In this paper, two new sinusoidal signal frequency estimators calculated on the basis of four equally spaced signal samples are presented. These estimators are called four-point estimators. Simulation and experimental research consisting in signal frequency estimation using the invented estimators have been carried out. Simulation has also been performed for frequency tracking. The simulation research was carried out applying the MathCAD computer program that determined samples of a sinusoidal signal disturbed by Gaussian noise. In the experimental research, sinusoidal signal samples were obtained by means of a National Instruments PCI-6024E data acquisition card and an Agilent 33220A function generator. On the basis of the collected samples, the values of four-point estimators invented by the authors and, for comparison, the values of three- and four-point estimators proposed by Vizireanu were determined. Next, estimation errors of the signal frequency were determined. It has been shown that the invented estimators can estimate a signal frequency with greater accuracy.
Focus of the vibration expert community shifts more and more towards diagnosing machines subjected to varying rotational speeds and loads. Such machines require order analysis for proper fault detection and identification. In many cases phase markers (tachometers, encoders, etc) are used to help performing the resampling of the vibration signals to remove the speed fluctuations and smearing from the spectrum (order tracking). However, not all machines have the facility to install speed tracking sensors, due to design or cost reasons, and the signal itself has to then be used to extract this information. This paper is focused on the problem of speed tracking in wind turbines, which represent typical situations for speed and load variation. The basic design of a wind turbine is presented. Two main types of speed control i.e. stall and pitch control are presented,. The authors have investigated two methods of speed tracking, using information from the signal (without relying on a speed signal). One method is based on extracting a reference signal to use as a tachometer, while the other is phase-based (phase demodulation). Both methods are presented and applied to the vibration data from real wind turbines. The results are compared with each other and with the actual speed data.
Condition monitoring of machines working under non-stationary operations is one of the most challenging problems in maintenance. A wind turbine is an example of such class of machines. One of effective approaches may be to identify operating conditions and investigate their influence on used diagnostic features. Commonly used methods based on measurement of electric current, rotational speed, power and other process variables require additional equipment (sensors, acquisition cards) and software. It is proposed to use advanced signal processing techniques for instantaneous shaft speed recovery from a vibration signal. It may be used instead of extra channels or in parallel as signal verification.