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Guo et al Detection of damaged wheat kernels ACTA ACUSTICA UNITED WITH ACUSTICA. Vol 102 2016, nance duration For further study in addition to the dis. criminant features used before the di erential spectrum. and the maxima in short time windows were used as dis. criminant features and the stepwise discriminant analysis. routine was exploited for selecting a small feature subset. Using a neural network 98 of undamaged wheat kernels. and 87 of insect damaged ones were correctly classi ed. In addition to high accuracy the new sorting method pro. vided celerity with a throughput of 40 wheat kernels s. On this basis a new adaptive time frequency analysis. and classi cation method using impact acoustics was pro. posed to separate three types of damaged wheat kernels. IDK pupal and scab from undamaged wheat kernels, 16 Discriminant features were extracted from the adap. tively segmented acoustic signal and were post processed Figure 1 Schematic of experimental apparatus. by principal component analysis PCA Using a lin, ear discriminant classi er these three types of damaged. By using the vibration feeder the wheat kernels were. wheat kernels were separated from undamaged ones with. channeled into a single le stream The freely falling. 96 82 and 94 accuracies respectively Furthermore, wheat kernels impacted the stainless steel and the impact. the algorithm presented adaptation capability to the time. acoustic signals were acquired and saved in the computer. frequency patterns of signals making it a more universal. method for grain kernel classi cation, In this report a new scheme based on EEMD using im 3 Signal processing.
pact acoustics is proposed for detection of IDK The dis. criminant features including the IMF kurtosis IMF form Traditional time frequency analysis methods such as the. factors IMF third order R nyi entropies and the mean of short time Fourier transform STFT Wigner Ville distri. the degree of stationarity are extracted as the inputs into bution WVD as well as the wavelet transform WT. a SVM classi er and the resultant detection accuracy is are not very suitable for processing non stationary and. measured non linear signals because of lack of self adaptive basis. functions Huang Shen and Long et al put forward a, 2 Experimental apparatus method the Hilbert Huang transform whose core is em. pirical mode decomposition EMD which is able to pro. Figure 1 shows the experimental apparatus for dropping cess the non stationary and non linear signals 17 How. wheat kernels onto an impact plate and collecting the im ever the problem of mode mixing cannot be avoided. pact acoustic signals The experimental apparatus includes which is the primary drawback of EMD. a vibration feeder an impact plate a microphone and a To overcome the problem of mode mixing in EMD a. computer equipped with a sound card The impact sounds new method called ensemble empirical mode decomposi. are a ected by the structural properties of the substrate To tion EEMD was proposed 18 EEMD is based on the. compare suitabilities of di erent substrates 2000 wheat local characteristic time scales of a signal and the sig. kernels were tested 700 on glass 700 on wood and 600 nal can be self adaptively decomposed into several IMFs. on stainless steel plates The di erences between uctua where each of the IMF components contains a di erent lo. tion properties of the signals from undamaged wheat ker cal characteristic time scale Unlike EMD the nite white. nels and IDK during the resonance decay process were noise which is uniformly full of the whole time frequency. larger when using stainless steel so the impact plate was plane is added to the signal by using EEMD Then the. determined to be a block of stainless steel The dimensions components of signals in di erent scales are automatically. Author s complimentary copy, were adjusted to maximize the resonance properties of the separated into appropriate scales of reference With su. impact plates which ultimately were set at approximately cient numbers of trials the white noise can be eliminated. 24 11 0 06 cm Then 600 wheat kernels including to achieve better decomposition results 18 Based on its. 300 undamaged wheat kernels and 300 IDK were used in capability for suppressing mode mixing EEMD is widely. the experiment To avoid the circumstance that the wheat used in the eld of fault diagnosis 19 20 and signal de. kernels bounce twice before leaving the impact plate the tection 21. incline angle was set 30 above the horizontal and the drop The EEMD algorithm can be described as follows. distance from the feeder to the impact plate was set at 1 Add a white noise series to the original signal to obtain. 50 cm through trial and error a general signal, The impact acoustic signals were collected by using. Xi t x t i t i 1 2 K 1,a condenser microphone SHURE BG 4 1 The micro. phone was connected to a computer equipped with a sound where x t represents the original signal i t is the ith. card MAYA44 sampling at 48 kHz with 18 bit resolu added white noise series and Xi t is the general signal. tion of the ith trial, ACTA ACUSTICA UNITED WITH ACUSTICA Guo et al Detection of damaged wheat kernels.
