Diagnosis from logs

Example 1 Separating imbalance with an FFT

Simulated X-axis acceleration sampled at 1,000 Hz for 3 seconds while hovering at 5,000 rpm with 2-blade propellers, before and after a hard landing.

import numpy as np

FS, T = 1000, 3.0                              # Hz, s
RPM, BLADES = 5000, 2
f1 = RPM / 60
t = np.arange(0, T, 1 / FS)
rng = np.random.default_rng(7)

def accel(a_1x):                               # m/s², 1x component from imbalance
    return a_1x * np.sin(2 * np.pi * f1 * t) + 3.0 * np.sin(2 * np.pi * BLADES * f1 * t) + rng.normal(0, 1.0, t.size)

print(f"1x = {f1:.1f} Hz, blade pass = {BLADES * f1:.1f} Hz, resolution = {1 / T:.2f} Hz")
for name, a in (("before", 0.8), ("after", 6.0)):
    x = accel(a)
    amp = np.abs(np.fft.rfft(x)) * 2 / x.size
    f = np.fft.rfftfreq(x.size, 1 / FS)
    k1, kb = np.argmin(abs(f - f1)), np.argmin(abs(f - BLADES * f1))
    print(f"{name:<6} peak at {f[np.argmax(amp)]:.1f} Hz | 1x {amp[k1]:.2f} | blade pass {amp[kb]:.2f} | 1x/blade {amp[k1] / amp[kb]:.2f}")

1x = 83.3 Hz, blade pass = 166.7 Hz, resolution = 0.33 Hz
before peak at 166.7 Hz | 1x 0.81 | blade pass 2.99 | 1x/blade 0.27
after  peak at 83.3 Hz | 1x 6.02 | blade pass 2.97 | 1x/blade 2.03

Before the hard landing, the largest peak is at the blade-pass frequency, as expected. After it, the $1\times$ peak has grown several times to become the largest, while the blade-pass peak has barely changed. This pattern points to imbalance in a rotating part (a chipped propeller or bent shaft) rather than a loose damping mount, which usually raises vibration at all frequencies. In real data the four motors turn at slightly different speeds, so the peaks are broader, and finding which motor is at fault takes a physical inspection.

Example 2 Finding a faulty IMU with the median

Z-axis rotation rates (deg/s) from three IMUs with the drone stationary on the ground over 5 samples. The team treats a difference from the median of more than 1.0 deg/s as abnormal (simulated values).

import statistics as st

gyro_z = {                                     # deg/s while stationary
    "IMU0": [0.05, -0.02, 0.03, 0.01, -0.04],
    "IMU1": [0.02, 0.01, -0.03, 0.04, 0.00],
    "IMU2": [1.62, 1.58, 1.71, 1.66, 1.60],
}
LIMIT = 1.0
n = len(next(iter(gyro_z.values())))
for k in range(n):
    med = st.median(v[k] for v in gyro_z.values())
    bad = [name for name, v in gyro_z.items() if abs(v[k] - med) > LIMIT]
    print(f"sample {k}: median {med:+.2f} deg/s, outliers {bad or 'none'}")
bias = {name: st.mean(v) for name, v in gyro_z.items()}
print("mean while stationary:", {k: round(v, 2) for k, v in bias.items()})

sample 0: median +0.05 deg/s, outliers ['IMU2']
sample 1: median +0.01 deg/s, outliers ['IMU2']
sample 2: median +0.03 deg/s, outliers ['IMU2']
sample 3: median +0.04 deg/s, outliers ['IMU2']
sample 4: median +0.00 deg/s, outliers ['IMU2']
mean while stationary: {'IMU0': 0.01, 'IMU1': 0.01, 'IMU2': 1.63}

IMU2 has a constant offset of about 1.6 deg/s even though the drone is still, while the other two are near zero. A 1.6 deg/s difference is below the 5 deg/s pre-arm threshold, so the aircraft arms and flies normally; passing pre-arm does not mean the sensors are healthy. The result says IMU2 is wrong but not why: it could be an old calibration, temperature or impact damage. Recalibrate and test again, and if it is still wrong, replace the board or disable that IMU according to the manual.