Damage Analysis III: Object Densities, Presented Surfaces Based on Exposure, Geometry and Damage Models

Abstract

The chapter covers basic approaches to the damage assessment modeling in the case of trajectory based damage, e.g. fragment and debris impact. In its initial steps, it is an example for the physical-engineering modelling of damage effects, in its final steps it also shows the application of empirical-statistical damage models. The use of distributions for further damage modelling is only indicated as well as how to use the presented surfaces in risk analysis approaches. The presented surfaces are used to determine damage probabilities of objects. This information enters risk computations: local and non-local, for individuals and groups. To avoid as far as possible object-specific modelling, the chapter first uses geometry information only. It is shown how to compute the presented surface, i.e. the surface that could be damaged in case of explosive fragment and debris impact. The same arguments hold true for other types of trajectory-based impact, e.g. in case of hail or ice rain, objects that are torn from buildings or structures due to heavy wind, or debris generated by accidents of airplanes or aerial drones, as well as a set of malicious events in the aerial domain, e.g. aerial drones that discharge objects. The presented surface is computed using analytical and numerical approaches. In the case of simple geometrical objects, fast analytical approaches are feasible. In the case of more complicated or composed geometries, a Monte Carlo integration approach is employed. The chapter introduces the notion of a relevant surface with respect to a set of damage criteria. This links presented surfaces with damage models. Typically it suffices to suitably combine a rather small number of damage models for a single object along with their respective different volume and surface elements to obtain a sufficient overall damage model for an object. It is indicated how this is achieved for an object using only one discrete damage model. To model unknown positions and orientations of objects, the chapter introduces in detail two concepts. Object exposure densities and the homogeneous integration (averaging) over an unknown orientation parameter. The latter case illustrates under which assumptions unknown parameters can be considered in an adequate way. The former example allows a similar approach at a later risk analysis step, e.g. for computing collective ricks.