Penetration signal Analysis based on RLS Adaptive

International Journal of Engineering Science Invention Research & Development; Vol. II Issue IV October 2015 www.ijesird.com e-ISSN: 2349-6185 Penetration signal Analysis based on RLS Adaptive Wavelet Transformation Uday Kumar Rai1, Rajesh Mehra2, Rajesh Kumar3 Department of Electronics and Communication1,3, National Institute for Technical Teachers Training and Research, Sector -26, Chandigarh, 160019 1 2 3 Udayrai13@gmail.com, Rajeshmehra@yahoo.com, Rajeshrana1040@gmail.com Abstract — The hard target penetration process is very complex, it contains axial de-acceleration vibration and some weak interfering random signals. This is a non-stationary random vibrating signal. Although filtering method based on Hard threshold and Soft threshold method is effective on some extend, but it cannot completely remove the high-g acceleration signal components which is related to vibration and interference. As such this paper proposes a new method which analyzes the multivariate signal through Recursive Least Squares Adaptive Wavelet Transformation. Further with the similar signal and multivariate processing this paper compares the RLS Adaptive and Hard/Soft Threshold in Mat lab Simulation Software. simulation software. II BLOCK WAVELET ALGORITHM In terms of the type of the wavelet transform being used, the paper present the DWT based WTAF. D-WTAF could also be use for adaptive filtering in different time’s domains, the BeforeReconstruction structure that correspond to adaptive filtering in the scale-domain and the AfterReconstruction structure that correspond to adaptive Keywords— complex, random, soft threshold, hard threshold, filtering in the time-domain. In the sub band error RLS adaptive filtering, based D-WTAF, the error signal in each sub band is I. INTRODUCTION used as input to the LMS algorithm. In order to Based on the filtering method that exists, the speed up the calculation, this paper developed the paper present a method which uses the different block RLS based WTAF, that modifies the weights wavelet function to decompose noise. First the of the adaptive filter block-by-block instead of original measured signal is decompose by using sample-by-sample. We observe that the signal-towavelet function into low frequency and high noise ratio (SNR) was greatly increased by applying frequency signal. Then, the block adaptive filter these WTAFs. This makes a possibility of lower design selected for the Recursive Least Square sampling rate, and greatly improves the system algorithm allow the low frequency and high speed to meet faster testing requirements. A conventional block adaptive filter is depicted in frequency signal to pass through this filter model. The method by which the error signal is detected by Fig. 1. using Wavelet Transform’ Adaptive Filter (WTAF) [1] is known as Wavelet Transform Adaptive Signal processing. The adaptive filtering on the sub band signal which is obtained by wavelet decomposition and reconstruction is the application of WTAF. The Adaptive filtering technique provides good convergence and low computational complexity that can be easily adaptable to non-stationary signal as well. At the output the signal is reconstruct by using the filtered low frequency and the high frequency signal. In this paper, we choose similar penetration signal and RLS algorithm in mat lab Uday Kumar Rai, Rajesh Mehra and Rajesh Kumar u(n) Serial-toparallel converter Block FIR filter w parallel to serial convert Mechanism for performing block correlation mechanism f or sectioning serial to parallel e(n) convert er y(n) ∑ + d(n) Fig. 1 Conventional block adaptive filter ijesird , Vol. II (IV) October 2015/238 International Journal of Engineering Science Invention Research & Development; Vol. II Issue IV October 2015 www.ijesird.com e-ISSN: 2349-6185 The serial to parallel converter