Condition Monitoring of Rotating Machinery via Harmonic Subset Analysis

December 7th 2012

Simon Freijer-Poulsen Cloutier SID 3826890

Vibration Monitoring Explained

Existing Methodologies Described

Harmonic Subset Analysis (HSA) Defined

Algorithm (DS-MF) Defined

SHarD Filter

ChaFF Diagnostic

Experimental Results, Observations

Continued Development

Rotating components, such as bearings and gears, are some of the most common machine elements in existence.

These components suffer continuous wear. Condition monitoring is an important factor in limiting downtime and avoiding system breakdowns.

Source: Rexnord.com Source: Arrowgear.com Source: Scoobymods.com

Vibration Analysis is a well-studied and widely used method for monitoring the condition of rotating machinery.

Faults in rotating elements commonly manifest as cracks or chips on sliding surfaces. Impulses are created as parts slide across (and strike) the fault.

Impulses are created at a fixed rate relative to the machine‟s speed. This is a Characteristic Frequency.

The machine‟s characteristic frequency is thus 1.

Vibration Analysis is a well-studied and widely used method for monitoring the condition of rotating machinery.

When picked up by an accelerometer, they will appear as a peak in the frequency domain at that characteristic frequency x machine speed.

As a periodic signal, the fault will also generate Harmonic peaks, which appear at integer multiples of the base frequency.

Common Industrial Method: Extract statistical measures of signal energy. High signal energy equates to a faulty system.

Simple, fast and well-proven approach.

Kurtosis, RMS particularly popular. [1]

Multiple measures can be combined through simple fusion (fuzzy logic, normalised mean, etc.).

Output is nonspecific (Fault/No-Fault), and susceptible to interference.

A variety of theoretical solutions exist.

Pattern matching systems, such as Support Vector Machines, Neural Networks [2], or Particle Swarm Optimisation, are „taught‟ using sets of known-state data.

The Wavelet Transform can be applied to either signal enhancement or feature extraction [3].

Results are significantly more precise.

Individual faults can be identified.

Interference can be filtered out.

System requirements inhibit practical usage.

Pattern Matching Systems require a „training set‟ of data with known conditions.

They are also vulnerable to small changes.

The Wavelet transform‟s high computational costs present issues with real-time usage.

Most current methods tend to process the signal/spectrum as a singular whole.

HSA is ultimately a noise reduction algorithm

The frequencies of interest within a signal (Machine speed, Fault impulses) will generate spectral harmonics.

By extension, frequencies lacking harmonic behaviours can be considered irrelevant.

Evaluate Frequencies based on their harmonics rather than their amplitudes.

More direct measure of relevance.

Create a harmonic subset for each frequency. This is a vector of the spectral amplitudes at all integer multiples of the source frequency (harmonics). The Harmonic Subset of 35.2 Hz below will take the

amplitudes at [35.2, 70.4, 105.6, ..., 457.6, 492.8].

Each subset is evaluated to form a single relevance value, which replaces the base frequency‟s amplitude in analysis.

Subsets which correspond to impulses will be more energetic than those of noise or interference, leading to higher relevance values.

Shaft Speed: 25Hz

Low-Frequency Impulses are enhanced

High-Frequency Impulses are smeared

Decimated Spectrum – Model Fitting Monitor

Practical application of HSA.

Automated condition monitoring algorithm offering continuous speed tracking and fault detection with only a minimal knowledge of the target machine. Operating parameters are all static machine properties.

No training data or pre-prepared material is needed.

The system is intended for rapid deployment on machines whose design is known, but whose present condition is uncertain.

The algorithm consists of two main stages: SHarD Filtering applies the concept of HSA to perform

point-by-point de-noising of the signal. The result is removal of upwards of 99% of the spectrum while retaining the harmonics that mark system features.

ChaFF Diagnosis compares the decimated spectrum to lists of characteristic frequencies, and with this is able to rapidly determine the machine‟s speed as well as which faults, if any, are present within the system.

