## 8 Calibration of Instrumentation for Aerodynamic Testing
### Instrument Calibration Using the Analyzed Algorithms  
Semiconductor-based piezoresistive MEMS pressure sensors exhibit inherent temperature dependence [69], requiring suitable temperature compensation in practice. Similarly to other types of sensors, there are also deviations from the ideal linear model, including offset, \(\beta^{i}\), gain, \(\alpha^{i}\), and nonlinearity, \(v^{i}_{\text{r}}\), which must also be minimized. The best results can be achieved by using digital signal-processing methods. In the case of the above-mentioned pressure scanner, we use a method based on a polynomial model, whose parameters are determined by _initial calibration_. In general, the initial calibration is performed by measuring the output signal values of all individual pressure-sensing elements at a multitude of different pressure and temperature values, distributed over the respective operating ranges of the instrument. The recorded values are then used to determine the mathematical model parameters for each of the sensing elements. Depending on the choice of model, this method minimizes the offset, the temperature drift of the offset and gain, and the sensor nonlinearity, resulting in measurement uncertainties lower than 0.1 % in a wide temperature range (see (1)). However, being connected to a fixed moment of time, the initial calibration cannot take into account internal or external time-varying changes of the instrument characteristics, which can lead to small drifts in offset and/or gain. In the most demanding applications, the influence of these drifts on the measurement performance can be significant, so that _re-calibration_ (after the initial calibration) has to be performed during operation. However, re-calibration in the classical sense, i.e., performed by applying a set of known pressure values, is not feasible during typical aerodynamic experiments, so that there is a need for a different approach, i.e., for blind calibration. The algorithms presented in this work are well suited for this purpose by the very definition of the adopted design methodology. There are two important additional aspects connected to the above-presented pressure-sensing instrument:  
(1) The instrument utilizes multisensor chips with several pressure-sensing elements instead of a general array of discrete pressure sensors; thus, it follows that there is an _inherent similarity between the monolithtically integrated pressure-sensing elements_ in terms of their characteristics, i.e., formally, the parameters \(\beta^{i}\), \(\alpha^{i}\), and nonlinear terms \(v^{i}_{\text{r}}\) in the sensor models (1) can be expected to be very close to each other for all \(i\). It follows then, in this case, that Remarks 5 and 10 (given above) can be applied, so that one can achieve a significant reduction in the influence of the nonlinearities to the entire calibration procedure. (2) Aerodynamic testing experiments are usually performed in such a way that there are time intervals, \(T_{k}\geq 10\) min, \(k=1,2,\ldots\) (typically after each consecutive measurement is taken), during which all the sensing elements are exposed to the _same slowly time-varying pressure signal_, \(x_{t}\). Consequently, the general real-time calibration strategy for the described instrument can be based on applying the developed algorithms regularly during each \(T_{k}\), \(k=1,2,\ldots\), eliminating any need for considering the difficult problem of constructing a spacial model for the signals in the general case (which itself requires complex offline computation). A static nonlinearity is included in a very general way in the parametric mathematical model of the pressure sensors, according to (1). Such a definition encompasses a very large range of nonlinear functions, under the only assumption that the nonlinear term is bounded. This nonlinearity is always reduced through the initial calibration (the measurement uncertainty is less than 0.1% before the application of the described blind calibration algorithms).