dc.description.abstract | The time-frequency analysis is a brand-new new numerical technique. The energy distribution pattern of a signal can be demonstrated simultaneously on the time domain and frequency domain, it′s a powerful tool for the observation of a time-variant system. The Hilbert-Huang Transform (HHT) is one of the time-frequency analysis methods. The good local adaption and the posteriori base are the unique specialities of the HHT. With these characteristics, HHT is found useful for the nonlinear and non-stationary signal analysis. Additionally, the definition of the Intrinsic Mode Function (IMF) makes the calculation of the instantaneous frequency (IF) possibly. The physical meaning of IF was also clearly demonstrated by the HHT.
The original signal is decomposed into the summation of the production of amplitude temporal modulated function and the frequency temporal modulated function by the HHT. Meanwhile, the Foruier decompose the signal into the summation of the production of constant amplitude function and the constant frequency function. The time-varriant characteristic of the Hilbert Transform makes the analysis for the non-stationary system possible. The Hilbert-Huang Transform, the improved Hilbert Transform, the speciality of the posteriori base makes the method totally adaptive. The decomposition procedures are not influenced by the base function anymore. The limitations and congenital defects coming from the base function (sinusoid or wavelet function) are totally disappeared. Contrary to almost all the previous methods, the HHT method is intuitive, direct, a posteriori, and adaptive, with the basis of the decomposition based on and derived from the data. The HHT might not be efficient for the artificial communication signal problems. It’s found suitable for the geophysical related analysis.
The earthquake energy was generated from hypocenter tectonic activities. The released energy passed through underground geographic media, reached on the specific site conditions, impacted the surface of the ground. Seismologically speaking, the earthquake waveform can be decomposed into several different wave phases. With several phases, the earthquake is not a stationary signal. Furthermore, for a strong earthquake, the destructive energy makes the underground geographic media into the nonlinear deformation stage. For a strong-motion earthquake record, it′s not only a non-stationary signal but also having nonlinear characteristics. In this article, we use HHT to analyze the strong-motion records of structures. The observations on the time-frequency spectrum are what we planned to extract detail dynamic properties of building. Structural Health Monitoring (SHM) parameters and information can be extracted from the HHT result directly. The IF is also introduced to explain the vivid difference of the SHM condition.
The theoretical solution of a Multiple-Degree-Of-Freedom (MDOF) structure excited by horizontal force is the combination of several individual modes that are supported by mechanical theorems and mathematical formulas. When we directly demonstrate the waveform from the building strong-motion response waveform on the time-frequency spectrum, the energy distribution usually concentrates at some frequencies, and also the temporal variations of each frequency band are clearly shown as well. Those temporal variations of the frequencies are the actual performances of structure during the vibration, even though those "modal behaviors" are not coming from the solution of the theoretical linear and stationary governing equations. By the vantages of the HHT, the modal behaviors of a real building can be obtained easily by directly reading the time-frequency spectrum of the acceleration response record.
In addition to read the response on the spectrum, some numerical steps are found even more helpful on collecting SHM information, including the signal enhancement skills, the newly defined time-frequency domain amplification function (T.F.AF) ,the extraction of modal temporal variation curve (MTVC), and the SHM application of the IF. We develop a new method called the HHT SHM method which integrated all the numerical steps mentioned above. The measurement of shaking-table experiment and the real building observation data are used to show the performance and the method-validation.
The procedures are described step by step as follows. First, the original nonlinear and nonstationary real building strong-motion response signal is firstly been transferred into the wave-propagating properties, the T.F.AF. The T.F.AF which is the core of the method can give dynamic parameters results through all the phases in an earthquake event. Then, after adopting selective and mechanical judgment, the useful structural modal information can be extracted from the T.F.AF, which is called the MTVC. The MTVC contains detail information of SHM that enable observers to read the structural modal behavior directly without traditional mechanical calculation. It is a new and crucial way for us to explore useful SHM information from the real building records. Examining these MTVCs can explore the vivid differences of structure healthy condition that might be ignored by other observers.
The specialities of the new method are the following three: 1. The results are totally obtained by the vibration data, it’s an adaptive and data-driven method. 2. The structural and mechanical concepts of the theoretical linear and stationary governing equations are included in the new method. 3. The traditional linear and stationary model and modal calculations are not included in the new method. We had demonstrated the excellent performances of the new method. The vivid differences of the MTVCs from different earthquake events showed the corresponding slight structural differences of a healthy building.
The T.F.AF is a new-created tool for the observation for a simple time-variant system. The energy density and instantaneous frequency distribution pattern on the time-frequency spectrum are the curical information for the observers. The vivid differences of the system can be easily found from T.F.AF. Now, the vibration-based results are having a drastic differnce with the theoretical solution. With new-created T.F.AF and the new HHT SHM method, useful dynamic information is explored and showed. These results might be helpful for the academic improvement of the basic mechanical model in the future. We showed a lot of observational results from real building and shaking-table experiment in the article, including SDOF and MDOF structures. Some of the behaviors are case unique and some are common phenomenon. We introduce a new observation tool; wish this helps to improve the performance of theoretical model in the future by researchers.
Keywords: Time-frequency analysis, Hilbert-Huang Transform, Strong-motion building response analysis, Vibration-based analysis, Structural Health Monitoring, Two-station method, Time frequency amplification function, Modal temporal variation curve. | en_US |