灰色模型在非等步长变形监测数据处理中的应用

Application of Gray Model to the Unequal-Step Deformation Monitoring Data Processing

常规变形监测数据处理中的GM(1,1)灰色模型是以等时间间隔观测值为原始序列,经一次累加处理,建立生成数列的一阶微分方程,并利用最小二乘求解未知参数的建模方法;但实际监测过程中,因受诸多因素影响,采集到的原始数据多呈现非等间隔分布,引入时间权重思想建立改进的GM(1,1)灰色模型,通过对沉降数据进行建模分析及精度检验,扩大了灰色模型的适用范围,验证了该模型的可靠性和科学性。

The application of GM（1,1） model is based on the time interval of the observation value of the original sequence,generated by the cumulative time processing,the establishment of a series of first order differential equations,and the use of least squares to strike the unknown parameters.Due to many factors,the raw data collected from actual monitoring process shows non-interval distribution,so the weight of time to create an improved GM（1,1） gray model by the settlement data is introduced,and the scope of the gray model’s application is expanded.The mode analysis and accuracy tests show that the model is reliable and scientific.