## 7 Results Interpretation  
### ANN Test Flow via Dedicated Virtual Instrumentation  
For a thorough verification of all the ANN calculations with a totally separated test flow, a dedicated National Instruments Virtual Instrument was built in LabVIEW. The virtual instrument (VI) diagram (detailed in Appendix D) illustrates how test data, individually or as a block (of 62 sets in our main use case, exercised in most other implementations, Sections 5.1-5.4 and 6.1), could be fed as an Input.csv file, together with the reference parameters computed from the statistic of the training data (184 sets in our main use case): the Means.csv and StdDev.csv files, as detailed in Appendix A.  
The implemented virtual instrument could be used for various ANN coefficient sets (weights and bias parameters) for more two-layer models with ReLU activation. Specifically, the versatility of this VI implementation is given by its scalability to changes in the dimensions of the two hidden layers that can have even different numbers of neurons/layers.  
Figure 20 shows four examples of the compact code (6.1) run with the corresponding virtual instrument (VI) test verifications.  
For this \"edge AI\" smart device presented in Section 6.1 (\"AI in a nutshell), the ANN verification is given in Table 3.  
As the optimization criterion was MAE, the mean of the absolute error, 0.01992755, was also considered relevant. Half of this value gives a relative precision of the estimation equal to 0.9963%. The interpretation of precision as relative to standard deviation is a matter of discussion; in this case, RMSE division should have been done not to 2\(\sigma\) but to larger intervals up to max-min. For such cases, the relative precision would be significantly better. However, spurious extreme values, erroneous measured values that happen to be outside the inputs' statistic (even if occurring once), can make the max-min difference a \"span\" that is useless as reference for the precision. Regarding such \"outliers\",  
Figure 19: LXDE (light-weight X11) directives, intranet ANN invoking, and Pe prediction publishing using a normal browser.  
Figure 20: Examples of the compact edge AI code run (black) with the corresponding virtual instrument (VI) test verification (grey) for un-normalized values.  
the MAE criterion is more robust (due to the squaring of the errors, the MSE was more distorted by spurious inputs).  
As seen in Figure 17, the 12 bit outputs of the ADC, between 0 and 4095 = 2\({}^{12}\) - 1 (for the converters' analog input range 0-3.3 V as detailed in Appendix E), were re-shifted by subtracting 2048 (half of the binary span). Re-scaling was not done by division to 2048 but to 4096 (written 4096.0, to switch the computing into real numbers). This means that, related to normalization, inputs should be allowed to be between \(-2\sigma\) and \(2\sigma\) and not only between \(\pm\)\(\sigma\). This compromise (the overlaying of the less probable greater inputs) only affected the MSB (most significant bit) of the digital input.  
Nevertheless, the greater time-constants in vehicular applications (particularly in diesel engine ECUs) allow for some over-sampling of inputs (even if analog channels are multiplexed to the input of a single ADC)--e.g., with a sampling frequency 2\({}^{\rm n}\) times greater than f\({}_{\rm Nyquist}\) (double the maximum frequency in the spectrum of the continuous signal), an effective number of bits, ENOB = n + the number of bits/sample at the ADC output, can be obtained if a moving average (with a 2\({}^{\rm n}\) broad window centered on each ADC output) can be computed.