Pothole data smoothing and detection of accelerometer data
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Pothole data smoothing and detection of accelerometer data

by zacharoni16 on Sun Jan 27, 2013 4:26 am

I wanted to start a separate thread concentrating on smoothing filtering and detecting bumps and potholes with an Arduino and my Accelerometer. I'm using an Analog Accelerometer set to 50HZ bandwidth sampling at 100HZ. I'm plotting data with MegunoLink (GREAT tool BTW). My delemma is that the accelerometer readings are noisy as hell, especially in a car with the engine running and road noise. What would be the best way to filter out the noise? I'm sampling at 100HZ I'm not sure how to implement at filter that wont affect the sampling rate... Also, I'm not sure if 100HZ is enough to sample at, it seems to catch the bump events pretty well though (graphs posted).

Accelerometer is a KXPS5-3157

I converted the accelerometer output to Gforce, should I be using Gforce, or should I use raw voltage or it doesn't matter for potholes application

Here is my code so far:
Code: Select all | TOGGLE FULL SIZE
/* ***********************************************************************************************************
    Send data to MegunoLink for plotting.
   
    Read analog Z-axis acceloremeter data , bandwidth set to 50HZ by
    external capacitors per the datasheet
   
    According to Nyquist we need to sample the accelerometer at least twice the bandwidth
   
    Set Serial UART to 115200 to handle more than 100HZ sampling rate to plot to Meguno
   
    115200 baud means 115200 bit-times/second, and there are 10 bit-times per byte transmitted on the UART
    (start bit, 8 data bits, and stop bit).
   
    So 115200 / 10 = 11520 bytes / second = 11.520 bytes / millisecond.
   
   ************************************************************************************************************/

#include <GraphSeries.h>

GraphSeries g_aGraphs[] = {"Z"}; //Z acceleration graph label for Meguno

// GLOBALS

long previousMillis = 0;
long interval = 10; // interval in milliseconds (10ms => 100Hz)
int data = 0;

//CALIBRATION DATA FOR ACCELEROMETER
float one_G = 647.0; // OFFSET OF 1G Z axis
float neg_G = 372.0; // OFFSET OF -1G Z axis
// Our ZERO G Reference should be in the middle of these two readings
float mZ = (one_G + neg_G) / 2.0; // ZERO_G REFERENCE FOR Z AXIS
// Estimate Z axis specific sensitivity difference of 2G between readings
float senZ = (one_G - neg_G) / 2.0;
float sensitivity = 440.0; // FROM DATASHEET TYPICAL SENSIVITIY 440mV/G

void setup()
{
  // The data is sent via the serial port. Initialize it.
  Serial.begin(115200);
  analogReference(EXTERNAL); // ACCELEROMETER IS 3.3VOLT
}


void loop()
{
 
  ReadAccelerometer();
 
}

void ReadAccelerometer()
{
   unsigned long currentMillis = millis();
   if((currentMillis - previousMillis) > interval) {
      previousMillis = currentMillis;

      // Read values from the ADC converter and send them out the serial port.
      data = analogRead(2); // READ ANALOG PIN 2 100uS
     
      //float GForceG = ((float)data - mZ) / senZ; // Convert ADC value to G force with gravity
      float GForce = ((float)data - (one_G)) / senZ; // ZERO BASE WITHOUT GRAVITY
 
     
     
     
      g_aGraphs[0].SendData(GForce); // SEND Z AXIS G FORCE
    }
}


Pothole at 25 MPH
Image

Pothole at 25 MPH zoomed

Image

I have two graphs at approximately 25 MPH the pothole event is obvious, then there was a subtle bump afterwards The other graph is the same data, but zoomed in slightly

I'm not sure how to detect the actual pothole event, if I could use FFT, standard Deviation threshold, running average?

Any advice, suggestions, input, wisdom is greatly appreciated!


