ACARS-based flight state anomaly detection method

Abstract

The invention provides a flight state anomaly detection method based on an ACARS, and relates to the technical field of aviation network security. The method comprises the following steps: constructing a CNN network, and defining a step length, a convolution kernel size and a pooling mode; aCARS data are acquired and preprocessed; training a CNN (Convolutional Neural Network) based on the preprocessed ACARS data; and acquiring ACARS data in flight of the aircraft, preprocessing the ACARS data, inputting the preprocessed ACARS data into the trained CNN network, performing flight state anomaly detection, and outputting a category label of an aircraft state. According to the method, through a CNN deep learning technology, automatic anomaly detection of ACARS data can be realized, and requirements of different aircraft types and flight environments can be met. The method can improve the flight safety, reduce the accident risk and improve the flight efficiency.

Description

Technical Field

[0001] The present invention relates to the field of aviation network security technology, and in particular to a flight status anomaly detection method based on ACARS. Background Art

[0002] In recent years, the civil aviation industry has developed rapidly and its safety has been significantly improved. Compared with other modes of transportation, such as cars and trains, airplanes have a higher safety factor in terms of both the number of casualties caused by accidents and the casualty rate. Although the probability of civil aviation accidents is extremely low, once they occur, there is a high possibility of serious consequences.

[0003] Therefore, in order to understand the real-time status of the aircraft, flight tracking is required. For flight tracking, existing commercial real-time flight tracking systems, such as Flightradar24 system and VariFlight, are based on data such as automatic dependent surveillance-broadcast, which can display information such as aircraft track, arrival time and flight delay, and are often used to monitor the location of flights. However, it is impossible to determine the status of an aircraft by monitoring its flight status parameters.

[0004] Flight tracking includes normal flight tracking, abnormal flight tracking and flight distress tracking. Abnormal flight tracking is used to locate abnormal flight or crashed aircraft in order to quickly respond to emergencies and conduct search and rescue.

[0005] ACARS (Aircraft Communications Addressing and Reporting System) uses communication links such as VHF (Very High Frequency), HF (High Frequency) and SATCOM (Satellite Communications) to achieve data transmission. It is an air-to-ground data communication network for automatic transmission and exchange of information between airborne equipment and ground data centers. Among them, the ACARS position report can be used for aircraft positioning and tracking. ACARS data contains multiple flight status parameters, but the aircraft health detection, real-time flight monitoring, and performance analysis systems that have been developed do not include positioning functions when dangerous situations occur or the aircraft is in an abnormal state. In other words, existing technologies cannot detect abnormal flight status, and there is currently no mature and feasible solution for abnormal tracking. Summary of the invention

[0006] In order to solve the above-mentioned technical problems existing in the prior art, the present invention aims to provide a flight status abnormality detection method based on ACARS, which can be used to ensure aviation safety in flight status monitoring and provide more information for aviation search and rescue and flight accident investigation.

[0007] Specifically, a technical solution of a flight status abnormality detection method based on ACARS includes the following steps:

[0008] Step S1: Build a CNN (Convolutional Neural Networks) network and define the step size, convolution kernel size and pooling method;

[0009] Step S2: Acquire ACARS data and pre-process;

[0010] Step S3: training a CNN network based on the preprocessed ACARS data;

[0011] Step S4: Obtain the ACARS data of the aircraft in flight, input it into the trained CNN network after preprocessing, perform flight status anomaly detection, and output the category label of the aircraft status.

[0012] Preferably,

[0013] In step S2, obtaining ACARS data is specifically step S21;

[0014] Step S21: Obtain a wav file containing acars information;

[0015] Preprocessing ACARS data includes steps S22 to S26;

[0016] Step S22: Enter the program through acarsdec.c, use the acars.c file to initialize the wav file, read the configuration, and set the input and output;

[0017] Step S23: Use soundfile.c to read the wav file and initialize the channel information;

[0018] Step S24: Divide the ACARS data in the wav file according to the channels and store them in the corresponding dm_buffer;

[0019] Step S25: transfer the ACARS data in the wav file to msk.c for demodulation;

[0020] Step S26: pass the demodulated ACARS data to label.c for parsing, obtain the acars message and output it.

