Rotating machine speed estimation using a vibration statistical approach

Nowadays, we are witnessing an awareness of the importance of preventative maintenance on production sites. Industrials want to implement condition monitoring and use reliable diagnostic techniques to anticipate any failure. In order to reach this objective, advanced signal processing tools need to be used, which generally require parallel and synchronous measurement of vibration and speed signals (via accelerometers and encoders, respectively). Unfortunately, in many cases, the industrial environment and the reduced footprint on the shaft make it impossible to install speed sensors. Moreover, the very high cost associated with this type of sensor acts as a brake on its implementation in condition monitoring systems. Therefore, the development of methodologies for reconstructing the instantaneous speed information of the machine using vibratory signals is required. This paper presents a new statistical approach in order to extract the instantaneous speed for rotating machines using only a vibration signal. The new method is implemented in two steps. The first step consists of filtering the initial data of a vibration spectrogram into a cloud of points characterised by (t_i, y_i), where t_i is the time and y_i is the corresponding frequency. The second step involves the clustering of this cloud based on the models of probabilistic mixture and, more precisely, the expectation-maximisation (EM) algorithm. In particular, we use the formalism of regression mixtures, taking into account a relatively slow evolution of the data over time and making it possible to extract the different spectral harmonics present in the vibration signal. The results obtained from simulated and industrial vibration signals prove the effectiveness of the method.