Enhancing Motion Trajectory Prediction for Site Safety by Incorporating Attitude toward Risk

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1 425 Enhancing Motion Trajectory Prediction for Site Safety by Incorporating Attitude toward Risk Khandakar M. Rashid 1 and Amir H. Behzadan 2 1 Graduate Student, Dept. of Technology and Construction Management, Missouri State Univ., 901 S. National Ave., Springfield, MO khandakar201@live.missouristate.edu 2 Associate Professor, Dept. of Technology and Construction Management, Missouri State Univ., 901 S. National Ave., Springfield, MO abehzadan@missouristate.edu Abstract The unscripted nature of construction jobs puts equipment and workers in close proximity of one another which can lead to near-miss situations or contact collisions. Previous research has primarily focused on location-aware methods to improve construction safety from a technological perspective, but has fallen short in investigating the role of individuals in creating or avoiding safety accidents. This paper presents a preemptive safety framework that incorporates not only positional data but more importantly, workers perception of and attitude toward safety. First, a comprehensive review of previous work related to construction safety, resource tracking, trajectory prediction, and risk behavior is presented. Next, the designed methodology is explained and tested which incorporates worker s risk index (a measure of affinity for or aversion to risky behavior near hazards) with conventional trajectory modeling in order to better predict the worker s future position, and detect potential contact collisions in advance. In particular, we examine the reliability of polynomial regression and hidden Markov model (HMM) in predicting a worker s position given his/her positional data collected by a smartphone s GPS sensor. Next, HMM prediction is further modified by considering the worker s past walk trajectory near hazard zones. Preliminary results demonstrate that the developed motion trajectory prediction can reliably detect unsafe movements and near future collision events. The outcome of this research contributes to improving current practices of site safety monitoring. INTRODUCTION AND BACKGROUND Workers and equipment continuously interact in construction sites, and can come to close proximity of each another due to random movements and ever-changing site layout (Sacks, Rozenfeld, & Rosenfeld, 2009). Without proper coordination and site planning, such events can lead to contact collisions and threaten the safety and health of construction crew (Teizer, Ben, Clare, & Jimmie, 2010). Therefore, proactive safety monitoring and prevention that could alert workers before a hazardous situation occurs would be of great value. In the past, researchers have developed proximity safety warning and alert systems in construction. For instance, Tizer et al. (2010) used radio frequency (RF) to give an audio-visual alert to workers and equipment operators. Dinga et al. (2013) created a safety management tool which integrates fiber Bragg

2 426 grating (FBG) sensors and a radio frequency identification (RFID) system for labor tracking. Results of the experiment indicated an improvement in monitoring, detecting, and safety warning. Another research based on location-aware technologies that combined wireless communication, GPS, and GIS, enabled real time safety warning by automatically detecting the hazard, and alerting drivers to avoid collision (Wu, et al., 2013). Nonetheless, collecting timely field data to improve jobsite safety still remains a challenging task. The research presented in this paper takes advantage of mobile location-aware technologies, and investigates construction safety from a slightly different perspective by trying to answer the question of how much in advance can a worker be reliably alerted of hazardous encounters (e.g. close proximities) to avoid an accident? It is imperative that sending a warning message to a worker who is already inside a hazard zone may not serve the purpose. To this end, a framework that couples proximity analysis with motion trajectory prediction is developed. Trajectory prediction has been used in robotics (Bennewitz, Burgard, Cielniak, & Thrun, 2005), aerospace (Gong & McNally, 2004), maritime traffic management (Perera, Oliveira, & Guedes, 2012), physics and mechanics (Choi & Hebert, Learning and predicting moving object trajectory: a piecewise trajectory segment approach., 2006), and meteorology (Kim, Han, & Park, 2015) using clustering techniques, and learning and prediction algorithms (Vasquez & Fraichard, 2004). This research investigates and critically compares two trajectory prediction techniques, namely polynomial regression, and a more advanced method based on the hidden Markov model (HMM). A key point of departure in this research is that a conglomeration of factors (a.k.a risk profile) that influence one s behavior will be considered in trajectory prediction. Research has shown that a person s risk profile is directly influenced by age, gender, and level of experience (Salminen 2004, Cooper 2003, Charness & Gnezzy 2012). In summary, this research introduces a methodology that uses worker s positional data (captured by built-in smartphone GPS sensor), robust trajectory prediction, and worker s attitude towards risk to compile and send out preemptive proximity warnings before a contact collision occurs. RESEARCH METHODOLOGY As explained earlier, the developed methodology uses sensor data (smartphone GPS), coupled with risk attitude to predict a person s immediate future position, and generate safety alerts if he/she is in close proximity to hazards. Given that the accuracy of GPS sensors depends on several variables, a pilot test was performed to determine the average, minimum, and maximum errors obtained from an LG Nexus 5 device using five benchmark locations with known coordinates. The error values, calculated using the Haversine distance formula, were 3.63m, 2.17m, and 4.73m, respectively. Two separate prediction models are developed and tested: a polynomial regression model, and a hidden Markov model (HMM). Details of each model are explained below. Trajectory Prediction by Polynomial Regression Model. To establish a benchmark for position prediction, first a polynomial regression technique is developed to predict the motion trajectory of moving objects (i.e. workers, equipment). In this approach, positional data obtained in the past s time intervals are used to predict an object s position in interval s+1. Selecting the value for s is critical; a large s may result in a complicated regression model, while a small s may yield a low-accuracy model. In addition, finding the best polynomial degree n is key, since a high n value can result in overfitting, while a low n value can lead to underfitting. In this work,

