Denoising Process on Body Vibration Signals from Caterpillar Nodule Collector on the Soft Quality Bottom of the Sea

Regarding the diversity and complexity of the road conditions on the soft sediment seabed, in order to improve the driving control precision of the caterpillar nodule collector, this study, focusing on the noise disturbance of the nodule collector body, adopts the methods of wavelet packet decomposition algorithm and Hilbert-Huang transformation algorithm to reconstruct the nodule collector body vibration signals, which are targeted by HilberHuang transformation algorithm to reach IMF fraction in the process of Empirical Mode Decomposition. Therefore, through the Hilbert spectrum analysis of IMF component, IMF component power characteristics are achieved, the available IMF component is optioned to reconstruct signals and the disturbance of the noise is eliminated. Comparing to the approach of wavelet decomposition, Hilbert-Huang transformation’s analysis and algorithm of the collector body’s vibration signals’ reconstruction are more accurate, providing valid control parameter to control the drive of caterpillar nodule collector on the soft quality bottom of the sea more precisely.


INTRODUCTION
In the deep-sea mining system, caterpillar nodule collector is applied to collect polymetallic nodule, which, during its operation, is affected by coincident and complicated environmental factors, including wind, wave, sea current and submarine high-voltage, etc.Its performance in the fields of kinematics and dynamics is complex enough to bring immense challenge to the control system of the caterpillar nodule collector that runs on the soft sediment (Dai and Shao-Jun, 2009;Wang and Liu, 2004;Liu et al., 2003).
In the control system, the collected collector's vibration signals are unavoidably interrupted by noise.Furthermore, as the measured signals and the disturbing signals are non-stationary signals, it is a tough job to eliminate the noise by adopting the filtering method.For example, while using Fourier filtering method to filter the noise (Alsdorf, 1997), Gaussian noise as well as some important high-frequency information is destroyed; while using spline fitting method (Xian-Liang et al., 1996), though Gaussian noise is perfectly ceased, some invalid information will enter the control system.
This study mainly aims to apply the approaches of wavelet decomposition and Hilbert-Huang changes (Wei et al., 2010;Rai and Mohanty, 2007;Li et al., 2008;Dong et al., 2008a, b)  This study, concentrating on the significant importance of the accuracy of control system which ensures the possibility of the caterpillar nodule collector's on the soft quality bottom of the sea, has great academic value and perspective for wide application in construction.

INTRODUCTON OF WAVELET DECOMPOSITION THEORY
Wavelet packet: Consider Orthogonal wavelet basis's Filter coefficients as h (n) and g (n) respectively, in addition that criterion function φ (t) is changed into ω 0 (t) and wavelet function ψ (t) into ω 1 (t).Then, twoscale equations about scale function φ (t) and wavelet function ψ (t) are: H (ω) and G (ω) are the Fourier transformation for h (n) and g (n) respectively: Fourier transformation for two-scale equations is: A new space U l j is proposed as a united representation for scale space V j and a wavelet Space W j .Suppose that: Hence, multiple resolving power space's orthogonal decomposition V j-1 = V j ⊕ W j is able to be united by U I j 's decomposition: It is to define subspace U l j to be function ω 1 (t)'s closure space, but U 2l j is function ω 2l (t)'s closure space.Then ω l (t) is fit to the following two-scale equations: Wavelet packet {ω l (t)} is defined as a correspondent function set, including scale function ω 0 (t) = φ (t) and wavelet function ω 1 (t) = ψ (t).

INTRODUCTION OF HIBERT-HUANG CHANGES
The basic idea of EMD decomposition (Loutridis, 2004 The medium value of two envelop lines are marked as m 1 , the difference between X and m 1 is h 1 : If h 1 (t) satisfies IMF's condition, h 1 (t) is an IMF and h 1 (t) is the first component for X (t).• If h 1 can't satisfy IMF's definition, h 1 (t) is considered as original data, the repetition of the former procedure leads to: where, m 11 (t) is the average of the upper and lower envelope and then it's time to judge whether h 11 (t) satisfies IMF's definition.In case that satisfaction fails, the loop will be repeated k times to reach an answer h 1k (t) = h 1 (k-1) (t) -m 1k (t), which is enough to enable m 1k (t) to satisfy IMF's definition with a mark c 1 = h 1k .• The following result embodies by separating c 1 from data X: And then turn r 1 (t) into new original data and repeat the procedures above once and again.As a result, the second fraction c 2 is reached to satisfy IMF.The repeated loops come to: In order to determine the signal processing is no longer with IMF, IMF component is generally taken to end the loop.Now that it's harsh to have IMF components satisfy condition (2), width wave is supposed to be deleted in a physical sense.For this reason, condition (2) should follow more valid quantity criterion to make sure that every IMF is in width and frequency's physical sense.The standard is provided owing to Eq. ( 5): where, m 1k (t) : Medium envelop realized by algorithm of this looping of IMF components' extracting modules m 1 (k-1) (t) : Medium envelop in the last loop 0, …, T : All the time points that medium envelop line contains The ideal SD value should be between 0.2-0.3.Those two conditions above that satisfy IMF components not only lay foundations of the consequent Hibert changes, but also render every component meaningful in a physical sense.Not until r n (t) becomes a monotonic function that is impossible to be extracted to meet IMF components, the loop comes to an end.So the initial data is the sum of IMF components and the final remnant and expressed as follows:  When the Eq. ( 8), ( 9) and (10) are possible, the instantaneous envelop a i (t) and frequency ω i (t) will be reached: [ ( )] ( ) arctan ( ) Original signal X (t) is the real component for Eq. ( 11) after Hilbert transformation of every IMF components.

