To reduce the safety risk posed by small Unmanned Aircraft System (UAS) to persons on the ground, one of the mitigating measures is to equip the UAS with an airbag in combination with a parachute, both of which are deployed in case of an uncontrolled descent. In literature, methods for the evaluation of the effect of a parachute alone have been developed. This paper develops a method to assess the safety risk for persons on the ground posed by a UAS that is both equipped with an airbag and a parachute. For the descent phase of the UAS to the ground, existing models are used. The novel part is the dynamical simulation of the effect on a human body of impact and interaction of a UAS with airbag. For the human impact simulation, use is made of Multi Body System (MBS) model for the UAS and the human; in combination with Finite Element (FE) model of the airbag. This method is applied for a specific parcel delivery UAS, of 15 kg weigh, for cases with and without airbag. The results obtained show that the combination of parachute and airbag can reduce the safety risk posed to people on the ground by more than one order in magnitude. Comparison with existing models for parachute alone, show that the novel method is much better in taking UAS design and material properties into account. The paper also shows that the dynamical simulation results obtained provide effective feedback to the further improvement of the airbag design.

The transition kernel of an ℝ ⁿ-valued diffusion or jump diffusion process {X _t} is known to satisfy the Feller property if {X _t} is the solution of an SDE whose coefficients are Lipschitz continuous. This Lipschitz route to Feller falls short if {X _t} is the solution of an SDE whose coefficients depend on a state-dependent regime-switching process {θ _t}. In this paper it is shown that pathwise uniqueness and the Feller property are satisfied under mild conditions for a regime-switching jump diffusion process {X _t, θ _t} with hybrid jumps, i.e. jumps in {X _t} that occur simultaneously with {θ _t} switching.

Advantages of commercial UAS-based services come with the disadvantage of posing third party risk (TPR) to overflown population on the ground. Especially challenging is that the imposed level of ground TPR tends to increase linearly with the density of potential customers of UAS services. This challenge asks for the development of complementary directions in reducing ground TPR. The first direction is to reduce the rate of a UAS crash to the ground. The second direction is to reduce overflying in more densely populated areas by developing risk-aware UAS path planning strategies. The third direction is to develop UAS designs that reduce the product (Formula presented.) in case of a crashing UAS, where (Formula presented.) is the size of the crash impact area on the ground, and (Formula presented.) is the probability of fatality for a person in the crash impact area. Because small UAS accident and incident data are scarce, each of these three developments is in need of predictive models regarding their contribution to ground TPR. Such models have been well developed for UAS crash event rate and risk-aware UAS path planning. The objective of this article is to develop an improved model and assessment method for the product (Formula presented.) In literature, the model development and assessment of the latter two terms is accomplished along separate routes. The objective of this article is to develop an integrated approach. The first step is the development of an integrated model for the product (Formula presented.). The second step is to show that this integrated model can be assessed by conducting dynamical simulations of Finite Element (FE) or Multi-Body System (MBS) models of collision between a UAS and a human body. Application of this novel method is illustrated and compared to existing methods for a DJI Phantom III UAS crashing to the ground.

For diffusions, a well-developed approach in rare event estimation is to introduce a suitable factorization of the reach probability and then to estimate these factors through simulation of an Interacting Particle System (IPS). This paper studies IPS based reach probability estimation for General Stochastic Hybrid Systems (GSHS). The continuous-time executions of a GSHS evolve in a hybrid state space under influence of combinations of diffusions, spontaneous jumps and forced jumps. In applying IPS to a GSHS, simulation of the GSHS execution plays a central role. From literature, two basic approaches in simulating GSHS execution are known. One approach is direct simulation of a GSHS execution. An alternative is to first transform the spontaneous jumps of a GSHS to forced transitions, and then to simulate executions of this transformed version. This paper will show that the latter transformation yields an extra Markov state component that should be treated as being unobservable for the IPS process. To formally make this state component unobservable for IPS, this paper also develops an enriched GSHS transformation prior to transforming spontaneous jumps to forced jumps. The expected improvements in IPS reach probability estimation are also illustrated through simulation results for a simple GSHS example.

This paper focuses on estimating reach probability of a closed unsafe set by a stochastic process. A well-developed approach is to make use of multi-level MC simulation, which consists of encapsulating the unsafe set by a sequence of increasing closed sets and conducting a sequence of MC simulations to estimate the reach probability of each inner set from the previous set. An essential step is to copy (split) particles that have reached the next level (inner set) prior to conducting a MC simulation to the next level. The aim of this paper is to prove that the variance of the multi-level MC estimated reach probability under fixed assignment splitting is smaller or equal than under random assignment splitting methods. The approaches are illustrated for a geometric Brownian motion example.

UAS-based commercial services such as urban parcel delivery are expected to grow in the upcoming years and may lead to a large volume of UAS operations in urban areas. These flights may pose safety risks to persons and property on the ground, which are referred to as third-party risks. Path-planning methods have been developed to generate a nominal flight path for each UAS flight that poses relative low third-party risks by passing over less risky areas, e.g., areas with low-density unsheltered populations. However, it is not clear if risk minimization per flight works well in a commercial UAS operation that involves a large number of annual flights in an urban area. Recently, it has been shown that when using shortest flight path planning, a UAS-based parcel delivery service in an urban area can lead to society-critical third-party risk levels. The aim of this paper is to evaluate the mitigating effect of state-of-the-art risk-aware path planning on these society-critical third-party risk levels. To accomplish this, a third-party risk simulation using the shortest paths is extended with a state-of-the-art risk-aware path-planning method, and the societal effects on third-party risk levels have been assessed and compared to those obtained using shortest paths. The results show that state-of-the-art risk-aware path planning can reduce the total number of fatalities in an area, but at the cost of a critical increase in safety risks for persons living in areas that are favored by a state-of-the-art risk-aware path-planning method.

Commercial aviation distinguishes three indicators for third party risk (TPR): i) Expected number of ground fatalities per aircraft flight hour; ii) Individual risk; and iii) Societal risk. The latter two indicators stem from TPR posed to population by operation of hazardous installations. Literature on TPR of Unmanned Aircraft System (UAS) operations have focused on the development of the first TPR indicator. However the expected increase of commercial UAS operations requires an improved understanding of third party risk (TPR). To support such improvement, this paper extends the existing TPR model for UAS operations with societal and individual risk indicators. The extension is developed both at modelling level and at assessment level. Subsequently the extended approach is applied to a hypothetical UAS based parcel delivery service in the city of Delft. The results obtained for the novel UAS TPR indicators show that this aligns commercial UAS operations with land use policies and standing TPR regulation for airports and hazardous facilities.