Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/08—Learning methods
  • G06N3/084—Backpropagation, e.g. using gradient descent
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/04—Architecture, e.g. interconnection topology
  • G06N3/045—Combinations of networks
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/04—Architecture, e.g. interconnection topology
  • G06N3/0499—Feedforward networks
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/08—Learning methods
  • G06N3/09—Supervised learning
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N3/00—Computing arrangements based on biological models
  • G06N3/02—Neural networks
  • G06N3/04—Architecture, e.g. interconnection topology
  • G06N3/048—Activation functions

Definitions

• the present invention relates generally to control systems and in particular to a device and a method for predicting the value of a quantity intended for use by a control system.
• the prediction device comprises a first neural network-based predictor configured to calculate an estimate of said non-explicit parameter and a second neural network-based predictor configured to calculate an estimate of said value of the magnitude from the estimation of the non-explicit parameter, the two predictors receiving a set of input data, each neural network being associated with a set of weights.
• the prediction device is configured to apply a plurality of iterations of a single learning function to the two predictors, the learning function comprising: The invention improves the situation.
• a device for predicting the value of a quantity intended for use by a control system implemented on a computer, the quantity depending on several parameters, the parameters comprising a non-explicit parameter.
• the prediction device comprises a first neural network-based predictor configured to calculate an estimate of said non-explicit parameter and a second neural network-based predictor configured to calculate an estimate of said value of the magnitude from the estimation of the non-explicit parameter, the two predictors receiving a set of input data, each neural network being associated with a set of weights.
• the prediction device is configured to apply a plurality of iterations of a single learning function to the two predictors, the learning function comprising:
• a forward propagation block configured to calculate, based on the input data of the two predictors, the gradient of a minimization function of a cost function of the first predictor;
• a backpropagation block configured to update the weights of the neural networks of the two predictors by backpropagating the gradients calculated by the forward propagation block.
• the prediction device is configured to estimate said value of the magnitude at a future instant, after said iterations of the learning function, by applying input data to the neural networks of the two predictors using the weights updated by the learning function.
• the back propagation block can be configured to update the weights of the second predictor, while the weights of the first predictor are frozen.
• the first predictor may comprise a neural network receiving generic input data, the block of
• the first predictor can comprise a set of elementary neural networks each receiving specific input data.
• the second predictor can be configured to apply the predicted value as input to the first predictor.
• the first predictor can be configured to broadcast the output value of the non-explicit parameter to external systems.
• control system is an air traffic control system
• the prediction device then being configured to predict the arrival time of a given aircraft making a trajectory between a starting point and a point arrival point, the non-explicit parameter being relative to the arrival point of the airplane.
• the non-explicit parameter may be the congestion rate at the end point.
• the non-explicit parameter can be a global delay parameter.
• the input data of the first predictor can include characteristics relating to the given aircraft, information relating to the aircraft arriving at the point of arrival, and a number representing the maximum number of aircraft associated with the point d 'arrival.
• the input data for aircraft arriving at the point of arrival may include the number and type of aircraft scheduled to land at the point of arrival by time range.
• the input data of the second predictor can include characteristics relating to the given aircraft, information relating to the aircraft. arriving at the point of arrival, and capacity information associated with the point of arrival.
• the input data for the second predictor may further include a time slot representing the expected landing range for the given aircraft, and a history of values of the non-explicit parameter over a period of time.
• the embodiments thus improve the prediction of the value of quantities depending on a non-explicit parameter, by the use of two jointly trained neural networks, the predicted quantity thus being more precise and improving the control performed by the systems. control using the predicted value.
• FIG. 1 shows an example of an environment using a prediction device, according to embodiments of the invention.
• FIG. 2 is a diagram showing an example of a neural network used to implement a predictor of the prediction device, according to one embodiment.
• FIG. 3 is a diagram illustrating the learning function implemented to jointly train two neural networks corresponding to two predictors of the prediction device, according to certain embodiments.
• FIG. 4 represents the first neural network-based predictor, in an example of application of the invention to predicting the time of arrival of an aircraft.
• FIG. 5 represents the second neural network-based predictor, according to the exemplary embodiment of Figure 6.
• FIG. 6 shows the interactions between the first predictor and the second predictor in the learning phase, according to the example embodiment of Figures 5 and 6.
