Insurance Automata Engine

Introduction

Overview of the App

Insurance Automata uses a cellular automata model to simulate the spread of fire across a house. The app allows users to place objects within a virtual house and observe how a fire might spread under various conditions. This guide provides an explanation of the parameterization process used in the underlying logic. It covers the data sources and methods used to determine the frequency of fires, the probability of different fire sources, and the simulation of fire spread. Additionally, the guide explains how the values of objects and the parameters for fire spread were determined.

By providing a detailed overview of the parameterization process, this guide helps users understand the underlying mechanics of the simulation and the factors that influence the simulation results. It also serves as a valuable resource for those interested in developing similar simulation tools or forking and altering this tool.

Data Collection

Data Sources for Fire Frequency

The frequency of fires in the simulation is based on data provided by the National Fire Protection Association (NFPA). The NFPA is a reputable organization that conducts extensive research on fire safety and provides valuable data on fire incidents, including their frequency and causes. By utilizing this data, the simulator can accurately reflect real-world fire occurrence patterns.

To calculate the frequency of house fires, the simulator uses data from the NFPA and the U.S. Census Bureau. The NFPA reports that there were an average of 343,100 house fires annually between 2016 and 2020. The U.S. Census Bureau provides data on the number of housing units in the United States for each year. By dividing the mean annual number of fires by the average number of housing units between 2016 and 2020, the simulator calculates the fire frequency.

Data Sources for Fire Source Probability

The probability of different fire sources in the simulation is also derived from data provided by the NFPA. This data includes information on the likelihood of fires starting from various sources, such as stoves, heaters, candles, barbecues, fireplaces, and lightning strikes. By incorporating this data, the simulator can realistically model the chances of fires originating from different sources.

The simulator uses the FEMA U.S. Fire Administration National Fire Incident Reporting System (NFIRS) dataset to determine the probability of different fire sources. The dataset categorizes fire causes into codes, which are then mapped to specific sources in the simulator. For example, the "Cooking" cause code is mapped to the "Stove" source, the "Heating" cause code is mapped to the "Heater" source, and the "Open Flame" cause code is mapped to the "Barbecue", "Fireplace", and "Candle" sources.

In addition, there is a 1% chance of a lightning strike causing a fire. This probability is not based on data from the NFPA.

Amount of Data and Analysis

One may be surprised by the small amount of data used to determine the fire frequency and fire source probability, as well as the basic nature of the analysis. However, the data is sufficient for the purposes of the simulator. It simply needs to simulate the occurence of a fire and the ignition source. Of course, this could be based on a much more complicated model, accounting for weather, time of day, usage, age of appliances, and other factors. However, such a model would be overkill for the purposes of this simulator. The goal is to provide a simple demonstration of how a fire might spread in a house, not to create a complex model that accounts for every possible factor.

With the advent of big data and advanced machine learning, it is easy to forget that simple statistical analysis can still be useful and not every problem requires a massive dataset and advanced algorithms.

Fire Frequency Simulation

Overview of the Poisson Process

The Poisson process is a mathematical model used to describe events that occur randomly and independently over time. It is characterized by a single parameter, λ (lambda), which represents the average rate of events per unit of time. In the context of the simulator, the Poisson process is used to model the occurrence of fires, where λ represents the average fire frequency derived above.

Calculating Fire Frequency

The simulator calculates the fire frequency by generating Poisson random variables based on the average fire frequency parameter, λ. It continues generating these random variables until their sum reaches the specified number of fires to simulate. This approach is used because the simulator only simulates when a fire occurs. For example, if the simulator is set to run 10 simulations, it will generate Poisson random variables until it accumulates a total of 10 fires. The simulator then calculates the mean of the sum of the random variables divided by the number of random variables generated. This mean represents the simulated fire frequency, providing an estimate of the average number of fires that occur in a given time period.

Cellular Automata Basics

Cellular automata are mathematical models used to simulate complex systems by dividing them into a grid of cells. Each cell can be in one of a finite number of states, and the state of each cell at a given time step is determined by the states of its neighboring cells and a set of rules. Cellular automata are particularly well-suited for simulating phenomena that evolve over time and space, such as the spread of fire.

In the context of the fire spread simulation, the cellular automata model divides the virtual house into a grid of cells. Each cell represents a small area of the house. The state of each cell at each time step is determined by the states of its neighboring cells and a set of rules that govern how fire spreads from one cell to another.

The cellular automata model allows the simulator to capture the spatial and temporal dynamics of fire spread. It provides a simple yet powerful framework for modeling the complex interactions between different parts of the house as the fire spreads.

The Grid

The grid represents the house and is the basis of the cellular automata model used to simulate the spread of fire. It is a two-dimensional array of cells, where each cell represents a small area of the house.

