A lossless compression method incorporating sensor fault detection for underwater acoustic sensor array

Abstract

This article proposes an efficient lossless compression method for an underwater acoustic sensor array. The proposed method first decides whether the input signal is coming from a normal or a faulty sensor. In particular, such sensor fault detection is performed using a root-mean-square crossing rate and a zero crossing rate. If a sensor is determined to be faulty, then a pre-processing technique is applied prior to signal compression to make the signal from this sensor meaningful for further use. After that, multi-channel sensor signals are encoded by the MPEG-4 audio lossless coding encoder, where the indices of faulty sensors are also sent to the decoder, which applies a post-processing technique on the MPEG-4 audio lossless coding decoded signals for the faulty sensors. The performance of the proposed method is evaluated using three different sensor arrays deployed in real underwater environments by measuring the precision of faulty sensor detection and comparing the compression ratios between normal and faulty sensors. The evaluation shows that the fault detection of the proposed method works correctly for the experiments, and the compression ratios are decreased by 0.43% and 4.57%, respectively, in the faulty sensor signal send and non-send modes, compared to the MPEG-4 audio lossless coding reference software.

Keywords

Sonar system lossless compression MPEG-4 audio lossless coding underwater acoustic sensor sensor fault detection

Introduction

Various studies on sonar technologies are currently ongoing for military and commercial applications. Sonar systems are widely used in commercial applications such as medical imaging, fish finding, marine exploration, and seismic exploration,^1,2 and it is used in military applications to detect, classify, and track underwater obstacles, submarines, torpedoes, mines, and surface ships.¹

Sonar can be further classified into two basic types: passive and active. An active sonar system estimates the direction and distance of underwater targets such as submarines or mines by detecting the reflected signals from targets using ping signals transmitted from a transducer. Active sonar systems usually detect signals over tens of kilohertz. Meanwhile, passive sonar systems detect the self-radiated noises from ship or submarine machinery such as engines and propellers. Since the frequencies of these machinery noises are mainly distributed in the lower frequency band within 1 kHz, passive sonar systems mainly detect signals within a range of several kilohertz. In addition, it is often possible to determine the type of target by analyzing its radiated noise frequencies using passive sonar.² Due to absorption loss, low-frequency acoustic waves with small bandwidth and long wavelengths can travel longer distances than high-frequency acoustic waves.³ This is a common reason that passive sonar systems have a lower resolution but a larger detection range than active sonar systems.

The main factors that influence sonar system performance are frequency and directivity. Low frequency sound is used to increase the sonar detection range because the absorption loss is proportional to the sound frequency. However, this lowers the directivity resolution, and mobility is restricted because the weight of the sonar is increased to avoid spatial aliasing.² Nowadays, the received target signal is very weak because own-ship noise reduction technologies and sound absorption materials for submarines and warships have been developed while environmental noise increases due to high marine traffic and sea waves. Consequently, the target signal may be invisible due to the low signal-to-noise ratio (SNR) at the sensor output stage. In addition, acoustic sensor modules that have high piezoelectric effects and amplify electrical signals are used to achieve a higher sensor output,⁴ but this method includes many physical constraints. Therefore, there are many ongoing studies associated with sonar systems that attempt to increase directivity and reduce noise.⁵

Figure 1 illustrates the general structure of a sonar system. As shown in the figure, sonar systems are composed of acoustic sensor arrays, a signal acquisition unit, a signal processing unit, an information processing unit, and a display unit. An acoustic sensor array generally consists of one or more hydrophones for multi-channel underwater acoustic sensing. It is common for passive sonar to use multi-channel sensor signals with a sampling rate of up to mid-thousands of hertz according to which ship noises are typically distributed.¹ However, the sampling rate of the active sonar varies depending on the objects to be detected. For example, in order to detect smaller objects such as divers and swimmers, the sampling rate must be set to higher than 100 kHz. Therefore, the data rate for multi-channel sensor signals is huge for real-time data acquisition and processing. In particular, when sensors are installed on the seabed or the shore but information processing is done in a system that is located remotely, it is necessary to communicate between the sensor signals and the system through a medium wirelessly or a long-distance optical cable.

Figure 1.

The general structure of a sonar system.

Both the bandwidth and data rate of acoustic underwater communications over underwater sensor networks are extremely low. In addition, the power supply to the underwater sensors is limited, thus it is difficult to replace a discharged battery with a new one.⁶ Therefore, a low-complexity source compression technique should be applied to the sensor signals for real-time operation in a limited power and bandwidth environment.

