Method for carrying out group intention recognition through dynamic distribution probability image

Abstract

The invention discloses a method for identifying group intention through a dynamic distribution probability image, which comprises the following steps of: processing measurement related to each invading aircraft through EKF (Extended Kalman Filter) to obtain an estimated state and a related covariance matrix; constructing a DDP image based on the estimated state and the covariance matrix corresponding to the estimated state, wherein the DDP image is an image capable of representing the state of the invading aircraft group estimated at the current moment; extracting a first feature of the DDP image through a CNN neural network, and extracting a second feature through a BP neural network; and inputting the first feature and the second feature into a GRU neural network, outputting probabilities of different intentions by the GRU neural network, and further determining the group intention of the invading aircraft group. The group intention recognition method disclosed by the invention has a more accurate recognition rate.

Description

Technical Field

[0001] The invention relates to a method for identifying group intentions through a dynamic distribution probability image, and belongs to the technical field of image recognition. Background Art

[0002] In air defense, it is critical to quickly and accurately identify the intentions of an invading group.

[0003] Traditional recognition methods mainly focus on single-target applications and are highly effective in single-aircraft scenarios, but these methods ignore the disturbance introduced by measurement noise and have difficulties when applied to group recognition.

[0004] In addition, existing methods also use a tandem support vector machine and a dynamic Bayesian network, combined with low-correlation features, to extract information and infer the intention of the intruding aircraft. However, although this method includes multiple intruding aircraft, it still mainly identifies the intention of each intruding aircraft in a sequential manner. In essence, this method emphasizes a single intention and still has difficulty in effectively handling the recognition of group intentions.

[0005] In order to address the deficiencies in research algorithms in the field of group intent recognition, various countermeasures have been proposed in the prior art, such as the deep learning architecture of W-CPCLSTM, intent recognition models based on behavioral analysis and unsupervised learning clustering, and double-box models, however, these methods fail to integrate active measures against noise. In real-world scenarios, sensor measurements are rarely flawless and are often contaminated by noise. Traditional methods are mainly data-centric and show a higher sensitivity to data quality. Although noise can be artificially introduced into the training database to simulate real-world conditions, neural networks are essentially like capacities to analyze noise in a targeted manner, and this operation may reduce training efficiency. In addition, current research lacks a specific formation strategy, which is actually a key aspect that affects group intent.

[0006] Therefore, it is necessary to further study the existing group intention recognition methods to solve the above problems. Summary of the invention

[0007] In order to overcome the above problems, the inventors have conducted in-depth research and proposed a method for identifying group intentions through a dynamic distribution probability image, which includes the following steps:

[0008] S1. Process the metrics associated with each intruder aircraft through the EKF to obtain the estimated state and its associated covariance matrix;

[0009] S2, constructing a DDP image based on the estimated state and its corresponding covariance matrix, wherein the DDP image is an image capable of representing the estimated state of the invading aircraft group at the current moment;

[0010] S3. Extract the first feature of the DDP image through the CNN neural network, and extract the second feature through the BP neural network; input the first feature and the second feature into the GRU network, and the GRU neural network outputs the probabilities of different intentions, thereby determining the group intention of the invading aircraft group.

[0011] In a preferred embodiment, in S1, an extended Kalman filter is constructed for each intruding aircraft, the input of the i-th extended Kalman filter is the measurement information of the i-th intruding aircraft, and the output is the state of the i-th aircraft and the related covariance matrix.

[0012] In a preferred embodiment, the extended Kalman filter is expressed as:

[0013]

[0014] Where k represents the time, k+1|k represents the prediction of k+1 time based on k time, subscript i represents the i-th extended Kalman filter, P i (k+1|k) represents the error covariance matrix of the i-th extended Kalman filter predicting the k+1 moment at the k moment, Ψ i represents the linear constant velocity model in the extended Kalman filter, P i (k) represents the covariance matrix at time k, Q represents the covariance, S i (k+1) represents the covariance of the innovation process, represents the estimated state at time k, H() represents the measurement matrix of the extended Kalman filter, R represents the noise covariance matrix, K i (k+1) represents the Kalman gain at time k+1, M i (k+1) represents the measurement information at time k+1.

