passive sonar signature estimation using bispectral ... - Google Sites

PASSIVE SONAR SIGNATURE ESTIMATION USING BISPECTRAL TECHNIQUES 1

R.K. Lennartsson, 1

J.W.C. Robinson,

1

L. Persson,

2

M.J. Hinich

3

and S. McLaughlin

Defence Research Establishment, SE 172 90 Stockholm, Sweden. e-mail:

2

1

fron,john,[email protected]

Applied Research Laboratories, University of Texas at Austin, Austin, TX 78713-8029. e-mail: [email protected]

3

Dept. of Electronics and Electrical Eng.

University of Edinburgh, Edinburgh EH9 3JL, UK.

e-mail: [email protected]

ABSTRACT

An important task in underwater passive sonar signal processing is the determination of target signatures based on the narrow-band signal content in the received signal. To achieve good classi cation performance it is important to be able to separate the dierent sources (e.g. engine, hull and drive) present in the signature, and to determine the distinct frequency coupling pattern of each of these sources. In this work we demonstrate how this can be done using bispectral techniques applied to data recorded at a sea trial in the Baltic Sea. As a target we used a 23 ft berglass motor boat powered by a 4-cylinder, 4-stroke, turbo-charged diesel engine connected to a stern drive with two counter rotating propellers. Data was recorded with a bottom mounted hydrophone array as well as with accelerometers mounted on the engine and hull. It was found that the harmonics that propagated through water are engine related at low speeds and drive related at high speeds. The hull vibrations are only present at very low speeds. Moreover, we found that normalized bispectrum measures (skewness) could provide additional coupling information not visible in the standard bispectrum. 1.

INTRODUCTION

In passive sonar signature estimation it is important to be able to separate the dierent narrow-band contributions that are present in the received signal. If the source is a vessel with a conventional engine/drive con guration a good rst characterization can often be obtained with the power spectrum alone, but for a more precise characterization the phase couplings between harmonics must be uncovered. The phase coupling patterns can be used to separate the dierent sources

present in the signature. However it is a well-known fact that conventional power spectral techniques are phase-blind and cannot be used to track phase couplings, hence the use of bispectral techniques [1]. A stationary signal with narrow-band content at the frequencies 1 2 and 1 + 2 will show peaks in the power spectrum at these frequencies. In the bispectrum however, a peak at the bifrequency ( 1 2) will occur if and only if the signals are phase-coupled. The ability of the bispectrum to detect phase-couplings has been utilized in such diverse areas as diagnosis of heart conditions [2], nonlinear wave interaction in tidal waves [3], and machine monitoring [4]. In the present work we report on an experiment on harmonic characterization of (hydro-)acoustic signals performed in shallow waters using a small motor boat with a diesel engine and a stern drive as a source. Our main objective has been to determine if the phase coupling pattern between harmonics present in the engine, drive and hull are preserved after propagation through (shallow) water, and if it is possible to utilize this information for classi cation purposes. More speci cally, the focus has been on the possibility to separate the dierent generating sources (engine, drive and hull) in hydrophone data. A secondary objective has been to compare bispectrum and skewness based techniques in this particular application. f ;f

f

f

f ;f

2.

SPECTRUM, BISPECTRUM AND SKEWNESS

Given a discrete time series ( ) obtained by sampling with frequency s a (zero-mean, second-order stationary) process ( ). The power spectrum ( ) of ( ), for discrete frequency =
with
= s , can be estimated by conventional averaging of perix n

f

x t

f

k

f

P k

x n

f

f =M

Power [dB]

Amplitude

0.2 0.1 0 −0.1 −0.2 70

70.05

70.1

0 −20 −40 −60 0

70.15

Time [sec]

200

400 600 Frequency [Hz]

800

1000

200

400 600 Frequency [Hz]

800

1000

20

1

Power [dB]

Amplitude

2

0 −1 −2 70

70.05

70.1

70.15

Time [sec]

0 −20 −40 0

Figure 1: Typical time series of the signals; engine accelerometer (top) and hydrophone (bottom).

