Calibration of contributing factors for model-based predictive analysis algorithm using polynomial chaos expansion methods

To improve operational flight safety, a model-based predictive analysis algorithm to quantify the occurrence probabilities of airlines' incidents or accidents has been developed at the Institute of Flight System Dynamics. An incident model based on physics is built to map the relationship between the incident metric and corresponding contributing factors, which are recorded directly or identified indirectly from the operational flight data. The incident metric distribution can be obtained via propagating uncertainties of the contributing factors through the incident model. A calibration step is necessary to ensure that the generated incident metric distribution does represent the reality before prediction. Except for the model simplification error, the deviation between simulation and reality also arises from the measurement error, identification error or distribution fitting error of contributing factors and the incident metric. Therefore, the basic strategy of calibration is to reduce those errors via solving an optimization problem and then justify if the deviation between the calibrated and recorded incident metric is acceptable for the subsequent prediction. A calibration framework using the polynomial chaos expansion method and optimization method is proposed in the paper. Meanwhile, the dependence structure of contributing factors has been considered and integrated into this framework based on Copula. This approach has been shown to be convergent and greatly improve efficiency because it is not required to run the Monte Carlo simulation again during each iteration of optimization. Finally, this calibration algorithm is implemented for a runway overrun incident model.