Audio data compression has been intensively studied in the field of communications due to the proliferation of mobile phones, multimedia players, and the Internet. It can be categorized by lossy and lossless algorithms depending on whether the original sampled signal can be accurately recovered from the compressed data. Various studies on audio coding techniques including the standardization of lossless coding have been carried out according to the demand for multi-channel and high-quality audio.^7–10 Among them, lossy compression algorithms such as linear predictive coding (LPC), MPEG-2 audio layer III (MP3), and advanced audio coding (AAC)^11,12 have been developed to deliver audio or speech signals through limited capacity communication channels with minimal perceptual degradation using auditory masking techniques based on psychoacoustics. Lossy compression algorithms achieve a higher compression rate with some acceptable distortion compared to lossless compression. On the other hand, lossless audio compression algorithms such as MPEG-4 audio lossless coding (ALS), MPEG-4 scalable lossless coding (SLS), and free lossless audio codec (FLAC)^11,12 enable the perfect reconstruction of the original signal so that the audio signal may be compressed without any loss of perceptual quality.¹³ However, these lossless audio compression algorithms require high computational complexity. As such, there still exists an implementation issue associated with computational complexity suitable for low-power embedded devices.^9,14

Unlike general audio systems for listening purposes, the target acoustic signal for sonar systems is very weak because it is easily affected or masked by marine environmental noise. Furthermore, false alarms due to signal distortion can be fatal in a tactically urgent situation involving a military sonar system. Therefore, a lossless coding technique is required for the compression of sonar sensor signals to minimize the deterioration of detection performance due to the loss of information.

Compared to conventional communications channels, either a sensor fault or failure may occasionally occur due to physical or electrical shocks in the sonar system. In these cases, the detection performance of the sonar system will degrade due to the influx of electrical noise or a reduced directivity index.^2–4 As a remedy to this problem, according to the sensor fault information sent by a transmitter, the signals coming from faulty sensors can be excluded from processing, which could improve the performance in terms of compression efficiency and encoder complexity. Moreover, it is possible to prevent the degradation of the detection performance by eliminating the faulty sensor signal at the signal processing stage.

Therefore, an MPEG-4 ALS-based signal compression method is proposed here by incorporating a sensor fault detection scheme for an underwater acoustic sensor array where the sensor fault detection scheme operates based on the analysis of both a root-mean-square crossing rate (RMSCR) and a zero crossing rate (ZCR). The goal of the scheme proposed in this article is to compress underwater acoustic sensor signals losslessly with a high compression ratio using the well-known MPEG-4 ALS tool. This is because there is no coding tool standardized or available for compressing underwater acoustic sensor signals. However, instead of directly using the MPEG-4 ALS, the proposed scheme incorporates a sensor fault detection scheme in order to increase the compression performance for multi-channel signals from hundreds of acoustic sensors.

Following this introduction, section “Review of MPEG-4 ALS audio coding for compressing multi-channel signals” briefly reviews the MPEG-4 ALS for multi-channel audio signals.^11–14 Section “Proposed sensor signal compression method” proposes an MPEG-4 ALS-based sensor signal compression method and a sensor fault detection scheme. After that, section “Performance evaluation” evaluates the performance of the proposed method using three different sensor arrays deployed in real underwater environments by measuring the precision of faulty sensor detection and the compression ratio of the normal and faulty sensors. Finally, section “Conclusion” concludes this article.

Review of MPEG-4 ALS audio coding for compressing multi-channel signals

MPEG-4 ALS is a lossless audio coding standard that compresses multi-channel audio signals based on linear prediction. It provides joint channel coding to improve the compression ratio of multi-channel audio streams by utilizing the inter-channel correlation of multi-channel signals^13,14 and also it supports floating-point audio signal compression. Linear prediction is applied for a given audio signal and then the residual signal from the linear prediction is encoded using the Rice and block Gilbert-Moore codes.^11,12 It is noted here that the MPEG-4 ALS is not limited to the encoding of audio signals but includes the compression of other fixed-size, one-dimensional, correlated multi-channel signal types such as seismic and medical data.^11,12 In fact, the MPEG-4 ALS can compress signals whose sampling rate and number of channels are up to 192 kHz and 65,536, respectively. In addition, the bit-resolution of signals can be covered by 32 bits, and IEEE754 32-bit floating-point signals can be supported by the MPEG-4 ALS.¹³

Figure 2 shows a block diagram of the MPEG-4 ALS encoder and decoder.¹³ First, the input signal is divided into a consecutive number of frames. These frames are then divided into audio channels, and each channel may be subdivided into several audio sample blocks for the subsequent prediction and encoding process.¹¹ As shown in the figure, short-term and subsequent long-term predictors predict audio samples in each block, which results in residual signals. The MPEG-4 ALS adopts forward adaptive prediction with up to 1023 prediction orders. In addition, the input channels are joined by either difference coding or multi-channel coding (MCC) to eliminate inter-channel redundancy. The residual signals are encoded by entropy coders such as Rice and block Gilbert-Moore codes. Since the linear prediction and joint channel coding methods are the main features of the MPEG-4 ALS, the following subsections will explain them in detail.

Figure 2.