Figure 2: Typical power spectra of the signals; engine accelerometer (top) and hydrophone (bottom).

odograms by dividing the time series ( ) into (possibly overlapping) blocks, each of length , and computing (possibly using tapering) the point DFT for each block. The estimated power spectrum ^( ) at frequency bin is then obtained as K ^( ) = 1 ( )2

AD31/DP) having an engine/drive gear ratio of 2.3:1. The drive was tted with two counter-rotating propellers (VP type A7) having 3 (front) and 4 (rear) blades, respectively. 2 Engine and hull vibrations were recorded with two one-axis accelerometers, one tted directly on the engine mount and one to the hull close to the engine. Water-propagated sound was recorded using a hydrophone array, with four wideband omnidirectional hydrophones horizontally equally spaced, but at various depths. In the subsequent analysis presented in this work one hydrophone mounted at a depth of 17 meters was utilized. In order to separate the dierent sources involved (e.g. engine, hull and drive), several recordings were made at various rpm, both with the boat drifting freely with the drive disconnected and with the boat moving with the drive connected. In each of the recordings where the boat was powered by its drive it was run on a straight track, at constant throttle, passing directly above the hydrophone array. Ambient sea noise was recorded and analyzed to ensure that it had negligible eect on the end result. The weather conditions during the sea trial were good with wind speeds below 5 m/s. The sound velocity pro le was also measured, and was found to be approximately at over the whole water depth. All data was recorded with a sampling rate of 25 kHz, which was considered to be suÆciently high since most signal and noise power was below 5 kHz and virtually no power was present over 10kHz. To ensure that the phase relations in the recorded signal

x n

K

M

M

P k

X

k

P k

K

j=1

j

jX

k j ;

where j ( ) is the DFT over block at frequency bin . In a similar way (assuming third-order stationarity) the bispectrum ( ) and skewness 1 2( ), for discrete bifrequency ( 1 2) = (

), can be estimated with the direct method. The (averaged) bispectrum and skewness estimates ^ ( ) and ^2( ), respectively, are then given by [5] K ^( ) = 1 j ( ) j ( ) ( + ) X

k

j

k

B k; `

f ;f

k

f; `

B k; `

B k; `

X

K

j=1

X

k X

j

` X

k

S

k; `

S

k; `

f

` ;

^( ) 2 ^2( ) = ^( ) ^( ) ^( + ) where ( ) denotes complex conjugation. S

jB k; ` j

k; `

P k P ` P k

;

`




3.

SEA TRIAL

The sea trial was conducted in the Baltic Sea o the east coast of Sweden, in shallow waters of approximately constant depth, 30 meters. As target a 23 ft berglass motor boat (Botnia Marine model Targa23) was used, powered by a 4-cylinder, 4-stroke turbocharged Volvo Penta (VP) diesel engine (type AD31PA) equipped with a VP Aquamatic stern drive (type 1A

square-root of it is called bicoherence index in [1].

2 The

most

notable

advantage

with

having

two

counter-

rotating propellers, rather than one single, is less noise and vibration.

Hence, the power in drive related signals from this vessel

can be expected to be lower than with other forms of drives.

8

183

80

5

70

4.5

122 60 50 40 61 30

Frequency f2 [Hz]

Frequency f2 [Hz]

x 10 5.5

183

90

4

122

3.5 3 2.5 61

2 1.5

20

1

10 0 0

61 122 Frequency f1 [Hz]

183

0.5

0 0

61 122 Frequency f1 [Hz]

183

Figure 3: Bispectrum magnitude for the hull accelerometer time series from the 1830 rpm straighttrack run (at CPA). The grid spacing is 15 25 Hz which corresponds to half the engine axis rotation frequency.