[0021] Preferably,

[0022] In step S2, obtaining ACARS data is specifically step S21;

[0023] Step S21: Connecting a radio receiver to receive acars signal;

[0024] Preprocessing ACARS data includes steps S22 to S25;

[0025] Step S22: Enter the program through acarsdec.c, use the acars.c file to initialize the wav file, read the configuration, and set the input and output;

[0026] Step S23: Initialize the radio receiver and set receiving parameters;

[0027] Step S24: The radio receiver receives the radio frequency signal in the air and converts it into a digital signal, and transmits it to msk.c for demodulation;

[0028] Step S25: pass the demodulated ACARS data to label.c for parsing, obtain the acars message and output it.

[0029] Preferably, step S3 specifically includes:

[0030] Step S31: input the pre-processed ACARS data into the CNN network for convolution, and extract features by learning the weights of the convolution kernel;

[0031] Step S32: Apply activation function to perform nonlinear transformation on features and perform pooling;

[0032] Step S33: Connect the pooling result to the fully connected layer through the flattening layer for integration to obtain a feature vector, and output the category label of the aircraft state according to the feature vector;

[0033] Step S34: define the loss function L of the CNN network,

[0034]

[0035] In the formula, l is the sample number, y is l is the true label of the flight status corresponding to the lth ACARS data, is the predicted probability that the flight status corresponding to the lth ACARS data is normal;

[0036] Step S35: Update the parameters θ of the CNN network through the back propagation algorithm to minimize the loss function L; wherein the back propagation algorithm formula is as follows:

[0037]

[0038] Where α is the learning rate.

[0039] Preferably, the convolution operation formula is:

[0040]

[0041] Where (i, j) is the feature point of the output feature map obtained by convolution after traversing the ACARS data, O(i, j) is the value of the output feature map at the feature point (i, j), k is the size of the convolution kernel, (m, n) is the coordinate position on the convolution kernel, I(i+m, j+n) is the value of the preprocessed ACARS data at the coordinate position (i+m, j+n), K(m, n) is the weight of the convolution kernel at the coordinate position (m, n), and b is the bias term.

[0042] Preferably, an activation function is applied to perform a nonlinear transformation on the convolved ACARS data, specifically:

[0043] The ReLU function f(·) is used in the activation function to introduce nonlinear transformation.

[0044] f(x)=max(0,x);

[0045] Where x represents the input of the ReLU function.

[0046] Preferably, pooling is specifically:

[0047]

[0048] Where (i, j) is the feature point of the output feature map obtained by convolution after traversing the ACARS data, P(i, j) is the pixel value of the output feature map at the feature point (i, j), (m, n) is the coordinate position on the convolution kernel, p is the pooling window size, s is the step size of the pooling operation, and I(i·s+m,j·s+n) is the pixel value of the output feature map at position (i·s+m,j·s+n) in the pooling window.

[0049] The technical solution provided by the present invention can realize automatic anomaly detection of ACARS data through CNN deep learning technology, and can adapt to the needs of different aircraft models and flight environments. The method can improve flight safety, reduce accident risks, and improve flight efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Schematic diagram of ACARS data collection and preprocessing process in one embodiment of the present invention.

[0051] Figure 2 Schematic diagram of the process of training a CNN model in one embodiment of the present invention.

[0052] Figure 3 The figure is a flow chart of abnormal flight status detection in one embodiment of the present invention. DETAILED DESCRIPTION

[0053] The technical solution provided by the present invention will be further elaborated below in combination with embodiments and drawings.

[0054] Currently, the practice of analyzing recorded data and using it for daily monitoring is becoming more and more common in the aviation industry. By regularly accessing recorded flight parameters, the safety of flight operations and engine performance can be evaluated, and daily operations can be understood. Incorporating accident and incident data into daily monitoring and analyzing this data can help predict safety hazards before an event or accident occurs, thereby reducing the risk of flight accidents and better ensuring flight safety.

[0055] Compared with other communication methods, ACARS data transmission is fast and timely, and supports airlines to customize their free messages according to their needs. In addition to the conventional waypoint location and arrival time, estimated arrival time, destination airport, and flight altitude, ACARS messages also include meteorological information such as wind speed, wind direction, temperature, and engine thrust, fuel consumption, temperature, pressure, avionics, hydraulics, fuel, and other key system status information. Compared with the common flight tracking technologies ADS-B (Automatic Dependent Surveillance-Broadcast) and ADS-C (Automatic Dependent Surveillance-Contract), ACARS's ground base station communication area covers a wider range, basically covering all routes. In addition, the usage rate of the ACARS system in civil aviation aircraft is also much higher than the other two.