A block diagram of the MPEG-4 ALS encoder and decoder.¹³

Prediction

Linear prediction is commonly used for encoding speech and audio in order to predict the current sample using a linear combination of the K immediate predecessors.¹⁰ A finite impulse response (FIR) linear predictor of the Kth order predicts the current audio sample, $x (n)$ , as

\hat{x} (n) = \sum_{k = 1}^{K} a_{k} x (n - k)

(1)

where $a_{k}$ is the kth predictor coefficient. The residual signal, $e (n)$ , is then computed as

e (n) = x (n) - \hat{x} (n)

(2)

If the prediction is successful, the variance of $e (n)$ is smaller than that of $x (n)$ . Since it is more efficient to encode $e (n)$ than $x (n)$ using an entropy encoder,¹¹ $e (n)$ is encoded and transmitted to the decoder. Simultaneously, the linear prediction coefficients, ${a_{1}, a_{2}, \dots, a_{K}}$ , should be transmitted to the decoder using a quantizer. After transmitting the code sequence of $e (n)$ , an entropy decoder is utilized. Thus, a predicted sample of $x (n)$ , $\hat{x} (n)$ , is obtained by applying the inverse of the linear prediction filter described in equation (1).

Joint channel coding

The MPEG-4 ALS supports up to 65,536 channels, which is why the encoder and decoder should exploit inter-channel correlations and dependencies. There are two schemes for MCC in the MPEG-4 ALS, difference coding and MCC; these are both implemented in the MPEG-4 ALS and either may be used. In particular, joint channel coding is one MCC scheme which may be used to exploit the dependencies between any two channels of a multi-channel signal. In difference coding, the inter-channel correlation between two channels is eliminated by computing the difference between the two channel signals, $x_{i} (n)$ and $x_{i + 1} (n)$

d_{i} (n) = x_{i + 1} (n) - x_{i} (n)

(3)

The stronger the correlation between $x_{i} (n)$ and $x_{i + 1} (n)$ , the closer the difference value, $d_{i} (n)$ , will go to zero. This means that $d_{i} (n)$ in equation (3) has a smaller variance than either $x_{i} (n)$ or $x_{i + 1} (n)$ and encoding $d_{i} (n)$ and either $x_{i} (n)$ or $x_{i + 1} (n)$ is more efficient than directly encoding $x_{i} (n)$ and $x_{i + 1} (n)$ . The selection of two signals from among $x_{i} (n)$ , $x_{i + 1} (n)$ , and $d_{i} (n)$ is done by comparing the size of the bitstream after encoding $x_{i} (n)$ , $x_{i + 1} (n)$ , and $d_{i} (n)$ individually. In the case of a multi-channel signal, difference coding is applied to a pair of multi-channels according to a channel pairing scheme.¹³ As described in section “Prediction,” in MCC, the residual signal for a given channel is first estimated using the linear predictor, which is referred to as $e_{r} (n)$ . The residual signal of another cth channel, $e_{c} (n)$ , can then be predicted using $e_{r} (n)$ .^13,15 Essentially, the MPEG-4 ALS decides which coding scheme is proper for a given frame by comparing the size of the bitstream from MCC and the difference coding, then it selects whichever provides a smaller compression ratio.

Proposed sensor signal compression method

Figures 3 and 4 show the block diagram of the proposed sensor signal compression encoder and decoder, respectively. As shown in Figure 3, the encoding procedure in the proposed method is composed of two steps, sensor fault detection and encoding. In order to encode sensor signals, several candidates may be selected from state-of-the-art lossless audio codecs.^11,16 According to the study done by H Huang,¹⁶ three codecs are considered in this article: (1) MPEG-4 ALS, (2) FLAC, and (3) WavPack, as shown in Table 1. In fact, these three codecs can operate in several different compression modes, thus two different modes for each codec are selected as described in the third column of Table 1. Next, the compression ratio, $C_{R}$ , of each codec and compression mode is computed as^11–13

C_{R} = \frac{Compressed file size}{Original file size} \times 100 (%)

(4)

Figure 3.

A block diagram of the proposed sensor signal compression encoder.

Figure 4.

A block diagram of the proposed sensor signal compression decoder.

Table 1.

The list of candidate codecs and their compression modes applicable to the compression of underwater acoustic sensor signals.

Candidates	Codec	Compression mode
A-1	MPEG-4 ALS	Adaptive prediction order
A-2	MPEG-4 ALS	Fixed prediction order (12th)
B-1	FLAC	Fast mode
B-2	FLAC	High-quality mode
C-1	WavPack	Fast mode
C-2	WavPack	High-quality mode

Notice that an encoder with a low compression ratio is desirable.

Figure 5 compares the compression ratios of three different candidate codecs with two different compression modes, as shown in Table 1, where 30-s sensor signals are used from three different sensor arrays. Array 1 and Array 2 operate in the same coastal area, and the other is in a different coastal area. In addition, the three arrays are composed of six sensors, and the distance between adjacent sensors is 8 m. As shown in the figure, MPEG-4 ALS (A-1 and A-2) provides a lower compression ratio than the others. Based on these preliminary results, the MPEG-4 ALS encoder is selected as an encoder for the proposed scheme. Moreover, since the compression ratio of A-1 is similar to that of A-2, but the complexity of A-2 is lower than that of A-1, it was eventually decided that A-2 should be used in the proposed scheme.

Figure 5.

The comparison of compression ratios for three different candidate codecs with two different compression modes.

