The article discusses the task of classifying projectiles (A - (a-ammunition), A/M - (a/m-ammunition), A/P - (armor-piercing), A/PС - (armor-piercing-cumulative), M - (m-ammunition), P - (armor-piercing ammunition)) using an MLP perceptron with the aim of determining the type of projectile (artillery or missile). This allows: the military to quickly respond and apply an effective strategy and tactics during military operations; civilian organizations and law enforcement agencies to determine whether a projectile has a potentially dangerous nature that can pose a threat to the safety of citizens; in regions with military conflict or after its completion, it is important to identify unexploded projectiles for their safe removal and disposal; scientific institutions to study the properties and characteristics of new types of projectiles. The classification of projectiles was carried out using an MLP perceptron with two-, three-, five-, sixhidden layers, which have respectively the number of neurons (33 and 8), (33, 16 and 8), (33, 16, 16 and 8), (33, 16, 16, 16 and 8) with activation functions relu, logistic, tanh. The dependence of the accuracy of projectile classification on the number of hidden layers for activation functions relu, logistic, tanh was experimentally investigated. It is shown that the highest accuracy of projectile classification (95.9%) is achieved by a neural network with two hidden layers and the number of neurons 33 and 8 with Tanh activation functions respectively and an output layer with six neurons with the Softmax activation function. The results of the study of the influence of the components of the input feature vector (x1 - position_x1, x2 - position_y1, x3 - position_h1, x4 - velocity, x5 - taget_class, x6 - explosion_x2, x7 - explosion_y2, x8 - explosion_h2, x9 - hour, x10 - minute, x11 - second, x12 - angle_big_tick, x13 - angle_small_tick, x14 angle_degrees, x15 - angle_rotation_degrees, x16 - distance_2d, x17 - distance_3d, x18 - flight_time) on the accuracy of classification are visualized in the form of diagrams. The height, speed, and angle have the greatest influence on the values of the outputs of neurons in the output layer.
The task of neural network classification of projectiles (A - (a-ammunition), A/M -
(a/mammunition), A/P - (armor-piercing), A/PС - (armor-piercing-cumulative), M - (m-ammunition),
P - (armor-piercing ammunition) is relevant, as its solution automatically solves the problem of
determining the type of projectile [
0000-0002-7481-8628 (I. Peleshchak); 0000-0002-5665-5423 (D. Koshtura); 0000-0002-2196-252X ((M. Luchkevych); 0000-0002-3549-2813 (V. Tymchuk) © 2024 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
The aim of the work is to develop an optimized morphology of the MLP perceptron to ensure
high accuracy metrics (accuracy, precision, recall, f1-score) when classifying projectiles. The
optimization of the MLP perceptron morphology is achieved by determining the necessary
number of hidden layers [
In the context of modern technological products and the needs of the defense sector, the task of
data classification, in particular the determination of types of projectiles, is an important task [
The training sample was formed by choosing a multifunctional complex with flexible hardware
and algorithmic support that easily adapts to perform various combat tasks - 1L220U-KS [
Main technical characteristics of the 1L22OU-KS/IL22OU complex [
After analyzing the characteristics of such a complex, the following tasks can be identified for
which data can be generated based on materials [
The coordinates position_x1 (x coordinates from where the projectile was launched), position_y1
(y coordinates from where the projectile was launched), position_h1 (height h from where the
projectile was launched), explosion_x2 (x coordinates where the explosion occurred),
explosion_y2 (y coordinates where the explosion occurred), explosion_h2 (height h where the
explosion occurred) are initially generated in the SK-42 coordinate system - a cartographic
coordinate system [
It divides the earth's surface into 60 numbered zones each 6 degrees of longitude wide. The values of the extreme meridians of six-degree zones will have values: the first zone 0 - 6 °, the second zone 6 - 12 °, the third zone 12 - 18 ° and so on.
