Jakub Obuchowski

Stochastic Modeling of Time Series with Application to Local Damage Detection in Rotating Machinery

Raw vibration signals measured on the machine housing in industrial conditions are complex and can be modeled as an additive mixture of several processes (with different statistical properties) related to normal operation of machine, damage related to one (or more) of its part, some noise, etc. In the case of local damage in rotating machines, contribution of informative process related to damage is hidden in the raw signal so its detection is difficult. In this paper we propose to use the statistical modeling of vibration time series to identify these components. Building the model of raw signal may be ineffective. It is proposed to decompose signal into set of narrowband sub-signals using time-frequency representation. Next, it is proposed to model each sub-signal in the given frequency range and classify all signals using their statistical properties. We have used several parameters (called selectors because they will be used for selection of sub-signals from time-frequency map for further processing) for analysis of sub-signals. They have base in statistics theory and can be useful for example in testing of normality of data set (vibration time series from machine in good condition is close to Gaussian, damaged not). Results of such modeling will be used in the sub-signals classification procedure but also in defects detection. We illustrate effectiveness of novel technique using real data from heavy machinery system.

Impulsive Noise Cancellation Method for Copper Ore Crusher Vibration Signals Enhancement

In this paper, we deal with a problem of local damage detection in bearings in the presence of a high-energy impulsive noise. Such a problem was identified during diagnostics of bearings in raw materials crusher. Unfortunately, classical approaches cannot be applied due to the impulsive character of the noise. In this paper we propose, a procedure that cancels out impulsive noise rather than extracts signal of interest. The methodology is based on the regime switching model with two regimes: first corresponding to high-energy noncyclic impulses and second to the rest of the signal. We apply the proposed technique to a simulated signal as well as to the real one. Effectiveness of the method is presented graphically using time series, time-frequency spectrogram, and classical envelope analysis. The obtained results indicate efficiency of the method in impulsive noise cancellation and improve the ability to detect a damage.

Procedures for Decision Thresholds Finding in Maintenance Management of Belt Conveyor System – Statistical Modeling of Diagnostic Data

Belt conveyors are a key component in material transportation system in both opencast lignite mining and underground copper mines in Poland. Regardless of the structure of the mine, the problem of maintenance of belt conveyors is important (from the entire mining process point of view) for many reasons, such as: (a) conveyors are spatially distributed over a large area, (b) they create logically structured form of complex and heavy components, (c) they are operating in harsh mining environmental conditions, (d) failure of any belt conveyor might result in downtime of the entire production line or its major part. The paper discusses the issue of maintenance of gearboxes used in the conveyor drive systems. The authors have developed a CMMS-class system using GIS technology to support management of conveyors’ network. Its fundamental role is to make right decisions for the exchange of components of the drive systems or allow them to continue their work. Such defined problem requires determination of complex decision rules and the definition of appropriate thresholds of diagnostic parameters. The article presents the procedures for determining decision thresholds, based on statistical modeling of diagnostic data and multidimensional data clustering. By selection of suitable distribution of the data and appropriate statistical parameters, multidimensional data analysis has been performed to determine threshold values for the effective identification of the condition of machines and their components.

Recent Developments in Vibration Based Diagnostics of Gear and Bearings Used in Belt Conveyors

Local damage detection in bearings/gearboxes is one of the most intensively explored problems in condition monitoring literature. Also for mechanical systems used in mining industry this issue might be critical due to short time local overloading of surfaces in contact in gear-pair or bearings that often happens during operation. In general, the problem of local damage detection is well defined in literature, however, specific factors related to the mining industry, require adaptation of existing methods or even developing new approaches. In the paper, some of the most promising techniques with mining machinery context are briefly re-called. The key problems identified for mining machines are: operation under time-varying load/speed conditions, presence of time varying signal to noise ratio and non-Gaussian noise (impulses that appear incidentally, randomly, not with expected cycle or cyclically, however with different cycle related to another damage). All these situations motivated us to find novel solution. The paper might be considered as brief review of recent achievements in the field rather that comprehensive, holistic description of the problem.

Periodic Autoregressive Modeling of Vibration Time Series From Planetary Gearbox Used in Bucket Wheel Excavator

Vibration signals acquired from machines operating under non-stationary operations are difficult to process due to their time varying spectral content, statistical properties, signal to noise ratio etc. In case of damaged machine vibration analysis, the classical damage detection approach might be defined as informative and non-informative contents separation. It can be done in many ways, including model based approaches. One of the most known solutions for constant load/speed operations exploits autoregressive (AR) modeling of the deterministic high energy components that often mask the weak impulsive and stochastic part of the signal. After establishing the model, the residual signal is extracted and further analyzed. In the case presented here, AR modeling is considered inappropriate because of the variation of speed/load conditions. To illustrate importance of the problem and novelty of our approach, a planetary gearbox vibration will be analyzed. The gearbox operates in a bucket wheel excavator (heavy duty mining machine) subjected to cyclic load/speed variation due to the digging/excavating process. Due to periodicity of the excavation process, it seems appropriate to assume a periodic autoregressive (PAR) model for the deterministic high energy components. In the chapter several topics will be discussed: real data inspired motivation for PAR modeling, estimation details, simulations and PAR based inverse filtering for extraction of the informative stochastic part of the signal. Finally, we present some comparison of PAR and AR for modeling the deterministic high energy part.

