Researching on solution of improving the quality of underwater signal classification in shallow waters applying aritificial intelligence

TABLE OF CONTENTS

LIST OF ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . vii

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

CHAPTER 1.OVERVIEW ON THE CLASSIFICATION OF BI-

OTIC AND ABIOTIC UNDERWATER SIGNALS

IN SHALLOW WATERS 7

1.1 Biotic-Abiotic underwater signals and uderwater signal clas-

sification system in shallow waters . . . . . . . . . . . . . . . . 7

1.1.1 The ocean and acoustic propagation characteristics in shal-

low waters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.1.2 Biotic and Abiotic sound sources . . . . . . . . . . . . . . . . 11

1.1.3 Underwater signal detection system based on sonar principle 13

1.2 Classical approaches in underwater signal classification . . . 19

1.2.1 Time-frequency domain transformation . . . . . . . . . . . . 19

1.2.2 LOFAR algorithm . . . . . . . . . . . . . . . . . . . . . . . . 22

1.2.3 CMS algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 23

1.2.4 DEMON algorithm . . . . . . . . . . . . . . . . . . . . . . . . 24

1.3 Modern approaches in underwater signal classification . . . 26

1.3.1 Restricted Boltzmann Machine . . . . . . . . . . . . . . . . . 27

1.3.2 Auto-Encoder . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.3.3 Convolution Neural Network . . . . . . . . . . . . . . . . . . 29

1.4 The current state of research in underwater signal classifi-

cation and limitation . . . . . . . . . . . . . . . . . . . . . . . . . 30

1.4.1 The sole use of artificial intelligence . . . . . . . . . . . . . . 32

1.4.2 The use of pre-processing combined with artificial intelligence 35

1.4.3 The use of transfer learning . . . . . . . . . . . . . . . . . . . 38

1.4.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

iv

1.5 Research directions of the thesis and actual underwater

datasets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

1.5.1 Research directions of the thesis . . . . . . . . . . . . . . . . 41

1.5.2 Actual underwater datasets used in the thesis . . . . . . . . 43

1.6 Chapter 1 conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 48

CHAPTER 2.CLASSIFICATION OF PROPELLER SHIP SIGNALS

USING THE SOLUTION OF PROPOSED SPEC-

TRAL AMPLITUDE VARIATION COMBINED WITH

A CUSTOMIZED CONVOLUTION NEURAL NET-

WORK 49

2.1 The formation process of the propeller ship signals during

movement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.1.1 Signals generated from moving propeller ships . . . . . . . . 49

