# Algorithms Utilized for Creep Analysis in Torque Transducers for Wind Turbines
## 13 Conclusions  
Algorithmic approaches for analyzing creep study in measuring torque transducer were proposed. An algorithm of approximate polynomial fit-straight line, a polynomial of the third degree to a series of points determined at intervals, is presented. Fit parameters and an averaged corridor of uncertainty were determined. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type of Function \(\boldsymbol{\xi(t)}\)** & **Torque** & \(\boldsymbol{u(\theta_{1 min})}\) & \(\boldsymbol{u(\theta_{0 min})}\) & \(\boldsymbol{\rho_{\theta_{0}}}\boldsymbol{\theta_{1}}\) \\ \hline \(\xi(t)=t\) & 0 & \(1.4\times 10^{-5}\) mV/sV & 0.0012 mV/V & \(-1\) \\ \(\xi(t)=t\) & 2000 & \(3.5\times 10^{-5}\) mV/sV & 0.0013 mV/V & \(-1\) \\ \(\xi(t)=t^{3}+\beta_{1}t^{2}\) & 0 & \(1.3\times 10^{-10}\) mV/sV & 0.000 04 mV/V & \(-0.8\) \\ \(\xi(t)=t^{3}+\beta_{1}t^{2}\) & 2000 & \(2.4\times 10^{-9}\) mV/sV & 0.000 28 mV/V & \(-1\) \\ \(\xi(t)=t^{3}+\beta_{1}t^{2}+\beta_{2}t\) & 0 & \(2.5\times 10^{-10}\) mV/sV & 0.001 mV/V & \(-1\) \\ \(\xi(t)=t^{3}+\beta_{1}t^{2}+\beta_{2}t\) & 2000 & \(1.7\times 10^{-8}\) mV/sV & 0.001 mV/V & \(-1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The uncertainties of the estimated parameters of the straight line \(y=\theta_{1}\xi+\theta_{0}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Estimated Value** & **Estimated Value** & **Estimated Value** \\
**Type of** & **for 0 kN\(\cdot\)m** & **for 2000 N\(\cdot\)m** & **for Difference** \\
**Uncertainties** & \(\boldsymbol{u_{L}}\) & \(\boldsymbol{u_{H}}\) & \(\sqrt{\boldsymbol{u_{L}^{2}+u_{H}^{2}}}\) \\  & **(mV/V)** & **(mV/V)** & **(mV/V)** \\ \hline \(u_{EA}(y)\) & \(2.5\times 10^{-5}\) & \(8.4\times 10^{-5}\) & \(8.8\times 10^{-5}\) \\ \hline \(u_{R}(y)\) & \(2.89\times 10^{-5}\) & \(3.41\times 10^{-5}\) & \(4.45\times 10^{-5}\) \\ \hline \(u_{A}(y)\) & \(2.8\times 10^{-5}\) & \(2.42\times 10^{-4}\) & \(2.4\times 10^{-4}\) \\ \hline \(u_{p1}=\sqrt{<u_{p1}^{2}>_{t}}\) & \(1.34\times 10^{-4}\) & \(3.34\times 10^{-4}\) & \(3.6\times 10^{-4}\) \\ \hline \(u_{p2}=\sqrt{<u_{p2}^{2}>_{t}}\) & \(3.3\times 10^{-5}\) & \(4.5\times 10^{-4}\) & \(4.5\times 10^{-4}\) \\ \hline \(u_{p3}=\sqrt{<u_{p3}^{2}>_{t}}\) & \(5.8\times 10^{-5}\) & \(7.37\times 10^{-5}\) & \(9.4\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Estimator of standard deviation: the uncertainties of low and high levels. This article provides an analysis of the metrological properties of the creep process during the calibration of the torque transducer. The relative electrical signal (given in electrical units, mV/V) as a function of torque measured was monitored at intervals of time. To fit the data, the weighted method of least squares with both a straight line and a cubic spline curve was used to measure low and high levels of transducer in static measurement. To find the estimated measurand value at 2 kN\(\cdot\)m and 0 kN\(\cdot\)m, a few estimators of averages (arithmetical, middle spread, average of integral) have been applied, as well as for estimators of deviation like experimental deviation, Allan's spread, and the integral average of coverage corridor. In the results, we chose the appropriate estimators for the average of the signal and uncertainty, which are not typical statistical estimators. Due to the mechanical similarity of the tested 2 kN\(\cdot\)m torque transducer to the 5 MN\(\cdot\)m torque transducer, the proposed algorithms may be useful for optimizing the creep signal and its uncertainty for mechanically similar transducers. In conclusion, torque transducers are vital components in wind energy applications, enabling the measurement of torque data critical for power optimization and turbine performance analysis. Various parameters, including temperature, applied load, calibration frequency, and environmental factors, influence the creep behavior of these transducers. Understanding and considering these parameters allows for accurate and reliable measurements, ensuring the efficient and safe operation of wind turbines.