# Hazards in Motion: Development of Mobile Geofences for Use in Logging Safety

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{i}is the delay for the ith intersection, P

_{i}is the predicted intersection time for the ith intersection calculated using the recorded GNSS coordinates, and O

_{i}is the field-recorded National Institute of Standards and Technology (NIST) time when the faller crossed the ith intersection point.

_{ijkl}is ith time delay, a

_{j}is the jth intersection angle, s

_{k}is the kth standard deviation, and r

_{l}is the lth geofence radius.

## 3. Results

#### 3.1. Field Results

#### 3.2. Simulation Results

^{−16}.

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Illustration of the potential use of global navigation satellite system (GNSS) technology paired with radio frequency transmission (GNSS-RF) on a timber sale. GNSS-RF personal location devices (PLDs) receive positional information from GNSS satellites and send that information to nearby units using radio frequency transmission. In this figure, geofences with radii of approximately two tree lengths surround the manual fallers, delineating virtual perimeters associated with occupational hazards. Audible or sensory (e.g., vibration) alerts are triggered when other PLDs cross into the hazard areas, which move with individual workers.

**Figure 2.**Illustration showing field experiment setup. The manual faller carried a T5 transponder (PLD) and a chainsaw along a 300-m route. Alpha 100 units recorded the GNSS data and were located at the start and end of the route. The six stationary PLDs located perpendicular to the route are shown. This figure shows the manual faller surrounded by mobile geofences of three radii, illustrating three possible intersection angles.

**Figure 3.**Box-and-whisker plot of field results showing geofence intersection alert delay as a function of the geofence radius-intersection angle combinations. The panels are grouped by pace (30, 45, and 60 bpm).

**Figure 4.**Distance traveled over time as a function of walking pace. The slope of each line corresponds to the mean observed speed for each level of pace. Positive distances indicate how far the faller has walked into or past the geofence boundary when the alert is generated (i.e., a positive, late warning). Negative distances indicate how far ahead of the intersection point the faller is when the alert is generated (i.e., a negative, early warning).

**Figure 5.**Box-and-whisker plot of simulation results showing geofence alert delay as a function of intersection angle grouped by radius and GNSS standard deviation. To improve clarity, the figure is a subset of factor-level combinations, representing three geofence radii (r = 50, 80, and 110 m) and three standard deviations (s = 1, 3, and 5 m). Upper panel numbers are GNSS standard deviation and lower panels represent geofence radii.

**Figure 6.**Visualization of GNSS error bearings resulting in early alerts. In each cell, the black circle is a stationary geofence and the blue circle represents a mobile geofence located 20 m from its initial intersection point with the stationary geofence. In the first column, the geofence intersection angle will be 0°. In the second and third columns, the intersections will occur at 45° and 90°, respectively. The red circle in each cell illustrates the location of the mobile geofence if it were moved 20 m from its true location, with each row representing one of eight possible directions in which that 20-m error might occur. Arrows in each cell indicate the directionality of error, with light blue arrows indicating movements that result in early intersection alerts. Black arrows indicate movements that do not result in early intersection alerts. The top row depicts all eight error directions in each column below and summarizes which of those directions result in early alerts.

**Figure 7.**Proportion of error bearing angles that result in early alert plotted as a function of the intersection angle. Calculations were done for five intersection angles (0°, 22.5°, 45°, 67.5°, and 90°). The upper panel labels represent the four starting locations (d = 1, 4, 7, and 10 m from the true intersection point) and the lower panels are the three GNSS standard deviations (s = 1, 3, and 5 m).

**Table 1.**Table showing the seven different mobile geofence radii and their intersections with the six different PLDs. The resulting intersection angles are shown.

PLD | Radius (m) | Angle (Degrees) |
---|---|---|

1 | 30 | 0 |

2 | 30 | 90 |

1 | 45 | 0 |

2 | 45 | 42 |

1 | 60 | 0 |

2 | 60 | 30 |

3 | 60 | 90 |

1 | 75 | 0 |

2 | 75 | 24 |

3 | 75 | 53 |

1 | 90 | 0 |

2 | 90 | 19 |

3 | 90 | 42 |

4 | 90 | 90 |

1 | 105 | 0 |

2 | 105 | 17 |

3 | 105 | 35 |

4 | 105 | 59 |

1 | 120 | 0 |

2 | 120 | 14 |

3 | 120 | 30 |

4 | 120 | 49 |

5 | 120 | 90 |

**Table 2.**Analysis of variance (ANOVA) results comparing models with and without autoregressive error structure. Model 1 was fit without correlated errors while Model 2 was fit with autoregressive error structure.