To convert coordinates from the SK-42 system to the WGS84 system (longitude and latitude), you can use the converter: https://sk42.org/en/. This converter uses the ST_Transform() postgis method, which converts the output coordinates of SK-42, the SK-42 zone to latitude and longitude.
For example, coordinates: SK-42: 5445007, 07366730 with zone: SK-42: 7 will be converted to latitude: 49.122917949468516, longitude: 37.172574626199335. In this work, coordinates in the SK-42 system will be used for training and testing. y coordinates from where the SK-42 projectile was launched
Projectile class x coordinates explosion occurred y coordinates explosion occurred where where the SK-42
occurred measurement - meters
(16:45:56) Large division of the protractor One division of the protractor =
protractor = 360’ = 6° Small division of the protractor One division of the protractor =
360 Measurement - degrees, from 0 to 360
position of the projectile and the point of its explosion
The division of the protractor ("thousandth") is a central angle, the length of the arc of which is equal to 1/6000 of the length of the circle. The formula for calculating the angle in degrees (angle_degrees) uses both the large and small part of the angle, which allows you to get complete information about the position and orientation of the data.
The length of the arc of angle ∪AB of one protractor division is equal to:
2 2 ∙ 3,14 ∙ 1
∪AB = = = = 0,001105 ≈ 0,001 ,
6000 6000 955
introduces a systematic error of 4.5% (rounded - 5%) [
So, the central angle, which is based on an arc equal to 0.001 R, that is, a division of the protractor, is called a thousandth.
A circle contains 360°, or 21600'. One division of the protractor is equal to 21600/6000 = 3.6'. One large division of the protractor is equal to 3.6·100 =360’ = 6°. One degree is approximately equal to 6000/360 = 16.66 p.k. = 17 p.k. (P.k. - division of the protractor). To convert angle values expressed in protractor divisions to values expressed in degrees and minutes, and vice versa, the following ratios are used: 60-00 =360°, 30-00 = 180°, 15-00 = 90°, 1-00 = 6°, 0-01 = 3.6' Vector of output features for projectile classification (А – 1, А/М – 2, А/Р – 3, А/РС – 4, М – 5, Р – 6)
[A - 1 (ammunition), A/M - 2 (a/m-ammunition), A/R - 3 (armor-piercing), A/RC - 4 (armor-piercingincendiary), M - 5 (ammunition), R - 6 (armorpiercing ammunition)] (2) (3) (4)
For the data preprocessing, criteria will be defined using Table 1 and Table 2.
Before the data processing for the classification of projectiles collected from the 1L220U-KS complex, it is necessary to perform the generation of new values. This is done to increase the size of the training set and help the MLPClassifier_2HL_T neural network acquire generalizing properties.
The generation of new values uses the method of pseudo-random noise with a normal distribution. New values are generated closer to the values in the training sample, taking into account the standard deviation of each characteristic.
Generation of a new value:
∗ = + ∙ (0,1), where ∗ – is the new value of the i-th characteristic, – is the initial value of the i-th characteristic, – is the standard deviation of the i-th characteristic, (0,1)– is the function for generating pseudo-random values with a normal distribution (mean = 0, standard deviation = 1).
Calculation of the standard deviation: = √ ∑( − )2 where – is the i-th value of the characteristic, – is the mean value of the i-th characteristic, N – is the size of the training sample.
In this article, data were generated: position_x1, position_y1, position_h1, velocity, taget_class,
explosion_x2, explosion_y2, explosion_h2, hour, minute, second, angle_big_tick, angle_small_tick,
angle_degrees, angle_rotation_degrees, distance_2d, distance_3d, flight_time from the study [
Normalization: ′ = − where ′ - is the normalized value of the i-th characteristic, – initial value of the i-th characteristic, – is the mean value of the i-th characteristic, is the standard deviation of the i-th characteristic.
Each row of the table needs to be checked for compliance with certain conditions: validity of time, coordinates, velocity, angle, and others. This allows identifying and filtering acceptable data rows.