After detecting faulty sensors, which will be described in section “Sensor fault detection,” the signals from the normal sensors and faulty sensors are clustered separately based on the detection results. While the signals from normal sensors are directly encoded by the MPEG-4 ALS encoder, the signals from faulty sensors are first pre-processed. After that, it is decided whether the signal encoding for the faulty sensor should be skipped, which is called the send mode indicator. According to the indicator’s determination as being in send mode or non-send mode, the pre-processed signal is encoded by the MPEG-4 ALS encoder if the send mode indicator is in send mode. Thus, the proposed method may decrease the encoding complexity and increase the coding efficiency. Consequently, the encoded MPEG-4 ALS bitstream is transmitted to the proposed sensor signal compression decoder, where the send mode indicator from the sensor fault detector is merged with the side information from the pre-processor into the encoded bitstream.

As mentioned in section “Review of MPEG-4 ALS audio coding for compressing multi-channel signals,” the MPEG-4 ALS encoder compresses multi-channel signals by joint channel coding. This means that the residual signal of a channel must be correlated with that of another channel. The performance of this coding scheme in the MPEG-4 ALS encoder is dependent on how highly the two channel signals are correlated with each other.¹¹ However, the cross-correlation between multi-channel signals obtained from an underwater sensor array depends on the array structure, and it is lower than typical audio signals due to ambient noise and long sensor-to-sensor spacing.^1,17 To make sure of this, the signals are acquired from three equally spaced sensor arrays, where each array is composed of 12 sensors with different sensor-to-sensor spacing. That is, the distances between adjacent sensors from Array 4, Array 5, and Array 6 are 8, 4, and 2 m, respectively.

Figure 6 shows the cross-correlation between the signal from the fourth sensor and the adjacent sensors of each array. As shown in the figure, it may be observed that cross-correlation decreases due to the length of sensor-to-sensor spacing. That is, the cross-correlation of Array 4 is lower than those of Array 5 and Array 6. The figure also shows that the cross-correlation is reduced with the distance between sensors. This is because acoustic sensors must be arranged at intervals of $wavelength (λ) / 2$ in order to avoid spatial aliasing.²

Figure 6.

An illustration of the cross-correlation between the fourth sensor signal and its adjacent sensor signals acquired from three different sensor arrays composed of equally spaced sensors: (a) Array 4, (b) Array 5, and (c) Array 6.

Therefore, it is reported that it is essential to focus on the efficient compression of ambient noise rather than specific sound sources for underwater sound.⁹ Figure 7 compares the compression ratios of four different arrays with or without applying joint stereo (JS) coding, that is, difference coding, and/or the MCC operation of MPEG-4 ALS to sensor signals. As shown in the figure, the JS coding and MCC had marginally lower compression ratios for all the arrays. Considering the complexity, it is decided that the JS and MCC operations can be deactivated in the MPEG-4 ALS encoder, as shown in Figure 3.

Figure 7.

Comparison of compression ratios of three arrays composed of equally spaced sensors: (a) Array 4, (b) Array 5, and (c) Array 6.

After receiving the bitstream, the decoding process is performed as shown in Figure 4. The received bitstream is first divided into an MPEG-4 ALS bitstream for the sensor signals, the send mode indicator of the sensor fault detection, and the pre-processing side information. If the send mode indicator is in send mode, the signal from the faulty sensor is decoded using the MPEG-4 ALS decoder. If the send mode indicator is in non-send mode, the beamformer of the signal processing unit, as shown in Figure 4, excludes the sensor signal that corresponds to the faulty sensor to avoid degrading the performance of the sonar system.

Sensor fault detection

Sonar systems are generally composed of single or multiple arrays, which are themselves composed of a number of hydrophones. In these, some failures generate electrical noise and cause performance degradation in the sonar system.^2–4 The cause of a sensor malfunction can be classified as a fault or failure.¹⁸ Generally, it is more difficult to detect sensor faults than sensor failures because faulty sensors still output a signal that appears normal even if the sensor signal is actually corrupted. Figures 8 and 9 illustrate the sensor signals obtained from two different sensor arrays (Array A and Array B), and each array has two faulty sensors (the third and fifth sensors). As shown in Figure 8, the faulty sensors output uncertain constant values. In such a case, it is easy to identify the faulty sensors. However, as mentioned above, faulty sensors may also produce signals that are difficult to distinguish from normal signals, as shown in Figure 9. Compared to Figure 8, it is generally more difficult to identify the integrity of a signal than to detect its absence.¹⁸

Figure 8.

An illustration of sensor signals for Array A in (a) normal and (b) noisy environments.

Figure 9.

An illustration of sensor signals for Array B in (a) normal and (b) noisy environments.

In passive and active sonar systems, the arrival direction of a target sound is used as a cue to predict the bearing or position of a target. In addition, such systems attempt to improve the SNR of sensor signals. These are accomplished by array signal processing, which is applied to multi-channel sensor signals acquired from the hydrophone array.^5,19 That is, sonar systems use visual or acoustic information with the SNR using the array signal processing results to identify target contacts. Because these systems display or use the integrated output of multiple sensors, it is difficult to recognize single sensor fault immediately. Moreover, faulty sensors continuously generate incorrect signals.¹⁸ Thus, it is difficult to distinguish an actual target from artificial noise caused by faulty sensors in a display unless the faulty sensors completely fail. It is therefore necessary to minimize the performance degradation of sonar systems by integrating an automatic sensor fault detection technique into sonar systems to eliminate faulty sensor signals. Furthermore, if sensor fault detection is performed in a signal acquisition unit as shown in Figure 1, the transmission efficiency may be expected to improve by excluding the faulty sensor signal in the bitstream.

