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Polynomial Regression Surface (PRS) is a commonly used surrogate model for its simplicity, good interpretability, and computational efficiency. The performance of PRS is largely dependent on its basis functions. With limited samples, how to correctly select basis functions remains a challenging problem. To improve prediction accuracy, a PRS modeling approach based on multitask optimization and ensemble modeling (PRS-MOEM) is proposed for rational basis function selection with robustness. First, the training set is partitioned into multiple subsets by the cross validation method, and for each subset a sub-model is independently constructed by optimization. To effectively solve these multiple optimization tasks, an improved evolutionary algorithm with transfer migration is developed, which can enhance the optimization efficiency and robustness by useful information exchange between these similar optimization tasks. Second, a novel ensemble method is proposed to integrate the multiple sub-models into the final model. The significance of each basis function is scored according to the error estimation of the sub-models and the occurrence frequency of the basis functions in all the sub-models. Then the basis functions are ranked and selected based on the bias-corrected Akaike’s information criterion. PRS-MOEM can effectively mitigate the negative influence from the sub-models with large prediction error, and alleviate the uncertain impact resulting from the randomness of training subsets. Thus the basis function selection accuracy and robustness can be enhanced. Seven numerical examples and an engineering problem are utilized to test and verify the effectiveness of PRS-MOEM.

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The satellite constellation network is a powerful tool to provide ground traffic business services for continuous global coverage. For the resource-limited satellite network, it is necessary to predict satellite coverage traffic volume (SCTV) in advance to properly allocate onboard resources for better task fulfillment. Traditionally, a global SCTV distribution data table is first statistically constructed on the ground according to historical data and uploaded to the satellite. Then SCTV is predicted onboard by a data table lookup. However, the cost of the large data transmission and storage is expensive and prohibitive for satellites. To solve these problems, this paper proposes to distill the data into a surrogate model to be uploaded to the satellite, which can both save the valuable communication link resource and improve the SCTV prediction accuracy compared to the table lookup. An effective surrogate ensemble modeling method is proposed in this paper for better prediction. First, according to prior geographical knowledge of the SCTV distribution, the global earth surface domain is split into multiple sub-domains. Second, on each sub-domain, multiple candidate surrogates are built. To fully exploit these surrogates and combine them into a more accurate ensemble, a partial weighted aggregation method (PWTA) is developed. For each sub-domain, PWTA adaptively selects the candidate surrogates with higher accuracy as the contributing models, based on which the ultimate ensemble is constructed for each sub-domain SCTV prediction. The proposed method is demonstrated and testified with an air traffic SCTV engineering problem. The results demonstrate the effectiveness of PWTA regarding good local and global prediction accuracy and modeling robustness.