Soldadura

There are a significant number of alternative and more advanced signal processing and feature extraction methods that have been investigated for condition monitoring applications. Some of these techniques, such as the Wavelet transform, have received attention in machining process monitoring literature, but there are also many techniques used in other condition monitoring applications that are yet to be thoroughly tested on machining applications. Given the breadth of the field of signal processing, not all methods are reviewed in this chapter. Several methods reported in the literature have been summarised below.

Windowed Fourier Transform

When the spectral content of a signal changes with time, neither the time nor frequency domain features alone are sufficient to describe the signal properties.

The windowed Fourier transform method effectively divides a signal up into segments before Fourier analysis is applied, then giving information on how the spectral content varies with time. It makes the assumption that the signal is stationary in each segment. For a finite section of data this method is called the Short Time Fourier Transform (STFT). The limitation of this technique is the tradeoff between time resolution and frequency resolution; for smaller windows, the frequency resolution is decreased, whereas for larger windows, the time resolution is decreased. The STFT can be written as:

𝑋(𝜏, 𝜔) = ∫ 𝑥(𝑡)𝑤(𝑡 − 𝜏)𝑒−𝑗𝜔𝑡

∞ −∞

𝑑𝑡 ₍₆₎

where 𝑤(𝑡) is the window function.

Time-Frequency Analysis

Many time-frequency analysis methods are covered extensively by Cohen [97]. Popular methods for time-frequency analysis for machining applications include the Gabor transform, the Wigner-Ville distribution and the Choi-Williams distribution.

These methods have been particularly popular for acoustic emission sensor signals, such as that presented by Marinescu and Axinte in [91]. The authors developed a monitoring system for the milling process which used time-frequency approaches on an AE sensor signal. The sensor features were shown to indicate missing or damaged cutting edges on an indexable end mill. It was not clear whether these techniques offered any advantage over time or frequency domain data alone.

The Wavelet Transform

The wavelet transform has also been classed as time-scale analysis. Like the Fourier transform, wavelets can be classed as continuous or discrete.

Discrete wavelet transforms have been used for machining process monitoring applications, where the magnitude of wavelet coefficients in a specified frequency band have been used as signal features.

Li et al. [92] used the discrete wavelet transform for tool breakage monitoring in the drilling of steel. The system successfully detected drill breakage using AE and spindle power sensor data. The wavelet transform features were not compared to alternative time or frequency domain features, so it could not be concluded whether there was an advantage to applying this technique.

Cyclostationarity

A cyclic function is one where the function itself changes with respect to time. E.g. Fn(x), where n is the cyclic order of the function. A periodic function is one where the function generates a signal which contains oscillations, e.g. 𝑓(𝑡) = 𝑓(𝑡 + 𝜏), ∀𝜏, where τ is the period. The use of cyclostationary signal processing techniques allows signal features to take into account random effects produced periodically with the rotation of the system being monitored. The outputs of the various methods found in the literature allow the angular position and frequency content of periodic transient signals to be determined. Detailed reviews of analysing cyclostationary signals have been published by Antoni [98], [99].

Lamraoui [100] applies time domain, frequency domain and time-frequency domain (in this case, the STFT) analysis to accelerometer measurements from a milling process. The results are then compared to cyclostationary analysis techniques. Four different cyclostationary methods were covered; Wigner-Ville, spectral correlation, cyclic autocorrelation function and instantaneous autocorrelation function. Both chatter vibration and tool wear conditions were tested when full slotting an aluminium work piece with two and three flute solid carbide milling tools. Whilst the signal processing theory was comprehensive, it was not clear that the cyclostationary analysis provided any advantage, either in terms of computational cost or reliability, when compared to more familiar techniques such as time and frequency domain feature extraction.

Time Synchronous Averaging

Time Synchronous Averaging (TSA) is a signal processing technique commonly used when monitoring rotating machinery, such as gearboxes. The method allows periodic waveforms to be extracted from noisy data. The review paper by Bechhoefer and Kingsley [101] describes six methods of TSA and tests them on an accelerometer signal for fault detection in a gearbox. No application of TSA for machining process monitoring could be found.

Spectral Kurtosis

A method for using spectral kurtosis of vibration signals for fault detection in rotating machinery is presented by Antoni and Randall [102]. Both fault detection and fault identification methods were proposed. A faulty condition is shown to be detectable without the need for historical or non-faulty measurement data. The difference of the dB-spectrum from the vibration signal of non-faulty and faulty condition is comparable to the spectral kurtosis of the faulty signal on its own. The technique is reliant on the noise signal being Gaussian, therefore having a spectral kurtosis close to zero.