1 Introduction

Due to the complex physical properties of Sonar targets, classification of the real target and the false alarms has become a significant and widely used area for researchers and industrialists working in this field. Unwanted signals in the underwater environment have various sources including noise, reverberation and clutter [1]. Since the reverberation has the same domain and are homogenous with original ping, it is easy to distinguish them from the real target [2]. When the seabed changes a lot and when there are different kinds of beds, echoes returning from the seabed will have target-like properties, in a way that even probability density function of the real target and the seabed are very much alike. This false alarm is called clutter [3]. Due to the great similarity of their reflected echoes, it’s very hard to classify clutter and real target.

In recent years the use of NNs to classify sonar targets has been very common and many efforts have been put into this area [4]. For most applications of MLP NNs, optimized [5] or standard back-propagation algorithms [6] are used as learning methods. Many methods based on differentiation have been used for training the neural network, including gradient descent, Kalman filter, decoupled Kalman filter, and back- propagation. Back-propagation algorithm is based on the gradient which has some deficiencies such as slow convergence [7] and applicability in small areas [8]; therefore, it’s not reliable for practical applications.

The ultimate goal of the learning process in NNs is to find the best combination of their weights and biases, so that we’d have the lowest error in training the network and in the test samples [9]. Reference [10] shows that the meta-heuristic optimization algorithms can replace the gradient-based learning algorithms, since the Stochastic nature of these algorithms prevents getting stuck in local optimum, increases the convergence speed, and reduces classification errors [11].

Here we briefly mention the NFL theorem, in which the abbreviation stands for “No free lunch” [12, 13]. This theorem logically proves that there is no appropriate meta-heuristic algorithm for solving all the optimization problems. In other words, a specific meta-heuristic algorithm could have promising results for a set of problems, but do poorly over another set. Obviously, the NFL makes this field of study very active and leads to the promotion of current methods and proposition of new meta-heuristic algorithms every year. Meta-heuristic methods used for training NNs in recent years include Genetic Algorithms (GA) [14], Simulated Annealing (SA) [15, 16], Magnetic Optimization Algorithm (MOA) [17], Biogeography-Based Optimization (BBO) [18] and Gray Wolf and Modified Grey Wolf Optimizer (GWO) [19].

One of the aspects of the similarity of meta-heuristic algorithms is dividing the search space into two phases: exploration and exploitation. Exploration phase occurs when the algorithm converges towards reliable solutions. In this phase, the population undergoes slight changes. In many cases, due to the stochastic nature of meta-heuristic algorithms, there is no clear boundary between the two phases; in other words, the imbalance between the two phases makes the algorithm stuck in a local minimum. DA easily recognizes the boundary between the exploration and the exploitation phase and converges towards more reliable solutions. Due to the two aforementioned reasons, i.e. NFL theorem and the DA’s ability for regulating exploitation and exploration phase, this paper suggest the use of AD for training an MLP NN to classify sonar targets with high accuracy and in real time.

The rest of the paper is organized as follows. Section 2 introduces MLP NNs. Section 3 discusses the general aspects of DA. The proposed training scheme is described in Sect. 4. Section 5 presents the various sonar data sets. Simulation results are discussed in Sect. 6. Finally, Sect. 7 concludes the article.

2 MLP NN

Figure 1 shows a three-layer MLP NN where, n represents the number of input nodes, h represents the number of hidden nodes and m denotes the number of output nodes [19]. As show, there are one-way connections between the nodes of the MLP NN which is from the family of Feed forward NNs. The output of the MLP NN is calculated by Eq. 1:

$$S_{j} = \mathop \sum \limits_{i = 1}^{n} \left( {W_{ij} \cdot X_{i} } \right) - \theta_{j} , \quad j = 1, 2 \ldots h$$
(1)

where n is the number of input nodes, Wij is the weight connecting the i-th (in the input layer) to j-th-node (in the hidden layer), θij denotes j-th bias node (in the hidden layer), and X-i represents the input to the i-th node (in the input layer). The output of each hidden node is calculated using a sigmoid function as in Eq. 2.

