When components overlap, the aircraft multiple-hit vulnerability analysis usually consists of two steps. The first is to determine the aircraft unique existent states using vulnerable area decomposition method, and the second is to calculate the aircraft cumulated probability of kill using Markov chain method for exact solution or Monte Carlo method for solving the combinatorial explosion problem. This article proposes a direct simulation method for calculating the aircraft multiple-hit vulnerability in order to avoid the complex vulnerable area decomposition issue. In this method, random method is adopted to produce the multiple-hit locations and Bernoulli trial is used to determine the kill or no kill of each component hit by one shot line, and kill tree is checked to determine aircraft existent states during one simulation. When the number of times of simulation is large enough, the aircraft multiple-hit vulnerability can be statistically obtained. Analysis shows that the proposed direct simulation method can provide good accuracy compared with Markov chain method and avoid the combinatorial explosion problem, and does not need the complex vulnerable area decomposition and can directly calculate the aircraft multiple-hit vulnerability. Another important finding is the binomial or Poisson simplified approach is sometimes very poor in accuracy, and should be used cautiously.
This article, firstly, categorizes aircraft＇s presented area in a particular hit aspect into non-vulnerable region, non-overlapping vulnerable region and overlapping vulnerable region. Then, the aircraft＇s unique existing states are divided into kill states, intermediate states and no kill states. The parameters pertinent to aircraft＇s existing states in the above-mentioned regions are analyzed by using the shot line scanning method. Finally, the method provides two kinds of shot line geometric descriptive data： （1） component＇s vulnerable area and presented area in each region, which can be used to calculate the component＇s single-hit vulnerability and （2） aircraft＇s unique existing states and the areas corresponding to each state, which can be used to calculate the aircraft＇s single-hit and multi-hit vulnerability. Examples show that the proposed method can provide the parameters of the aircraft＇s or its component＇s area under threat being hit through tracing the shot line path thereby enabling the vulnerability calculated results to conform with reality to larger extent. In addition, the method solves the generality problem in dealing with overlapping components.
