A Hierarchical Bayesian Model of Workers’ Responses to Proximity Warnings of Construction Safety Hazards: Towards Constant Review of Safety Risk Control Measures
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Xiaochun Luo1; Heng Li2; Fei Dai3; Dongping Cao4; Xincong Yang5; Hongling Guo6
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Hong Kong. E-mail:
[email protected]
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E-mail:
[email protected]
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Senior Research Fellow, Dept. of Building and Real Estate, Hong Kong Polytechnic Univ., Hung Hom, Kowloon,
Chair Professor, Dept. of Building and Real Estate, Hong Kong Polytechnic Univ., Hung Hom, Kowloon, Hong Kong.
Assistant Professor, Dept. of Civil and Environmental Engineering, West Virginia Univ., Morgantown, WV 26506-
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6103, USA. E-mail:
[email protected]
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Kong. Email:
[email protected]
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Email:
[email protected]
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Beijing, China (corresponding author). Email:
[email protected]
Postdoctoral Fellow, Dept. of Building and Real Estate, Hong Kong Polytechnic Univ., Hung Hom, Kowloon, Hong
PhD Candidate, Dept. of Building and Real Estate, Hong Kong Polytechnic Univ., Hung Hom, Kowloon, Hong Kong.
Associate Professor, Dept. of Construction Management, Tsinghua University, Qinghuayuan, Haidian District,
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Abstract
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Quickly changing and complicated workplace conditions, which are typical of construction projects, have
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always been contributing to the poor safety record of the construction industry. However, few of existing
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approaches to reviewing control measures take into account or effectively tackle them. This paper
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introduces a three-level (i.e., individual hazards, hazard types, and generic hazards) hierarchical Bayesian
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model based on workers’ responses to proximity warnings of safety hazards to address the problem. The
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proposed model distinguishes between two uses of proximity warnings (i.e., as the primary control measure
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and as the secondary measure), takes as input observational response rates, takes into account prior
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knowledge on workers’ responses to similar hazards, and finally produces as output estimated response
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rates (ERRs). These ERRs are the primary indicator of the effectiveness of a given control measure as well
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as the validity of a previously identified safety hazard. A 17-day field experiment was conducted to test the
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proposed approach preliminarily using a location-based proximity warning system, which was featured to
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warn workers of safety hazards and record their responses to warnings. The experimental results
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demonstrated the potential of the proposed approach. The limitations of the present study and the
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directions for future research are also discussed.
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Keywords
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Proximity warning system; Safety risk management; Control measure review; Hierarchical Bayesian
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modeling
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Introduction
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Safety risk management is traditionally conducted in the form of four sequential tasks: hazard identification,
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risk evaluation, risk control, and control measure review (Manuele, 2005; Safe Work Australia, 2011). In
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practice, the approaches to hazard identification are also used in control measure review (Safe Work
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Australia, 2011), but with a different focus: identification focuses on finding newly-presented hazards, while
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review focuses on validating those already identified. Hazards can be identified, or control measures
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reviewed, through a general engineering evaluation based on previous data and operational history (an
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informal approach), or a formal approach using well-developed identification/review techniques
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(Kumamoto and Henley, 1996). These approaches are either reactive where information is analyzed after
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accident occurrence or proactive where identification is based on historical data from similar hazards
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(Khanzode, et al., 2012).
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Although these reactive and proactive approaches do facilitate construction safety risk management, few
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of them effectively take into account quickly changing and complicated workplace conditions, which have
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always been contributing to the poor safety record of the construction industry (Haslam, et al., 2005; Hide,
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et al., 2003). In Hong Kong, the numbers of fatal accidents in construction in 2013, 2014, and 2015 were
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respectively 37, 38, and 43 (Occupational Safety and Health Branch, 2015; Occupational Safety and Health
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Branch, 2016). Quickly changing and complicated workplace conditions were identified to have directly
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accounted for over 30% of these accidents. There is a need to review safety risk control measures effectively
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with the consideration of quickly changing and complicated workplace conditions.
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Over the years, numerous variations and applications of proximity warning systems (PWS’s) have been
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published in the literature (Carbonari, et al., 2011; Luo, et al., 2016b; Teizer and Cheng, 2015). Among them,
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location-based PWS’s first detect dangerous proximities and then alert those people affected (Luo, et al.,
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2016b); they acquire locations of both potential hazards and objects to be protected, and then evaluate the
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relative distances between them to identify dangerous situations. These applications possess the ability to
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monitor construction processes continuously. This study attempts to introduce a method of constantly
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reviewing safety risk control measures based on workers’ responses to proximity warnings of safety hazards.
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Review of Construction Safety Risk Management
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The four steps in safety risk management (i.e., hazard identification, risk assessment, risk control, and
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control measure review) can be organized into a cycle in that the output of the final step can meaningfully
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inform and supplement the first step (see Fig. 1). This section reviews the literature concerning the four
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stages together on account of (1) hazard identification and control review traditionally share most of their
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methods, (2) the methods for risk assessment were used to enlighten the method design in this study with
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respect to their dynamic nature, and (3) the hierarchical risk control methods were referenced to distinguish
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between two primary uses of proximity warnings, which structure the proposed review logic (detailed in
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next section).
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Fig. 1. Safety risk management cycle
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Hazard Identification
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Hazard means “the inherent property or ability of something to cause harm” (Holt, 2001) and identification
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is to identify the potential hazards. Khanzode, et al. (2012) group the hazard identification methods into
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three categories. The first is referred to as the biased reactive approach, which is adopted after accident
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occurrence. Examples of it are general engineering evaluations. The second is named as the biased
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proactive approach, which is based on information from similar construction systems or methods of
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previous data from the same system or method. Examples include fault-tree analysis and event-tree analysis.
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The last is the unbiased proactive approach, which is adopted without waiting for the events to occur, and
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without any restrictive assumptions about the presence of specific hazards, but with a focus on searching
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potential hazardous elements and targets.
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However, hazard identification and definition can become a major challenge due to the large-scale, dynamic,
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and complex nature of construction projects. In fact, the hazard identification levels are far from ideal and,
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for example, a studied project within both the railway and general construction industry only reported a
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66.5% hazard identification level (Carter and Smith, 2006). Efficiency problem becomes outstanding on the
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traditional identification approaches.