• FIG. 7 is a flowchart showing the method of learning the two predictors, according to certain embodiments.
• FIG. 8 is a flowchart representing the method for predicting the non-explicit quantity implemented by the first predictor, in a generalization phase, according to one embodiment.
• FIG. 9 represents the method for predicting the value of magnitude implemented by the second predictor, in the generalization phase, according to one embodiment.
• FIG. 10 represents a plurality of elementary neural networks used by the first predictor to take account of specific data, according to an exemplary embodiment.
• FIG. 1 shows an example of an environment using a prediction device 100, according to embodiments of the invention.
• the prediction device 100 is configured to calculate (or predict) an estimate of the value that a magnitude P (also called 'control magnitude') will take at a final instant in response to the triggering or to the occurrence of an event between an initial instant Ti and a final instant Tf.
• the magnitude P depends on a plurality of parameters comprising at least one 'non-explicit' parameter Q.
• the predicted value P is intended for use by a computer implemented control system 200 for optimization purposes.
• a 'non-explicit' parameter refers to a parameter having no reality in the field, such as for example a parameter having no explicit formula, not defined by a formula or values and / or of which only the link with the other parameters on which the magnitude P depends.
• a “non-explicit” parameter can also be defined as a parameter calculated from a method based on the data.
• the predicted quantity may be the estimated time of arrival ETA (ETA is the acronym for "Estimated Time of Arrivai” literally meaning “ Estimated Time of Arrival) ”of an airplane in a given airport (destination airport), for a given flight from a departure airport, the event being the flight that occurs between the take-off time (initial time Ti) and the arrival time (final instant Tf).
• the predicted quantity P depends on a set of parameters relating to the event (such as the flight plan, the weather forecast on the route of the aircraft, etc.), to data relating to past occurrences of the event (for example historical data of one or more relative parameters flight over given past periods).
• the non-explicit parameter Q may for example be a
• the prediction device 100 comprises a first predictor 101, based on a neural network, configured to calculate an estimate of the 'non-explicit' Q parameter (for example, the parameter total instantaneous delay on the arrival airport for a prediction of an ETA) and a second predictor 102, based on neural networks, configured to calculate an estimate (or prediction) of the value P (for example ETA) from a first predictor 101, based on a neural network, configured to calculate an estimate of the 'non-explicit' Q parameter (for example, the parameter total instantaneous delay on the arrival airport for a prediction of an ETA) and a second predictor 102, based on neural networks, configured to calculate an estimate (or prediction) of the value P (for example ETA) from
• Both predictors 101 and 102 are configured to receive a set of input data.
• Each neural network corresponding to the predictors 101 and 102 is also associated with a set of weights.
• the non-explicit parameter Q, delivered at the output of the first predictor 101 can for example be a data vector.
• the non-explicit parameter Q provided by the first predictor 101 is intended to improve the estimate made by the second predictor.
• FIG. 2 is a diagram representing the neuron network corresponding to each predictor 101 or 102.
• a neural network constitutes a computational model imitating the functioning of biological neural networks.
• a neural network 2 comprises neurons interconnected with one another by synapses generally implemented in the form of digital memories (resistive components for example).
• a neural network 2 can comprise a plurality of successive layers, comprising an input layer carrying the input signal and an output layer carrying the result of the prediction made by the neural network (result of the network), and a or more intermediate layers.
• the first entry layer contains dummy neurons that pass the supplied inputs to the network.
• Each layer of a neural network takes its inputs from the outputs of the previous layer.
• the number of neurons on each layer is equal to the number of inputs from neurons in the next layer.
• a given layer of neural network 2 is thus composed of a set of generalization neurons taking their inputs from the neurons of the previous layer.
• the signals propagated at the input and at the output of the layers of the network can be digital values (information encoded in the value of the signals), or electrical pulses in the case of pulse encoding (information encoded temporally according to the order arrival of pulses or according to pulse frequency).
• the pulses can come from a sensor.
• a neural network 2 comprises a set of input data 20 (also called 'input coefficients'), denoted xi, and output data 25 (also called' coefficients of output '), denoted Oj.
• the output coefficients Oj correspond to the output values of the neurons of the neural network 2.