Fig. 1
figure 1

An MLP NN with a hidden layer

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$$S_{j} = sigmoid\left( {s_{j} } \right) = \frac{1}{{\left( {1 + { \exp }\left( { - s_{j} } \right)} \right)}}, \quad j = 1, 2 \ldots h$$
(2)
$$o_{k} = \mathop \sum \limits_{j = 1}^{h} \left( {W_{jk} \cdot S_{j} } \right) - \theta_{k}^{'} , \quad k = 1, 2 \ldots m$$
(3)

After calculating the values of the hidden nodes, the finals output can be defined as follows:

$$O_{k} = sigmoid\left( {o_{k} } \right) = \frac{1}{{\left( {1 + exp\left( { - o_{k} } \right)} \right)}}, \quad k = 1, 2 \ldots m$$
(4)

where Wjk is the weight connecting the j-th node (in the hidden layer) to the k-th node (output layer), and θk represents the k-th bias node (in the output layer). The most important parts of MLP NNs are weights and the bias of the nodes. As we observed above, weights and the biases, define the final output values. Training a MLP NN includes finding the best value for the weights and the biases, in order to obtain the desired output per specific input.

3 Dragonfly Algorithm

3.1 The Operators for Exploration and Exploitation

According to Reynolds’ theory, collective (group) behavior follows three basic principles [21]:

  • Separation, which refers to avoiding collision with neighbors.

  • Alignment, which represents the speed adjustment relative to the neighbors.

  • Cohesion, which points to the tendency of moving toward the average position of the neighbors.

The main purpose of collective life is to survive; therefore, all the members should be attracted to the food sources and divert the attention of the external enemies. According to these two behaviors and following Fig. 2 five main factors of the group members will be updated.

Fig. 2
figure 2

Five main factors of the members of the updating group

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Each of these behaviors is mathematically modeled as follows. Separation is calculated as follows [22].

$$S_{i} = - \mathop \sum \limits_{j = 1}^{N} X - X_{j}$$
(5)

where X is the specific position of each member, Xj represents the j-th position of adjacency for each member and N is the number of members’ neighbors. The alignment is calculated as follows:

$$A_{i} = \frac{{\mathop \sum \nolimits_{j = 1}^{N} V_{j} }}{N}$$
(6)

where Vj is the speed of j-th adjacency for each member. Cohesion is calculated as follows:

$$C_{i} = \frac{{\mathop \sum \nolimits_{j = 1}^{N} X_{j} }}{N} - X$$
(7)

where X is the specific position for each member, N represents the number of neighbors, and Xj denotes the j-th position of adjacency for each. Gravity and attraction toward a food source is calculated as follows:

$$F_{i} = X^{ + } - X$$
(8)

where X is the specific position of each member and X+ shows the location of a food source. Distracting the enemy is calculated as follows:

$$E_{i} = X^{ - } + X$$
(9)

where X is the specific position of each member and X− is the position of the enemy. It is assumed that the behavior of dragonfly is a combination of the five patterns mentioned in this article. We consider two vectors to update the position of the artificial dragonfly in a search space and simulate its movements: step vector (ΔX) and position vector (X).

Step vector is similar to the velocity vector in PSO, and DA has been developed based on the framework of PSO algorithm. The step vector shows the direction toward which the dragonfly moves and it is defined as follows. It should be noted that the position update model for artificial dragonflies has been defined in one dimension; however, it can be developed to higher dimensions.

$$X_{t + 1} = \left( {sS_{i} + aA_{i} + cC_{i} + fF_{i} + eE_{i} } \right) + w\Delta X_{t}$$
(10)

where s, a, and c are the separation, alignment, and cohesion weights, respectively while \(S_{i}\), \(A_{i}\) and \(C_{i}\), respectively denote the separation, alignment, and cohesion of the i-th member. f is a factor for food and Fi represents the food source for the i-th member. e is a factor for enemy and \(E_{i}\) is the position of the i-th member of the enemy and also w is the inertia weight and t counts the number of repetitions. After calculating the step vector, the position vector is calculated as follows:

$$X_{t + 1} = X_{t} + \Delta X_{t + 1}$$
(11)

where t is the number of repetitions. By incorporating separation, alignment, cohesion, absorption of food and repulsing the enemy agents (s, a, c, f and e), we can obtain various exploration and exploitation behaviors during the course of optimization. The neighbors of a dragonfly are very important, so that an adjacency is defined as a specific radius around each dragonfly. As Fig. 3 shows, dragonflies show only two types of mass movement: the static and the dynamic movements.