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Automating hazard identification that is an intuitive approach to addressing the efficiency problem above
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is implemented primarily with two strategies. The first strategy is to identify construction activities’ safety
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hazards in conjunction with construction schedules. For example, Navon and Kolton (2006) investigated
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how to automate fall prevention procedures and developed an automated model that identifies the
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dangerous activities in project schedules, which in turn lead to the identification of fall hazards. Hallowell,
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et al. (2011) proposed a safety risk interaction matrix to quantify the impact that pairwise spatial and
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temporal interactions on the base-level risk of 25 common highway construction tasks in the United States.
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Based on that matrix, Esmaeili and Hallowell (2013) introduced a system to produce predictive plots of
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safety risk over time based on the temporal and spatial interactions among concurrent activities.
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The second strategy is to utilize building information models (BIM) to identify latent safety hazards,
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primarily by rule-based reasoning, where geometric information of building elements is checked against
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safety rules to determine dangerous conditions and factors (Kiviniemi, et al., 2011). For example, rule-based
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fall hazard identification can be implemented in two steps: the first goes to identify if there are hazardous
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openings or edges, and the second is to determine if adequate protection facilities (e.g., guardrails) are put
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in place (Zhang, et al., 2011; Zhang, et al., 2015; Zhang, et al., 2013). Similarly, Hammad, et al. (2012)
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reported a study to prevent falls from a height by automatically identifying hazardous slab edges and
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generating corresponding virtual fences. More recently, Kim, et al. (2016) reported a method of automated
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hazard identification based on the deviation between optimal routes, which were shortest paths
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determined by BIM, and actual routes of workers, which were collected with a real-time location system.
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Risk Assessment
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Risk means “the chance or probability of loss”, and an evaluation of the potential for failure (Holt, 2001).
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Risk assessment methods can be classified as qualitative methods producing as output a qualitative risk
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level and quantitative methods providing a quantitative score (Luo, et al., 2016a). However, the traditional
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and prospective methods are criticized as ignoring the actual execution of construction activities
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(Mitropoulos and Namboodiri, 2010) and being subject to safety officers’ experience and diligence.
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Furthermore, officers can be overwhelmed due to the changing and complex working place situations and
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concurrent involvement of numerous resources on construction sites (Behzadan, et al., 2008). To address
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this problem, Luo, et al. (2016a) introduced a dynamic risk assessment method by quantifying workers’
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hazard exposure amounts based on real-time location data of workers and construction equipment.
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Similarly but more specifically, Teizer and Cheng (2015) proposed a leading safety indicator, “proximity
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hazard indicator,” by automatically gathering and analyzing the spatial–temporal conflicts between
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workers-on-foot and large construction equipment. Continuous informational feeding and feedback
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between workplaces and workers are essential to the methods envisaged to monitor dynamic construction
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processes.
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Risk Control
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The measures of controlling safety risks can be meaningfully organized into a six-level hierarchy in terms of
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their effectiveness (Manuele, 2005): (1) eliminate hazards through system design and redesign, (2) reduce
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risks by substituting less hazardous methods and materials, (3) incorporate safety devices, (4) provide
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warning systems, (5) apply administrative controls, and (6) provide personal protection equipment. The first
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three levels are more useful because they are preventive actions that reduce risk by design, substitute
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methods and materials, and most importantly, rely least on personnel performance (Manuele, 2005). The
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last three levels rely significantly on human behavior and thus are believed to be less effective.
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However, research attributes the majority of safety accidents to human behavior. Heinrich (1939) stated
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that unsafety acts cause around 85% of accidents. Blackmon and Gramopadhye (1995) found that unsafe
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behavior causes 98% of accidents. Therefore, measures at the last three levels are critical to reducing safety
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accidents on sites. In this context, the authors have developed a PWS, the Proactive Construction
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Management System (PCMS), which pertains to the fourth level, “provide warning systems”, and has been
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introduced in detail in (Luo, et al., 2016a; Luo, et al., 2016b).
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Control Measure Review
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To ensure control measures work as planned, they should be reviewed, and if necessary, revised (Manuele,
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2005; Safe Work Australia, 2011). Thus, control measure review is an integral step in the effective problem-
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solving technique (Manuele, 2005). The dynamic nature of construction sites, which can turn the engaged
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measures ineffective, or give rise to a new safety risk that these means may be not adequate to handle,
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intensifies the need to examine control measures (Safe Work Australia, 2011). In the former case, the
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engaged control measures should be revised. In the latter case, the approaches toward hazard identification
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are used in reviewing control measures (Safe Work Australia, 2011); control measure review focuses on
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validating the hazards already identified, while hazard identification focuses on finding newly-presented
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hazards. However, review processes with these methods seldom take into account or effectively tackle
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quickly changing workplace conditions; they are primarily based on previous information from similar
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hazards or factual information after accident occurrence.
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In summary, rapidly changing workplace conditions pose the greatest challenge to existing methods for
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reviewing safety risk control measures, which take the form of either reactive analysis or proactive
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projection. However, the engaged control measures can quickly become invalid due to an entirely new
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hazardous situation or a sharp change in the envisaged position. Therefore, continuously reviewing those
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employed risk control measures is critical for making a prompt and efficient response to situational changes.
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Research Objective, Scope, and Definitions
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The objective of this paper was to introduce a novel method for continuous review of safety risk control
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measures according to workers’ responses to proximity warnings of safety hazards. The PCMS was used to
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track workers and record their answers to proximity warnings. Note that the hazards investigated in this
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paper were restricted to those that can be addressed by proximity warnings. These hazards are classified
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into static hazards, e.g., unprotected roof edges, roof and floor openings, and dynamic hazards, e.g., tower
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crane hooks, excavators and bulldozers (Luo, et al., 2016b). They are defined in the form of virtual fences
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at the backend of the PCMS to identify dangerous proximities of objects to be protected.