The training dataset will contain the following characteristics:
Initial projectile coordinates: position_x1: X coordinate of the initial point, position_y1: Y coordinate of the initial point, position_h1: Z coordinate, height of the initial projectile position.
Velocity: velocity: projectile velocity.
Target class: target_class: class of the target aimed at by the projectile (categorical variable).
Coordinates of the final projectile position: explosion_x2: X coordinate of the final point, explosion_y2: Y coordinate of the final point, explosion_h2: Z coordinate, height of the final projectile position.
Time: hour: hour of projectile launch, minute: minute of projectile launch, second: second of projectile launch.
Angles: angle_big_tick, angle_small_tick, angle_degrees, angle_rotation_degrees.
Distances: distance_2d: 2D distance between initial and final points, distance_3d: 3D distance between initial and final points.
Flight time: flight_time: projectile flight time.
For neural network training, the launch time was divided separately into hours: hour, minutes: minute, seconds: second, and these values were saved in separate columns.
The angle value was also divided into two parts: the large (angle_big_tick) and small (angle_small_tick) divisions of the angle, calculation of the total angle in degrees (angle_degrees), using the values angle_big_tick and angle_small_tick for an accurate calculation of the angle.
These transformations are aimed at increasing the data set and reflecting new aspects that may be important for further research and modeling, as shown in Table 1.
The rotation angle (angle_rotation_degrees) is a parameter that defines the rotation angle between the position and the point of explosion, which can be important when considering the trajectory of the projectile. The distances between the position and the point of explosion are calculated to determine the spatial position of the projectile. This data can be useful in analyzing the trajectory and impact of the projectile – 2D and 3D distances.
Calculation of 2D and 3D distances between the position and the point of explosion:
The three-layer perceptron architecture used for the classification of dynamic objects (A - 1, A/M - 2, A/R - 3, A/RC - 4, M - 5, R - 6) in the work is optimized in terms of the number of hidden layers and the number of neurons in them, with the following morphology: two hidden layers and one output layer. The input sensory layer has 18 neurons, because the input feature vector has 18 components; the first hidden layer has 33 neurons with Tanh activation functions; the second hidden layer has 8 neurons with Tanh activation functions; the output layer has 6 neurons with Softmax activation functions, because 6 objects are classified. =1 =1 =1 where yi – is an element of the output vector of probabilities related to each class of projectiles, fsoftmax – is the softmax activation function, ftanh – is the tanh activation function, wli – is an element of the weight matrix between the second hidden layer and the output layer, wij – is an element of the weight matrix between the first and second hidden layers, wjk – is an element of the weight matrix between the input layer and the first hidden layer. The model receives the input feature vector ̅ = ( 1, 2, … , 18), where x1 - position_x1, x2 - position_y1, x3 - position_h1, x4 – velocity, x5 - taget_class, x6 - explosion_x2, x7 - explosion_y2, x8 - explosion_h2, x9 – hour, x10 – minute, x11 – second, x12 - angle_big_tick, x13 - angle_small_tick, x14 - angle_degrees, x15 - angle_rotation_degrees, x16 - distance_2d, x17 - distance_3d, x18 - flight_time.
The experimental results investigated the influence of the number of hidden layers on the model's accuracy. The accuracy graph (Figure 3) showed that increasing the number of hidden layers improves the classification accuracy. The graph (Figure 3) displays three different activation functions: ReLU, Logistic, and TanH.
As seen from the graph (Figure 3), the accuracy of MLP classifiers increases with the increase
in the number of hidden layers with ReLU and TanH activation functions. However, after 3 hidden
layers with Logistic activation functions, the accuracy of MLP classifiers starts to decrease. This
happens because complex networks can be overly adapted to the training data and may not
perform well on new data [
In this case (Figure 3), MLP classifiers with three and two hidden layers and TanH activation functions have the highest accuracy. To optimize computational resources, it is advisable to use an MLP classifier with two hidden layers and TanH activation functions.
