Metrics for Evaluating Survivability in Dynamic Multi-Attribute Tradespace Exploration

Abstract

Survivability engineering is critical for minimizing the impact of disturbances to the operation of space systems. To improve the evaluation of survivability during conceptual design, metrics are proposed for the assessment of survivability as a dynamic, continuous, and path-dependent system property. Two of these metrics, time-weighted average utility loss and threshold availability, are then incorporated into a tradespace study on the survivability of future space tug vehicles to orbital debris. A value-based design approach, Dynamic Multi-Attribute Tradespace Exploration, is taken to evaluate survivability based on the relationship between stochastic space tug utility trajectories and changing stakeholder expectations across nominal and disturbed environmental states. Results of the tradespace study show that moderate levels of bumper shielding and access to an on-orbit servicing infrastructure benefit space tugs with large exposed cross-sectional areas while active collision avoidance only delivers value to extremely risk-averse decision makers. Timeweighted average utility loss and threshold availability are found to be discriminating metrics for navigating survivability tradespaces of thousands of design alternatives. NomenclatureA T = threshold availability CS = campaign-level survivability ∆V = change in velocity F(t) = failure likelihood as a function of time MoME = measure of mission effectiveness MTAT = mean time above critical value threshold MTBF = mean time between repair MTTR = mean time to repair P K = probability of kill P K|E = probability of kill for multiple-shot engagement P K|SS = probability of kill from single-shot P S = probability of survival P S|E = probability of survival for multiple-shot engagement P H = probability of hit (susceptibility) P K|H = probability of kill given hit (vulnerability) R(t) = reliability as a function of time T dl = time of design life T r = permitted recovery time U ‾ L = time-weighted average utility loss from design utility, U 0 ‾ U t = time-weighted average utility U(t) = utility delivery over time; multi-attribute utility trajectory V e = emergency value threshold V(t) = value delivery over time V x = required value threshold

Multi-Attribute Tradespace Exploration for Survivability: Application to Satellite Radar

“…Interestingly, every design comprising the 198-count Pareto set incorporates the minimum number of constellation spares of 0. As demonstrated previously in the survivability analysis of an orbital transfer vehicle, 6 the mitigating impact of survivability enhancement features on environmental disturbances is not accounted for in the static tradespace. However, the mass penalty of purchasing constellation spares adds lifecycle cost.…”

“…These changes are operationalized by characterizing stakeholder needs over time through a required utility threshold (i.e., zero utility in nominal environments), an emergency utility threshold (i.e., zero utility in perturbed environments), and a permitted recovery time (i.e., allowable time before performance expectations return to nominal). 6 However, for the case of a constellation of military radar satellites, tactical user expectations for GMTI do not change as a function of localized disturbances from the natural space environment. Therefore, it is assumed that the required utility threshold of the decision-maker is equivalent to the emergency utility threshold (i.e., U x =U e =0).…”

“…4,5 To improve the evaluation of survivability in tradespaces, metrics were developed to assess survivability as a dynamic, continuous, and path-dependent system property. 6 These respective efforts enable consideration of survivability strategies that prevent losses across the entire disturbance lifecycle and an ability to rapidly filter thousands of design alternatives in tradespace studies. However, the design principle framework and survivability metrics have not been integrated into a general methodology for survivability design and analysis.…”

“…The utility trajectory outputs from the dynamic analysis (i.e., distributions of multi-attribute utility over time) may be then evaluated using the survivability metrics as summary statistics. 6 Integrating the deterministic assessment of lifecycle cost and mission utility (at beginning of life) with the stochastic survivability metrics allows decision-makers to navigate an integrated tradespace of lifecycle cost, mission utility, and operational survivability. Figure 1 provides a flow chart of MATE for Survivability and identifies relationships with the legacy MATE process (i.e., either unchanged from MATE, evolved from MATE, or new to MATE).…”

“…6 This dynamic characterization of survivability was then operationalized using two metrics: time-weighted average utility loss and threshold availability. 6 Time-weighted average utility loss assesses the difference between the design utility (at beginning-of-life), U o , and the time-weighted average utility achieved over the system design life, T dl :…”