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I have an acceleration vibration signal (m/s^2) pic(1) and I need to calculate displacement from this signal, as I know first I have to integrate acceleration I will get vibration velocity [mm/s] pic(2) after that, I have to do it again integration of vibration velocity and I will get vibration displacement [μm] pic(3) Am I right? But the result of the second integration is weird. Displacement should be also decries as I understand.

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    $\begingroup$ Discrete integration is tricky. What algorithm did you use? Keep in mind that a continuous integrator has infinite gain at 0 Hz, so having any type of bias in your signal will turn into the drift you see. In general, double integration will amplify any low frequency noise greatly, so there should some sort of high pass filter in there to manage this. $\endgroup$
    – Hilmar
    Apr 14, 2022 at 13:36
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    $\begingroup$ Welcome to SE.SP! The usual way of finding velocity and displacement estimates from an accelerometer signal is to use a Kalman filter. This tends to deal with some of the issues @Hilmar raises in his comment. $\endgroup$
    – Peter K.
    Apr 14, 2022 at 14:50

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Besides the offset and drift issues that can occur in practical implementation, the graphs and interpretation of the graphs make sense:

We integrate acceleration to get velocity- I can't tell from the acceleration curve if the velocity would truly be positive or if there is an offset error involved, but assuming the velocity was positive, this would give us a positive displacement. As we move forward in time, the velocity decreases, but it is still positive-- so the displacement MUST continue to increase in the positive direction, albeit at a lower rate as the velocity goes down. The only way to be the displacement start to go down instead of up is to introduce a velocity in the opposite direction. This is all given mathematically as the time integration of the velocity curve.

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