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Air traffic control is an important tool to ensure the safety of civil aviation. For the departments that do the work of air traffic control, reducing the percentage of unsafe event is the core task of safety management. If the relationship between the percentage of unsafe event and their influencing factors can be effectively clarified, then the probability of unsafe event in some control department can be predicted. So, it is of great importance to improve the level of safety management. To quantitatively estimate the probability of unsafe event, a three-layer BP neural network model is introduced in this paper. First, a probabilistic representation of unsafe event related to air traffic control department is made, and then, the probability of different classes of unsafe events and safe events is taken as the outputs of the BP neural network, the factors influencing occurrence of unsafe event connected with air traffic control is taken as inputs, and the sigmoid function is chosen as activation function for the hidden layer. Based on the error function of neural network, it is proved that the general BP neural network has two drawbacks when used for the training of small probability events, which are as follows: the pattern does not ensure that the sum of probability of all events is equal to one and the relative error between the actual outputs and desired outputs is very large after the training of neural network. The reason proved in this paper is that the occurrence rate of the unsafe event is much smaller than that of the safe event, resulting in each weight in the hide layer being subjected to the desired outputs of the safe event when using the gradient descent method for network training. To address this issue, a new mapping method is put forward to reduce the large difference of the desired outputs between the safe event and unsafe event. It is theoretically proved that the mapping method proposed in this paper can not only improve the training accuracy but also ensure that the sum of probability is equal to one. Finally, a numeric example is given to demonstrate that the method proposed in this paper is effective and feasible.

In this paper, a new kind of method is developed to analyse the bit-error rate for a free-space optical communication system, which is based on the three most important parameters of scintillation statistics, i.e. fraction of time of fade and surge, mean frequency of level crossings, and mean duration of fade and surge. By using this method, the relationship between the bit-error rate and scintillation is clearly identified. The tip-tilt error deteriorates the performance of a free-space optical communication system. Fine tracking ability of adaptive optics ( through tip-tilt compensation) can overcome this difficulty. The fade and surge statistical parameters with tip-tilt compensation are evaluated for the plane wave model. The bit-error rate as a function of the scintillation statistical parameters ( with tip-tilt compensation) is developed. The results show that the bit-error rate is reduced notably through tip-tilt compensation for free-space optical communication.