Fig. 3
figure 3

Dynamic versus static dragonfly swarms

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It may be seen in Fig. 3 that dragonflies are willing to adapt their flight, and this occurs when the collective and dynamic separation and adhesion are appropriate. In a group of static dragonflies compliance is low while cohesion, due to the attack on the prey, is high. As a result, while exploring the search space, we assign high compliance and low cohesion to dragonflies. When compliance is low and the cohesion is high, the search space is being exploited.

To transfer between exploration and exploitation, the radius of adjacency increases proportional to the number of iterations. Another way to balance exploration and exploitation, is the compatibility of the adjustments of collective factors (s, a, c, f, w, and e) during the optimization. Here the question is how to ensure convergence of the DA during the optimization. Dragonflies need to change their alignment weight in order to transfer from exploration to exploitation phase in the search space. It is assumed that the dragonflies tend to adjust their flight path as an optimization improvement. In other words, the adjacency expands; thereby, in order to allow for the optimization and converge towards the local optimum, a large herd of them become one group.

Food sources and the enemies are among the best and the worst solutions found by swarming and collective movement. It makes the convergence move towards the mentioned search spaces while the divergence to be outside. To reach stochastic improvement and when there is no solution around the adjacency, we use the random behavior and exploration of this dragonfly which should fly around the search space. In this case, the position of dragonfly is updated using the following relations.

$$X_{t + 1} = X_{t} + Le^{\prime}vy\left( d \right) \times X_{t}$$
(12)

where t is the current iteration and d is the distance from the position vector (Fig. 4).

Fig. 4
figure 4

Pseudo-codes of DA

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$$Le^{\prime}vy\left( x \right) = 0.01 \times \frac{{r_{1} \times \sigma }}{{\left| {r_{2} } \right|^{{\frac{1}{\beta }}} }}$$
(13)

where r1, r2 are two random numbers in the range of [0,1], β is a constant (in this work, equal to 1.5) and σ is calculated as follows:

$$\sigma = \left( {\frac{{\varGamma \left( {1 + \beta } \right) \times \sin \left( {\frac{\pi \beta }{2}} \right)}}{{\varGamma \left( {\frac{1 + \beta }{2}} \right) \times \beta \times 2^{{\left( {\frac{\beta - 1}{2}} \right)}} }}} \right)^{{\frac{1}{\beta }}}$$
(14)

where \(\varGamma \left( x \right) = \left( {x - 1} \right)!\)

4 Training an MLP NN Using Dragonfly Algorithm

In general, there are three methods of using meta-heuristic algorithms to train MLP NNs. The first method consists of applying meta-heuristic algorithms in order to find a combination of weights and bias nodes to have the least amount of errors in an MLP NN. The second method is the use of meta-noise curves received by hydrophone, Fourier transformheuristic algorithms to find an appropriate structure for an MLP NN in a particular problem, and the last method includes the use of meta-heuristic algorithms to find the gradient descent based methods’ parameters like learning rates and momentums. In this paper, DA, is applied to an MLP NN using the first approach. In order to design an algorithm for training an MLP NN, it is necessary to appropriately present the connection weights and the node biases (Fig. 5).

Generally, there are three ways to show the connection weights and the node biases including vectors, matrices and the binary method. In vectors, matrices and binary method, each element is represented respectively by a vector, a matrix, and a string of binary bits. Each of these methods has deficiencies and advantages which could be of use in certain cases.

