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Bridge pier settlement prediction in high-speed railway via autoregressive model based on robust weighted total least-squares

机译：基于鲁棒加权总最小二乘的自回归模型预测高速铁路桥墩沉降

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摘要

The autoregressive model for time series prediction is a common method in settlement prediction. In the traditional parameter estimation of autoregressive model, least-squares (LS) is the method, which only considers the errors in the observation vector. However, the errors in the coefficient matrix have not been considered. To solve this issue, weighted total least-squares (WTLS) method is developed for parameter estimation. However, it does not consider the possible gross errors in observations, which may lead to a reduction in the robustness and reliability of parameter estimation. In order to solve this problem, in this study, robust WTLS (RWTLS) method is proposed to estimate parameters of autoregressive model for bridge pier settlement prediction in high-speed railway. A comparison with LS, robust LS (RLS) and WTLS methods is conducted for bridge pier settlement prediction and two sets of observed data are used in this evaluation. The results of experiments show that the variance components and the mean absolute values of predictive residuals obtained by WTLS and RWTLS methods are smaller than those by using LS and RLS methods in the case of modelling data without gross errors, and the variance component and the mean absolute value of predictive residuals obtained by RWTLS method is the smallest in the case of modelling data with gross errors. It shows that autoregressive model settlement prediction for bridge pier by using RWTLS method is more reliable and accurate than LS, RLS and WTLS methods in high-speed railway.
机译：时间序列预测的自回归模型是沉降预测中的常用方法。在传统的自回归模型参数估计中，最小二乘（LS）是仅考虑观测向量误差的方法。但是，尚未考虑系数矩阵中的误差。为了解决这个问题，开发了加权总最小二乘法（WTLS）用于参数估计。但是，它没有考虑观测值中可能出现的严重误差，这可能会导致参数估计的鲁棒性和可靠性降低。为了解决这个问题，本研究提出了一种鲁棒的WTLS（RWTLS）方法来估计高速铁路桥梁墩台沉降预测的自回归模型参数。与LS，鲁棒LS（RLS）和WTLS方法进行了比较，以进行桥墩沉降预测，并且在此评估中使用了两组观测数据。实验结果表明，在没有明显误差的情况下，WTLS和RWTLS方法获得的预测残差的方差成分和平均绝对值均小于LS和RLS方法得到的预测残差的方差成分和均值。对于具有严重误差的数据，通过RWTLS方法获得的预测残差的绝对值最小。结果表明，在高速铁路中，使用RWTLS方法进行桥墩自回归模型沉降预测比LS，RLS和WTLS方法更可靠，更准确。

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