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Introduction
There are more and more opportunities for customers to request data collection and data analysis from manufacturing processes.
Even if you can collect data from the manufacturing floor, there are many ways to turn it into analytical results that help solve problems.
This time, we will focus on the downsampling of vibration data and introduce some of the preparatory processes for data analysis.
What is data preprocessing?
When analyzing the collected data, processing the data into a form that is easy to analyze by aligning the data format is called preprocessing.
Preprocessing of sensing data (data collected using sensors) mainly includes "downsampling", "joining division of data", "normalization", and "offset processing".
Among them, thinning out data by downsampling is the point.
Why data preprocessing is necessary
The vibration sensed by the analog vibration sensor changes continuously as time progresses. Sampling (sampling) this at regular intervals becomes digitized vibration data.
In order to collect the vibration data necessary for data analysis, it is necessary to sample at a sampling rate (sampling frequency) that is at least twice the maximum frequency required to capture features.
The higher the sampling rate, the larger the amount of data, which increases the analysis load.
actually thin out
It is necessary to apply an LPF (Low Pass Filter) as processing before thinning out the data.
Why is LPF necessary in advance?
This is because thinning without applying LPF changes the features required for data analysis.
Let's compare and verify the thinning results of "without LPF" and "with LPF" to see how it changes.
(1) Create a waveform that combines three frequencies
First, create a waveform that combines three frequencies.
Normal vibration data is the overlay of vibration data at different frequencies (sensed by a vibration sensor).
In this verification, we will use sine wave data with frequencies of 1 Hz, 3 Hz, and 14 Hz to make it easier to understand the changes in data characteristics (Fig. 1). The data below was verified at a sampling rate of 100 Hz.
(2) Check the frequency spectrum of the composite waveform
Synthesize the sine wave data of the above three frequencies (Fig. 2).
When we confirm the frequency components by applying FFT (Fast Fourier Transform) to the synthesized data, we can see that there are peaks in the frequencies of the three synthesized data (Fig. 3).
(3) Failure to perform LPF adversely affects analysis results
The amount of data is reduced to 1/5 by thinning so that one out of every five data is left (Fig. 4).
Here, the 100Hz sampling rate is decimated to 1/5, so it corresponds to data with a 20Hz sampling rate.
Notice the frequency peaks in the synthesized data in Figure 5.
If you check the frequency spectrum, you can see a component around 6Hz that corresponds to 14Hz, which cannot be expressed at a sampling rate of 20Hz after thinning.
This is called aliasing (aliasing noise).
The analysis results are affected because the 6 Hz vibration shows a frequency characteristic that should not exist.
④ Downsampling using anti-aliasing
An LPF that prevents aliasing is called an anti-aliasing filter.
What would happen if we used an anti-aliasing filter to decimate?
Checking the frequency spectrum in Fig. 7, the upper frequency limit of the data after thinning shown in orange is 10 Hz, and the peak at 14 Hz does not appear.
The aliasing at 6 Hz, which was visible when the data volume was simply thinned to 1/5 (Fig. 5), does not occur.
Antialiasing enables downsampling without aliasing altering the data characteristics.
Summary
This time, we introduced the points of data preprocessing, focusing on downsampling of vibration data.
point
・ To collect vibration data, sample at a sampling rate that is at least twice the highest frequency required.
・ Be sure to apply LPF as processing before data thinning
・ Aliasing occurs without LPF, which adversely affects analysis results
・ Antialiasing enables downsampling without being affected by aliasing.
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