• the output values Oj are calculated from the inputs xi and the synaptic weights 21, denoted Wij.
• Each output output coefficient Oj is calculated by applying an activation function f to the input coefficients xi (block 23).
• Each neuron of the neural network is configured to calculate a weighted sum of its inputs xi (20) using a combination function ⁇ (block 22) and the weights Wij (block 21), before applying the function d 'activation f (block 23) at this resulting weighted sum to produce its output Oj:
• a 'non-explicit' parameter refers to a parameter having no reality in the field, such as for example a parameter having no explicit formula, not defined by a formula or values and / or of which only the link with the other parameters on which the magnitude P depends.
• a “non-explicit” parameter can also be defined as a parameter calculated from a method based on the data.
• the predicted quantity may be the estimated time of arrival ETA (ETA is the acronym for "Estimated Time of Arrivai” literally meaning “Estimated Time of Arrival” of a plane in a given airport (destination airport), for a given flight from a departure airport, the event being the flight which occurs between the take-off time (initial instant Ti) and the arrival time (final instant Tf).
• the predicted quantity P depends on a set of parameters relating to the event (such as the flight plan, the weather forecast on the path of the airplane, etc.), to data relating to occurrences past periods of the event (for example historical data of one or more parameters relating to the flight over given past periods).
• the non-explicit parameter Q may for example be a
• the prediction device 100 comprises a first predictor 101, based on a neural network, configured to calculate an estimate of the 'non-explicit' Q parameter (for example, the parameter total instantaneous delay on the arrival airport for a prediction of an ETA) and a second predictor 102, based on neural networks, configured to calculate an estimate (or prediction) of the value P (for example ETA) from a first predictor 101, based on a neural network, configured to calculate an estimate of the 'non-explicit' Q parameter (for example, the parameter total instantaneous delay on the arrival airport for a prediction of an ETA) and a second predictor 102, based on neural networks, configured to calculate an estimate (or prediction) of the value P (for example ETA) from
• Both predictors 101 and 102 are configured to receive a set of input data.
• Each neural network corresponding to the predictors 101 and 102 is also associated with a set of weights.
• the non-explicit parameter Q, delivered at the output of the first predictor 101 can for example be a data vector.
• the non-explicit parameter Q provided by the first predictor 101 is intended to improve the estimate made by the second predictor.
• FIG. 2 is a diagram representing the neuron network corresponding to each predictor 101 or 102.
• a neural network constitutes a computational model imitating the functioning of biological neural networks.
• a neural network 2 comprises neurons interconnected with each other by generally implemented synapses in the form of digital memories (resistive components for example).
• a neural network 2 can comprise a plurality of successive layers, comprising an input layer carrying the input signal and an output layer carrying the result of the prediction made by the neural network (result of the network), and a or more intermediate layers.
• the first input layer contains dummy neurons that pass the supplied inputs to the network.
• Each layer of a neural network takes its inputs from the outputs of the previous layer.
• the number of neurons on each layer is equal to the number of inputs from neurons in the next layer.
• a given layer of neural network 2 is thus composed of a set of generalization neurons taking their inputs from the neurons of the previous layer.
• the signals propagated at the input and at the output of the layers of the network can be digital values (information encoded in the value of the signals), or electrical pulses in the case of pulse encoding (information encoded temporally according to the order arrival of pulses or according to pulse frequency).
• the pulses can come from a sensor.
• a neural network 2 comprises a set of input data 20 (also called 'input coefficients'), denoted xi, and output data 25 (also called' coefficients of output '), denoted Oj.
• the output coefficients Oj correspond to the output values of the neurons of the neural network 2.
• the output values Oj are calculated from the inputs xi and the synaptic weights 21, denoted Wij.
• Each output output coefficient Oj is calculated by applying an activation function f to the input coefficients xi (block 23).
• Each neuron of the neural network is configured to calculate a weighted sum of its inputs xi (20) using a combination function ⁇ (block 22) and the weights Wij (block 21), before applying the function d 'activation f (block 23) at this resulting weighted sum to produce its output Oj:
• the activation function f can take different values depending on the value of the weighted sum of the weights of the neural network with respect to a threshold (also called 'bias'):
• the neuron is in a transition phase
• the threshold therefore represents the threshold from which a neuron will emit a signal.