There are several main causes of faulty sensors. One of these is that the internal module of a sensor fails. In this case, electrical noise occurs occasionally, meaning that sensor signals can be distorted due to the noise, which may generate a false target signal in the detection equipment. Another is the failure of the multiplexer that supplies power, controls the acoustic gain of each acoustic sensor, and performs A/D conversion. If the power is not properly supplied to a sensor, such a faulty sensor tends to output an uncertain constant value, as shown in Figure 8. In other cases, the output of the faulty sensor is biased to a specific value, as shown in Figure 9. In such cases, the measured root-mean-square (RMS) value of the faulty sensor signal becomes high or invariant compared to that of a normal sensor signal. The RMS is defined as

r_{i} = \sqrt{\frac{1}{N} \sum_{n = 1}^{N} {| x_{i}^{〈 T 〉} (n) |}^{2}}, i = 1, \dots, M

(5)

where $x_{i}^{〈 T 〉} (n) = \frac{1}{T} \sum_{k = 1}^{T} x_{i} ((n - 1) T + k)$ and $x_{i} (n)$ denote the sample values of each input frame of the ith sensor. In addition, M, N, and T denote the number of sensors, frame length of the array, and the linear integration time, respectively.

It is important to select a reliable decision factor to correctly identify valid sensors, even in noisy underwater environments, by analyzing the features of sensor signals. A conventional detection method measures the RMS continuously from all sensors, and a sonar operator or a monitoring system detects faulty sensors by observing the RMS difference between adjacent sensors.²⁰ However, the analysis of the RMS difference cannot be a reliable decision factor for sensor fault detection because the RMS of a normal sensor signal is similar to that of faulty sensor signals in noisy underwater environments. This kind of condition makes it harder for the sonar operator or the monitoring system to detect faulty sensors accurately and quickly. In our previous work,^21,22 a sensor fault detection method has been proposed by comparing RMS and/or RMSCR. Exhaustive experiments have demonstrated that the RMS did not always work well in noisy underwater environments. On the other hand, the proposed method in this article further utilizes the relative values of ZCR. In other words, the proposed method detects faulty sensors using a combination of RMSCR and ZCR ratios.

Figure 10 shows a flowchart of the proposed sensor fault detection method that is composed of two decision modes depending on the computational complexity: a low-complexity (LC) decision mode and a high-complexity (HC) one. The LC decision mode is based on ZCR.²³ That is, the LC decision mode compares the ratio between the ZCR of a sensor and the average ZCR of all sensors. However, the HC decision mode compares the ratio between the RMSCR of a sensor and the average RMSCR of all sensors.²¹ Comparing both modes, the HC decision mode requires higher computation with a better accurate detection performance than the LC decision mode because the RMS should be calculated for RMSCR and RMS computation requires additional operations such as $(M \times (N + 1))$ multiplications, $M \times N$ additions, and M square-root computations for M sensors and N samples per sensor compared to the LC decision mode. For the proposed method, the ZCR and RMSCR are defined as

Z_{i} = \frac{1}{N - 1} \sum_{n = 2}^{N} | v (x_{i}^{〈 T 〉} (n)) - v (x_{i}^{〈 T 〉} (n - 1)) |

(6)

R_{i} = \frac{1}{N - 1} \sum_{n = 2}^{N} | w (x_{i}^{〈 T 〉} (n)) - w (x_{i}^{〈 T 〉} (n - 1)) |

(7)

where $v (0) = 0$ and $v (x)$ is equal to 1 or −1 if $x > 0$ or $x < 0$ , respectively. In addition, $w (x) = v (x - r_{i})$ , where $r_{i}$ is the RMS, as defined in equation (5).

Figure 10.

A flowchart of the proposed sensor fault detection method.

Tables 2 and 3 compare ZCR and RMSCR for several sensors of Array B under two different underwater conditions where the average RMS is measured at −21.6 and −13.1 dB, respectively. As indicated in the last column of each table, the third and fifth sensors are faulty. The linear integration time, T, is set to 2 to compute RMS, ZCR, and RMSCR. As shown in Tables 2 and 3, the RMS value of a faulty sensor is higher than that of a normal sensor, but ZCR and RMSCR for a faulty sensor are zero or very low compared to those from a normal sensor. Note that ZCR and RMSCR in Table 2 become zero for faulty sensors. This is because the signal from a faulty sensor is biased toward a negative value without any zero crossings, as shown in the third and fifth subplot of Figure 8(a). As shown in Table 2, which is the result in a noisy environment, the RMS value of a normal sensor becomes similar to that of a faulty sensor. In addition, ZCR is also increased for faulty sensors because noise makes the signal from a faulty sensor fluctuate across zero even if the signal is biased to a negative value, as may be observed in the third and fifth subplot of Figure 8(b).

