Data compression in wireless sensors network using

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Data compression in wireless sensors network using MDCT and embedded harmonic coding Jaafar K. Alsalaet a,n, Abduladhem A. Ali b a b

Department of Mechanical Engineering, College of Engineering, University of Basrah, Basrah, Iraq Department of Computer Engineering, College of Engineering, University of Basrah, Basrah, Iraq

art ic l e i nf o

a b s t r a c t

Article history: Received 31 July 2013 Received in revised form 10 September 2014 Accepted 30 November 2014 This paper was recommended for publication by Dr. Didier Theilliol.

One of the major applications of wireless sensors networks (WSNs) is vibration measurement for the purpose of structural health monitoring and machinery fault diagnosis. WSNs have many advantages over the wired networks such as low cost and reduced setup time. However, the useful bandwidth is limited, as compared to wired networks, resulting in relatively low sampling. One solution to this problem is data compression which, in addition to enhancing sampling rate, saves valuable power of the wireless nodes. In this work, a data compression scheme, based on Modified Discrete Cosine Transform (MDCT) followed by Embedded Harmonic Components Coding (EHCC) is proposed to compress vibration signals. The EHCC is applied to exploit harmonic redundancy present is most vibration signals resulting in improved compression ratio. This scheme is made suitable for the tiny hardware of wireless nodes and it is proved to be fast and effective. The efficiency of the proposed scheme is investigated by conducting several experimental tests. & 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Keywords: Wireless sensors network Data compression MDCT Embedded coding

1. Introduction Main challenges in WSN are limited bandwidth and power requirements [1]. The bandwidth of wireless networks is much lower than that of wired systems. Wireless nodes in general are built on tiny hardware to reduce cost and power requirement on the expense of data transmission rate. For example, most of ZigBee nodes have maximum data rate of 250 kbps. When using high accuracy AD converters, such as 16- bit or 24- bit converters, the sampling rate will be limited to a small quantity especially in hierarchical network topologies. Machinery diagnostic analysis is based on vibration data streaming at moderate and high sampling rates especially when it is required to analyze vibration of special parts such as bearings and gears [1–3]. On the other hand, health monitoring of important civil structures requires large number of wireless nodes, in access of several hundred nodes [1,4–6]. Therefore, the total amount of data will be very large even when the sampling rate per node is not high. Furthermore, wireless transmissions consume most of the node energy and significantly reduce battery life [1,7]. For the above reasons, it is desirable to reduce sensory data before transmission and this can be achieved by data compression. n

Corresponding author. Tel.: þ 964 780 5650 844. E-mail addresses: [email protected] (J.K. Alsalaet), [email protected] (A.A. Ali).

Data compression techniques are extensively applied in many fields as it is well known to the reader. Data compression techniques can be divided into two main categories, lossless and lossy [8]. In the lossless compression techniques, original data can be retained exactly without any loss but on the expense of compression ratio and system complexity. Examples of lossless data compression techniques are Run Length Encoding (RLE), Huffman coding, arithmetic coding and Lempel–Ziv (LZ) coding. On the other hand, lossy data compression permits a certain degree of inaccuracy in the reconstructed data but the compression ratio will be significantly high. Examples of lossy compression techniques are prediction, quantization, fitting, transform coding and compressive sensing. Some compression techniques may use combination of two or more techniques such as encoders of multimedia data [8]. MDCT is a transform coding scheme which is widely employed in the commercial audio coding products such as MPEG-1, MPEG-2, MP3, AAC, AC-3 encoder/ decoders, etc. [9–11]. It has many advantages over other transform coding schemes including energy compaction, blocks effect cancellation and reduced calculations. Hence, it is selected in this work as the main compression technique. To further improve compression ratio, the MDCT coefficients are encoded using Embedded Harmonic Components Coding algorithm to exploit any harmonic redundancy in vibration signals. The EHCC is a sort of lossless coding since MDCT coefficients can be retrieved exactly when the encoding process proceeds up to the least significant bit.

http://dx.doi.org/10.1016/j.isatra.2014.11.023 0019-0578/& 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Please cite this article as: Alsalaet JK, Ali AA. Data compression in wireless sensors network using MDCT and embedded harmonic coding. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2014.11.023i

