# Demodulation of EM Telemetry Data Using Fuzzy Wavelet Neural Network with Logistic Response
## 4 Examples
### Comparison of the FWNN with BP Using Pseudo-Synthetic Data  
In general, artificial learning methods rely heavily on large amounts of training data that significantly creates the wide characteristic filter required for accurate prediction over a wide range of scenarios. Therefore, to work out the effectiveness of the FWNN method with real data, we adopted the complete data processing workflow with adaptive processing in removing ELF-EM band noise and demodulating generated pseudo-synthetic EMT data. Pseudo-synthetic EMT data was adopted to fill the void of cogent field data. The pseudo-synthetic EMT data were generated by means of combining binary phase shift key code modulation and actual field noise. Figure 13 shows a typical schematic diagram of the EMT/EM MWD signal processing workflow with signal code recovery. Electromagnetic telemetry data were acquired during a drilling operation in Sichuan province, China. The starting depth of the downhole transceiver was about 2000 m. A phase-shift-coded signal with a center frequency of 10 Hz and a shift frequency of 2 Hz was  
Figure 13: Full-stack EMT/EM MWD data processing workflow. transmitted from the insulating gap along the drill string, which was outside the borehole casing. The electrode array used in EM telemetry signal measurement is described in [12]. The voltage difference between dipoles (L1 to L10) was recorded using the DRU 45 system developed by the Institute of Geology and Geophysics, Chinese Academy of Sciences, at a sampling frequency of 2400 Hz. In this study, we considered the performance of the technique by considering only the field noise characteristics and convolving it with the generated binary phase shift signal. The amount of generated data set was 465, and all of them were of sizes 1275 \(\times\) 1. Moreover, these data were randomly divided into three sets. Specifically, 350 of these data were used as the training set, 65 as the validation set, and the remaining 50 were used for testing. Large parts of the initially generated data were included in the training set, increasing the total training data set to 720. Considering a sinusoidal carrier, if it is modulated by a bi-polar bitstream, its polarity will be reversed every time the bitstream changes polarity. This, for a sinewave, is equivalent to a phase reversal (shift), and the output is similar to the adopted BPSK signal. A binary phase shift signal was generated using a sample rate of 2400 Hz, signal frequencies of 10 Hz, and a period of 0.5 s. In assessing the effectiveness of the FWNN technique, the BPSK signal amplitude was varied between 0.05 and 0.0002 V to allow for an assessment of the technique under different signal-to-noise ratios (SNRs). Figures 14-16 show the variation in the adaptive processing result, with changes in the signal-to-noise ratio from 8.3 \(\times\) 10\({}^{-2}\) to 8.3 \(\times\) 10\({}^{-4}\) and the FWNN-recovered code. As observed in Figure 14, the adaptive processing result was excellent and easy to decode using the FWNN technique. However, as the SNR reduces, the effectiveness of the adaptive processing reduces, considering the same processing time for all the signals. However, the accuracy of the FWNN techniques remained constant, thereby retrieving the transmitted code effectively. The obtained results reiterate the effectiveness of the proposed workflow. Likewise, the above techniques do not require the spectral characteristics of EMT/EM MWD data in the real-time denoising and demodulation of the acquired data. Additionally, the inclusion of the FWNN in the coded signal recovery process reduces the pressure on adaptive processing in producing totally smoothly varying processed data. The above point, therefore, reduces the working time for coded signal recovery by eliminating the  
Figure 14: Description of a fuzzy wavelet neural network for EM MWD response demodulation with a logistic response. The generated signal signal-to-noise ratio is \(8.3\times 10^{-2}\).