2.1.2 Cavitation phenomenon . . . . . . . . . . . . . . . . . . . . . 51

2.2 Proposal of spectral amplitude variation pre-processing . . 52

2.2.1 Drawbacks of the DEMON algorithm . . . . . . . . . . . . . 52

2.2.2 Mathematical analysis of the proposed algorithm . . . . . . . 54

2.2.3 Structure of the proposed algorithm . . . . . . . . . . . . . . 57

2.2.4 Evaluation of the proposed algorithm on actual ship data . . 60

2.2.5 Evaluation of the proposed algorithm on actual diver breath

data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

2.3 Proposal of a customized convolution neural network . . . . 69

2.3.1 Reasons for choosing convolution neural network . . . . . . . 69

2.3.2 Proposed network configuration . . . . . . . . . . . . . . . . . 70

2.3.3 Evaluation of the proposed convolution neural network com-

plexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

2.4 Classification results using the combination of two proposed

solutions on propeller signals . . . . . . . . . . . . . . . . . . . . 76

2.4.1 Classification results of DEMON-Hilbert combined with LeNet

and VGG19 as control results . . . . . . . . . . . . . . . . . . 77

2.4.2 Classification results of the proposed spectral amplitude vari-

ation algorithm with LeNet and VGG19 . . . . . . . . . . . . 78

v

2.4.3 Classification results of DEMON-Hilbert and the proposed

spectral amplitude variation algorithm combined with the

proposed CNN . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

2.4.4 Evaluation of the proposed network . . . . . . . . . . . . . . 83

2.5 Chapter 2 conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 85

CHAPTER 3.CLASSIFICATION OF MARINE MAMMAL AND

PROPELLER SHIP SIGNALS USING THE PRO-

POSED SOLUTION OF CUBIC SPLINES INTER-

POLATION COMBINED WITH PROBABILITY DIS-

TRIBUTION IN THE HIDDEN SPACE DOMAIN 88

3.1 Marine mammals communication signal structure . . . . . . 88

3.2 Proposal of the cubic-splines interpolation pre-processing . 89

3.2.1 Theoretical basis for using cubic-splines interpolation . . . . 90

3.2.2 Interpolations on the frequency domain and proposed solutions 91

3.2.3 Structure of the proposed algorithm . . . . . . . . . . . . . . 95

3.2.4 Evaluation of the proposed algorithm on actual marine mam-

mal data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.3 Proposal of probability distribution in the hidden space for