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2. Related works Vibration signals must be sampled at rates as twice as the highest frequency to be considered to prevent aliasing. For wireless sensors networks, this will produce large amount of data packets especially when there are many signals sampled at the same time. One solution to this problem is to compress vibration data. Vibration signals can be loosely compressed as long as the system parameters can be extracted at a reasonable accuracy. Some works conducted in this area includes sensory data compression which include the work of Staszewski [4], Liu and Cheng [5] and Todorovska and Tzong [6] to compress vibration of civil structures using wavelet transform. Another work done by Myong et al. [3] in which the Discrete Wavelet Transform (DWT) is used to compress machinery vibration data. Chan and Tse [2] proposed a novel method for data compression based on Empirical Mode Decomposition (EMD) and Differential Pulse Code Modulation (DPCM). The EMD is a time consuming scheme which involves some mathematical steps such as envelope extraction, cubic spline interpolation and sifting process. It relies mainly on downsampling process to reduce the number of samples therefore it is suitable for low-frequency signals only. After downsampling, the samples are processed by DPCM coder for further compression. Tharini and Ranjan [7] presented a modified Huffman coding algorithm to exploit spatio–temporal correlation among WSN nodes. Their method is suitable only for very low sampling rates. Compressive sensing is a promising technique to compress signals efficiently. One of the recent works on this novel signal compression technique includes the work of Lei et al. [12] in which they proposed a multiscale reconstruction model based on wavelet analysis and evolutionary programming to compress signals. Most of the above works are unsuitable for machinery vibration data compression. For example, wavelets are ill suited to represent and capture oscillatory patterns. Some of the schemes mentioned are inappropriate for tiny resources of wireless nodes due to complexity and lengthy calculations. Since vibration signals are almost stationary and deterministic, trigonometric-functions-based transforms, such as FFT, Discrete Cosine Transform (DCT) and MDCT are more suitable to compress them. FFT suffers from a number of limitations such as window effect and complex nature of the coefficients. DCT suffer from blocking effect or artifacts, therefore, MDCT is best suited for the purpose of vibration data compression [13]. Too many papers are published to discuss application of MDCT in multimedia data compression such as images, audio and video files, see [9–11] for example. However, application of MDCT in vibration data compression has never been discussed before the work of [13] according to our knowledge. Following any transform, the correlation between signal components will be exploited resulting in less number of significant coefficients having most of the signal energy. To achieve higher compression ratios, the resulting coefficients must be coded properly before transmission or storage. This can be achieved by using for example, Run Length Encoding (RLE), Huffman, Lempel–Ziv (LZ) or arithmetic coding. Some other techniques applied in DWT include thresholding and denoising by eliminating certain portions of the transform. Another method of coding includes construction of significant components table which contains the position and value of each component then applying some other scheme to encode the table. In 1993 Shapiro introduced his famous Embedded Zerotree Wavelet (EZW) algorithm which is very simple and effective to compress images after applying 2-Dim DWT [14]. In EZW the encoder can terminate encoding at any point providing certain degree of compression and corresponding distortion to be met. Following that, Said and Pearlman made some enhancement to EZW coding and proposed a new and different implementation based on the Split Partitioning In Hierarchical Tree (SPIHT) method [15]. SPIHT algorithm

is also applied after 2-Dim DWT of the image blocks but it has better performance than EZW. Davis and Chawla [16] extended the idea of embedded coding to 2-Dim 8  8 DCT blocks of images using the EZW and SPIHT algorithms. They proposed an algorithm to select the optimum significance tree structure for both DWT and DCT coefficients. Since that too many papers have been published about zerotree selection and enhancement to EZW and SPIHT algorithms, for example, see [17–20]. In 2005, Strahl et al. proposed an adaptive tree embedded coding scheme to compress audio signals based on applying SPIHT algorithm to 1-Dim MDCT coefficients [21]. The method involved designing of a number of significance trees and then dynamically selecting one of them during encoding of successive MDCT blocks. Hansen et al. [22] presented improvements to embedded coding of MDCT of audio signals based on psychoacoustic weighting and spectral envelope restoration to enhance perceptual performance of the coder. They suggested band-wise weighting of the MDCT coefficients with the inverse masking threshold before applying SPIHT algorithm.

