On the x-axis of the file in Figure 4.5 we can see the corresponding frequency of each vibration detected by the sensors. When referring to the occurrence of a repeating event it is convenient to do it in terms of multiples of running speed rather than absolute Hz. This is because of varying RPM values, which make the scale in frequency inconsistent for different files. So instead of indicating the specific frequency it is more advantageous for vibration analysis to know the frequency relative to the input speed. To achieve this, we convert frequencies into orders. It is
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beneficial to use orders for analysis of vibration signals, as they help with ignoring the noise of irrelevant rotating components.
If a vibration signal is equal to twice the input speed RPM from a thruster, then the order is two, with the first order being the input speed rotation value. By utilizing the orders we can track each individual component with more ease.
To obtain the orders we use Equation4.2. Remember, that frequency is the number of events per unit of time, so by multiplying with 60 seconds we discover the number of events per minute.
Order = Frequency (Hz) × 60
Input Speed (RPM). (4.1)
Accordingly for each individual frequency fi for i ∈ [1, 2622], which are all the data points, we use the RPM measurement for each file and calculate the new axis in orders. For example to acquire the order corresponding for an amplitude value with fi and input speed s we have
Orderi = fi × 60
s , (4.2)
where s is the input speed, for the respective file of 2622 data points, and is measure in RPM.
Figure 4.5 was used to calculate the orders for all 2662 data points. The converted x-axis, in orders, is visible in in Figure4.6. The input speed for this file was 600 RPM, thus using Equation 4.2we get a maximum order value of 100. Note that the amplitudes are still the same, essentially only the x-axis labels are different.
Figure 4.6: A spectra file after order normalization has been applied. After obtaining the orders it is easier to find peaks corresponding to the components of interest.
Figure 4.6 still seems quite complicated for analysis. The analysts focus on specific orders which correspond to parts of the thruster. Usually this would amount to approximately the first 40-50 orders.
To clarify the analysis of the data, we will inspect the first part of the file like the analysts and identify what the peaks correspond to. As shown in Figure4.7we examine the same file of Figure 4.6 but this time we focus on the first 30 orders. Specifically we noted a number of interesting peaks. Since we use the orders now at the first order we always have the peak at the running speed of the thruster.
Using units of orders, we can therefore find the source of each vibration in a more straightfor-ward manner. At the 8th order we can see the pole pass peak rising higher than the noise floor
CHAPTER 4. APPROACH
created by the rest of the peaks. The noise floor can be thought as the horizontal line set by the majority of the peaks, in this case ' 0.015 m/s2. The orders that correspond to different mechanical parts are known to the analysts and they are referred to as forcing frequencies [24].
As can be seen in Figure4.7, at the 16th order, the 1st harmonic of the pole pass frequency is visible. Harmonics are a series of evenly spaced peaks that are multiples of any forced frequency, and are common in periodic signals in vibration analysis. Locating all sets of harmonics is of great importance during the analysis process because they verify that an anomaly is present, if both the fault frequency and the 1st harmonic amplitudes are significantly high.
Figure 4.7: Analysing a file for the first 30 orders. Peaks are visible at 1st and 2nd order. These peaks correspond to the input speed of the thruster and its first harmonic. The peaks visible at 8th and 16th orders correspond to the pole pass frequency. This is considered a common pattern for the spectra files
4.2.1 Data Interpolation
As explained in chapter4.2the input speed of each file, measured in RPM, is utilized and thus the values for the orders are calculated. However, the thruster is operating at different speed values, when the sampling process takes place. The RPM values varies from file to file and this causes an inconsistency in the analysis of the files. An input speed of 600 RPM for the thruster will lead to maximum order of 100 as depicted in Figure4.8, while a file with input speed of 180 RPM leads to a maximum order of approximately 330, also shown in Figure4.9. This inconsistency is caused because the file in Figure4.9is spread across a broader scale of orders while the file of Figure4.8 is more compressed due to the higher thruster speed during sampling.
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Figure 4.8: A file with input speed of 600 RPM. Note that the spectrum is limited to 100 orders.
Figure 4.9: A file with input speed of 170 RPM. Notice how the scale for orders is extended to almost 350.
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Figure 4.10: Misalignment of spectra with varying input speed in RPM. The figure shows how a file with higher RPM value results in a more compact file. [36]
Figure 4.2.1 shows more clearly the effect of the fluctuating RPM on the order scale. On the x-axis we have the orders, the y-axis the amplitudes and z-axis showcases the RPM for the different files. Naturally, files with higher RPM values appear more condensed than than those with lower RPM. Again, it should be mentioned that the data points are still the same size for all files. Now, each measurement of the available 2622, corresponds to a different order.
This irregularity for the data is troublesome for the analysts. Since the current PCMS anomaly detection is based on comparing the latest data with the old, the analysts use files that are approximately of the same thruster speed for their analysis work. This is even more complicated if we take into consideration that the availability of data in a certain period can be low.
To solve this complication the data was interpolated to a limited range of orders with an explicit number of new data points ˆxi with i ∈ {1, . . . , 1600}. The number of resampled data points was made with respect to the desired precision, necessary for the analysis of the data. After consulting with the analysts in W¨artsil¨a and the current analysis technique, it was found that a precision of 3 data points for a range of 0.1 order is appropriate.
Therefore all files are cut off at the maximum of 50 orders and then interpolated with 1600 points. xk = x1, x2, . . . , x2622 → ˆxi = ˆx1, ˆx2, . . . , ˆx1600
The new frequency orders ˆfiare of a fixed range with a discrete set of values needed for analysis.
By implementing a limit of 50 orders and i ∈ {1, . . . , 1600} this leads to a step of approximately 0.03 order for each data point ˆxi.
This is a crucial part of the proposed solution as it solves the challenge of inconsistent data point frequency. Since we want to use an autoencoder to learn the relation between the data points, we need a fixed input space for training. However, the input speed for each file differs.
This causes the amplitude values for the first 50 orders, which are required for analysis, to be of different amounts. This effect proves problematic for the analysts, because in most instances the
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analysis has to be for files with almost the same input speed. This limitation is solved by using a NN.
4.2.2 Scaling the Data
Before the training of the NN we use two different scaling methods to scale the data. This is crucial when dealing with datasets containing varying values and ranges, like the one used for the current thesis project. In cases of data features expressed in great magnitude, in DL it is customary to scale the data before used for the models.
Minimum - Maximum Scaler
The Min-Max scaling method is considered the simplest scaler. This method rescales the data in such a way that all values are in the range [0, 1]. Function (4.4) provides the rescaled data points.
x0= xi− min(x)
max(x) − min(x), (4.4)
where x0 is the normalized values and x is the original value.
Robust Scaler
Robust scaler uses a similar approach to the Min-Max scaler. Instead of using the minimum and maximum vales of the data set, the robust scaler uses the interquartile ranges of the data, as noted by Function (4.5). Because the robust scaler is based on quartiles it is not strongly influenced large outliers.[5]
x0= xi− Q1(x)
Q3(x) − Q1(x) (4.5)
where x0 is the normalized values, x is the original value and Q1, Q3 are the first and third quartiles respectively. After experimenting with both scalers, robust scaler was found to provide slightly better results.