Siamese triple loss network . . . . . . . . . . . . . . . . . . . . . 101

3.3.1 Structure of Siamese triple loss network . . . . . . . . . . . . 101

3.3.2 Structure of Rep-VGG model . . . . . . . . . . . . . . . . . . 102

3.3.3 Proposed solution using probability distribution in the hid-

den space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

3.3.4 Proposed solution using SNN-VAE model . . . . . . . . . . . 105

3.4 Classification results using the combination of two proposed

solutions on marine mammal and propeller signals . . . . . . 108

3.4.1 Classification results of the proposed SNN-VAE on propeller

signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

3.4.2 Classification results of the proposed cubic-splines interpola-

tion and SNN-VAE on marine mammal signals . . . . . . . . 113

3.4.3 Classification results of the proposed cubic-splines interpola-

tion and SNN-VAE on marine mammal and propeller signals 119

vi

3.5 Chapter 3 conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 125

CONCLUSION 127

LIST OF SCIENTIFIC PUBLICATION 130

REFERENCES 132

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er to select an effective processing technique, it is necessary to analyze the physical nature and the effects of the phenomenon of bubble cavitation. Figure 2.2: The water bubbles burst during cavitation The rotating propeller blades will absorb the torque of the engine and convert it into thrust to propel the ship in the water environment. According to Bernoulli’s law [76], when the ship moves in the water using the propeller, a positive pressure will appear on the surface of the propeller blade and a negative pressure will appear behind it. This pressure difference is a physical phenomenon that cannot be avoided in the process of converting torque into the ship’s propulsive force, and it also creates air bubbles around the propeller. These bubbles appear and burst when the force acting on the bubbles exceeds the tensile strength of the water’s outer 52 surface, as shown in Figure 2.2 [117], producing energy pulses that propagate in the water environment [44]. This process generates a wideband noise (around 15-20 kHz) that is modulated by the propeller blades rotation cycle [23]. The surface of the propeller blades also creates a uniform flow on each rotation. Changes in the velocity of the inflowing stream are due to the resistance force of the ship’s hull, causing a sudden decrease in inflow velocity, changing the angle of attack and rapidly reducing the pressure on the surface of the propeller blades. This phenomenon increases the process of bubble cloud formation and cavitation. As a result, the wideband noise generated by these bubbles is modulated in amplitude at the frequency of the propeller blade’s rotational speed multiplied by the number of blades [47]. The repetition of such mechanical processes creates unique characteristics of each ship and each class of ship. Therefore, a underwater signal recording may contain two main noise components: the additive component and the modulated compo- nent [82], respectively corresponding to the approach of the LOFAR and DEMON algorithms [98], which will be used to process the underwater signal generated by ship propeller. Depending on the specific problem and practical conditions, the LOFAR and DEMON algorithms will be applied to process the propeller noise signal. 2.2. Proposal of spectral amplitude variation pre-processing 2.2.1. Drawbacks of the DEMON algorithm Traditional techniques based on the DEMON algorithm have been a well-known solution for processing and classifying propeller underwater signals, which have been applied in nearly all military sonar systems from World War II to the Cold War era, such as the USA’s SURTASS [53], Sweden’s HAWKeye [40], and modern devices as Israel’s BlackFish [19] and Norway’s KongBerg [21], demonstrating the applicability and accuracy of the DEMON algorithm and its variants in practice. However, faced with the requirements of modern underwater signal classification problems, the DEMON algorithm also faces two limitations that affect the pro- cessing results of underwater signals, namely: • The first : limitation is the design of bandpass filters. In theoretical simula- 53 tions or real systems, this is a task assigned to sonar operators who rely on their experience and formal training to adjust the bandwidth manually to se- lect the periodic components in the sonar signal related to the modulation of the cavitation signals. A solution to replace humans at this stage with adaptive filtering based on fuzzy logic analysis [73] has been proposed, but it still boils down to the traditional DEMON algorithm, meaning that a specific bandpass filter still needs to be selected; • The second : limitation is the improvement of the new types of propeller thruster engines. A new trend in ship engines was opened up by the well- known Schottel engine company in 2015 by introducing versions of a new type of thruster engine system with solutions for propeller and SRT thruster en- gines. The new product SRT (Schottel Rim Thruster) [147] is an