program data 1038). In a particular aspect, the system memory 1030, the storage device 1050, or both contain tangible computer-readable media. In a specific aspect, one or more of the storage devices 1050 are external to the computing device 1010.

[0104] One or more input / output interfaces 1040 enable the computing device 1010 to communicate with one or more input / output devices 1070 to facilitate user interaction. For example, one or more input / output interfaces 1040 may include a display interface, an input interface, or both. For example, the input / output interface 1040 is adapted to receive input from a user, receive input from another computing device, or a combination thereof. In some implementations, the input / output interface 1040 conforms to one or more standard interface protocols, including serial interfaces (e.g., Universal Serial Bus (USB) interfaces or Institute of Electrical and Electronics Engineers (IEEE) interface standards), parallel interfaces, display adapters, audio adapters, or custom interfaces ("IEEE" is a registered trademark of the Institute of Electrical and Electronics Engineers, Piscataway, New Jersey). In some embodiments, the input / output device 1070 includes one or more user interface devices and a display, including some combination of buttons, keyboards, pointing devices, displays, speakers, microphones, touchscreens, and other devices. In a specific configuration, the input / output interface 1040 may include Figure 2 inputs 202, outputs 242, or some combination thereof.

[0105] The processor 1020 is configured to communicate with a device or controller 1080 via one or more communication interfaces 1060. For example, one or more communication interfaces 1060 may include a network interface. The device or controller 1080 may include, for example, device 104, Figure 1 a training data set 142 of, Figure 2 inputs 202, a data preprocessing system 206, outputs 242, or some combination thereof.

[0106] In some implementations, a non-transitory computer-readable medium (e.g., a computer-readable storage device) stores instructions that, when executed by one or more processors, cause the one or more processors to initiate, execute, or control operations to perform some or all of the functionality described above. For example, the instructions may be executable to implement Figures 1 - 9 one or more operations or methods of. In some embodiments, one or more operations or methods of may be implemented by one or more processors executing the instructions (e.g., one or more central processing units (CPUs), one or more graphics processing units (GPUs), one or more digital signal processors (DSPs)), by dedicated hardware circuitry, or any combination thereof. Figures 1 - 9 Some or all of one or more operations or methods of.

[0107] In combination with the described embodiments, a device includes a unit for receiving input data corresponding to trajectory data of an aircraft flight. For example, the unit for receiving input data includes a computing device 102, Figure 1 a processor 106 of, Figure 2 inputs 202 of,Figure 10 a computing device 1010, an input / output interface 1040, a processor 1020, one or more other circuits or components configured to input data corresponding to the trajectory data of the flight of the aircraft, or any combination thereof.

[0108] The apparatus further includes a unit for generating a set of input parameters based on the trajectory data, where the set of input parameters includes a first subset of input parameters corresponding to the takeoff phase of the flight and a second subset of parameters corresponding to the climb phase of the flight. For example, the unit for generating the set of input parameters 118 includes Figure 1 a computing device 102, one or more processors 106, an input parameter generator 110, Figure 10 a computing device 1010, one or more processors 1020, one or more other circuits or components configured to generate the set of input parameters based on the trajectory data, where the set of input parameters includes a first subset of input parameters corresponding to the takeoff phase of the flight and a second subset of parameters corresponding to the climb phase of the flight, or any combination thereof.

[0109] The apparatus further includes a unit for processing the set of input parameters using a trained model to generate an estimate of the takeoff weight of the aircraft. For example, the unit for processing the set of input parameters includes Figure 1 a computing device 102, (one or more) processors 106, an input parameter processor 112, Figure 2 a regression method system 232, Figure 10 a computing device 1010, (one or more) processors 1020, one or more other circuits or components configured to process the set of input parameters using a trained model to generate an estimate of the takeoff weight of the aircraft, or any combination thereof.

[0110] The illustrations of the examples described herein are intended to provide a general understanding of the structures of different implementations. These illustrations are not intended to serve as a complete description of all elements and features of the devices and systems that utilize the structures or methods described herein. After reviewing the present invention, many other embodiments will be apparent to those skilled in the art. Other implementations can be utilized and obtained from the present disclosure such that structural and logical substitutions and changes can be made without departing from the scope of the present disclosure. For example, method operations can be performed in a different order than shown in the figures or one or more method operations can be omitted. Accordingly, the present disclosure and the figures are considered to be illustrative rather than restrictive.

