Processing And Forecasting Of Deformation Data Based On Modal Decomposition And Gaussian Process Regression

The current research hotspot in the field of deformation monitoring data processing is to use mathematical theory and signal processing technology to analyze the non-stationary and non-linear deformation signals of the deformation object,and obtain the deformation characteristic information reflecting the deformation law,so as to achieve the stability analysis and deformation prediction of the deformation object and effective early warning.However,the deformation monitoring data often contains random noise components,and because different types of deformation objects use different data collection methods and are affected by a variety of factors,there is a certain difference in the noise content level of the monitored data.This has different degrees of adverse effects on the stability of the deformation analysis and the accuracy of the prediction results.In order to effectively grasp the deformation law of the deformation object,it is usually necessary to take corresponding methods to preprocess the monitoring data to reduce the disturbance effects caused by various types of random noise.Therefore,according to the characteristics of different types of monitoring data with different signal-to-noise ratios,this paper uses modal decomposition method combined with entropy theory to form different combined noise reduction methods,which are respectively applied to the GPS elevation time series of IGS reference stations with lower signal-to-noise ratio characteristics,dam horizontal displacement sequence and deformation sequence of foundation pit settlement with higher signal-to-noise ratio characteristics.In addition,using a reasonable prediction model to accurately predict the future deformation development trend of the deformed body is another major research direction in the field of deformation monitoring.This paper uses Gaussian Process Regression(GPR)as the core,aiming at the limitations of the single prediction model and the shortcomings of the GPR model,the modified fruit fly optimization algorithm was used to optimize it and build a combined prediction model.The specific research work is as follows:(1)Aiming at the problem that GPS elevation time series is affected by various types of noise,which makes it difficult to extract useful information,this paper researches a threshold denoising method based on overall empirical mode decomposition(EEMD)and multi-scale permutation entropy(MPE).EEMD can adaptively decompose the original signal into a series of intrinsic modal function(IMF),and use MPE as an indicator to subdivide it into noise IMF,hybrid IMF,and information IMF,and then use the threshold function to process the mixed IMF to achieve secondary noise reduction.Finally,the data and information IMF are reconstructed to obtain the noise reduction result,and the noise reduction error ratio(dn SNR)index is introduced to evaluate the noise reduction quality.By analyzing the simulation signals and examples,it is verified that the new method has the best noise reduction effect and can better reflect the non-linear change characteristics of the time series itself.(2)Aiming at the problem that the noise components contained in the deformation monitoring data are difficult to effectively filter out,which affects the accuracy of the prediction results,a variational mode decomposition method(VMD)is introduced to process the deformation monitoring data,and the VMD is combined with the sample entropy(SE)to construct the VMD-SE noise reduction method.First use VMD to decompose the original monitoring sequence into K band-limited intrinsic modal functions(BIMF)with different center frequencies,and then directly remove the components of the high-frequency BIMF sample entropy greater than the set threshold as noise components,and finally reconstruct the remaining Component to obtain the noise reduction sequence.The validity and feasibility of the method are verified by simulation examples and two engineering examples.(3)In order to avoid the shortcomings of Gaussian Process Regression(GPR)using conjugate gradient method to obtain hyperparameters,this paper uses a modified fruit fly optimization algorithm(MFOA)to optimize the Gaussian Process Regression(GPR)to construct a MFOA-GPR prediction model.First,modify the flavor concentration function of the standard fruit fly optimization algorithm(FOA)to expand the scope of the solution;meanwhile,a search radius dynamic adjustment parameter is introduced to enable the algorithm to dynamically adjust the global search ability and local development ability during the iterative optimization process;The modified fruit fly optimization algorithm is directly applied to the hyperparameters optimization of GPR.The analysis and inspection through three actual tunnel engineering examples not only verify the effectiveness and feasibility of the MFOA-GPR method,but also confirm that the combination of the new method and the VMD-SE method can further improve the prediction accuracy and has good applicability.