What is a Cell

Contents of Cell

Each cell in the simulation represents a 1x1x3 volume within the virtual house. The cell is divided into three sections: top, middle, and bottom. The top section represents the roof, while the middle and bottom sections represent the contents of the cell. The roof is always the same volume and material for all cells and is not modeled directly. If the cell is burning and is part of the structure, it is assumed that the roof is burning too. The floor cells burn based on the roof, and the cost is calculated using a constant roof value. The contents of the cell are assumed to have some volume made of wood, representing furniture and other items.

Each cell holds the following information:

• Coordinates: The cell's position in the simulation grid, represented by the x and y coordinates.
• Object: The structural component of the cell, such as a wall or floor.
• Material: The material of the object, such as wood or tile.
• Temperature: The current temperature of the cell in Kelvin.
• Initial Fuel: The initial amount of fuel in the cell, calculated based on the object's volume and the material's density.
• Fuel: The current amount of fuel in the cell.
• Is Burning: A boolean value indicating whether the cell is currently burning.
• Proportion Burned: The proportion of the cell that has been burned.
• Value: The value of the cell, calculated based on the object's and material's parameters, the roof value, and the contents value.
• Item: An optional item within the cell, such as a stove or heater.
• Defence: An optional defence within the cell, representing a fire protection measure.

Object

The object in a cell represents the structural component of the cell, such as a wall or floor. Each object has a set of parameters that define its characteristics, including its volume, heat resistance, whether it contributes to the cost of the cell, and its base value. The object's parameters are defined in the ObjectParamsMap.

The following objects are available in the simulation:

• Earth
• Floor
• Wall
• Door
• Window

Each object can be made of different materials, which are defined in the AllowedMaterialsMap. For example, a wall can be made of brick or wood, while a floor can be made of wood, tiles, or carpet.

Material

The material in a cell represents the material of the object, such as wood or tile. Each material has a set of parameters that define its characteristics, including its density, fuel consumption rate, heat value, specific heat, combustion point, heat decrease rate, and base value multiplier. These parameters affect the behavior of the cell during the simulation, including how quickly the fire spreads and how much heat is generated.

The following materials are available in the simulation:

• Dirt: Represents the ground.
• Grass: Represents the grass on the ground.
• Wood: Represents wooden objects, such as walls and floors.
• Brick: Represents brick walls.
• Tiles: Represents tiled floors. Tiles and carpet are considered under roof floor materials, so they are given wood's values as it is assumed the roof is burning and made of wood.
• Carpet: Represents carpeted floors.
• Metal: Represents metal objects, such as doors.
• Glass: Represents glass windows.

Each material's parameters affect the cell's behavior during the simulation. For example, the density of the material affects the initial fuel in the cell, while the fuel consumption rate affects how quickly the fuel is consumed. The heat value and specific heat determine how much heat is generated and absorbed by the material, while the combustion point determines the temperature at which the material ignites. The heat decrease rate affects how quickly the temperature decreases, and the base value multiplier affects the value of the cell.

Item

An item in a cell represents a specific object within the cell, such as a stove or heater. Items can be added to a cell and have their own parameters, which can affect the cell's behavior during the simulation. Items are optional and can be added or removed from a cell as needed.

Defence

A defence in a cell represents a fire protection measure, such as a sprinkler system or fire-resistant material. Defences can be added to a cell and have their own parameters, which can affect the cell's behavior during the simulation. Defences are optional and can be added or removed from a cell as needed.

Item

An item in a cell represents a specific object within the cell that can potentially ignite and start a fire. Each item has a set of parameters that define its characteristics, including its name, fire probability, and value. The item's parameters affect the behavior of the cell during the simulation, including the likelihood of the item igniting and starting a fire.

The following items are available in the simulation:

• Stove
• Heater
• Candle
• Fireplace
• Barbecue

Defence

A defence in a cell represents a fire protection measure that can help prevent or mitigate the spread of fire. Each defence has a set of parameters that define its characteristics, including its name, fuel reduction rate, max temperature, alerted status, radius of effect, response time, remaining uses, and chance of failure. The defence's parameters affect the behavior of the cell during the simulation, including how effectively the defence can prevent or mitigate the spread of fire.

The following defences are available in the simulation:

• Extinguisher
• Sprinkler
• Blanket
• Detector

Each defence's parameters affect the cell's behavior during the simulation. The fuel reduction rate of the defence determines how effectively the defence can reduce the fuel in the cell. The max temperature of the defence determines the maximum temperature at which the defence can operate effectively. The alerted status of the defence indicates whether the defence has been alerted to the presence of fire. The radius of effect of the defence determines the area around the defence that is affected by its actions. The response time of the defence determines how quickly the defence can respond to the presence of fire. The remaining uses of the defence indicate how many times the defence can be used before it is depleted. The chance of failure of the defence determines the likelihood of the defence failing to operate effectively.