• the activation function of f neurons can be, for example, a sigmoid or thresholding function capable of introducing non-linearity.
• the input signal propagates from one layer of the neural network to another until the output, with or without activating the neurons.
• Synaptic weights can be determined by learning in a learning phase. Random values are initially assigned to the weights of the neural network and then a set of data xi is used to perform the training. Learning a neural network involves determining the optimal values of synaptic weights, for each neuron in the neural network, from the last layer of the network to the first, using a learning function.
• the learning phase can implement a plurality of iterations of the learning function, each iteration comprising a forward propagation step ('forward) and a backward' step for correct the errors between the outputs obtained in the forward propagation phase and the outputs expected for the input sample considered.
• 'forward forward propagation step
• backward' step for correct the errors between the outputs obtained in the forward propagation phase and the outputs expected for the input sample considered.
• the learning phase thus makes it possible to compare the output obtained with respect to the expected output (in the case of a supervised method), and according to this comparison, to update the links between the neurons represented. by synaptic weights to improve the final result (weights can be changed to strengthen or inhibit the bonds between neurons).
• the signal corresponding to the input sample is propagated forward in the layers of the neural network from the first layer, from one layer (k-1) to the next layer (k) until the last layer .
• the activation function f and the synaptic weights connecting neurons of a previous layer (k-1) and a subsequent layer (k) are used.
• any errors obtained by a neuron are back-propagated to its synapses and to the neurons which are connected to it.
• the backpropagation can be a gradient backpropagation to modify the synaptic weights while taking into account their impact on the errors generated.
• the synaptic weights that contribute to causing a large error can be changed more significantly than the weights that cause a smaller error.
• the error ei between the output yi output calculated by the neural network and the expected output ti in the current sample is determined, using the derivative of the activation function cp '.
• the error is then back-propagated backwards from the last layer, layer by layer, to the first layer.
• the synaptic weights are then modified by a gradient descent algorithm.
• each iteration of the learning function makes it possible, from a sample at the input of the network, to calculate the output of the network, to compare it with the expected output and to back-propagate an error signal in the network to modify synaptic weights.
• examples of each class are provided at the input of the neural network 2 (input data) and the output provided by the neural network in response to these input data represents the number of the class considered.
• the network is then driven by the gradient descent algorithm to minimize the error between the obtained output and the expected output (by applying a cost minimization function), which leads to the modification of the weights of the neurons at each iteration of the learning algorithm.
• the duration of the training phase may depend on the size of the database storing the samples used for training and on the size of the network. It can therefore be relatively long.
• a so-called generalization phase which is faster, is implemented.
• the weights learned from the learning phase are used (static neural network in which the weights are frozen).
• Input data is presented to the neural network and a response from the neural network is obtained (for example, representing the number of the class to which the input data for a classification network belongs).
• the prediction device 100 is configured to apply a single function
• Figure 3 is a diagram illustrating the learning function implemented to jointly train the two neural networks 2A and 2B (commonly designated by the reference 2 'in Figure 2) corresponding to the predictors 101 and 102.
• the common learning function 3 applied to the two predictors 101 and 102 comprises two blocks 31 and 32 called successively at each iteration of the learning function:
• a forward propagation block 31 ⁇ forward ' configured to calculate, at each iteration, the gradient of a set of minimization functions of the cost function of the first predictor 101 (P2), in response to the data of entry applied two predictors 101 and 102;
• back-propagation block 32 (“backward") configured to update the weights of the neural networks of the two predictors 101 and 102 by back-propagating the gradients calculated by the forward propagation block, at the current iteration.
• the cost function of the first predictor 101 can for example be the quadratic error on the learning base which consists in minimizing the sum of the squares of the errors between the value yi obtained at the output of the neural network 2A and the value expected ti at the output of the neural network 2A.
• the cost function of the first predictor 101 can be cross entropy.
• the cost function of the first predictor 101 is not limited to squared error or cross-entropy and may be defined by other functions.
• the minimization of the cost function of the first predictor 101 uses the calculation of the gradient of the cost function with respect to the weights of the network.
