# Novel Hierarchical Fall Detection Algorithm Using a Multiphase Fall Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. Fall Detection Algorithm

#### 2.2.1. Threshold-Based Fall Detection Algorithms

^{2}) upper fall threshold for the trunk had the highest specificity, and suggested that the trunk was the optimal wearing position for a fall sensor. Kangas et al. [27] used a single threshold–based fall detection algorithm with posture detection after the fall with a tri-axial accelerometer attached at the waist, wrist, or head to investigate the placement of a fall detection sensor. The results showed that the head-worn accelerometer provided perfect results, and the authors suggested that the head was a reasonable wearing position for fall detection. Designing more complex algorithms than the single threshold–based fall detection algorithms, Kangas et al. [28] evaluated different low-complexity fall detection algorithms using accelerometers attached at the waist, wrist, and head. The results ultimately indicated that the effective sensor placements were the waist and head. The sensor at the head level had the highest accuracy, but the usability and user’s acceptance should be considered in more detail, i.e., ergonomics. In conclusion, an accelerometer worn on the waist might be an optimal choice for a wearable sensor–based fall detection algorithm.

#### 2.2.2. Machine Learning–Based Fall Detection Algorithms

## 3. Materials and Methods

#### 3.1. Hierarchical Fall Detection Algorithm

_{xyz}is defined as the Euclidean norm of tri-axial accelerations as calculated by Equation (1), where ${a}_{x}$, ${a}_{y}$, and ${a}_{z}$ are the acceleration (g) in the x-, y-, and z-axes, respectively. Then the time index corresponding to a maximum of Norm

_{xyz}is identified as the critical point. Finally, the data frame is determined by taking 1.5 s (128 Hz × 1.5 s = 192 samples) before the critical point and 2.5 s (128 Hz × 2.5 s = 320 samples) after the critical point, corresponding to a time window of 513 samples (192 + time index of the critical point + 320).

_{xyz}and Norm

_{hori}. Norm

_{xyz}is used to describe the spatial variation of acceleration during the falling interval. Norm

_{hori}is defined as the Euclidean norm of acceleration in the horizontal plane and can be calculated by Equation (2), which is used to describe the change of velocity in the horizontal plane of the body. The threshold is determined by observing the distribution of the maximum Norm

_{xyz}and Norm

_{hori}of the data frames. The Norm

_{xyz}and Norm

_{hori}distribution of falls and ADLs are presented in Figure 3.

_{xyz}and Norm

_{hori}corresponding to ${F}_{train}$ that can be presented as ${V}_{train}=\left\{{v}_{i}^{train}\right|i=1,2,\dots ,{N}_{train}\}$ and ${W}_{train}=\left\{{w}_{i}^{train}\right|i=1,\text{}2,\dots ,{N}_{train}\}$, respectively. According to the distribution of ${V}_{train}$ and ${W}_{train}$, two thresholds, including ${T}_{fall}^{Nor{m}_{xyz}}$ and ${T}_{fall}^{Nor{m}_{hori}}$, for the absolute fall detection can be determined, where ${T}_{fall}^{Nor{m}_{xyz}}$ and ${T}_{fall}^{Nor{m}_{hori}}$ are the maximum Norm

_{xyz}and Norm

_{hori}values of ADLs, respectively. Additionally, two thresholds, including ${T}_{ADL}^{Nor{m}_{xyz}}$ and ${T}_{ADL}^{Nor{m}_{hori}}$, for the absolute ADL identification can be determined, where ${T}_{ADL}^{Nor{m}_{xyz}}$ and ${T}_{ADL}^{Nor{m}_{hori}}$ are the minimum Norm

_{xyz}and Norm

_{hori}values of falls, respectively. Similarly, two sets of maximum Norm

_{xyz}and Norm

_{hori}values corresponding to ${F}_{test}$ can be presented as ${V}_{test}=\left\{{v}_{i}^{test}\right|i=1,\text{}2,\dots ,{N}_{test}\}$ and ${W}_{test}=\left\{{w}_{i}^{test}|i=1,\text{}2,\dots ,{N}_{test}\right\}$, respectively. Finally, the threshold-based classifier applied to the testing set can be defined as follows:

_{xyz}is closer to 0g has been studied in various durations, including 120–200 ms [22], 300–500 ms [21], and 400–800 ms [43]. The impact phase is determined by the person hitting the ground and has a signal pattern with a sharp pulsation, usually less than one second. In the rest phase, the person remains motionless in a prone or supine position and usually has a mitigating signal pattern. There is potential for the multiphase fall model to be improved, involving important aspects of the fall event. The knowledge-based fall detection algorithm using a multiphase fall model is proposed to provide the system with advanced functionality to deal with unidentified data frames.

