Research On Tensor Model Interpolation Algorithm For Landslide Data Based On Bayesian Inference

The development of landslide monitoring technology is accelerating,and automated intelligent monitoring methods have gradually replaced manual monitoring to become the main monitoring technology.With the increase in monitoring content,the expansion of monitoring fields,and the increasing variety of data acquisition sensors,it is inevitable that the deformation monitoring system will generate missing data due to various factors.For research analysis that requires a complete dataset,reasonable and effective interpolation methods are particularly important.In order to improve the research value of landslide data,under the premise of ensuring the integrity of the data structure,this paper introduces the concept of tensor,combines Bayesian theorem,and proposes three tensor model algorithms based on Bayesian inference for landslide data with different characteristics to fill in the missing landslide data.The main work is as follows:(1)A Bayesian truncated Normal CP decomposition algorithm(BTCP)is proposed to deal with the missing data problem of landslide time series data.The BTCP algorithm uses the Bayesian inference theory method based on probabilistic models and Bayesian theorem to obtain prior distributions of parameters for landslide data that follows a truncated normal distribution.The Gibbs sampling model is then obtained through Markov Chain Monte Carlo algorithm,and interpolations are conducted accordingly.By processing measured landslide data with multiple missing rates and types into tensors,the algorithm achieves missing data interpolation and evaluates interpolation performance using root mean square error.Results show that the BTCP model can achieve better results in interpolating missing landslide data than other interpolation algorithms.(2)A Bayesian structural vector autoregression tensor factorization algorithm(BSTF)is proposed to deal with large-scale missing landslide data.The BSTF algorithm uses tensor factorization to model time series and structural vector autoregression to model time-factor matrices.By integrating structural vector autoregression and tensor factorization into a single model,large-scale time series data can be effectively modeled,and experimental results can be obtained using Bayesian inference and Gibbs sampling methods.Results indicate that the BSTF model can achieve better results in handling third-order tensor landslide data with smaller root mean square error,improving interpolation performance,and showing good stability for different types of missing data.(3)A Bayesian cosine-transform tensor completion algorithm(BCTC)is proposed to deal with the multidimensional characteristics of interpolated landslide data.The BCTC algorithm first models the missing landslide data and expresses it as a third-order tensor.The tensor is decomposed into the product form of the core tensor and the external tensor of cosine transformation and corresponding probability model and prior distribution are presented.Bayesian inference is used to optimize the interpolation result and complete the interpolation of missing landslide data.Experimental results show that this algorithm performs well in dealing with completely random missing types of landslide data interpolation problems.In conclusion,the combination of Bayesian inference and tensor models using three algorithms can better handle the discontinuity and missing problems in deformation monitoring data caused by various factors.By combining with the root mean square error evaluation index,the tensor model algorithm based on Bayesian inference demonstrates excellent interpolation performance.