3. The proposed compression scheme Some rotating machinery faults excite harmonically related frequency components due to some kind of impacting or striking. For example, mechanical looseness in the fixing plate or bearing housing will generate many multiples of 1  RPM or 1x component [23]. Sometimes, up to 5x or even more harmonics are generated. Another fault that generates harmonics is severe offset misalignment in couplings [23]. Defected gear trains and roller bearings mostly generate many types of harmonics at high frequencies. For example, misaligned gears excite Gear Mesh Frequency (GMF¼number of teeth  RPM) and its second and third order 2 and 3  GMF with sidebands at 1  RPM at both sides of each GMF component [23]. Some defects in roller bearings generate bearing related frequencies and their harmonics in severe cases [23]. Consequently, vibration signals may contain several harmonically related frequency components or even random and high frequency components. Due to the oscillatory nature of vibration signals, MDCT is best suited to represent them as discussed in [13]. The transform coding involves segmentation of the input signal into blocks, applying antileakage window and applying MDCT. Then, the resulting coefficients are coded using the proposed embedded coding scheme. The term “embedded coding” implies that the coefficients are transmitted progressively in multi-precision fashion where encoding information are embedded in the beginning of bit stream [14,15]. The proposed method is inspired by the set partitioning in hierarchical trees (SPIHT) algorithm presented by Said and Pearlman [15]; however, it employs different plan for indexes coding and a hierarchical structure that is suitable for vibration signals. SPIHT [15] is suitable for image compression using 2-Dim DWT where significant coefficients are mainly concentrated at lower subbands. For vibration data, this is not always true because vibration signals commonly have high-frequency components hence, another hierarchical structure must be adopted to exploit harmonic redundancy. On the host side, the decoder will reconstruct the MDCT coefficients from the bit stream and then apply Time-Domain Aliasing Cancellation (TDAC) scheme to obtain the time signal.

3.1. The MDCT The MDCT has been extensively employed in audio data compression due to its ability to remove time domain aliasing through Modulated Lapped Transforms (MLT) [9,10]. The MDCT of

Please cite this article as: Alsalaet JK, Ali AA. Data compression in wireless sensors network using MDCT and embedded harmonic coding. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2014.11.023i

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a block size of N is given by:     N 1 π N ð2k þ 1Þ ; 2iþ 1 þ X k ¼ ∑ xi cos 2 2N i¼0

N k ¼ 0; 1; 2:…  1 2

ð1Þ

It is clear that the number of MDCT coefficients is only half of the number of original samples and hence, it is expected that there will be information loss. In fact, this lack of representation can be treated by overlapped transforms with 50% overlapping percentage [13]. So far, the information contained in the lapped portion will be perfectly encoded in the coefficients of the two overlapped transforms. The backward transform is given by:     N=2  1 π N x~ i ¼ ∑ X k cos ð2k þ 1Þ ; i ¼ 0; 1; 2:…N  1 2i þ 1 þ 2 2N k¼0 ð2Þ The backward transform yields a scrambled version of the original ~ This scrambling can be signal and therefore it is denoted by x. removed by overlapping and adding the successive backward transforms using the so called algorithm time-domain aliasing cancellation (TDAC). The efficient implementation of MDCT and its inverse is extensively discussed in [13]. However, the encoding algorithm of MDCT coefficients in [13] is simple and not optimized. Here, the EHCC is applied to further increase the compression ration and provide the embedded feature of transmission process. 3.2. The Embedded Harmonic Components Coding (EHCC) algorithm Embedded coding refers to the fact that coefficients are transmitted according to their significance progressively. Transmission can be stopped at any instant and the signal can be reconstructed at accuracy proportional to the number of transmitted bits. Examples of embedded transmissions are multi-precision pictures sent over the internet and dynamic video and audio quality in remote conferencing applications. The EZW and SPIHT coding schemes are used to encode DWT coefficients depending on the fact that most signal power is concentrated in the low-frequency components while the higher band coefficients, corresponding to finer resolutions are diminishing successively [14]. In EZW, each coefficient in a certain band is considered as parent node for three related coefficients of the same orientation in the higher bands. From experience, Shapiro concluded that if the coefficient in a parent node is insignificant then all the related coefficients in the child nodes are likely insignificant [14]. This hierarchical organization will dramatically improve compression ratio by categorizing coefficients into significant and insignificant (zero) and progressively transmit them according to their importance. The locations of the coefficients can easily be interpreted from the hierarchical structure. As an improvement to EZW, SPIHT utilizes the same hypothesis of Shapiro about DWT coefficients but it is based on re-arrangement of the coefficients in descending form before transmission [15]. This will results in better compression since some bits can be excerpted from the order itself. However, the scheme includes an advanced ordering (component picking) algorithm which was the main contribution of Said and Pearlman [15]. Details of EZW and SPIHT are not given here due to shortage of space but the interested reader can consult the two papers [14,15]. Both EZW and SPIHT cannot be applied to encode MDCT coefficients due to many reasons:

 They are suitable for DWT coefficients structure (Shapiro hypothesis).

 Applied for 2-Dim DWT such as in image and video comp

3

method is named Embedded Harmonic Components Coding (EHCC). The main idea behind this scheme is that vibration frequency components are almost harmonically related (multiples of machine speed) and hence, this harmonic redundancy can be exploited by proper selection of the significance tree. A typical MDCT coefficient shown in Fig. 1 where three harmonics are identified by the components indexes of 20, 40 and 60. This transform may be obtained from analyzing some vibration problem such as severe misalignment [23]. It will be shown later how to detect the first component and its harmonics. The proposed scheme supposes that there are root nodes as many as components from 1 up to the fundamental (first identified) component which is 20 in this example. Each root node constitutes a chain of harmonically related components with certain number of elements. This can be called as one to one mapping since each node is associated with one descendant and one antecedent except the root and leave nodes. The root nodes arrangement will start at the most significant component down to X(1) component. The node will be indexed by two subscripts, root or chain index as row counter and harmonic index as column counter. In our example, Node(0,0) is actually X(20), Node(0,1) is X(40), Node(1,0) is X(19) and Node(1,1) is X(39) and so on. In other words Nodeði; jÞ ¼ XðH 0 i þ j  H 0 Þ

ð3Þ

where H0 is the index of the fundamental component (20 in the above example). The hierarchical structure for the above example is shown in Fig. 2. This harmonically related multi-chain structure is useful to improve compression ratio by categorizing the components into groups of as much identical components as possible. The benefit of this process is to minimize the “hole” bits which identify insignificant components during transmission. These hole bits are encountered when one or more insignificant component is positioned between two significant components. In the beginning of encoding process, the first power-of-two number higher than the maximum absolute coefficient is found and the threshold (TH) is set to half of this number in the first level of encoding. Components above this

Node(0,2)

Node(0 1) Node(0,1) Node(0,0) 20

0

60

40

Fig. 1. Typical MDCT plot including several harmonics.

Chain 1

X(20)

X(40)

X(60)

X(80)

Chain 2

X(19)

X(39)

X(59)

X(79)

Chain 3

X(18)

X(28)

X(58)

X(78)

Chain H0

X(1)

X(21)

X(41)

X(61)

ression. Suitable for low-frequency signals.

For the above reasons, a new method is proposed by the authors to efficiently encode MDCT coefficients of vibration signals. This

Fig. 2. The proposed tree structure.

