Sparse Stochastic Libraries for Hazard Risk Assessment
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Solution Overview
Problem
Existing methods for assessing hazard risks, such as wildfires, rely on averages that fail to capture spatial correlations and can lead to erroneous decisions, particularly in non-technical management contexts.
Innovation Solution
The development of a practical approach that conveys the full distribution of hazard intensity while preserving spatial correlations, using Sparse Monte Carlo and event Polygons to reduce storage requirements and facilitate chance-informed decision-making.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If average hazard intensity is used to assess risk, then decision-making is simplified, but spatial correlations and simultaneous risk events are lost leading to erroneous decisions
Solution Approach 1:
The patent segments the hazard assessment into two distinct components: (1) marginal hazard distributions for individual locations, and (2) a copula function that captures spatial correlations. This segmentation allows decision-makers to use simplified marginal distributions while preserving critical spatial dependency information through the copula structure, thereby resolving the contradiction between simplicity and information completeness.
Solution Approach 2:
The copula function serves as an intermediary element that connects individual hazard distributions at different locations while preserving spatial correlations. This intermediary structure enables the model to maintain detailed spatial dependency information without requiring decision-makers to directly process complex multivariate data, thus bridging the gap between information completeness and ease of use.
2Loss of information
If full hazard simulation data is stored for all locations and time steps, then complete spatial correlation information is preserved, but storage requirements become prohibitively large
Solution Approach 1:
The patent extracts only the essential spatial correlation information from the full simulation data by fitting a copula function to the joint hazard distributions. Instead of storing complete multivariate simulation results for all locations and time steps, the model extracts and stores only the copula parameters that capture spatial dependencies, dramatically reducing storage requirements while preserving the critical spatial correlation structure.
Solution Approach 2:
The patent transforms the full hazard simulation data into a reduced-parameter representation by fitting copula functions. This parameter change converts complex multivariate spatial-temporal hazard fields into a smaller set of copula parameters that encapsulate the essential spatial correlation information, thereby reducing data storage requirements from O(N×M) to O(N) where N is the number of locations and M is the number of time steps.
3Measurement precision
If detailed spatial hazard distributions are used, then accurate risk assessment is achieved, but computational complexity and processing time increase significantly
Solution Approach 1:
The patent segments the computational process into two independent stages: (1) generating marginal hazard distributions for each location using standard hazard models, and (2) combining these marginals using copula functions to preserve spatial correlations. This segmentation allows each stage to be computed independently and efficiently, reducing overall computational complexity while maintaining accurate risk assessment through the copula-based spatial dependency modeling.
Data Source
AI summary
A method according to an embodiment conveys the full distribution of hazard intensity while preserving spatial correlations, including the chances of simultaneous risk events. Sparse Monte Carlo and event Polygons reduce storage requirements by orders of magnitude compared to Pixel based approaches.