# What exactly was my car's tire pressure monitor doing?November 17, 2018 9:33 PM   Subscribe

I recently had to add some air to my tires due to cold weather. Afterwards, I had to "reset" the TPMS, and then drive around for a while while a progress bar ticked from 0 to 99 percent. In as much detail as possible, what was my car (and its computer) actually doing during this time?

I gather that somehow this kind of TPMS uses the rotation speed of the tires to infer tire pressure. But what data was actually being collected -- like, specifically, what was being measured? How is this data aggregated into an estimate of tire pressure? What algorithm was being used to do this, and what exactly did the progress percentage represent?

I would really like to know this, for some reason. If there are any journal articles about this, I would love to at least skim them.
posted by vogon_poet to Computers & Internet (15 answers total) 2 users marked this as a favorite

Wheel speed. The diameter of the tyre is affected by tyre pressure (higher pressure is stiffer sidewall, is a bigger 'disc' if you will) and the sensor uses a rotational speed differential to note low pressure - ie a lower pressure tyre will have a smaller diameter and so rotate faster than a fully inflated one.

No algorithm. It's really not that clever, it's just if one is bigger than that the other there is a problem with the faster turning wheel.
posted by Brockles at 10:49 PM on November 17, 2018 [3 favorites]

Further - there is a reason these systems are cheaper and were dropped for more expensive cars, because they are unable to detect all four tyres deflating (because there is no speed differential) and also they can be confused by front to rear axle differences. They are a crude way of checking tyre pressure *effects* but they do not in any way check pressures themselves.
posted by Brockles at 10:52 PM on November 17, 2018 [3 favorites]

Yeah, but what was it actually doing to go from measured rotation speed to approx. tire pressure? Is it sampling the time for many repeated wheel rotations? Why did it take 10 minutes of driving to complete this process, and why did the progress meter move at different rates during that time?
posted by vogon_poet at 8:01 AM on November 18, 2018 [1 favorite]

I’ve never seen a car do the progress bar thing. What kind of car is it?
posted by jeffamaphone at 8:23 AM on November 18, 2018 [1 favorite]

It might be establishing a new baseline for tire pressure as it increases (after inflation) over a set distance as the tire heats up.

The recommended inflation pressures are always given as cold pressure. The computer possibly is assuming the new inflation is "cold" and it reads the pressure increase as the tire heats up. This establishes an acceptable range which would not cause a warning.
posted by Thorzdad at 8:35 AM on November 18, 2018

but what was it actually doing to go from measured rotation speed to approx. tire pressure?

It's not calculating tyre pressure at all. It is just comparing wheel size (circumference more precisely). There will be a natural variation in distance travelled by each wheel on the car through cornering (inside tyres will travel less distance) so it needs to go a predetermined distance to be able to discard noise readings and set a baseline. It probably needs a certain percentage of time at zero steering angle (or something) to be able to get a solid reading. So any cornering you did or wheel movement or whatever meant the time taken to complete the sampling amount necessarily got longer.

Also: establishing a new baseline for tire pressure as it increases (after inflation) over a set distance as the tire heats up.

This may also be a factor. Tyres absolutely should (assuming the same air source within them and so consistent moisture content) expand with heat at the same rate but having a hot comparison (so a data set of x miles taken y miles after starting) as well as a cold one is maybe in there too.
posted by Brockles at 8:57 AM on November 18, 2018 [2 favorites]

I think those two things together explain the behavior I saw pretty well. It was mainly when making turns that the progress seemed to stop. And there was a period of time near the end where progress was stuck at 99% -- I assume it was waiting for the tires to warm up enough to finish up a second set of readings. Thank you!
posted by vogon_poet at 9:29 AM on November 18, 2018

I would tend to assume that the progress bar, like most progress bars, was essentially cosmetic. It probably is programmed to fill up according to some fairly simplistic algorithm that is not actually connected in any way to actual readings from the TPMSes, and then it hangs at 99% until the TPM system is actually satisfied. It gives a rough approximation of how far along in the calibration process you likely are, but that's it. In most cars, when you need to calibrate the TPMSes all that happens is the warning light stays on for a bit, sans explanation, and then eventually just turns off, also sans explanation. This is a bit confusing for drivers who aren't already in the know. The progress bar eliminates some of that confusion but any impression that it's reflective of actual reality is probably illusory.
posted by Anticipation Of A New Lover's Arrival, The at 9:36 AM on November 18, 2018 [1 favorite]

It was mainly when making turns that the progress seemed to stop.