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A 2-second rule was introduced to evaluate if a worker responds to a proximity warning in light of the earlier
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research on driver brake reaction time (Green, 2000; Summala, 2000), which found that a driver could react
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to surprise events, such as an object suddenly moving into their path, in roughly 1.5 seconds. In
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consideration of that, most of the time workers and equipment on construction sites move at a slower
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speed than cars do on highways, the effective response time threshold was set as 2 seconds (Luo, et al.,
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2016a). As a result, a reaction is viewed as a response only if a worker does not walk closer to a hazard after
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2 seconds from receiving a personal hazard-specific warning until they leave the hazard area, or it is viewed
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as a neglect. The response rate (RR) of a particular hazard can be observational and defined as the ratio of
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the number of responses to the number of warnings occurred in the hazard area in a unit time, which was
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a workday in this study. The observational RR is abbreviated as ORR for the sake of convenience.
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However, it is desirable to view RRs from a comprehensive perspective since safety hazards on construction
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sites are dynamic in nature. Usually, construction activities at different stages by multiple trades are
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involved, and site situations change quickly. The observational numbers of responses to and neglects of
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warnings can conceal safety hazards with higher risks or overstate those with lower risks. Prior knowledge
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on workers’ responses to similar hazards can be utilized to counterbalance the impact of the simplification
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of only using observational data.
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Hierarchical Bayesian modeling is an appropriate approach to accommodating all these concerns due to its
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potential to overrule classical frequentist statistics in applications where respondents give multiple
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observational data (Gelman, et al., 2014). It describes a statistical model in a hierarchical form of various
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levels estimating the parameters of the posterior distribution using the Bayesian method (Allenby, et al.,
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2005). To this end, this paper introduces a three-level (i.e., individual hazards, hazard types, and generic
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hazards) hierarchical Bayesian model based on workers’ responses to proximity warnings of safety hazards.
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Therefore, control measures can be hierarchically reviewed based on the prior knowledge on workers’
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responses to warnings of similar hazards as well as the observational warnings and responses. The posterior
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estimates of RRs at different levels are also referred to as estimated response rates (ERRs) in this study,
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which are the primary indicator to review the effectiveness of a given control measure as well as the validity
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of a previously identified safety hazard.
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This study differentiates between two uses of proximity warnings (see Fig. 2), namely as the secondary risk
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control measure and as the primary control measure. In contrast with those more effective control
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measures such as elimination, substitution, and safety devices (Manuele, 2005), providing warning systems
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is a second or supplementary choice. When those more effective control measures are adopted, warnings
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can be a complementary prevention. In this case, warnings are referred to as a secondary control measure.
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In practice, however, elimination, substitution, and safety devices are not employed to cope with all risk
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situations, due to tight time schedules or technical reasons. For example, on those congested construction
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sites, workers-on-foot can frequently be observed working around large construction equipment such as
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excavators and trucks, and moving near lifting areas, openings that are not defended for material convey.
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In these situations, proximity warnings are used as the primary control measure. As a result, the decision
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tree for reviewing control measures is formed as follows:
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(1) When proximity warnings are used as the primary risk control measure of a hazard, the higher the ERR
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is, the more effective the control would be. In this situation, when the ERR arrives at a level, more
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effective control strategies such as elimination, substitution, or safety devices should be considered.
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On the contrary, a small ERR denotes that proximity warnings are little meaningful to workers, and the
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virtual hazard can be removed in the PCMS.
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(2) When warnings are used as the secondary risk control, the higher the ERR is, the less effective the
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primary control would be. In this situation, the primary control should be adjusted in response to the
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changed workplace conditions. However, if the ERR is small, safety officers are suggested to involve the
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review decision in that the fact can be either the primary control is effective, or the hazard is invalid. In
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the former situation, it is adequate to maintain the status quo. In the latter case, it is suggested that
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the virtual hazard is removed in the PCMS to reduce false warnings.
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Fig. 2. Decision tree for reviewing control measures
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Hierarchical Bayesian Modelling
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Fig. 3 shows the hierarchical Bayesian model, which was proposed to implement the control measure
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review logic, and defined by latent data intermediate between the observational data and underlying
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parameters. In this model, the observational data precisely consists of (1) the number of warnings 𝑛𝑖
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occurred in hazard area i, (2) the number of responses 𝑥𝑖 observed in hazard area i, (3) the number of
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hazard areas 𝑁ℎ , and (4) the number of hazard types 𝑁𝑡 . The underlying parameters were organized into
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a three-level structure: individual hazards, hazard types, and generic hazards, and thus the estimate of the
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parameter of any particular hazard depends on the estimates of the parameters of its hazard type, which
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in turn depend on the estimates of the parameters of generic hazards.
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Fig. 3. Bayesian hierarchical model
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In the hierarchical model, the level of individual hazards was designed to describe workers’ responses to
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proximity warnings in a particular hazard area i, which belongs to a specific hazard type j. As a result, the
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number of responses 𝑥𝑖 depends on the number of warnings 𝑛𝑖 and the RR 𝜃𝑖 in the form of a binomial
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distribution, expressed as Equation 1. This modeling section recognized that site workers tend to have
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different RRs to various hazards because of the distinct and complicated nature of the workplace conditions
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that form individual hazards, and other complex factors such as task urgency and complexity, workers’
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safety knowledge and experience (Luo, et al., 2016a).
252 𝑥𝑖 ~𝐵(𝑛𝑖 , 𝜃𝑖 )
(1)
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The RR 𝜃𝑖 obviously is not a constant and was supposed to be distributed as a beta density with shape
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constants 𝑎𝑗 and 𝑏𝑗 , expressed as Equation 2, where the subscript j indicates that hazard i falls into hazard
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type j. This treatment assumes that workers’ responses to a type of hazards are similar and thus can be
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clustered. It enables that ERRs of various hazards of an identical hazard type can be meaningfully compared
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and evaluated.