electrically driven thrust system without a gearbox or transmission shaft. The stationary part of the electric motor is attached to the outside of the connecting tube. The propeller blades are attached to the inside of the rotating chamber. This creates a space-saving and lightweight thrust device that reduces transmission line losses, limits engine noise to a very low level, and attenuates signals in the rotating chamber before they are emitted into the environment. This is the main reason that has changed the structure of cavitation noise signals, significantly affecting the detection performance of the DEMON algorithm, which only focuses on processing frequency information about the envelope of cavitation noise. Based on the technique of transforming the second-order periodic components in the torque signal of a flipper into functions containing first-order periodic through signal envelope transformation and signal processing techniques in the time-frequency domain, which have been effective approaches to date. However, the dependence on selecting the range of the bandpass filter makes DEMON-type algorithm unable to operate adaptively and automatically, and the stability of the results depends entirely on the skill of the operator. Therefore, the thesis proposes an approach based on processing the variance of the amplitude frequency components in the received signal to extract characteristic frequencies, thereby improving the classi- fication results of propeller signals. 54 2.2.2. Mathematical analysis of the proposed algorithm From the theoretical analyses in Section 1.2.4 and Section 2.1, the noise signal generated by the propeller s(t) is modeled as a modulated periodic signal m(f, t) with a cycle of Tk = 2π/k, and the cavitation noise nk(t) is modulated by ampli- tude modulation. Using equation (1.18) from Nielsen [98], the signal s(t) is expanded as formula (2.1) below: s(t) = mwk(t)nk(t) (2.1) The modulated signal mwk(t) with a cycle of Tk is the result of the propeller blade passing through the flow, creating the signal. Although mwk(t) is periodic and can be represented by a Fourier transform to find the rotation frequency of the fan, its specific modulated waveform is difficult to determine, making it challenging to determine the Fourier coefficients accurately. The two components of propeller cavitation noise can be considered statistically independent because the structure of the flow that creates the mwk(t) signal and the shape and structure of the propeller blade as well as the water bubble cloud that generates the nk(t) signal are not directly related to each other. In the discrete- time domain, the cavitation noise is a discrete-time signal composed of a sequence of uncorrelated random variables with a mean of 0 and a finite variance, so the spectrum of the signal x(t) can be regarded as white noise. According to the Rosenblatt central limit theorem [111], the signal s(t) follows a Gaussian distribution because s(t) consists of the total weight of the formation and bursting processes of water bubbles, and the bubble bursting process is balanced in all directions, so the mean value of s(t) is 0. Thus, this signal has a normal distribution of amplitude and an expected value of 0. Based on the signal model in equation (2.1), let ϕi(t) be a family of basis functions for the orthogonal projection of the signal x(t) onto the spatial domains. The basis functions are chosen such that the projections of the signal onto different basis functions are uncorrelated with each other. If the observation time T is chosen to be sufficiently large to observe the pro- 55 jected signal, then the signal is defined by the formula: xi = ∫ T 0 x(t)ϕi(t)dt (2.2) for i = 0, 1, 2, ...∞. Since the projected signals xi are orthogonal, each pair of signals xi and xj must follow the rule of the orthogonal function [137], which is given by the formula: E{xixj} = λiδij, (2.3) where E is the expected value, δij is the Dirac-delta function with a value of 1 if i = j, and 0 if i ̸= j. The observation time T is much larger than the cycle Tk of the modulated signal to ensure that the signal s(t) can be observed. By substituting formula (2.3) into formula (2.2), then: λiδij = E (∫ T 0 x(t)ϕi(t)dt ∫ T 0 x(u)ϕj(u)du ) = ∫ T 0 ϕi(t) ∫ T 0 E{x(t)x(u)}ϕj(u)dudt, (2.4) According to formula (2.3), formula (2.4) satisfies only if it satisfies the integral formula: λjϕj(t) = ∫ T 0 E{x(t)x(u)}ϕj(u)du (2.5) The covariance function of the cavitation noise is given by the formula: E{s(t)s(u)} = E{mwk(t)nk(t) ·mwk(u)nk(u)} = mwk(t)mwk(u)E{nk(t)nk(u)} (2.6) Since nk(t) is white noise, E(nk(t)nk(u)) = 0, hence E(s(t)s(u)) = 0 if u ̸= t. If t = u, then: E{s(t)s(u)} = E{s2(t)} = m2wk(t)E{n2k(t)} = m2wk(t)σ 2 k, (2.7) where σ2k is the power spectral density of the cavitation white noise nk(t). By substituting formula (2.7) into formula (2.6), the covariance function of the 56 spreading sequence is given by the formula: E{s(t)s(u)} = mwk(t)mwk(u)σ2kδ(t− u), (2.8) From the covariance function (2.8), solving the integral function (2.5) as follows: λjϕj(t) = ∫ T 0 E{x(t)x(u)}ϕj(u)du = ∫ T 