When the car isn't going straight, the tires on one side are rotating faster than the tires on the other side. So it makse sense that it pauses this calibration task during turns.
posted by humboldt32 at 9:45 AM on November 18, 2018 [1 favorite]

And there was a period of time near the end where progress was stuck at 99%

Weird. Wouldn't expect that a car would be Windows based, but... well. That's pretty compelling evidence.
posted by Brockles at 9:48 AM on November 18, 2018 [4 favorites]

The system brockles is describing is called "rolling radius" indirect pressure detection and is pretty much outdated. It simply compares the wheel speed of all four wheels and detects when one is spinning more rapidly than the other three. It has the drawback of being unable to detect when all four tires are low because is only compares the tires to each other.

The newer indirect pressure detection systems are much more sophisticated. They use what is called "resonant frequency" analysis to determine pressure. This is becoming more prevalent on newer cars and replacing the older direct pressure sensors embedded in the tire stems. These direct pressure sensors are expensive, and prone to failure and radio frequency interference.

The resonant frequency systems use the wheel speed sensors that are already present for the automatic braking system (ABS) so require no new hardware. All they add is some fancy software and software is free, eh?

This is how the resonant frequency systems work. The ABS wheel speed sensors consist of a toothed wheel on the axle that typically has 40 to 45 teeth. A magnetic sensor detects the passage of each tooth as the wheel turns and generates a pulse, allowing a computer to calculate the speed of rotation of the wheel.

There is a torsional vibration associated with the turning of the wheel because the wheel and axle are solid steel but the tire is flexible rubber. There is a minute rotational vibration as the solid wheel tugs the flexible rubber tire around and the tire stretches and snaps back in a twisting motion as it rotates.

This resonant frequency changes as the pressure in the tire changes, shifting up by one or two Hz as pressure increases and the tire becomes stiffer, and shifting down by one or two Hz as pressure decreases and the tire becomes less stiff. You can think of it as the tone change when you tune a guitar string.

The computer analyzes the readings it gets from the wheel speed sensor and detects this twisting vibration as small changes in the frequency of the wheel sensor pulses as the teeth rotate around. The computer performs a Fourier analysis of thousands of samples and extracts the resonant frequency of each tire.

After you carefully adjust the proper air pressure in your tires, it takes 30 to 60 minutes of driving to train the system to recognize and record the normal resonate "tone" of each tire with proper pressure. It takes thousands of samples and lots of number crunching math to do this, called Fourier analysis. That is what is happening as you are driving around watching the progress bar. It is measuring the resonant frequency "tone". Thereafter, the system looks for a deviation in the resonant "tone" to detect low pressure.

According to the Federal Motor Vehicle Safety Standards, the tire pressure monitoring system must detect within 10 minutes when the tire pressure is 25% below normal.

I expect many manufacturers to move toward this newer resonant frequency indirect monitoring in the future because it is less expensive and less prone to failure. One drawback is that it doesn't work as well on very low profile tires. Because of their stiffness, the torsional resonant frequency is much higher and lower magnitude. So low profile tires will likely stick to the traditional direct pressure sensors embedded in the tire valves.
posted by JackFlash at 12:31 PM on November 18, 2018 [7 favorites]

Are there any sources where the math is documented? I would like to read about exactly what is happening. (Or maybe it's all patented and internal to manufacturers.)
posted by vogon_poet at 9:27 PM on November 19, 2018

What year and make is your car? Is it on this list: http://www.tirereview.com/indirect-tpms-imports/
posted by Brockles at 9:37 PM on November 19, 2018

Are there any sources where the math is documented?

Each manufacturer has their own proprietary algorithms and there are a lot of patents involved if you search for "resonant frequency TPMS". Audi, for example, combines the rolling radius method and the newer resonant frequency method together. Others are combining inputs from the electronic stability control accelerometers with resonant frequency.

Here is one example article that shows the mathematical foundations of TPMS resonant frequency analysis. It probably won't mean a lot to you unless you understand the basics of Fourier spectral analysis and digital filtering. But it has a few graphs showing the resonant frequency shift as tire pressure changes.

http://users.isy.liu.se/rt/fredrik/reports/02reglermotetpi.pdf

The important thing to keep in mind is that they are measuring the torsional vibration of the tire belt around the solid wheel. The belt/tread of the tire oscillates clockwise and counter-clockwise back and forth around the steel wheel, like the balance wheel in a watch, due to the flex of the sidewalls at a resonant frequency typically around 40 Hz. This vibration is transmitted to the wheel and picked up by the speed sensors on the wheel axles. The pitch/frequency of the oscillation changes very slightly, a couple of Hz, as tire stiffness changes with air pressure.
posted by JackFlash at 8:03 AM on November 20, 2018

The linked article was very good. I don't know that much about time series analysis but I was able to get the basic ideas (they're assuming some functional form generates the data, and just fitting the MLE, working in the frequency domain). This is exactly what I had hoped for when I asked this question!
posted by vogon_poet at 11:47 AM on November 30, 2018

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