259 𝜃𝑖 ~𝐵𝑒𝑡𝑎(𝑎𝑗 , 𝑏𝑗 ) 260
(2)
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However, to convert a prior belief expressed in terms of central tendency and sample size into equivalent,
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the values of 𝑎𝑗 and 𝑏𝑗 in the beta distribution were re-expressed with the mode ω𝑗 , and concentration
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κ𝑗 of the beta distribution: 𝑎𝑗 = 𝜔𝑗 (𝜅𝑗 − 2) + 1 and 𝑏𝑗 = (1 − 𝜔𝑗 )(κ𝑗 − 2) + 1 for κ𝑗 > 2 , where
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𝜔𝑗 = (𝑎𝑗 − 1)/(𝑎𝑗 + 𝑏𝑗 − 2) and κ𝑗 = 𝑎𝑗 + 𝑏𝑗 . Therefore, concerning hazard type j, 𝜔𝑗 represents a
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prior belief about 𝜃𝑖 , its posterior estimate is the ERR of hazard type j, and the value of κ𝑗 governs how
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near 𝜃𝑖 is to 𝜔𝑗 , with larger values of κ𝑗 generating values of 𝜃𝑖 more concentrated near 𝜔𝑗 (Kruschke,
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2014). Consequently, Equation 2 was re-written as Equation 3.
268 𝜃𝑖 ~𝐵𝑒𝑡𝑎(𝜔𝑗 (𝜅𝑗 − 2) + 1, (1 − 𝜔𝑗 )(𝜅𝑗 − 2) + 1)
(3)
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Besides, the study supposed the distribution over 𝜔𝑗 as another beta distribution expressed as Equation
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4. Similarly, the parameters 𝜔 and 𝜅 denote the mode and the concentration of the distribution over 𝜔𝑗 .
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Most importantly, 𝜔 and 𝜅 are the parameters at the generic hazard level constraining the estimates of
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the parameters at the hazard type level, which in turn limit the estimates at the individual hazard level. The
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posterior estimate of 𝜔 is the ERR of the generic hazards.
275 𝜔𝑗 ~𝐵𝑒𝑡𝑎(𝜔(𝜅 − 2) + 1, (1 − 𝜔)(𝜅 − 2) + 1)
(4)
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In real situations, the value of 𝜅𝑗 is not well known in advance, and instead, this paper used the previously
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observational data to inform its credible values. Intuitively, when the data from different hazards of hazard
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type j shows very similar RRs, 𝜅𝑗 is large. But when the data shows diverse RRs, then 𝜅𝑗 is small. To
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express prior uncertainty about 𝜅𝑗 , the hierarchical model includes a prior distribution on 𝜅𝑗 . Because the
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value of 𝜅𝑗 2 must be non-negative, the prior distribution on 𝜅𝑗 2 must not allow negative values. A
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gamma distribution was adopted to represent its density, as in Equation 5, where S𝜅 and 𝑅𝜅 are its shape
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and rate parameters. Similarly, at the generic hazard level, 𝜅 was treated in the same way with 𝜅𝑗 and
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supposed to be distributed as another gamma distribution as in Equation 6, which shares the shape and
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rate parameters with 𝜅𝑗 .
286 (𝜅𝑗 − 2)~𝐺𝑎𝑚𝑚𝑎(S𝜅 , 𝑅𝜅 )
(5)
(𝜅 − 2)~𝐺𝑎𝑚𝑚𝑎(S𝜅 , 𝑅𝜅 )
(6)
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The prior distribution over 𝜔 was selected as a beta distribution as in Equation 7, where 𝐴𝜔 and 𝐵𝜔 are
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constants determined by prior knowledge on the RR of generic hazards. In this case, it is believed that ω is
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typically near the mode of the distribution, (𝐴𝜔 − 1)/(𝐴𝜔 + 𝐵𝜔 − 2).
291 𝜔~𝐵𝑒𝑡𝑎(𝐴𝜔 , 𝐵𝜔 )
(7)
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In summary, the proposed hierarchical Bayesian model consists of three levels. At the individual hazard
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level, the parameters to be estimated are their RRs < 𝜃1 , 𝜃2 , … , 𝜃𝑁ℎ > . At the hazard type level, the
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parameters to be estimated are the modes < 𝜔1 , 𝜔2 , … , 𝜔𝑁𝑡 >, which represent the RRs of hazard types,
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and the concentrations < 𝜅1 , 𝜅2 , … , 𝜅𝑁𝑡 >. At the generic hazard level, the parameters to be estimated are
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the mode 𝜔 representing the RR of generic hazards, and the concentration 𝜅. Therefore, the continuous
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review of safety risk control measures is transformed into estimating these model parameters according to
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the observational data and the prior knowledge on the prior distributions of 𝜅𝑗 , 𝜔, and 𝜅.
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Experiment
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The specific technologies and techniques of the PCMS have been introduced in the authors' previous
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research. For example, Li, et al. (2015) focused on evaluating various real-time location technologies,
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including chirp spread spectrum, global positioning system, radio-frequency-identification, and ultra-wide
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band. Luo, et al. (2016b) further concentrated on risk assessment by dynamically quantifying workers’
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hazard exposure based on the real-time trajectories of workforce and equipment. Workers’ responses to
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proximity warnings were also investigated (Luo, et al., 2016a) and the findings were used as the prior
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knowledge in establishing the prior parameters of the proposed model.
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Experimental Settings and Procedure
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The experiment was carried out on a viaduct construction project in Shanghai, China. A total of 72 male
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worker volunteers aged between 21 and 55 participated and the trial lasted 17 workdays between 12
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January 2015 and 21 April 2015. To initialize the PCMS, a latest site layout drawing was uploaded to its
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backend, and location anchors were marked on the layout and deployed physically on-site, location tags
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were mounted on workers’ safety helmets, and most importantly, hazard zones were defined in the form
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of virtual fences at the system’s backend, as shown in Fig. 4. In running system, when workers were detected
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entering an unauthorized hazard zone, a signal was sent to their tags, and a personal hazard-specific
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warning (e.g., “ground uneven,” “vehicle approaching,” and “lifting hook approaching”) would sound.
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Finally, warnings and workers’ reactions regarding the response time were recorded for further analysis.
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Readers are referred to the articles by Luo, et al. (2016a) and Luo, et al. (2016b) for more details about the
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application of the PCMS. Additionally, to ensure the protection of participants’ rights and welfare, the
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authors had clearly explained the use of location devices and the functioning mechanism of the warnings
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to them. Most importantly, they were allowed to switch off the location tags to quit the experiment if they
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feel uncomfortable.
