Abstract: The time-varying weighted combination forecast based on polynomial approximation formulas of unary and binary functions is proposed and used to model and forecast the structural response time-series of some aircrafts. Taking the unbiasedness and nonnegativity constraints into consideration, the relaxation variables are introduced to transform the inequality constraint to equality constraint, and the new objective function of the combination forecast is constructed based on penalty function. The Gene Algorithm is used to acquire the numerical solution of all variables and the function of time-varying weights. The application results verify the efficiency of this method.

Key words: vibration and wave, combination forecast, time-varying weights, relaxation variable, penalty function.

摘要： 提出一种基于一元多项式逼近和二元多项式逼近的时变权重组合预测方法，并将之应用于飞行器结构响应序列的建模与预测。充分考虑权重的无偏性和非负性，通过引入松弛变量将不等式约束转化为等式约束并基于惩罚函数构造新的组合预测目标函数；最后采用遗传算法获得未知变量的数值解及组合预测时变权重表达式。应用结果表明预测方法有效。

关键词: 振动与波, 组合预测, 时变权重, 松弛变量, 惩罚函数