Please cite this article as: Alsalaet JK, Ali AA. Data compression in wireless sensors network using MDCT and embedded harmonic coding. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2014.11.023i

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threshold are significant and those below it are insignificant. This threshold value is halved in each upcoming encoding level till it reaches a certain small value such as unity. Defining LIC(i, j) as the set of indexes of insignificant coefficients, NIC(i) as the number of insignificant coefficients in chain i, LSC(i, j) as the set of indexes of significant coefficients, NSC(i) as the number of significant coefficients in chain i. Let us also define D(i, j) as the set of all descendants of Node(i, j), S0(i, j) as the significance flag (1- bit) for Node(i, j), and Sd(i, j) as significant flag for all descendants of Node(i, j), i.e. (   1 if Nodeði; jÞ Z TH S0 ði; jÞ ¼ 0 otherwise (   1 if any Dði; jÞ Z TH ð4Þ Sd ði; jÞ ¼ 0 otherwise Also, let P0(i) as a bit be the significance flag for chain i and Ps(i) is the significance flag for all chains following it. So far P0(i) is zero when there is no significant node in chain i and 1 otherwise. Also, Ps(i) is zero when there is no significant node in all the chains following chain i and 1 if there exist at least one significant chain. (   1 if any Nodeði; jÞ Z TH P 0 ðiÞ ¼ 0 otherwise ( P s ðiÞ ¼

1

  if any P 0 ðkÞ ¼ 1; k ¼ i þ 1 … H 0

0

otherwise

ð5Þ

where j covers all yet insignificant harmonics contained in a chain. The process of encoding MDCT coefficients is similar to successive approximation of the ADC which represents an analog voltage by a number of bits in progressive resolution. However, in the proposed algorithm the most significant bit will be excerpted from the significance flag during multi-level thresholding. Moreover, the position of the coefficients (its index) can be decoded from the position of the significance flag in the bit stream and the predefined hierarchical structure of the nodes. The algorithm can be viewed as dynamic thresholding process where threshold value is halved successively. It can be divided into four steps, initialization, splitting, refinement and threshold adjustment. In the first step, the first threshold value is estimated and LIC(i, j) is initialized to the indexes of all the nodes defined in Eq. (3) while LSC(i, j) is initialized to null. In the splitting step, indexes will be moved from LIC(i, j) to LSC(i, j) according to the significance of the corresponding coefficient. The significance flags for individual nodes and chains will be estimated and emitted. If S0(i, j) of a node is 1 then it will be followed by Sd(i, j) which judge whether splitting process continues for the current chain or not. If Sd(i, j)¼ 1 then there is one or more significant descendant need to be found. If S0(i, j) is zero then it will not be followed by Sd(i, j) but splitting continues to check the descendant nodes. For example the significance flags stream {1, 1, 0, 0, 0, 1, 0} indicates that the first and fifth components are significant while other components are insignificant including those component beyond the fifth one. Also, when S0(i, j)¼ 1 then the sign of corresponding coefficient is emitted. The same scheme is followed for chain significance identification by estimating P0(i) and Ps(i), if P0(i) is 1 it will be followed by Ps(i) which indicate whether to continue splitting for the next chains or not. By moving significant components to LSC(i, j), they will not be checked for significantly in the next levels rather than their relevant bits are emitted in the refinement step. Doing so will results in less and less number of flags bits as encoding process proceeds. In the threshold adjustment step, the threshold is halved and the splitting step is repeated till all components are moved to the list of significant components or a certain threshold is reached. The algorithm can be illustrated in the following descriptive steps:

Step (1): Initialization 1.1 Get or calculate H0 1.2 Calculate the number of harmonics in each chain according to MDCT block size Nh(i) 1.3 Set NIC(i) to Nh(i) and NSC(i) to zero for all chains 1.4 Set LIC(i, j) to all indexes of MDCT coefficients corresponding to Node(i, j) defined from Eq. (3) and initialize LSC(i,k) to nothing, assuming all nodes are insignificant initially 1.5 Calculate the first power-of-two number greater than the maximum absolute coefficient and set threshold TH to half of this number Step (2): Splitting 2.1 For each i in the H0 chains do: 2.1.1 Calculate P0(i) and emit it 2.1.2 If P0(i)¼ 0 then consider next i, else continue as below 2.1.3 For each j in NIC(i) do: 2.1.3.1 Calculate S0(i, j) and emit it 2.1.3.2 If S0(i, j)¼1 then: emit the sign of Node(i, j) move the index of Node(i, j) from LIC(i, j) to LSC(i, j) update both NIC(i) and NSC(i) accordingly 2.1.3.3 Calculate Sd(i, j) and emit it only when j is less than NIC(i) 2.1.3.4 If Sd(i, j)¼ 0 then exit j-loop 2.1.5 Calculate Ps(i) and emit it only when i is less than H0 2.1.6 If Ps(i)¼ 0 then exit i-loop Step (3) Refinement 3.1 For each index in LSC(i, k) found in previous level(s), send the relevant bit of the absolute value of the coefficients Step (4) Threshold Adjustment 4.1 Update threshold level, TH ¼TH/2 and go to Step (2) until TH is less than or equal to a specific small value or all components are identified as significant.

