摘要
由于Verhulst模型的精度依赖结构参数α,且初值选取为(1)x(1)会造成误差积累。因此基于信息覆盖原理对结构参数α进行优化,利用加权平均优化预测模型初值,改进了Verhulst模型;结合改进的Verhulst模型与双曲线模型的优缺点,利用最优加权将两种模型进行组合。通过实例,对比了几种模型的预测精度,以应变片2为例,改进后的Verhulst模型、传统Verhulst模型、双曲线模型、组合模型平均相对误差分别为0.0094、0.0183、0.0356、0.0070。结果表明:改进后的Verhulst模型预测精度显著高于传统模型;改进的Verhulst模型与双曲线模型的组合模型预测精度高于单一的改进的Verhulst模型和双曲线模型。说明本文对Verhulst模型的改进及模型组合对提高样本数据预测精度可行有效。
Verhulst accuracy of the model is dependent on the structural parameters α, and the initial value will result in error accumulation. Therefore, based on the principle of information covering, structure parameter α is optimized, and model initial value is predicted by using the weighted average optimization and the Verhulst model is improved. The improved Verhulst model and the hyperbolic model are combined by using the optimal weighted method. The prediction accuracies of several models are compared through examples. Taking the strain gauge 2 as an example, the average relative error of the improved Verhulst model, the traditional Verhulst model, the hyperbolic model and the combined model are 0.0094, 0.0183, 0.0365 and 0.0070 respectively. The results show that prediction accuracy of the improved Verhulst model is significantly higher than the traditional model. And the improved Verhulst model and the combination model of the hyperbolic model are higher than the single Verhulst model or the hyperbolic model. In this paper, the improvement of the Verhulst model and the combination of the models are feasible and effective for the improvement of the accuracy to the sample data.
出处
《应用力学学报》
CAS
CSCD
北大核心
2016年第1期86-92,183,共7页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(51178398)
