Testing of Trend Detection Algorithm

Once the threshold values have been selected, the trend detection algorithm defined in Figure 6.6 can be tested. Using the threshold values in Table 6.1, the percentage of false alarms and missed detections is calculated over 5000 new samples of noisy data and are given in the Table 6.1. These noisy sam- ples are different from those used for creating the thresholds. For the ΔEGT and ΔWF measurement, there are a considerable number of missed detec- tions, if the threshold is selected to minimize false alarms. However, for the rotor speeds ΔN1 and ΔN2, we can obtain thresholds such that the false and missed detections are both zero. The high rotor speed ΔN2 turns out to be the best measurement to monitor for trend detection.

It should be noted that other measurements besides rotor speed might pro- vide an indication of engine distress for certain type of faults. In general, rotor speed shifts are small, and so the true signal-to-noise ratio would be different for different faults. The ΔEGT and ΔWF signals are then more likely to reflect engine health. In general, the establishment of detection thresholds is a trade-off between false alarms and missed detections. These thresholds can also be set or tuned by the end user or by some automated system based

0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 ∆N2 Threshold (C) 1.9 Missed detections False alarms 25 20 15 10 5 Alarms (% ) 0 FIGURE 6.12

Missed detections and false alarms for trend shift detection with varying values of thresh- old on ΔN2. (From Ganguli, R., and Dan, B., Journal of Engineering for Gas Turbine and Power 126(1):55–61, 2004. With permission.)

on historical data. Individual sensor signal-to-noise ratios will determine the achievable false alarm and missed detection ratio.

Finally, we point out that one of the benefits of the trend shift detection approach proposed in this chapter is that it will work regardless of whether the trend shift is from zero or from some other nonzero quasi-steady-state measurement value. This is because of the use of gradient information for edge detection.

It should also be pointed out that there are specific trend shift cases that the algorithm developed in this chapter alone would not detect. This includes intermittent shifts that the median filter would discard as outliers. It also includes gradual trend shifts that occur over several samples that the edge detector would not necessarily detect. The cascaded RM filter with edge detection is best suited for sharp trend shifts in gas path measurements.

6.9 Summary

Fast and effective trend shift detection requires filtering of the data for removing the high-frequency noise while preserving the sharp edges. Among nonlinear filters, cascaded recursive median filters, of increasing order, are found to have the capability of noise removal with accurate sig- nal feature preservation. They are also very fast converging; i.e., only one pass is required to obtain the accurate root signal, and are well suited for software and hardware implementations. For testing the filters, simulated faulty data, indicating the effect of the fault in the engine on ΔEGT, ΔWF, ΔN1, and ΔN2, are passed sequentially through a three-point RM filter and five-point RM filter. A substantial noise reduction of about 38% is found after a single pass. The task of trend shift detection is accomplished by using a combination of a gradient edge detector and a Laplacian edge detector. This combination is also found to be very effective. A suitable choice of thresh- old value for the gradient of the filtered data, along with the Laplacian edge detector used for cross-checking, can be chosen to minimize false alarms. For the particular faults and noise levels considered in this chapter, only the low and high rotor speeds were found to be able to give zero false alarms and zero missed alarms. In general, measurements with less noise are more suited to trend  detection. One of the benefits of the trend shift detection approach proposed in this chapter is that it will work regardless of whether the trend shift is from zero or from some other nonzero quasi-steady-state measurement value.

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7

Optimally Weighted Recursive

Median Filters

The previous chapters have showcased a number of signal processing approaches for gas turbine diagnostics. In general, the filters have become more complex and powerful from Chapter 2 to Chapter 6. The issue of non- Gaussian noise remains an important aspect for filters developed for fault detection. For example, Yoshida [71] points out that non-Gaussian noise occurs in health signals because damage tends to be concentrated in a spe- cific part of the structure. He used a Monte Carlo filter to address the issue of non-Gaussian noise in structural damage detection for structures following earthquakes. However, the computer time requirements for such a filtering method can be very large.

We have seen in the earlier chapters that median filters can be used to preprocess health signals before subjecting them to fault detection and isola- tion algorithms. There is a possibility of significantly enhancing the median filters for diagnostics preprocessing applications. Progressive improvements in advancing median type algorithms were made over the last decade. In Chapter 6, the use of recursive median filters was studied, and it was found that such filters have excellent noise removal properties. Comparing wavelets with recursive median filters for denoising frequency time series for improved operational diagnostics, it was found that wavelets provide greater levels of noise reduction, and recursive median filters provide good results and are much simpler to develop and implement. Moreover, the non- linear nature of the median type filters makes them useful for the removal of outliers [66, 67].

Figure  1.1 shows a schematic of a gas turbine diagnostics system. We address the noise removal function in this chapter. Noise removal enhances both the automated and human-driven actions for diagnostics. In this chapter, the weighted recursive median filter is introduced for diagnostics applications. The concept of determining the optimal weights for different types of health signals is explored. A comprehensive study of this filter struc- ture shows superior performance compared to the filters discussed earlier. The optimally weighted recursive median filters are the tools that can be of great use for denoising of signals before performing fault detection and iso- lation functions. This chapter is based on the research by Uday and Ganguli [72], who proposed the use of the optimally weighted recursive median filter for gas turbine diagnostics.