427 given the versatility and randomness of movements on the jobsite, only the last 60 seconds of an object s movement are considered to predict its future position.

e. current longitude or r latitude) collected from the four sub- segmentss of the positional data, Eq. (1) Different values for n (from 1 to 5) are tested to find the best polynomial degree.

This can be attributed to the fact that predicted latitude and longitude values are expressed as functions of time.

3 427 given the versatility and randomness of movements on the jobsite, only the last 60 seconds of an object s movement are considered to predict its future position. This 60-second segment is further divided into four equal sub-segments (last 15, 30, 45, and 60 seconds). Equation (1) is the general polynomial formulation in which is the regression outpu (i.e. predicted longitude or latitude), and is the input (i.e. current longitude or r latitude) collected from the four sub- segmentss of the positional data, Eq. (1) Different values for n (from 1 to 5) are tested to find the best polynomial degree. In each step, predictedd values are compared with the actual (collected) values, and a discrepancy factor ( ) is calculated. Results indicate that tends to be larger for higher value of n. This can be attributed to the fact that predicted latitude and longitude values are expressed as functions of time. So, for a higher degree polynomial, a small error in prediction results in a significantly large. For this reason, a linear regression model (n = 1) is selected to minimize in polynomial regression. Trajectory Prediction by Hidden Markov Model (HMM). The major shortcoming of the linear regression model is that it does not fully capture the randomness of the worker s trajectory. To overcome this problem, a new trajectory prediction method based on HMM was examined in which trajectories are consideredd as discretee stochastic processes (i.e. random walks). A moving object s trajectory can be broken down into a number of short trajectory sections, as shown in Figure 1. A group of short sections with common statistical features (e.g. mean, variance, and covariance) are bundled into one cluster which is represented by a single average section ( a.k.a. latent segment) (Choi & Hebert, Learning and predicting moving object trajectory: a piecewise trajectory segment approach., 2006). Considering the limited horizon assumption, which states that the probability of a future location depends only onn the currentt location and not on the path by whichh the current location is achieved (Ramage, 2007), given a sequence of latent segments S 0, S 1, S2,.S n, the probability of a future latent segment, S n+1 to occur depends only on the current latent segment, S n, as stated in Equation (2),,,.. Eq. (2) Figure 1. Key elements of the HMMM prediction model. In HMM, these probabilities are termed transition probabilities and together create the transition matrix. Within a cluster of sections, the likelihood of a trajectory section to be generated from a specific latent segment is calculated from multivariate Gaussian probability distribution function.