Figure 4: Bispectrum magnitude for the hydrophone time series from the 1830 rpm straight-track run (at CPA). The grid spacing is the same as in Fig. 3.

and noise were preserved no pre ltering was used.

axis frequency. Here, and in all subsequent gures involving the bispectrum, the values are quantized to 10 levels with white indicating the lowest level and the other levels given by the grayscale on the right. It can be seen that there are strong coupled modes, induced mainly by the torque variations of the engine due to inertia, piston angular velocity and gas pressure variations. This is an example of the \second order" harmonics appearing at twice the engine axis rotation frequency [6], which are moreover coupled to the associated fourth order harmonics. Coupled second and third order engine axis harmonics are also visible. The corresponding bispectrum for the hydrophone is seen in Fig. 4 (same grid spacing as in Fig. 3) where the only visible (o-diagonal) peak is at bifrequency (approx) (61 40) Hz, which represents a coupling between an engine and a drive harmonic. In Figures 5 and 6 the bispectra for the hull accelerometer and hydrophone data, respectively, for the 2712 rpm straight-track run is shown. The grid used in Fig. 5 is 22.6 Hz, which is half the engine axis frequency. Also one can see strong coupled engine harmonics in the hull accelerometer data, at the second and third order. Moreover, one can see couplings between the engine and drive, at bifrequencies (approx) (117 20) Hz and (136 20) Hz. The grid spacing used in Fig. 6 is 19 5 Hz, which corresponds to the propeller axis frequency, and several frequency couplings are visible. Notable in particular is the peak at bifrequency (approx) (137 20) Hz (and its neighbors), and the band-like structure of peaks around 2 = 156 Hz. It appears that all the peaks fall on the grid. Hence, these harmonics are drive related. This can be explained by

:

4.

DATA ANALYSIS AND RESULTS

In the following we will show the results of an analysis of time series from three dierent rpm straight-track recordings, at 1830, 2712 and 3549 rpm, respectively. The data and results presented here are taken from a time frame of 15 seconds duration around the closest point of approach (CPA) to the hydrophone array. In the bispectrum estimates the number of blocks was = 22 and the number of points in the DFTs was = 16384. The same number of points in the DFTs were used in the skewness estimates but to achieve a consistent estimate an overlap of 12288 was used yielding a total number of blocks = 88. A Hamming tapering was applied to data in all DFT computations. Figure 1 displays a typical example of time series from the hull accelerometer and the hydrophone. The corresponding power spectra of the time series in Fig. 1 are seen in Fig. 2. By conventional power spectral based analysis it is diÆcult to separate and relate the peaks of dierent sources (engine, drive and hull). However, with bispectral analysis it is easier to identify and separate the sources. K

M

K

;

;

;

:

4.1.

Bispectrum

In Figure 3 the estimated absolute value of the bispectrum for the hull accelerometer data from the 1830 rpm straight-track run at CPA is displayed. The grid spacing is 15.25 Hz which corresponds to half the engine

;

f

7

180.8

x 10 160

10

100

90.4

80 60

468 Frequency f2 [Hz]

Frequency f2 [Hz]

140 120

11

546

9 8

390

7 312 6 234

5

156

4

40

3 78

0 0

2

20 90.4 Frequency f1 [Hz]

180.8

Figure 5: Bispectrum magnitude for the hull accelerometer time series from the 2712 rpm straighttrack run (at CPA). The grid spacing is 22.6 Hz, which is half the engine axis frequency. the fact that the propeller noise increases dramatically when the speed increases and that the engine load, and hence vibrations, are lower at the higher speed since the boat is then hydrofoiling. In Figures 7 and 8 the bispectra of the hull accelerometer and hydrophone data, respectively, from the 3549 rpm straight-track run are displayed. The results are about the same as the ones obtained at 2712 rpm. In the accelerometer bispectrum in Fig. 7, where the grid spacing is 29 6 Hz corresponding to half the engine axis frequency, again one can see a few engine-engine coupled harmonics, at the expected orders, and some additional engine-drive coupled harmonics. In the hydrophone bispectrum in Fig. 8, where the grid spacing is 25 6 Hz, which corresponds to the propeller axis frequency, a very rich coupling structure is again visible. Also here it appears as if all peaks fall on the grid and hence the harmonics are all drive related. :

0 0

78

156

234 312 390 Frequency f1 [Hz]

468

546

Figure 6: Bispectrum magnitude for the hydrophone time series from the 2712 rpm straight-track run (at CPA). The grid spacing is 19.5 Hz which corresponds to the propeller axis rotation frequency. are quantized to 10 levels and displayed using the upper half of the grayscale on the right. There are several peaks that do not fall on the grid, most notably the ones at (approx) (286 86) Hz, (335 166) Hz and (334 263) Hz. Moreover, these peaks do not fall on the grid corresponding to multiples of half of the engine axis frequency either. Therefore, it is conceivable that these coupled frequencies are sums or dierences between multiples of the engine and drive frequencies, possibly generated by quadratic phase coupling. However, further study is needed to determine the nature of these peaks. ;

;

;

:

4.2.