section the written in terms of the block time as follows incoming data sequence u(n) into L- block[1] which n = kL+i , i =0, 1, …, M-1 (2) is applied to an FIR filter of length M, one block at Let the input signal vector v(n) the same as a time. The adaptive filter tap weight is held fixed before. Then, at time n the output y(n) produced and the filtering is done block by block rather than by the filter in response to the input signal vector sample by sample as in standard LMS algorithm [2]. v(n) is defined by the inner product The Wavelet Transform (WT) processes both y(n) = wT (k)v(n) (3) stationary as well as non-stationary signal, thus the Equivalently, in light of (2) we may write WT is used to separate the signal into sub bands y(kL+i) = wT (k)v(kL+ i) , and is subsequently applied to block adaptive i=0, 1…M-1 (4) filtering algorithm. The Block Wavelet Transform Let Adaptive Filter [1]-[4] is shown in Fig. 2 d(n) = d(kL+i) (5) Denote the corresponding value of the desired response. An error signal e(n) is produced by comparing the filter output y(n) against the desired response d(n) , as shown in Figure 1, Block Wavelet Block u(n) y(n) FIR sectioning which is defined by Subband filter Coding e(n) = d(n)-y(n) (6 ) or equivalently, e(kL+i) = d(kL+ i) -y(kL+ i) (7) Thus, the error signal is permitted to vary at the d(n) e(n) sampling rate as in the standard LMS algorithm. Block ∑ The error signal is sectioned into L-point blocks in RLS a synchronous manner with v(n) and then used to + calculate the modification of the tap weights of the filter. For each block of data we have different values of the error signal to use in the adaptive Fig. 2 Block wavelet transform Adaptive Filter process. For the kth block, we define an average estimate of the gradient vector, as shown by[2] The input signal u (n) is processed by wavelet   (k) decomposition and reconstruction Filter banks, and Now using the optimum solution for Adaptive the sub band signal v(n) is obtained. The properly filter, we have the following update equation for the sectioned sub band vector input of v(n) is tap-weight vector of the block LMS algorithm subsequently processed by the Block FIR Filter w(k+1)=w(k)+µ∑i=0v(kL+i)e(kL+i) (9) [1], whose weights held fixed during the block. Where µ is the step-size parameter and the factor The estimated output y(n) is compared with the 1/L is absorbed into µ. desired signal d(n) to obtain the error signal e(n) . The Block LMS algorithm finally adjust the III HARD/SOFT THRESHOLD FILTERING weights of the block FIR filter based on the error signal e(n) , and the block FIR filter is now ready In the process of signal analysis and filtering hard to process the next sub band block. threshold and soft threshold are often mentioned Let k refer to block time, and w(k) denote the and are used for the purpose of filtering. The tap-weight vector of the filter for the kth block, as equation for hard threshold and soft threshold are shown by given as w(k) =[w0(k),w1(k),...,wM-1(k)]T , k = 0, 1.. (1) The index n is reserved for the original sample time, Uday Kumar Rai, Rajesh Mehra and Rajesh Kumar ijesird , Vol. II (IV) October 2015/239 International Journal of Engineering Science Invention Research & Development; Vol. II Issue IV October 2015 www.ijesird.com e-ISSN: 2349-6185 (10) d(n) e(n) and scale N=1 (11) scale N=2 Recursive least square algorithm y(n) x(n) f f w -t scale N=N Fig.4 RLS adaptive filtering based on a wavelet filtering -t t Fig.3 (a) hard threshold (b) Soft threshold From the given equation and the diagram, it is found that when the absolute value is smaller than the threshold value, it is set to zero. In hard threshold filtering it generate interrupt at some points such that we get poor continuity of wavelet coefficient and form oscillatory reconstructed signal. Whereas soft threshold constantly shrink boundary by