4 428 These likelihood values are stored in the likelihood matrix. The HMM is trained to compute normalized trajectory sections, latent segments, and transition and likelihood matrices. Th model first checks the likelihood matrix to find the latent segment that best resembles the observed trajectory section. Next, it determines the most probable future latent segment using the transitionn matrix, and finally provides the most likely trajectory segment from the likelihood matrix. Learning Latent Segments. In this research, training trajectory data is collected at 1 Hz frequency from 26 individuals resulting in a total of 1,166 minutes of data (latitude, longitude). Each trajectory is divided into 12-second short sections. As shown in Figure 2, since trajectories have different starting positions, directions, and velocities, they are first normalized by translation to the origin (0, 0), rotation so that the initial direction is (1, 0), and scaling so that the initial velocity is unit velocity. This results in 4,662 normalized short trajectory sections extracted from the training data. After normalization, each short trajectory section is represented by a 22-dimensional vector consisting of x and y coordinates at 1-second intervals. Next, K- means clustering (Choi & Hebert, Learning and predicting moving object trajectory: a piecewise trajectory segment approach., 2006) is applied to find statistically similar trajectory sections. In this research, 8 clusters were found to best represent all short trajectory sections. Each cluster is describedd by a single latent segment the attributes of which are contained in a 5-by-12 characteristics matrix. In particular, five statistical features (means of x and y coordinates, variances of x and y coordinates, and covariance of x, y coordinate) are calculated for 12 data points (times t 1, t 2,.,t 12 ) of all trajectory segments in a cluster. Figure 2. Normalization of trajectory sections. HMM Training and Prediction. Training the Markov model involves calculating the transition probabilities between all latent segments. These probabilities form an 8-by-8 transition matrix which contains the probability of any given latent segment to be followed by other latent segments. Next, the likelihood of a normalized section to be generated from a latent segment is calculated using a bivariate normal probability distribution function. From Bayes theorem, it can be said that the latent segment with the highest probability of generating a trajectory section is the one with the highest likelihood. Since each segment consists of 12 data points, at least 12 points are required to create one segment and launchh the prediction. The process starts by observing and normalizing the latest segment (l n ) whichh contains the last 12 data points. Next, the likelihood matrix is used to select the latent segment (S n ) thatt most closely resembles the normalized l n (maximum likelihood probability). Then,, the most probable next latent segment (S n+1 ) is computed from the transition matrix. Subsequently, the likelihood matrix is used to find the trajectory segment which is most likely to be generated from S n+1. Finally, the trajectory segment is denormalized to generate the predicted futuree trajectory (l n+1 ). The first two points of

429 l n+1 are patched to the existing trajectory. seconds in advance. Therefore, the HMM model can predict up to 10 Incorporating Risk-Taking Behavior into Trajectoryy Prediction.

Two types of risk factors aree considered: angular risk factor (α), and linear risk factor (m). The overall risk factor (k) is the product of angular and linear risk factors.

To this end, an individual s aggregate risk factor is calculated and updated based on the historyy of his/her movements in the vicinity of hazards.

If a worker moves directly towards the hazard, α is 1 (risk-taker), and if he/she movess in the opposite direction of the hazard, α is 0 (risk-averse) person.

The linear risk factor (m), on the other hand, is based on the discrepancy between predicted and actual positions, and represents how much radial error the prediction has relative to actual position,

5 429 l n+1 are patched to the existing trajectory. seconds in advance. Therefore, the HMM model can predict up to 10 Incorporating Risk-Taking Behavior into Trajectoryy Prediction. In general, for a risk-takeshe is more likely person, the predictedd future location is moved closer to the hazard since he or to be on a collision course. Two types of risk factors aree considered: angular risk factor (α), and linear risk factor (m). The overall risk factor (k) is the product of angular and linear risk factors. To yield accurate results, it is important to properly quantify the risk attitude (referred to in this paper as the aggregate risk factor or µ) of each worker. To this end, an individual s aggregate risk factor is calculated and updated based on the historyy of his/her movements in the vicinity of hazards. In particular, α is calculated based on the worker s actual path. If a worker moves directly towards the hazard, α is 1 (risk-taker), and if he/she movess in the opposite direction of the hazard, α is 0 (risk-averse) person. For all other directions of move, α ranges between 0 and 1. The linear risk factor (m), on the other hand, is based on the discrepancy between predicted and actual positions, and represents how much radial error the prediction has relative to actual position, with the hazard zone at the center of the circle. In Figure 3, the predicted position is shown as 4ʹ. Distances d between actual position (4) and hazard, and d 1 between 4ʹ and hazard can be calculated using the haversine formula. Knowingg d and d 1, k is calculated using Equation (3). The aggregate risk factor (µ) is initially zero and workers are assumed neutral (neither risk- taker nor risk-averse). This will be modifiedd over time as positional data is collected. In the next iteration, point 4ʹ is shifted k units toward H. The adjusted position is labeled as 4ʹʹ. Next, given k and d 1, the modifiedd linear distance d 2 (between H andd 4ʹʹ) is calculated and compared with a predefined proximity radius (R 1 ) which is a function of the hazard type. If d 2 R 1, the worker is too close to the hazard and an alert is generated. If risk factor m is negative, it is changed to zero, thus no adjustment is made (4ʹʹ=4ʹ), whichh makes the analysis more conservative. Next, µ is updated for the next step using the weighted average of k values from previous steps. Eq. (3) Figure 3. Linear risk factor and adjustment of prediction.