[0056] In the existing technology, deep learning is good at mining abstract feature representations from raw input data, and convolutional neural network is one of the classic and widely used structures, which has achieved good performance in various signal and information processing tasks. Its biggest highlight is that its characteristics such as local connection, weight sharing and pooling operation can effectively reduce the complexity of the network and the number of training parameters.

[0057] Based on the above considerations, this patent proposes a flight status anomaly detection method based on ACARS messages. This method aims to promptly notify the ground operation control center when the aircraft is in an abnormal state, and assist the crew members in handling abnormal situations based on the data. Through the ACARS datagram transmitted to the ground during the flight, combined with CNN, the ACARS message is automatically analyzed, and the aircraft status is judged using multiple parameters such as pressure altitude, pitch angle, wing speed, etc., to achieve real-time monitoring and abnormal tracking of flight data.

[0058] Example 1

[0059] This embodiment provides a method for analyzing ACARS messages using a convolutional neural network to determine abnormal flight status. Figure 1 As shown, it specifically includes steps S1 to S4:

[0060] Step S1: Input the ACARS signal (including ACARS data, such as altitude, pitch angle, latitude and longitude, remaining fuel, cabin altitude, roll angle and rotation angle) received by SDRplay (Software Defined Radio play) in wav format. Enter the program through acarsdec.c, and use the acars.c file to initialize it, read the configuration, and set the input and output.

[0061] Step S2: Initialize the radio receiving device used;

[0062] Step S21: Use the files corresponding to the device, namely sdrplay.c, soapy.c and rtl.c, to initialize the device and set receiving parameters such as frequency, sampling rate, etc. The program controls the device through the API (Application Programming Interface) of SDRplay to ensure that the device can start receiving RF signals.

[0063] Step S3: signal reception and modulation and demodulation;

[0064] Step S31: After initialization, the SDRplay device starts to receive the RF signal in the air and converts it into a digital signal, which is then passed to msk.c for demodulation.

[0065] Step S4: The demodulated data will be passed to label.c for parsing the ACARS message. By parsing the format of the data frame, including the start flag, end flag and data part, useful information such as flight number, location, etc. is extracted. The output results are converted into network form, MQTT (Message Queuing Telemetry Transport) form and file form using the three files netout.c, mqttout.c and fileout.c, respectively, and finally outputted using the output.c file.

[0066] The C language files include:

[0067] acars.c, the main logic for processing ACARS messages;

[0068] acarsdec.c, the main program file, contains the program entry and overall control logic;

[0069] label.c, logic for processing label information;

[0070] msk.c, handles the logic of MSK modulation and demodulation;

[0071] sdrplay.c, soapy.c, rtl.c, soundfile.c handle different inputs;

[0072] netout.c, mqttout.c, fileout.c, output.c, handle the logic of various outputs.

[0073] Furthermore, after the above data collection and preprocessing, Figure 2 As shown, the CNN network is trained based on the ACARS data set composed of ACARS messages, and the following steps are also included:

[0074] Step R1: Construct the CNN network structure and define the convolution kernel size, step size and other parameters, as well as the pooling method. The CNN network consists of sequentially connected convolution layers, connection layers (pooling layers), LSTM layers, fully connected layers, activation functions (such as ReLU) and loss functions. Among them, the activation function can enhance the model's expressiveness and anomaly detection performance by introducing nonlinearity.

[0075] Step R2: Input the preprocessed ACARS data into the CNN network.

[0076] Step R3: Perform convolution operation on the input data and extract features by learning the weights of the convolution kernel;

[0077] Among them, the convolution operation formula is:

[0078]

[0079] Where i, j are used to traverse each pixel or feature point of the output feature map, O(i, j) is the value of the output feature map at the feature point (i, j), the two variables (m, n) represent the coordinate position on the convolution kernel, k is the size of the convolution kernel, I(i+m, j+n) is the value of the input processed ACARS data at the coordinate position (i+m, j+n), K(m, n) is the weight of the convolution kernel at the coordinate position (m, n), and b is the bias term.

