Fire Risk of Electrical Installations: A Fuzzy Petri Net Approach Applied to the National Museum of Brazil

doi:10.21203/rs.3.rs-4902374/v1

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Fire Risk of Electrical Installations: A Fuzzy Petri Net Approach Applied to the National Museum of Brazil

https://doi.org/10.21203/rs.3.rs-4902374/v1

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Over time, electrical fires have been recurring disasters around the world. As a common preventive strategy, the use of a standard checklist has become a traditional technique widely adopted today. However, this procedure might not capture the full spectrum of risk levels or address interconnected issues, thus potentially compromising effective risk management. Conversely, allowing for prioritization and immediate remediation of fire hazards, the incorporation of expert knowledge and data-driven insights to gauge risk factors is noteworthy. In this context, the approach proposed, rooted in fuzzy Petri nets, optimizes resource allocation by focusing on the highest-risk elements, leading to a more substantial risk reduction. In this paper, an enhanced methodology, which surpasses the absence of statistical data in real-life assessments, was implemented, considering the pre-fire conditions at the Brazilian National Museum. Simulation results indicate that simple corrections in the electrical installation could have significantly reduced the fire risk, possibly preventing the tragedy. These findings underscore the method's effectiveness, emphasizing the importance of thorough electrical risk management. It suggests that the catastrophe might have been avoided had the risks been appropriately addressed. The model emerges as an essential instrument for enhancing risk assessment and strategic resource allocation, especially vital in resource-constrained environments characteristic of developing countries like Brazil.

electrical failures

electrical fires

fuzzy petri net

fuzzy knowledge representation

National Museum Fire

Checking the safety of an electrical installation is a critical issue that ensures the proper functioning of electrical equipment, prevents unexpected shutdowns, and most importantly, protects people from potential electrical fire hazards. Usually, the safety checks in electrical installations are carried out through adherence verification addressed to the current standards [1], [2], conducted through inspections and tests that identify non-conformities. However, it is understood that these standards do not have the ability to propose a corrective/preventive strategy considering the detected problems.

This lack of hierarchy can be a challenge, especially in older installations where, often due to budget constraints, a complete upgrade is not possible. This situation puts the onus on the maintenance personnel, as they are the ones responsible for evaluating which issues are more severe and require immediate intervention. However, this judgement-based approach can lead to errors. Due to the complexity and diversity of electrical issues, the professionals might overlook or misjudge certain problems, thus potentially exacerbating the risk. This issue is a concern particularly when dealing with older systems, where wear or outdated equipment might complicate the evaluation process [3] [4].

Electrical fires in historic and ancient buildings are regrettably frequent, leading to the loss of invaluable cultural heritage worldwide. Notable examples include the National Museum of Brazil in Rio de Janeiro, which was devastated by a fire in September 2018, reportedly initiated due to a short-circuit in an air conditioner. The iconic Notre-Dame Cathedral in Paris experienced a severe fire in 2019. Although the exact cause was still under investigation, ongoing electrical work was speculated as a possible source. São Paulo's Museum of the Portuguese Language was hit by a fire in December 2015, with suspicions pointing to a short-circuit. The historic Windsor Castle, located in Berkshire, England, was impacted by a fire in 1992. While the exact cause wasn't confirmed as electrical, electrical issues were among the considered possibilities.

Before a devastating fire, an adequate maintenance regime could have potentially averted the disaster. However, the individuals responsible for maintenance were unable to accurately identify the severity of the numerous existing problems, resulting in a failure to take corrective actions in a timely manner. If a thorough risk assessment has been conducted, it could have brought many critical issues to light. Such assessment would involve a comprehensive survey of all electrical systems, detecting potential hazards and evaluating their risk levels. Then, the mitigation measures would be based on this analysis, prioritizing high-risk issues, and allocating resources accordingly to address them.

This adequate practice can be confronted with a tragedy occurred in the National Museum, located in Rio the Janeiro city, Brazil. Unfortunately, the electrical challenges faced by the edification were largely overlooked. The absence of a strategic risk assessment and a proper maintenance plan led to neglect of these significant problems. Additionally, the lack of a structured system to prioritize problems based on their risk level resulted in critical issues being overlooked [5].

A fire at the National Museum, Rio de Janeiro, Brazil, occurred on the evening of September 2^nd, 2018. According to reports, the flames were noticed around 7:30 p.m., when the historic 200-year-old building, which served as the museum's headquarters, was already closed to the public. The fire quickly spread through the building, consuming its three floors. Firefighters arrived on the scene about 40 minutes after the fire outbreak, but the flames were already out of control and compromising the palace's structures. Throughout the night, the fire could be seen from various parts of the city of Rio de Janeiro, Brazil, lighting up the night sky and casting a dense black smoke into the air. The firefighters' efforts extended throughout the night, trying to control the flames and prevent the complete collapse of the building. Despite the effort, a large part of the museum's collection was destroyed by the fire.

Among the losses were invaluable archaeological artifacts, paleontological, anthropological, and biological collections, as well as historical records and documents. One of the most well-known items lost was the "Luzia" fossil, the oldest human skeleton found in Americas. After hours of fighting the flames, firefighters were able to control the fire in the morning after, but the building was practically destroyed, and much of its collection was lost. Figure 1 depicts the National Museum, located in Rio de Janeiro, Brazil, post-fire.

Following the devastating fire that destroyed most of the collection of the National Museum of Rio de Janeiro, Brazil, on September 2^nd, 2018, a series of investigations were initiated to determine the cause of the fire and assess the extent of the damage. The Brazilian Federal Police were tasked with the criminal investigation to determine the cause of the fire. In their report [5], published in April 2019, they have concluded that the fire likely started due to a short-circuit in one of the air conditioning units in the building's auditorium. Figure 2 and Figure 3 ilustrates some damaged components by the fire.

The report also pointed out a series of deficiencies in the building's fire safety system. There were no sprinklers, and the nearest hydrants were without adequate pressure at the time of the fire. Furthermore, the museum had no fire brigade, and the building had not been inspected by the Fire Department for many years. While the absence of a comprehensive and functional fire protection system indeed amplified the fire's impact, allowing flames to rapidly spread and consume a significant portion of the museum's irreplaceable collection, it wasn't the fundamental origin of the disaster.

Summing up, the reported circumstances underscore the urgent necessity for a robust system for evaluating and managing risks in electrical installations. An efficient approach would not only detect problems, but also assess their severity and determine the urgency of their resolution. Then, mitigate fire risks, the development of specialized systems stands out.

In this context, based on a proper characterization of the electrical condition verified on an installation prior to the fire, this paper deals with a methodology proposition grounded in the use of a fuzzy Petri net, which models the chain of electrical failures involved in electrical fires. The enhanced approach presents its relevance to combine expert knowledge with a probabilistic model, overcoming the lack of statistical data in real-life application. The results highlighted the capability of this approach in assessing electrical fire risks [6].