In the selected configuration, it showed high results on the test dataset. Tables 2 and 3 provide metrics for evaluating the accuracy of the three-layer neural network classifier using the ScikitLearn library.
The model of a feedforward neural network (MLPClassifier) [
Using train_test_split, the data was split into training (80%) and test (20%) sets for efficient model validation. The random_state=42 was set for result reproducibility. The random_state parameter in the train_test_split function determines the method of selecting a random permutation for dividing the data into training and test sets. Setting random_state to a specific value (in this case, 42) ensures that the same random permutation will be used for data splitting at each program run. This makes the data split repeatable and suitable for result reproducibility [10[].
LabelEncoder is used for numerical encoding of categorical class labels. LabelEncoder is used
to transform categorical labels into numerical values. We create LabelEncoder and MinMaxScaler
[
In particular, the accuracy on the training set is 0.979, and the accuracy on the test set is 0.959.
Besides accuracy, other metrics such as precision, recall, and F1-score also have high values: on the training set: accuracy: 0.9786, precision: 0.9788, recall: 0.9786, F1-score: 0.9787; on the test set: accuracy: 0.9585, precision: 0.9617, recall: 0.9585, F1-score: 0.9592.
The MLP model used SHAP (SHapley Additive exPlanations) [
SHAP is used to estimate the importance of features. For each component of the input feature vector and class i, the SHAP value determines the weight of and is described as follows: | |! ( − | | − 1)!
! where 0 – is the base value, ( , )– is the model output for the subset of features .
Using the shap.sample function, a subset of data is determined for analysis. 100 random objects are used for this sample to reduce the number of computations required for SHAP analysis because the dataset is very large. Using shap.KernelExplainer [14], an explainer is created, which is passed the model.predict function for prediction and the X_train_sample sample. The explainer is ready to use to obtain SHAP values. SHAP uses the Shapley method to analyze the impact of each feature on the model's prediction. This allows to reveal how each feature contributes to or decreases the likelihood of a specific prediction [15].
( ) = 0 + ∑ ⊆ { } [ ( ∪ { }, )− ( , )], (8)
Using the explainer.shap_values method, SHAP values are obtained, indicating how each individual feature affects the model's predictions. After executing this command, shap_values will contain a matrix of SHAP values, where each row corresponds to a sample from X_train_sample, and each column corresponds to a specific feature [16].
The values in the matrix show the influence of each feature on the model's prediction for the corresponding sample. By the sign of the value, it can be understood whether this feature contributes (positive value) or decreases (negative value) the prediction. Using shap.summary_plot, a feature importance plot is generated. This plot shows the importance of each feature, helping to understand which features have the greatest impact on the model's predictions.
Parameter values are presented on the x-axis, and SHAP values are presented on the y-axis. SHAP values represent how strongly each parameter affects the model output.
As shown in Figure 4, the parameters of altitude, speed, and angle have the greatest impact on the model output. An increase in speed by 1 unit leads to an increase in the SHAP value by 3 units. An increase in the angle by 1 unit leads to an increase in the SHAP value by 2 units [17]. These variables have the greatest impact because they directly affect the classification of the projectile [18]. Speed determines how fast the projectile flies, maximum altitude determines how high it climbs, and altitude position determines where it stops. Flight time determines how long the projectile flies before falling [19]. Other parameters also have some impact on the model output, but it is smaller. For example, an increase in maximum altitude by 1 unit leads to an increase in the SHAP value by 1 unit [20].
The plot_confusion_matrix and plot_result_area functions are used to visualize classification results, specifically to display the confusion matrix and detailed classification report.
In the work, classifiers were trained on training data and evaluated on test data [21]. The main steps include copying training and test data, initializing classifiers, and calling the perform_training_cycle function for training and evaluating each classifier. The perform_training_cycle function trains each classifier and computes quality metrics for training and test data. The results are stored in the reporting DataFrame training_report_df_fulldata and presented in Figure 5.
