基于背景值与初始条件优化的非等间距GM（1,1）模型

摘要

利用非等间距GM(1,1)模型一次累加生成序列近似满足指数规律优化其背景值，再利用最小二乘法，由模拟序列和原始序列的一次累加生成值的偏差平方和最小对模型的时间响应函数的参数进行优化，从而建立基于背景值与初始条件同时优化的非等间距GM(1,1)模型，并通过实例验证此模型的有效性与可行性。%The background value of the unequal interval GM(1, 1) model is optimized while its first accumulated generating series satisfy the approximate exponential rules. According to the method of least squares, the pending coefficient of the time response function is optimized when the sum of the squared differences of the first accu-mulated generating values and the simulative values is the smallest, then the unequal interval GM(1, 1) model optimized both the background value and the original condition is obtained. This optimized model doesn ’t need to select the initial condition, and an example is given to show the effectiveness and feasibility of this model.