0 mwk(t)mwk(u)σ 2 kδ(t− u)ϕj(u)du = m2wk(t)σ 2 kϕj(t) ∫ T 0 δ(t− u)du = m2wk(t)σ 2 kϕj(t), (2.9) Since the covariance function exists only if and only if t = u, from formula (2.9), then λj = m 2 wk (t)σ2k. The expected value of each spreading sequence sample will be 0 because the mean value of the cavitation noise along the phases of the cavitation noise is 0, then: mi = E{s(ti)} = E{mwk(ti)nk(ti) + n(ti)} = mwk(ti)E{nk(ti)}+ E{n(ti)} = 0, (2.10) Therefore, the variance of s(t) according to the Gaussian distribution is calcu- lated by the formula: λj = m 2 wk (t)σ2k (2.11) Environmental noise in cases that follow the Gaussian distribution will have a mean of 0 and a variance of N0/2 where N0/2 is the power spectral density of the white noise. Therefore, the ith signal of the spreading sequence will also have a mean power of 0 and a variance of σi calculated by the formula (2.12) as follows: λj = m 2 wk (ti)σ 2 k +N0/2 (2.12) 57 Thus, if a distribution at time ith of the signal is defined as: Ps(s(ti)/wk) = 1√ 2πσ2i exp ( − x 2(ti) 2σ2i ) (2.13) then the general formula (2.14) applies to all time steps ti of the signal when m2wk(ti) is periodic with characteristic frequency wk. Ps(s(ti)/wk) = 1√ 2π(m2wk(ti) · σ2k +N0/2) exp ( − ( x2(ti) 2(m2wk(ti) · σ2k +N0/2) )) (2.14) Next, the STFT transfor is used to overcome the inflexibility when using the FFT transform of the DEMON algorithm. The STFT adds a time dimension to the parameters of the base function by multiplying an infinite complex exponential function with a window. b(w, t0)(t) := w(t− t0)exp(iwt) (2.15) where w(t) is a window function and (w, t0) is the time-frequency coordinate of the base function. The general formula for STFT is given by the formula: S{s(t)}(w, t0) = ∫ ∞ −∞ w(τ)exp(−iwτ)s(τ)dτ (2.16) Formula (2.16) provides information on both the time and frequency domains by selecting the size of the window. The result of this transformation can also be regarded as a bandpass filter with a Fourier transform of the window function w(t) shifted to the center frequency w. Therefore, filter have the same bandwidth. In summary, the proposed amplitude variation algorithm aims to improve the ac- curacy of extracting characteristic frequencies from underwater acoustic signals by computing the variance of the amplitude gradient and the probability distribution combined with the time-frequency domain transformation. 2.2.3. Structure of the proposed algorithm Based on the variance transformation formula (2.11), signal distribution for- mula (2.14), and time-frequency domain transformation formula (2.16), the block diagram of the proposed algorithm is presented in Figure 2.3. The algorithm ex- ecution steps and flowchart are depicted in Figure 2.4 to enhance the ability to 58 extract characteristic frequencies from underwater acoustic signals. Figure 2.3: Block diagram of the proposed algorithm The execution steps of the proposed algorithm include the following: • Step 1: Consider the input to the algorithm as underwater acoustic signals that are segmented into equal-length samples. Then, the frequency variance variation calculation is applied to each segment of the signal. • Step 2: The signal spectrum is calculated by STFT transformation so that the nominal frequency resolution is 1Hz. Then, a 2D spectrum matrix is obtained, with one axis representing frequency in Hz and the other axis representing the number of samples over time in seconds. • Step 3: The frequency amplitude of each segment is averaged over the entire range to obtain a unique value as the feature peak. • Step 4: The stack-piling technique is used to reduce the variance and increase the signal-to-noise ratio (SNR) value. This technique divides the underwater acoustic signal x(t) into overlapping consecutive segments. As the signal is divided into more overlapping segments, the variance will decrease accordingly, and the probability of accurately estimating the characteristic frequency of the signal will increase. 59 M_Sample[rate/2] = Mean(Sample) Rate, α, maxFreq Sample[60 x (rate/2)] i = rate/2, j = maxFreq Start i = i-1 i = 0 + Finish S_Sample = M_Sample * Hamming[8] SD_Sample = Standard deviaon(S_Sample) maxSample[rate/2] = maxFreq M_maxSample[rate/2] = Mean(maxSample) S_maxSample = M_maxSample * Hamming[8] j = j - 1 + var = S_maxSample[j] - S_maxSample[j-1] AV[j] = var3 Detect var > 0 AV[j] > (SD_Sample[j]*α) Detect + + True False True False True False Figure 2.4: Flowchart of proposed algorithm for processing propeller signals 60 2.2.4. Evaluation of the proposed algorithm on actual ship data The results of the proposed algorithm for variable instantaneous frequency es- timation are verified and compared with the DEMON algorithm using the Hilbert filter presented in Figure 1.11 in Section 1.2.4 on actual propeller ship signal sam- ples from the ShipEar dataset [114]. To fully evaluate the effectiveness of extracting characteristic frequency components from raw data, the proposed algorithm and the DEMON-Hilbert algorithm [106] will be tested on recordings containing charac- teristic operational states of ships in shallow