Operating Principles:

HSA is used as described above – Each frequency is assigned a harmonic subset, then that subset is evaluated using fuzzy fusion of several metrics to produce a relevance rating that is assigned to the original frequency.

The highest scoring frequencies are kept, and the rest are discarded.

The result is heavy filtering, with output sets as small as 1% of the original spectrum while retaining important harmonics at lower frequencies.

Spectral Harmonic Decimation Filter

Example: Machine speed is 25 Hz. Shaft harmonics are preserved even at the low end where individual frequencies appear weak.

Operating Principles: In a rotating system, the locations of spectral peaks are

fixed relative to the machine‟s speed. These relative positions are defined as characteristic frequencies (CFs)

Faults in rotating components have well-defined CFs.

These are often available from the manufacturer.

Ignoring amplitude, a spectrum can thus be described using CFs and harmonics.

The SHarD filter de-noises so aggressively that it is possible to perform model fitting between the position of peaks in the decimated spectrum and a CF-based model.

Operating Principles:

When preparing the algorithm, two lists of CFs are produced.

A Known set lists all CFs that are naturally produced by the machine and is used to establish the machine‟s speed by finding the closest fitting base frequency.

An Unknown set lists all CFs that are tied to component faults. Once the machine‟s speed is found, the degree of fit with each of these CFs indicates the presence of that particular fault.

The Spectrum is fit to the Known model to determine speed, and the unknown models to determine fault presence.

Model Fitting Metrics: Absolute Error: The difference between the

frequencies in the spectrum, and those in the known vector.

Clustering: The average distance from the candidate to each other candidate. This considers smearing effects.

Impulsiveness: Impulsive candidates are less likely to be the shaft and more likely to be faults.

Characteristic Frequency Fitting Diagnosis

Example: Machine speed is 35 Hz. A fault is present in the bearing‟s outer race (ORF).

Maximum Likelihood is found at 35.2 Hz.

Example: Machine speed is 35 Hz. A fault is present in the bearing‟s outer race (ORF).

Fitting Strength at 35.2 Hz is indicative of fault.

Experimental data collected from MFS.

Assorted bearing faults & machine speeds.

Accelerometer Data:

Signal Duration: 5sec

Sampling Rate: 12 kHz

DS-MF Parameters:

Speed Band: [5.0 50.0], Physical limits.

Search Band: [5.0 3.0E4], Full spectrum.

Filtering Percentage: 0.4%, 120 samples.

Slip Compensation: 1%, Standard value.

Harmonic Count: 3, Empirical

Speed Identification: 93.0%

Mean Harmonics Retained: 5.43

Fault Identification: 93.0%

Mean Harmonics Retained: 2.4

Success Rate (Speed & Fault): 89.3%

Mean Run Time: 8.3s

Computational Cost: 166%

Filtering retains useful quantities of harmonics.

Diagnosis with limited information is accurate.

Algorithm‟s computational cost is suitable for continuous operation.

Successful proof of concept.

Improve Harmonic Retention.

Current retention rates are mediocre.

Improve sensitivity to low-energy signals.

Current metrics selected for rapid calculation.

Augment with more complex metrics.

In-Depth testing with non-bearing machinery.

Gearboxes are a promising environment for DS-MF.

[1] A. Sadoughi, S. Tashakor, M. Ebrahimi, “Intelligent Diagnosis of Bearing Faults by Using Frequency and Time Aspects of Vibration Signal”, The 14th international conference on electrical engineering, ICEE 2006, Iran

[2] H. Henao et al., “Bearing Faults Detection by a Novel Condition Monitoring Scheme based on Statistical-Time Features and Neural Networks”, IEEE Transactions on Industrial Electronics, September 2012

[3] W.Yang, P.J. Tavner, M.R. Wilkinson, “Condition monitoring and fault diagnosis of a wind turbine synchronous generator drive train”, IET Renewable Power Generation, Vol.3 No.1, pp.1-11, December 2008