Fire Simulation Process

This section describes the process used by the simulator to simulate a fire.

Determining the Initial Fire Source

The simulator determines the initial fire source by randomizing the ignition point among a set of predefined ignition sources. Each ignition source has an associated probability of ignition, which represents the likelihood of that source being the initial point of the fire. This is what the fire source probability data from the NFPA is used for.

First, the simulator adds a random chance of a lightning strike as an ignition source. It generates random coordinates within the simulation grid to represent the location of the lightning strike. The probability of a lightning strike is set to 0.01, or 1%.

The simulator then shuffles the ignition sources, including the lightning strike, to randomize the order in which they are considered. It loops through the shuffled ignition sources and generates a random number between 0 and 1 for each source. If the random number is less than the ignition probability of the source, that source is selected as the initial fire source, and the loop is terminated.

This process ensures that the initial fire source is determined randomly based on the probabilities of the different ignition sources. It allows the simulator to model the unpredictability of real-world fire ignition scenarios.

Fire Spread Rules

The simulation progresses in discrete steps, and during each step, the state of each cell is updated based on its current state and the states of its neighboring cells.

The simulation follows these steps:

1. For each cell that has been altered in the previous step, the cell undergoes self-interaction, which updates its state based on its current properties.
2. The cell's neighbors are identified, and the impact of the neighbors on the cell is calculated. The cell's state is updated based on the states of its neighbors.
3. The impact of the cell on its neighbors is calculated. The states of the neighboring cells are updated based on the state of the cell.
4. If the cell has a defence, such as a sprinkler or fire extinguisher, the defence is checked for its alert status, readiness, and remaining uses. If the defence is ready and has remaining uses, it responds to the fire in the neighboring cells by reducing their fuel based on the defence's fuel reduction rate.
5. The cost of the fire is calculated based on the states of the cells.

The simulation continues in this manner, updating the states of the cells and calculating the cost of the fire at each step. The simulation ends when the loss of value has not changed for 10 steps, or at 1,000 steps.

Self Interaction

The self interaction of a cell is a crucial part of the simulation process. It determines how a cell behaves based on its current state, including its temperature, fuel, and whether it is burning. The self interaction process follows these steps:

1. First, the cell checks its remaining fuel. If the fuel is depleted (fuel <= 0), the cell cools down.
2. Next, the cell checks its temperature and whether it is already burning. If the temperature is greater than or equal to the combustion point of the material and the cell is not already burning, the cell ignites.
3. If the cell is burning and still has fuel, it continues to burn. The burning process updates the cell's temperature and fuel based on the material's properties.

The self interaction process is repeated for each cell in the simulation at every step. It ensures that the cells behave realistically based on their current states and the properties of the materials they are made of.

Neighbor Interaction

The interaction between neighboring cells is another essential aspect of the simulation process. It determines how a cell is affected by its neighbors and how it affects them in return. The neighbor interaction process follows these steps:

1. First, the cell checks if it is already burning. If it is, the interaction process is skipped for this cell.
2. Next, the cell retrieves the parameters of the object it represents, including its heat resistance.
3. The cell calculates the temperature difference between itself and its neighbor.
4. If the temperature difference is positive (the neighbor is hotter than the cell), the cell calculates the heat transfer based on the temperature difference, a constant heat transfer rate, and the inverse square of the distance between the cells.
5. The cell updates its temperature based on the calculated heat transfer and its heat resistance.

The neighbor interaction process is repeated for each cell and its neighbors in the simulation at every step. It ensures that the cells interact with each other and spread heat realistically based on their current states and the properties of the objects they represent.

Defence

The defense mechanism in the simulation is responsible for mitigating the spread of fire. It is implemented in the form of defense parameters associated with each cell. The defense process follows these steps:

1. First, the cell checks if the defense is out of uses. If it is, the defense process is skipped for this cell.
2. Next, the cell checks if the defense has an unlimited radius. If it does, the defense is immediately alerted.
3. The cell retrieves the neighbors within the defense's radius of effect. It checks if any of these neighbors are burning. If any are, the defense is alerted.
4. If the defense is not alerted, the cell updates its state and continues to the next step in the simulation.
5. If the defense is alerted, it checks if it is ready to respond. If the defense has a response time greater than zero, it decrements the response time and updates the cell's state.
6. Once the defense is ready to respond, it iterates over each neighbor within its radius of effect. If the neighbor is burning and its temperature is below the defense's maximum temperature, the defense checks if it fails based on a random number and its chance of failure. If it fails, the defense's remaining uses are decremented. If it succeeds, the neighbor's fuel is reduced based on the defense's fuel reduction rate.

The defense process is repeated for each cell with defense parameters in the simulation at every step. It ensures that the cells interact with each other and mitigate the spread of fire based on their current states and the properties of the defense mechanisms they have.