This paper is structures as follows: session 2 introduces the background and the model foundation. The proposed methodology is presented in session 3. After that, the results and the model application are reporter in session 4. The conclusion and a further discussion are the focus of the sessions 5 and 6 respectively.

2.1. Electrical installation conditions

Despite some renovations and updates over time, the electrical infrastructure of older buildings like the National Museum, Rio de Janeiro, Brazil, often incorporates components that are several decades old. In the case of the National Museum, the current electrical components were estimated to have more than 30 years old. These aged components may not only exhibit reduced efficiency but may also fail to meet contemporary safety standards.

A variety of issues can arise due to this aging of electrical installations. For instance, the insulation around wires could deteriorate over time, exposing the conductive material, which can result in short-circuits or electric shocks. Similarly, the wear and tear of connectors and junction boxes can lead to loose connections, which can subsequently cause arcing and overheating, posing a significant fire hazard [7].

Moreover, outdated components may not be compatible with more modern devices and electrical loads, causing imbalances in the system. This incompatibility can lead to overloaded circuits, a condition conducive to electrical fires. Similarly, old electrical panels may not have the capacity to handle the electricity demands of today's equipment and appliances, leading to the panel overheating, another potential fire risk. In the following, some pertinent issues presented in the National Museum report will be explained [7].

2.1.1. Lack of proper routine inspections

The condition of the installation suggested a lack of routine inspections, with corrective interventions only occurring when a more serious issue manifested itself. This reactive approach to maintenance and the absence of regular safety checks heightened the potential for undetected issues to escalate into major problems, further compounding the possible electrical malfunctions and failures that could escalate into severe consequences, such as fires.

Before the unfortunate incident, multiple sources had indicated concerns about the quality of the National Museum's electrical installations. Staff members at the institution frequently reported potential problems with the building's electrical system, and photographs taken before the event suggest a lack of consistent upkeep in the museum's electrical infrastructure.

These accounts often highlighted the inconsistent nature of electrical maintenance and the prevalence of makeshift repairs. Frequently, patchwork wiring, loosely secured connections, and a general disarray in the electrical system were evident. Such practices potentially increase the risk of electrical faults, like short-circuits and overloads.

Additionally, signs of wear and tear were evident on some electrical installations and components, indicating their advanced age. Older electrical components may not meet current safety standards and can be more susceptible to malfunctions due to their material properties degrading over time. Such issues can increase the likelihood of electrical fires. These various factors point towards a significant need for improved electrical safety and maintenance procedures in older buildings like the National Museum.

2.1.2. Issues in the overcurrent protection system

Overcurrent protection devices, such as fuses and circuit breakers, are designed to automatically interrupt an electrical circuit whenever the current exceeds a certain level for a specified period. This mechanism protects the electrical system from damage caused by excessive current, short-circuits, or overheating that could potentially lead to fires [8]. In the case of older buildings like the National Museum, an efficient overcurrent protection system becomes even more crucial. Despite updates and renovations over time, the existing electrical components often retain elements several decades old, potentially falling short of current safety standards and escalating the chances of electrical faults.

A fundamental mistake in the design of overcurrent protection systems can be the incorrect specification of the overcurrent protection devices. This could arise from miscalculating the circuit's load or neglecting to update the system's protection after modifications that increase the load. In the case of the National Museum, this issue was seemingly present. According to the administrative direction of the National Museum, there were reports of overloading problems in the power circuit for the auditorium's air conditioning units. It was pointed out that this was due to an improper branch, made to power the canteen's equipment. This inappropriate alteration likely increased the load on the circuit without a corresponding upgrade to the overcurrent protection devices. Such situations underscore the importance of ensuring that any changes to an electrical system are accompanied by a thorough evaluation of the potential impacts on the system's overall integrity, including its overcurrent protection design [9].

In addition, the air conditioning units in the auditorium were not provided with individual protection devices as recommended by the manufacturer. Instead, a single protection device was assigned to all units. This practice goes against the manufacturer's specifications, which call for separate protection devices for each air conditioning unit, as shown Fig. 5 and Fig. 6

Additionally, to the potential of deficiencies in overcurrent protections contributing to the fire's inception, the failure of these devices to respond during short-circuits sparked by the fire itself could have further amplified the event's magnitude. According to the local power company, there was a failure in the building's overall protection system, which resulted in the shutdown of the medium-voltage transmission line powering the museum. As outlined in the investigation report, it was discovered after the event that the substation was operating without the main circuit breaker, which had been removed for maintenance. This operational lapse points to an alarming oversight in the facility's electrical safety measures, further complicating the escalation of the fire.

Furthermore, the circuit breaker in the electrical panel (see Fig. 9) that powered the air conditioning units also failed to act. This failure allowed an insulation fault to escalate into a short-circuit potent enough to rupture the conductor. The ineffective response of the circuit breaker to this severe fault indicates a considerable lapse in the overcurrent protection scheme, further contributing to the extent of the electrical failure and potentially the fire's progression.

The rupture of a cable due to a bolted short-circuit, likely caused by insulation damage due to extreme temperatures (see Fig. 7 and Fig. 8). This type of damage signifies the passage of an exceedingly high current, which should have triggered the overcurrent protection devices. The fact that the overcurrent protections did not act as expected in such a situation reinforces the presence of deficiencies in the electrical safety system of the building.

The failure of the overcurrent protection devices to act as expected during the fire event could be attributed to a range of factors. Over time, such devices may degrade, especially in older installations where components have been in use for decades. The lack of routine maintenance could also contribute to their impaired functionality. Furthermore, if these devices were originally underspecified - that is, they lacked the necessary interrupting capacity to handle the current levels present during the fire - they would be unable to perform their protective role effectively.

The installation lacked design documentation and calculation records for the circuits and protection system. Additionally, as evidenced in Fig. 10, critical information regarding the equipment has been erased. Specifically, it was not possible to determine the interrupting capacity of the breaker that malfunctioned.

2.1.3. Poor electrical connections

In the context of electrical installations, the quality and durability of connections are critical elements in maintaining, both in terms of system's functional efficiency and safety [10], [11]. Ideally, in well-designed and maintained systems, connections should be securely enclosed within junction boxes. Exposed connections can expose the system to moisture intrusion, physical degradation, and inadvertent contact, which could lead to electrical malfunctions. In more severe cases, these conditions can lead to electrical fires. Indeed, many electrical safety experts have identified poorly maintained connections as a recurrent cause of electrical fires, underscoring the importance of meticulous installation processes and regular maintenance of electrical systems.

However, in the case of the National Museum, it appears these vital safety protocols were not consistently followed. Observations made during the investigation revealed several instances of exposed electrical connections and wiring. A significant example was the electrical supply circuit for the auditorium's air conditioning units, which exhibited clear signs of exposed connections (as shown in

Figure 11). Moreover, these connections showed signs of humidity and oxidation, further compromising their safety and performance. These findings highlight the gravity of the safety oversights in the museum's electrical installations.