comparing discontinuous points and prevent interruption, and the reconstruction of the signal become very smooth. Now the decomposed continuous wavelet coefficients are good. However if the coefficient of the decomposed wavelet is large, deviation could appear with the real coefficient resulting reconstruction error. The Adaptive filtering is also used to remove noise signal. The effect of its filtering depends on filtering algorithm [8]. During the filtering process it update and adjust the weighting coefficient for each sample of the input signal x(n) as per the algorithm used. We can obtain the Recursive least square error between the output sequence and the desired signal sequence. The diagram for the RLS adaptive filtering is shown in figure 4. Uday Kumar Rai, Rajesh Mehra and Rajesh Kumar The main determining factors for filtering in this model are: 1. Type of wavelet: Different type of wavelet show different decomposition. So paper used Daubechies 2 as mother wavelet which has the orthogonality, compactness and proximity with penetration [2]. 2. Wavelet decomposition layers: The number of layer to be used with Daubechies 2 [2] wavelet requires special analysis. Adoptive algorithm: There are many algorithms that determine the filtering effect of the high frequency coefficient of wavelet decomposed and the reconstructed signal after filtering. The paper uses the Recursive least square algorithm for verification. IV PROCESSING METHODS To verify the proposed adaptive filter model, the paper adopts the white noise signal that is similar to penetration signal and the simulation is done in mat lab. The paper uses Heursure soft threshold method, Sqtwolog hard threshold method and the proposed method. ijesird , Vol. II (IV) October 2015/240 International Journal of Engineering Science Invention Research & Development; Vol. II Issue IV October 2015 www.ijesird.com e-ISSN: 2349-6185 1st wavelet decompose Original signal 1 6 4 2 0 -2 Observed signal 1 500 1000 Original signal 2 0 500 1000 Observed signal 2 0 500 1000 Original signal 3 5 0 -5 500 1000 Original signal 4 0 500 1000 15 10 0 500 1000 Denoised signal 3 0 500 1000 Observed signal 4 500 5 0 -5 0 100 200 300 400 500 600 0 500 1000 Denoised signal 4 10 5 0 -5 0 25 20 5 0 -5 10 5 0 -5 8 6 4 2 0 -2 -4 30 0 500 1000 Denoised signal 2 0 500 1000 Observed signal 3 5 0 -5 0 35 4 2 0 -2 -4 -6 5 0 -5 2 0 -2 -4 45 40 8 6 4 2 0 -2 -4 8 6 4 2 0 -2 -4 0 Denoised signal 1 1000 second wavelet decompose 25 20 0 500 1000 15 10 Fig.5 Hard threshold De-noising 5 0 Original signal 1 Observed signal 1 10 5 0 6 4 2 0 0 500 1000 Original signal 2 0 500 1000 Observed signal 2 0 500 1000 Original signal 3 5 0 -5 0 500 1000 Observed signal 3 0 500 1000 Original signal 4 0 500 1000 0 500 1000 Denoised signal 2 500 1000 -25 0 100 200 300 400 500 600 Fig.7 db2 wavelet decomposition mse 400 0 500 1000 Denoised signal 4 350 300 8 6 4 2 0 -2 0 -20 0 500 1000 Denoised signal 3 0 500 1000 Observed signal 4 10 5 0 -5 8 6 4 2 0 -2 -4 -15 5 0 -5 5 0 -5 -5 -10 4 2 0 -2 -4 5 0 -5 2 0 -2 -4 Denoised signal 1 8 6 4 2 0 -2 250 0 500 1000 Fig.6 Soft threshold De-noising 200 150 100 50 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Fig.8 MSE Uday Kumar Rai, Rajesh Mehra and Rajesh Kumar ijesird , Vol. II (IV) October 2015/241 International Journal of Engineering Science Invention Research & Development; Vol. II Issue IV October 2015 www.ijesird.com e-ISSN: 2349-6185 [6] error estimates 25 20 [7] 15 [8] 10 5 Weile Yan, Chunling Du, Chee Khiang Pang, Multirate Adaptive Feedforward FIR Filter for Suppressing Disturbances to the Nyquist Frequency and Beyond, 2015 IEEE 978-1-4799-3633-5/15. Xiao-Ping Zhang and M.. Desai, Nonlinear Adaptive noise Suppression Based on Wavelet Transform, Proc. Of ICASSP 98, Seattle, Washington, May 12-15, 1998. Shashi Kant Sharma, Rajesh Mehra, LMS and RLS based Adaptive Filter Design for Different Signals, ICRTIET-2014 conference proceeding, 30th -31st Aug. 2014. 