[0080] Step R4: Apply activation function to the convolution result for nonlinear transformation;

[0081] Step R41: Use the ReLU function in the activation function to introduce nonlinear transformation:

[0082] Among them, the ReLU function formula is:

[0083] f(x)=max(0,x);

[0084] In the formula, for any input x, if x is positive, then the output is x; if x is non-positive (i.e. x≤0), then the output is 0.

[0085] Step R5: In the connection layer, perform pooling operation on the activated data to reduce the data dimension;

[0086] Among them, the pooling operation formula is:

[0087]

[0088] In the formula, P(i,j) is the pixel value of the output feature map at the coordinate position (i,j), I(i·s+m,j·s+n) is the pixel value of the input feature map at the position (i·s+m,j·s+n) in the pooling window, p is the pooling window size, and s is the step size of the pooling operation. The step size determines the moving distance of the pooling window when sliding on the input data.

[0089] Step R6: Connect the data output by the pooling layer to the fully connected layer through the flattening layer for prediction results. Specifically, the flattening layer in this embodiment is implemented using an LSTM network (Long Short-Term Memory).

[0090] The fully connected layer receives and integrates the information into a feature vector, which contains the representation of multiple key parameters such as the aircraft's position, speed, acceleration, altitude, temperature, attitude, pressure, oil pressure, etc.

[0091] Corresponding to different tasks, the output layer of the fully connected layer will output the corresponding prediction results. In the classification task, the output is the category label of the aircraft status, including normal and abnormal.

[0092] Step R7: Define the loss function of the CNN network to measure the difference between the model output and the true label and determine the accuracy of the detection result;

[0093] Among them, the cross entropy loss function formula is:

[0094]

[0095] In the formula, y i is the true label of the i-th sample (0 or 1, corresponding to normal and non-normal), is the predicted probability that the corresponding flight state of the i-th sample is normal (the probability value output by the model, between 0 and 1);

[0096] Step R8: Update the parameters in the CNN network through the back-propagation algorithm to minimize the loss function and thus improve the accuracy of the model.

[0097] Among them, the back propagation algorithm formula is:

[0098]

[0099] In the formula, θ represents the network parameters, α is the learning rate, is the gradient of the loss function with respect to the parameters.

[0100] Finally, if Figure 3 As shown, the real-time ACARS data in flight is input into the trained CNN network for abnormal detection. The specific process is consistent with step R3 to step R6. If the flight status is normal, the training detection is carried out, otherwise the alarm device is triggered and an alarm message is issued.

[0101] The thresholds for abnormal events are as follows: the descent rate is the height difference between the aircraft per second and the previous second. Within 10 seconds, the descent rate is greater than 75 feet per second; except for the takeoff and landing phases, the pitch angle is greater than 10 degrees; the cabin altitude is greater than 9,000 feet; the roll angle is greater than 40 degrees; the remaining fuel is less than 10%. When any of the above parameters exceeds the threshold, the corresponding abnormal warning is issued.

[0102] Example 2

[0103] The ACARS message data collection and preprocessing method provided in this embodiment includes:

[0104] Step 1: Monitoring direction This method passes a wav file containing acars information, enters the program through acarsdec.c, and uses the acars.c file to initialize it, read the configuration, and set the input and output.

[0105] Step 2: Initialize the incoming wav file; use soundfile.c to read the contents of the file, initialize its channel information, and then for each channel, separate the read data according to the channel and store it in the corresponding dm_buffer.

[0106] Step 3: Signal reception and modulation and demodulation; the data in the wav file is passed to msk.c for demodulation.

[0107] Step 4: The demodulated data will be passed to label.c for ACARS message parsing. By parsing the format of the data frame, including the start flag, end flag and data part, useful information such as flight number and location can be extracted. The output results are converted into network form, MQTT form and file form using the three files netout.c, mqttout.c and fileout.c respectively, and finally outputted using the output.c file.

[0108] Furthermore, after collecting and preprocessing the ACARS data from step 1 to step 4, the process of processing the ACARS message using the CNN network is as follows:

[0109] 1) Build the CNN network structure, define the convolution kernel size, step size and other parameters, as well as the pooling method.

[0110] 2) Input the preprocessed ACARS data into the CNN network.