_{xyz}larger than 6g, and the other is the maximum of Norm

_{xyz}less than 6g. The impact phase of the first situation is determined by taking 10 samples before and after the critical point, and a total of 21 samples (10 + critical point + 10) while the maximum of Norm

_{xyz}is larger than 6g. The impact phase of another situation is determined by taking 10 samples before, and 20 samples after, the critical point, for a total of 31 samples (10 + critical point + 20) while the maximum of Norm

_{xyz}is less than 6g. Then, the rest phase is determined by taking the following samples after the defined impact phase within the data frame. Finally, the free fall phase is determined by taking 32 samples before the impact phase. The proposed multiphase fall segmentation is sufficient for the knowledge-based fall detection algorithm to identify multiple situations, so that the necessary information can be obtained. The illustration of the multiphase fall segmentation for two situations is shown in Figure 4, and there are three phases, in turn: the free fall phase, impact phase, and rest phase.

#### 3.2. Performance Evaluation Criteria

## 4. Results and Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

**Table A1.**The total testing data of falls and ADLs in each round of five-fold cross-validation rounds.

Round | Stand | Stand up | Sit down | Walk | Stoop | Jump | Walk Backward | Stand from Sit | Stand from Squat | Sit (Normal) | Sit (Fast) | Lie (Normal) | Lie (Fast) | Go up Stairs | Go down Stairs | Walk (Normal) | Walk (Fast) | Jump (Ground) | Jump (Bed) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 15 | 15 | 16 | 16 | 15 | 15 | 3 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 6 | 6 |

16 | 15 | 15 | 15 | 15 | 15 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 8 | 6 | 6 | 6 | 6 | 6 | |

15 | 15 | 15 | 15 | 16 | 16 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 5 | 6 | |

15 | 16 | 15 | 15 | 15 | 15 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 6 | 6 | |

15 | 15 | 15 | 15 | 15 | 15 | 4 | 6 | 6 | 6 | 6 | 5 | 6 | 8 | 5 | 6 | 6 | 6 | 6 | |

2 | 15 | 15 | 15 | 16 | 15 | 15 | 4 | 6 | 6 | 6 | 6 | 5 | 6 | 7 | 5 | 6 | 6 | 6 | 6 |

16 | 15 | 15 | 15 | 15 | 16 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 5 | 6 | |

15 | 16 | 16 | 15 | 15 | 15 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 8 | 6 | 6 | 6 | 6 | 6 | |

15 | 15 | 15 | 15 | 16 | 15 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 8 | 6 | 6 | 6 | 6 | 6 | |

15 | 15 | 15 | 15 | 15 | 15 | 3 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 6 | 6 | |

3 | 15 | 15 | 15 | 15 | 15 | 15 | 3 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 5 | 6 |

15 | 15 | 15 | 16 | 15 | 15 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 6 | 6 | |

15 | 15 | 15 | 15 | 15 | 16 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 6 | 6 | |

15 | 16 | 15 | 15 | 16 | 15 | 4 | 6 | 6 | 6 | 6 | 5 | 6 | 8 | 6 | 6 | 6 | 6 | 6 | |

16 | 15 | 16 | 15 | 15 | 15 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 8 | 5 | 6 | 6 | 6 | 6 | |

4 | 16 | 15 | 16 | 15 | 15 | 15 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 8 | 6 | 6 | 6 | 6 | 6 |

15 | 16 | 15 | 16 | 15 | 15 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 6 | 6 | |

15 | 15 | 15 | 15 | 15 | 15 | 3 | 6 | 6 | 6 | 6 | 5 | 6 | 8 | 5 | 6 | 6 | 6 | 6 | |

15 | 15 | 15 | 15 | 15 | 15 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 6 | 6 | |

15 | 15 | 15 | 15 | 16 | 16 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 5 | 6 | |

5 | 16 | 15 | 15 | 16 | 15 | 15 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 6 | 6 | 6 | 6 | 6 |

