基于尖点突变理论的高层建筑沉降变形预测分析

Prediction analysis of settlement deformation of high rise building based on cusp catastrophe theory

为建立一个全面且系统的高层建筑变形预测模型,本文首先利用卡尔曼滤波对变形数据进行去噪处理,分离出趋势项和误差项,再利用GA-BP模型和LS-GM(1,1)模型对趋势项进行预测,并通过组合得到趋势项预测值;其次,利用马尔科夫链对累计误差序列的进行修正,进一步提高预测精度;最后,利用尖点突变理论对高层建筑的稳定性进行评价,以验证预测模型的有效性。结果表明:半参数型卡尔曼滤波具有较好的滤波效果,且在趋势项的预测过程中,通过对BP神经网络的优化将平均预测精度由4.02%提高到了2.44%,而优化GM(1,1)模型则将平均预测精度由4.29%提高到了2.76%,说明本文的优化方法切实可行。通过误差修正,验证样本中的最大相对误差仅为1.63%,说明误差修正模型达到了进一步提高预测精度的目的,尖点突变理论的分析结果与预测结果相符,均得出高层建筑处于稳定状态,其后期变形将会持续减弱。

To establish a comprehensive and systematic high-rise building deformation prediction model,this paper uses Calman filter for deformation data denoising,separation of trend and the error term,and then use GA-BP model and LS-GM（1,1） model to predict the trend,and obtain the trend prediction by combination;secondly,the cumulative the error data is corrected using the Markov chain,further improve the prediction accuracy;finally,the cusp catastrophe theory of stability of high-rise buildings are evaluated to verify the validity of prediction model.The results show that the semi parametric Calman filter has good filtering effect.In the process of forecasting trend,by optimization of the BP neural network,the average prediction accuracy was increased from 4.02% to 2.44%,and the optimization of GM（1,1） model increased the average prediction accuracy from 4.29% to 2.76%,showing that the optimization method in this paper is feasible.Through error correction,the maximum test sample in relative error is only 1.63%,indicating that the error correction model can further improve the prediction accuracy.Catastrophe theory and prediction results were consistent,the high-rise building is in a stable state,and its deformation will continue to be weakend.