Probit Analysis for Energetic Sensitivity CDF Determination

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Solution Overview

Problem

Existing methods for determining the sensitivity of energetic materials to explosive shock, such as the Bruceton analysis, are influenced by the shape of the cumulative distribution function (CDF) and the number of tests performed, leading to inaccurate results when the CDF diverges from a step function.

Innovation Solution

A system and method that calculate the actual shape of the CDF by conducting tests at predetermined levels, using electronic processors to determine the 50% sensitivity level and associated confidence interval, employing probit modeling and statistical analysis to analyze sensitivity test data and fit curves to determine the precise sensitivity of energetic compositions.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If Bruceton analysis is used to determine sensitivity, then the method is simple and quick, but the accuracy is influenced by the shape of the CDF and the number of tests performed

Engineering Contradiction:

Improvespeed of sensitivity determinationVSAvoidaccuracy of 50% sensitivity level

Core Design Contradiction:

ProductivityVSMeasurement precision

Solution Approach 1:

The patent changes the analytical approach by transitioning from simple Bruceton analysis to probit analysis that models the CDF shape explicitly. This involves changing the mathematical parameters used in the analysis to account for different CDF shapes (normal, lognormal, Weibull, etc.), thereby improving accuracy without significantly increasing the number of tests required.

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent replaces the simple mechanical counting method of Bruceton analysis with a statistical modeling system that uses probit analysis and CDF fitting. This substitution of the analytical mechanism allows for more accurate determination of the 50% sensitivity level by modeling the underlying probability distribution rather than relying on simple step-function assumptions.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Measurement precision

If more tests are performed to improve accuracy, then the 50% sensitivity level becomes more precise, but the time required for testing increases

Engineering Contradiction:

Improveaccuracy of 50% sensitivity levelVSAvoidtesting time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent implements feedback through iterative CDF fitting and probit analysis. The system analyzes the test data, fits appropriate CDF curves, and uses this feedback to determine the 50% sensitivity level with confidence intervals. This feedback mechanism allows for more accurate results to be achieved with fewer tests by efficiently utilizing the data that is collected.

Inventive Principle:

Principle #23Feedback

Solution Approach 2:

The patent changes the statistical parameters and modeling approaches to maximize information extraction from each test. By using probit analysis and comparing multiple CDF shapes (normal, lognormal, Weibull), the system extracts more meaningful data from a smaller number of tests, thereby reducing the time required while maintaining or improving accuracy.

Inventive Principle:

Principle #35Parameter changes

3Ease of operation

If Bruceton analysis is used, then the starting point and number of tests do not matter, but the results are inaccurate when CDF diverges from step function

Engineering Contradiction:

Improvesimplicity of test procedureVSAvoidaccuracy of sensitivity determination

Core Design Contradiction:

Ease of operationVSMeasurement precision

Solution Approach 1:

The patent replaces the simple Bruceton analysis mechanism with a sophisticated probit analysis system that explicitly models CDF shapes. This substitution allows the system to handle cases where the CDF diverges from a step function by fitting appropriate continuous distributions (normal, lognormal, Weibull) to the data, thereby maintaining ease of operation while significantly improving accuracy.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent changes the mathematical modeling parameters from simple step-function assumptions to continuous CDF models with adjustable shape parameters. This allows the analysis to adapt to different underlying distributions of sensitivity data, improving accuracy when the CDF is not a step function while keeping the overall procedure straightforward through automated fitting and analysis.

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS9836560B1Computer simulation of probit method of cumulative distribution function determination of energetic sensitivity

Publication Date: 2017.12.05 THE UNITED STATES OF AMERICA AS REPRESENTED BY THE SECRETARY OF THE NAVY

AI summary

Embodiments of the invention simulate the actual shape of a cumulative distribution function (CDF) that describes the energetic sensitivity of an energetic composition. Sensitivity tests and historical data are input into an electronic processor. Response data points are obtained through electronic analysis and a best fit curve is produced through the response points and produced as output in a tangible medium.