There is a wide range of signal processing methods in the field of machine condition monitoring, which are used in feature extraction and fault diagnosis. Derivation and integration are very common and important operations in vibration signal processing. Often, a signal that has been measured using an accelerometer is integrated to obtain a velocity or displacement signal. These commonly-used three signals and an infinite number of other signals can be obtained by means of fractional order derivation. Especially in challenging fault and process cases, signals whose order of derivation is a real or complex number could be clearly more sensitive to fault detection than the commonly-used signals. This paper discusses the application of complex order derivation to acceleration signals in order to detect various faults at an early stage.

Liquid steel is typically stirred in a vacuum tank using argon gas injection to achieve a homogeneous composition and high‐purity steel. The aim of this work is to study the effect of vessel vibration on the operational state monitoring of the gas stirring in a vacuum tank degasser. Following an extensive analysis of vibration features, the root mean square (RMS) of vertical velocity is found to be the best feature for the measurement of the stirring intensity caused by the volumetric gas injection rate into the ladle. Smoothing is conducted using a centered median filter with a window length of 21 s. In this work, the operational state monitoring of gas stirring is described using a ladle responsiveness value (LRV). This describes the ability of a ladle to generate the maximum amount of vibration with the minimum amount of argon gas. The LRV summarized for each ladle reveals significant differences between them. Correspondingly, a rolling ladle responsiveness value (rLRV) is used for online monitoring of possible gas leakages. The rLRV can also be used for the online monitoring of the stirring efficiency and as its comparison with the overall efficiency of a specific ladle or all ladles.

The regularity of the vibration signals measured from a rotating machine is often affected by the condition of the machine. The fractional order of regularity can be measured using the definition of Hölder continuity. In this paper, we review the connection between the pointwise Hölder regularity of a signal and its wavelet transform. We calculate the wavelet transform modulus of acceleration measurements from a test rig. The effects of different faults were recorded, such as unbalance, the coupling misalignment of a claw clutch, the absence of lubrication in a ball bearing, the absence of the bearing's cage, and their combinations. An analysis of the estimated isolated pointwise regularities from the wavelet transform modulus maxima ridges shows that the faults often cause irregularities in the signals and that their locations and frequencies can be used in diagnosing the faults. Coupling misalignment and the absence of lubrication in a ball bearing both cause impact-like vibrations, but these impacts have positive and negative regularities in the case of a coupling misalignment and mainly negative in the case of a dry bearing. Unbalance is best diagnosed from the integrals of the acceleration signals using traditional methods. In diagnosing the misalignment, bearing problems and simultaneous faults, the local regularity analysis outperforms the use of high order norms of differentiated acceleration measurements (i.e. jerk and snap signals). Using just three features (the number of local irregularities in an acceleration signal, their mean Hölder regularity and the arithmetic mean of the absolute values of a velocity signal), a quadratic classifier can be constructed whose estimated classification error is only 0.3 %.

Hot metal desulfurization is the main process step for removing sulfur in blast furnace‐based steelmaking. A desulfurization reagent is pneumatically injected into the hot metal through a submerged lance causing it to vibrate. The aim of this study is to develop a mechanical vibration measurement‐based method that can detect changes in the gas‐forming properties of the reagent. The detection is performed using Elastic Net regression and eXtreme Gradient Boosting‐based classification models the classification performance of which is compared. The lance aging causes changes in its dynamic characteristics, and the disturbing effect of this is removed from the measured data of the lance vibration prior to classification by means of a developed cleaning algorithm. The best classification performance in detecting changes in the gas‐forming properties, with an area under the receiver operating characteristic curve of 0.916 and Matthews correlation coefficient of 0.699, is achieved using an Elastic Net regression‐based classification model. The results of this work serve as a basis for developing industrial applications in which the effective utilization of the excitation, such as vibrations generated by the gas formation can be utilized for process monitoring and as a soft sensor for predicting the reagent‐induced process variance.

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