# Algorithms Utilized for Creep Analysis in Torque Transducers for Wind Turbines
## 2 Creep Study
### Experimental Conditions
Therefore, the creep analysis is based on the least squares method with the use of polynomial and linear regression, whereby, in general, the nonlinear function is adjusted to the individual measuring points. For this purpose, both a linear function with two parameters, which represent the direction of the creep at each measurement point, and a third-degree polynomial function with three and four parameters were used. Third-degree polynomial functions, thanks to having saddle points, take into account the nonlinear effects of the time dependence of the signal. For measurement points under load, in most cases it is an increasing trend, but for measurement points without load, no clear trend can be distinguished. Further analysis of the line of best fit in the figure indicates that the scatter of the data about the line is not random but exhibits a definite trend. In order to adjust the parameters of a given nonlinear function, the measured values of the points and their estimated uncertainties are necessary. The combined standard uncertainty associated with a single measuring point is determined using eight contributions by the equation:  
\[u_{\text{TSM}}^{2}=\sum_{i=1}^{8}u_{i}^{2} \tag{1}\]  
where:  
\(u_{1}\)--standard uncertainty of calibration results of reference transducers when cubic fitting functions are used;  
\(u_{2}\)--standard uncertainty due to short-term creep of reference transducers;  
\(u_{3}\)--standard uncertainty associated with the long-term drift of reference transducers;  
\(u_{4}\)--standard uncertainty due to misalignment of the device under calibration;  
\(u_{5}\)--standard uncertainty associated with the resolution and stability of the indicating device (amplifier);  
\(u_{6}\)--standard uncertainty associated with using reference transducers in partial ranges;  
\(u_{7}\)--standard uncertainty due to stability of torque transmission on shafts;  
\(u_{8}\)--standard uncertainty due to the influence of the variation in temperature on reference transducers. Figure 3: The measurement of torque at selective points in time from a level of 2000 N-m to zero: dependence on the time of the measurement cycle; the left side with the series of sixteen points of signal (upper part) for 2000 N-m of torque (and the right side with the series of sixteen points of signal for zero torque (lower part). The blue dots represent the measured data. In addition, a single measurement point at a given moment of time in general is determined by a total of 13 uncorrelated corrections, 8 of which are directly related to the standard measurement uncertainty of the torque generation. The measurement points in a successive moments of time do not indicate the same value of the signal from the transducer. The final values of the signal after the equilibrium state has been established do not represent the measured value either. It is a time relationship \(y=f(t)\) that reflects a measurement that is entirely a stochastic process, and therefore the use of standard methods will be insufficient to determine the average value of the measured level. For example, to determine the uncertainty value of the time-dependent signal measurement, the deviation is often called Allan's deviation, or square root of Allan's variance, which is not used in stationary systems where the time dependence is no longer important. In this case, the assumption about the stationarity of the signal measurement process is doomed to be unreliable. In order to determine the characteristics of the torque converter, it is necessary to determine the average signal level \(y\) from the transducer measured at preset intervals. This signal is subject to so-called creep, changing its value at each sampled moment of time. In Figure 4a, a sample relationship of the signal as a function of time is presented, \(y(t)\), including the expanded uncertainty of the coverage corridor, which is also a function of time in general, \(U(t)\).