Table 2.

Comparison of RMS, ZCR, and RMSCR for several sensors from Array B, where the average RMS for normal sensors is −21.6 dB and the third and fifth sensors are faulty.

Sensor	RMS (r_i) (dB)	ZCR (Z_i)	RMSCR (R_i)	Fault
1	−21.61	0.77	0.43	No
2	−21.83	0.76	0.41	No
3	−10.42	0.00	0.00	Yes
4	−21.85	0.73	0.41	No
5	−10.51	0.00	0.00	Yes
6	−21.62	0.74	0.42	No

RMS: root-mean-square; ZCR: zero crossing rate; RMSCR: root-mean-square crossing rate.

Table 3.

Comparison of RMS, ZCR, and RMSCR for several sensors from Array B, where the average RMS for normal sensors is −13.1 dB and the third and fifth sensors are faulty.

Sensor	RMS (r_i) (dB)	ZCR (Z_i)	RMSCR (R_i)	Fault
1	−11.51	0.89	0.45	No
2	−11.82	0.83	0.46	No
3	−9.45	0.56	0.04	Yes
4	−10.83	0.84	0.42	No
5	−9.16	0.52	0.05	Yes
6	−11.12	0.89	0.46	No

RMS: root-mean-square; ZCR: zero crossing rate; RMSCR: root-mean-square crossing rate.

Fault detection becomes a difficult task in a noisy underwater environment because the faulty sensor signal fluctuates more often across the zero value as the environmental noise becomes more severe. As such, the fault detection in the environment as shown in Table 3 is more difficult than that in Table 2. Moreover, ZCR and RMSCR can be used to more reliably detect faulty sensors than RMS, which is the reason why ZCR and RMSCR are used for the LC and HC decision modes, respectively. The reliability of ZCR and RMSCR for fault detection are improved by normalizing them with their respective averages, such as

ρ (Z_{i}) = \frac{Z_{i}}{\bar{Z}}

(8)

ρ (R_{i}) = \frac{R_{i}}{\bar{R}}

(9)

where $\bar{Z} = \frac{1}{M} \sum_{i = 0}^{M - 1} Z_{i}$ and $\bar{R} = \frac{1}{M} \sum_{i = 0}^{M - 1} R_{i}$ . After that, $ρ (R_{i})$ and $ρ (Z_{i})$ are compared with pre-defined decision thresholds. If $ρ (Z_{i}) < θ_{zcr}$ , then the ith sensor is regarded as a faulty sensor in the LC decision mode. Similarly, if $ρ (R_{i}) > θ_{rmscr}^{high}$ or $ρ (R_{i}) < θ_{rmscr}^{low}$ , then the HC decision mode classifies the ith sensor as faulty.

Figures 11 and 12 illustrate the cumulative plot of $ρ (R_{i})$ and $ρ (Z_{i})$ , correspond to the acquired eight frame signals from Array A and Array B, respectively, for different average RMS values. The preliminary experiments on threshold setting for faulty sensor detection show that it is better to set the threshold at a fixed value rather than to set it adaptively. In the experiments, the standard deviations of $ρ (R_{i})$ and $ρ (Z_{i})$ of normal sensors are measured as below than 0.2. Thus, the upper and lower thresholds for the detection are set to 0.4, which is twice the value of 0.2. T, $θ_{zcr}$ , $θ_{rmscr}^{low}$ , and $θ_{rmscr}^{high}$ are set to 2, 0.6, 0.6, and 1.4, respectively. Note that the number of sensors for Array A and Array B is M = 80 and M = 100, respectively. As shown in the figures, $ρ (R_{i})$ and $ρ (Z_{i})$ , which correspond to six sensors in Array A and the three sensors in Array B, are smaller than $θ_{zcr}$ and $θ_{rmscr}^{low}$ because the signals from the faulty sensors are biased toward negative values. In a noisy underwater environment such as in Figure 12(b), $ρ (R_{i})$ remains low while $ρ (Z_{i})$ increases. This implies that the faulty sensors in the RMSCR-based approach could be detected better than when using the ZCR-based approach in noisy underwater environments with a low integration time.

Figure 11.

Illustrations of $ρ (R_{i})$ and $ρ (Z_{i})$ from Array A when the average RMS is (a) –21.1 dB (normal environment) and (b) −12.6 dB (noisy environment).

Figure 12.

Illustrations of $ρ (R_{i})$ and $ρ (Z_{i})$ from Array B when the average RMS is (a) –21.3 dB (normal environment) and (b) −13.7 dB (noisy environment).

Pre/post-processing

As described above, the proposed method deals with faulty sensor signals in either non-send or send mode. In non-send mode, the status information on faulty sensors is transmitted without encoding the faulty sensor signal. However, when it is determined that the faulty sensor signal is particularly needed at the signal processing unit, send mode processing is applied as follows. In the proposed encoder, the signal from a faulty sensor is pre-processed and followed by the application of the MPEG-4 ALS encoder as shown in Figure 3. The signal from the faulty sensor is decoded from the transmitted bitstream using the MPEG-4 ALS decoder and the decoded signal is post-processed as shown in Figure 4.

