Analysis of non-stationary structural systems by using a band-variable filter

One of the main tools used to study the dynamic response of structural systems is certainly the Fourier Transform. This tool is very useful and reliable to investigating the response of a stationary system, i.e. a generic system that does not changes its characteristics over time. Conversely, the Fourier Transform is no longer reliable if the main goal is to study the evolution of the dynamic response of a system whose features rapidly vary with time. To this regard, several mathematical tools were developed to analyze time-variable dynamic responses. Soil and buildings, subject to transient forcing such as an earthquake, may change their characteristics over time with the initiation of nonlinear phenomena. This paper proposes a new methodology to approach the study of non-stationary response of soil and buildings: a band-variable filter based on S-Transform. In fact, with the possibility of changing the bandwidth of each filtering window over time, it becomes possible to extract from a generic record only the response of the system focusing on the variation of individual modes of vibration. Practically, it is possible to extract from a generic non-stationary signal only the phase of interest. The paper starts from examples and applications on synthetic signals, then examines possible applications to the study of the non-stationary response of soil and buildings. The last application focuses on the possibility to evaluate the mode shapes over time for both numerical and scaled model subjected to strong motion inputs.

[1]  MansinhaL..  Localization of the complex spectrum , 1996 .

[2]  Gerard T. Schuster,et al.  Migration methods for imaging different‐order multiples , 2007 .

[3]  Martin Schimmel,et al.  The inverse S-transform in filters with time-frequency localization , 2005 .

[4]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[5]  Rocco Ditommaso,et al.  A fast method for structural health monitoring of Italian reinforced concrete strategic buildings , 2010 .

[6]  J. Mayer,et al.  On the Quantum Correction for Thermodynamic Equilibrium , 1947 .

[7]  Rocco Ditommaso,et al.  Effect of a single vibrating building on free-field ground motion: numerical and experimental evidences , 2010 .

[8]  Angelo Masi,et al.  Analysis of RC Building Dynamic Response and Soil-Building Resonance Based on Data Recorded during a Damaging Earthquake (Molise, Italy, 2002) , 2004 .

[9]  Stefano Parolai,et al.  Denoising of Seismograms Using the S Transform , 2009 .

[10]  L. Cohen,et al.  Time-frequency distributions-a review , 1989, Proc. IEEE.

[11]  Lalu Mansinha,et al.  Localization of the complex spectrum: the S transform , 1996, IEEE Trans. Signal Process..

[12]  Juan José Dañobeitia,et al.  The S-Transform and Its Inverses: Side Effects of Discretizing and Filtering , 2007, IEEE Transactions on Signal Processing.

[13]  Randy K. Young.  Wavelet theory and its applications , 1993, The Kluwer international series in engineering and computer science.

[14]  David J. Ewins,et al.  Application of MAC in the frequency domain , 2000 .

[15]  Dennis Gabor,et al.  Theory of communication , 1946 .

[16]  Hamid Reza Siahkoohi,et al.  Ground roll attenuation using the S and x‐f‐k transforms , 2007 .

[17]  Felice Carlo Ponzo,et al.  Short Note Buildings as a Seismic Source: Analysis of a Release Test at Bagnoli, Italy , 2006 .

[18]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[19]  Roel Snieder,et al.  Extracting the Building Response Using Seismic Interferometry: Theory and Application to the Millikan Library in Pasadena, California , 2006 .

[20]  Michael S. Ford,et al.  The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science , 2003 .

[21]  Kojiro Irikura,et al.  Nonlinearity, liquefaction, and velocity variation of soft soil layers in Port Island, Kobe, during the Hyogo-ken Nanbu earthquake , 1997, Bulletin of the Seismological Society of America.

[22]  T. Heaton,et al.  VARIATIONS IN THE DYNAMIC PROPERTIES OF STRUCTURES : THE WIGNER-VILLE DISTRIBUTION by S Case , 2005 .

[23]  Paul S. Addison,et al.  The Illustrated Wavelet Transform Handbook Introductory Theory And Applications In Science , 2002 .

[24]  Anil K. Chopra,et al.  Dynamics of Structures: Theory and Applications to Earthquake Engineering , 1995 .

[25]  Arun Kumar Pandey,et al.  Damage detection from changes in curvature mode shapes , 1991 .

[26]  Carlo Rainieri,et al.  Automated output-only dynamic identification of civil engineering structures , 2010 .

[27]  Mohammad Javad Dehghani.  Comparison of S-transform and Wavelet Transform in Power Quality Analysis , 2009 .

[28]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[29]  Rocco Ditommaso,et al.  Monitoring the response and the back-radiated energy of a building subjected to ambient vibration and impulsive action: the Falkenhof Tower (Potsdam, Germany) , 2010 .

[30]  C. Robert Pinnegar,et al.  Application of the S transform to prestack noise attenuation filtering , 2003 .