Figure 5 shows the results of the experiment for the test datasets. The table presents the model names: MLPClassifier_2HL_T, SVC, MLPClassifier_2HL_R, MLPClassifier_2HL_R, where 2HL is the number of hidden layers (two in this case), R is the Relu activation function, L is the Logistic activation function, T is the Tanh activation function, and others, including accuracy, precision, recall, and F1-score for each model [22].
As seen from the results and experiment, the best results were obtained by the MLPClassifier_2HL_T model, which achieved an accuracy of 95.85%, precision of 96.17%, recall of 95.85%, and F1-score of 95.92% on testing. Compared to other models, the MLPClassifier_2HL_T model demonstrated high training and testing accuracy. This is because the model has two hidden layers, allowing it to better represent complex dependencies between the data [23].
The performance of the models suggests that a neural network with two hidden layers and the tanh activation function is well-suited for the classification task. This finding is consistent with the notion that deeper networks can capture more complex patterns in the data.
The SHAP (SHapley Additive exPlanations) values were used to determine the importance of input features in the classification process [24]. The analysis revealed that the speed and launch angle had the most significant impact on the classification decision.
The study's results were compared with previous research on projectile classification using different methodologies. The comparison showed that the MLPClassifier_2HL_T model outperformed other models used in previous studies [25], demonstrating the effectiveness of the chosen approach.
The high performance of the MLPClassifier_2HL_T model suggests its potential application in real-world scenarios, such as military operations or security systems, where the classification of projectiles is essential for decision-making.
Overall, the study demonstrates the effectiveness of using neural networks for projectile classification and highlights avenues for further research to enhance the model's performance and applicability.
Developed an optimized three-layer network with two hidden layers, consisting of 33 neurons in the first hidden layer and 8 neurons in the second hidden layer, using Tanh activation functions, and an output layer with 6 neurons using Softmax activation for classifying projectiles (A - (antipersonnel), A/M - (anti-personnel high-explosive), A/P - (anti-personnel high-explosive antitank), A/PC - (high-explosive), M - (high-explosive anti-tank)) with an accuracy of 95.85%.
Experimentally determined that the MLP classifier (95.85% accuracy) with two hidden layers, 33 neurons in the first hidden layer, and 8 neurons in the second hidden layer using Tanh activation functions, and an output layer with 6 neurons using Softmax activation, achieved the highest accuracy.
Found that increasing the number of hidden layers, starting from 3, decreases the accuracy of projectile classification.
Demonstrated that the most significant input features influencing the accuracy of projectile classification are the projectile's speed, initial height, and launch angle. [14] Jeon, Jueun, Jong Hyuk Park, and Young-Sik Jeong. "Dynamic analysis for IoT malware detection with convolution neural network model." IEEE Access 8 (2020): 96899-96911 [15] Li, Guang, et al. "Research on the natural language recognition method based on cluster analysis using neural network." Mathematical Problems in Engineering 2021 (2021): 1-13 [16] Rashid, Muhammad, et al. "A sustainable deep learning framework for object recognition using multi-layers deep features fusion and selection." Sustainability 12.12 (2020): 5037. [17] Sharifzadeh, Foroogh, Gholamreza Akbarizadeh, and Yousef Seifi Kavian. "Ship classification in SAR images using a new hybrid CNN–MLP classifier." Journal of the Indian Society of Remote Sensing 47 (2019): 551-562. [18] Desai, Meha, and Manan Shah. "An anatomization on breast cancer detection and diagnosis employing multi-layer perceptron neural network (MLP) and Convolutional neural network (CNN)." Clinical eHealth 4 (2021): 1-11. [19] Fekri-Ershad, Shervan. "Bark texture classification using improved local ternary patterns and multilayer neural network." Expert Systems with Applications 158 (2020): 113509. [20] Wen, Junhao, et al. "Convolutional neural networks for classification of Alzheimer's disease:
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