Skewness

Given the fact that apparently all visible coupled harmonics in the hydrophone data for higher speeds (2712 and 3549 rpm) fall on frequencies commensurable with the drive frequency a natural question is if a more careful analysis, using for instance the skewness, would reveal additional coupling information. This indeed turns out to be the case, as shown in Fig. 9 where the skewness for the 2712 rpm straight-track run is shown using a grid spacing of 19.5 Hz, which corresponds to the propeller axis frequency. Here, only the values exceeding half of the full range are shown, and these values

5.

CONCLUSION

Only for low speeds (1830 rpm) is it possible to see engine harmonics in the hydrophone data, despite the presence of such harmonics in the hull data. Thus, the hull does not act as a \projector" for engine vibrations. Instead, the dominating source at medium (2712 rpm) to high speed (3549 rpm) is the drive and at high speed only the drive is visible in the bispectrum from hydrophone data. However, using the skewness it is possible to detect coupled harmonics that are neither strictly engine related nor strictly drive related. The propeller leaves a clear trace in both the bispectrum and skewness for medium speeds, in terms of peaks at 7,8, and 9 times the propeller axis frequency, which might be useful in determining the propeller con guration.

354.9

200 180 9

x 10

236.6

140

2.2

120

2

512

1.8

118.3

80 60 40

0 0

118.3 236.6 Frequency f1 [Hz]

Frequency f2 [Hz]

100 409.6

1.6 1.4

307.2

1.2 1

204.8

0.8

354.9

Figure 7: Bispectrum magnitude for the hull accelerometer time series from the 3549 rpm straighttrack run (at CPA) with frequency grid corresponding to half the engine axis frequency. REFERENCES

[1] C.L. Nikias and M.R. Raghuver, \Bispectrum Estimation: A Digital Signal Processing Framework," Proc. IEEE, Vol. 75, No. 7, pp. 869{891, 1987. [2] M. Shen and L. Sun, \The Analysis and Classi cation of Phonocardiogram Based on Higher-Order Spectra," Proc. IEEE Workshop on Higher-order statistics, Ban, Alta., Canada, 21{23 July, 1997, pp. 29{33. [3] A.G. Beard, N.J. Mitchell, P.J.S. Williams and M. Kunitake, \Non-linear Interactions Between Tides and Planetary Waves Resulting in Periodic Tidal Variability," J. Atmosph. Solar Terrest. Phys., Vol. 61, pp. 363{376, 1999. [4] R.W. Barker and M.J. Hinich, \Statistical Monitoring of Rotating Machinery by Cumulant Spectral Analysis," Proc. IEEE Workshop on Higher-Order Statistics, South Lake Tahoe, CA, USA, 7{9 June, 1993, pp. 187{191. [5] J.W.A. Fackrell, S. McLaughlin and P.R. White, \Bicoherence Estimation Using the Direct Method. Part 1: Theoretical Considerations," Applied Sig. Process., Vol. 3, pp. 155{168, 1995. [6] C.F. Taylor, The Internal-Combustion Engine in Theory and Practice, Revised ed., Vol. 2, MIT Press, 1985.

0.6 102.4

0 0

0.4 0.2 102.4

204.8 307.2 409.6 Frequency f1 [Hz]

512

Figure 8: Bispectrum magnitude for the hydrophone time series from the 3549 rpm straight-track run (at CPA) with grid spacing equal to the propeller axis rotation frequency.

390

10 9.5

312 Frequency f2 [Hz]

Frequency f2 [Hz]

160

9 8.5

234

8 156

7.5 7

78 6.5 0 0

6 78

156 234 Frequency f1 [Hz]

312

390

Figure 9: Skewness for the hydrophone time series from the 2712 rpm straight-track run (at CPA). The grid spacing is 19.5 Hz which equals the propeller axis frequency.