Future Event Simulation Using PDF Convolution Instead of Monte Carlo
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Solution Overview
Problem
Existing Monte Carlo simulation methods for complex computational simulations, such as Integrated Master Schedules, are inefficient due to the need for numerous iterations and the use of random number generators, leading to prolonged processing times and imprecise results.
Innovation Solution
A system and method utilizing TriCoBi processing, which combines and merges probability density functions (PDFs) sequentially without iterations, employing convolution theory to achieve faster and more accurate simulations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If brute force Monte Carlo simulation is used, then statistical significance can be achieved, but processing time increases significantly
Solution Approach 1:
The patent segments the simulation process by dividing the probability density function into discrete bins and processing each bin independently through convolution operations. This segmentation allows the system to achieve statistical significance through systematic mathematical operations rather than relying on numerous random iterations, thereby reducing processing time while maintaining reliability
Solution Approach 2:
The patent replaces the mechanical iteration process of brute force Monte Carlo simulation with a mathematical convolution-based system. Instead of mechanically repeating random sampling thousands of times, the system uses convolution of probability density function bins to directly compute results, eliminating the time-consuming iterative mechanism while preserving statistical accuracy
2Measurement precision
If numerous iterations are performed to obtain statistically significant results, then accuracy improves, but the process becomes time-consuming
Solution Approach 1:
The patent performs preliminary action by pre-defining and binning the probability density functions before the simulation process. By preparing the PDF bins in advance and organizing the data structure, the system eliminates the need for time-consuming iterations during actual simulation, achieving both high accuracy and efficiency through upfront preparation
Solution Approach 2:
The patent substitutes the iterative mechanical process with a direct mathematical convolution approach. The convolution operation on pre-binned PDFs directly yields accurate results without requiring repeated sampling iterations, thereby achieving measurement precision without the associated time cost
3Ease of operation
If random number generators are used for each task, then individual task simulation is achieved, but overall simulation time increases
Solution Approach 1:
The patent merges the simulation approach by combining probability density functions through convolution operations. Instead of separately simulating each task with random number generators, the system merges task PDFs mathematically to produce aggregate results, maintaining ease of operation while dramatically improving simulation speed and productivity
Data Source
AI summary
A system and method for performing simulations of uncertain future events may use statistical analysis via computerized simulations associated with processes including project scheduling; project budgeting, project risk assessments (or confidence percentages), strategic decision-making of alternatives, investment alternatives, etc. In some embodiments, the system and method may utilize probability and convolution theory to arrive at ideal theoretical probabilistic solutions (PDF [probability density function] and “S” Curve [cumulative distribution function] outcomes).