Special issue: recent advances in acoustic black hole research
NIC Methodology: A probabilistic methodology for improved informative frequency band identification by utilizing the available healthy historical data under time-varying operating conditions

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Abstract

Effective incipient fault detection requires a method that can separate fault signatures under constant and time-varying operating conditions. In this work, we focus on improving informative frequency band identification methods for applications under constant and time-varying operating conditions. Many automatic band selection techniques exist and have proven effective under constant speed and load conditions. However, it has been shown that these techniques occasionally identify frequency bands that contain non-damage related information, especially under fluctuating operating conditions and at low damage levels. With this research, a new methodology is proposed which makes use of popular informative frequency band selection techniques, such as the Fast Kurtogram, to effectively identify damage under constant and fluctuating speed and load conditions. A key step in this methodology, the NICogram, requires healthy historical data, which is used to identify frequency bands that contain novel information in unclassified signals. The methodology uses multiple signals to identify whether a component is damaged or not through a probabilistic approach. It is shown that the method performs much better than the conventional informative frequency band identification methods on synthetic and experimental data.

Introduction

A vibration signal may contain much information related to the condition and health of a rotating machine and its subcomponents. The difficulty however, lies in separating and extracting the useful diagnostic information from the baseline healthy state and interfering noise. Dominant signal components and high noise levels which manifest in the vibration signal could make detecting the damage more difficult [1]. Therefore, the ability to autonomously extract the relevant signals and diagnose a machine’s health with non-invasive techniques during normal operation, has numerous benefits for condition-based maintenance (CBM). It allows for cost effective maintenance planning of scheduled downtime and reduces the risk of sudden significant failure [2].

Many fault diagnosis methodologies have been proven to be well-suited for stationary operating conditions, however, performing condition monitoring under time-varying operating conditions remains challenging [3]. Some investigations have been performed on data acquired under independently varying speed [1], [4], [5] and varying load [6], [7] conditions, but performing condition monitoring under simultaneously varying load and varying speed conditions still offers large scope for further research.

This article pays specific attention to informative frequency band (IFB) selection methodologies. The aim of an IFB method is to identify an optimal frequency band for fault detection that contains fault signatures while simultaneously filtering out any vibration components not related to the damage before computing the squared envelope spectrum [8]. Antoni and Randall [9] proposed the spectral kurtosis as a way of designing optimal filters for filtering out the mechanical signature of faults, which lead to the development of the Kurtogram. The Kurtogram is a two dimensional representation of the spectral kurtosis as a function of frequency and of spectral resolution. The maximum node of the Kurtogram provides the optimal parameters from which a band-pass filter can be designed, for instance as a precursor to envelope analysis. In a succeeding paper, Antoni [10] proposed a multirate filterbank as a solution for fast computation of the Kurtogram known as the Fast Kurtogram. The Fast Kurtogram identifies informative frequency bands based on their impulsivity, by calculating the kurtosis of multiple combinations of frequency bands, whereafter the frequency band with the highest kurtosis is used for further analysis.

The Fast Kurtogram paved the way for multiple other IFB methods based on unique features. These include the Sparsogram [11], [12], Enhanced Kurtogram [13], Infogram [14], Envelope Harmonic-to-Noise-Ratio (EHNR) method, referred to as the EHNRogram, [15] and the Autogram [16], all of which are used in this article and will be referred to in a general sense as the Grams. All of the Grams have been proven effective under constant operating conditions. Wang et al. [1] successfully used the Fast Kurtogram in unknown variable speed applications in an adaptive noise cancellation algorithm. However, the performance of the other Grams under fluctuating operating conditions is not well documented.

The conventional Grams also make no use of historical data, meaning that potentially valuable information is unused during the diagnostic process. Schmidt et al. [17] developed a pre-processing methodology that incorporates healthy data to identify frequency bands that contain significant novel information by using a model that was fitted on the Grams of historical reference data. Wang et al. [18] proposed using a spectral kurtosis ratio (SKR) between a single baseline signal from a healthy gearbox to that of an unclassified measured signal. A new SKRgram is constructed using this method by calculating the ratio between the baseline Fast Kurtogram and the unclassified Fast Kurtogram to highlight the presence of bearing damage in a planetary gearbox. This method was applied to both simulated and experimental data under constant speed and load applications and proved to be an effective damage detection method.

However, the aforementioned methods only focus on constant operating conditions and do not use a probabilistic approach. Hence, this article proposes a generalization of the SKRgram applicable to all Grams and incorporates a probabilistic approach to damage detection under varying operating conditions. Neither the SKRgram nor its extension, the NICogram, are probabilistic. However, the NIC methodology is probabilistic due to the fact that the NICogram is applied to many healthy signals. In summary, the following contributions are made:

  • A new Gram, the NICogram, which is a generalization of the SKRgram.

  • A new methodology, the NIC methodology, is proposed which is capable of identifying frequency bands that contain novel information under time-varying operating conditions.

  • The NIC methodology is investigated on datasets acquired under time-varying operating conditions where it is shown that it performs very well.

  • The NIC methodology uses multiple healthy signals to allow a probabilistic interpretation of the results as opposed to other methods.

The layout of the paper is as follows: In Section 2, the methodology is presented in detail, whereafter the model and experimental setup used to obtain data are presented in Section 3. The methodology is applied on numerical and experimental data in Section 4. Conclusions are drawn and recommendations are made in Section 5. Appendix A contains additional information related to the numerical gearbox model presented in Section 3 and Appendix B contains a motivation for the selection of a damage threshold.

Section snippets

Proposed novelty information criterion - NIC methodology

Data acquisition in a CBM plan generally occurs over a long period of time. During this time, machine components are assumed to go from a healthy state to some unknown damaged state with vibration samples captured at regular intervals. This means that healthy historical data is readily available which may offer valuable insights into the condition of the machine. A probabilistic approach for incipient fault detection can be used by incorporating all the healthy data samples into the diagnostic

Gearbox model and experimental setup

The analytical model used in this work is the phenomenological model developed by Abboud et al. [3]. Furthermore, an experimental setup is used to confirm the abilities of the methodology on real vibration signals.

NIC Methodology evaluation

To evaluate the proposed methodology, both phenomenological and experimental data are used. The phenomenological signal allows for the testing of many hypothetical scenarios without the expensive and time consuming procedure involved with collecting actual data. Then, once it has been shown that the proposed method is an effective approach, experimental data can be used to further validate its performance on signals that can be typically expected from industrial gearboxes.

Conclusion

In this article an automatic informative frequency band selection methodology is developed for applying envelope analysis under fluctuating operating conditions in the presence of strong noise and deterministic components. The proposed NIC methodology was designed and compared to the popular Gram approach that makes use of features such as kurtosis, negentropy, sparsity, amongst many others, to identify incipient bearing faults. The method requires no a priori information regarding the fault

CRediT authorship contribution statement

Willem N. Niehaus: Conceptualization, Methodology, Software, Writing - original draft. Stephan Schmidt: Supervision, Writing - review & editing. P. Stephan Heyns: Supervision, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors gratefully acknowledge the Eskom Power Plant Engineering Institute (EPPEI) for their financial support in the execution of this research.

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