[0111] 3) Perform convolution operation on the input data to obtain the output feature map, and extract features by learning the weights of the convolution kernel;

[0112] Among them, the convolution operation formula is:

[0113]

[0114] Where i, j are used to traverse each pixel or feature point of the output feature map, O(i, j) is the value of the output feature map at the feature point (i, j), the two variables (m, n) represent the coordinate position on the convolution kernel, k is the size of the convolution kernel, I(i+m, j+n) is the value of the input processed ACARS data at the coordinate position (i+m, j+n), K(m, n) is the weight of the convolution kernel at the coordinate position (m, n), and b is the bias term.

[0115] Among them, corresponding to the ACARS data, the features include altitude, pitch angle, longitude and latitude, remaining fuel, cabin altitude, roll angle and rotation angle.

[0116] 4) Apply activation function to the convolution result for nonlinear transformation;

[0117] Furthermore, the ReLU function is used in the activation function to introduce nonlinear transformation:

[0118] Among them, the ReLU function formula is:

[0119] f(x)=max(0,x);

[0120] In the formula, for any input x, if x is positive, then the output is x; if x is non-positive (i.e. x≤0), then the output is 0.

[0121] 5) Perform pooling operation on the activated data to reduce the data dimension;

[0122] Among them, the pooling operation formula is:

[0123]

[0124] Where P(i,j) is the pixel value of the output feature map at the coordinate position (i,j), I(i·s+m,j·s+n) is the pixel value of the input feature map at the coordinate position (i·s+m,j·s+n) in the pooling window, p is the pooling window size, and s is the step size in the pooling operation, which determines the moving distance of the pooling window when it slides on the input data I.

[0125] 6) The data output by the pooling layer is connected to the fully connected layer through the flattening layer for prediction results;

[0126] The fully connected layer receives and integrates the information into a feature vector, which contains the representation of multiple key parameters such as the aircraft's position, speed, acceleration, altitude, temperature, attitude, pressure, oil pressure, etc.

[0127] Corresponding to different tasks, the output layer of the fully connected layer will output the corresponding prediction results. In the classification task, the output is the category label of the aircraft status, including normal and abnormal.

[0128] 7) Define the loss function of the CNN network to measure the difference between the model output and the true label and determine the accuracy of the detection results;

[0129] Among them, the cross entropy loss function formula is:

[0130]

[0131] In the formula, y i is the true label of the i-th sample (0 or 1, corresponding to normal and non-normal), is the predicted probability that the corresponding flight state of the i-th sample is normal (the probability value output by the model, between 0 and 1);

[0132] 8) Update the parameters in the CNN network through the back-propagation algorithm to minimize the loss function and thus improve the accuracy of the model.

[0133] Among them, the back propagation algorithm formula is:

[0134]

[0135] In the formula, θ represents the network parameters, α is the learning rate, is the gradient of the loss function with respect to the parameters.

[0136] Finally, the real-time ACARS data in flight is input into the trained CNN network for anomaly detection. The specific process is consistent with step R3 to step R6. If the flight status is normal, the training detection is carried out, otherwise the alarm device is triggered and an alarm message is issued.

[0137] The above two embodiments can write ACARS signal modulation and demodulation programs in C language, which can analyze the ACARS signal WAV files collected in the past, and can also connect SDR to collect and parse ACARS messages at the same time. ACARS is the most widely used data link system in the field of civil aviation aircraft communication. The hardware conditions for tracking and monitoring flights using the ACARS system are relatively low. And the method is simple to implement. It only needs to use the editable free message in the ACARS message, and can also increase other data that the monitoring user is concerned about, such as the remaining fuel volume, to monitor the safety of the aircraft in flight. Using advanced convolutional neural networks, the original data is directly input into the network, and then implicitly learns the network from the training data, which can avoid the shortcomings of manual feature extraction leading to error accumulation. Combined with feature selection and optimization technology, it can automatically learn message features from ACARS data through multi-layer nonlinear transformation. Compared with the rule-based judgment method, the method based on convolutional neural networks can better adapt to message garbled and error, detection accuracy and system adaptability. In addition, the analysis of ACARS signals is suitable for various common software-defined radio tools such as rtl_sdr, airspy and sdrplay devices, and can decode the input of multiple channels at the same time; the decoding selects the libacars library, which supports the ACARS signals defined by the ARINC-622 protocol, and the decoding process is simple and efficient.

