## 8 Calibration of Instrumentation for Aerodynamic Testing
### Instrument Calibration Using the Analyzed Algorithms
In the case of silicon piezoresistive MEMS pressure sensors operating in air, i.e., without a separation membrane and oil filling (the type used in the described instrument), hysteresis is negligible, because single-crystal silicon can be considered to be an ideallyelastic material, up to the breaking point (the rupture of the sensor's diaphragm.) Therefore, the consideration of hysteresis and other memory effects in sensors is not needed in this case. As far as the piece-wise nonlinearities are concerned, they belong to the bounded nonlinearities, provided that A2 is satisfied. All the above-presented simulations are obtained by using nonlinearities composed of pieces of polynomials and exponential and trigonometric functions chosen at random (see Section 7). According to practice, the online real-time calibration of the instruments like the presented one is primarily concerned with offset corrections; gain corrections are less frequently needed. Keeping this in mind, we performed extensive simulations and experimenting in order to test the calibration algorithms presented in Section 3 under circumstances close to reality, encompassing the nonlinearity terms, \(v_{t}^{i}\), and measurement noises, \(\xi^{i}\); thus, we assumed that the communication noise can been neglected (since communications between sensors are mostly performed internally within the multichannel instruments themselves). Figure 11 presents the time evolution of the corrected offsets generated by the algorithm with reference \(f_{ref}^{1}=0\), implemented according to (4). The following conditions have been adopted: \(\|v_{t}^{i}\|+\|\xi_{t}^{i}\|<0.1\%\) of the full-scale approach (as mentioned above); \(\delta_{t}=1/(\mu+vt^{0.55})\) with \(\mu\) and \(\
u\) found by trial and error; sampling rate equal to 10 Hz; \(\gamma_{ij}\) chosen in such a way as to provide equal weights to all the nodes; network topology is chosen at random, according to A3. It is possible to note from the figure that the convergence to the predefined reference values is fast and accurate, with a very low variance. In addition, Figure 12 gives the evolution of the corrected gains obtained by the algorithm with reference presented in Section 4. It has been adopted that \(g_{ref}^{1}=1\), while the algorithm is implemented according to (16), with instrumental variables and \(\tau=2\). Convergence to the desired value is obvious. It must be emphasized that the computational effort required by the proposed calibration algorithm is minimal. In order to shed full light on this important aspect, we present in the following text the pseudo-code (Algorithm 1). for all the computations performed  
Figure 11: Time evolution of corrected offsets; algorithm with reference; multichannel pressure scanner. Different colors represent different node’s estimates. in one iteration of the algorithm. The hardware in which the algorithms are embedded is more than sufficient to meet the needs of the proposed algorithms. Both examples indicate that the consensus-based calibration methodology, using selected reference values, can be successfully applied to the developed multichannel instrument as a reliable real-time calibration tool.