Termination

The simulation continues to run until a termination condition is met. The termination condition is based on the cost values calculated at each step of the simulation. The simulation checks the last 10 cost values and determines if they have converged, meaning that the difference between consecutive cost values is less than 0.1. If the cost values have converged, the simulation terminates. However, this check is only performed after a minimum number of steps have been completed to ensure that the simulation runs for a sufficient amount of time.

The termination condition ensures that the simulation stops once the fire has reached a steady state, and further simulation steps would not provide any additional insights. By checking the convergence of the cost values, the simulation can efficiently determine when to stop running and provide the final results.

Determining Fire Spread Parameters and Object Values

Fire spread parameters are crucial for accurately simulating the behavior of a fire. These parameters influence factors such as the rate of fire spread and the intensity of the fire. I determined the intensity of the fire through research and online searches to populate reasonable estimates of the parameters. However, fire simulation is a complex topic, and there is no one-size-fits-all solution. The parameters I chose are based on my research and are not guaranteed to be accurate for all situations.

Above we saw that the each cell defines properties for objects, including volume and heat resistance. Properties for materials include density, fuel consumption rate, heat value, specific heat, combustion point, and heat decrease rate.

For example, the Wood material has a density of 500.0 kg/m³, a fuel consumption rate of 1%/step, a heat value of 15,000 J/kg, a specific heat of 2,000 J/kg·K, a combustion point of 573.0 K (300.0°C) and a heat decrease rate of 5%/step.

These parameters are used to simulate the behavior of a fire as it spreads through a space, taking into account the properties of the objects and materials involved. However, it is important to note that the simulation is a simplified representation of fire spread, and the parameters used are only indicative.

Object values represent the estimated monetary value of objects within the simulation, such as furniture, appliances, and structural elements. These values are used to calculate the total loss incurred in the event of a fire.

To determine object values, I used online searches to find the average cost per square foot of various objects and structural elements. I then converted these values to cost per square meter for consistency within the simulation. It is important to note that these values are only indicative and should not be relied upon for actual financial assessments. In a more realistic simulation, object values would be provided by the user based on their specific circumstances and property.

It is essential to emphasize that the object values used in this simulation are only for illustrative purposes. In a real-world scenario, object values would be determined based on a variety of factors, including the specific materials used, the age and condition of the objects, and their location within the property.

Ultimately, the object values used in this simulation serve as a starting point for understanding the potential financial consequences of a fire. However, they should not be used as a substitute for a comprehensive assessment of property value and potential loss in the event of a fire. Their primary purpose is to show the impact of including fire defense mechanisms in the simulation.

Conclusion

Summary of the Guide

Insurance Automata is an app that uses a cellular automata model to simulate the spread of fire across a house. This guide has provided a comprehensive overview of the parameterization process used in the app's underlying logic. It has covered the data sources and methods used to determine the frequency of fires, the probability of different fire sources, and the simulation of fire spread. Additionally, the guide has explained how the values of objects and the parameters for fire spread were determined.

By utilizing data from reputable sources such as the NFPA and the U.S. Census Bureau, the simulator accurately reflects real-world fire occurrence patterns. The app allows users to place objects within a virtual house and observe how a fire might spread under various conditions. The simulation process involves determining the initial fire source, spreading the fire using cellular automata, and calculating the cost of the fire based on the states of the cells.

The guide has also discussed the properties of cells in the simulation, including their coordinates, object, material, temperature, fuel, burning status, proportion burned, value, item, and defence. The parameters associated with objects, materials, items, and defences have been explained, and their impact on the simulation has been discussed.

It is important to note that the simulation is a simplified representation of fire spread, and the parameters used are only indicative. The object values used in the simulation are also for illustrative purposes and should not be relied upon for actual financial assessments.

Future Work and Improvements

While the current version of Insurance Automata provides a valuable tool for simulating the spread of fire in a house, there are several areas where future work and improvements could enhance the app's functionality and realism. These include:

• Expanding the Data Sources: Incorporating additional data sources and more detailed fire statistics could improve the accuracy of the fire frequency and fire source probability calculations.
• Enhancing the Simulation Model: Incorporating more complex fire spread models, such as those that account for weather, time of day, usage, age of appliances, and other factors, could provide a more realistic simulation of fire spread.
• Improving the User Interface: Enhancing the user interface to allow for more customization of the simulation parameters, object placement, and fire defence mechanisms could provide a more interactive and user-friendly experience.
• Adding More Objects and Materials: Expanding the list of available objects, materials, items, and defences could provide a more comprehensive simulation of a house and its contents.
• Conducting Validation Studies: Comparing the simulation results with real-world fire incidents could help validate the accuracy of the simulation model and identify areas for improvement.

By addressing these areas, future versions of Insurance Automata could provide an even more powerful and realistic tool for simulating the spread of fire in a house and understanding the potential consequences of a fire.