全信息变权缓冲算子的拓展、优化及其应用

针对冲击扰动系统的建模预测问题,对全信息变权缓冲算子进行拓展,提出两类含幂指数的全信息变权缓冲算子,并从理论上揭示强化缓冲算子与弱化缓冲算子的转换关系.在此基础上,给出新算子参数优化机理以及具体算法,并探讨算法的时间复杂度问题.最后,以全国风力发电装机容量的冲击扰动数据预测为例,验证算子的有效性和优越性.结果表明:所提出的新算子及其优化算法在不增加时间复杂度的条件下,能够显著提高缓冲算子对冲击扰动系统的适应能力和灰色模型的预测精度.此外,全信息变权强化(弱化)缓冲算子为新算子的特殊形式,当幂指数取值为1时,新算子退化为全信息变权强化缓冲算子;当幂指数取值为-1时,新算子退化为全信息变权弱化缓冲算子.

Extension, optimization and application of variable-weight buffer operators with perfect information

For the modeling and forecasting problems of shock perturbation systems, this paper expands the variable-weighted buffer operator with full information, and proposes two kinds of perfect information variable weighted buffer operators with a power index, and theoretically reveals the conversion relationship of the buffer operator. On this basis, this paper gives a new operator parameters optimization mechanism and specific algorithm, and discusses the time complexity of the algorithm. Finally, the forecast of disturbance data of the installed capacity of wind power in the country is taken as an example to verify the effectiveness and superiority of the new operator. The results show that the new operator proposed and its optimization algorithm significantly improve the adaptability of the buffer operator to the shock perturbation system and the accuracy of the gray model without increasing time complexity. In addition, the perfect information variable weighting strengthening(weakening) buffer operator is a special form of the new operator; When the power index is 1, the new operator degenerates into the perfect information variable weighted strengthening buffer operator; when the power index is taken as the value at -1, the new operator degenerates into the perfect information variable weight weakening buffer operator.