Figures 13(a) and (b) show a block diagram for pre-processing faulty sensor signals in the proposed encoder and that for post-processing the decoded faulty sensor signals in the proposed decoder, respectively. As mentioned in section “Sensor fault detection,” the faulty sensor signals are either biased to a specific value or may output an uncertain constant value. The bias of the faulty sensor signal is removed at the pre-processing stage using a short-time average for the signal before applying the linear prediction analysis in the MPEG-4 ALS.

Figure 13.

Block diagrams for (a) pre-processing and (b) post-processing faulty sensor signals in send mode.

The short-time average is computed once for every frame of the input signal and is defined as

μ_{i}^{m} = \frac{1}{N} \sum_{n = 1}^{N} x_{i}^{m} (n)

(10)

where i is the faulty sensor channel, m is the frame index, and N is the number of samples within a frame. Actually, $μ_{i}^{m}$ is encoded using a 16-bit scalar quantizer such that ${\bar{μ}}_{i}^{m} = Q^{- 1} (Q (μ_{i}^{m}))$ , where $Q (\cdot)$ and $Q^{- 1} (\cdot)$ , respectively, denote the scalar quantizer and its inverse quantizer. Next, the mth frame of the ith faulty sensor signal, $x_{i}^{m} (n)$ , is normalized by subtracting ${\bar{μ}}_{i}^{m}$ as follows

{\hat{x}}_{i}^{m} (n) = x_{i}^{m} (n) - {\bar{μ}}_{i}^{m}, k = 1, \dots, N

(11)

The normalized signal, ${\hat{x}}_{i}^{m} (n)$ , is then brought to the MPEG-4 ALS encoder. In addition, $Q (μ_{i}^{m})$ and the send mode indicator, non-send or send mode, should also be sent to the decoder in send mode. The send mode indicator is extracted from the bitstream and ${\bar{μ}}_{i}^{m}$ is decoded for the send mode in the proposed decoder. Finally, the post-processing stage is applied to recover $x_{i}^{m} (n)$ from the decoded signal, ${\hat{x}}_{i}^{m} (n)$ , and ${\bar{μ}}_{i}^{m}$ , such that ${\bar{x}}_{i}^{m} (n) = {\bar{\hat{x}}}_{i}^{m} (n) + {\bar{μ}}_{i}^{m}, k = 1, \dots, N$ .

Framing

The multiplexer at the encoder configures the encoded frame every second for the entire sensor signal. Figure 14 shows the frame structure in the proposed method. As shown in the figure, the frame consists of a frame header (56 bits) and M encoded channel blocks, where M is the number of sensors. The frame header includes the current frame number, array identifier (ID), the send mode indicator, and M. Each encoded channel block is composed of a sensor channel header (48 bits) and an MPEG-4 ALS bitstream of variable length. Note here that the encoded channel blocks corresponding to the respective channels are sequentially arranged. In addition, the short-time average is packed into the sensor channel header in accordance with the send mode indicator. The frame is only composed of the sensor channel header for the failure sensor channel block if non-send mode is indicated.

Figure 14.

Illustration of the frame structure for transmitting the bitstream in the proposed sensor signal compression method.

Performance evaluation

Figure 15 shows the signal acquisition flow for the experiment. As shown, sensor signals were acquired from three different real underwater sensor arrays that operated in different coastal areas, as shown in Table 4. Similar to a towed line array sonar system deployed and towed by naval ships to detect underwater targets,² the underwater acoustic sensor arrays were connected to signal acquisition equipment at the shore station through long fiber-optic cables of several tens of kilometers for reliable communication.²⁴ Every sensor signal simultaneously captured by a multiple hydrophone array¹ was converted into a digital signal through the use of an analog-to-digital (A/D) converter. Next, the digital signal was again converted into an electrical-to-optical (E/O) signal for long range transmission. Typically, these A/D and E/O converters were equipped on an inter-connecting module that assembled the sensors and cables. Finally, the E/O converted signals were subsequently transmitted to a signal acquisition unit via fiber-optic cables. At the signal acquisition unit, the transmitted sensor signal was converted back into an electric digital signal through the use of an optical-to-electrical (O/E) converter and then re-arranged and framed for the following signal processing stages.

Figure 15.

Illustration of a signal acquisition flow for the experiment.

Table 4.

Configurations of three different sensor arrays used for the experiment.

Sensor array	Number of sensors
Sensor array	Normal	Faulty	Total
A	97	3	100
B	74	6	80
C	70	10	80

The performance of the proposed sensor signal compression method was evaluated in two ways: the precision of faulty sensor detection and the compression ratios for the send and non-send modes. Table 4 shows the sensor configuration of each of the three sensor arrays. Each sensor array was composed of 80 or more sensors, and the number of faulty sensors in each array ranged from 3 to 10. Each faulty sensor was manually determined in advance by judging whether the gain control was normally operated and by monitoring the RMS value of the sensor.²¹ In addition, the purity of the data received through the sensor array was verified by an additional sensor that could monitor the acquisition status of the sensor signal. This approach confirmed whether the faulty signal came from an error due to the sensor unit or some other reasons. The sensor signals were obtained over the course of 56 s from each sensor array. The A/D converter used in this article had a maximum value of ±5 V. Thus, each sensor signal was sampled at 2048 Hz and uniformly quantized with 16-bit resolution at a quantization level of $5 [V] / 2^{15}$ .