I want to be able to detect and count potholes and bumps and also eventually score them on how "rough" they are to the passenger/driver probably based on a subjective scale or a human g force scale
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Re: Pothole data smoothing and detection of accelerometer data

by Arctic_Eddie on Sun Jan 27, 2013 10:13 am

If you want to try an FFT, you can use the FFFT library. It has a timer generated interrupt running at 9615Hz and collects 128 samples on ADC0. There is another library from France, the PlainFFT library, which does the transform after you have collected the data independently. It has more versatility than FFFT. However, I doubt if either will be fast enough for what you're trying to do. The alternative is either an analog or digital filter.

The analog version can be several stages of op-amps configured as a bandpass filter. Your sketch would then collect the data on ADC0 and do the analysis. The disadvantage is the lack of adjustments without changing circuit components.

The better choice would be a IIR Butterworth 3rd or 5th order bandpass filter. Set the two corner frequencies to encompass the equivalent frequency of your shock pulse. The link below leads to a filter worksheet. It will calculate the filter coefficient data, show a graph of the response curve, and list a C coded program. This can be copied directly into your sketch. In use, the filter takes one new data point, which overrides the oldest, and calculates the newest output value. Your sketch would then count the pulses above a threshold and evaluate the amplitude.

http://www-users.cs.york.ac.uk/~fisher/mkfilter/

Just for kicks, you could put an accelerometer on each front wheel A-frame, add the Ultimate GPS and micro SD card reader, and create a pothole map of your area.
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Re: Pothole data smoothing and detection of accelerometer data

by zacharoni16 on Sun Jan 27, 2013 2:07 pm

Thanks artic eddie for the information:)

I wonder if I should add it to the dashboard of the car the accelerometer, and it would be subjected to damped harmonic oscillolator type signal from the suspension, or on the Suspenion A arm (unsprung mass) it will receive direct road input. Would the A-arm attachment be easier to detect potholes? You would have to filter out the road noise

I just realized the Accelerometer has built in 32K resistors so Ok the Accelerometer has 32k resistors built in that I didn't see before haha that makes it easy, so I can design a single pole RC filter if I want a 10HZ cutoff C = 1 / [2πRf] C = 1 / (2π * 32000 * 10HZ) = 497nF capacitor? This will be better than the 50HZ I currently have since the frequency of a pothole or bump on a cars suspension is very low

I'm upping the sampling rate since it seems like the pothole event is a very fast and large impulse to 1000 samples a second

I have a few ideas I can keep testing and find a threshold that potholes generate, the only problem is if I only look at the peak threshold with some sort of peak filter or peak detector it will consider everything as a pothole basically, speed bumps, expansion joints, manhole covers, road kill, etc

If I would use say a half-wave rectifier because the voltage swings negative, the pothole event has +G and -G components since the tire goes into and out of the hole and count the peaks?

Use standard deviation of the z axis data?

Could FFT be used to find the pattern of a pothole? and then look for the pattern continuously?
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Location: Washinston, PA

Re: Pothole data smoothing and detection of accelerometer data

by Arctic_Eddie on Sun Jan 27, 2013 4:48 pm

The best place to detect potholes will be on the upper A-frame just above the top ball joint. The dashboard would be a good place to detect passenger jolts and a comparison of what the suspension is seeing.

The output RC filter is a good place to eliminate the high frequency noise. The sensor already has a 1KHz digital low pass filter internally. The RCs corner frequency should be somewhat higher than the equivalent frequency of the pothole jolt. A frequency value twice as high would be a good place to start. If you make the capacitors plug into a two pin header then they can be changed later without any soldering. Use Mylar instead of ceramic for stability. The -3dB corner frequency is that which has a capacitive reactance equal to 32K. Your calculations are correct.

You can estimate the jolt frequency by assuming that one pulse is a half cycle. With your higher sampling rate, you should see the time lapse easily.

A pothole should produce a particular waveshape. The leading edge will depend on the diameter across the pothole in the direction of travel as it controls how much of the tire falls onto the bottom surface. The trailing edge will depend on how sharp the back edge of the hole is and the tire pressure. You can characterize the pulse by measuring the time from first threshold crossing to peak then peak to second threshold crossing.