[0111] In addition, although specific examples have been shown and described herein, it should be understood that any subsequent arrangements designed to achieve the same or similar results may replace the specific implementations shown. The present disclosure is intended to cover any and all subsequent adaptations or variations of different implementations. After reviewing this description, combinations of the above implementations and other implementations not specifically described herein will be apparent to those skilled in the art.

[0112] Submitting the abstract of the present disclosure, it should be understood that it is not used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing detailed description, for the purpose of streamlining the present disclosure, different features may be combined together or described in a single implementation. The above examples illustrate but do not limit the present disclosure. It should also be understood that many modifications and variations are possible in accordance with the principles of the present invention. As reflected in the following claims, the claimed subject matter may cover fewer features than all the features of any disclosed example. Therefore, the scope of the present disclosure is defined by the appended claims and their equivalents.

[0113] Furthermore, the present disclosure includes embodiments according to the following examples:

[0114] According to Example 1, a method includes: receiving input data corresponding to trajectory data of an aircraft flight; generating a set of input parameters based on the trajectory data, wherein the set of input parameters includes a first subset of parameters corresponding to the takeoff phase of the flight and a second subset of parameters corresponding to the climb phase of the flight; and processing the set of input parameters using a trained model to generate an estimated value of the takeoff weight of the aircraft.

[0115] Example 2 includes the method according to Example 1, wherein the set of input parameters further includes a third subset of parameters corresponding to the ground roll phase of the flight, the cruise phase of the flight, or the landing phase of the flight.

[0116] Example 3 includes the method according to Example 1 or Example 2, wherein the set of input parameters further includes subsets of parameters corresponding to each of the ground roll phase of the flight, the cruise phase of the flight, and the landing phase of the flight.

[0117] Example 4 includes the method according to any one of Examples 1 to 3, wherein the input data corresponds to publicly available surveillance data associated with the flight of the aircraft.

[0118] Example 5 includes the method according to Example 4, wherein the publicly available surveillance data includes automatic dependent surveillance - broadcast data from the aircraft.

[0119] Example 6 includes the method according to any one of Examples 1 to 5, and further includes adjusting parameters of a planned flight of the aircraft, the planned flight being after the flight of the aircraft.

[0120] Example 7 includes the method of Example 6 and further includes providing a verification indication of the initial weight of the aircraft before a planned flight.

[0121] Example 8 includes the method of any one of Examples 1 to 7, and further includes training a training model with a set of training data, the set of training data including a set of quick access recorder data, synthetic data, or a combination thereof.

[0122] Example 9 includes the method according to Example 8, wherein a portion of the synthetic data is generated from a basis of an aircraft data model of the aircraft.

[0123] Example 10 includes the method according to Example 8 or Example 9, and further includes: extracting a plurality of features; determining a feature importance value for each of the plurality of features; and selecting a set of the plurality of features based at least on the feature importance value, wherein the set of the input parameters corresponds to the selected set of the plurality of features.

[0124] Example 11 includes the method according to Example 10, wherein the feature importance value is associated with a specific aircraft type.

[0125] Example 12 includes the method according to Example 10 or Example 11, wherein the set of the plurality of features includes a subset of features corresponding to the ground roll phase of the flight, the subset of features including maximum ground speed, average flap angle, weight estimate, ground roll distance, or some combination thereof.

[0126] Example 13 includes the method according to any one of Examples 10 to 12, wherein the set of the plurality of features includes a subset of features corresponding to the takeoff phase of the flight, the subset of features including average specific energy of the aircraft, time span, maximum acceleration, maximum specific energy gradient, or some combination thereof.

[0127] Example 14 includes the method according to any one of Examples 10 to 13, wherein the set of the plurality of features includes a subset of features corresponding to the climb phase of the flight, the subset of features including climb thrust, specific energy gradient, one or more climb feature rates, maximum climb angle, or some combination thereof.

[0128] Example 15 includes the method according to any one of Examples 10 to 14, wherein the set of the plurality of features includes a subset of features corresponding to the cruise phase of the flight, the subset of features including maximum specific energy, travel duration, maximum altitude, maximum Mach, maximum calibrated airspeed, or some combination thereof.

[0129] Example 16 includes the method according to any one of Examples 10 to 15, wherein the set of multiple features includes a subset of features corresponding to the landing phase of the flight, and the subset of features includes a weight estimate value, an approach speed, an average flap angle, or some combination thereof.