Poorly executed or deteriorating electrical connections, resulting from inappropriately joined wires or decaying connection points, can generate excessive heat due to increased resistance and the occurrence of series arc faults. This surge in temperature could potentially ignite proximate flammable materials, thus instigating a fire. Given the nature of a museum environment, which often includes a variety of potentially combustible materials, the risk associated with such electrical hazards is significantly magnified.

In addition, the museum had multiple instances of loosely tightened connections, further intensifying the potential risk of electrical malfunctions and fires. Loose connections can lead to intermittent contact between conductors, resulting in sparking and excessive heat generation, and possibly initiating a fire.

These issues serve to emphasize that ensuring the integrity of electrical connections is not just about maintaining system functionality: it is a critical element in the prevention of catastrophic fire incidents. Regular inspections, appropriate and timely interventions, and consistent adherence to safety protocols are all essential in maintaining the safety of electrical installations, especially in environments as rich and historically significant as the National Museum.

2.1.4. Improper cable lines

Electrical lines that lack proper protection are vulnerable to mechanical damage, which can come in the form of impacts, abrasion, or excessive tension. Any of these mechanical solicitations can compromise the insulation of the wires, thereby exposing the live conductors. This exposure could lead to electrical faults, such as short-circuits or arc flashes, both have the potential to spark fires [12], [13].

Moreover, these non-protected electrical lines are also at risk from various environmental threats, which can inflict further damage on the cable insulation. These threats can include moisture, heat, and pests, all of which can degrade the insulation and accelerate the occurrence of electrical faults. For example, moisture can heighten the conductivity of the material surrounding the wire, potentially causing stray currents. Similarly, exposure to heat, such as from the sun’s rays, can cause the insulation to degrade and crack over time, thereby exposing the conductive wires within. Pests, particularly rodents, have also been known to gnaw on electrical cables, a behavior that can damage the protective insulation and expose the conductive wires.

To mitigate these risks, it is crucial that electrical lines are properly installed within protective conduits or enclosures, thereby shielding them from potential hazards. Compliance with industry standards and regulations, along with regular inspections and maintenance, are critical steps in preventing fires that could result from non-protected electrical lines [14].

In the case of the National Museum fire, the investigation revealed the presence of several electrical lines improperly exposed to humidity, solar radiation, and rodent activity, as shown in Fig. 11 and Fig. 12.

Cables exposed to sunlight need to be specifically designed with UV-resistant sheathing to prevent degradation over time. Sunlight can deteriorate the insulation material on the cables, leading to the potential exposure of the conductive wires. This deterioration can increase the risk of electrical faults such as arc faults and short-circuits, which can cause fires in the presence of flammable materials [15].

In the instance of the National Museum, there were reports of cables lacking UV-resistant sheathing being exposed to sunlight. Given the building’s age and potential for outdated aspects of the electrical installation, it’s possible that this risk factor was not adequately addressed. This situation illustrates the importance of using suitable materials for specific environments in electrical installations and ensuring updates are made to older installations to align with current safety standards.

One clear indicator of this deterioration is the fading of the cable’s color. Over time, UV light can break down the chemical bonds in the color dyes used in the cable sheathing, resulting in a faded or bleached appearance. This color fading is not merely a cosmetic issue, but a warning sign of the degradation of the cable’s material properties.

2.1.5. Rodent infestation

Rodent infestations pose a significant risk to electrical installations due to their destructive behavior. Particularly, rats and mice tend to gnaw on almost anything to maintain the size of their teeth, and unfortunately, electrical cables often fall victim to this gnawing. This can lead to insulation removal and exposure of conductive wires, escalating the risk of electrical faults, short-circuits, and even fires if these exposed wires contact flammable materials [16].

In the case of the National Museum, signs of rodent infestations were evident. Rodents, including rats, were found in the cable ducts. Disturbingly, the remains of a possum, another type of rodent, were discovered in the aftermath of the fire, revealing its unfortunate demise due to the blaze. This evidence further attests to the presence of this hazard and its potential contribution to the fire's ignition or spread.

These findings serve to emphasize the importance of pest control in the maintenance and management of such historical infrastructure. Proactive measures should be adopted to prevent rodent infestations, and if present, to swiftly address and eliminate the issue. Contextualizing, Fig. 13 and Fig. 14 illustrate some evidences of rodent infestation in National Museum.

2.1.6. Poor grounding and bonding

Grounding and bonding are essential aspects of any electrical system, providing protection against electrical shock hazards and ensuring the correct operation of overcurrent protection devices like fuses and circuit breakers. Grounding refers to connecting an electrical system to the earth with grounding electrodes, which helps stabilize the system’s voltage, safeguarding it against potential surges. Bonding, on the other hand, involves electrically connecting all metallic non-current-carrying components in a system to guarantee they have the same electrical potential, which reduces the risk of shock or electrocution.

However, the repercussions of poor grounding and bonding can be grave. Without a robust connection to the ground, voltage surges could cause substantial damage to an electrical system, and there wouldn’t be a direct path for electrical current to follow in the event of a short-circuit. This can lead to hazardous situations where electrical equipment or other objects become unintentionally energized. Poor bonding can lead to potential differences between different parts of an electrical system, creating a risk of shock [17], [18].

In the National Museum, the grounding and bonding system had deficiencies. Without suitable grounding and bonding, the electrical system was vulnerable to irregular performance and safety risks. In the event of a fault condition, these deficiencies could have hindered protective devices’ operation, escalating the electrical fire’s severity. This aspect underscores the need for regular inspections and maintenance of the grounding and bonding system to maintain its integrity and effectiveness.

Even though the Brazilian`s Federal Police report does not provide detailed information about the complete grounding system and its corresponding tests, it does note that the air conditioning units were grounded independently (see Fig. 16) of the main installation; in other words, they were not bonded. This lack of bonding can lead to an uneven voltage distribution and exacerbate risks related to potential electrical faults [5]

2.2. Fire risk indexing according to the Non-Compliances Found

Before the tragic fire, an evaluation of the museum's fire risk using an indexing approach could have potentially prevented the disaster. Fire risk indexing is a methodology that identifies, assesses, and compares risks in a structured way. It allows for the prioritization of mitigation strategies based on the risk evaluation.

In the context of the National Museum, such a risk index could have considered a range of factors, including: the age and condition of the electrical installation; compliance with electrical standards; the presence and functionality of fire safety systems and the vulnerability of the building and its contents.

An in-depth evaluation of these factors could have highlighted the significant electrical risks present in the museum. For instance, the aging electrical infrastructure and violations of electrical standards could have been identified as high-risk factors.

A comprehensive fire risk index, had it been in place, could have served as a warning signal, prompting more urgent and focused attention on the museum's electrical safety. It could have informed the allocation of resources, prioritizing the most critical safety upgrades.

However, it is crucial to note that currently, a comprehensive methodology for quantifying electrical fire risk does not exist. One reason could be the complexity of the failure mechanisms involved. A multitude of factors such as: the condition and age of the electrical installation; the nature of the building and its contents and the presence or absence of fire safety measures contribute to the risk of electrical fires.

