# An Effective Surrogate Ensemble Modeling Method for Satellite Coverage Traffic Volume Prediction
## 1 Introduction
[16] employ the weighted average surrogate to solve the problem of computationally expensive function evaluations in optimization. [PERSON] et al. [17] construct the ensemble of PRS, Kriging, RBF, and SVR for the approximation of an occupant protection system. For ensemble modeling, on one hand, the prediction accuracy of the ensemble is greatly influenced by the performance of the contributing surrogates. [PERSON] et al. [18] find that adding inaccurate surrogates into the ensemble is likely to result in loss of accuracy. On the other hand, the weight factors also have a significant effect on the prediction accuracy of the ensemble. To obtain the ensemble with better performance, some research focuses on how to solve the appropriate weights considering the regional characteristics of the objective function to be approximated or predicted [19]. [PERSON] et al. [20] determine the weight of each contributing surrogate based on the local measure of accuracy in the pertinent trust region. [PERSON] et al. [21] divide the design space into multiple sub-domains, each of which is assigned a set of optimized weights. These optimized weights are determined by minimizing the error metric of the training points in the corresponding sub-domains. [PERSON] et al. [22] propose a pointwise ensemble which calculates the weights based on the \(v\)-nearest points cross-validation error. Although these studies could enhance the positive effects of the accurate contributing surrogates by increasing their weights in the local area, they do not completely eliminate the negative influences of the inaccurate contributing surrogates, leading to the relatively low accuracy of the ensemble model [23]. Moreover, for the SCTV prediction problem, the specific practical problem features should be considered for effective ensemble modeling. In this paper, an effective surrogate ensemble modeling method is proposed for the SCTV prediction. First, the global earth surface domain is split into multiple sub-domains according to the prior geographical knowledge of the SCTV distribution, and then multiple different candidate surrogates are constructed on each sub-domain, respectively. Second, to fully exploit these surrogates and combine into a more accurate ensemble, a partial weighted aggregation method (PWTA) is developed. Because each sub-domain has distinct SCTV features, and different surrogates have different performance, PWTA adaptively selects the candidate surrogates with higher accuracy as the contributing models (the negative inaccurate surrogates are eliminated) for each sub-domain, based on which the ultimate ensemble is constructed in each sub-domain. In this way, for the sub-domains, there are independent positive contributing surrogates and weights so that the ensembles are more suitable for the corresponding sub-domains. Thus, the proposed surrogate ensemble modeling method could capture the regional SCTV features better in each sub-domain. The method proposed in this paper mainly has two contributions: (a) instead of constructing candidate surrogates in the global domain, multiple independent candidate surrogates are built for each sub-domain. (b) In each sub-domain, unlike integrating all the candidate surrogates to build an ensemble, the candidate surrogates are adaptively selected as contributing surrogates to construct a single ensemble. The rest of the paper is organized as follows. In Section 2, a brief review of PRS, Kriging, RBF, the weighted aggregation method, and the BestGMSE surrogate are introduced. In Section 3, the satellite coverage traffic volume model is described, and the partial weighted surrogate ensemble modeling method is developed in detail. In Section 4, the proposed surrogate ensemble modeling method is testified in the SCTV prediction problem with engineering data, followed by the conclusions in the final section.