[0015] In a preferred embodiment, the measurement matrix is ​​set as:

[0016]

[0017] X i =[x i ,y i ,v x,i ,v y,i ] T

[0018] Among them, X i represents the state of the i-th invading drone, x i ,y i represents the position of the i-th invading aircraft, v x,i ,v y,irepresents the speed of the i-th invading aircraft.

[0019] In a preferred embodiment, in S2, the probability of each intruding drone being located at a specified point (x, y) is obtained based on the estimated states of different intruding aircraft and their associated covariance matrices;

[0020] By superimposing the probability of all invading drones being located at any point, the comprehensive spatial distribution of the invading group is obtained, which is used to reflect the probability of the existence of invading drones.

[0021] The probability of invading drones is mapped to grayscale values ​​and then converted into a DDP image.

[0022] In a preferred embodiment, the probability that each intruding drone is located at a specified point (x, y) is expressed as:

[0023]

[0024] Among them, p I (x, y, k) represents the probability that the i-th invading drone is located at point (x, y) at time k, represents the spatial distance between the i-th invading drone and the point (x, y), D M,i (x,y,k) represents the Mahalanobis bias distance between the i-th intruder drone and the point (x,y).

[0025] In a preferred embodiment, the Mahalanobis bias distance is expressed as:

[0026]

[0027]

[0028] Among them, e i (x, y, k) represents the spatial distance between the i-th invading drone and point (x, y), x i (k),y i (k) is the estimated state Obtained in.

[0029] In a preferred embodiment, the probability of the existence of an intruding drone is expressed as:

[0030]

[0031] Where N represents the number of invading drones.

[0032] In a preferred embodiment, the first feature and the second feature are summed and used as the input of the GRU neural network.

[0033] In a preferred embodiment, the output layer of the GRU neural network uses a softmax function to obtain the probability of each intent, expressed as:

[0034] p(k)=[p1(k),p2(k),...,p M (k)] T =softmax(w out h G (k)+b out )

[0035] Among them, the subscripts 1, 2, ..., M represent different intention numbers, [p1(k), p2(k), ..., p M (k)] represents the probability of different intentions, w out represents the weight of the output layer, h G (k) represents the output state of the GRU neuron in the last GRU hidden layer, b out Represents the bias of the output layer.

[0036] The beneficial effects of the present invention include:

[0037] (1) Has a more accurate recognition rate;

[0038] (2) It has robust noise resistance and excellent training efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A schematic flow chart of a method for identifying group intentions through a dynamic distribution probability image according to a preferred embodiment of the present invention is shown;

[0040] Figure 2 A schematic diagram showing the group intention of an invading aircraft group according to a preferred embodiment of the present invention is shown;

[0041] Figure 3 The movement trajectory of the intruder aircraft group with search and attack intentions in Example 2 is shown;

[0042] Figure 4 The curve showing the probability of different intentions changing with recognition time in Example 2;

[0043] Figure 5 The curve showing the probability of different intentions changing with recognition time in Comparative Example 2 is shown. DETAILED DESCRIPTION

[0044] The present invention will be further described in detail below through the accompanying drawings and embodiments. Through these descriptions, the characteristics and advantages of the present invention will become more clear and distinct.

[0045] The word "exemplary" is used exclusively herein to mean "serving as an example, embodiment, or illustration." Any embodiment described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments. Although various aspects of the embodiments are shown in the drawings, the drawings are not necessarily drawn to scale unless otherwise noted.

[0046] According to a method for identifying group intentions through a dynamic distribution probability image provided by the present invention, Figure 1 As shown, the following steps are included:

[0047] S1. Process the metrics associated with each intruder aircraft through the EKF to obtain the estimated state and its associated covariance matrix;

[0048] S2, constructing a DDP image based on the estimated state and its corresponding covariance matrix, wherein the DDP image is an image capable of representing the estimated state of the invading aircraft group at the current moment;

[0049] S3. Extract the first feature of the DDP image through the CNN neural network, and extract the second feature through the BP neural network; input the first feature and the second feature into the GRU network, and the GRU neural network outputs the probabilities of different intentions, thereby determining the group intention of the invading aircraft group.

[0050] In S1, an extended Kalman filter is constructed for each intruding aircraft. The input of the i-th extended Kalman filter is the measurement information of the i-th intruding aircraft, and the output is the state of the i-th aircraft and the related covariance matrix.