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Fig. 4. System deployment in the experiment
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In contrast with (Luo, et al., 2016a), this study focused on demonstrating the hierarchical Bayesian model’s
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capability of continuously reviewing safety risk control measures. To this end, the review time interval was
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selected as one workday and the hazard zones that lasted more than one workday were counted as separate
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ones. As a result, a total of 50 nominal static hazard zones (namely 30 independent hazard zones), which
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fell into nine hazard types, were identified and defined manually in the 17-workday experiment and a total
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of 5391 warnings were recorded. Table 1 summarizes the experimental settings and procedure as well as
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the warnings and responses observed, which were fed into the proposed model for estimation.
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Table 1. Experimental settings and procedure, and recorded warnings and responses
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In the experiment, the values of 𝐴𝜔 and 𝐵𝜔 were set at 30 and 30 respectively, which denoted there were
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30 responses and 30 neglects in a genetic hazard area in a unit time (a work day) and the concentration
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(𝐴𝜔 + 𝐵𝜔 ) was 60, on account of the median of responses in all hazard zones was 35 and that of neglects
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was 36.5. The two numbers (35 and 36.5) were established according to the prior knowledge on workers’
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responses obtained in the last two years of the development and trial of the PCMS. The adopted values
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were slightly smaller than actually possible numbers of responses and neglects with an aim to reflect more
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influence of the observational data on the estimates of model parameters.
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To establish the values of S𝜅 and 𝑅𝜅 , the mode 𝜔𝜅 was selected as 58, which was also the concentration
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(𝐴𝜔 + 𝐵𝜔 ) minus 2, and the standard deviation 𝜎𝜅 was 58, denoting the significant variation of the
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warning numbers in various hazard areas. Finally, S𝜅 , 2.6180, and 𝑅𝜅 , 0.0279, were derived according to
349
𝑆𝜅 = 1 + 𝜔𝜅 𝑅𝜅 , where 𝑅𝜅 = (𝜔𝜅 + √𝜔𝜅 2 + 4𝜎𝜅 2)/2𝜎𝜅 2 (Kruschke, 2014).
350 351
Computational Algorithm
352
Ideally, the posterior estimates can be calculated analytically, but for the experimental model with 70
353
parameters < 𝜃1 , 𝜃2 , … , 𝜃50 , 𝜔1 , 𝜔2 , … , 𝜔9 , 𝜅1 , 𝜅2 , … , 𝜅9 , 𝜔, 𝜅 > , an analytical calculation is almost
354
infeasible. In this situation, two approaches are available (Salvatier, et al., 2016): (1) finding the maximum
355
a posteriori (MAP) point using optimization methods, and (2) computing summaries based on samples
356
drawn from the posterior distribution using Markov Chain Monte Carlo (MCMC) sampling methods. Since
357
the MAP approach gives point estimates of the parameters and can be biased if the model isn’t
358
representative of the distribution (Salvatier, et al., 2016), this paper adopted one of the MCMC methods —
359
the Metropolis algorithm, which was placed among the ten algorithms that have had the greatest influence
360
on the development and practice of science and engineering in the 20th century (Beichl and Sullivan, 2000).
361
PyMC3, which is a Python module for Bayesian statistical modeling and model fitting which focuses on
362
advanced MCMC fitting algorithms (Salvatier, et al., 2016), was adopted to compute the posterior estimates.
363 364
Results and Analysis
365
The total number of simulation steps was 51,000 and the first 1,000 steps in the burn-in period were
366
removed in the final results due to their unrepresentativeness. Fig. 5 shows the traces of several parameters,
367
which are selected to illustrate the simulation process. Table 2 summarizes the estimates of the posterior
368
parameters in the form of quantiles, and Fig. 6 is a box-and-whisker plot showing all omegas and thetas,
369
which are grouped by hazard types. In this section, for the sake of succinctness, the estimates of the
370
parameters implicitly refer to their medians, unless they are explicitly specified.
371 372
Fig. 5. Trace plot of several selected parameters, where the burn-in step number is 1,000 and the thin
373
value 20 resulting in there are only (51,000 – 1,000)/20 = 2,500 steps shown.
374 375
Table 2. Quantiles of parameter estimates
376 377
Fig. 6. Box-and-whisker plot of ERRs (omegas and thetas), where ‘*’ indicates that proximity warnings
378
are used as the secondary safety control measure in those hazard areas; those without ‘*’ use proximity
379
warnings as the primary control measure. The red dashed line indicates the ERR of the generic hazards,
380
̂ (0.528), and the red horizontal span represents its interquartile range, which is the namely 𝝎
381
difference between the lower quartile (0.503) and the upper quartile (0.552). Similarly, the yellow
382
dash-dot line in each column shows each hazard type ERR and the yellow horizontal span represents
383
the interquartile range between its lower and upper quartiles. For example, in the first column
384
̂ 𝟏 ) was about 0.487 with its interquartile range representing the welding areas, their hazard type ERR (𝝎
385
between the lower quartile (0.466) and the upper quartile (0.510), which is represented by the yellow
386
horizontal span. The estimates of individual hazards are represented in the form of boxes with
387
whiskers.
388 389
Use 1: Proximity warnings as the primary risk control measure
390
In this situation, the higher the ERR is, the more effective the primary control would be. As shown in the
391
second column of Fig. 6, proximity warnings in laydown areas, as the primary control measure to reduce
392
the risk of being struck by moving or dropping objects, had a relatively high hazard type ERR (𝜔 ̂2 was about
393
0.648). However, the ERRs varied in this type of hazards (𝜅̂ 2 was about 63.9). For example, Hazard 24 had
394 395
62 responses out of 77 warnings, which led its ERR to the highest in this type (𝜃̂24 was about 0.733). By contrast, Hazard 28 had the lowest ERR in this hazard type (𝜃̂28 was about 0.572 originated from 104
396
responses of 191 warnings). Although the higher ERRs justified the effectiveness of the control measure for
397
these hazards, more effective engineering control measures (e.g., separating average workers from the
398
laydown areas using caution tape) were supposed to be adopted.
