As shown in the screenshot, the processed data given by this sensor show that x_max_acc_G < x_rms_acc_G, y_max_acc_G < y_rms_acc_G and z_max_acc_G < z_rms_acc_G. It does not make sense mathematically. Why is that?
My understanding is x_rms = sqrt( (x_1^2 + x_2^2 + …+x_n^2) / n) <= sqrt( (x_max^2 + x_max^2 + …+x_max^2) / n) = sqrt( n * x_max^2 /n) = x_max. So, theoretically x_rms <= x_max, but the computing results from the sensor said otherwise.
This is actually expected behavior for the Standalone Smart Vibration Sensor v4 and is mathematically consistent when considering how the sensor processes vibration data.
The confusion usually stems from the assumption that the signal is a simple, single-frequency sine wave. In industrial environments, vibration is complex and composed of many different frequencies. Here is why the RMS can be greater than the MAX
MAX (x_max_acc_G): This value represents the amplitude of the single largest frequency component (the highest peak) identified in the FFT spectrum. It is a “Peak-of-Peaks” measurement.
RMS (x_rms_acc_G): This represents the total energy of the entire vibration spectrum. It is calculated by taking all components of the signal into account.
The Math:
While your formula for a single discrete series is correct, the sensor is comparing a single spectral peak against the integrated energy of the whole signal. If your spectrum has multiple significant peaks (e.g., motor vibration, bearing noise, and structural resonance), the RMS combines them:
In your case, because there are multiple vibration components contributing to the signal, the total energy (RMS) exceeds the amplitude of the single highest peak (MAX)
If the vibration were a perfect, clean sine wave with only one frequency, you would see the “normal” relationship where Max \approx RMS \times \sqrt{2}. However, in real-world machinery, the presence of multiple peaks and background noise often pushes the total RMS energy above the value of the highest individual peak.