The encoding process can be stopped at any level and the coefficient can be reconstructed at accuracy proportional to the deepness of thresholding level. It is worth mentioning that the arrangement of chains in descending form will enhance compression efficiency by reducing the number of bits required to indicate chains significantly in the first few encoding steps. For that reason, the first node is selected as the identified fundamental component. For the same reason, it is not surprising that the compression ratio will be better if the higher harmonics are decreasing or diminishing progressively. In the decoder side, the algorithm can easily be reversed to obtain MDCT coefficients from the embedded information in the bit stream. It should be noted that when the signal to be encoded is noisy, there will be small MDCT coefficients spreading through the transform which may degrade compression efficiency due to position and level encoding. To overcome this problem, encoding can be stopped when threshold attains small value such as 2 when the MDCT coefficients are represented by sufficiently large numbers. This will dramatically increase compression ratio while leaving very small effect on the accuracy of the decoded signal. 3.3. The MDCT–EHCC algorithm Vibration signals are divided into 256-points blocks for transform coding by MDCT with 50% overlapping. The small amplitude signals may be adjusted to larger values before MDCT to ensure good transform accuracy. H0 can be read from the host based on previous knowledge of machine specifications. If the machine parameters are not yet known or when analyzing non-stationary signals, such as during machine run-up and coast-down tests,

Please cite this article as: Alsalaet JK, Ali AA. Data compression in wireless sensors network using MDCT and embedded harmonic coding. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2014.11.023i

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optimum H0 can be obtained from variable length pattern comparison scheme. The resulting MDCT coefficients are encoded by using EHCC algorithm and progressively sent to the host which can interrupt encoding process upon some condition. For example, when network congestion is encountered, the host can terminate encoding process for some wireless nodes early. Similar action may be taken by the host for those wireless nodes with low battery condition to extend their operating lifetime.

4.1. The effect of optimum H0 To investigate the effect of choosing the optimum value of H0, vibration data of severe misalignment problem was captured at 1024 Sample/s from Machinery Vibration Simulator (MVS-1) by tailor made wireless nodes as shown in Fig. 3. MDCT is applied to compress time signal by dividing it into a number of 50% overlapped blocks of size 256 samples. The first local maximum component index is 20 and there are four harmonics as can be seen in the MDCT plot in Fig. 4. The variable length pattern comparison is applied to find the optimum harmonic interval which was 20. The encoding algorithm is repeated at different values of H0 starting from 14 to 26 and the compression ratio, defined in Eq. (6) is calculated at various quantization steps q. original data size compressed size

that increasing H0 beyond its optimum value has less harmful effect than decreasing it in general. This is due to the fact that decreasing H0 will produce fewer chains with more number of harmonics and hence, the effect of disharmony will be relevant. Another useful observation from Table 1 is that increasing quantization step q reveals the effect of optimum H0 selection due to the fact that more zero components will be encountered in the higher frequency bands and higher chain orders resulting in more compact bit stream. 4.2. Efficiency of the proposed scheme

4. Results and discussion

CR ¼

5

ð6Þ

It has been found that the best compression ratio is obtained at H0 ¼20 as shown in Table 1. As H0 diverge from the optimum value, compression ratio decreases in general. Also, it is obvious from Table 1