Fig. 5
figure 5

The training scheme used in the paper

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In the first method, it is easy to convert the elements to a vector, a matrix, or to strings of binary bits; however, the retrieving process will be complicated. That’s why this method is often used in simple NNs. In the second method for NNs with complex structures, the decoding process is easier than coding the elements. This method of learning algorithms in generic NNs is very appropriate. In the third method, variables need to be displayed in the binary form. In this case, when the structure of the network becomes complicated, the length of each element also increases. So the process of encoding and decoding would be very complicated.

Since we are not dealing with complex MLP NNs in this work, the vector method is used. In order to reduce the execution time of MLP NN, the general toolboxes of MATLAB are not used. As an example of this style of coding, we have used the final vector of MLP NN shown in Fig. 6 which is presented in Eq. 15.

Fig. 6
figure 6

An MLP NN with structure 2-3-1

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$$Position = [w_{13} w_{23} w_{14} w_{24} w_{15} w_{25} w_{36} w_{46} w_{56} \theta_{1} \theta_{2} \theta_{3} \theta_{4} ]$$
(15)

5 Dataset

The main strategy of this study is to use three dataset as follows:

  • Using Sejnowski & Gorman’s [24, 25] dataset in order to have a reference dataset to compare the proposed classifiers with the works of other researchers.

  • Planning test scenarios and collecting data in the cavitation tunnel in order to use as inactive sonar data [26].

  • Planning test scenarios and collecting data by the designed sonobuoy in order to use as an active sonar dataset.

In the following, the data collection mentioned is briefly described.

5.1 The Sonar Dataset of Sejnowski & Gorman

Sonar data used in this section have been derived from Sejnowski and Gorman’s test in [24, 25]. In this experiment, there are two types of echoes; the first is of a metallic cylinder (the real target) and the second, a rock with the same size as the cylinder (clutter or the false target). In this test, a metal cylinder with the length of 5 feet and a rock with the same size have been placed at a sandy seabed and a chirped wide-band linear FM (ka = 55.6) is sent towards them. Based on the received echo’s SNR, 208 echoes of 1200 collected echoes which had a SNR in the range of 4-15 db were selected. One hundred and eleven of these 208 echoes belong to the metallic cylinder and 97 to the rock. Figure 7 shows samples of echoes received from the rock and the metal cylinder. As it is observed, echoes of the real target (the cylinder) and the clutter (rock) are very similar to each other and cannot be separated by a linear or non-linear low-order classifier.

Fig. 7
figure 7

An example of the echoes returned from the rock and the metal cylinder

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Preprocessing used to obtain the spectral envelope is shown in Fig. 8. Figure 8a presents a set of sampling valves. In Fig. 8b, the set of sampling valves have been located on the two-dimensional spectrogram for Fourier transform of Sonar data. The spectral envelope is obtained by collecting the effects of each valve. In this test, the spectral envelope consists of 60 samples which have been normalized in the range of 0–1. Each of these numbers represents the total energy contained in its associated sampling valve; for instance, the energy contained, after being normalized, would be the first number of the sixty numbers in the characteristics vector.

Fig. 8
figure 8

Preprocessing used to obtain the spectral envelope

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5.2 The Passive Datasets (Cavitation Tunnel)

To perform this test and obtain reliable datasets, three types of propellers in classes A, B and C were tested in the cavitation tunnel. At this test, which was performed in the cavitation tunnel of the hydrodynamic, three propellers with different speeds to simulate the working conditions of different vessels were examined. This dataset was collected by the authors using the cavitation tunnel model B&K 8103. The complementary information and whole dataset is available in [26].

5.2.1 The Presentation of the Collected Noise

From left to right, respectively, Fig. 9 presents noise curves received by hydrophone, Fourier transform, and noise power spectrum in decibels for the various modeled propellers [25,26,27].

5.2.2 Active Datasets (Sonobouy)

This dataset has been collected by the Port and Maritime Organization’s sonobuoy [29]. In this experiment, 6 objects including 4 targets and 2 non-targets have been placed at the sandy bed of the sea. In this study, the transmitted signal is a wide-band linear frequency modulated pulse which covers the frequency range of 5-110 Hertz. An electric motor rotates the objects (at the bottom of the sea) through 180 degrees, with a precision of one degree. In this position, the returning echoes are collected within 10 m of them.

