An interval process expansion method based on standard orthogonal bases
Compared with traditional stochastic process models that rely on precise probability distributions,the interval process model uses upper and lower boundary functions.This method is adept at describing dynamic or time-varying uncertainty parameters,providing a new tool for solving engineering problems such as uncertainty dynamics analysis.This article proposes an interval process series expansion method that leverages standard orthogonal bases to efficiently characterize the temporal characteristics of dynamic uncertainty parameters.First,we propose a truncated series expansion approach tailored for practical use,coupled with error analysis,to ensure reliability.Second,a sampling method designed for interval processes is introduced.Third,leveraging the truncated series expansion form,we propose a sampling method for interval processes.This method can simulate interval processes with high accuracy in the time domain.Finally,the effectiveness of the proposed method is verified by simulating three interval processes with typical types of auto-correlation coefficient functions.
interval processorthogonal series expansionstandard orthogonal basesinterval process simulation
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