Furthermore, the lack of suitable statistical data hampers the application of robust models. Traditional risk assessment methodologies often rely heavily on historical data to inform probabilistic analyses. The absence of an extensive, reliable database of electrical fire incidents impedes the development and refinement of these models.

To overcome the data deficiency, many studies have started using expert systems to create mathematical models. These models are designed to represent the chain of events or failures that can lead to an accident or fire. By simulating different scenarios and potential outcomes, these models can help assess the overall risk associated with an electrical installation. These expert systems leverage the knowledge of specialists in the field to compensate for the lack of extensive historical data, utilizing a rule-based approach to model various scenarios and evaluate potential risks. While not a replacement for traditional risk assessment methodologies, expert systems offer a complementary tool that can provide a deeper understanding of potential hazards and inform preventative efforts. This approach, combining expert judgement and mathematical modeling, offers a promising path forward in the effort to improve the assessment and mitigation of electrical fire risks. Through the development and refinement of such models, it becomes possible to prioritize and address safety issues more effectively and efficiently, ultimately reducing the potential for electrical fires[19][20][21] [22].

To calculate the risk of an electrical fire resulting from violations of electrical codes and related risk factors, a specialist system as suggested in [6], was applied, considering the electrical infrastructure of the National Museum. This methodology offered a thorough risk evaluation in the period before the unfortunate fire.

The chosen methodology for risk indexing employs a fuzzy Petri net to represent the sequence of states and transitions associated with electrical failure mechanisms capable of causing fires. Fuzzy Petri nets are used in the construction of expert systems due to their ability to represent reasoning and knowledge through fuzzy production rules [23].

A fuzzy Petri net's graphical representation (as shown in Fig. 17) consists of places and transitions connected by directed arcs [24]. 'Places' can signify various elements within the system, including risk factors, physical or chemical processes, electrical malfunctions, or outright failures. Each place in the network may illustrate a specific condition that can influence the overall state of the electrical. The true value of each preposition (places) may reflect scenarios that vary from an increased risk factor due to the aging of a component, to the physical process of insulation breakdown, to a malfunction such as a loose connection, or an absolute failure like a short-circuit.

Transitions, on the other hand, represent events that could cause a change in the state of the electrical system. They may denote occurrences such as the overheating of a component due to an excessive electrical load or the onset of a short-circuit due to worn-out insulation. Arcs illustrate the causal relationships between places and transitions, providing a roadmap for the potential sequence of events that could lead to an electrical fire. This comprehensive representation helps in formulating a clear picture of the complex interplay of factors that may lead to potential electrical fires.

The fuzzy transition rules encapsulate the dynamics and transition logic of a fuzzy Petri network. There are essentially three types of rule productions with which any complex system can be represented: Type 1 (Simple); Type 2 (Logical AND) and Type 3 (Logical OR) [25].

Type 1 rules, also referred to as Simple rules, are straightforward in that they transition based on a singular condition. If that condition is satisfied, the transition happens.
Type 2 rules, or Logical AND rules, signify that a transition is dependent on the satisfaction of multiple conditions simultaneously. In essence, all the specified conditions must be satisfied for the transition to occur.
Lastly, Type 3 rules, or Logical OR rules, signify that a transition can occur if at least one of the specified conditions is satisfied. Thus, the transition is not contingent on all conditions being met, but rather any single one. Figure 18 depicts these three rule types.

To represent these relationships, FPRs use fuzzy operators, which allow for the representation of linguistic (fuzzy) variables. The fuzzy simulation theory adopts ‘‘MIN” operator to manage ‘‘AND” problems and ‘‘Max” operator to manage ‘‘OR” problems. [25], as shown Table 1.

Table 1

Fuzzy production rule fuzzy operators
Relationship	Production Rule	Fuzzy Operator
AND	If $\:\alpha\:\left({p}_{i1}\right)\:$AND $\:\alpha\:\left({p}_{i2}\right)$ THEN $\:\beta\:\left({p}_{i}\right)$	$\:min\:$($\:\alpha\:\left({p}_{i1}\right),\:\alpha\:\left({p}_{i2}\right))$
OR	If $\:\alpha\:\left({p}_{i1}\right)\:$OR $\:\alpha\:\left({p}_{i2}\right)\:$THEN $\:\beta\:\left({p}_{i}\right)$	$\:max\:$($\:\alpha\:\left({p}_{i1}\right),\:\alpha\:\left({p}_{i2}\right))$

The minimum operator is used to represent the logical AND operator in fuzzy logic. It is used to determine the degree of support for a rule based on the weakest premise. In FPRs, the minimum operator is used to calculate the degree of membership of a fuzzy set. The maximum operator is used to represent the logical OR operator in fuzzy logic. It is used to determine the degree of support for a rule based on the strongest premise. In FPRs, the maximum operator is used to calculate the degree of membership of a fuzzy set [26].

Together, these rules allow for the comprehensive representation and simulation of intricate complex systems within a fuzzy Petri network. This approach, using expert systems and fuzzy Petri nets, provides a comprehensive understanding of the potential chain of events leading to a fire. It thereby helps identify potential weaknesses and risks in the electrical system, allowing for a prioritization of mitigation efforts based on the assessed risks. The complete failure chain is shown in Fig. 21.

3.1. Matrix representation

The matrix representation of WFPNs provides an effective way to perform computational simulations of the system. By representing the system as a two-dimensional matrix, it is possible to perform various operations on the system, such as fire sequence determination of transitions and the behavior analysis of the system under different conditions.

One advantage of the matrix representation is that it allows for efficient computation of the system's behavior. The matrix can be updated based on the firing of transitions, allowing for real-time simulations, leading for rapid prototyping and testing of complex systems before their implemented in the real-life [27].

In addition, the matrix representation of WFPNs allows for the use of various mathematical and computational tools to analyze the system. For example: it is possible to use linear algebra techniques to analyze the matrix and determine the steady-state behavior of the system.

One of these approaches is presented in Liu H. et al. [28], where the authors introduce a matrix representation that enables computational simulation of complex systems. The Dynamic Adaptative Fuzzy Petri net (DAFPN) can be defined as an 11-tuple [26]

$\:\text{D}\text{A}\text{F}\text{P}\text{N}=\:\left(\text{P};\:\text{T};\:\text{I};\:\text{O};\:\text{D};\:{\alpha\:};\:{\beta\:};\:\text{W};\:\text{U};\:\text{T}\text{h};\:\text{M}\right)$ , where:

$\:\text{P}=\left\{{\text{p}}_{1},\:{\text{p}}_{2},\dots\:,\:{\text{p}}_{\text{m}}\right\}$ denotes a finite nonempty set of places; $\:\text{T}=\left\{{\text{t}}_{1},\:{\text{t}}_{2},\dots\:,\:{\text{t}}_{\text{n}}\right\}$ denotes a finite nonempty set of transitions.

$\:\text{I}\::\text{P}\times\:\text{T}\to\:\left\{0,\:1\right\}$ is an $\:\text{m}\:\times\:\text{n}$ input incidence matrix defining the directed arcs from place to transitions.

