The method of determining the trend equation for predicting vertical displacements by the search method of nonlinear programming

Abstract

Observing the settlement of buildings and structures often gives rise to the question of their prediction. This primarily requires determining the form of the time series trend equation, which would describe by a single law all sequences of the time series compiled from geodetic data. The procedure for determining the trend equation of the time series is carried out by linear and nonlinear regression analysis. However, these methods have a number of drawbacks. In this connection, the case study of changing the benchmarks values of one of the deformation marks is considered in order to analyze the possibility to apply the search method of nonlinear programming for determining the trend equation on the basis of the geodetic measurements data. A method of constructing a trend equation for a predictive model based on geodetic data is presented, including: 1) determining the trend equation by a search method of nonlinear programming using a VBA-based search program; 2) assessment of the accuracy of determining the coefficients of the trend equations by using the search method of nonlinear programming; 3) assessment of the adequacy of trend models obtained by the search method. Based on the results of the analysis and calculations, an adequate trend model in the form of a logarithmic equation was established. The correctness of the conclusions was proved by the calculations carried out in Microsoft Excel and Statistica, which coincided with the results obtained. The predicted values of the deformation benchmarks were determined.

Keywords

• geodetic measurements
• forecasting
• trend equation
• time series
• the adequacy of the model
• search method of nonlinear programming
• sdgs