[0130] Example 17 includes the method according to any one of Examples 8 to 16, wherein training the training model includes training a plurality of trial models and selecting one of the trained plurality of trial models based on a performance criterion.

[0131] Example 18 includes the method of Example 17, and further includes partitioning the training data set into a training data subset and a test data subset, and wherein the performance criterion is based on the test data subset.

[0132] Example 19 includes the method according to Example 18, wherein the training data subset includes synthetic data, and the test data subset includes real data.

[0133] According to Example 20, a device includes: one or more processors configured to receive input data corresponding to trajectory data of an aircraft flight; generate a set of input parameters based on the trajectory data, wherein the set of input parameters includes a first subset of parameters corresponding to the takeoff phase of the flight and a second subset of parameters corresponding to the climb phase of the flight; and process the set of input parameters using a training model to generate an estimate of the takeoff weight of the aircraft.

[0134] Example 21 includes the device according to Example 20, wherein the set of input parameters further includes a third subset of parameters corresponding to the ground roll phase of the flight, the cruise phase of the flight, or the landing phase of the flight.

[0135] Example 22 includes the device according to Example 20 or Example 21, wherein the set of input parameters further includes a subset of parameters corresponding to each of the ground roll phase of the flight, the cruise phase of the flight, and the landing phase of the flight.

[0136] Example 23 includes the device according to any one of Examples 20 to 22, wherein the input data corresponds to publicly available surveillance data associated with the flight of the aircraft.

[0137] Example 24 includes the device of Example 23, wherein the publicly available surveillance data includes automatic dependent surveillance - broadcast data from the aircraft.

[0138] Example 25 includes the device according to any one of Examples 20 to 24, wherein the one or more processors are further configured to adjust parameters of a planned flight of the aircraft, the planned flight being after the flight of the aircraft.

[0139] Example 26 includes the apparatus of Example 25, wherein one or more processors are further configured to provide a verification indication of an initial weight of an aircraft prior to a scheduled flight.

[0140] Example 27 includes the apparatus according to any one of Examples 20 to 26, wherein one or more processors are further configured to train a training model with a set of training data, the set of training data including a set of quick access recorder data, synthetic data, or a combination thereof.

[0141] Example 28 includes the apparatus of Example 27, wherein a portion of the synthetic data is generated from a basis of an aircraft data model of the aircraft.

[0142] Example 29 includes the apparatus according to Example 27 or Example 28, wherein one or more processors are further configured to extract a plurality of features; determine a feature importance value for each of the plurality of features; and select a set of the plurality of features based at least on the feature importance value, wherein the set of the input parameters corresponds to the selected set of the plurality of features.

[0143] Example 30 includes the apparatus according to Example 29, wherein the feature importance value is associated with a particular aircraft type.

[0144] Example 31 includes the apparatus according to Example 29 or Example 30, wherein the set of the plurality of features includes a subset of features corresponding to a ground roll phase of a flight, the subset of features including a maximum ground speed, an average flap angle, a weight estimate, a ground roll distance, or some combination thereof.

[0145] Example 32 includes the apparatus according to any one of Examples 29 to 31, wherein the set of the plurality of features includes a subset of features corresponding to a takeoff phase of a flight, the subset of features including an average specific energy of the aircraft, a time span, a maximum acceleration, a maximum specific energy gradient, or some combination thereof.

[0146] Example 33 includes the apparatus according to any one of Examples 29 to 32, wherein the set of the plurality of features includes a subset of features corresponding to a climb phase of a flight, the subset of features including a climb thrust, a specific energy gradient, one or more climb feature rates, a maximum climb angle, or some combination thereof.

[0147] Example 34 includes the apparatus according to any one of Examples 29 to 33, wherein the set of the plurality of features includes a subset of features corresponding to a cruise phase of a flight, the subset of features including a maximum specific energy, a travel duration, a maximum altitude, a maximum Mach, a maximum calibrated airspeed, or some combination thereof.

[0148] Example 35 includes the apparatus according to any one of Examples 29 to 34, wherein the set of multiple features includes a subset of features corresponding to the landing phase of a flight, and the subset of features includes a weight estimate, an approach speed, an average flap angle, or some combination thereof.

[0149] Example 36 includes the apparatus according to any one of Examples 27 to 35, wherein the one or more processors are further configured to train a training model, including training multiple trial models and selecting one of the trained multiple trial models based on a performance criterion.