$\:{\text{I}}_{\text{i}\text{j}}=1$ , if there is a directed arc from pi to t_j, and $\:{\text{I}}_{\text{i}\text{j}}=0$, I_ij if there is no directed arcs from pi to $\:{\text{t}}_{\text{j}}$, for p_i to $\:\text{i}=1,\:2,\:\dots\:,\:\text{m}$ and $\:\text{j}=1,\:2,\:\dots\:,\:\text{n}$.

$\:\text{O}\::\text{T}\times\:\text{P}\to\:0,\:1$ is an $\:\text{m}\:\times\:\text{n}$ output incidence matrix defining the directed arcs from transitions to places. $\:{\text{O}}_{\text{i}\text{j}}=1$, if there is a directed arc from p_i to $\:{\text{t}}_{\text{j}}$, and $\:{\text{O}}_{\text{i}\text{j}}=0$ if there is no directed arcs from p_i to $\:{\text{t}}_{\text{j}}$, for $\:\text{i}=1,\:2,\:\dots\:,\:\text{m}$ and $\:\text{j}=1,\:2,\:\dots\:,\:\text{n}$, $\:\text{D}=\left\{{\text{d}}_{1},\:{\:\text{d}}_{2},\dots\:,\:{\text{d}}_{\text{m}}\right\}$ denotes a finite set of propositions.

$\:\text{P}\cap\:\text{T}\cap\:\text{D}=\:{\varnothing}$ , $\:\left|\text{P}\right|=\left|\text{D}\right|$. $\:{\alpha\:}\::\text{P}\to\:\left[0,\:1\right]$ is an association function which maps from places to real values between 0 and 1.

$\:{\beta\:}\::\text{P}\to\:\text{D}$ is an association function representing a bijective mapping from places to propositions.

$\:\text{W}\::\text{I}\to\:\left[0,\:1\right]$ is an input function and it can be expressed as a $\:\text{m}\:\times\:\text{n}$-dimensional matrix. The value of an element in $\:\text{W}$, $\:{\text{w}}_{\text{i}\text{j}}\in\:\left[\text{0,1}\right]$, is the weight of the input place, which indicates how much the place p_i impacts its following transition $\:{\text{t}}_{\text{j}}$ connected by $\:{\text{I}}_{\text{i}\text{j}}$.

$\:\text{U}\::\text{O}\to\:\left[0,\:1\right]$ is an output function and can be expressed as a $\:\text{m}\:\times\:\text{n}$-dimensional matrix. The value of an element in $\:\text{U}$, $\:{{\mu\:}}_{\text{i}\text{j}}\in\:\left[\text{0,1}\right]$, is the value of certainty factor, which indicates how much a transition t_j impacts its output places $\:{\text{p}}_{\text{i}}$, if the transition fires.

$\:\text{T}\text{h}\::\text{O}\to\:\left[\text{0,1}\right]$ is an output function which assigns a certainty value between 0 and 1 to each output place of a transition, $\:\text{T}\text{h}=\:{\left({{\tau\:}}_{\text{i}\text{j}}\right)}_{\text{m}\text{x}\text{n}},\:\text{i}=1,\:2,\:...,\:\text{m};\text{j}=1,\:2,\:\dots\:,\:\text{n}$, denoting the output threshold of this place. $\:{{\tau\:}}_{\text{i}\text{j}}\in\:\left[\text{0,1}\right]$, if there is a direct arc from $\:{\text{t}}_{\text{j}}$ to pi, and $\:{{\tau\:}}_{\text{i}\text{j}}=+{\infty\:}$, if there are no direct arcs from $\:{\text{t}}_{\text{j}}$ to p_i, for $\:\text{i}=1,\:2,\:...,\:\text{m}\:\text{a}\text{n}\text{d}\:\text{j}=1,\:2,\:...,\:\text{n}$. $\:\text{M}$ denotes a marking of the Petri Net, $\:\text{M}=\:{\left({\alpha\:}\left({\text{p}}_{1}\right),\:{\alpha\:}\left({\text{p}}_{2}\right),\:\dots\:,\:{\alpha\:}\left({\text{p}}_{\text{m}}\right),\right)}^{\text{T}}\:$, where $\:{\alpha\:}\left({\text{p}}_{1}\right)$ is the truth value of place p_j. The initial marking is denoted by $\:{\text{M}}_{0}$. Its determination should be based on an actual status. Hence, its value could be understood as the dynamic input and directly influence the dynamic behavior of DAFPN.

The evolution of failures chain depends on the execution of production rules, related to a fire of transitions mechanisms.

The notation $\:\text{I}\left(\text{t}\right)=\left\{{\text{p}}_{\text{I}1},\:{\text{p}}_{\text{I}2},\dots\:,{\text{p}}_{\text{m}},\:\right\}$ represents the input with corresponding weights $\:{\text{w}}_{\text{I}1}$, $\:{\text{w}}_{\text{I}2},\dots\:,\:{\text{w}}_{\text{I}\text{m}}$, Similarly, $\:\text{O}\left(\text{t}\right)=\left\{{\text{p}}_{\text{O}1},\:{\text{p}}_{\text{O}2},\dots\:,{\text{p}}_{\text{n}},\:\right\}$ represents the output with corresponding output thresholds $\:{{\tau\:}}_{\text{O}1},\:{{\tau\:}}_{\text{O}2},\:\dots\:,\:{{\tau\:}}_{\text{O}\text{n}}$ and certainty factors $\:{{\mu\:}}_{\text{O}1},\:{{\mu\:}}_{\text{O}2},\:\dots\:,\:{{\mu\:}}_{\text{O}\text{n}}$. The enabling and firing rules are specified as follows.

Enabling rule: $\:\forall\:\text{t}\in\:\text{T}$, $\:\text{t}$ is enabled and fired if $\:\forall\:{\text{p}}_{\text{I}\text{j}}\in\:\text{I}\left(\text{t}\right)$,

$$\:\left\{{\alpha\:}\left({\text{p}}_{\text{i}\text{j}}\right)>0\right\}\wedge\:\left\{{\mu\:}\left(\text{t}\right)\ge\:\text{min}\left({{\tau\:}}_{\text{O}\text{K}}\right)\right\},\:\text{j}=1,\:2,\:\dots\:,\:\text{m};\text{k}=1,\:2,\:\dots\:,\:\text{n}.$$

Where $\:{\alpha\:}\left({\text{p}}_{\text{i}\text{j}}\right)$, $\:\:{\alpha\:}\left({\text{p}}_{\text{i}\text{j}}\right)\in\:\left[\text{0,1}\right]$, is the fuzzy truth value in place $\:{\text{p}}_{\text{I}\text{j}},\:{\text{p}}_{\text{I}\text{j}}\in\:\text{I}\left(\text{t}\right)\:$, wich indicates the truth degree of proposition $\:{\text{d}}_{\text{I}\text{j}},$ if $\:{\beta\:}\left({\text{p}}_{\text{I}\text{j}}\right)=\:{\text{d}}_{\text{I}\text{j}};\:{\mu\:}\left(\text{t}\right)=\:\sum\:_{\text{j}=1}^{\text{m}}{\alpha\:}\left({\text{p}}_{\text{i}\text{j}}\right){\text{w}}_{\text{I}\text{j}},\:\text{j}=1,\:2,\:\dots\:,\:\text{m}$ is the equivalente fuzzy truth of input places at transitions when $\:\text{t}$ is enabled.

