Researches On End Condition Algorithm Design And Its Application On Spectral Data Process

The empirical mode decomposition(EMD)plays an important role in non-linear and non-stationary signal processing and analysis.As the precondition of EMD,the end condition method attracts much attention.This paper focus on the algorithm design of end condition method and the application on quantitative retrieval of organics of black soil spectral.The main contents of this paper include the following three topics.The first is related to the algorithm design of end condition method,the second is the theoretical description and interpretation on the affecting factors and mechanism of end effect,and the third is the quantitative retrieval application on organics of black soil spectral combined with the spectral data denoising with EMD-based filtering method and absorption signatrues extraction based on the filtered spectral data.As to the algorithm design on end condition method,the topics of this paper cover the mathematical interpretation and theoretical description on original mechanism,affecting factors and variation rule of the end effect.Meanwhile,two end condition methods are proposed,in which one is designed based on the three-moment method of cubic spline,and the other is based on the Hermite interpolation cubic spline.Furthermore,the following six achievements are also produced in this paper.1)It has been pointed out that the algorithm design of the end condition method is not just a prediction problem of the extened points,but a prediction problem together with the determination of the first or second derivative of the extened points.2)Two regular principles used to design the end condition method are proposed.3)This paper provides a microscopic level to understand and define the end effect,that is,to define the end effect as the difference between the original envelope and extended envelope of the signal.4)The end effect can be quantitatively estimated,and the correlation coefficient and the vector angle cosine can be taken as two performance criteria of the end effect.5)The sifting process of EMD to extrct the IMFs will not converge uniquely.So,the end effect can not be eliminated totally based on experimental results.6)Three theorems are proved to indicate how the cubic spline change when the initial condition of the first derivative of the endpoints varied,which can also be the theory basis on how to design the end condition method and how to intepret the end effect.As to the application of the spectral data process with EMD,the EMD-based filter method is used to denoise the black soil spectral data,then the absorption signatures are extracted after the denoising procedure.Finally,the quantitative retrieval of the black soil organics are calculated with multiple linear regression,multiple linear stepwise regression and BP(back propagation)neural network.The innovations of this paper include the following threer points.1)Two new end condition methods are proposed and designed based on the three-moment method cubic spline and Hermiter interpolation cubic spline.Experimental results show that the performance of the proposed methods are improved when IO and MSE are taken as the criteria.Also,two regular principles used to design end condition method are pointed out.Further,a new opinion is pointed tout that the algorithm design of the end condition method is not just a prediction problem of the extened points,but a prediction problem together with the determination of the first or second derivative of the extened points.2)Three theorems are proved to describe three cased on how the cubic spline change when the initial condition of the first derivative of the endpoints varied.Here,three cases mean the left side perturbation,the right side perturbation and both of the left and right sides perturbation of the initial condition.These theorems provide an interpretation in theory on how the envelopes change while the derivative property of the extended points are varied,which can also be the reason for the end effect of EMD.3)The absorption signatures are extracted based on the EMD-based filter spectral data and the clustered results of the black soil organics,then followed by the quantitative retrieval of the black soil organics.The results show that the performance of the BP nonlinear retrieval is better than that of the multiple linear regression statistic model.