[0138] In summary, the technical solution provided by the present invention can realize automatic anomaly detection of ACARS data through CNN deep learning technology, and can adapt to the needs of different aircraft models and flight environments. This method can improve flight safety, reduce accident risks, and improve flight efficiency.

Claims

1. A flight status abnormality detection method based on ACARS, characterized in that: The following steps are involved: Step S1: Build a CNN network and define the step size, convolution kernel size and pooling method; Step S2: Acquire ACARS data and pre-process; Step S3: training a CNN network based on the preprocessed ACARS data; Step S4: Obtain the ACARS data of the aircraft in flight, input it into the trained CNN network after preprocessing, perform flight status anomaly detection, and output the category label of the aircraft status.

2. The method for detecting abnormal flight status based on ACARS as claimed in claim 1, characterized in that: In step S2, the obtaining of ACARS data is specifically step S21; Step S21: Obtain a wav file containing acars information; The preprocessing includes steps S22 to S26; Step S22: Enter the program through acarsdec.c, use the acars.c file to initialize the wav file, read the configuration, and set the input and output; Step S23: Use soundfile.c to read the wav file and initialize the channel information; Step S24: Divide the ACARS data in the wav file according to the channels and store them in the corresponding dm_buffer; Step S25: transfer the ACARS data in the wav file to msk.c for demodulation; Step S26: pass the demodulated ACARS data to label.c for parsing, obtain the acars message and output it.

3. The method for detecting abnormal flight status based on ACARS as claimed in claim 1, characterized in that: In step S2, the obtaining of ACARS data is specifically step S21; Step S21: Connecting a radio receiver to receive acars signal; The preprocessing includes steps S22 to S25; Step S22: Enter the program through acarsdec.c, use the acars.c file to initialize the wav file, read the configuration, and set the input and output; Step S23: Initialize the radio receiver and set receiving parameters; Step S24: The radio receiver receives the radio frequency signal in the air and converts it into a digital signal, and transmits it to msk.c for demodulation; Step S25: pass the demodulated ACARS data to label.c for parsing, obtain the acars message and output it.

4. The method for detecting abnormal flight status based on ACARS as claimed in claim 1, characterized in that: Step S3 specifically includes: Step S31: input the pre-processed ACARS data into the CNN network for convolution, and extract features by learning the weights of the convolution kernel; Step S32: Apply activation function to perform nonlinear transformation on features and perform pooling; Step S33: Connect the pooling result to the fully connected layer through the flattening layer for integration to obtain a feature vector, and output the category label of the aircraft state according to the feature vector; Step S34: define the loss function L of the CNN network, In the formula, l is the sample number, y is l is the true label of the flight status corresponding to the lth ACARS data, is the predicted probability that the flight status corresponding to the lth ACARS data is normal; Step S35: Update the parameters θ of the CNN network through the back propagation algorithm to minimize the loss function L; wherein the back propagation algorithm formula is as follows: Where α is the learning rate.

5. The method for detecting abnormal flight status based on ACARS as claimed in claim 4, characterized in that: The convolution operation formula is: Where (i, j) is the feature point of the output feature map obtained by convolution after traversing the ACARS data, O(i, j) is the value of the output feature map at the feature point (i, j), k is the size of the convolution kernel, (m, n) is the coordinate position on the convolution kernel, I(i+m, j+n) is the value of the preprocessed ACARS data at the coordinate position (i+m, j+n), K(m, n) is the weight of the convolution kernel at the coordinate position (m, n), and b is the bias term.

6. The method for detecting abnormal flight status based on ACARS as claimed in claim 4, characterized in that: The application activation function performs nonlinear transformation on the convolved ACARS data, specifically: The ReLU function f(·) is used in the activation function to introduce nonlinear transformation. f(x)=max(0,x); Where x represents the input of the ReLU function.

7. The method for detecting abnormal flight status based on ACARS as claimed in claim 4, characterized in that: The pooling is specifically as follows: Where (i, j) is the feature point of the output feature map obtained by convolution after traversing the ACARS data, P(i, j) is the pixel value of the output feature map at the feature point (i, j), (m, n) is the coordinate position on the convolution kernel, p is the pooling window size, s is the step size of the pooling operation, and I(i·s+m,j·s+n0) is the pixel value of the output feature map at position (i·s+m,j·s+n) in the pooling window.

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