You should not need a diode on the input signal as the device is ratiometric or a proportion of a single positive supply voltage. Zero G should be half of the supply voltage and 1 G should be part of your full scale value away from center. If the signal bottoms out near 0.0V then you would have to select a higher G scale. If it actually went negative then you could bias it up at the input of an op-amp buffer. The device also has I2C communication. You can set a lot of parameters this way, and also retrieve data. An ADXL345 breakout board is another alternative. I use one on an aerial photo stable platform.

You can use a running average of the standard deviation on the Z-axis then use that as your threshold. Four s.d. would be a good starting point.

You could use the FFT in the PlainFFT library to analyze the pulse after crossing the first threshold and characterize the jolt by relating several of the dominant frequencies. That library uses double precision floating point math and provides complex input and output. You might need to use a Mega board because memory usage will go up.

I would start with a sensor mounted anyplace convenient, the simple RC filter, and some form of data logging. Later, you can add a Butterworth 5-pole low pass filter and move the sensor to the A-frame. After seeing many jolt waveforms, then decide on a bandpass filter and perhaps FFT analysis. There are likely better filters for pulse work with less ringing. I use SciDAVis as my plotting and analysis program. It's free and comes in Windows and Linux versions.
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Re: Pothole data smoothing and detection of accelerometer data

by zacharoni16 on Sun Jan 27, 2013 11:11 pm

Wow thank you for the great ideas , I wanted to first try to mount it on the dashboard or flood inside the car for conveince and to see how many G'a the riders are experiencing.

I had a question about driving up hills, in my accelerometer calibration I subtract 1G acting on the sensor al times by subtracting an offset to zero the sensor. When going up a hill gravity will be split across two vectors , and it would be something like g/ sin angle of tilt


I was wondering if I would have to have a gyroscope or tilt angle sensor to send the angle of the car to correct the gravity offset while driving up slopes, or could I use latitude data right off the gps or do you think I even have to correct it

Also what is " four s.d will be a good starting point " I'll be sampling at 1000hz I was wondering how much samples I should be doing running average and standard deviation how to handle 1000 samples a second and averaging them all ?


Or should I wait for buffer to fill up completely after the standard deviation and send the buffer all at once over serial rather than one data sample at a time. Not sure how to keep all the processing code from bogging down the sampling rate



Thank you
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Location: Washinston, PA

Re: Pothole data smoothing and detection of accelerometer data

by Arctic_Eddie on Mon Jan 28, 2013 10:11 am

Tilt will not cause a notable problem in your case. A slope of 15° is probably the most you will see and that is only a 3% loss in the Gz axis. If you want to calculate tilt then use the equation:

angle = arctan( Gx / Gz ); // Assuming X is forward and Z is down. The function is in <math.h> and needs double as it's input data type.

Because your filters will allow frequencies up to the jolt equivalent, you will need to use a running average filter for the tilt calculation. This will run in parallel with the jolt detector but as an independent data array. You would collect the new data point and add it to both the jolt[] array and the tilt[] array. Next, you would update the jolt filter and tilt filter. If the data crosses any kind of threshold, then perform the needed calculations.

You won't need a gyro sensor as the accelerometer will do the job.

The "four s.d." term is just my way of saying four standard deviations. Three s.d.(+/-) will contain 99% of the data so four s.d. out either side is an event you might want to evaluate.

The sampling rate does not want to be greater than 1KHz as the sensor has a built-in filter set at the same value. I would set the rate such that you have enough time in the loop() routine to collect a data point, filter jolt and tilt, detect an event, and act on the event. This will be the worse case situation and limit the maximum sampling rate. The lower limit will be the Nyquist value for the highest digital filter corner frequency. The value is twice that frequency. If your upper value is 10Hz then you will have to sample at 20Hz or greater. I suspect that 100Hz will give a good picture of the road conditions and still allow plenty of time for the Arduino to process the worse case data situation. I think the Mega board will be your best choice. That's the one I use on my Dynamixel servo stabilized aerial photo platform.
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Re: Pothole data smoothing and detection of accelerometer data

by zacharoni16 on Mon Jan 28, 2013 9:07 pm

I adjusted the sampling rate and lowered the LPF on the accelerometer to 15HZ. I have obtained better data, I see the negative and postive peaks in a pothole, it seems to oscillate and dampen with time making a "beat" type pattern. I wonder how the pattern could be programmatic ally found?

