Explicit Exact Solution of Damage Probability for Multiple Weapons against a Unitary Target
| Autor: | Hong Zhou, Cardy Moten, Hongyun Wang, Morris Driels, Don Grundel |
|---|---|
| Přispěvatelé: | TRADOC Analysis Center, Mechanical and Aerospace Engineering (MAE), Applied Mathematics |
| Rok vydání: | 2016 |
| Předmět: |
Physics::Physics and Society
Exact Solution 021103 operations research 0211 other engineering and technologies General Engineering 02 engineering and technology Function (mathematics) Expression (computer science) Ellipse Carleton Damage Function Optimal Distribution of Aimpoint Combinatorics Distribution (mathematics) Exact solutions in general relativity 0202 electrical engineering electronic engineering information engineering Applied mathematics Multiple Weapons with Dependent Errors 020201 artificial intelligence & image processing Point (geometry) Damage Probability Random variable Mathematics Free parameter |
| Popis: | The article of record as published may be found at http://dx.doi.org/10.4236/ajor.2016.66042 We study the damage probability when M weapons are used against a unitary target. We use the Carleton damage function to model the distribution of damage probabil- ity caused by each weapon. The deviation of the impact point from the aimpoint is attributed to both the dependent error and independent errors. The dependent error is one random variable affecting M weapons the same way while independent errors are associated with individual weapons and are independent of each other. We con- sider the case where the dependent error is significant, non-negligible relative to in- dependent errors. We first derive an explicit exact solution for the damage probabil- ity caused by M weapons for any M. Based on the exact solution, we find the optimal aimpoint distribution of M weapons to maximize the damage probability in several cases where the aimpoint distribution is constrained geometrically with a few free parameters, including uniform distributions around a circle or around an ellipse. Then, we perform unconstrained optimization to obtain the overall optimal aim- point distribution and the overall maximum damage probability, which is carried out for different values of M, up to 20 weapons. Finally, we derive a phenomenological approximate expression for the damage probability vs. M, the number of weapons, for the parameters studied here. TRAC-M |
| Databáze: | OpenAIRE |
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