To compare the performance of the MDCT–EHCC scheme with some other techniques, a mechanical looseness vibration problem was studied. The mechanical looseness was introduced in the bearing housing of the machinery vibration simulator MVS-1 in addition to attaching unbalance mass to the rotor to generate the 1  RPM and its multiples 2, 3, 4 and 5  RPM. Vibration signal of the free end support was sampled at 1024 Sample/s with total number of samples of 4096. The signal is segmented into blocks of 256-sample size for transformation. The resulting coefficients are quantized at different steps for each compression scheme to obtain higher compression ratios. To evaluate the accuracy of the compression techniques at different compression ratios, the Peak Signal to Noise Ratio, given in Eq. (7) is calculated after reconstruction of the compressed signal. Peak Value RMSE sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 1 N1  ∑ x  x^ i where RMSE ¼ Ns i ¼ 0 i

PSNR ¼ 20log 10

ð7Þ

where N is the total number of samples, x^ is the reconstructed signal and RMSE represents the Root Mean Square Error. So far, high PSNR indicates good compression accuracy or small distortion. To encode the quantized coefficients, EHCC and Huffman coding algorithms are applied. Huffman coding is a lossless, entropy encoding algorithm which can be considered optimum Table 1 Compression ratios for different harmonic interval and quantization steps. H0

Wireless Node

Main Station

14 16 18 19 20 21 22 24 26

Compression ratio q¼4

8

16

64

128

1.91 1.90 1.92 1.93 1.96 1.93 1.93 1.92 1.92

2.20 2.20 2.21 2.22 2.27 2.23 2.23 2.23 2.19

2.61 2.60 2.64 2.64 2.74 2.69 2.68 2.63 2.62

4.98 5.03 5.05 5.16 5.59 5.45 5.32 5.11 5.13

10.14 9.99 9.89 10.42 12.19 11.38 11.41 10.21 10.32

Fig. 3. Machinery vibration simulator.

Fig. 4. MDCT plot for mechanical looseness.

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Table 2 PSNR at different compression ratios. CR

MDCT–EHCC

MDCT [13]

MDCT–Huff

DCT–EHCC

DWT–Huff

2.0 4.0 6.0 8.0 10.0

63.98 40.74 35.06 32.14 29.98

63.74 39.53 32.42 26.74 24.39

51.13 35.67 31.67 27.74 25.14

60.34 39.01 33.43 29.70 27.01

38.91 29.21 24.24 20.14 17.01

only low frequency components. Most machinery faults excite high frequency vibration such as mechanical looseness, bearing defects gears problems and other problems. Moreover, it is impractical to over-sample a signal when the relevant frequency range is limited because over-sampling is redundant by itself. The compression efficiency of MDCT–EHCC is nearly independent on the frequency of the signal, hence, it is more suitable in general to compress machinery vibration signals. 4.3. Enhancement to wireless nodes

Table 3 Compression ratio and PRD at 2400 RPM. Vibration case

Unbalance Misalignment

MDCT–EHCC

EMD [2]

DWT-D4

CR

PRD%

CR

PRD%

CR

PRD%

16.25 11.07

2.95 3.74

15.87 5.30

2.95 3.74

3.82 3.20

2.95 3.74

Table 4 Streaming rate and Energy saving vs. compression ratio. CR

Max. streaming rate (KByte/s)