waters. Specifically, three main cases are considered: • The first case: a ship is moving with complex speed variations; • The second case: a ship is moving steadily at a constant speed against a noisy background; • The third case: a ship is starting to move at a slow speed. The pre-processing and testing process is conducted on a Dell T3600 Xeon 8- core workstation with an NVIDIA K2200 4GB graphics card running Ubuntu 18.04 operating system with kernel CUDA 10.1 and Cudnn 7.6.5. A. The DEMON algorithm using the Hilbert filter is applied to process: - The first case: Figure 2.5: Signal detection by DEMON-Hilbert on Record-1 61 - The second case: Figure 2.6: Signal detection by DEMON-Hilbert on Record-2 - The third case: Figure 2.7: Signal detection by DEMON-Hilbert on Record-3 The results in Figure 2.5 indicate that the DEMON-Hilbert algorithm missed many neighboring frequency components due to the tendency to consider neigh- boring frequencies to be within a single signal envelope. For signals generated from a ship moving steadily, the DEMON-Hilbert algorithm extracted the correct 62 characteristic frequency components as shown in Figure 2.6, but could not detect low-frequency components with weak intensity as in Figure 2.7 when the ship began to move. B. The proposed algorithm is applied to process: - The first case: Figure 2.8: Signal detection by the proposed AV algorithm on Record-1 - The second case: Figure 2.9: Signal detection by the proposed AV algorithm on Record-2 63 - The third case: Figure 2.10: Signal detection by the proposed AV algorithm on Record-3 In the first case, when the ship speed changes in a complex manner, the char- acteristic frequencies of the propeller also change in a complex way. The proposed algorithm has extracted neighboring characteristic frequency components, thereby reducing false alarms as seen in Figure 2.5 and Figure 2.8. In case two, when the ship signal operates at a stable speed, even in a noisy background, the DEMON-Hilbert algorithm produces classification results equivalent to those of the proposed algo- rithm as shown in Figure 2.6 and Figure 2.9. In the case of slow-moving ships, the resulting characteristic frequencies caused by wheel slip will also be low. The pro- posed algorithm has extracted all characteristic frequencies while DEMON-Hilbert failed to detect them. Due to the nature of DEMON’s use of a square filter over the entire range, the ship signal can be difficult to detect when mixed in with noise, as in many cases this will affect signal processing quality as shown in Figure 2.7 and Figure 2.10. The DEMON algorithm considers the set of neighboring frequen- cies as a bounding curve, so in many cases DEMON can only detect a single peak frequency. Meanwhile, the proposed algorithm focuses on calculating the variation in amplitude between neighboring frequencies, then extracting and analyzing the frequency changes along the signal spectrum, making it easier to extract and detect the characteristic frequency peaks. 64 The Blackman window is used in the proposed algorithm because the Blackman filter structure has advantages when processing complex and variable signals with irregular patterns mixed in a complex background noise. In practical problems, using different windows in the frequency domain will trade off two conditions: having a narrow main lobe width will result in a large side lobe decay and vice versa. When compared to some commonly used windows such as Hanning and Hamming, the first side lobe of Hamming is smaller (meaning the Hamming filter will filter the signal better) than the first side lobe of Hanning, but the farther side lobes from the main lobe of Hanning are smaller than those of Hamming. The Blackman window has a wider main lobe width than Hanning and Hamming, which presents some difficulties when extracting the central frequency, but it has much smaller side lobes, which brings advantages in extracting neighboring frequency components. The results using the proposed algorithm in generating spectrogram images with frequency on one axis and time on the other axis, with the intensity representing the strength of the signal, are shown in Figure 2.11. (a) Spectrogram of the Record-1 (b) Spectrogram of the Record-3 Figure 2.11: Spectrograms of some actual records of ShipEar dataset The raw hydroacoustic data is stored in .wav files and divided into 3300 records (1800 records contain propeller signals, and 1500 records contain only background noise) overlapped to ensure data continuity. The original raw data from the ShipEar dataset [109] consisted of 5-minute-long records, which were split into smaller 65 records of 1 minute to increase the amount of dataset. The records were processed using the DEMON-Hilbert algorithm [126] and a proposed algorithm for spectral amplitude variation. The results were cross-checked with public parameters from the dataset to evaluate accuracy and false alarm probability. Comparing with other published results using the ShipEar dataset, the proposed algorithm achieved a de- tection rate of 98.22% (Table 2.1), which is higher than the published rates