Image

Data looks to be expected with the matlab model, Large negative -G spike falling edge then damping oscillating G's with a +G spike out of the pothole and suspension going to equilibrium I only model with a 2DOF quarter car model though to compare. Usually one wheel hits a pothole in a discernible sample time

I know the derivative of acceleration would be "jerk" I'm wondering if the pothole data could be recognized by a series of decrementing jerks? The pattern is also negative though too, there has to be a signature to search for to find the pothole and count it. The only time there will be negative G's in the Z axis of a car is if the tire goes into a hole, or the car is airborne for a brief moment and hits the ground, so a negative "jerk" would be a good signature right?
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Re: Pothole data smoothing and detection of accelerometer data

by Arctic_Eddie on Tue Jan 29, 2013 9:33 am

The one characteristic I see for a pothole is a series of -G pulses over some period of time and exceeding a threshold value. It would take both of those conditions to distinguish the pothole from rough road noise.

You might also get MatLab to integrate the data(maybe twice) over time. The resulting trace(s) might be easier to parse for certain events. The second integral might be a measure of suspension deflection and be a better indicator. If it produces suspension displacement then you would have a profile of the pavement surface. You may need to mount the sensor on the A-frame to get good data.
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Re: Pothole data smoothing and detection of accelerometer data

by zacharoni16 on Tue Jan 29, 2013 9:52 am

I was thinking of something simple like this, the suspension seems to dampen the pothole very fast approximately 1 second to 1.2 seconds, I'm sampling at 200HZ, if I fill a running buffer of 200 elements with data from the accelerometer, it creates a "window", Then I would have code that counts -G peaks over a threshold, if it's > then say 5 then that would be a pothole?

5 -G peaks in a second window
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Re: Pothole data smoothing and detection of accelerometer data

by Arctic_Eddie on Tue Jan 29, 2013 10:38 am

That would work.

Try the double integration of your sample data. I'm curious as to how well it will show the road profile. Do you have the data in a text file that you could send? I would like to try it in SciDAVis.
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Re: Pothole data smoothing and detection of accelerometer data

by zacharoni16 on Tue Jan 29, 2013 10:44 am

I'm at work now, I can post it later, I'm curious too :) thanks for your help on this.

I actually want to put one accelerometer on the A-arm and one on the dash and compare the results. Another thing I was thinking, if I could find the peaks in the signal considering that a peak is above two adjacent lower values, I could count the peaks, also I could find the the logarithic decrement I believe that would be able to tell damping ratio and maybe could use that to scan for when the suspension is "damping" meaning it has been set into oscillation by a road event

Would double integration be way too process intensive on the Arduino MEGA?
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Re: Pothole data smoothing and detection of accelerometer data

by Arctic_Eddie on Tue Jan 29, 2013 1:02 pm

Yes, the two sensor locations will tell you how well the suspension is working, including the shock absorbers.

Using the peak heights after the highest are data points for exponential decay, A*e^(-u*t), where u is the damping coefficient.

I don't think the incremental time integral is too much of a chore for the Mega. You would have two more arrays, velocity[] and displacement[]. They would be filled "on the fly" with the same index(idx) as used to fill the accel[] array. Integrate accel[] to get velocity[] then velocity[] to get displacement[]. You could try it with your sample data. The three plots on the same time scale would be interesting to view. When viewed together, the pothole signature might be easier to recognize.

I am designing a tri-axial FFT metal detector for road side bomb detection. It uses the Mega and has the following arrays.