NODULE COLLETOR'S BODY VIBRATION SIGNAL RECONTRUCTION
The collected signals in experiments were caterpillar nodule collector's body vibration signals when it runs on the soft quality bottom of the sea.In the first Fig. 1, there were 500 mixed signal data about collector's body vibration, including the noise.In each process of decomposition, the nth frequency band of upper level j will be further divided into j+1's 2nth and 2n+1'Th frequency bands.Therefore, the frequency domain on k level will be divided into 0~fs/2k, fs/2k~2fs/2k,…, 2k-1 fs/2k~fs, among which fs has the highest frequency.
Based on the standard of coiflets4 wavelet packet, the decomposition of the signal in 3 levels will gain 8 wavelet packet in all, ranging from s (3, 0) ~s (3, 7) which are shown in the Table 1.
From the power characteristics of every frequency band and the percentage, wavelet packets s (3, 0), s (3, 1), s (3, 2), s (3, 4) with a wealth of wavelet packet feature information are regarded as distinctive wavelet packets, which are extracted and reconstructed and shown in Fig. 2.

Reconstruction of body vibration signals through hilbert-huang changes:
Body vibration signals are decomposed and IMF components from IMF1 to IMF9 are obtained and shown in Fig. 3.
IMF1~IMF9 represent the gradually adaptive development from the low-level IMF components (the high-frequency elements are major in number) to the high-level IMF components (the low-frequency elements are major in number), through the process, the frequency components of the caterpillar nodule collector's body vibration signals will be extracted from

;•
Chang and Lee, 2009; Jia-Qiang et al., 2008): Find signals' all local minimums and use line transect three times to string all the local maximum points and local minimum points to form upper and below envelope, which contain all the data points.

Fig. 2 :
Fig. 2: Wavelet packet decomposition reconstruction of collector's body vibration signals Wavelet decomposition reconstruction of collector's body vibration signals: Wavelet basis is a crucial element in wavelet transform.Reasonable option of wavelet means a lot to extract accurate signals and characteristics.Through the analysis of wavelet basis, it is known that Daubechies wavelet, Symlets wavelet and Coitlets wavelet are appropriate for vibration signal analysis of wavelet.Coiflets4 wavelet is chosen.Decompose signals with closure algorithm in K levels.In each process of decomposition, the nth frequency band of upper level j will be further divided into j+1's 2nth and 2n+1'Th frequency bands.Therefore, the frequency domain on k level will be divided into 0~fs/2k, fs/2k~2fs/2k,…, 2k-1 fs/2k~fs, among which fs has the highest frequency.Based on the standard of coiflets4 wavelet packet, the decomposition of the signal in 3 levels will gain 8 wavelet packet in all, ranging from s (3, 0) ~s (3, 7) which are shown in the Table1.From the power characteristics of every frequency band and the percentage, wavelet packets s (3, 0), s (3, 1), s (3, 2), s (3, 4) with a wealth of wavelet packet feature information are regarded as distinctive wavelet packets, which are extracted and reconstructed and shown in Fig.2.

Fig. 5 :
Fig. 5: IMF components' Hilbert spectrum of caterpillar nodule collector's body vibration signals The outcome of practical test notes that the major cause for the irregular waves of the collector's body vibration signals derives from diverse factors, consisting of wind, wave, current and high pressure of sea bottom etc, while it's running on the soft quality bottom of the sea.So the diesel's body vibration signals with noise are initially implemented EMD decomposition.Judging from the analysis of IMF components' Hilbert spectrum, such as illustrations in Fig. 4, it unveils that the power of collector's vibration signals is intensive on IMF1, IMF2, IMF3, IMF4, IMF9, so that except IMF5, IMF6, IMF7与IMF8, the rest of IMF components are about to be reconstructed for the purpose of getting collector's body vibration signals after denoising according to Fig. 5.The test for the real displacement during the process of collector's body vibration displays the fact that the reconstructed to deal with crawler-style set tub's vibration signals, in the meantime, those respectively received reconstructed signals and the practical vibration signals are compared and contrasted.It is shown that reconstructed vibration signals with Hilbert-Huang changes are more accurate.

Table 1 :
The band wavelet packet power percentage