After $\:\text{t}$ is fired, the tokens in input places are copied, and tokens with fuzzy truth are put into each output place whose output thresholds are lesser than the equivalent fuzzy truth. The new fuzzy truth values of output places are defined as:

$$\:{\alpha\:}\left({\text{p}}_{\text{O}\text{i}}\right)=\left\{\begin{array}{c}{{\mu\:}}_{\text{O}\text{i}}\mu\:\left(\text{t}\right),\:\mu\:\left(t\right)\ge\:{{\tau\:}}_{\text{O}\text{i}}\\\:0,\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mu\:\left(t\right)<{{\tau\:}}_{\text{O}\text{i}}\:\end{array}\right.\text{i}=1,\:2,\:\dots\:,\:\text{n}.$$

If a place has more than one input transition and more than one of its input transitions fires, then the transition produces the new fuzzy truth value of the output place with the maximum fuzzy truth.

3.1. Reasoning process for risk indexing using a failure chain model

The assessment of electrical fire risk through a failure chain model is a systematic process that unfolds in several stages. Each stage is critical to understanding the overall fire risk, providing insights that can guide preventative measures and mitigation efforts. By combining inspection, expert knowledge, data analysis, and mathematical modeling, this method offers a comprehensive view of the potential risks associated with an electrical installation. Figure 20 summarizes the involved reasoning in the failure chain model. In the following, the associated five stages are delved.

Installation verification: The first step involves a thorough inspection of the electrical installation to assess its condition. In the case study under consideration, this evaluation is conducted using photographic records from the investigation report.

Completion of the questionnaire: The next stage involves filling out a questionnaire about the risk factors relevant to the occurrence of an electrical fire. This questionnaire is designed based on electrical standards and the knowledge of experts in the field.

Initial state matrix (M ₀ ) definition: Following the identification of risk factors, the next step is to establish the current state of the installation, represented in the mathematical model by the initial matrix M_o. This matrix serves as the input for the computational simulation of the electrical failure chain.

Computational simulation: Based on the fuzzy production rules, which represent the logic of interaction and evolution of electrical problems as modeled by experts, the mathematical model, implemented in the Matlab platform, is simulated iteratively, calculating the transitions considering the evolution of states.

Final state matrix (M _k ): Finally, when the system reaches stability (when the truth value of the propositions stops changing), it's possible to check the likelihood of occurrence of each of the states (failures/events). This indicates the chances of a fire occurring in accordance with the electrical problems found, mathematically represented by the matrix M_k.

By following these steps, the process provides a systematic and comprehensive assessment of electrical fire risks, enabling effective prioritization and management of mitigation efforts.

3.2. Evaluation of electrical installation condition

A significant percentage of structural fires are linked to electrical faults associated with wiring or wiring devices [29]. The museum's infrastructure exhibited a series of non-conformities pertaining to current electrical standards, according to the images captured by law enforcement and the pre-fire photographic evidence included in the investigation report [5]

The utilized methodology curates a comprehensive list of primary electrical hazards and malfunctions. If present within an installation, these factors have the potential to escalate into a critical failure. This strategy seamlessly merges the directives of electrical codes and incorporates domain-specific knowledge, facilitating the construction of the initial state of prepositions that characterize the conditions of the electrical installation. Based on the evidence indicated in the report, an expert in the electrical field completed the questionnaire proposed by the methodology to compose the input matrix (M_o) for the computational simulation of the model, showcased in Table 2.

Table 2

Script to Determine the Condition of the Electrical Installation
		[X]	$\:{\varvec{p}}_{\varvec{i}}$=1.0
1)	Has the installation more than 30 years old?	[X]	p01
2)	Are there lack of periodic maintenance and inspections?	[X]	p02
3)	Are there inconsistencies in the design of circuit breakers and/or RCCB?	[X]	p03
4)	Are there reports of frequent breaker tripping?	[X]	p04
5)	Have automatic switching devices problems in functional tests?	[ ]	p06
6)	Are there any problems between the neutral of the installation and the grounding of the system?	[ ]	p07
7)	Is the same neutral shared for more than one circuit?	[ ]	p09
8)	Are there circuits passing through materials used for thermal insulation?	[ ]	p12
9)	The levels of harmonic distortion are above the limit recommended by the standard?	[ ]	p14
10)	Is there a marked difference between the currents of each phase?	[ ]	p16
11)	Are there equipment or heat sources causing cable heating?	[ ]	p18
12)	Are thermal anomalies verified through thermographic inspections?	[ ]	p19
13)	Are there poorly executed cable splices, lack of signaling?	[X]	p20
14)	Does the installation use aluminum conductors in low voltage circuits?	[ ]	p21
15)	Are loose connections found in outlets, switches, or do you have breaker terminals?	[X]	p22
16)	Are there connections outside junction boxes or sealing problems in electrical cabinets?	[X]	p23
17)	Are there conductors exposed to mechanical damage?	[X]	p24
18)	Are there partially broken conductors?	[ ]	p25
19)	Is there excessive dust or moisture on electrical connections or terminals?	[X]	p29
20)	Are there direct connections between copper and aluminum?	[ ]	p31
21)	Are there signs of oxidation on electrical connections?	[X]	p32
22)	Are glowing connections found?	[ ]	p33
23)	Are there non-protected PVC cables exposed to direct sunlight?	[X]	p34
24)	Are there wires exposed to sun showing color fading?	[X]	p36
25)	Are there wires with cracks in their insulation?	[ ]	p37
26)	Are there any wires with signs of charred insulation?	[ ]	p40
27)	Are there wires with signs of melting?	[ ]	p42
28)	There are signs of rodent existence?	[X]	p43
29)	Are there any cables with their cover damaged?	[ ]	p44
30)	Are there issues with the grounding and bonding system?	[X]	p45
31)	Is there no SPD in the main electrical panel?	[X]	p46
32)	Are there live parts exposed, with risk of accidental contact?	[ ]	p50
33)	Is insulation resistance below recommended?	[ ]	p53

Each proposition is identified by a number (pi) and can represent a risk factor, characteristic, non-compliance, malfunction, or electrical failure. The input format for system simulation is composed of a matrix M₀ (60x1), where each row of the column represents one of the propositions. When a factor is marked, as per Table 1, the value of this entry changes from 0 to 1, indicating the presence of this risk factor in the system.

3.3. Model parametrization

This comprehensive fuzzy Petri net simulation provides a probabilistic risk index for various electrical fault events that can lead to a fire. Each proposition represents events or states, which in this context can be physical and chemical mechanisms, risk factors, electrical malfunctions, and fires. The value assigned to each proposition represents the likelihood of occurrence of each of these events or states.