2 double[128]
10 int[128]
9 int[64]

It captures one int[128] at 8KHz, converts to double[128], clears another double[128], processes the FFT, then analyzes both raw and transformed data for 3D display. The Mega still works but someday I'd like to move to the Due. The IDE for the Due and it's library calls have some serious flaws so I'll wait awhile.
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Re: Pothole data smoothing and detection of accelerometer data

by zacharoni16 on Tue Jan 29, 2013 1:17 pm

WOW awesome I'd love to see a video of that project when it's done. Thanks for your help and insight, do you think I should implement a HPF, the pothole "spikes" seem to have fast rise time compared to the nosie and road oscillation noise. I figured like 50-200HZ HPF would help isolate and smooth out the peaks?
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Re: Pothole data smoothing and detection of accelerometer data

by Arctic_Eddie on Tue Jan 29, 2013 2:50 pm

I would stay with the LPF until you have collected more data from dash and a-frame. The integrals may show a lot more useful info that keep the filtering code at a minimum.

The metal detector code is complete and I'm now working on coil design. I need more forward sensitivity so the assembly doesn't get too close too the blast area. That will be the limiting factor.
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Re: Pothole data smoothing and detection of accelerometer data

by zacharoni16 on Tue Jan 29, 2013 10:03 pm

Hey man :)

Here is the RAW DATA for 1 SECOND window of hitting a pothole

Seems maybe my Z axis is upside down O.o? lol

DATA was collected using only the 25HZ RC LPF on the end of the accelerometer Z-axis output no software filtering

Code: Select all | TOGGLE FULL SIZE
ZACCEL,TIME,GFORCE

Z,0.01,-0.01
Z,0.02,0.02
Z,0.03,0.06
Z,0.04,0.02
Z,0.05,0.04
Z,0.06,0.09
Z,0.07,0.07
Z,0.08,0.00
Z,0.09,-0.10
Z,0.10,-0.04
Z,0.11,-0.03
Z,0.12,-0.05
Z,0.13,-0.13
Z,0.14,-0.12
Z,0.15,-0.19
Z,0.16,-0.16
Z,0.17,-0.09
Z,0.18,-0.17
Z,0.19,-0.18
Z,0.20,0.04
Z,0.21,0.20
Z,0.22,0.04
Z,0.23,-0.12
Z,0.24,-0.25
Z,0.25,-0.15
Z,0.26,-0.17
Z,0.27,0.03
Z,0.28,0.08
Z,0.29,-0.09
Z,0.30,-0.26
Z,0.31,-0.30
Z,0.32,-0.04
Z,0.33,0.20
Z,0.34,0.36
Z,0.35,0.04
Z,0.36,-0.20
Z,0.37,-0.38
Z,0.38,-0.40
Z,0.39,-0.25
Z,0.40,-0.17
Z,0.41,0.40
Z,0.42,0.93
Z,0.43,0.69
Z,0.44,0.01
Z,0.45,-0.17
Z,0.46,-0.42
Z,0.47,-0.54
Z,0.48,-0.21
Z,0.49,0.22
Z,0.50,0.83
Z,0.51,0.65
Z,0.52,0.18
Z,0.53,-0.15
Z,0.54,-0.12
Z,0.55,-0.25
Z,0.56,-0.49
Z,0.57,0.01
Z,0.58,-0.04
Z,0.59,0.37
Z,0.60,0.36
Z,0.61,-0.29
Z,0.62,-0.27
Z,0.63,0.04
Z,0.64,0.06
Z,0.65,-0.09
Z,0.66,-0.04
Z,0.67,0.01
Z,0.68,0.01
Z,0.69,0.28
Z,0.70,-0.08
Z,0.71,-0.18
Z,0.72,-0.11
Z,0.73,-0.10
Z,0.74,0.11
Z,0.75,0.15
Z,0.76,0.01
Z,0.77,-0.11
Z,0.78,-0.33
Z,0.79,-0.14
Z,0.80,0.12
Z,0.81,0.04
Z,0.82,0.01
Z,0.83,0.17
Z,0.84,0.09
Z,0.85,-0.02
Z,0.86,-0.07
Z,0.87,-0.04
Z,0.88,0.04
Z,0.89,0.04
Z,0.90,0.02
Z,0.91,0.09
Z,0.92,0.05
Z,0.93,-0.01
Z,0.94,0.01
Z,0.95,0.01
Z,0.96,-0.07
Z,0.97,0.07
Z,0.98,0.08
Z,0.99,0.12
Z,1.00,0.01


