Application Of Hybrid Proper Transformation To Simulation Of Stochastic Time Series

Hybrid Proper Transformation combines two types of Proper Orthogonal Decomposition -- uses Covariance Proper Transformation to reject the higher covariance modes, in order to enhance the speed of simulating wind area by Spectral Proper Transformation1. Proper orthogonal is used to simulate and rebuild wind area in wind structure. Because of the different aims, the two uses were independent. Simulating wind area is based on proper decomposition of spectrum matrix got by estimated experience, called Spectral Proper Transformation. Rebuilding wind area is based on its covariance matrix, called Covariance Proper Transformation.According to the relation of spectrum matrix and covariance matrix, author uses Covariance Proper Transformation to reject the higher covariance modes, in order to enhance the speed of simulating wind area by Spectral Proper Transformation. The new simulating method is called Hybrid Proper Transformation.2. When predecessor were analyzing the effects of simulations, because of without true time-area curve of the aim spectrum, they only measured the effect in frequency area. Contrast of efficiency between the two simulations has been done a little.Author puts the spectrum got by experiment as aim spectrum, and simulates the random area. Not only in frequency area, but also at first in time area author analyzes and contrast the accuracy and efficiency of the two methods.3. The number of retain covariance modes is a key number both of covariance proper transformation and hybrid proper transformation. Accumulated energy ratio and covariance ratio had been used to decide the number of retain covariance modes in covariance proper transformation.Author compares and analyzes the advantages and disadvantages of the two ratios in hybrid proper transformation. Then analyze the effects of efficiency and accuracy caused by the number of retained covariance modes in hybrid proper transformation.4. The choice of orthogonal increment process is done in computer. This process doesn't affect the accuracy in frequency area. Because of the lack of true time curve, its effect to accuracy in time area is not done.Author compares three time curves produced by three different orthogonal increment processes, and analyzes its effects to time accuracy.