The model allows for prioritizing corrections based on the obtained results. The ability to discern which factors pose the greatest risk and are more readily correctable can guide effective intervention strategies.

3.3.1. General fire risk indexing before the fire

Figure 21 illustrates the influence of each risk factor on others, specifically concerning the mechanisms involved in electrical fires. Based on fuzzy arithmetic, events with feedback don't result in an "overflow" of the proposition's value. This facilitates an effective depiction of the intricate interplay between risk factors.

The circles in black represent the issues within the museum's electrical installation prior to the fire, in accordance with the investigation report, serving as inputs to the developed mathematical model. The green color circles represent events/states with a zero probability, i.e., implying unlikely. The color scale, ranging from yellow to red, denotes the occurrence possibility for each event, where yellow and red suggest the lowest and highest likelihood respectively. The onset risk of a fire is signified by the proposition p60, displayed in orange, highlighted by the black arrow in Fig. 19. This signifies a tangible fire possibility, given the reported conditions and characteristics of the electrical installation.

This outcome clearly signifies the urgent need for corrective interventions in the installation, which were unfortunately neglected, potentially resulting in the fire incident. Despite financial constraints cited by the museum staff, it seems there was a misjudgment in evaluating the severity of existing issues, given that addressing many of the non-conformities would not necessarily have required substantial investment.

3.3.2. Hazard ranking through the application of the methodology

This study enables the hazardous hierarchization by applying the proposed methodology, simulating the individual impact of each risk factor on the probability of fire ignition (p60) as depicted in Fig. 19. The hierarchy is derived from calculating the value of each proposition through computational simulation, representing the likelihood of occurrence for each event. This method provides a more strategic approach to risk management. By identifying, quantifying, and prioritizing risks, it aids in making better-informed and efficient decisions, ultimately enhancing the overall safety of electrical installations. Considering a range from 0 to 1, Table 2 showcases the impact on safety for each electrical issue found in the National Museum of Rio de Janeiro, Brazil.

Table 3

Impact on the safety of each electrical issues.
Relevance	Place	Electrical issues found	Likelihood of fire p(60)
1	p32	Are there signs of oxidation on electrical connections?	0.500
2	p22	Are there loose connections?	0.375
3	p03	Are there inconsistencies in the design of circuit breakers and/or RCCB?	0.281
4	p29	Is there excessive dust or moisture on electrical connections or terminals?	0.250
5	p04	Are there reports of frequent breaker tripping?	0.211
6	p20	Are there poorly executed cable splices, lack of signaling?	0.141
7	p23	Are there connections outside junction boxes or sealing?	0.125
8	p45	Are there issues with the grounding and bonding system?	0.125
9	p01	Has the installation more than 30 years old?	0.094
10	p02	Are there lack of periodic maintenance and inspections?	0.094
11	p24	Are there conductors exposed to mechanical damage?	0.094
12	p36	Are there wires exposed to sun showing color fading?	0.079
13	p43	Are there signs of rodent existence?	0.047
14	p46	Is there no SPD in the main electrical panel?	0.031
15	p34	Are there non-protected PVC cables exposed to direct sunlight?	0.020

Based on the data in Table 2, the following rationale can be provided for the varying criticality of different failures:

Signs of Oxidation on Electrical Connections (weight = 0.500): Oxidation increases the resistance at electrical connections. This, in turn, can lead to excessive heating during current flow, which has the potential to ignite nearby materials, hence the high fire risk.
Loose Connections in Outlets, Switches, Breaker Terminals (weight = 0.375): Loose connections can cause electrical arcing. This phenomenon generates a significant amount of heat that can potentially start a fire, explaining its high fire risk.
Inconsistencies in Circuit Breakers/RCCB Design (weight = 0.281): Circuit breakers and RCCBs are crucial protective devices in an electrical system. Any inconsistency in their design can prevent them from functioning properly during overloads or short-circuits, thereby escalating the risk of an electrical fire.
Excessive Dust or Moisture on Electrical Connections/Terminals (weight = 0.250): Dust and moisture could lead to short-circuits or provide fuel for a potential fire. Moisture can also cause corrosion, which increases resistance and generates heat.
Frequent Breaker Tripping (weight = 0.211): This often indicates an underlying issue in the electrical system, such as overloading or short-circuits, both of which can cause excessive heat or sparks and potentially lead to fires.
Poorly Executed Cable Splices, Lack of Signaling (weight = 0.141): Poorly executed splices increase resistance, generate heat, and can also cause arcing. The lack of signaling may lead to using the system in unsafe conditions, unknowingly.
Connections Outside Junction Boxes or Sealing Problems in Electrical Cabinets (weight = 0.125): These issues expose electrical connections to environmental factors that could lead to short circuits or fires.

The other risk factors from the middle to the bottom of the list, such as the existence of rodents or non-protected PVC cables exposed to sunlight, while still posing a risk, are less direct or immediate in their potential to cause a fire. Rodents could cause damage over time, and unprotected cables could degrade under sunlight, but these risks are slower acting and thus less likely to cause a fire within a short time frame.

The prioritization of electrical issues can serve as an indicative guide for initiating corrections. However, the individual contribution of each risk factor may vary due to its interaction with other present factors, akin to what occurs in real life scenarios. While an issue might initially seem less critical, its significance can increase substantially when combined with other factors within a particular environment or situation. Consequently, understanding the interplay between these elements is just as crucial for effective and comprehensive risk management as identifying the individual issues. This complexity mirrors real-life situations where multiple variables coexist and interact in ways that can escalate or mitigate potential risks.

The proposed approach adopted in this study provides an invaluable tool for assessing the impact on safety that rectifying non-compliance corrections can have. Seven distinct simulations were conducted to demonstrate the impact of rectifying different non-compliance issues within the real-world context (Table 4). These simulations show the intricate intricacies of real-world systems, emphasizing that enhancing safety is not merely a result of rectifying isolated non-compliance factors. Instead, it's the collective interplay of multiple interconnected factors that leads to a significant improvement in safety.

Table 4 The influence on safety that rectifying instances of non-compliance can exert.

4.1 Individual Rectifications within the Real-World Scenario

The initial simulation, labeled 'correction 1,' highlights the consequences of addressing the most detrimental factor, p32, which is associated with the presence of oxidation in electrical connections. Addressing this single issue resulted in a noteworthy 15% enhancement in safety compared to the original scenario. Subsequent corrections, from 2 to 4, focused on factors p22, p03, and p29 respectively. Intriguingly, rectifying these factors individually did not yield a discernible increase in overall safety. This observation underscores the complex synergies and interactions among the array of factors in real-world settings.

4.2 Compound Rectifications in the Real Scenario

In the final series of simulations, represented as corrections 5 through 7 in Table 2, combinations of various factors were addressed. The most striking result was observed in correction 7, which showcased a remarkable risk reduction of 52% by rectifying the factors p32, p22, p03, and p29. Essentially, addressing just over a quarter of the non-compliance factors cut the fire risk by more than half. This finding emphasizes the significance of addressing specific combinations in real scenarios and highlights the potential of strategic interventions to considerably boost electrical fire safety.