• the gradient can be defined as the sum of all the partial gradients calculated for each of the examples of the learning base:
• the modification of the weights of the two neural networks 2A and 2B of the predictors 101 and 102 can be carried out after each partial gradient calculation or alternatively after the total gradient calculation.
• the prediction device 100 is further configured to then implement a generalization phase in which the synaptic weights thus updated are fixed.
• the prediction device 100 applies input data received at the input of the neural networks of the two predictors 101 and 102 and calculates the response to these inputs using the weights determined during the learning phase, this which provides an estimate (or prediction) of the value of the quantity P (for example ETA).
• P for example ETA
• the remainder of the description will be given with reference to an example of application of the invention to the prediction of the time of arrival of an aircraft (ETA).
• ETA time of arrival of an aircraft
• the invention applies similarly to the prediction of other parameters whose value depends on a non-explicit parameter, the predicted parameter P and the non-implicit parameter Q depending on the nature. of the control system 200.
• the invention can be applied to the prediction of the time of arrival at another intermediate point of the trajectory of the aircraft ETO (acronym for 'Estimated Time of Overflight' meaning Time of Overflight Valued').
• the prediction of 4D trajectories is a major issue in many fields.
• the prediction of the ETA arrival time of an aircraft makes it possible in particular to optimize the management of aircraft flows by an air traffic control system 200. It is however useful to be able to have a prediction that is as reliable as possible. in order to be able to deduce therefrom a prediction of the instants of passage of the aircraft from one sector to another or to predict flight delays.
• the trajectory of an airplane between a departure airport and an arrival airport is estimated by an airline, according to available information relating to the departure and arrival airports, weather conditions and aircraft characteristics.
• the flight plan of an airplane is conventionally planned taking into account the information available on the departure and arrival airports, weather forecasts on the path of the airplane, the weight of the airplane and the aircraft fuel.
• the flight plans are then transmitted before the departure of the aircraft and processed by the ATC air traffic control center. Enroute updates of these flight plans may be made as a function of events occurring during the journey, such as exceptional weather conditions, and / or incidents en route or at the arrival airport.
• the updates are then carried out by operators between the various ATC centers concerned by the flight (arrival ATC center, departure ATC center).
• arrival ATC center departure ATC center
• Such approaches can be supplemented by calculating an estimated time of arrival from historical flight data, representing data relating to flights made between the departure airport and the arrival airport over a past period of time, such as that the weather and air traffic conditions observed on such past flights.
• ETAs conventionally calculated on the basis of formulas and / of historical data lack precision.
• the prediction device 100 improves the prediction of I ⁇ TA by using the two predictors 101 and 102 which interact and are jointly trained by a single learning function.
• the prediction device can thus provide an I ⁇ TA prediction that can be used by an air traffic control system to optimize traffic in the arrival airport.
• FIG. 4 represents the first predictor 101 based on a neural network, in an example application of the invention to the prediction of the estimated time of arrival ETA of an aircraft on a route between an arrival airport and a departure airport.
• the first predictor 101 is used to predict the non-explicit parameter Q which can represent for example the instantaneous overall delay at the arrival airport or a congestion parameter at the arrival airport such as the congestion of arrival airport (global congestion parameter).
• the first predictor 101 can receive as input information relating to estimates calculated for the aircraft considered and to a set of planes (hereinafter referred to as “arriving planes”) whose arrival is planned at the same airport. arrival that the aircraft considered, such as:
• the first predictor 101 can more generally take into account the capacity of the arrival airport and the traffic information expected at each instant (number of planes with the same ETA).
• the first predictor 101 thus continuously provides a future prediction of the non-explicit parameter Q (for example instantaneous global delay parameter or congestion parameter).
• the outputs of the first predictor 101 can be represented in the form of a prediction table providing the congestion parameter of the arrival airport per interval. of future time.
• the time interval can be a future time range corresponding to the next hours with respect to the current instant (corresponding to the instant at which the prediction method is launched by the first predictor 101).
• FIG. 4 shows an example of the implementation of the neural network 2A of the first predictor 101, in an example of the application of the invention to the estimation of the time of arrival of an airplane.
• the neural network 2A of the first predictor 101 can be activated by a set of inputs which can include capacity information of the arrival airport (for example number of runways of the airport, status indicator runways, etc.), outputs from arrival management systems configured to manage and optimize aircraft arrivals.
