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通过分析地基沉降预测模型,指出最小二乘的病态性会导致模型参数求解失败。应用正则化理论,基于矩阵求逆理论,提出了一种沉降预测模型参数的正则化无偏估计算法,说明了新算法的无偏性和方差最小性。在一定条件下,证明了新算法中正则参数的存在性,并给出了正则参数的计算公式。结合文献和工程实例进行的分析表明,新算法降低了矩阵条件数,减轻矩阵病态程度,能有效求得地基沉降预测模型参数。
By analyzing the foundation settlement prediction model, it is pointed out that the pathological condition of the least squares will lead to the failure of solving the model parameters. Based on the theory of regularization, a regularization unbiased estimation algorithm of settlement prediction model parameters is proposed, which shows the unbiasedness and minimum variance of the new algorithm. Under certain conditions, the existence of the canonical parameters in the new algorithm is proved, and the formula of the canonical parameters is given. The analysis based on the literature and the engineering examples shows that the new algorithm reduces the number of matrix conditions, alleviates the ill-conditioned matrix and effectively determines the parameters of the foundation settlement prediction model.