Analysis And Reconstruction For Ground Settlement Based On The Compressive Sensing

Nowadays, more and more subways are built to ease the heavy traffic in big cities.The analysis and assessment must be made to ensure the safety of the subway constructionand avoid the potential ground collapse, while the accurate and reliable monitored data isthe foundation of them. At present, these sampled data is manually gained. Since there aresome unavoidable reasons, such as the construction characteristics, different observingenvironments, measuring instrument error and so on, all of the data usually don’t haveequal time intervals and maybe incomplete in some monitoring process when the numberof sampled data is casual to each monitoring and there is no fixed sampling frequency.In most cases, one can recover the incomplete data by using the interpolationmethods, while it tends to make large error when there is much noise in the sampled dataor the number of data achieved is relatively small. In order to decrease this error and makeaccurate monitoring, this paper proposes a method to reconstruct the incomplete groundsettlement data. Furthermore, we shall also give a method to determine the lower limit ofthe sampling frequency for its casual changes, thus providing theoretical support for thefurther optimization of the safety monitoring standard.This paper firstly has made a brief analysis of the ground settlement laws, andestablished the Poisson curve model whose parameters are calculated by using thethree-point method and three-step method respectively. Simulation result shows that theformer method is better than the latter one. Then the theory of Compressive Sensing isintroduced whose validity of reconstructing the incomplete data is analyzed bygeometrical methods. A study on the structural design principle of measurement matrix insingle-pixel camera has been made, on the basis of this, a ground settlement basedmeasurement matrix is designed which is used to reconstruct the incomplete sampled data.Several case results demonstrate that the Compressive Sensing method is better than cubicspline and linear interpolation method when the sampled data has much noise or thenumber of sampled data is very small. Finally, simulation study is used to analyze thelower boundary on the monitoring number to guarantee that one can reduce the number ofsampled data while the original data can be recovered accurately, thus giving a method tofind the lower limit of the sampling number by applying the compressive sensing theory.