[0051] It is generally known to those skilled in the art that the extended Kalman filter includes a motion model and a transition model, and preferably the motion model adopts a linear constant velocity model to optimize computational efficiency.

[0052] Preferably, the transition model Ψ of the linear constant velocity model t It is expressed as:

[0053]

[0054] Among them, δ t Indicates the sampling time.

[0055] In a preferred embodiment, the extended Kalman filter is expressed as:

[0056]

[0057] Where k represents the time, k+1|k represents the prediction of k+1 time based on k time, subscript i represents the i-th extended Kalman filter, P i(k+1|k) represents the error covariance matrix of the i-th extended Kalman filter predicting the k+1 moment at the k moment, Ψ i represents the linear constant velocity model in the extended Kalman filter, P i (k) represents the covariance matrix at time k, Q represents the covariance, S i (k+1) represents the covariance of the innovation process, represents the estimated state at time k, H() represents the measurement matrix of the extended Kalman filter, R represents the noise covariance matrix, K i (k+1) represents the Kalman gain at time k+1, M i (k+1) represents the measurement information at time k+1.

[0058] Preferably, the covariance Q satisfies a normal distribution.

[0059] Preferably, the measurement matrix is ​​set as:

[0060]

[0061] X i =[x i ,y i ,v x,i ,v y,i ] T

[0062] Among them, X i represents the state of the i-th invading drone, x i ,y i represents the position of the i-th invading aircraft, v x,i ,v y,i represents the speed of the i-th invading aircraft.

[0063] The above measurement matrix fully considers the problem that the measurement values ​​of the intruding aircraft in the display scene are polluted by the environmental noise, and sets these noises to zero-mean Gaussian white noise.

[0064] In S2, the probability of each intruding drone being located at a specified point (x, y) is obtained based on the estimated states of different intruding aircraft and their associated covariance matrices, which is expressed as:

[0065]

[0066] Among them, p I (x, y, k) represents the probability that the i-th invading drone is located at point (x, y) at time k, represents the spatial distance between the i-th invading drone and the point (x, y), D M,i(x,y,k) represents the Mahalanobis bias distance between the i-th intruder drone and the point (x,y).

[0067] According to the Gaussian distribution principle, the probability obviously decreases by more than three standard deviations. In the present invention, if the Mahalanobis bias distance between the ith invading drone and the point (x, y) is less than 3, the ith invading drone is considered to exist within the triple standard deviation range of the point (x, y), that is, it has a probability of existence. Otherwise, the probability of the ith invading drone at the point (x, y) is considered to be 0.

[0068] Preferably, the Mahalanobis bias distance is expressed as:

[0069]

[0070]

[0071] Among them, e i (x, y, k) represents the spatial distance between the i-th invading drone and point (x, y), x i (k),y i (k) is the estimated state Obtained in.

[0072] By superimposing the probability of all invading drones being located at any point, we can obtain the comprehensive spatial distribution of the invading group. In the comprehensive spatial distribution, the probability of the existence of an invading drone can be expressed as:

[0073]

[0074] Where N represents the number of invading drones.

[0075] The probability of invading drones is mapped to grayscale values, and then converted into a DDP image. Preferably, the mapping is performed in a linear transformation manner. More preferably, the mapping process is expressed as:

[0076] τ(x,y,k)=p(x,y,k)×255

[0077] Among them, τ(x,y,k) represents the grayscale value of the image, and (x,y) is the pixel position in the image.

[0078] In S3, the first feature extracted by the CNN neural network is the data centered on the formation.

[0079] The BP neural network is used to analyze the group state, and the second feature obtained is kinematic information.

[0080] Specifically, CNN consists of three layers: convolutional layer, pooling layer and fully connected layer. The convolutional layer receives the DDP image as its input and uses a set of convolutional filters to extract features in the image. Unlike the fully connected layer, it establishes sparse connections to scan local areas of the image. After the convolutional layer, the goal of the pooling layer is to downsample the feature map while retaining key information. After the pooling operation, the simplified feature map is flattened into a one-dimensional vector, which is then input into a fully connected layer to obtain the first feature.