Two-Stage Data Driven Filtering for Local Damage Detection in Presence of Time Varying Signal to Noise Ratio

Local damage detection in rotating machinery can become a very difficult issue due to time-varying load or presence of another damage reflected in amplitude modulation of the raw vibration signal. In this paper a two-stage filtering method is presented to deal with this problem. The first stage is based on autoregressive (AR) modeling. It is incorporated to suppress high-energy components that mask an informative signal. High-energy amplitudes of mesh harmonics modulated by other damage or load variation can affect selectors of optimal frequency band as well, so they have to be suppressed. The second stage relies on filtering the AR-residual signal using a linear filter based on an informative frequency band selector. Here as a selector we propose to use the average horizontal distance on quantile-quantile plot. We compare the result of the second stage with the spectral kurtosis. The procedure is illustrated by real data analysis of a two-stage gearbox used in a belt conveyor drive system in an open-pit mine.

Stochastic Modelling as a Tool for Seismic Signals Segmentation

In order to model nonstationary real-world processes one can find appropriate theoretical model with properties following the analyzed data. However in this case many trajectories of the analyzed process are required. Alternatively, one can extract parts of the signal that have homogenous structure via segmentation. The proper segmentation can lead to extraction of important features of analyzed phenomena that cannot be described without the segmentation. There is no one universal method that can be applied for all of the phenomena; thus novel methods should be invented for specific cases. They might address specific character of the signal in different domains (time, frequency, time-frequency, etc.). In this paper we propose two novel segmentation methods that take under consideration the stochastic properties of the analyzed signals in time domain. Our research is motivated by the analysis of vibration signals acquired in an underground mine. In such signals we observe seismic events which appear after the mining activity, like blasting, provoked relaxation of rock, and some unexpected events, like natural rock burst. The proposed segmentation procedures allow for extraction of such parts of the analyzed signals which are related to mentioned events.

Cyclic modulation spectrum — An online algorithm

Many profitable methods of damage detection in rotating machines involve cyclostationarity. This approach exploits the fact that vibrations of a damaged machinery possess a periodic envelope. The frequency related to this periodic behavior is strictly related to one of the characteristic frequencies associated with design and specific operation of the considered machine. Nowadays, such methods are rarely implemented in industrial condition monitoring systems for several reasons. One of the main reasons is related to computational complexity. Algorithms that calculate cyclostationary features are said to be computationally expensive, thus their involvement in monitoring systems is limited. This drawback becomes critical in online systems in which the monitored features are updated just after arrival of the next measurement. Because of complexity of cyclostationary approach other tools are preferred instead, especially those which do not require intensive computations. In this paper we discuss algorithms for calculation of a basic cyclostationary tool, namely cyclic modulation spectrum (CMS). In this paper we provide several novel algorithms that update CMS when new measurements arrive.

New Criteria for Adaptive Blind Deconvolution of Vibration Signals from Planetary Gearbox

In the paper performance of the adaptive blind deconvolution algorithm in application to a vibration signal with time-varying informative frequency band (IFB) is analyzed. The time-varying nature of the IFB might be caused by e.g. time-varying load or speed, time-varying signal-to-noise ratio (SNR), presence of other damages with distributed nature or time-varying transmission path, especially for source signals that propagate through a rolling element bearing or a planetary gearbox. Linear time-invariant filters cannot follow such phenomena, i.e. they might indicate too wide or too narrow frequency band as informative. Thus, the filtered signal contains too much noise or does not contain the whole information about the damage, respectively. Adaptive blind deconvolution is a time-varying filter which in each step tends to a filter that minimizes or maximizes given criterion of the deconvolved signal. In the classical version it maximizes kurtosis of the deconvolved signal, since high kurtosis (impulsiveness) is expected in the case of local damage. There exist also alternative measures that might provide equivalent results, or sometimes better in specific cases. Such combination of impulsiveness detection and ability of adaptation due to non-stationary operational conditions seems to be very promising. The methodology is illustrated by analysis of real data representing vibration acceleration of a heavy-duty rotating machinery (planetary gearbox used in bucket wheel excavator) operating in industrial conditions of an open-pit mine. The analyzed signal reveals strong dependency between time-varying load applied to the gearbox and properties of cyclic impulses related to damage.

Vibration Analysis of Copper Ore Crushers Used in Mineral Processing Plant—Problem of Bearings Damage Detection in Presence of Heavy Impulsive Noise

Vibration analysis of rolling element bearings (REB) used in copper ore crushers is discussed in the paper. The purpose of the analysis is to detect localized damage in REB. The problem of damage detection in REB is widely described in literature, in general. However, known techniques might be not successful in case of crushers due to presence of heavy non-Gaussian, impulsive noise. Impulsiveness of the signal from bearings is commonly used as an indicator of damage as well as a filter optimization criterion in order to enhance raw observation (to extract informative part—signal of interest (SOI)). A crusher is a kind of machine which use a metal surface to crumble materials into small fractional pieces. During this process, as well as during entering material stream into the crusher, a lot of impacts/shocks appear. They are present in vibration signal acquired from bearing’s housing. These non-periodic, strong impulses are non-informative from diagnostic point of view and should be removed from the raw signal before further processing, because they mask completely informative, cyclic impulses related to damaged part of REB. Unfortunately, impulsiveness cannot be basis for signal extraction anymore. So, commonly used kurtosis-based optimization of pre-filtering (kurtogram, spectral kurtosis) cannot be used here. Promising approach is to search for cyclic/periodic nature of impulses (envelope analysis, spectral correlation density, protrugram, etc.). However, as mentioned, even before enveloping there is also a need to pre-filter the signal. In the paper we will introduce the problem including description of the machine, investigation on structure of vibration and we will present preliminary results of vibration processing using protrugram approach. At the end, we will propose an enhancement of protrugram in order to identify cyclo-stationary signal in presence of randomly spaced impulses and narrowband amplitude modulation of discrete components.