Vol 102 2016, Figure 2 Examples of impact acoustic signals from an undam. aged wheat kernel a and an IDK b, 2 Apply EMD to Xi t then each of the IMF components. cj i can be obtained where cj i represents the jth IMF. component of the ith trial, 3 Add a di erent white noise series i t to the original. signals and repeat steps 1 and 2 until K trials,4 Calculate the ensemble mean of K trials. cj t cj i t 2, Figure 3 EEMD of the signals from an undamaged wheat kernel.
j 1 2 m i 1 2 K where m is the number a and an IDK b. of IMF components,Author s complimentary copy, 5 Eventually the original signal x t can be represented. as peak values of the signals are quite variable so they are. not very useful for distinguishing IDK from undamaged. x t cj t rm t 3 wheat kernels However the signals of undamaged wheat. j 1 kernels typically have larger uctuation during the reso. nance decay process Relative to the signals of undamaged. where cj t represents the jth IMF component and wheat kernels the signals of IDK have more stable decay. rm t is the residue trends associated with the intrinsic characteristics and the. Generally the result of decomposition will be closer to the resonance e ects of their impacts on the steel plate. actual value if more trials are taken Usually K 100 Figure 3 demonstrates the EEMD of the signals from an. Typical impact acoustic signals from an undamaged undamaged wheat kernel and an IDK The main signal en. wheat kernel and an IDK are shown in Figure 2 Compared ergy exists in the rst several IMF components This char. with the signal from the IDK the signal from the undam acteristic indicates that the features should be extracted in. aged wheat kernel may have a larger peak value but the the rst several IMFs. Guo et al Detection of damaged wheat kernels ACTA ACUSTICA UNITED WITH ACUSTICA. Vol 102 2016, Figure 4 The mean and SD dot and error bars of IMF kurtosis Figure 5 The mean and SD of IMF form factors for 300 undam. for 300 undamaged wheat kernels and 300 IDK aged wheat kernels and 300 IDK. 4 Results Figure 5 shows the mean and SD of IMF form fac. tors for 300 undamaged wheat kernels and 300 IDK The. 4 1 Feature extraction by EEMD method change trends of the mean of IMF form factors for undam. aged kernels and IDK are generally similar The two types. In this paper 5000 data points were acquired for each im. of kernel can be distinguished because the mean of IMF. pact beginning 20 points before the maximum magnitude. form factors for undamaged wheat kernels are larger than. of the whole signal The IMF kurtosis IMF form factors. for IDK before the 9th IMF The rst 8 IMF form factors. IMF third order R nyi entropies as well as the mean of the. were extracted as discriminant features, degree of stationarity were extracted as the discriminant. features The details of feature extraction are as follows 4 1 3 The IMF third order R nyi entropy. 4 1 1 The IMF kurtosis For the jth IMF component cj j 1 2 m the IMF. R nyi entropy is, The kurtosis a dimensionless parameter re ects the distri. bution characteristics of signals For a discrete signal the N. IMF kurtosis can be expressed as R cj ln, Kurtcj 4 where is the order of R nyi entropy here 0 and.