[0081] Preferably, the pooling layer adopts a maximum pooling operation, that is, the features are divided and mapped to non-overlapping areas, and the maximum value is selected from each area.

[0082] In a preferred embodiment, before the DDP image is input into the BP neural network, the pixels in the image are normalized. Since the attributes of data in different pixels may be different, the normalization operation ensures that during the network training process, attributes with a larger span will not cover up those with a narrower range.

[0083] More preferably, the normalization is performed using a commonly used maximum-minimum method.

[0084] In a preferred embodiment, the BP neural network uses ReLU as the activation function.

[0085] According to the present invention, the first feature and the second feature are summed and used as the input of the GRU neural network.

[0086] In a preferred embodiment, the GRU neural network consists of four layers, including an input layer, two GRU hidden layers and an output layer.

[0087] In a preferred embodiment, the output layer of the GRU neural network uses a softmax function to calculate the probability of each intent, expressed as:

[0088] p(k)=[p1(k),p2(k),...,p M (k)] T =softmax(w out h G (k)+b out )

[0089] Among them, [p1(k),p2(k),...,p M (k)] represents the probability of different intentions, subscripts 1, 2, ..., M represent different intention numbers, and w out represents the weight of the output layer, h G (k) represents the output state of the GRU neuron in the last GRU hidden layer, b outRepresents the bias of the output layer.

[0090] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in the present disclosure can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document is not limited here.

[0091] Example

[0092] Example 1

[0093] Conduct a simulation experiment to simulate the recognition of group intentions. The recognition of group intentions includes the following steps:

[0094] S1. Process the metrics associated with each intruder aircraft through the EKF to obtain the estimated state and its associated covariance matrix;

[0095] S2, constructing a DDP image based on the estimated state and its corresponding covariance matrix, wherein the DDP image is an image capable of representing the estimated state of the invading aircraft group at the current moment;

[0096] S3. Extract the first feature of the DDP image through the CNN neural network, and extract the second feature through the BP neural network; input the first feature and the second feature into the GRU network, and the GRU neural network outputs the probabilities of different intentions, thereby determining the group intention of the invading aircraft group.

[0097] In S1, an extended Kalman filter is constructed for each intruding aircraft. The input of the i-th extended Kalman filter is the measurement information of the i-th intruding aircraft, and the output is the state of the i-th aircraft and the related covariance matrix.

[0098] The extended Kalman filter is expressed as:

[0099]

[0100] The measurement matrix is ​​set up as:

[0101]

[0102] X i =[x i ,y i ,v x,i ,v y,i ] T

[0103] In S2, the probability of each intruding drone being located at a specified point (x, y) is obtained based on the estimated states of different intruding aircraft and their associated covariance matrices, which is expressed as:

[0104]

[0105]

[0106] By superimposing the probability of all invading drones being located at any point, we can obtain the comprehensive spatial distribution of the invading group. In the comprehensive spatial distribution, the probability of the existence of an invading drone can be expressed as:

[0107]

[0108] The probability of invading drones is mapped to grayscale values ​​and then converted into a DDP image. The mapping process is expressed as:

[0109] τ(x,y,k)=p(x,y,k)×255

[0110] In S3, the GRU neural network consists of four layers, including an input layer, two GRU hidden layers and an output layer. The output layer of the GRU neural network uses a softmax function to calculate the probability of each intent, which is expressed as:

[0111] p(k)=[p1(k),p2(k),...,p M (k)] T =softmax(w out h G (k)+b out )

[0112] During the simulation process, an intention database is established to train the CNN neural network, BP neural network and GRU neural network.

[0113] According to experience, the group intentions of the invading aircraft groups set in the database include penetration, detour, reconnaissance, search and attack, fast passage, continuous attack and salvo attack.

[0114] Among them, penetration means that the goal of the invading aircraft group is to penetrate the opponent's defenses or facilitate the attack on important targets outside these defense systems, such as Figure 2 (a)

[0115] Detours are when the goal of an invading aircraft swarm is to bypass the opponent's defenses, induce the opponent to reposition away from their best defensive position, and increase the options for a successful follow-up attack, such as Figure 2 (b)

[0116] Reconnaissance is the extensive surveillance of an area by a swarm of intruder aircraft, such as Figure 2 (c)

[0117] Search and attack refers to the intruder aircraft group identifying and attacking potential targets in a designated area, such as Figure 2 (d)

[0118] A fast pass is when a group of intruder aircraft quickly moves through a specific area, usually maintaining a dense formation, e.g. Figure 2 (e)

[0119] A continuous attack is when a group of invading aircraft systematically attacks a target within a predetermined time interval, such as Figure 2 (f)

[0120] Salvo attack means that the target of the invading aircraft group is attacked synchronously to increase the probability of successful attack, such as Figure 2 (g) as shown.

