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| Stockwell transform based power spectrum estimation of non-stationary stochastic process |
| Received:February 15, 2013 Revised:June 10, 2013 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx201404005 |
| KeyWord:Stockwell transform power spectrum density stochastic process earthquake excitation |
| Author | Institution |
| 孔凡 |
同济大学土木工程学院 建筑工程系, 上海 |
| 李杰 |
同济大学土木工程学院 建筑工程系, 上海 ;同济大学 土木工程防灾国家重点实验室, 上海 |
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| Abstract: |
| The evolutionary power spectrum density (EPSD) of the non-stationary stochastic process is estimated via the Stockwell transform (S transform).The approach depends on the slowly varying pro-perty of the modulating function of the stochastic process, compared to the kernel of the S transform.This yields the phase-modified S transform of the process on a certain frequency can be viewed as a stochastic process with the EPSD given in terms of the EPSD of the original one.Further, an equation between the mean square value of the instantaneous S-transform and the EPSD of the process is derived.The solution of the equation is sought by representing the EPSD of the process as a sum of squared modulus of Gaussian shape functions of the S transform on the different frequency points, modulated by time-depended coefficients.Finally, the time-dependent coefficients can be determined by a linear algebra equation.Since the system matrix in the algebra equation only depends on the Gaussian shape function of the S transform, the algorithm shows high computational efficiency.Both the uniformly and non-uniformly modulated stochastic process is employed to demonstrate the accuracy of the proposed approach. |