15 | 15 | 16 | 15 | 16 | 15 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 7 | 5 | 6 | 6 | 6 | 6 | |

15 | 15 | 15 | 15 | 15 | 15 | 4 | 6 | 6 | 6 | 6 | 5 | 6 | 7 | 6 | 6 | 6 | 5 | 6 | |

15 | 16 | 15 | 15 | 15 | 16 | 4 | 6 | 6 | 6 | 6 | 6 | 6 | 8 | 6 | 6 | 6 | 6 | 6 | |

15 | 15 | 15 | 15 | 15 | 15 | 3 | 6 | 6 | 6 | 6 | 6 | 6 | 8 | 6 | 6 | 6 | 6 | 6 | |

total | 380 | 380 | 380 | 380 | 380 | 380 | 95 | 150 | 150 | 150 | 150 | 145 | 150 | 185 | 145 | 150 | 150 | 145 | 150 |

**Table A2.**The total testing data of false predictions for falls and ADLs using the knowledge-based algorithm.

Round | Stand | Stand up | Sit down | Walk | Stoop | Jump | Walk Backward | Stand from Sit | Stand from Squat | Sit (Normal) | Sit (Fast) | Lie (Normal) | Lie (Fast) | Go up Stairs | Go down Stairs | Walk (Normal) | Walk (Fast) | Jump (Ground) | Jump (Bed) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 1 | |||||||||||||||||

1 | 1 | ||||||||||||||||||

1 | |||||||||||||||||||

2 | 2 | ||||||||||||||||||

1 | |||||||||||||||||||

1 | |||||||||||||||||||

1 | 1 | ||||||||||||||||||

3 | 1 | ||||||||||||||||||

1 | |||||||||||||||||||

1 | |||||||||||||||||||

1 | |||||||||||||||||||

1 | 1 | ||||||||||||||||||

4 | 1 | ||||||||||||||||||

1 | |||||||||||||||||||

1 | |||||||||||||||||||

1 | |||||||||||||||||||

2 | |||||||||||||||||||

5 | 1 | 1 | |||||||||||||||||

1 | |||||||||||||||||||

1 | |||||||||||||||||||

1 | |||||||||||||||||||

total | 0 | 0 | 0 | 0 | 5 | 0 | 0 | 0 | 0 | 0 | 0 | 8 | 15 | 0 | 0 | 0 | 0 | 0 | 0 |

**Table A3.**The total testing data of false predictions for falls and ADLs using the machine learning–based algorithm.

Round | Stand | Stand up | Sit down | Walk | Stoop | Jump | Walk Backward | Stand from Sit | Stand from Squat | Sit (Normal) | Sit (Fast) | Lie (Normal) | Lie (Fast) | Go up Stairs | Go down Stairs | Walk (Normal) | Walk (Fast) | Jump (Ground) | Jump (Bed) |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 1 | 2 | 1 | ||||||||||||||||

1 | |||||||||||||||||||

1 | |||||||||||||||||||

1 | |||||||||||||||||||

2 | 1 | ||||||||||||||||||

1 | 1 | ||||||||||||||||||

1 | 2 | 3 | |||||||||||||||||

3 | 1 | ||||||||||||||||||

1 | |||||||||||||||||||

2 | |||||||||||||||||||

2 | 2 | ||||||||||||||||||

4 | 1 | 2 | |||||||||||||||||

1 | |||||||||||||||||||

1 | 1 | 1 | 1 | 1 | |||||||||||||||

2 | |||||||||||||||||||

1 | |||||||||||||||||||

5 | 1 | 1 | 1 | ||||||||||||||||

1 | 1 | ||||||||||||||||||

1 | |||||||||||||||||||

3 | |||||||||||||||||||

1 | 1 | ||||||||||||||||||

total | 0 | 0 | 3 | 0 | 8 | 2 | 5 | 0 | 0 | 0 | 4 | 8 | 11 | 0 | 0 | 1 | 4 | 1 |

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**Figure 1.**(

**a**) Wearing position and the axial direction of sensor; (

**b**) Schematic view of the participant wearing a helmet, waist, knee, and elbow guards.

**Figure 3.**The illustration of the Norm

_{xyz}and Norm

_{hori}distribution of falls and ADLs. The left seven activities are falls and the right 12 activities are ADLs. The green line is determined by the maximum Norm

_{xyz}value of ADLs. The purple line is determined by the minimum Norm

_{xyz}value of falls. (

**a**) The boxplot of maximum Norm

_{xyz}values for falls and ADLs; (

**b**) The boxplot of maximum Norm

_{hori}values for falls and ADLs.