Expert systems offer a tool for simulating complex systems, especially in situations where there is limited statistical data available for risk quantification. This study highlights the utility of methodologies, including the fuzzy Petri net simulation, for risk identification, quantification, and prioritization. It demonstrates how expert systems can support more informed decision-making processes in risk management.

A notable aspect of the model used in this study is the presence of subjectivity, resulting from the incorporation of expert knowledge. This subjectivity underscores the value of ongoing refinement and adaptation, suggesting the inclusion of insights from a broader range of professionals to enrich the model's accuracy and reliability.

Expert systems are inherently adaptable, providing an avenue for continuous improvement. As such, there is an opportunity to expand and refine the knowledge base. This could involve gathering perspectives from a more diverse set of professionals to fine-tune risk factors and their interrelationships, as well as their associated weights. Additionally, exploring advanced fuzzy Petri net algorithms could enhance the model's simulation accuracy and effectiveness. Future efforts might also focus on validating the model using real-world case studies or historical incident data when available, ensuring the system remains relevant and aligned with real-world contexts.

This proposed fuzzy Petri net simulation method offers a more nuanced and actionable understanding of electrical fire risks, making it far superior to a standard checklist approach, such as a mere compliance with electrical safety standard or codes. A standard checklist often provides a binary perspective, i.e., whether a condition is met or not. Although this common-sense approach is, undoubtedly, a useful tool for compliance, it may not account for the varying levels of risk posed by different issues, or the interconnections between them. This lack of prioritization and contextual understanding can limit the effectiveness of risk management efforts.

Conversely, the fuzzy Petri net simulation incorporates expert knowledge and data-driven insights to quantify the likelihood of various risk factors. It not only identifies the presence of potential issues but also assigns them a risk score based on their probability of occurrence. This nuanced understanding enables to prioritize the highest-risk factors for immediate correction, making it a more efficient risk management tool.

Moreover, by identifying and prioritizing risks, this method aids in the effective allocation of financial resources. In scenarios where financial resources are scarce, as is often the case in old buildings particularly in developing countries like Brazil, the importance of strategic resource allocation becomes even more critical. Instead of spreading resources thinly over all potential issues, which may not be feasible given the financial constraints, funds can be directed towards correcting the highest-risk factors. This focused approach brings about the most significant risk reduction, thereby optimizing the use of limited resources.

It is important to underscore that this fuzzy Petri net simulation analysis is based on the electrical problems detailed in the investigation report following the fire. However, due to the extensive damage caused by the fire, there were undoubtedly additional checks and verifications that could not be performed. Consequently, some potential electrical issues may not have been accounted for in this analysis. Hence, the actual risk associated with the electrical installation prior to the fire could have been higher than what the simulation suggests. If these additional checks were possible, the risk factors and their associated likelihood of occurrence might have been greater, thereby raising the overall risk rating of the installation.

This underscores the importance of regular inspections, thorough maintenance, and comprehensive risk assessments in mitigating fire risks in old electrical installations. Moreover, it highlights the significant potential of techniques such as the fuzzy Petri net simulation in identifying, quantifying, and prioritizing these risks, ultimately enabling more informed and effective risk management and resource allocation decisions. In essence, the fuzzy Petri net simulation offers a more dynamic, risk-based approach, aligning safety measures more closely with actual on-the-ground conditions and facilitating a more efficient and effective management of electrical fire risks.

The incident at the National Museum highlights the significance of regular maintenance and oversight of electrical systems, particularly in historic structures. Currently, the museum is undergoing reconstruction. It is anticipated that maintenance routines for the museum will be comprehensively reviewed and updated. Moreover, it's hoped that this event will prompt a reassessment of maintenance protocols in other buildings with similar conditions. Such events underscore the need to enhance methodologies for assessing fire risks in electrical installations, aiming to reduce the number of occurrences through appropriate risk management.

Finally, the flexibility afforded by the methodology used in this study intimates that the approach could signify a substantial progression in electrical fire safety. With its capacity to identify, quantify, and prioritize risks, the fuzzy Petri net simulation empowers a more strategic and effective decision-making process for resource allocation and interventions. This progress in handling electrical risks carries a potential to avert similar catastrophes in the future, particularly pertinent in developing nations where updates to electrical installations may be neglected due to constrained financial resources.

7.1 Clinical Trial Number

Not applicable.

7.2. Ethical Approval

Not applicable.

7.3. Funding

Not applicable.

Author Contribution

G.S.d.R. conceptualized the study, developed the fuzzy Petri net methodology, and conducted the computational simulations. J.P.C.R. and D.d.S.G. had equal contributions, providing input on the theoretical framework and assisting with data analysis. G.S.d.R., J.P.C.R., and D.d.S.G. collaboratively wrote the main manuscript text. All authors reviewed and approved the final manuscript.

Availability of data and materials

Not applicable.

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No competing interests reported.

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You are reading this latest preprint version

Fire Risk of Electrical Installations: A Fuzzy Petri Net Approach Applied to the National Museum of Brazil

Status:

Version 1

Abstract

Figures

1. Introduction

2. Background and model foundations

2.1. Electrical installation conditions

2.1.1. Lack of proper routine inspections

2.1.2. Issues in the overcurrent protection system

2.1.3. Poor electrical connections

2.1.4. Improper cable lines

2.1.5. Rodent infestation

2.1.6. Poor grounding and bonding

2.2. Fire risk indexing according to the Non-Compliances Found

3. Methodology Adopted for Fire Risk Assessment

3.1. Matrix representation

3.1. Reasoning process for risk indexing using a failure chain model

3.2. Evaluation of electrical installation condition

3.3. Model parametrization

3.3.1. General fire risk indexing before the fire

3.3.2. Hazard ranking through the application of the methodology

4. Impact of Rectifications on Fire Risk

4.1 Individual Rectifications within the Real-World Scenario

4.2 Compound Rectifications in the Real Scenario

5. Discussion

6. Conclusion

Declarations

7.3. Funding

Author Contribution

Availability of data and materials

References

Additional Declarations

Status:

Version 1

Relationship	Production Rule	Fuzzy Operator
AND	If \(\:\alpha\:\left({p}_{i1}\right)\:\)AND \(\:\alpha\:\left({p}_{i2}\right)\) THEN \(\:\beta\:\left({p}_{i}\right)\)	\(\:min\:\)(\(\:\alpha\:\left({p}_{i1}\right),\:\alpha\:\left({p}_{i2}\right))\)
OR	If \(\:\alpha\:\left({p}_{i1}\right)\:\)OR \(\:\alpha\:\left({p}_{i2}\right)\:\)THEN \(\:\beta\:\left({p}_{i}\right)\)	\(\:max\:\)(\(\:\alpha\:\left({p}_{i1}\right),\:\alpha\:\left({p}_{i2}\right))\)