README.rst

Signal Analysis

Setup

virtualenv env
source env/bin/activate
pip install requirements.txt

Run the ipython notebook notebook

ipython notebook

Analysing vibration events

1. Import all the necessary library to process:

#importing libraries for plotting
%matplotlib inline
import matplotlib.pyplot as plt
import json
import math
import numpy as np

2. Helper code for processing the data

def splitAndConvert(value,splitter = ' '):
    return map(float,value.split(splitter))

def getRMSData(x,y,z):
    return [ math.sqrt((x[i]*x[i])+(y[i]*y[i])+(z[i]*z[i]))  for i in xrange(0,2048)]


def loadEvents():
    events = []
    with open('vibration.json') as data_file:
            for line in data_file:
                    event = json.loads(line)
                    event['x'] =  splitAndConvert(event['value']['x']);
                    event['y'] =  splitAndConvert(event['value']['y']);
                    event['z'] =  splitAndConvert(event['value']['z']);
                    event['rms'] = getRMSData(event['x'],event['y'],event['z'])
                    del event['value'];
                    events.append(event)
    return events


def processPSD(events, axis):
    psds = []
    for event in events:
            signal = np.array(event[axis], dtype=float)
            fourier = np.fft.fft(signal*np.hanning(2048))
            psd = 2*((fourier.real * fourier.real)/(1600*2048))
            psds.append(psd)
    return psds


def consolidatePSD(psds):
            dArray = np.array(psds)
            #print 'Data type                :', dArray.dtype
            #print 'Total number of elements :', dArray.size
            #print 'Number of dimensions     :', dArray.ndim
            #print 'Shape (dimensionality)   :', dArray.shape
            #print 'Memory used (in bytes)   :', dArray.nbytes
            vibrationTable = []
            for i in xrange(0,2048):
                    vibrationTable.append(np.sum(dArray[:,i])/len(psds))

            return vibrationTable

def processData():
    events = loadEvents()
    table = {}
    table['x'] = consolidatePSD(processPSD(events,'x'))
    table['y'] = consolidatePSD(processPSD(events,'y'))
    table['z'] = consolidatePSD(processPSD(events,'z'))
    table['rms'] = consolidatePSD(processPSD(events,'rms'))
    return table

3. Display sample data for 3 axis

data = loadEvents()
print "No of Events recorded :", len(data)
plt.plot (data[0]['x'], label="x")
plt.plot (data[0]['y'], label="y")
plt.plot (data[0]['z'], label="z")
plt.plot (data[0]['rms'],  label="rms")
plt.legend(loc='upper left')

No of Events recorded : 334

<matplotlib.legend.Legend at 0x105f3fd50>

4. Display a sample signal with hanning window and after psd analysis

import numpy as np
signal = np.array(data[0]['z'], dtype=float)
plt.subplot(2,2,1)
plt.plot(signal,label="normal signal")
plt.legend(loc='lower left')
plt.subplot(2,2,2)
plt.plot(signal* np.hanning(2048),label="Signal after hanning window")
plt.legend(loc='lower left')
plt.figure()
fourier = np.fft.fft(signal*np.hanning(2048))
n = signal.size-3
timestep = 0.000625
freq = np.fft.fftfreq(n, d=timestep)
psd = (fourier.real * fourier.real)/(1600*2048)
psd  = np.array(psd, dtype=float)
psd[2:n-1] =  2* psd[2:n-1]
plt.plot(freq[2:n/2], 10*np.log10(psd[2:n/2]),label="Signal after psd analysis")
plt.legend(loc='center left')

<matplotlib.legend.Legend at 0x10c782590>

5. Consolidating the report

data = processData()
from scipy.integrate import simps, trapz
graph = data['x'][2:n/2-1]
# Compute the area using the composite trapezoidal rule.
area = trapz(graph, dx=5)
print("trapezoidal area x=", area)

# Compute the area using the composite Simpson's rule.
area = simps(graph, dx=5)
print("Simpson x =", area)

graph = data['y'][2:n/2-1]
# Compute the area using the composite trapezoidal rule.
area = trapz(graph, dx=5)
print("trapezoidal area y=", area)

# Compute the area using the composite Simpson's rule.
area = simps(graph, dx=5)
print("Simpson y =", area)

graph = data['z'][2:n/2-1]
# Compute the area using the composite trapezoidal rule.
area = trapz(graph, dx=5)
print("trapezoidal area z=", area)

# Compute the area using the composite Simpson's rule.
area = simps(graph, dx=5)
print("Simpson z =", area)

graph = data['rms'][2:n/2-1]
# Compute the area using the composite trapezoidal rule.
area = trapz(graph, dx=5)
print("trapezoidal area rms=", area)

# Compute the area using the composite Simpson's rule.
area = simps(graph, dx=5)
print("Simpson rms =", area)

n = signal.size-3
timestep = 0.000625
freq = np.fft.fftfreq(n, d=timestep)
plt.figure(figsize=(20, 6))
plt.subplot(1,2,1)
plt.plot(freq[2:n/2-1], data['x'][2:n/2-1],label = 'x axis' )
plt.legend(loc='upper right')
plt.subplot(1,2,2)
plt.plot(freq[2:120], data['x'][2:120],label = 'x axis' )
plt.legend(loc='upper right')
plt.show()
plt.figure(figsize=(20, 6))
plt.subplot(1,2,1)
plt.plot(freq[2:n/2-1], data['y'][2:n/2-1],label = 'y axis' )
plt.legend(loc='upper right')
plt.subplot(1,2,2)
plt.plot(freq[2:120], data['y'][2:120],label = 'y axis' )
plt.legend(loc='upper right')
plt.show()
plt.figure(figsize=(20, 6))
plt.subplot(1,2,1)
plt.plot(freq[2:n/2-1], data['z'][2:n/2-1],label = 'z axis' )
plt.legend(loc='upper right')
plt.subplot(1,2,2)
plt.plot(freq[2:120], data['z'][2:120],label = 'z axis' )
plt.legend(loc='upper right')
plt.show()
plt.figure(figsize=(20, 6))
plt.subplot(1,2,1)
plt.plot(freq[2:n/2-1], data['rms'][2:n/2-1],label = 'rms axis' )
plt.legend(loc='upper right')
plt.subplot(1,2,2)
plt.plot(freq[2:120], data['rms'][2:120],label = 'rms axis' )
plt.legend(loc='upper right')
plt.show()

('trapezoidal area x=', 0.12360196506596299)
('Simpson x =', 0.12375189082977331)
('trapezoidal area y=', 0.1416781518529569)
('Simpson y =', 0.1417611851789779)
('trapezoidal area z=', 0.32075644988274854)
('Simpson z =', 0.32102093319348385)
('trapezoidal area rms=', 0.29523818043622763)
('Simpson rms =', 0.29480228984341683)