Fig. 9
figure 9figure 9

From left to right, respectively, noise curves received by hydrophone, Fourier transform, and noise power spectrum in decibels versus sound power reference of water(1 μPa) for various modeled floaters

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A proper dataset plays a critical role in the classification of sonar data. Due to the high volume of raw data obtained in the previous step, a high complexity in calculations is anticipated. In order to reduce the complexity of the feature classifier and extractor, conducting a possible target detection process for all the incoming data is necessary. For this purpose, the intensity of the received signal is used.

Due to the shallowness of the sea, phenomena such as multipath propagation, secondary reflections and echoes are inevitable in this environment. After the detection phase and before the feature extraction, we remove the effects of theses artifacts, using a filter in the field of matched filters. After this step, we use inverse filtering to restore the original reflected signal. At this point, we have taken advantage of the fact that separating these artificial processes in the field of matched filter is much simpler than in the time domain. The whole process of pre-processing takes place in four stages as follows:

  1. 1.

    Scaling: To eliminate the effect of amplifier gain, filter and etc. in the data collection stage, it converts the raw signal to a scaled signal.

  2. 2.

    Downsampling: the main sampling rate is 2 MHz which is much higher than the main bandwidth. In order to reduce the sampling rate so that the useful information is not lost, we have used Ref. [26]. In this reference, using environmental data such as water depth, frequency, area under surveillance etc., a fixed number of points are selected for each ping in the sampling stage [30]. Here, 2048 points are selected in a way that the useful information for feature extraction is not missed.

  3. 3.

    The process of removing the artifacts and multipath: In this method, using cross-correlation of backscattering signal with transmitted signal at every angle, the maximum output of matched filter is assigned as x. Then a window covering [x-left: x + right] is applied on the signal. Here, the right and the left are equal to 300 and 211, respectively, resulting in a window with 512 points. In order to maintain the original size of the signal, it is segmented, zero-padded and then inverse-filtered through Eq. 16 to eliminate the effect of transmitted signals.

    $$H\left( k \right) = \frac{X\left( k \right)}{{\left| {X\left( k \right)} \right|^{2} + c}}$$
    (16)

    where X(k) the Fourier transform of the transmitted signal and c = 0.0025(\(\left| {X\left( k \right)} \right|^{2}\)) for solving the singularity problem are added to the Eq. The output of this step is the net backscattered signal without the effects of artificial phenomena.

  4. 4.

    ‏Normalization: finally, we scale each objective so that they all have the same target strength. To do this, we divide each backscattered signal using SAR with the highest range which is less than 90% of the maximum received ranges.

Figure 10 shows examples of the signals received from different objectives which are functions of their frequency and direction.

5.3 Feature extraction

After the preprocessing and receiving detected frames which contain the sounds of backscattered signals, the detected sounds whose effects of artificial phenomena has been eliminated and transferred to the frequency domain (named S(k)) are delivered to the feature section (Figs. 11, 12). At this step, first the spectral of the signal is calculated by Eq. 17.

Fig. 10
figure 10

Examples of echoes returning from different target and non-target objects

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Fig. 11
figure 11

Block diagram of preprocessing and feature extraction steps

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Fig. 12
figure 12

Convergence curves for Gorman & Sejnowshki dataset

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$$\left| {S\left( k \right)} \right|^{2} = S_{r}^{2} \left( k \right) + S_{i}^{2} \left( k \right)$$
(17)

where \(S_{r}^{2}\)(k) and \(S_{i}^{2}\)(k) are the real and the imaginary parts of the Fourier transform for the detected signal. Then the spectral energy is filtered by a Mel-scaled triangular filter. The output energy of the lth filter is calculated by Eq. 18.

$$E\left( l \right) = \mathop \sum \limits_{k = 0}^{N - 1} \left| {S\left( k \right)} \right|^{2} H_{l} \left( k \right)$$
(18)

where N is the number of discrete frequencies used for FFT in the preprocessing stage and \(H_{l} \left( k \right)\) is the transfer function of the given filter where l = 0, 1,…, Ml.