399 400
On the contrary, the lower the ERR is, the less valid the hazard would be. In this situation, the virtual hazard
401
defined at the backend of the PCMS can be removed to reduce false warnings. Take the easy-to-stumble
402
areas as an example. They had the lowest ERRs, which informed the estimate of the hazard type’s ERR (𝜔 ̂5
403
was about 0.412), which was lower than the overall ERR (0.528). Thus, as the primary control measure,
404
proximity warnings of the easy-to-stumble risk were ineffective, probably due to there were full of this kind
405
of hazards on construction sites; warnings of the risks were little meaningful to workers. Specifically, Hazard
406
30 received 24 responses out of 80 warnings, and this led to the lowest ERR (𝜃̂30 was about 0.356) during
407
the whole experiment, which indicated that workers just ignore the majority of the warnings. Therefore,
408
these easy-to-stumble areas should be removed from the PCMS.
409 410
Use 2: Proximity warnings as the secondary risk control measure
411
In this situation, the higher the ERR is, the less effective the primary control would be. Workers believe that
412
the warnings are valid and perceive the high risks even with the main control measure engaged. For
413
example, the warnings in the hazard areas related to floor openings had the highest ERR (𝜔 ̂7 was about
414 416
0.795). Among this type of hazards, Hazard 47 had the lowest ERR (𝜃̂47 was about 0.763 derived according to 23 responses out of 33 warnings). Hazard 41 had the highest ERR (𝜃̂41 was about 0.829 derived according to 26 responses out of 28 warnings). In comparison with Hazard 41, the ERR of Hazard 42 (𝜃̂42 was about
417
0.807) was not the highest one in spite of all its six warnings got responses. The higher ERRs showed that
418
the primary control measure should be strengthened essentially or in a more visual way (e.g., fencing
419
openings with hand rails of high contrast colors showing the risk of fall from height relevant to the floor
420
openings).
415
421 422
On the contrary, when proximity warnings are adopted as the secondary control of a safety risk, a lower
423
ERR denotes that the primary control is effective, or the relevant hazard is not valid any longer. Take Hazard
424
3 as an example. In the experiment, its primary control was fencing the ground area that could be influenced
425
by dropping objects of the aerial work with yellow caution tape to prevent workers from entering
426
unwittingly. The virtual fence in the PCMS was defined by expanding the virtual ground area by 2 meters.
427
As shown in the sixth column of Fig. 6, Hazard 3 had a relatively low ERR (𝜃̂3 was about 0.435), which was
428
lower than that of all aerial work areas (𝜔 ̂6 was about 0.455). In turn, the type’s ERR (0.454) was lower
429
than the overall ERR (0.528). The result indicated that the primary control measure of the aerial work area
430
was effective, the risk of being struck by falling objects had been reduced to an acceptable level, and the
431
workers would not like to respond to the false warnings.
432 433
Discussions
434
This section first discusses the knowledge contribution of this study regarding its innovative points, which
435
are followed by its practical implication. Finally, the research limitations are discussed.
436 437
Contribution to Knowledge
438
This study primarily contributes to knowledge from two perspectives. First, workers’ responses to proximity
439
warnings of safety hazards are innovatively utilized to review safety control measures in the context of
440
dynamic and complicated construction sites. The proposed approach possesses the potential to make the
441
reviewing process continuous and meaningful because proximity warnings and workers’ responses are
442
hazard-specific, real-time, and objective. In the long term, a continuous and automatic method for
443
reviewing construction safety risk control measures is critical for implementing the roadmap of digital sites
444
(Bowden, et al., 2006).
445 446
Second, the proposed approach towards constant review of risk control measures takes into account both
447
the prior knowledge on safety risk management and observational process information. Specifically, the
448
hierarchical Bayesian modeling of workers’ responses to proximity warnings of safety hazards uses the
449
safety knowledge to establish prior parameters and the real-time ORRs to estimate posterior parameters.
450
The three-level structure of the model recognizes RR differences among various hazard types and
451
characteristics of individual hazards. Moreover, the parameter estimates of a specific hazard are
452
simultaneously informed by data from all the other hazards of an identical hazard type, since all these
453
parameters inform the parameters of higher levels (i.e., the hazard type level and, in turn, the generic
454
hazard level), which in reverse constrain the parameter estimates of all individual hazards.
455 456
Practical Implication
457
The proposed model takes into account two uses of proximity warnings and can be embraced to improve
458
the PCMS and other location-based PWS’s that depends on predefined virtual hazards. When proximity
459
warnings are used as the primary risk control measure, the higher ERR is, the more effective the control
460
would be; on the contrary, the lower ERR, the less valid the hazard. When they are used as the secondary
461
risk control, the higher ERR is, the less effective the primary control would be; in contrast, the lower ERR,
462
the more effective the primary control, or the less valid the hazard. Therefore, the simple logic can be coded
463
to reinforce the functions of the PCMS to make it more viable in practical application. For example, the
464
PCMS can be extended by adding the automatic hazard recognition and definition algorithms (Kiviniemi, et
465
al., 2011) and implementing the proposed hierarchical Bayesian model towards an automatic safety risk
466
management cycle.
467 468
Research Limitations
469
Despite the value of this research mentioned above, several research limitations need to be acknowledged.
470
First, the response differences between individual workers were ignored, and only the number of effective
471
responses and the number of warnings as an overarching group were collected. The authors believe that
472
this treatment has limited impact on the accomplishment of the research objective, which is to review risk
473
control measures continuously, rather than the RRs of individual workers.
474
475
Second, the selection of prior distributions and the value establishment of prior parameters seemed
476
subjective. In fact, these problems are inherent and typical of Bayesian statistics (Kass and Wasserman,
477
1996), which have been debated since Bayes (1763). Furthermore, there is an extensive literature on the
478
construction of priors, and the subject seems far from a definitive solution (Kass and Wasserman, 1993).
479
Priors can be selected using some methods (Carlin and Louis, 2008), including determination from past
480
information, elicitation from the purely subjective assessment of experts, symmetry or maximizing entropy
481
given constraints, etc. In this study, prior distributions were selected on account of if there were conjugate
482
priors with the aim of speeding up the fitting process of the model, and prior values were established
483
primarily based on past information accumulated in the development and trial of the PCMS.