k 1 1 For 1 with restriction of reaching 1 it reduces. to the Shannon entropy N is the number of data points. where cj k represents the kth data point of the jth IMF cj and Pcj k is the probability density. is the average of the jth IMF N is the number of data. points and cj is the standard deviation SD of the jth. IMF Figure 4 shows the mean and SD of IMF kurtosis Pcj k cj k cj k 7. for 300 undamaged wheat kernels and 300 IDK Before k 1. the 7th IMF component the mean of IMF kurtosis for un. where cj k is the kth data point of the jth IMF component. damaged wheat kernels are larger than for IDK However. Several empirical studies indicated that in addition to. there is little information in the last several IMF compo. Author s complimentary copy, appearing immune to the negative time frequency repre. nents The rst 6 IMF kurtosis components were extracted. sentation values that can invalidate the Shannon approach. for inclusion as discriminant features, the third order R nyi entropy seemed to measure signal. 4 1 2 The IMF form factors complexity 22 so the IMF third order R nyi entropies. Form factors re ect distributional characteristics of signals were computed for this report Figure 6 shows the mean. in the time domain For a discrete signal the IMF form and SD of IMF third order R nyi entropies for 300 un. factors are represented as damaged wheat kernels and 300 IDK The curves of the. two types present a general upward trend and it is evi. 1 N 2 dent that the mean of IMF third order R nyi entropies are. N k 1 cj k greater for IDK than for undamaged wheat kernels before. Kf c j N 5, the 7th IMF component Compared with the signals from. N k 1 cj k, undamaged wheat kernels the signals from IDK have a. where cj k represents the kth data point of the jth IMF and more stable decay trend Figure 2 therefore the relative. N is the number of data points complexities and the IMF third order R nyi entropies for. ACTA ACUSTICA UNITED WITH ACUSTICA Guo et al Detection of damaged wheat kernels. Vol 102 2016, where P is the Cauchy principal value and the analytic.
signal zj t is de ned as,zj t cj t iyj t aj t exp i j t 9. aj t cj t yj t,j t arctan yj t cj t,and the instantaneous frequency is de ned as. Applying the Hilbert transform to each IMF the original. Figure 6 The mean and SD of IMF third order R nyi entropies signal x t can be expressed as. for 300 undamaged wheat kernels and 300 IDK,x t aj t exp i j t. aj t exp i j t dt 11, Here the residue rm t is left out because it is either. a monotonic function or a constant Equation 11 also. enables us to represent the amplitude and the instanta. neous frequency as functions of time The frequency time. distribution of the amplitude is called Hilbert amplitude. spectrum H t or simply Hilbert spectrum De ne the,marginal spectrum h as.
h H t dt 12,then the mean marginal spectrum n is, where for a discrete signal N represents the number of. data points,The degree of stationarity is de ned as. DS 1 dt 14,For DS the higher the index value the more non. Author s complimentary copy, stationary is the process 17 Distributions of the degree. of stationarity from an undamaged wheat kernel and an. Figure 7 The degree of stationarity from an undamaged wheat IDK are shown in Figure 7 The degree of stationarity is. kernel a and an IDK b quite variable in di erent frequency ranges whether for the. undamaged wheat kernel or the IDK The degree of sta. tionarity for the undamaged wheat kernel tends to remain. IDK are larger This characteristic provides us with good. larger than for the IDK so we adopted the mean of the. detection features The rst 6 IMF third order R nyi en. degree of stationarity as one of the discriminant features. tropies were extracted as discriminant features, The mean values and SDs of the partial discriminant.
4 1 4 The mean of the degree of stationarity features of signals for randomly selected 300 undamaged. The Hilbert transform of the jth IMF cj t is wheat kernels and 300 IDK are shown in Table I for the. rst 4 IMF components c1 c4 of the kurtosis form fac. 1 cj tor and R nyi entropy as well as the mean of the degree. yj t P d 8 of stationarity The mean values and SDs from all features. Guo et al Detection of damaged wheat kernels ACTA ACUSTICA UNITED WITH ACUSTICA. Vol 102 2016, Figure 8 Scatter diagram of partial discriminant features from undamaged wheat kernels and IDK. Figure 9 Block diagram of the detection process,Author s complimentary copy. indicate that the extracted features enable good separation stationary signals and its suppression of mode mixing the. of di erences between the two types of wheat kernels Vi EEMD scheme was adopted Theoretically when the am. sual representations are presented in Figure 8 where the plitude of noise remains below a certain level the results. red marks and the green marks represent the feature values of decomposition will be closer to the actual value if more. amp 51 15 amp amp amp 5 amp amp amp 3 2 27 m9 mj27 2 0 amp 7 0 9 l 2 9 2 93m7 m 2 0 d 7427 l 0995 9 96 mj

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