• the output of the first predictor 101 can be a congestion parameter such as an instantaneous global delay parameter representing the landing delay of the airplane considered at the arrival airport or the representative congestion parameter. congestion at the arrival airport per future time interval.
• the global congestion parameter Q can be represented by an occupancy rate of the runways of the arrival airport with respect to the capacity maximum of the arrival airport, for each time slot (for example, a quarter of an hour or an hour).
• the neural network 2A of the first predictor 101 can be activated by a set of inputs which can include:
• FIG. 5 represents the second predictor 102 based on a neural network 2B, in the application of the invention to the prediction of the estimated time of arrival ETA of an aircraft on a route between an arrival airport and a departure airport.
• the second predictor 102 based on a neural network 2B, outputs a prediction of I ⁇ TA of the flight considered.
• the second predictor 102 can receive as input data relating to the flight plan of the aircraft, the weather conditions forecast on the trajectory, and / or landing time slot information as calculated for the aircraft. before the plane takes off.
• the second predictor 102 receives as input the non-explicit parameter Q determined at the output of the first predictor 101 (for example, the instantaneous global delay parameter).
• the second predictor 102 can also receive as input historical data of values of the non-explicit parameter Q output from the first predictor 101 over a past period of time.
• the input data of the second predictor 102 may include:
• Flight history data stored for example in a database or cache, the history data relating to previous flights corresponding to the route of the flight in question (between the place of origin and the place of
• the history can include information relating to a multitude of previous flights (millions of flights for example);
• the delay in take-off (“Delay at departure”) predicted at the time of take-off (it can be transmitted by the aircraft in the last message sent by the aircraft at the time of take-off); the delay corresponds to the difference between the actual take-off time and the initially planned take-off time (Estimated take-off time).
• the input data of the second predictor 102 comprises for example a set of K ’input characteristics
• the predictors 101 and / or 102 can be implemented by any form of neural network (such as convolutional networks, totally connected networks, etc.).
• the first predictor 101 can also be configured to broadcast the output parameter Q to the control systems of a plurality of airplanes which are on the way to neighboring sectors of the airport. arrival, using suitable means of communication.
• the means of communication can include one or more private and / or public networks that allow the exchange of data, such as the internet, a local area network (LAN), a virtual local area network (VLAN), an area network wide area (WAN), a cellular voice / data network, air-to-ground communication such as CPDLC (acronym for 'Control Pilot Data Link Communications' meaning 'Communications between Controller and Pilot via Data Link') and / or others types of communication networks of this kind.
• LAN local area network
• VLAN virtual local area network
• WAN area network wide area
• CPDLC air-to-ground communication
• CPDLC acronym for 'Control Pilot Data Link Communications' meaning 'Communications between Controller and Pilot via Data Link'
• Each communication network can use normal communication technologies and / or protocols such as HTTP (Hypertext Transport Protocol).
• the prediction device 100 can be configured to refine the estimate of the predicted value for the magnitude P constituting the response of the second predictor 102 using an initial estimate of the time of arrival ETA calculated from the speed, the path and the physical parameters of the airplane, this initial estimate being made when filing a flight plan, or intermediate estimates of the arrival time calculated from a formula or made by the device 100 at some point.
• FIG. 6 shows the interactions between the first predictor 101 and the second predictor 102 in the learning phase.
• the output Q of the first predictor 101 in this example, represents the congestion of the arrival airport which has no field reality available and therefore cannot be trained independently by a separate learning function.
• the non-explicit output Q of the first predictor 101 is supplied as the input of the second predictor 102, while in the phase
• the two predictors 101 and 102 are jointly trained using a single learning function for the two neural networks 2A and 2B, which makes it possible to reliably and accurately predict the value of the quantity P (ETA in l 'example considered) despite the non-explicit nature of the parameter Q.
• Such an arrangement of the two predictors makes it possible to capture the impact of the non-explicit parameter on the second predictor 102 in the learning phase. It further allows to provide a network (network of the first predictor 101) capable of predicting the non-explicit parameter in a way which also maximizes the precision of the second predictor 102, without the need to define an analytical function for this. setting.
• FIG. 7 represents the method of learning the two predictors 101 and 102, according to certain embodiments.
