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The authors propose a novel procedure for enhancement of the signal to noise ratio in vibration data acquired from machines working in mining industry environment. Proposed method allows performing data-driven reduction of the deterministic, high energy, and low frequency components. Furthermore, it provides a way to enhance signal of interest. Procedure incorporates application of the time-frequency decomposition,

Local damage detection in rotating machines is one of the most frequent topics in condition monitoring literature. Generation of such signal is well recognized ([

One might conclude that almost everything was done to be able to diagnose damage. However, in the practical applications there are plenty of challenging cases that prove difficult for the classical methods. In this paper we will present an interesting case related to heavy duty gearbox operating in harsh environment. Based on this example, we propose novel, data-driven procedure for damage detection. An important fact is that there are two damage types (with different nature and localization). One of them is easy to notice directly from raw signal. However, the second one produces weak signature and is hardly detectable. We have started with most popular tools as spectral kurtosis–based filter and envelope analysis. Unfortunately, the results are not satisfactory. So it motivates us to search for alternative solutions. As mentioned, it is expected that signal of interest (SOI) will be impulsive. There are plenty of techniques in time series analysis that are focused on data with such behavior. One can easily notice increasing number of publications concerning application of heavy-tailed distributions towards vibration and sound signals [

It motivates us to test our recently developed tools related for

Iterative

The paper is organized as follows: Section

In this section we present the methodology useful in the problem of local damage detection based on the analysis of the vibration signal. We propose the approach based on the analysis of subsignals obtained in time-frequency representation (spectrogram) of given signal. Mentioned subsignals are analyzed using appropriate statistics (called selectors). Till now, the most popular statistic was kurtosis, one of the measures that can point out these frequency bins on time-frequency map that reveals the most impulsive nature. When the kurtosis is applied to the appropriate subsignals, then it is called the spectral kurtosis (SK), [

Thus the spectral kurtosis (SK) statistic for input signal

However for some real signals the spectral kurtosis does not give expected results because it can be sensitive for impulses not related to damage (i.e., artifacts). Therefore, as it was mentioned, there are other statistics considered that can be applied instead of the kurtosis; see [

In this paper we propose not to calculate simple statistic for set of subsignals obtained by decomposition of raw data by spectrogram but to describe each subsignal by stochastic model that has similar properties as appropriate time series. One of the easiest stochastic models is based on the assumption that the vector of observations contains realizations of independent identically distributed random variables. The most known distribution is the Gaussian one. However, the Gaussian distribution is not appropriate to modeling data with impulses, like for instance subsignals from time-frequency representation (spectrogram) related to damage. It is more convenient to take under consideration more general distribution, that is, such that it can be appropriate to describe subsignals corresponding to informative frequency band (IFB) and from noninformative frequency bands. Of course for those regions the parameters of the chosen distribution will be different. One of the possibilities is the

We provide short description of distribution parameters. Stability parameter

Here, we use parameters

Subsignals coming from bands with high energy should have significantly higher scale parameter. High energy in the spectrogram of the vibration signal from gearbox is connected with the deterministic component of the signal. Combining such information one can construct filter characteristic which will allow for deterministic component attenuation. Filter construction is as follows. Let us assume that estimated parameters

We define stoppage criterion as minimum value of the stability parameter of the signal in the time domain. This parameter indicates impulsivity of the data. The lower the value of this parameter, the higher the impulsivity. One of the other approaches would be to use kurtosis as indicator. However, it is not suggested as it can be easily affected by single impulses that are not related to the fault.

Filtered signal is now assumed to be input signal for the spectrogram and whole procedure restarts at calculation of the spectrogram with repeated filtrations until

Flowchart of the procedure.

To prove efficiency of the proposed methodology we will show results of application of data-driven filtration to real vibration data from complex mechanical system operating in mining industry (Figure

Investigated machine.

In Figure

Spectrogram of the signal (a), time waveform of the signal (b), and its envelope spectrum (c).

Filter characteristics based on the

This subsection contains results of application of spectral kurtosis to the vibration data measured on the gearbox casing and moreover it contains authors’ procedure of

In Figure

Using obtained filter characteristics one can perform filtration of the raw signal. The following figures contain filtered signals in different domains. In Figure

Time waveforms of

However, comparing envelope spectra (Figure

Envelope spectra of

It can be seen here in Figure

Spectrograms of

Further iterations of

In this subsection one can denote that it contains results for the single

As for the comparison to the

Spectrogram of the signal (a), time waveform of the signal (b), and its envelope spectrum (c).

Based on results from

Each of the filtrations is based on the

Stability parameter for each

In Figure

Spectrogram of the signal (a), time waveform of the signal (b), and its envelope spectrum (c).

Combining results obtained using iterative application of

Spectrogram of the signal (a), time waveform of the signal (b), and its envelope spectrum (c).

In the paper a novel procedure for SOI denoising is proposed. It is

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work is partially (A. Wyłomańska) supported by the Framework Programme for Research and Innovation Horizon 2020 under Grant Agreement no. 636834 (DISIRE, Integrated Process Control based on Distributed In Situ Sensors into Raw Material and Energy Feedstock).