Table of Contents

• 1  Introduction
• 2  Data Source
• 3  Plot Time Series Data
• 4  Analysis in the Time Domain
  • 4.1  Easy Calculations of Peak, RMS and Crest Factor
    • 4.1.1  Calculate for Pure Sine Wave
  • 4.2  Integration to Velocity & Displacement
    • 4.2.1  First Compare Simple Sine Wave
    • 4.2.2  Calculate for Bearing Data
  • 4.3  Plot Integrated Velocity & Displacement
  • 4.4  Calculating RMS of Velocity and Displacement
• 5  Analysis in the Frequency Domain
  • 5.1  FFT Function
  • 5.2  Compare FFT and PSD Results for Simple Sine Wave
  • 5.3  Compare FFT and PSD of Bearing Data
  • 5.4  FFT of Bearing Data
  • 5.5  Calculate PSD
    • 5.5.1  Peak from PSD
  • 5.6  Show How PSD Relates to RMS
  • 5.7  Calculate Velocity & Displacement from PSD
    • 5.7.1  PSD
    • 5.7.2  RMS from PSD
  • 5.8  Build Octave Spaced PSD
    • 5.8.1  Build Frequency Ranges
    • 5.8.2  Compare PSD of Linear and Log Spaced Bins
    • 5.8.3  Plot Cumulative RMS of Linear & Log Spaced PSDs
  • 5.9  Find RMS within Arbitrary Range
  • 5.10  Calculate Pseudo Velocity Shock Spectrum & Peak
• 6  Compare Stats
  • 6.1  Table
  • 6.2  Plot Each Variable with a Drop Down
  • 6.3  Plot All Stats in One Dashboard
• 7  Appendix
  • 7.1  Installation
    • 7.1.1  Modules
  • 7.2  Ploting in Jupyter
    • 7.2.1  Matplotlib
    • 7.2.2  Plotly (My Favorite)
      • 7.2.2.1  Save Plot to Chart Studio
      • 7.2.2.2  Save Plot as HTML and PNG
  • 7.3  Manipulating .MAT Files from Case Western into Pandas CSV

Introduction

The first section references where we got this data, and the second shows how to manipulate the source data into something Python likes better. This dataset was then loaded online for public acces. So you can skip these sections and jump straight to plotting the time series data (which will reload the now "cleaned" data).

Data Source

Data was downloaded from the Case Western Reserve Bearing Data Center where they did some seeded fault testing and shared the data. This data can be downloaded here. An overview of the procedure is here.

For simplicity we will look at 4 data files:

• Normal
• Fan End Fault, Inner Race
  • Fault_007
  • Fault_014
  • Fault_007

All of these were when the motor was running at approximately 1772 RPM. The numbers in the fault file names signify the fault diameter in thousands of an inch. For example Fault_014 is a fan end bearing fault in the inner race measuring 0.014" in diameter.

In the appendix I show you how to pull out the data of interest from the source .MAT files. But I've uploaded the processed data into a CSV file which can be loaded directly from online. So we can skip those earlier steps (but they've been included for reference).

import pandas as pd
df = pd.read_csv("https://info.endaq.com/hubfs/Plots/bearing_data.csv")
df = df.set_index('Time')
fs = len(df)/(df.index[-1]-df.index[0])
print(fs)
df

12000.0

	Fault_021	Fault_014	Fault_007	Normal
Time
0.000000	-0.105351	-0.074395	0.053116	0.046104
0.000083	0.132888	0.056365	0.116628	-0.037134
0.000167	-0.056535	0.201257	0.083654	-0.089496
0.000250	-0.193178	-0.024528	-0.026477	-0.084906
0.000333	0.064879	-0.072284	0.045319	-0.038594
...	...	...	...	...
9.999667	0.095754	0.145055	-0.098923	0.064254
9.999750	-0.123083	0.092263	-0.067573	0.070721
9.999833	-0.036508	-0.168120	0.005685	0.103265
9.999917	0.097006	-0.035898	0.093400	0.124335
10.000000	-0.008762	0.165846	0.130923	0.114947

120000 rows × 4 columns

Plot Time Series Data

First let's plot the full dataset but render it as a SVG because it is so big.

import plotly.express as px
fig = px.line(df,
             labels={
                     "Time": "Time (s)",
                     "value": "Acceleration (g)",
                     "variable": "Data Set"
                 },
             title="Comparison of Bearing Acceleration Data")
fig.write_image("C:/Users/shanly/bearing-time-series.svg")
fig.show(renderer='svg',width=900, height=450)

Now let's get the full benefit of Plotly and render a the middle 1 second of the file as an interactive element. We'll also subtract 4.5 seconds from the time domain data so that these middle plots start at 0 and look good.

plot_start = 3.5
plot_end = 4.001

fig = px.line(df.loc[plot_start:plot_end],
             labels={
                     "Time": "Time (s)",
                     "value": "Acceleration (g)",
                     "variable": "Data Set"
                 },
             title="Interactive Comparison of Bearing Acceleration Data")
fig.write_html("C:/Users/shanly/Desktop/enDAQ/Marketing-Content/What-to-Monitor/bearing-time-series.html",full_html=False,include_plotlyjs='cdn')
fig.show()