The dynamic range of Mel-filtered energy spectrum is compacted by the logarithmic function as Eq. 19.

$$E\left( l \right) = log\left( {E\left( l \right)} \right)$$
(19)

Finally Mel-frequency cepstral coefficients are converted back to the time domain using Eq. 20 and discrete cosine transform (DCT).

$$C\left( n \right) = \mathop \sum \limits_{l = 1}^{M} e\left( l \right){ \cos }\left( {n\left( {l - \frac{1}{2}} \right)\frac{\pi }{M}} \right)$$
(20)

In this case and for all detected objectives, the characteristic vector will be in the form of Eq. 21.

$$X_{m} = \left[ {c\left( 0 \right){\cdot}c\left( 1 \right) \ldots c\left( {P - 1} \right)} \right]^{T}$$
(21)

All the steps outlined in the preprocessing and the feature extraction have been presented as a block diagram in Fig. 11.

6 Simulation results

In this section DA algorithm is measured by three different datasets. The datial of datasets are shown as Table 1. In each test, the efficiency of DA algorithm in terms of classification accuracy, convergence speed, and the probability of getting stuck in a local minimum are compared with other meta-heuristic algorithms. Comparison algorithms include: BBO, PSO, ACO, GWO, GSA, MVO and DA.

Table 1 The mean classification rate of various algorithms
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Required parameters and initial values have been presented in Table 2. Each network has been tested 10 times. After 10 runs, the best trained NN is selected and used for comparison. Classification rate and error percentage are two measures to compare the algorithms. To have a fairly good comparison, all algorithms stop after reaching a maximum of 250 iterations. Finally, to have a comprehensive comparison, the convergence of the results is examined. Since there are no standards regarding the selection of hidden nodes in the classification of datasets, we use the proposition in [30,31,32,33] and Eq. 22 based on the structure of MLP NNs.

Table 2 Parameters and initial values of the applied algorithms
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$$H = 2N + 1$$
(22)

where N is the number of inputs and H represents the number of hidden nodes. It should be noted that the simulations were performed in MATLAB using a PC with a 2.3 GHz processor and 4 GB RAM. The simulation results have been presented in Figs. 12, 13 and 14.

Fig. 13
figure 13

Convergence curves for passive dataset

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Fig. 14
figure 14

Convergence curves for active dataset

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As shown in Fig. 6, DA algorithm, compared to the classical algorithms, has much better results in all cases in terms of classification accuracy and convergence speed. The poor results of the ACO, PSO, and GWO algorithms are due to the nature of these algorithms. These algorithms have no operators for dramatic changes; therefore, they get stuck in local minimums. Moreover, PSO algorithm uses pheromone matrix increasing the learning capacity and efficiency of the algorithm, which is an advantage in combination problems, but also increasing the probability of getting stuck in a local minimum. PSO algorithms depend too much on the initial distribution of the particles and their primary drivers based on the attraction between them. If a large number of particles are caught in the local minimums, the algorithm to a low extent prevents the trapping of other particles.

The exploration and exploitation in this problem provide a heuristic behavior and a different recognition power. Shortly, we can say that the exploration power carries much weight in MLP NNs problems. Therefore, in order to avoid getting stuck in local minimums when solving complex problems using MLP NNs, we need random and instant search algorithms.

7 Conclusion

In this article, the sonar targets were categorized using MLP NNs. DA, BBO, GWO, ALO, ACO, GSA and MVO algorithms were used to train the MLP classifier. As it was shown, DA has a good ability in general optimal search. Due to the unique ability of DA in the exploration and exploitation phases, it has been used for solving the problems mentioned above which are more apparent in the case of data with high dimensions such as sonar data. The results show that the classifier based on DA has the most optimum classification accuracy for three different values of 92.14, 94.21 and 96.65 respectively. The speed of convergence of the algorithm is also higher than the six algorithms used.