[0150] Example 37 includes the apparatus according to Example 36, wherein the one or more processors are further configured to partition a training data set into a training data subset and a test data subset, and wherein the performance criterion is based on the test data subset.

[0151] Example 38 includes the apparatus according to Example 37, wherein the training data subset includes synthetic data and the test data subset includes real data.

[0152] According to Example 39, a non-transitory computer-readable medium includes instructions that, when executed by one or more processors, cause the one or more processors to: receive input data corresponding to trajectory data of a flight of an aircraft; generate a set of input parameters based on the trajectory data, wherein the set of input parameters includes a first subset of parameters corresponding to the takeoff phase of the flight and a second subset of parameters corresponding to the climb phase of the flight; and process the set of input parameters using a training model to generate an estimate of the takeoff weight of the aircraft.

[0153] Example 40 includes the non-transitory computer-readable medium according to Example 39, wherein the set of input parameters further includes a third subset of parameters corresponding to the ground roll phase of the flight, the cruise phase of the flight, or the landing phase of the flight.

[0154] Example 41 includes the non-transitory computer-readable medium according to Example 39 or Example 40, wherein the set of input parameters further includes a subset of parameters corresponding to each of the ground roll phase of the flight, the cruise phase of the flight, and the landing phase of the flight.

[0155] Example 42 includes the non-transitory computer-readable medium according to any one of Examples 39 to 41, wherein the input data corresponds to publicly available surveillance data associated with a flight of an aircraft.

[0156] Example 43 includes the non-transitory computer-readable medium according to Example 42, wherein the publicly available surveillance data includes automatic dependent surveillance-broadcast data from the aircraft.

[0157] Example 44 includes a non-transitory computer-readable medium according to any one of Examples 39 to 43, wherein the instructions, when executed by one or more processors, further cause the one or more processors to adjust parameters of a planned flight of an aircraft, the planned flight being after the flight of the aircraft.

[0158] Example 45 includes a non-transitory computer-readable medium according to Example 44, wherein the instructions, when executed by one or more processors, further cause the one or more processors to provide a verification indication of an initial weight of the aircraft before the planned flight.

[0159] Example 46 includes a non-transitory computer-readable medium according to any one of Examples 39 to 45, wherein the instructions, when executed by one or more processors, further cause the one or more processors to train a training model with a set of training data, the set of training data including a set of quick access recorder data, synthetic data, or a combination thereof.

[0160] Example 47 includes a non-transitory computer-readable medium according to Example 46, wherein a portion of the synthetic data is generated from a basis of an aircraft data model of the aircraft.

[0161] Example 48 includes a non-transitory computer-readable medium according to Example 46 or Example 47, wherein the instructions, when executed by one or more processors, further cause the one or more processors to extract a plurality of features; determine a feature importance value for each of the plurality of features; and select a set of the plurality of features based at least on the feature importance values, wherein the set of the input parameters corresponds to the selected set of the plurality of features.

[0162] Example 49 includes a non-transitory computer-readable medium according to Example 48, wherein the feature importance value is associated with a particular aircraft type.

[0163] Example 50 includes a non-transitory computer-readable medium according to Example 48 or Example 49, wherein the set of the plurality of features includes a subset of features corresponding to a ground roll phase of a flight, the subset of features including a maximum ground speed, an average flap angle, a weight estimate, a ground roll distance, or some combination thereof.

[0164] Example 51 includes a non-transitory computer-readable medium according to any one of Examples 48 to 50, wherein the set of the plurality of features includes a subset of features corresponding to a takeoff phase of a flight, the subset of features including an average specific energy of the aircraft, a time span, a maximum acceleration, a maximum specific energy gradient, or some combination thereof.

[0165] Example 52 includes a non-transitory computer-readable medium according to any one of Examples 48 to 41, wherein the set of multiple features includes a subset of features corresponding to the climb phase of the flight, and the subset of features includes climb thrust, specific energy gradient, one or more climb feature rates, maximum climb angle, or some combination thereof.

[0166] Example 53 includes a non-transitory computer-readable medium according to any one of Examples 48 to 52, wherein the set of multiple features includes a subset of features corresponding to the cruise phase of the flight, and the subset of features includes maximum specific energy, travel duration, maximum altitude, maximum Mach, maximum calibrated airspeed, or some combination thereof.

[0167] Example 54 includes a non-transitory computer-readable medium according to any one of Examples 48 to 53, wherein the set of multiple features includes a subset of features corresponding to the landing phase of the flight, and the subset of features includes weight estimate, approach speed, average flap angle, or some combination thereof.

