响应分布的线性化预测及矩信息的作用研究

LINEARIZATION PREDICTION OF RESPONSE DISTRIBUTION AND STUDY ON EFFECTS OF INFORMATION MOMENTS

以Duffing系统为例,探讨了非线性恢复力系统稳态随机响应线性化概率分布预测及矩信息的作用问题。分析了几种等效线性化方法及其解析解的精度。结果表明:采用线性化模型,仅利用已知方差信息的预测精度最高,线性化模型在一定程度上限制了信息的作用;存在一个体现系统线性因素影响力的综合指标,该指标越大,线性化模型预测精度越高。

Based on Duffing systems, the linearization prediction of the steady-state random response of non-linear restoring force systems and the effects of information of moments are studied. Some eguivalent methods of linearization and the precision of their analytical solutions are analyzed. The results indicate that adopting linearization models and using the known variance information only, the prediction precision is the highest; to a certain extent, linearization models restrict the available actions of information; there is a composite index that embodies the consequence of systematic linear factors, the bigger is the index value, the higher is the prediction oreeision of linearization models.