6 430 EXPERIMENTS AND RESULTS Evaluation of Position Prediction Models. To evaluate the reliability of regression and HMM models in position prediction, three trajectories are used, each representing a different level of complexity and randomness of movement. As shown in Figure 4, the first trajectory is simple, the second trajectory contains several sharp turns, and the third trajectory is the most extreme containing many frequent sharp turns. Figure 4 also shows the 95-percentile prediction error for all trajectories. For each trajectory, the prediction error increases with the time span (i.e. predicting 10 seconds in advance is more erroneous than predicting 5 seconds in advance). Another observation is that for both models, the error increases with an increase in trajectory complexity. For instance, using the polynomial regression model, the prediction error for 10 seconds in advance for trajectory 1 and trajectory 3 are 22.5 m and 41.2 m, respectively, and the same values using HMM are 14.1 m and 18.6 m, respectively. Conceivably, since trajectories are considered random walks, it is difficult to predict accurately in the presence of many sharp turns or sudden changes in direction. With the average human walking speed of 1.38 m/s, a 5-second advance prediction results in a collision event prediction at ~7 meters away from hazard. For the case of 5-second advance prediction in Figure 4, HMM results in significantly lower errors compared to polynomial regression. In particular, HMM reduces the error by ~42% for trajectory 1, ~50% for trajectory 2, and ~59% for trajectory 3. Trajectory 1 Trajectory 2 95% error (meter) Trajectory Prediction Error Second into future Regression_Traj 1 Regression_Traj 2 Regression_Traj 3 HMM_Traj 1 HMM_Traj 2 HMM_Traj 3 Figure 4. Prediction error using polynomial regression and HMM methods. Prediction of Potential Collision Events. To evaluate the robustness of HMM prediction, several experiments were conducted using both stationary (fixed) and moving hazards. In this Section, a scenario involving a moving hazard is described. In all experiments, a secondary radius (R 2 ) from the hazard is used to denote the buffer zone. The safety alert system is activated

431 when the worker is inside the buffer zone. In addition, a primary radius (R 1 ) from the hazard is used as the hazard zone.

Teizer et al. (2015) showed that blind spots of an excavator are 12 m (max) and 8 m (min).

Figure 5(a) shows a 30- minute log of positional data for the equipment moving between two points, and a worker moving in the peripheral area

Predictions are further adjusted considering the worker s risk attitude. Each adjusted position that falls inside the buffer zone is tagged as an event.

as in Figures 5 (b), (c), and (d). In total, there were 369 events, with 77 potential collisions (worker r in the hazard zone).

For instance, for 5-second advance prediction with risk, recall increasess by 6% from ~88% to ~94%, while precision falls only by 1% from ~89% to ~88% %.

00% 98.00% 96.00% 94.00% 92.00% 90.00% 1 6 Seconds into future HMM Prediction with Risk Factor HMM Prediction with Risk Factor Figure 5.