[0168] Example 55 includes a non-transitory computer-readable medium according to any one of Examples 46 to 54, wherein the instructions, when executed by one or more processors, further cause the one or more processors to train a training model, including training multiple trial models and selecting one of the trained multiple trial models based on a performance criterion.

[0169] Example 56 includes the non-transitory computer-readable medium according to Example 55, wherein the one or more processors are further configured to partition a training data set into a training data subset and a test data subset, and wherein the performance criterion is based on the test data subset.

[0170] Example 57 includes the non-transitory computer-readable medium according to Example 56, wherein the training data subset includes synthetic data and the test data subset includes real data.

[0171] According to Example 58, a device includes: a unit for receiving input data of trajectory data corresponding to an aircraft flight; a unit for generating a set of input parameters based on the trajectory data, wherein the set of input parameters includes a first subset of parameters corresponding to the takeoff phase of the flight and a second subset of parameters corresponding to the climb phase of the flight; and a unit for processing the set of input parameters using a training model to generate an estimated value of the takeoff weight of the aircraft.

[0172] Example 59 includes the device according to Example 58, wherein the set of input parameters further includes a third subset of parameters corresponding to the ground roll phase of the flight, the cruise phase of the flight, or the landing phase of the flight.

[0173] Example 60 includes the apparatus according to Example 58 or Example 59, wherein the set of input parameters further includes a subset of parameters corresponding to each of a ground roll phase of flight, a cruise phase of flight, and a landing phase of flight.

[0174] Example 61 includes the apparatus according to any one of Examples 58 to 60, wherein the input data corresponds to publicly available surveillance data associated with the flight of an aircraft.

[0175] Example 62 includes the apparatus according to Example 61, wherein the publicly available surveillance data includes automatic dependent surveillance - broadcast data from the aircraft.

[0176] Example 63 includes the apparatus of any one of Examples 58 - 62 and further includes a unit for adjusting parameters of a planned flight of the aircraft, the planned flight being after the flight of the aircraft.

[0177] Example 64 includes the apparatus of Example 63 and further includes a unit for providing a verification indication of an initial weight of the aircraft before the planned flight.

[0178] Example 65 includes the apparatus according to any one of Examples 58 to 64 and further includes a unit for training a training model using a set of training data, the set of training data including a set of quick access recorder data, synthetic data, or a combination thereof.

[0179] Example 66 includes the apparatus according to Example 65, wherein a portion of the synthetic data is generated from a basis of an aircraft data model of the aircraft.

[0180] Example 67 includes the apparatus according to Example 65 or Example 66, further comprising: a unit for extracting a plurality of features; a unit for determining a feature importance value for each of the plurality of features; and a unit for selecting the set of the plurality of features based at least on the feature importance values, wherein the set of the input parameters corresponds to the selected set of the plurality of features.

[0181] Example 68 includes the apparatus according to Example 67, wherein the feature importance value is associated with a specific aircraft type.

[0182] Example 69 includes the apparatus according to Example 67 or Example 68, wherein the set of the plurality of features includes a subset of features corresponding to a ground roll phase of flight, the subset of features including a maximum ground speed, an average flap angle, a weight estimate, a ground roll distance, or some combination thereof.

[0183] Example 70 includes the apparatus according to any one of Examples 67 to 69, wherein the set of multiple features includes a subset of features corresponding to the take-off phase of the flight, and the subset of features includes the average specific energy of the aircraft, the time span, the maximum acceleration, the maximum specific energy gradient, or some combination thereof.

[0184] Example 71 includes the apparatus according to any one of Examples 67 to 70, wherein the set of multiple features includes a subset of features corresponding to the climb phase of the flight, and the subset of features includes the climb thrust, the specific energy gradient, one or more climb feature rates, the maximum climb angle, or some combination thereof.

[0185] Example 72 includes the apparatus according to any one of Examples 67 to 71, wherein the set of multiple features includes a subset of features corresponding to the cruise phase of the flight, and the subset of features includes the maximum specific energy, the travel duration, the maximum altitude, the maximum Mach, the maximum calibrated airspeed, or some combination thereof.

[0186] Example 73 includes the apparatus according to any one of Examples 67 to 72, wherein the set of multiple features includes a subset of features corresponding to the landing phase of the flight, and the subset of features includes the weight estimate, the approach speed, the average flap angle, or some combination thereof.