[0121] Furthermore, a simulation system is used to build training and test databases through numerical simulation, and Latin hypercube sampling technique is used to set the application intent and intent parameters of each simulation. From the obtained trajectory clustering, 10% of the trajectories are randomly selected as the test database to ensure each intent. The remaining trajectories are designated for the training database. Therefore, although both the test database and the training database are built using the same method, they are still mutually exclusive and have no overlap.

[0122] A sliding window is used to extract samples, and labels are constructed using a one-hot encoding method. In the training dataset, all sample lengths are normalized to a predetermined length to facilitate efficient network training.

[0123] A total of 34,886 samples were extracted from the training set, of which 31,398 samples were used for training and the remaining 3,488 samples were used to test the generalization ability of the model. The Adam optimization algorithm was used during the training process, with the batch size of each iteration set to 64, the learning rate to 0.002, and the decay rate to 0.99 every 100 iterations. The hyperparameters of the Adam optimizer were selected as ∈ = 10 -8 ,η1=0.9andη2=0.999.

[0124] The performance of each intent is tested using the test set, and the recognition accuracy is recorded in Table 1.

[0125] Example 2

[0126] The same experiment as in Example 1 is conducted, except that the motion trajectory of a group of intruder aircraft with search and attack intentions is randomly selected for identification. Figure 3As shown in Figure 1, the intruder group includes a search intruder performing random surveillance maneuvers, and three attack intruders flying in a straight line to attack their own targets. The probability of the GRU neural network outputting different intentions changes with the recognition time as shown in Figure 1. Figure 4 shown.

[0127] Comparative Example 1

[0128] The W-cpclstm method is used to identify the intention of intruding aircraft groups. The training set in Example 1 is used to train the neural network in the W-cpclstm method. The test set is used to test the performance of each intention, and the recognition accuracy is recorded in Table 1.

[0129] Among them, the W-cpclstm method can be found in the literature: CHEN L, LIANG X, FENG Y, et al. Onlineintention recognition with incomplete information based on a weightedcontrastive predictive coding model in wargame[J]. IEEE Transactions on NeuralNetworks and Learning Systems, 2022.

[0130] Comparative Example 2

[0131] The W-cpclstm method is used to identify the intention of the intruding aircraft group. The training set in Example 1 is used to train the neural network in the W-cpclstm method. The motion trajectory of the intruding aircraft group with search and attack intentions randomly selected in Example 1 is identified. The results are as follows: Figure 5 shown.

[0132] The test results of the test set of Example 1 and Comparative Example 1 are shown in Table 1.

[0133] Table 1 Recognition accuracy of test set

[0134] intention Example 1 Comparative Example 1 penetration 0.9543 0.9133 detour 0.9347 0.9233 Investigation 0.9959 0.9714 Search and attack 0.9657 0.9778 Fast Track 0.9469 0.9143 Continuous Attack 0.9171 0.8987 Salvo Attack 0.9388 0.9343 average value 0.9505 0.9333

[0135] As can be seen from Table 1, the method in Example 1 provides higher recognition accuracy than Comparative Example 1 in all intended cases.

[0136] Comparing the results in Example 2 with those in Comparative Example 2, Figure 4 and Figure 5 , it can be seen from the figure that although at t = 0, the probability of each intention in Example 2 and Comparative Example 2 is equal at the beginning, but Example 2 ( Figure 4) converges quickly, with a probability of over 50% in identifying the true intent within 1 second. In contrast, the probability of Figure 5 ) takes significantly longer, reaching the same probability threshold after approximately 1.9 s.

[0137] The present invention has been described above in conjunction with preferred embodiments, but these embodiments are only exemplary and serve only as an illustration. On this basis, the present invention may be subjected to a variety of substitutions and improvements, all of which fall within the scope of protection of the present invention.

