Point Estimation Method for Non-Normal Variability Allocation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing point estimation methods (PEMs) in Civil Engineering and beyond are inefficient in estimating probability density functions, requiring a large number of function evaluations or simulation runs, and fail to effectively allocate variability to system components.
Innovation Solution
A second generation PEM design process that utilizes a customized multi-level experiment to estimate probability density functions with minimal function evaluations, assigning the number and values of levels for each design variable based on its contribution to response variability, and employing the Johnson family of probability densities to fit data to standardized moments, thereby reducing the need for regression modeling and allowing for non-normally distributed design variables.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional Monte Carlo methods are used to estimate probability density functions, then comprehensive sampling is achieved, but a large number of function evaluations or simulation runs are required
Solution Approach 1:
The system automatically determines the optimal number of levels and variable assignments without requiring external regression modeling or manual intervention. The PEM methodology self-configures the experiment design based on the transfer equation structure, eliminating the need for separate regression phases and reducing overall computational overhead
Solution Approach 2:
The methodology transforms the problem by changing from traditional Monte Carlo random sampling to structured multi-level sampling with specifically determined parameter values. By using the relationship between number of levels and estimation accuracy, the system optimizes sampling parameters to achieve the same precision with fewer evaluations
2Productivity
If customized multi-level experiments are designed with automatic level assignment, then the number of function evaluations is minimized, but the complexity of the design process increases
Solution Approach 1:
The system automatically determines the optimal number of levels and variable assignments without requiring external regression modeling or manual intervention. The PEM methodology self-configures the experiment design based on the transfer equation structure, eliminating the need for separate regression phases and reducing overall computational overhead
Solution Approach 2:
The methodology performs preliminary determination of the number of levels and variable assignments before conducting the actual experiment. By pre-calculating the optimal design parameters based on the transfer equation, the system prepares the experiment structure in advance, reducing the complexity of the execution phase
3Productivity
If second generation PEM methodology is used to reduce function evaluations, then computational efficiency improves, but the ability to handle non-normally distributed variables must be enhanced
Solution Approach 1:
The methodology assigns different numbers of levels to different variables based on their contribution to response variability, rather than using a uniform approach. This universal framework can accommodate any distribution type by adjusting the number of levels appropriately, making the system versatile for both normal and non-normal distributions while maintaining computational efficiency
Data Source
AI summary
A method for implementing a point estimation method (PEM) that predicts variability of a system output response based on variabilities of inputs includes building a customized designed experiment such that each input variable x for the designed experiment is assigned a number of variable values n based on the respective input variable's contribution p to overall response variability.