Wavelets Seismic Response Of Structure And Power Reliability Analysis

For the purpose of wavelet's basic concept and wavelet transform fundamental principle, four wavelets: Littlewood-Paley wavelet,meyer wavelet, harmonic wavelet and odd exponent wavelet are used to analyze structural response under earthquake; experimental investigation has been carried out for two-stories frame model; this paper also analyzes earthquake ground motion energy and structural energy response based on wavelet; this paper proposes dynamic reliability analysis for structure seismic response based on wavelet.It is shown by structural seismic response of four wavelets that Littlewood-Paley wavelet is not suitable for structural seismic response, because structural response is too small, meyer wavelet is a better wavelet for structural seismic response, for it's structural response is agreement with the finite element method, and also harmonic wavelet, structural response under earthquake is a little bigger than finite element method, structural response under odd exponent wavelet is also bigger than finite element method, this method is very simple by wavelet transform, wavelet transform method is different from old methods, one is with which not only knows the effects of earthquake wave detail frequency-band on structural response, but also considers earthquake wave's non-stationary of frequency and time-domain value, another is the second mode shape and higher mode shape response that don't attenuate so fast.It is shown by the two-stories frame model shake-table test that the contrast two response of acceleration based on wavelet and experiment draws on such conclusion: Littlewood-Paley wavelet does not agree with the test, so it is not suitable for structural seismic response, because structural acceleration response is too small. The wavelet transform result of acceleration response based on meyer wavelet, harmonic wavelet and odd exponent wavelet agree with the test, Thus they can be used to analyze structural seismic response.The analysis of earthquake ground motion energy and structural energy response based on these three wavelets(Littlewood-Paley wavelet,meyer wavelet, harmonic wavelet )shows that we can calculate earthquake ground motion energy by the record of acceleration, because the wavelet coefficient includes time-domain energy and frequency-domain energy. So the result is more accurate than old methods. The result of structural energy response based on wavelet provides a practicable method for structure design and design energy dissipation system in structure, this chapter's analysis and contrast tell us Littlewood-paley wavelet is not suitable for analyzing energy of earthquake ground motion and structural energy response. On the purpose of calculating energy, meyer wavelet must be modified so that its frequency integral is a constant, the result of energy by modified meyer wavelet and harmonic wavelet is practicable, only the later is bigger but in the same energy level.Dynamic reliability analysis for structure seismic response based on wavelet shows that whether signal of degree or multi of degree's system dynamic reliability analysis are practicable on theory, and also seismic response is to be considered nonstationary Gaussian process, these methods are easy to carry out. dynamic reliability under Littlewood-Paley wavelet is the biggest, dynamic reliability under modified meyerwavelet and harmonic wavelet are close. Analyzing the dynamic reliability of structure under odd exponent wavelet is very simple, it doesn't calculate Power Spectral Density function integral, it is only to calculate the square of displacement standard deviation and the square of velocity, then the dynamic reliability of structure can be concluded by max distribution. In addition the effects of upper limit is considered, when upper limit is smaller, the dynamic reliability of structure is less, that is, the damage possibility is bigger.At last, conclusion of the present investigation and suggestion for further study are presented...