Claims

1. A method for identifying group intentions through a dynamic distribution probability image, characterized in that: The following steps are involved: S1. Process the metrics associated with each intruder aircraft through the EKF to obtain the estimated state and its associated covariance matrix; S2, constructing a DDP image based on the estimated state and its corresponding covariance matrix, wherein the DDP image is an image capable of representing the estimated state of the invading aircraft group at the current moment; S3. Extract the first feature of the DDP image through the CNN neural network, and extract the second feature through the BP neural network; input the first feature and the second feature into the GRU network, and the GRU neural network outputs the probabilities of different intentions, thereby determining the group intention of the invading aircraft group.

2. The method for identifying group intentions through dynamic distribution probability images according to claim 1, characterized in that: In S1, an extended Kalman filter is constructed for each intruding aircraft. The input of the i-th extended Kalman filter is the measurement information of the i-th intruding aircraft, and the output is the state of the i-th aircraft and the related covariance matrix.

3. The method for identifying group intentions through dynamic distribution probability images according to claim 1, characterized in that: The extended Kalman filter is expressed as: Where k represents the time, k+1|k represents the prediction of k+1 time based on k time, subscript i represents the i-th extended Kalman filter, P i (k+1|k) represents the error covariance matrix of the i-th extended Kalman filter predicting the k+1 moment at the k moment, Ψ i represents the linear constant velocity model in the extended Kalman filter, P i (k) represents the covariance matrix at time k, Q represents the covariance, S i (k+1) represents the covariance of the innovation process, represents the estimated state at time k, H() represents the measurement matrix of the extended Kalman filter, R represents the noise covariance matrix, K i (k+1) represents the Kalman gain at time k+1, M i (k+1) represents the measurement information at time k+1.

4. The method for identifying group intentions through dynamic distribution probability images according to claim 3, characterized in that: The measurement matrix is ​​set as: X i =[x i ,y i ,v x,i ,v y,i ] T Among them, X i represents the state of the i-th invading drone, x i ,y i represents the position of the i-th invading aircraft, v x,i ,v y,i represents the speed of the i-th invading aircraft.

5. The method for identifying group intentions through dynamic distribution probability images according to claim 1, characterized in that: In S2, the probability of each intruding UAV being located at a specified point (x, y) is obtained based on the estimated states of different intruding aircraft and their associated covariance matrices; By superimposing the probability of all invading drones being located at any point, the comprehensive spatial distribution of the invading group is obtained, which is used to reflect the probability of the existence of invading drones. The probability of invading drones is mapped to grayscale values ​​and then converted into a DDP image.

6. The method for identifying group intentions through dynamic distribution probability images according to claim 5, characterized in that: The probability that each intruder drone is located at a given point (x, y) is expressed as: Among them, p I (x, y, k) represents the probability that the i-th invading drone is located at point (x, y) at time k, represents the spatial distance between the i-th invading drone and the point (x, y), D M,i (x,y,k) represents the Mahalanobis bias distance between the i-th intruder drone and the point (x,y).

7. The method for identifying group intentions through dynamic distribution probability images according to claim 6, characterized in that: The Mahalanobis bias distance is expressed as: Among them, e i (x, y, k) represents the spatial distance between the i-th invading drone and point (x, y), x i (k),y i (k) is the estimated state Obtained in.

8. The method for identifying group intentions through dynamic distribution probability images according to claim 6, characterized in that: The probability of the existence of an invading drone is expressed as: Where N represents the number of invading drones.

9. The method for identifying group intentions through dynamic distribution probability images according to claim 6, characterized in that: The first feature and the second feature are summed up and used as the input of the GRU neural network.

10. The method for identifying group intentions through dynamic distribution probability images according to claim 1, characterized in that: The output layer of the GRU neural network uses the softmax function to obtain the probability of each intent, expressed as: p(k)=[p1(k),p2(k),...,p M (k)] T =softmax(w out h G (k)+b out ) Among them, the subscripts 1, 2, ..., M represent different intention numbers, [p1(k), p2(k), ..., p M (k)] represents the probability of different intentions, w out represents the weight of the output layer, h G (k) represents the output state of the GRU neuron in the last GRU hidden layer, b out Represents the bias of the output layer.

Images