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Fig. 1. Stoniness classification process of forest soil, based on the excavator IMU data.

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Fig. 2. A drawing of the measurement setup and the coordinate axes in the excavator. The location of the measurement device is marked with the “IMU” label (IMU = inertial measurement unit).

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Fig. 3. Manual stoniness measurements at four different sites. The circles are the center points for the series of 10 bar insertions and the color indicates the year of the measurements. (Aerial photo © National Land Survey of Finland 2018).

Table 1. Initial features before feature selection.
Features for IMU signals
Basic descriptive statistics Mean Minimum
Median Maximum
Standard deviation (STD) 25th percentile
Variance 75th percentile
Median absolute deviation (MAD) Skewness
Interquartile range (IQR) Kurtosis
Signal metrics Peak to peak
Root-mean-square level (RMS)
Signal power
1-lag autocorrelation
Frequency domain properties Dominant frequency
Dominant frequency magnitude
Correlations Correlation coefficients between axes
Table 2. Features ranked highest by the ReliefF algorithm.
Ranked features for each axis by the ReliefF algorithm (Rank order)
Activity recognition Stoniness classification
Accelerometer X - Minimum (10)
Maximum (18)
Peak to peak (20)
Dominant frequency magnitude (21)
Autocorrelation (22)
Accelerometer Y Kurtosis (4)
Maximum (5)
MAD (11)
IQR (14)
75-percentile (24) 		Max (2)
Peak to peak (3)
Autocorrelation (5)
75-percentile (12)
STD (14)
Minimum (16)
Dominant frequency (23)
Power (24)
Variance (25)
Accelerometer Z Dominant frequency magnitude (7)
Autocorrelation (12)
Mean (15)
75-percentile (22)
Median (25) 		Autocorrelation (13)
MAD (15)
IQR (19)
Gyroscope X MAD (1)
Dominant frequency magnitude (10)
75-percentile (21) 		Autocorrelation (6)
Gyroscope Y - Autocorrelation (8)
Gyroscope Z Minimum (3)
75-percentile (6)
Median (8)
25-percentile (13)
Mean (20)
MAD (23) 		-
Correlation coeff. Acc. X – Acc. Y (2)
Acc. Y – Acc. Z (9)
Gyro. Y – Gyro. Z (19) 		Gyro. X – Gyro. Y (1)
Acc. Z – Gyro. Y (4)
Acc. X – Acc. Y (7)
Acc. Y – Gyro. X (9)
Acc. Z – Gyro. X (11)
Acc. X – Gyro. Z (17)
STD = standard deviation, MAD = Median absolute deviation, IQR = Interquartile range.
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Fig. 4. The misclassification rate with an increasing number of features selected by the ReliefF algorithm in (A) activity recognition and (B) stoniness classification.

Table 3. Selected features in activity recognition by the SFS algorithm.
Selected features for each axis by the SFS algorithm (activity recognition)
SVM BDTree KNN NaïveBayes LDA QDA
Accelerometer X RMS
Peak to peak 		Minimum - - - -
Accelerometer Y Variance STD Maximum
STD
Peak to peak 		STD Variance Variance
Accelerometer Z - - - - - -
Gyroscope X - - 25-percentile Median MAD MAD
Gyroscope Y - Peak to peak - - - -
Gyroscope Z - - - Mean Mean Mean
SVM = Support Vector Machine, BDTree = Binary Decision Tree, KNN = K-Nearest Neighbors, LDA = Linear Discriminant Analysis, QDA = Quadratic Discriminant Analysis. RMS = Root-mean-square level, STD = standard deviation, MAD = Median absolute deviation.
Table 4. Selected features in stoniness classification by the SFS algorithm.
Selected features for each axis by the SFS algorithm (stoniness classification)
SVM BDTree KNN NaïveBayes LDA QDA
Accelerometer X Dom. freq. - - - RMS
75-percentile
Dom. freq. mag. 		RMS
75-percentile
Dom. freq. mag.
Accelerometer Y Autocorrelation - - Mean
Skewness
Autocorrelation 		Median
Maximum
Variance
Power
Autocorrelation 		Median
Maximum
Variance
Power
Autocorrelation
Accelerometer Z STD
75-percentile 		- - Median
75-percentile 		Mean Mean
Gyroscope X Maximum - - - Maximum
Peak to peak 		Maximum
Peak to peak
Gyroscope Y Maximum - - MAD MAD
Kurtosis
Peak to peak 		MAD
Kurtosis
Peak to peak
Gyroscope Z Minimum Dom. freq. Dom. freq. - Minimum
Autocorrelation 		Minimum
Autocorrelation
Correlation coeff. - - - Acc. X – Acc. Y
Acc. X – Gyro. Y 		Acc. X – Gyro. Y Acc. X – Gyro. Y
SVM = Support Vector Machine, BDTree = Binary Decision Tree, KNN = K-Nearest Neighbors, LDA = Linear Discriminant Analysis, QDA = Quadratic Discriminant Analysis. RMS = Root-mean-square level, STD = standard deviation, MAD = Median absolute deviation.
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Fig. 5. The accuracy and percentage of false-positive predictions in the activity recognition using two feature-selection algorithms, ReliefF and Sequential Feature Selection (SFS).

Table 5. The stoniness prediction accuracy.
Stoniness prediction accuracy (%)
SVM BDTree KNN NaïveBayes LDA QDA ANN
Point prediction (ReliefF) 43.3 43.8 42.6 42.6 47.6 44.6 43.0
Point prediction (SFS) 45.0 37.7 45.6 44.6 44.6 40.8 43.0
Grid prediction (ReliefF) 66.1 69.6 37.5 64.3 35.7 57.1 62.5
Grid prediction (SFS) 75.0 26.8 46.4 50.0 28.6 53.6 62.5
SVM = Support Vector Machine, BDTree = Binary Decision Tree, KNN = K-Nearest Neighbors, LDA = Linear Discriminant Analysis, QDA = Quadratic Discriminant Analysis, ANN = a neural network model.
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Fig. 6. Predicted stoniness classes and manual measurements for the first site.

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Fig. 7. Predicted stoniness classes and manual measurements for the second site.

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Fig. 8. Predicted stoniness classes and manual measurements for the third site.

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Fig. 9. Predicted stoniness classes and manual measurements for the fourth site.

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Fig. 10. Entropy calculated for each grid cell in the first site.