**Figure 4.**The illustration of the multiphase fall segmentation for two situations. There are three phases, in turn: free fall phase, impact phase, and rest phase. (

**a**) The situation of the maximum of Norm

_{xyz}is larger than 6g, taking the data frame of the standing forward fall, for example; (

**b**) The situation of the maximum of Norm

_{xyz}is less than 6g, taking the data frame of the back-walking backward fall for example.

Article (Year) | Detection Algorithm (Methods) | Sensor(s) | Placement | Features Used for Fall Detection | Fall and ADL Types | Results |
---|---|---|---|---|---|---|

Kangas et al. (2008) [28] | Threshold-based | Tri-axial accelerometer | Waist Wrist Head | Beginning of the fall (SV_{TOT})Falling velocity Fall impact (SV _{TOT}, SV_{D}, SV_{MaxMin}, or Z_{2})Posture after impact | Falls: 9 ADLs: -- | Sn ^{2}: 97% (Waist)Sp ^{2}: 100% (Waist) |

Dinh et al. (2009) [34] | Machine learning–based (NB, RBF, SVM, C4.5 Ripple down rule learner) | Tri-axial accelerometer Dual-axial gyroscope | Thorax | Acceleration (X, Y and Z axis) Gyroscope (X and Y axis) | Falls: 4 ADLs: 3 | Naïve Bayesian Acc ^{2}: 97.3%Radial Basis Function Acc ^{2}: 95.8% |

Chao et al. (2009) [35] | Threshold-based | Tri-axial accelerometer | Chest Waist | Acceleration magnitude Acceleration cross-product | Falls: 8 ADLs: 13 | Sn ^{2}: 98.2% (Chest)Sp ^{2}: 92.4% (Chest)Sn ^{2}: 98.2% (Waist)Sp ^{2}: 89.9% (Waist) |

Bourke et al. (2010) [36] | Threshold-based | Tri-axial accelerometer | Waist | Upper fall threshold Lower fall threshold Vertical velocity | Falls: 8 ADLs: 4 | Velocity + impact + posture Sn ^{2}: 100%Sp ^{2}: 100%Less than 1 false positive a day |

Choi et al. (2011) [32] | Machine learning–based (NB) | SNA ^{1}:Tri-axial accelerometer, dual-axial gyroscope DNA ^{1}:Tri-axial accelerometer, one-axial gyroscope | SNA ^{1}: ChestDNA ^{1}: Chest,Thigh | SNA ^{1}:Acceleration (X, Y and Z axis) Gyroscope (X and Y axis) DNA ^{1}:Acceleration (X, Y and Z axis) Gyroscope (X axis) | SNA ^{1}: Falls: 4ADLs: 3 DNA ^{1}: Falls: 4ADLs: 4 | SNA ^{1}: Acc ^{2}: 99.4%DNA ^{1}: Acc ^{2}: 99.8% |

Rescio et al. (2013) [37] | Machine learning–based (SVM) | Tri-axial accelerometer | Waist | The product between the value of the acceleration peak and the change in the CPO | -- | Sn ^{2}: 97.7%Sp ^{2}: 94.8% |

Özdemir et al. (2014) [31] | Machine learning–based (kNN, LSM, SVM, Bayesian Decision Making, Dynamic Time Warping, ANN) | Tri-axial accelerometer Tri-axial gyroscope Tri-axial magnetometer | Head, Chest, Waist, Wrist, Thigh, Ankle | Minimum, Maximum Mean, Variance Skewness Kurtosis Autocorrelation Discrete Fourier transform | Falls: 20 ADLs: 16 | kNN Sn ^{2}: 100%Sp ^{2}: 99.91% |

Huynh et al. (2015) [38] | Threshold-based | Tri-axial accelerometer Tri-axial gyroscope | Chest | Upper fall threshold Lower fall threshold | Falls: 4 ADLs: 6 | Sn ^{2}: 96.55%Sp ^{2}: 89.50% |