484 485
Third, although workers’ responses to proximity warnings are determined by a combination of various
486
factors, including task urgency and complexity, safety knowledge and experience, existing risk control
487
measures, and hazard validity (Luo, et al., 2016a), this study primarily focused on the last two factors. Task
488
urgency and complexity were fused into the three-level structure of the model, namely individual hazards,
489
hazard types, and generic hazards. Safety knowledge and experience are closely related to the first
490
limitation and were treated indistinctly among workers. From a practitioner’s perspective, it is worth to
491
sacrifice somewhat pedantic integrity by fusing and simplifying some factors for the understandability of
492
the model and its computing efficiency.
493 494
Concluding Remarks
495
This paper introduced a three-level (i.e., individual hazards, hazard types, and generic hazards) hierarchical
496
Bayesian model based on workers’ responses to proximity warnings of specific hazards to review safety risk
497
control measures with the consideration of quickly changing and complicated workplace conditions. The
498
proposed model distinguishes between two uses of proximity warnings (i.e., as the primary control measure
499
and as the secondary measure), takes as input observational response rates, takes into account the prior
500
knowledge on workers’ responses to similar hazards, and finally produces as output ERRs of individual
501
hazards, hazard types, and generic hazards.
502 503
These ERRs are used as the primary indicator of the effectiveness of a given control measure as well as the
504
validity of a previously identified safety hazard. As a result, the control measure review logic consists of the
505
following rules: (1) when proximity warnings are used as the primary risk control measure, the higher the
506
ERR is, the more effective the control measure would be; on the contrary, the lower the ERR, the less valid
507
the hazard; and (2) when they are used as the secondary risk control, the higher the RR is, the less effective
508
the primary control would be; on the contrary, the lower the ERR, the more effective the primary control,
509
or the less valid the hazard.
510 511
To preliminarily test the proposed approach, a 17-day field experiment using the PCMS was conducted and
512
a total of 5391 warnings and 2712 responses in 50 hazards, which fell into nine types, were collected. The
513
observational data was fed into the model to estimate the model parameters. The analysis of experiment
514
results demonstrated how to utilize the estimates in practice as well as the potential of the proposed
515
approach to continuously reviewing safety risk control measures with the consideration of quickly changing
516
and complicated workplace conditions. Given more data collected in practical applications of the proposed
517
approach, the posterior estimates of the parameters, especially those of hazard types and generic hazards,
518
can be meaningfully referenced to establish their prior values, which in turn can significantly improve the
519
credibility of the estimates.
520 521
Automatic safety risk management cycle is an essential part of “the construction sites of the future”
522
(Bowden, et al., 2006), where context-aware and self-adapting sensor networks and decision support
523
systems monitor and complement workers' activities, at every level and in real time. The proposed review
524
approach could represent one step towards the vision. However, as indicated in the research limitations, to
525
ensure the short- and mid-term viability of the model, the Bayesian model fused and simplified some
526
factors, e.g., task urgency and complexity, and safety knowledge and experience. As the development of
527
data mining technologies and wireless sensor technologies, the indirect quantification of these factors
528
becomes possible, for example, by finding correlations in large data (Speed, 2011), which has the potential
529
to extend the proposed approach regarding comprehensiveness without undermining its viability.
530 531
Acknowledgements
532
The authors are in great debt to the site manager and the workers of the construction project for their
533
support during the experiment. Many thanks also go to Bo Ye, Wei Lu and Xintao Yang for their
534
indispensable efforts in the system development and experimental study. The work was supported by the
535
Innovation and Technology Commission of Hong Kong, under the public sector trial scheme of a project
536
"Location-based Technologies for Asset Tracking and Risk Management" (ITT/004/15LP), and the Research
537
Grants Council of Hong Kong with the grant titled “Proactively Monitoring Construction Progress by
538
Integrating 3D Laser-scanning and BIM” (PolyU 152093/14E).
539 540
541
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Table 1 Experimental settings and procedure, and recorded warnings and responses Zone Zone No.
Date
Num. of
Num. of
Zone Name
Zone No. Type
Warnings
Responses
Date
Zone
Num. of
Num. of
Type
Warnings
Responses
Zone Name
1
12-Jan-15
Dangerous goods
8
3
1
26
20-Mar-15
Dangerous goods
8
64
31
2
12-Jan-15
Welding area
1
12
8
27
20-Mar-15
Power distribution box
3
209
91
3
12-Jan-15
*Aerial work
6
77
32
28
20-Mar-15
Laydown area
2
191
104
4
19-Jan-15
Unprotected edge A
4
211
94
29
23-Mar-15
Lifting area
9
4
2
5
19-Jan-15
Unprotected edge B
4
55
18
30
23-Mar-15
Easy-to-stumble area
5
80
24
6
19-Jan-15
Lifting area
9
62
25
31
23-Mar-15
Welding area
1
32
14
7
19-Jan-15
Welding area
1
93
42
32
24-Mar-15
Lifting area
9
71
36
8
20-Jan-15
Unprotected edge A
4
312
125
33
24-Mar-15
Easy-to-stumble area
5
51
25
9
20-Jan-15
Unprotected edge B
4
58
19
34
24-Mar-15
Laydown area
2
69
43
10
20-Jan-15
Lifting area
9
54
18
35
25-Mar-15
Lifting area
9
63
34
11
20-Jan-15
Welding area
1
81
44
36
25-Mar-15
Easy-to-stumble area
5
97
39
12
21-Jan-15
Unprotected edge A
4
494
207
37
25-Mar-15
Laydown area
2
254
175
13
21-Jan-15
Unprotected edge B
4
49
24
38
31-Mar-15
Laydown area
2
104
67
14
21-Jan-15
Lifting area
9
72
30
39
3-Apr-15
Dangerous goods
8
168
92
15
21-Jan-15
Welding area
1
184
87
40
3-Apr-15
*Floor opening A
7
185
151
16
6-Feb-15
Unprotected edge
4
307
146
41
3-Apr-15
*Floor opening B
7
28
26
17
6-Feb-15
Dangerous goods
8
220
89
42
3-Apr-15
*Floor opening C
7
6
6
18
6-Feb-15
Lifting area
9
360
157
43
8-Apr-15
Power distribution box
3
39
27
19
17-Mar-15
Unprotected edge
4
23
13
44
8-Apr-15
Dangerous goods
8
16
6
20
17-Mar-15
Dangerous goods
8
63
39
45
8-Apr-15
Power distribution box
3
118
89
21
18-Mar-15
Lifting area
9
74
37
46
15-Apr-15
Lifting area
9
146
71
22
18-Mar-15
Welding area
1
58
26
47
15-Apr-15
*Floor opening
7
33
23
23
19-Mar-15
Power distribution box
3
120
52
48
15-Apr-15
Power distribution box
3
14
10
24
19-Mar-15
Laydown area
2
77
62
49
17-Apr-15
*Floor opening
7
16
15
25
19-Mar-15
Dangerous goods
8
188
98
50
17-Apr-15
Power distribution box
3
26
18
Zone type: 1, Welding areas; 2, Laydown areas; 3, Power distribution boxes; 4, Unprotected edges; 5, Easy-to-stumble areas; 6, Aerial work areas; 7, Floor openings; 8, Dangerous goods; 9, Lifting areas. ‘*’ indicates that proximity warnings are used as the secondary safety control measure in those hazard areas; the hazard areas without ‘*’ use proximity warnings as the primary control measure.
