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Probability of Kill Modeling for Hypersonic Vehicle Missions



OBJECTIVE: Create an optimization/sensitivity model that utilizes kill probability as the basis for assessment of alternative hypersonic system technologies.

DESCRIPTION: Hypersonic vehicles (HV) are designed to travel at high speeds pursuing deeply protected targets and seeking to impact them with sufficiently high energy. Thus, the Probability of Kill for a hypersonic weapon depends on both the ability to arrive at the target and to sufficiently damage it. Mathematically, the Probability of Kill (P_k) for a HV can be expressed as the product of the Probability of Arrival (P_a) multiplied by the Probability of Damage (P_d): P_k=P_a*P_d.The main challenge for developing an effective HV is that there are many vehicle performance and mission scenario parameters that influence P_k. Innovation is needed to develop a ‘system of systems’ analysis capability that models the many interdependent components and sub-components of P_k as a function of new technologies on the HV and then optimizes the family of technologies that maximizes P_k across relevant mission sets. The desired system of systems model will provide a framework to capture P_a and P_d under a variety of technology infusion scenarios and integrate these into assessments into the optimization of P_k of a new HV. The prototype framework should leverage both low- and high-fidelity models to robustly estimate the cost-benefit proposition (on P_k) from the injection of new technologies into the HV development and justify the robustness of the estimates with extensive sensitivity analysis.Estimating the P_a hinges on the ability to capture the behaviors and physical limitations of the HV itself, the supporting role of other blue-force systems, and the efficacy of any non-target red-force systems and their behaviors. In uncontested scenarios, this may be simply a function of time and geometry; however, in more complex scenarios that represent real-world scenarios, producing such a model requires incorporating capabilities of multiple interdependent systems. Estimating the P_d can be accomplished by a statistical model obtained by aggregating high-fidelity models and inputs. P_d can be calculated separately from the P_a by capturing the state information of the HV and pairing that with accepted models of threat systems. However, for any given mission and any given time, the state of HV at impact, again, is dependent on the blue-force support systems and the effect from red-force counter systems.The Phase II effort will likely require secure access, and SSP will process the DD254 to support the contractor for personnel and facility certification for secure access. The Phase I effort will not require access to classified information. If need be, data of the same level of complexity as secured data will be provided to support Phase I work.Work produced in Phase II may become classified. Note: The prospective contractor(s) must be U.S. owned and operated with no foreign influence as defined by DoD 5220.22-M, National Industrial Security Program Operating Manual, unless acceptable mitigating procedures can and have been implemented and approved by the Defense Counterintelligence and Security Agency (DCSA). The selected contractor and/or subcontractor must be able to acquire and maintain a secret level facility and Personnel Security Clearances, in order to perform on advanced phases of this project as set forth by DCSA and SSP in order to gain access to classified information pertaining to the national defense of the United States and its allies; this will be an inherent requirement. The selected company will be required to safeguard classified material IAW DoD 5220.22-M during the advanced phases of this contract.

PHASE I: Define and develop a conceptual framework for calculating P_k of HV based on modeling probability of arrival and probability of damage.Develop a concept for a system of systems modeling and simulation capability that can be flexibly and iteratively refined to include models of increasing fidelity blue and red force assets, including new and novel technologies within the major systems of HVs.The Phase I Option, if exercised, will include the initial design specifications and capabilities description to build a prototype solution in Phase II.Prepare a Phase II plan.

PHASE II: Deliver P_d models and P_A models that can be used to determine P_k for HVs. This will provide a framework to build a model for P_k that can be used to evaluate more complex systems. Validate the subsequent P_k results by comparison to field test data from HV flights.It is probable that the work under this effort will be classified under Phase II (see Description section for details).

PHASE III: Deliver an integrated toolset that assesses both P_d and P_A by integrating a representative set of low- and high-fidelity models of interest. Demonstrate P_k for real world scenarios by incorporating operational model HV and system of systems.The inherent functionality of the proposed analysis toolset would be applicable to any complex hypersonic vehicle application. For example, the design of planetary entry systems requiring precise targeting for landing would benefit from these innovations.

KEYWORDS: Probability of Kill, Probability of Damage, Probability of Arrival, Hypersonic Vehicles, System of Systems Analysis, Mission Effectiveness, Technology Assessments, Vehicle Design


1. Ezra, Kristopher L., DeLaurentis, Daniel A., Mockus, Linas and Pekny, Joseph F. "Developing Mathematical Formulations for the Integrated Problem of Sensors, Weapons, and Targets." Journal of Aerospace Information Systems, Vol. 13, No. 5, 2016, pp. 175-190. 2. Grant, Michael J., and Braun, Robert D. "Rapid indirect trajectory optimization for conceptual design of hypersonic missions." Journal of Spacecraft and Rockets 52.1, 2014, pp. 177-182. 3. Bogdanowicz, Zbigniew R., et al. "Optimization of weapon–target pairings based on kill probabilities." IEEE transactions on cybernetics, 43.6, 2012, pp. 1835-1844.

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