1.0 35 2.0 68 4.0 130 10.0 186

Transmission time Processing time Energy (ms) (ms) saving 468 248 131 58

0 47 48 48

0% 37% 62% 77%

for a stream of symbols with certain input probability distribution [9]. Five algorithms are studied; MDCT–EHCC, MDCT of [13], DCT– EHCC and DWT-Daubechies 4. To compare the PSNR of the selected schemes at a given compression ratio, the quantization level is adjusted for each scheme till the required CR is obtained. The obtained PSNRs for the selected compression ratios are shown in Table 2. It is clear that MDCT–EHCC has the highest PSNR at certain compression ratio as compared to other schemes. Application of EHCC to encode DCT coefficients also provide significant enhancement to the PSNR over Huffman encoding. The DWT has the lowest compression ratio due to its unsuitableness to represent high-frequency periodic patterns. Another test is conducted to compare the performance of the proposed scheme with that of Chan and Tse [2] and DWT technique. Two vibration problems are considered, unbalance and misalignment at rotation speed of 2400 RPM (40 Hz). The sequence length is 4096 samples at sampling rate of 1024 Sample/s. The Percentage Root Mean Square Difference (PRD) in time, employed by [2], is used as a criterion to measure the performance of the compression schemes. The PRD in time is defined in Eq. (8) and it is related to the inverse of PSNR. vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u u∑N  1 x  x^ 2 i i PRD ¼ t i ¼ 0N  1 2  100% ð8Þ ∑i ¼ 0 xi It can be concluded from Table 3 that the proposed algorithm has better compression ratio than the EMD and DWT for the same PRD in time for the unbalance problem. For the misalignment signal, the proposed method has much better compression ratio than the other schemes. This may be reasoned to the high frequency components contained in the misalignment signal which degrade the efficiency of EMD since it is based on downsampling. Despite the fact that EMD may perform better than the proposed algorithm for low frequency signal (when the dominant frequencies are much lower than the sampling rate, i.e. when the signal is over-sampled), it is seldom that vibration signals contain

An important advantage of the proposed scheme is its mathematical simplicity and suitability to the tiny resources of wireless nodes. A tailor made wireless node has been used to host the proposed data compression algorithm in order to investigate its effect on the performance of the node. This node employs nRF24L01þ wireless transceiver as the main wireless with current consumption of  11.5 mA at full power transmission state. The main processing and control unit is based on a LPC1343 Cortex-M3 microcontroller consuming about 12 mA at 36 MHz clock speed [24]. The maximum achievable link bandwidth of the node is 70 KByte/s when using 16-bit ADC accuracy to represent the sampled data. When data compression is employed, the useful bandwidth increment is found to be proportional to compression ratio. Furthermore, important battery energy saving is obtained because the processing time consumed by the microcontroller to compress the signals is lower than the time required by the transceiver to transmit the uncompressed signal. To investigate energy saving made, a misalignment vibration signal consisting of 16,384 samples is acquired from the MVS-1 and transmitted with different compression ratios. Table 4 shows the enhancement made to streaming rate and energy saving.

5. Conclusions An embedded coding scheme, based on exploiting harmonic redundancy in vibration signals and bit-stripping, has been proposed. The scheme can be applied to encode the MDCT or DCT coefficients efficiently in multi-precision embedded manner. The encoding process can be stopped at any encoding level to overcome some wireless networks problem such as congestion and low-battery conditions. The proposed method is proved to be more efficient in compressing vibration signals than other methods, such as Huffman coding and EMD, especially for signals with multiple harmonically-related components. Moreover, the proposed algorithm is fast and does not require a lot of program memory as compared to the Huffman coding algorithm. Therefore, it is more suitable for the tiny resources of wireless nodes. The scheme provides important enhancement to data streaming rate and energy saving especially for large compression ratios. References [1] Cao X, Chen J, Zhang Yan, Sun Y. Development of an integrated wireless sensor network micro-environmental monitoring system. (July). ISA Trans 2008;47(3):247–55. [2] Chan JC, Tse PW. A novel fast reliable data transmission algorithm for wireless machine health monitoring. IEEE Trans Reliab 2009;58(2). [3] Myong KJ, Lu J, Huo X, Vidakovic B, Chen D. Wavelet-based data reduction techniques for process fault detection. J Technometrics 2006;48(1):26–40. [4] Staszewski WJ. Wavelet based data compression and feature selection for vibration analysis. J Sound Vib 1998;211(5):735–60. [5] Liu S, Cheng L. Efficient data compression in wireless sensor networks for civil infrastructure health. In: Proceedings of the international workshop on wireless ad-hoc and sensor networks, New York City; 2006. [6] Maria I, Todorovska MI, Tzong YH. Representation and compression of structural vibration monitoring data using wavelets as a tool in data mining,

Please cite this article as: Alsalaet JK, Ali AA. Data compression in wireless sensors network using MDCT and embedded harmonic coding. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2014.11.023i

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Please cite this article as: Alsalaet JK, Ali AA. Data compression in wireless sensors network using MDCT and embedded harmonic coding. ISA Transactions (2014), http://dx.doi.org/10.1016/j.isatra.2014.11.023i