Sensor fault detection

Table 5 compares the sensor fault detection performance of the ZCR-based LC decision mode and RMSCR-based HC decision mode under different integration times and noise conditions for the three arrays. Both the ZCR-based and RMSCR-based methods provided nearly perfect precision for fault detection. However, the precision of the ZCR-based method for Array A was slightly lower for short integration times (T = 2 or 4) because the faulty sensor signal from Array A at a −13.1 dB average RMS changed so rapidly that $ρ (Z_{i})$ was not high enough to be detected within such a short integration time. However, the faulty sensors that were not detected by the ZCR-based approach were detected using the RMSCR-based ratio, $ρ (R_{i})$ , because the RMS value that was the reference value for the calculation of $R_{i}$ also increased in proportion with the ambient noise increase. Thus, $R_{i}$ and $ρ (R_{i})$ remained low. It may be concluded that the RMSCR-based approach was more robust for faulty sensor detection than the ZCR-based approach.

Table 5.

Experimental results of sensor fault detection: $θ_{zcr} = 0.6$ , $θ_{rmscr}^{low} = 0.6$ , and $θ_{rmscr}^{high} = 1.4$ .

Sensor array	Average RMS (dB)	T (s)	Precision (%)
Sensor array	Average RMS (dB)	T (s)	LC decision mode (ZCR-based)	HC decision mode (RMSCR-based)
A	−21.6	2	100	100
		4	100	100
		8	100	100
A	−13.1	2	78.6	100
		4	97.8	100
		8	100	100
B	−16.0	2	100	100
		4	100	100
		8	100	100
B	−12.4	2	100	100
		4	100	100
		8	100	100
C	−21.3	2	100	100
		4	100	100
		8	100	100
C	−11.6	2	100	100
		4	100	100
		8	100	100

RMS: root-mean-square; ZCR: zero crossing rate; RMSCR: root-mean-square crossing rate; LC: low complexity; HC: high complexity.

Compression performance

In this evaluation, the compression ratio of the bitstream encoded by the proposed compression method was compared with that of the MPEG-4 ALS reference software encoder.²⁵ Here, the prediction order and frame length were set to 20 and 2048, respectively, for the MPEG-4 ALS encoding.

Table 6 compares the compression ratios for the three different sensor arrays. The compression ratios for the proposed method were measured by setting the send mode indicator in either send mode or non-send mode. As shown in the table, the proposed method decreased the compression ratio by 0.43% and 4.57% in send mode and non-send mode, respectively, compared to the MPEG-4 ALS reference software. In send mode, the compression ratio was reduced with the assistance of pre- and post-processing for faulty sensors, even if the reduction was marginal. However, the compression ratio in non-send mode was decreased in accordance with the number of faulty sensors. In addition, non-send mode reduced the computational complexity by excluding the encoding process for faulty sensor signals.

Table 6.

The comparison of the compression ratios for the three different array signals.

Sensor array	Number of faulty sensors	Compression ratio, C_R (%)
		Proposed method		MPEG-4 ALS RM
		Send mode	Non-send mode	MPEG-4 ALS RM
A	3	76.08	73.18	76.12
B	6	66.67	64.48	67.64
C	10	69.65	62.33	69.94

Conclusion

This article proposed a lossless compression method for an underwater acoustic sensor array signal based on the standard MPEG-4 ALS coding. The proposed method included a sensor fault detection method using ZCR and RMSCR and two different send modes for reduced complexity and lowered compression ratio compared to the standard MPEG-4 ALS coding. In particular, the sensor fault detection in the proposed method was composed of two detection approaches depending on computational complexity: a ZCR-based LC approach and an RMSCR-based HC approach. The send mode incorporated pre-processing and post-processing to reduce the signal variance from faulty sensors, which resulted in a low compression ratio that did not damage the signal quality. In addition, a packet format was designed to accommodate all features together in the encoder.

The performance of the proposed sensor signal compression method was evaluated for two aspects: the precision of faulty sensor detection and the compression ratios for the send and non-send modes. Here, the performance evaluation was carried out using three real underwater sensor arrays that operated in different coastal areas. Comparing the precision of the faulty sensor detection between the ZCR-based and RMSCR-based approaches, it was shown that the RMSCR-based approach was more robust to faulty sensor detection than the ZCR-based approach for all sensor arrays and in noisy environments. In addition, the proposed method decreased the compression ratio by 0.43% and 4.57% in send mode and non-send mode, respectively, compared to the MPEG-4 ALS reference software.

Footnotes

Handling Editor: Jaime Lloret

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the government of Korea (MSIT) (No. 2015R1A2A1A05001687).

ORCID iD

Yong Guk Kim

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