Research On Time-frequency Analysis Method Of Ground Motion Vectors

The characteristics of ground motion are important contents of ground motion input research.In the previous ground motion research,the characteristics of ground motion are mainly described by three factors: amplitude,duration and spectrum.However,it is difficult to accurately determine the three elements.In order to more accurately and comprehensively describe the characteristics of ground motion,the non-stationary characteristics of ground motion are also indispensable under normal circumstances.The modern time-frequency analysis method is a powerful tool for the study of non-stationary characteristics of ground motion.Through the joint distribution information of time domain and frequency domain,the relationship between signal frequency and time can be clearly described,and the law of time-frequency distribution of signal energy is reflected.Most studies only consider the non-stationary characteristics of horizontal or vertical ground motion components separately,and considering ground motion as a vector is easier to fully reflect and reveal the nature of ground motion and the inherent vibration components.Spatial correlation.In the previous studies,the amplitude,spectrum and duration characteristics of the ground motion vector have been studied.Therefore,this paper takes the time-frequency non-stationary characteristic analysis method of vector ground motion as the main research content,and the results can provide theoretical analysis tools for the model research of the time-frequency characteristics of the subsequent vector ground motion,and provide basises for comprehensive understanding of the engineering characteristics of vector ground motion and the structure to provide a more reasonable vector ground motion input..In view of this,this paper firstly perfects the traditional ground motion analysis signal construction method,and directly constructs the ground motion analysis signal by using the ground motion vector,and then analyzes the time-frequency characteristics of the ground motion analysis signal.Secondly,on the basis of comparing different timefrequency analysis methods,some new methods of non-parameterization and parameterization for analyzing the time-frequency characteristics of vector signals are proposed.The research on ground motion characteristics is extended from the independent component research level to the overall research level of vectorization space.The main work and achievements are summarized into the following four aspects:(1)Based on the Duhamel integral,a new non-parametric time-frequency analysis method is proposed,which is similar in form to the short-time Fourier transform.The method is compared with the short-time Fourier transform,and the effectiveness of the method is verified by the actual time-frequency analysis of the ground motion signal.The advantages of the method compared with other non-parametric methods are studied,such as the analysis of the time-frequency window size.The adjustable and analytical results have a causality and a seismic response spectrum that can be directly derived from the analysis results.On this basis,the method is combined with the EMD method to analyze the time-frequency characteristics of the signal,which improves the limited Hilbert spectrum analysis in the Hilbert-Huang transform(HHT)method.(2)The HHT time-frequency analysis method is extended from one-dimensional to three-dimensional.Based on the energy superposition principle,the spectral characteristic representation method corresponding to the decomposition signal from the onedimensional to three-dimensional EMD method is realized,and the resolution and readability of the time-frequency analysis result are improved.Sexuality provides a new idea and method for vector ground motion analysis.(3)Considering the equivalence relation between the ARMA model parameters and the elastic single degree of freedom system,a time-frequency analysis method based on time-invariant ARMA model is established.The method has the advantages of high computational efficiency and high resolution of the spectrogram.Aiming at the problem of limited Hilbert spectrum analysis in HHT method,an improved method for calculating the instantaneous frequency of decomposed signals based on time-varying ARMA model is proposed.The Hilbert spectrum obtained by this method is smooth and has high resolution.(4)Based on two time-varying VARMA models(single input multiple output model and multiple input multiple output model),the vector ground motion is proposed to realize the time-frequency analysis of vector ground motion under different conditions,and the ideal analysis results are obtained.The VARMA model method is equally applicable to other multidimensional signals and can be applied to other signal research fields.The innovations of the paper include:(1)Taking the ground motion vector as the research object,it can reflect the spatial correlation between the components of the ground motion more comprehensively,and help to grasp the engineering characteristics of the ground motion as a whole.It is proposed to construct the analytical signal directly based on the orthogonal ground motion component.The idea makes the instantaneous frequency and the instantaneous amplitude have a clearer physical meaning,and has unique advantages in time-frequency analysis.An improved method of parameterized and non-parametric two-class vector ground motion time-frequency analysis is proposed respectively to reveal the vector earthquake.The dynamic time-frequency distribution feature provides an effective analysis tool.(2)Based on the Duhamel integral idea,a new time-frequency analysis method is proposed and applied.(3)Based on the equivalence relation between the time-invariant ARMA model and the elastic single degree of freedom system,a time-frequency analysis method based on time-invariant ARMA model is proposed.At the same time,two parameters based on time-varying VARMA model are proposed.The analytical method is applied to the actual vector ground motion time-frequency analysis.The vector ground motion time-frequency analysis method proposed in this paper provides an analysis tool for the subsequent vector ground motion energy-time domainfrequency domain distribution characteristics and regular model research,and lays a foundation for design vector ground motion input research.The method can be used for time-frequency analysis of multi-point and multi-dimensional seismic responses.Therefore,the research results of this paper have broad application prospects in the fields of structural seismic response prediction,system identification,health monitoring and damage identification.