of 88.92% (in 2021) [60] and 96.67% (in 2022) [154]. Table 2.1: Comparison of AV with published results on the same ShipEar dataset DEMON Proposed AV algorithm [60] [154] Detection 81,28% 98,22% 88,92% 96,67% False alarm 13,2% 3% - - According to the theory of algorithmic complexity [81], any algorithm can ac- curately estimate the total number of elementary operations required to perform the algorithm. The total input data n is a characteristic of the problem’s size, and an algorithm T applied to solve a problem of size n requires a total of T (n) ele- mentary operations, which is a characteristic of the efficiency of algorithm T . The complexity of the proposed algorithm differs from the DEMON algorithm and its variants in the steps performed, resulting in a significant difference in processing time for the same record. The processing time of two algorithms was verified on the same records, with length 5, 20, 40, and 60 seconds of some ship-type in the ShipEar and DeepShip datasets, as summarized in Table 2.2. Table 2.2: Processing time on the same records between DEMON and AV Ship 1 Ship 2 Ship 3 Ship 4 Records length 5 20 40 60 Proposed AV algorithm 0,002s 0,005s 0,008s 0,014s DEMON 0,351s 0,877s 1,239s 2,026s Number of difference 175 162 146 140 From the block diagram of the DEMON algorithm in Figure 1.9 and Figure 1.10 in Section 1.2.4, the complexity of DEMON depends on the order of operations: squaring the entire input data at the output of the bandpass filter, down-sampling, taking the square root, computing the average, and finally comparing the results to evaluate the characteristic frequency peak. Meanwhile, the proposed amplitude 66 variation algorithm computes the mean, standard deviation, variance, exponenti- ates and finally evaluates the peak. Therefore, on the same record with the number of memory accesses, the number of comparisons between samples, and the number of loop executions being the same, the space complexity required to process by DE- MON is greater than proposed algorithm. This is because the square magnitude of all points on the unprocessed data record and the variance of their magnitudes are different. Especially for low frequencies, small amplitudes, and complex variations, the magnitude of the variance between neighboring data points and with itself will be smaller. Therefore, the processing time efficiency of the proposed algorithm is maintained even when the length of the dataset samples increases. Moreover, the processing speed of the proposed algorithm with small duration records can gradually approach real time processing in practical systems. 2.2.5. Evaluation of the proposed algorithm on actual diver breath data Similar to the propeller signal, the diver using an open-circuit SCUBA will generate characteristic periodic signals that appear when the device’s release valves are in operation [72]. The pulses caused by the pressure vibration when the diver breathes as shown in Figure 2.12 have respiratory cycle-related characteristics, hence the DEMON algorithm is often used to detect the presence of diver [98]. Figure 2.12: The water bubbles of a diver with open-circuit SCUBA However, with the limitations of the DEMON algorithm discussed in Section 2.2.1 and experienced diver intentionally changing their breathing patterns to alter the cyclic structure of the signals, the performance of DEMON is affected. There- 67 fore, the proposed spectral amplitude variation and DEMON-Hilbert algorithm used in Section 2.2.4 will be verified for effectiveness in detecting diver breathing signals in two cases. The raw data was performed on an Ubuntu 18.04 operating system with CUDA 10.1 and Cudnn 7.6.5 kernel on a Dell T3600 Xeon 8-core workstation with an NVIDA k2200 4GB graphics card. A. The first case: regular diver does’t change breath patterns. Figure 2.13: Signal detection by DEMON-Hilbert on Record-4 Figure 2.14: Signal detection by the proposed AV algorithm on Record-4 68 B. The second case: experienced diver changes breath patterns. Figure 2.15: Signal detection by DEMON-Hilbert on Record-5 Figure 2.16: Signal detection by the proposed AV algorithm on Record-5 The DEMON-Hilbert algorithm used in Case A in Figure 2.13 provided a result that was close to the proposed spectral amplitude variation algorithm in Figure 2.14 for detecting diver breathing signals through the opening and closing of release valves. However, in Case B Figure 2.15, the DEMON-Hilbert algorithm failed to detect experienced diver breathing signals as well as the proposed algorithm in 69 Figure 2.16. The case of experienced divers manipulating their breathing patterns to alter the signal structure is similar to the case of modern ships placing flippers inside their rotating compartments to minimize the impact of noise generated by moving targets, as introduced in Section 2.2.1. Generally, passive sonar approaches for detecting diver breathing signals rely on accurately detecting frequency-related characteristic features from recordings in real environments. The performance of the passive sona

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