Table 2 Quantiles of parameter estimates Lower Parameter
Upper Median
Quantile
Lower Parameter
Quantile
Upper Median
Quantile
Quantile
𝜔 ̂
0.503
0.528
0.552
𝜃̂16
0.447
0.463
0.480
𝜅̂
14.350
19.566
26.785
𝜃̂17
0.410
0.431
0.453
𝜔 ̂1
0.466
0.487
0.510
𝜃̂18
0.425
0.441
0.457
𝜅̂ 1
72.322
105.634
147.619
𝜃̂19
0.424
0.456
0.490
𝜔 ̂2
0.626
0.648
0.672
𝜃̂20
0.520
0.552
0.586
𝜅̂ 2
41.774
63.856
94.026
𝜃̂21
0.448
0.474
0.501
𝜔 ̂3
0.560
0.589
0.621
𝜃̂22
0.442
0.473
0.504
𝜅̂ 3
19.089
27.688
39.021
𝜃̂23
0.432
0.462
0.492
𝜔 ̂4
0.414
0.430
0.446
𝜃̂24
0.702
0.733
0.763
𝜅̂ 4
76.438
109.140
151.330
𝜃̂25
0.494
0.514
0.535
𝜔 ̂5
0.381
0.412
0.443
𝜃̂26
0.464
0.494
0.525
𝜅̂ 5
51.257
79.079
118.147
𝜃̂27
0.430
0.453
0.476
𝜔 ̂6
0.412
0.455
0.501
𝜃̂28
0.548
0.572
0.593
𝜅̂ 6
53.160
81.782
126.450
𝜃̂29
0.423
0.461
0.496
𝜔 ̂7
0.768
0.795
0.821
𝜃̂30
0.324
0.356
0.388
𝜅̂ 7
50.994
80.145
118.544
𝜃̂31
0.442
0.476
0.507
𝜔 ̂8
0.480
0.501
0.522
𝜃̂32
0.452
0.479
0.506
𝜅̂ 8
55.432
81.035
117.973
𝜃̂33
0.408
0.444
0.482
𝜔 ̂9
0.441
0.458
0.475
𝜃̂34
0.607
0.636
0.665
𝜅̂ 9
77.079
107.227
151.841
𝜃̂35
0.460
0.488
0.517
𝜃̂1
0.452
0.495
0.537
𝜃̂36
0.377
0.406
0.434
𝜃̂2
0.469
0.507
0.548
𝜃̂37
0.661
0.680
0.697
𝜃̂3
0.401
0.435
0.470
𝜃̂38
0.617
0.644
0.671
𝜃̂4
0.421
0.441
0.460
𝜃̂39
0.508
0.531
0.555
𝜃̂5
0.367
0.396
0.425
𝜃̂40
0.790
0.808
0.825
𝜃̂6
0.410
0.438
0.467
𝜃̂41
0.798
0.829
0.861
𝜃̂7
0.444
0.471
0.495
𝜃̂42
0.768
0.807
0.842
𝜃̂8
0.393
0.410
0.425
𝜃̂43
0.604
0.647
0.689
𝜃̂9
0.367
0.395
0.423
𝜃̂44
0.440
0.480
0.518
𝜃̂10
0.387
0.418
0.445
𝜃̂45
0.694
0.721
0.749
𝜃̂11
0.486
0.511
0.540
𝜃̂46
0.453
0.474
0.497
𝜃̂12
0.408
0.421
0.436
𝜃̂47
0.726
0.763
0.795
𝜃̂13
0.421
0.449
0.479
𝜃̂48
0.579
0.627
0.682
𝜃̂14
0.414
0.441
0.468
𝜃̂49
0.782
0.818
0.852
𝜃̂15
0.457
0.478
0.500
𝜃̂50
0.589
0.637
0.681
Figures
Fig. 1. Safety risk management cycle Fig. 2. Decision tree for reviewing control measures Fig. 3. Bayesian hierarchical model Fig. 4. System deployment in the experiment Fig. 5. Trace plot of several selected parameters, where the burn-in step number is 1,000 and the thin value 20 resulting in there are only (51,000 – 1,000)/20 = 2,500 steps shown. Fig. 6. Box-and-whisker plot of ERRs (omegas and thetas), where ‘*’ indicates that proximity warnings are used as the secondary safety control measure in those hazard areas; those without ‘*’ use proximity warnings as the primary control measure. The red dashed line indicates the ERR of the generic hazards, ̂ (0.528), and the red horizontal span represents its interquartile range, which is the difference namely 𝝎 between the lower quartile (0.503) and the upper quartile (0.552). Similarly, the yellow dash-dot line in each column shows each hazard type ERR and the yellow horizontal span represents the interquartile range between its lower and upper quartiles. For example, in the first column representing the welding ̂ 𝟏 ) was about 0.487 with its interquartile range between the lower quartile areas, their hazard type ERR (𝝎 (0.466) and the upper quartile (0.510), which is represented by the yellow horizontal span. The estimates of individual hazards are represented in the form of boxes with whiskers.
