Results of the SE-EWT Algorithm

The results of this algorithm are based on the use of the SE to estimate the optimum scale index that gives the best estimation results, as discussed in Section 4.4. To show the functionality of this modified method, two examples of the estimation of the PPDs are demonstrated in Figure 42 and Figure 43. These figures show the estimated PPDs and Shannon entropy of wavelet coefficients (SEWCs) vs. scales in one plot. In both

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figures, the scale range was 1 to 100, where increasing the number of scales significant-ly increases the computational time of the WT.

The figures also explain the strategy of the employment of the SE to determine the PPDs, which is as follows. In the first, the SE is calculated for all WT coefficients, which results in SEWCs. In the second, the index of the minimum value of the SEWCs is selected, which represents the optimum scale index. Finally, the WT coefficients which correspond to this index are then selected and used in the estimation process by applying CC in conjunction with the curve fitting interpolation to these coefficients.

Figure 42: First example for using the SEWCs to select the optimum scale value (58) which delivers the PPD (20.59cm), where the actual PPD 21cm was.

In addition, the two examples illustrate the difference between the EWT-CC approach and the modified one. In the former, the PPDs were estimated at each scale value, repre-sented by the thick blue dots curves in both figures, and then the EWT-CC algorithm takes the average of these, whereas the latter only estimated the PPDs at the optimum scale value. In Figure 42, the estimated PPD using the modified method is 20.59cm while for multi-scale averaging it was around 22cm for the same example. Furthermore, in Figure 43, the SE-EWT delivered a value of 35.50cm in comparison to 36.82cm from the EWT-CC technique.

To conclude, both approaches provide almost the same results with respect to the actual PPDs which are 21cm and 36cm, and more examples are summarised in Table 9.

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ever, according to Table 7 the computational complexity of the EWT-CC method is higher than that of SE-EWT. This makes the latter approach more suitable to be em-ployed in wireless ASL applications if the time delays are intended to be extracted from the aliased versions of the acoustic signals captured at low sampling rates.

Figure 43: Second example for using the SEWCs to select the optimum scale value (59) which delivers the PPD (35.50cm), where the actual PPD 36cm was.

Table 9: Comparison between EWT-CC and SE-EWT algoritms.

Configuration of WU₁ WU₂ WU₃

PPDs (cm)

Estimated PPDs (cm) EWT-CC SE-EWT AVG STD AVG STD

P2 P2 P2

dm 00.00 1.12 0.80 1.00 0.78 dn 00.00 1.23 1.01 1.12 0.90

P₀ P₂ P₃

dm 15.00 15.19 2.60 14.99 3.01 dn 36.00 36.47 3.73 36.13 2.89

P1 P2 P3

dm 21.00 21.41 4.10 21.40 3.50 dn 15.00 15.62 4.50 15.03 3.91

105 4.7 Summary

Working with low sampling rates and localising a sound source using a centralised AWSN as well as from acoustic signals acquired at low sampling rates much below the Nyquist rate have been investigated. This includes the development of a new signal pro-cessing algorithm to be used for sound source localisation. The new technique has been implemented using an envelope-based wavelet transform cross-correlation (EWT-CC) in conjunction with a parabolic fit interpolation method. The intention of this technique is to globally extract the time delays from the aliased acoustic signals captured by the AWSN and received at a centralised collection point.

The proposed algorithm, offers a multi-resolution domain of analysis which shows po-tentially good performance in counteracting the ambiguity of peaks due to the low time resolution. The proposed approach enhances the spatial resolution of the localisation process in the following respects. Firstly, via the employment of the WT, it was possible to extract the characteristics hidden in the envelopes of the aliased versions looking for the closeness between them and the mother wavelet. Secondly, by applying the Shannon entropy, it was possible to select an optimum scale index that gives the best spatial reso-lution. Furthermore, the utilisation of curve-fitting interpolation enhances spatial resolu-tion by a factor of almost five based on the current setting of the developed wireless sys-tem. Finally, the use of the HEH mode in the MICAz platforms makes the data acquisi-tion operaacquisi-tion among acoustic wireless units more synchronised.

The approaches presented are proposed for the centralisation of data processing, which means that the individual wireless units are required to send the raw data to the central unit to be processed and analysed. This was performed for global off-line data pro-cessing, which still can overload the data transmission over WSNs if continuous online monitoring is involved. Therefore, the use of wireless sensing systems is obviously re-quired, which involves approaches for decentralised data processing in order to extract meaningful information or important features from content-based features with the use of low sampling rates. This provides the framework of the next chapter in conjunction with the implementation of a wireless in-situ SHM system on the top of WTBs for con-tinuous monitoring and further field study evaluations of the use of low sampling rates approach.

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