Palmerini et al. (2015) [39] | Threshold-based | Tri-axial accelerometer | Lower back | Continuous wavelet transform coefficients Upper peak value Lower peak value | Falls: 5 ADLs: -- | Wavelet Sn ^{2}: 90%Sp ^{2}: 89.7% |

He et al. (2016) [40] | Machine learning–based (kNN, NB, Bayes Net, ANN, Decision Tree, Bagging, Ripper) | Tri-axial accelerometer Tri-axial gyroscope | upper trunk | Resultant acceleration (α) Resultant angular velocity (ω) | Falls: 2 ADLs: 3 | kNN (k = 3) Sn ^{2}: 100%Sp ^{2}: 99.91%Acc ^{2}: 97.8548% |

Chen et al. (2016) [41] | Machine learning–based (SVM) | Tri-axial accelerometer | Waist | Maximum magnitude of the sum vector Rotation angle Slope Acceleration in the xy-plane Standard deviation of the sun vector | Falls: 6 ADLs: 6 | Sn ^{2}: 95.76%Sp ^{2}: 93.28%Acc ^{2}: 94.58% |

Gibson et al. (2016) [42] | Machine learning-based (ANN, kNN, RBF, Probabilistic Principal Component Analysis, Linear Discriminant Analysis) | Tri-axial accelerometer | Chest | Discrete wavelet transform | Falls: 6 ADLs: 5 | Radial Basis Function Sn ^{2}: 100%Sp ^{2}: 99.91%Linear Discriminant Analysis Sn ^{2}: 100%Sp ^{2}: 99.91% |

^{1}SNA: single-node analysis; DNA: double-node analysis;

^{2}Sn: sensitivity; Sp: specificity; and Acc: accuracy.

No. | Activities before Fall | Characteristics | |||

1 | Stand | Forward | Backward | Lateral (right and left) | |

2 | Stand up | Forward | Backward | Lateral (right and left) | |

3 | Sit down | Forward | Backward | Lateral (right and left) | |

4 | Stoop | Forward | Backward | Lateral (right and left) | |

5 | Walk | Forward | Backward | Lateral (right and left) | |

6 | Walk backward | -- | Backward | -- | |

7 | Jump | Forward | Backward | Lateral (right and left) | |

No. | Activities of Daily Living | Characteristic | No. | Activities of Daily Living | Characteristic |

1 | Stand up | From sit | 2 | Stand up | From squat |

3 | Sit down | Normal | 4 | Sit down | Fast |

5 | Lie on the bed | Normal | 6 | Lie on the bed | Fast |

7 | Go up stairs | Normal | 8 | Go down stairs | Normal |

9 | Walk | Normal | 10 | Walk | Fast |

11 | Jump | On the ground | 12 | Jump | On the bed |

Feature Vector, F = (f_{1}, f_{2}, …, f_{54}) $\in $ R_{54} | Feature Description |
---|---|

f_{1}~f_{3} | mean a_{x}(i); mean a_{y}(i); mean a_{x}(i), where i = 1, ..., m ^{1} |

f_{4}~f_{6} | mean a_{norm}(i) ^{2}; mean a_{verti}(i) ^{3}; mean a_{hori}(i) ^{4}, where i = 1, ..., m ^{1} |

f_{7}~f_{9} | std a_{x}(i); std a_{y}(i); std a_{x}(i), where i = 1, ..., m ^{1} |

f_{10}~f_{12} | std a_{norm}(i) ^{2}; std a_{verti}(i) ^{3}; std a_{hori}(i) ^{4}, where i = 1, ..., m ^{1} |

f_{13}~f_{15} | var a_{x}(i); var a_{y}(i); var a_{x}(i), where i = 1, ..., m ^{1} |

f_{16}~f_{18} | var a_{norm}(i) ^{2}; var a_{verti}(i) ^{3}; var a_{hori}(i) ^{4}, where i = 1, ..., m ^{1} |

f_{19}~f_{21} | max a_{x}(i); max a_{y}(i); max a_{x}(i), where i = 1, ..., m ^{1} |

f_{22}~f_{24} | max a_{norm}(i) ^{2}; max a_{verti}(i) ^{3}; max a_{hori}(i) ^{4}, where i = 1, ..., m ^{1} |

f_{25}~f_{27} | min a_{x}(i); min a_{y}(i); min a_{x}(i), where i = 1, ..., m ^{1} |