Model | DF ^{1} | AIC ^{2} | BIC ^{3} | Log Lik ^{4} | Test | L Ratio ^{5} | p-Value ^{6} |
---|---|---|---|---|---|---|---|

1 | 210 | 4394.911 | 5325.49 | −1987.456 | - | - | - |

2 | 211 | 4162.837 | 5097.848 | −1870.418 | 1 vs. 2 | 234.074 | <0.0001 |

^{1}Model degrees of freedom;

^{2}Akaike Information Criterion;

^{3}Bayesian Information Criterion;

^{4}Restricted log likelihood;

^{5}Likelihood ratio;

^{6}p-value associated with likelihood ratio statistic.

**Table 3.**ANOVA results from the full model showing all main effects and interactions. The response was the square root of the alert delay and the model was fit using autoregressive error structure.

Model Term | Num DF ^{1} | Den DF ^{2} | F-Statistic ^{3} | p-Value ^{4} |
---|---|---|---|---|

(Intercept) | 1 | 396 | 8.43367 | 0.0039 |

Rad Ang | 22 | 396 | 76.00023 | <0.0001 |

Pace | 2 | 16 | 1.24997 | 0.313 |

TI | 2 | 16 | 1.16111 | 0.3382 |

RadAng: Pace | 44 | 396 | 0.937 | 0.5896 |

RadAng: TI | 44 | 396 | 0.83993 | 0.7571 |

Pace: TI | 4 | 16 | 0.60202 | 0.6667 |

RadAng:Pace: TI | 88 | 396 | 1.24072 | 0.0874 |

^{1}Numerator degrees of freedom;

^{2}Denominator degrees of freedom;

^{3}F-statistic for Wald tests for model terms;

^{4}p-value associated with Wald tests for model terms.

**Table 4.**Summary of the exponential model (Equation (2)) fitted to the simulation results showing the estimate of each model coefficient, standard errors and p-values.

Parameter | Estimate ^{1} | Std. Error ^{2} | t-Statistic ^{3} | p-Value ^{4} |
---|---|---|---|---|

b0 | 3.86 × 10^{0} | 1.35 × 10^{-2} | 286.41 | <2 × 10^{−16} |

b1 | −5.79 × 10^{-2} | 3.64 × 10^{-4} | −159.06 | <2 × 10^{−16} |

b2 | 6.92 × 10^{-2} | 7.33 × 10^{-5} | 944.50 | <2 × 10^{−16} |

b3 | −2.00 × 10^{0} | 2.03 × 10^{-3} | −985.52 | <2 × 10^{−16} |

b4 | −4.29 × 10^{-3} | 1.27 × 10^{-4} | −33.76 | <2 × 10^{−16} |

^{1}Estimated model coefficient;

^{2}Standard error of estimated model coefficient;

^{3}t-statistic for each model coefficient;

^{4}p-value associated with the t-statistic for model coefficients.

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**MDPI and ACS Style**

Zimbelman, E.G.; Keefe, R.F.; Strand, E.K.; Kolden, C.A.; Wempe, A.M. Hazards in Motion: Development of Mobile Geofences for Use in Logging Safety. *Sensors* **2017**, *17*, 822.
https://doi.org/10.3390/s17040822

**AMA Style**

Zimbelman EG, Keefe RF, Strand EK, Kolden CA, Wempe AM. Hazards in Motion: Development of Mobile Geofences for Use in Logging Safety. *Sensors*. 2017; 17(4):822.
https://doi.org/10.3390/s17040822

**Chicago/Turabian Style**

Zimbelman, Eloise G., Robert F. Keefe, Eva K. Strand, Crystal A. Kolden, and Ann M. Wempe. 2017. "Hazards in Motion: Development of Mobile Geofences for Use in Logging Safety" *Sensors* 17, no. 4: 822.
https://doi.org/10.3390/s17040822