RAW DIRECT DATA PICTURE from accelerometer:

Image


Damn, excel filtered all the noise lol in the line graph version

Image

FFT on this seems to peak energy @ 12.5HZ, Would this be a good frequency to filter for?:

Image


HERE IS RAW DATA FOR driving at constant speed, hitting about 6 to 9 potholes and some rough patches in the road

Code: Select all | TOGGLE FULL SIZE
TIME,GFORCE
0,-0.06
0.01,-0.06
0.02,-0.07
0.03,-0.06
0.04,-0.04
0.05,0
0.06,0.01
0.07,0
0.08,-0.02
0.09,-0.04
0.1,-0.01
0.11,0.01
0.12,-0.02
0.13,-0.04
0.14,-0.04
0.15,-0.02
0.16,0
0.17,0
0.18,0.01
0.19,0
0.2,0.01
0.21,0
0.22,-0.01
0.23,0.01
0.24,0.04
0.25,0.04
0.26,0.01
0.27,-0.01
0.28,-0.01
0.29,-0.01
0.3,-0.01
0.31,-0.01
0.32,0.01
0.33,0.03
0.34,-0.01
0.35,0
0.36,0.01
0.37,0.04
0.38,0.07
0.39,0.06
0.4,0.03
0.41,0.01
0.42,0.02
0.43,0.02
0.44,0.03
0.45,0.04
0.46,0.07
0.47,0.07
0.48,0.01
0.49,0.04
0.5,0.07
0.51,0.07
0.52,0.05
0.53,0.04
0.54,0.04
0.55,0.02
0.56,0.03
0.57,0.02
0.58,0.04
0.59,0.02
0.6,0.01
0.61,0.01
0.62,0.03
0.63,0.02
0.64,0.01
0.65,0
0.66,-0.01
0.67,-0.01
0.68,0
0.69,0.02
0.7,0.04
0.71,0.01
0.72,0.01
0.73,0.01
0.74,0.02
0.75,0.01
0.76,-0.01
0.77,0.01
0.78,0.01
0.79,-0.01
0.8,0.01
0.81,0.01
0.82,0.01
0.83,-0.01
0.84,0.02
0.85,0.01
0.86,-0.03
0.87,-0.04
0.88,-0.01
0.89,-0.01
0.9,0
0.91,-0.03
0.92,-0.03
0.93,-0.04
0.94,-0.04
0.95,-0.01
0.96,-0.01
0.97,-0.01
0.98,0.01
0.99,-0.02
1,-0.04
1.01,-0.04
1.02,-0.01
1.03,0.02
1.04,-0.01
1.05,-0.01
1.06,-0.03
1.07,-0.02
1.08,0
1.09,0.01
1.1,0.01
1.11,0.01
1.12,0.01
1.13,0.03
1.14,0.03
1.15,0.01
1.16,-0.03
1.17,0
1.18,0.02
1.19,0.05
1.2,0.03
1.21,0
1.22,0
1.23,0.01
1.24,0.04
1.25,0.04
1.26,0.03
1.27,0
1.28,-0.01
1.29,0.01
1.3,0.02
1.31,0.04
1.32,0.02
1.33,0.02
1.34,0.01
1.35,0
1.36,0.01
1.37,0.06
1.38,0.04
1.39,0.02
1.4,0
1.41,0.01
1.42,0.01
1.43,0.01
1.44,0.03
1.45,0.07
1.46,0.05
1.47,0.03
1.48,0.01
1.49,0.02
1.5,0.03
1.51,0.01
1.52,0.02
1.53,0.03
1.54,0.01
1.55,-0.01
1.56,-0.02
1.57,0
1.58,0.01
1.59,0.01
1.6,0.01
1.61,0.02
1.62,0.03
1.63,0.03
1.64,0.01
1.65,0.01
1.66,-0.03
1.67,-0.06
1.68,-0.04
1.69,0.01
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zacharoni16
 
Posts: 25
Joined: Thu Aug 16, 2012 6:21 pm
Location: Washinston, PA