f_{28}~f_{30} | min a_{norm}(i) ^{2}; min a_{verti}(i) ^{3}; min a_{hori}(i) ^{4}, where i = 1, ..., m ^{1} |

f_{31}~f_{33} | range a_{x}(i); range a_{y}(i); range a_{x}(i), where i = 1, ..., m ^{1} |

f_{34}~f_{36} | range a_{norm}(i) ^{2}; range a_{verti}(i) ^{3}; range a_{hori}(i) ^{4}, where i = 1, ..., m ^{1} |

f_{37}~f_{39} | kurtosis a_{x}(i); kurtosis a_{y}(i); kurtosis a_{x}(i), where i = 1, ..., m ^{1} |

f_{40}~f_{42} | kurtosis a_{norm}(i) ^{2}; kurtosis a_{verti}(i) ^{3}; kurtosis a_{hori}(i) ^{4}, where i = 1, ..., m ^{1} |

f_{43}~f_{45} | skewness a_{x}(i); skewness a_{y}(i); skewness a_{x}(i), where i = 1, ..., m ^{1} |

f_{46}~f_{48} | skewness a_{norm}(i) ^{2}; skewness a_{verti}(i) ^{3}; skewness a_{hori}(i) ^{4}, where i = 1, ..., m ^{1} |

f_{49} | Correlation coefficient between a_{x} and a_{y} |

f_{50} | Correlation coefficient between a_{x} and a_{z} |

f_{51} | Correlation coefficient between a_{y} and a_{z} |

f_{52} | Correlation coefficient between a_{norm} ^{2} and a_{verti} ^{3} |

f_{53} | Correlation coefficient between a_{norm} ^{2} and a_{hori} ^{4} |

f_{54} | Correlation coefficient between a_{verti} ^{3} and a_{hori} ^{4} |

^{1}m: Determined size of data frame (or phase);

^{2}a

_{norm}: Euclidean norm of tri-axial acceleration;

^{3}a

_{verti}: Euclidean norm of acceleration on coronal plane;

^{4}a

_{hori}: Euclidean norm of acceleration on horizontal plane.

**Table 4.**The overall performance of five-fold cross-validation over five rounds for the knowledge-based fall detection algorithm. Std: standard deviation.

Knowledge-Based Fall Detection Algorithm | ||||||
---|---|---|---|---|---|---|

Round | 1 | 2 | 3 | 4 | 5 | Mean (Std) |

Sensitivity (%) | 100 (0) | 99.79 (0.47) | 99.58 (0.57) | 99.79 (0.48) | 99.79 (0.47) | 99.79 (0.43) |

Specificity (%) | 98.63 (1.36) | 98.62 (1.00) | 98.90 (0.61) | 98.62 (0.98) | 98.91 (0.61) | 98.74 (0.88) |

Precision (%) | 98.97 (1.03) | 98.96 (0.73) | 99.16 (0.47) | 98.97 (0.72) | 99.17 (0.47) | 99.05 (0.66) |

Accuracy (%) | 99.41 (0.59) | 99.29 (0.50) | 99.29 (0.26) | 99.28 (0.27) | 99.41 (0.42) | 99.33 (0.40) |

**Table 5.**The overall performance of five-fold cross-validation over five rounds for the machine learning–based fall detection algorithm.

Machine Learning–Based Fall Detection Algorithm | ||||||
---|---|---|---|---|---|---|

Round | 1 | 2 | 3 | 4 | 5 | Mean (Std) |

Sensitivity (%) | 99.58 (0.58) | 99.16 (1.37) | 99.36 (0.94) | 99.15 (0.89) | 98.95 (0.74) | 99.24 (0.89) |

Specificity (%) | 98.63 (1.68) | 98.63 (1.66) | 98.63 (2.37) | 97.80 (2.50) | 98.37 (1.48) | 98.41 (1.84) |

Precision (%) | 98.97 (1.26) | 98.95 (1.29) | 98.99 (1.73) | 98.35 (1.88) | 98.76 (1.10) | 98.81 (1.38) |

Accuracy (%) | 99.17 (0.90) | 98.93 (1.47) | 99.05 (0.90) | 98.56 (1.02) | 98.69 (0.49) | 98.88 (0.95) |

**Table 6.**The confusion matrix of the knowledge-based algorithm for each fall and ADL. The number of falls and ADLs is the total number of five-fold cross-validations over five rounds.