• the learning process comprises at least one iteration of the following steps:
• step 600 input data is applied to the input of the two
• step 602 a forward propagation is performed in which gradients of a set of minimization functions of the cost function of the first predictor 101 are calculated, in response to the application of the input data of the two predictors 101 and 102 and to the responses obtained by the neural networks of the predictors 101 and 102;
• step 604 the weights of the neural networks of the two predictors 101 and 102 are updated by backpropagation of the gradients calculated in step 602.
• FIG. 8 represents the method for predicting the non-explicit quantity Q implemented by the first predictor 101, in the generalization phase (after the learning phase) from several parameters, according to a method of embodiment, in an example of application of the invention to the estimation of the flight time of an airplane.
• the synaptic weights of the neural network used by the first predictor 101 are frozen in the generalization phase (static).
• step 700 input data relating to the arrival airport is applied to the first predictor.
• This input data may include:
• step 702 the output parameter Q of the first predictor (for example instantaneous global delay parameter) is generated as a function of the inputs received (response to the input data applied to the neural network of the predictor 101) .
• step 704 the response (output parameter Q) of the first predictor is transmitted to the second predictor.
• step 706 the output parameter Q can be further broadcast to all control systems of airplanes en route to sectors adjacent to the arrival airport, using suitable communications means.
• steps 704 and 706 are shown consecutively, in one embodiment these two steps can be carried out in a different order or substantially in parallel.
• FIG. 9 represents the method for predicting the value of the quantity P (I ⁇ TA of an aircraft in this example) implemented by the second predictor 102, in the generalization phase from the non-explicit parameter Q (the instantaneous global delay parameter in this example) transmitted by the first predictor 101, according to one embodiment.
• step 800 a set of input data are applied to the second predictor 102 comprising at least the output parameter Q of the first predictor 101 (which may for example be the instantaneous global delay parameter).
• step 802 the neural network of the second predictor 102 generates an output P in response to the input data, this output representing a prediction of the magnitude P (ETA of the aircraft considered, for example).
• step 804 the estimate P can be returned as the input of the first predictor 101 which, in response to this input data, can refine the estimate Q (by repeating steps 700 to 704).
• all input parameters can be updated (eg weather parameters) to improve the accuracy of the prediction.
• the predictions of the P value can be iterated periodically, according to a chosen period (eg every N minutes during the flight time for an estimate of an ETA).
• the neural network 2A of the first predictor 101 can receive as input data relating to a set airports, by way of non-limiting example.
• the prediction can be improved by using for the first predictor 101 a plurality of elementary neural networks 2Ai each relating to a specific airport, as illustrated in the example of FIG. 10.
• FIG. 10 shows for example 8 predictors 101 based on elementary neural networks (2A-1 to 2A-8), each neuron network being specific to a given airport (CGE, Atlanta, Mila, Guanghzhou, Heathrow, CdG, JFK, Abu Dhabi).
• Each elementary neural network 2A-i is trained together with the second predictor 102 as described above using the input data specific to the associated specific airport, which makes it possible to update the weights associated with each network of elementary neuron during learning.
• the weights of each elementary neural network 2A-i are only refined with data that corresponds only to the specific associated airport.
• the weights of the various neural networks 2A-i and 2B are frozen and for each airplane flight considered between an airport of departure and an arrival airport, only the neural network 2A-i corresponding to the arrival airport of the airplane is used.
• the systems or subsystems according to the embodiments of the invention can be implemented in various ways by hardware ("hardware"), software, or a combination of hardware and software, especially in the form of program code that can be distributed as a program product, in various forms.
• the program code may be distributed using computer readable media, which may include computer readable storage media and communication media.
• the methods described in the present description can in particular be implemented in the form of computer program instructions executable by one or more processors in a computer computing device. These computer program instructions may also be stored in computer readable media.
• the invention is not limited to the embodiments described above by way of nonlimiting example. It encompasses all the variant embodiments which may be envisaged by those skilled in the art. In particular, those skilled in the art will understand that the invention is not limited to the prediction of ETA quantities or more generally to air traffic control, and can be applied to other fields. Those skilled in the art will understand that the invention is also not limited to the examples of cost functions and cost function minimization described above.

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