7 431 when the worker is inside the buffer zone. In addition, a primary radius (R 1 ) from the hazard is used as the hazard zone. A collision event is logged when the worker is inside the hazard zone. R 1 and R2 can be selected using different rules such as equipment blind spots. Teizer et al. (2015) showed that blind spots of an excavator are 12 m (max) and 8 m (min). In the experiment presented here, R 1 = 10 m and R 2 = 20 m from a moving equipment. Figure 5(a) shows a 30- minute log of positional data for the equipment moving between two points, and a worker moving in the peripheral area occasionally crossing thee equipment path. Initially, a 1-second to 10-second advance prediction is made using HMM. Predictions are further adjusted considering the worker s risk attitude. Each adjusted position that falls inside the buffer zone is tagged as an event. Events are labeled as true positive (TP), false negative (FN), false positive (FP), or true negative (TN) for precision, recall, and accuracy analyses, as in Figures 5 (b), (c), and (d). In total, there were 369 events, with 77 potential collisions (worker r in the hazard zone). While precession, recall, and accuracy are less for farther prediction horizons, ncorporating risk attitude results in a higher recall. For instance, for 5-second advance prediction with risk, recall increasess by 6% from ~88% to ~94%, while precision falls only by 1% from ~89% to ~88% %. Precision i % 95.00% 90.00% 85.00% 80.00% 75.00% 70.00% 1 6 Seconds into future Accuracy Recall % 95.00% 90.00% 85.00% 80.00% 1 6 Seconds into future HMM Prediction with Risk Factor % 98.00% 96.00% 94.00% 92.00% 90.00% 1 6 Seconds into future HMM Prediction with Risk Factor HMM Prediction with Risk Factor Figure 5. Recall, precession, and accuracyy analyses (moving hazard). SUMMARY AND CONCLUSI IONS In order to achieve the ultimate goal of accident-free construction jobsites, a solid mathematical foundation and thought process is essential. To this end, this research presented a methodology for designing and evaluating trajectory prediction models for preemptive proximity safety alert

8 432 systems. First, a benchmark prediction was done using polynomial regression. Next, an HMMbased model was trained and tested using real trajectories collected from several human subjects in the field. Analysis showed that HMM outperformed polynomial regression in position prediction. Future work in this work will aim at improving prediction models to cover more complex trajectories in dynamic settings with multiple workers and hazard zones. REFERENCES Bennewitz, M., Burgard, W., Cielniak, G., & Thrun, S. (2005). Learning motion patterns of people for compliant robot motion. The International Journal of Robotics Research., 24(1), Charness, G., & Gneezy, U. (2012). Strong evidence for gender differences in risk taking. Journal of Economic Behavior & Organization., 83(1), Choi, P. P., & Hebert, M. (2006). Learning and predicting moving object trajectory: a piecewise trajectory segment approach. Robotics Institute, p Cooper, D. (2003). Psychology, risk and safety. Professional Safety, 48(11), Dinga, L. Y., Zhoua, C., Dengb, Q. X., Luoa, H. B., Yec, X. W., Nic, Y. Q., & Guoa, P. (2013). Real-time safety early warning system for cross passage construction in Yangtze Riverbed Metro Tunnel based on the internet of things. Automation in Construction, 36, Gong, C., & McNally, D. (2004). A methodology for automated trajectory prediction analysis. AIAA Guidance, Navigation, and Control Conference and Exhibit, Providence, Rhode Island. Kim, Y. K., Han, J., & Park, H. (2015). Trajectory Prediction for Using Real Data and Real Meteorological Data. Ubiquitous Computing Application and Wireless Sensor, Springer, Netherland. Perera, L. P., Oliveira, P., & Guedes, S. C. (2012). Maritime traffic monitoring based on vessel detection, tracking, state estimation, and trajectory prediction. Intelligent Transportation Systems, IEEE Transactions, 13(3), Ramage, D. (2007). Hidden Markov models fundamentals. Lecture Notes. < stanford. edu/section/cs229-hmm. pdf> Sacks, R., Rozenfeld, O., & Rosenfeld, Y. (2009). Spatial and temporal exposure to safety hazards in construction. Journal of contruction engineering and management 135(8), Salminen, S. (2004). Have young workers more injuries than older ones? An international literature review. Journal of safety research, 35(5), Teizer, J., Ben, S. A., Clare, E. F., & Jimmie, H. (2010). Autonomous pro-active real-time construction worker and equipment operator proximity safety alert system. Automation in construction, 19(5), Vasquez, D., & Fraichard, T. (2004). Motion prediction for moving objects: a statistical approach. IEEE International Conference on Robotics and Automation, 4, New Orleans, LA.

9 433 Waldron, I., McCloskey, C., & Earle, I. (2005). Trends in gender differences in accident mortality: Relationships to changing gender roles and other societal trends. Demographic Research, 13, Wu, H., Tao, J., Li, X., Chi, X., Li, H., Hua, X., Chen, N. (2013). A location based service approach for collision warning systems in concrete dam construction. Safety science, 51(1),

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