[0187] Example 74 includes the apparatus according to any one of Examples 65 to 73, wherein training the training model includes training a plurality of trial models and selecting one of the trained plurality of trial models based on a performance criterion.

[0188] Example 75 includes the apparatus according to Example 74 and further includes partitioning a training data set into a training data subset and a test data subset, and wherein the performance criterion is based on the test data subset.

[0189] Example 76 includes the apparatus according to Example 75, wherein the training data subset includes synthetic data and the test data subset includes real data.

Claims

1. A computer-implemented method comprising: receiving input data corresponding to trajectory data of the aircraft flight; generating a set of input parameters based on the trajectory data, wherein the set of input parameters includes a first subset of parameters corresponding to a takeoff phase of the flight and a second subset of parameters corresponding to a climb phase of the flight; as well as The set of input parameters is processed using a trained model to generate an estimate of a takeoff weight of the aircraft.

2. The computer-implemented method of claim 1 , wherein: The set of input parameters further includes a third subset of parameters corresponding to a ground roll phase of the flight, a cruise phase of the flight, or a landing phase of the flight.

3. A computer-implemented method according to any one of claims 1 and 2, wherein: The input data corresponds to publicly available surveillance data associated with the flight of the aircraft. 4 . The computer-implemented method of claim 1 , further comprising adjusting parameters of a planned flight of the aircraft, the planned flight subsequent to the flight of the aircraft. 5 . 5 . The computer-implemented method of claim 4 , further comprising providing a verified indication of an initial weight of the aircraft prior to the planned flight.

6. The computer-implemented method of any one of claims 1 to 5, further comprising training the training model using a training data set, the training data set comprising a set of Quick Access Recorder ("QAR") data, synthetic data, or a combination thereof.

7. The computer-implemented method of claim 6, further comprising: Extract multiple features; determining a feature importance value for each of the plurality of features; as well as A set of the plurality of features is selected based at least on the feature importance values, wherein the set of input parameters corresponds to the selected set of the plurality of features.

8. The computer-implemented method of claim 7, wherein: the set of the plurality of characteristics comprises a subset of characteristics corresponding to a ground roll phase of the flight, the subset of characteristics comprising maximum ground speed, average flap angle, weight estimate, ground roll distance, or some combination thereof; and / or wherein the set of the plurality of characteristics comprises a subset of characteristics corresponding to a takeoff phase of the flight, the subset of characteristics corresponding to a takeoff phase of the flight comprising an average specific energy, a time span, a maximum acceleration, a maximum specific energy gradient of the aircraft, or some combination thereof; and / or wherein the set of the plurality of characteristics comprises a subset of characteristics corresponding to a climb phase of the flight, the subset of characteristics corresponding to a climb phase of the flight comprising climb thrust, specific energy gradient, one or more characteristic rates of climb, maximum climb angle, or some combination thereof; and / or wherein the set of the plurality of characteristics comprises a subset of characteristics corresponding to the cruise phase of the flight, the subset of characteristics corresponding to the cruise phase of the flight comprising maximum specific energy, travel duration, maximum altitude, maximum Mach, maximum calibrated airspeed, or some combination thereof; and / or wherein the set of the plurality of features includes a subset of features corresponding to a landing phase of the flight, the subset of features corresponding to a landing phase of the flight including a weight estimate, an approach speed, an average flap angle, or some combination thereof.

9. The computer-implemented method of claim 6, wherein: Training the training model includes training a plurality of trial models and selecting one of the trained plurality of trial models based on a performance criterion.

10. The computer-implemented method of claim 9, further comprising dividing the training data set into a training data subset and a testing data subset, and wherein the performance criterion is based on the testing data subset.

11. The computer-implemented method of claim 10, wherein: The training data subset includes synthetic data, and the testing data subset includes real data. 12 . An apparatus for aircraft takeoff weight estimation, comprising one or more processors configured to execute the method of any one of claims 1 to 5.

13. The device according to claim 12, wherein: The one or more processors are further configured to perform the method according to any one of claims 6 to 11.

14. A non-transitory computer-readable medium comprising instructions which, when executed by one or more processors, cause the one or more processors to perform the method according to any one of claims 1 to 5.

15. The non-transitory computer readable medium of claim 14, wherein: The instructions, when executed by the one or more processors, further cause the one or more processors to perform the method according to any one of claims 6 to 11.

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