Predict Results and Measure Matrix | Fall (Ground Truth) | ADL (Ground Truth) | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Stand | stand up | Sit down | Walk | Stoop | Jump | Walk Backward | Stand from Sit | Stand from Squat | Sit (Normal) | Sit (Fast) | Lie (Normal) | Lie (Fast) | Go up Stairs | Go down Stairs | Walk (Normal) | Walk (Fast) | Jump (Ground) | Jump (Bed) | |

Fall (Predicted) | 380 | 380 | 380 | 380 | 375 | 380 | 95 | 0 | 0 | 0 | 0 | 8 | 15 | 0 | 0 | 0 | 0 | 0 | 0 |

ADL (Predicted) | 0 | 0 | 0 | 0 | 5 | 0 | 0 | 150 | 150 | 150 | 150 | 137 | 135 | 185 | 145 | 150 | 150 | 145 | 150 |

Sensitivity (%) | 100 | 100 | 100 | 100 | 98.68 | 100 | 100 | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- |

Specificity (%) | -- | -- | -- | -- | -- | -- | -- | 100 | 100 | 100 | 100 | 94.48 | 90 | 100 | 100 | 100 | 100 | 100 | 100 |

False positive rate (%) | -- | -- | -- | -- | -- | -- | -- | 0 | 0 | 0 | 0 | 5.52 | 10 | 0 | 0 | 0 | 0 | 0 | 0 |

False negative rate (%) | 0 | 0 | 0 | 0 | 1.32 | 0 | 0 | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- |

**Table 7.**The confusion matrix of the machine learning–based algorithm for each fall and ADL. The number of falls and ADLs is the total number of five-fold cross-validations over five rounds.

Predict Results and Measure Matrix | Fall (Ground Truth) | ADL (Ground Truth) | |||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Stand | Stand up | Sit down | Walk | Stoop | Jump | Walk Backward | Stand from Sit | Stand from Squat | Sit (Normal) | Sit (Fast) | Lie (Normal) | Lie (Fast) | Go up Stairs | Go down Stairs | Walk (Normal) | Walk (Fast) | Jump (Ground) | Jump (Bed) | |

Fall (Predicted) | 380 | 380 | 377 | 380 | 372 | 378 | 90 | 0 | 0 | 0 | 4 | 8 | 11 | 0 | 0 | 1 | 4 | 1 | 0 |

ADL (Predicted) | 0 | 0 | 3 | 0 | 8 | 2 | 5 | 150 | 150 | 150 | 146 | 137 | 139 | 185 | 145 | 149 | 146 | 144 | 150 |

Sensitivity (%) | 100 | 100 | 99.21 | 100 | 97.76 | 99.47 | 94.74 | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- |

Specificity (%) | -- | -- | -- | -- | -- | -- | -- | 100 | 100 | 100 | 97.33 | 94.48 | 91.86 | 100 | 100 | 99.33 | 97.33 | 99.31 | 100 |

False positive rate (%) | -- | -- | -- | -- | -- | -- | -- | 0 | 0 | 0 | 2.67 | 5.52 | 8.14 | 0 | 0 | 0.67 | 2.67 | 0.69 | 0 |

False negative rate (%) | 0 | 0 | 0.79 | 0 | 2.1 | 0.53 | 5.26 | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hsieh, C.-Y.; Liu, K.-C.; Huang, C.-N.; Chu, W.-C.; Chan, C.-T.
Novel Hierarchical Fall Detection Algorithm Using a Multiphase Fall Model. *Sensors* **2017**, *17*, 307.
https://doi.org/10.3390/s17020307

**AMA Style**

Hsieh C-Y, Liu K-C, Huang C-N, Chu W-C, Chan C-T.
Novel Hierarchical Fall Detection Algorithm Using a Multiphase Fall Model. *Sensors*. 2017; 17(2):307.
https://doi.org/10.3390/s17020307

**Chicago/Turabian Style**

Hsieh, Chia-Yeh, Kai-Chun Liu, Chih-Ning Huang, Woei-Chyn Chu, and Chia-Tai Chan.
2017. "Novel Hierarchical Fall Detection Algorithm Using a Multiphase Fall Model" *Sensors* 17, no. 2: 307.
https://doi.org/10.3390/s17020307