0 -5 Authors: -10 -15 -20 0 100 200 300 400 500 600 700 800 900 1000 Fig 9. Error Estimate V CONCLUSION Mr. Uday Kumar Rai: Mr. Uday is currently working as Senior Lecturer in Electronics & The fast and easy Computation make Wavelet communication Engineering Department at Sikkim RLS adaptive filter very attractive. RLS Adaptive Polytechnic (Center for Computer and filtering based on wavelet decomposition method Communication Technology), Chisopani in South not only provides good signal waveform but also Sikkim, India since 2003. He is pursuing his ME better signal to noise ratio (SNR) as compared to from ECE Department NITTTR, Chandigarh. He Hard/Soft Threshold method. has received his Bachelor of Engineering from NIT This method of filtering is done for non- Bhopal, Madhya Pradesh in the year 1993. Mr. stationary random vibrating signal with reference to Uday has 19 years of academic and industry high-g penetrating signal filtering. Since many experience. penetrating signal are relatively complex, more detail analysis are required, also the performance of this filtering may vary with different type of signal under consideration. Table SNR OF THREE FILTER METHOD Filtering Method SNR Hard Threshold 6.275 Soft Threshold 20.396 RLS adaptive decomposition 40.369 REFERENCES [1] [2] [3] [4] [5] Wensheng Huang, Wavelet Transform adaptive Signal Detection ,Raleigh 1999 pp47-51 Haifeng Zhao, Yan Guo, Ya Zhang, Shizhong Li, Penetration Signal Adaptive Cognitive Filtering model Based on Wavelet Analysis, Proc.2014IEEE 13th Int’l Conf.978-1-4799-6081-1/14. Jeena Joy, Salice Peter, Neetha John, Denoising Using Soft Thresholding, ,Int’l Journal Vol. 2, issue 3, March 2013. Milos Doroslovovacki and Hong Fan, Wavelet Based Adaptive Filtering, 1993 IEEE 0-7803-0946-4/93. Jinbiao Fan, Jing Zu, Yan Wang, Xu Peng, Triaxial Acceleration for Oblique Penetration of a Rigid Projectile into Concrete Target, 2008 IEEE 1-4244-1541-1/08. Uday Kumar Rai, Rajesh Mehra and Rajesh Kumar Dr. Rajesh Mehra: Dr. Mehra is currently associated with Electronics and Communication Engineering Department of National Institute of Technical Teachers’ Training & Research, Chandigarh, India since 1996. He has received his Doctor of Philosophy in Engineering and Technology from Panjab University, Chandigarh, India in 2015. Dr. Mehra received his Master of Engineering from Panjab Univeristy, Chandigarh, India in 2008 and Bachelor of Technology from NIT, Jalandhar, India in 1994. Dr. Mehra has 20 years of academic and industry experience. He has more than 250 papers in his credit which are published in refereed International Journals and Conferences. Dr. Mehra has 55 ME thesis in his credit. He has also authored one book on PLC & ijesird , Vol. II (IV) October 2015/242 International Journal of Engineering Science Invention Research & Development; Vol. II Issue IV October 2015 www.ijesird.com e-ISSN: 2349-6185 SCADA. His research areas are Advanced Digital Signal Processing, VLSI Design, FPGA System Design, Embedded System Design, and Wireless & Mobile Communication. Dr. Mehra is member of IEEE and ISTE. Er. Rajesh Kumar: Er. Rajesh is currently working as senior Lecturer in Electronics & Communication Engineering Department at MIT group Of Institutions, Hamirpur in Himachal Pradesh, India since 2012. He is pursuing his ME from ECE Department NITTTR, Chandigarh. He has received his Bachelor of Technology from IITT College Of engineering, Kalamb, Himachal Pradesh in the year 2006. Er. Rajesh has 9 years of academic and industry experience. He has about 4 papers under his credit which are published in international Journals & conferences. His Research areas are Advanced Digital Signal Processing &VLSI Design. Uday Kumar Rai, Rajesh Mehra and Rajesh Kumar ijesird , Vol. II (IV) October 2015/243