Experimental Modal Analysis of Civil Engineering Structures

Sound and Vibration, Jun 2006 by Cunha, �lvaro, Caetano, Elsa

The data acquisition and storage of dynamic data requires the use of an analog-to-digital (A/D) converter in the measurement chain. Raw data must be initially analyzed and processed; considering operations of scale conversion, trend removal, and decimation. Subsequently, the acceleration time history can be multiplied by appropriate time windows (Manning, Cosine-Taper, etc.), to reduce leakage effects, and subdivided into different blocks for evaluation of average spectral, auto spectral, and cross spectral estimates using the FFT algorithm. Finally, FRFs (frequency response functions) can be obtained using estimators H^sub 1^ or H^sub 2^.1 The automatic evaluation of FRFs requires appropriate software for analysis and signal processing, which is already available in commercial Fourier analyzers. These analyzers are sometimes implemented by a laptop PCMCIA card to allow either the acquisition of data through input channels or the control of a shaker through an output channel.

Input-Output Modal Identification Methods. There is a wide variety of input-output modal identification methods whose application relies either on estimates of a set of FRFs or on the corresponding impulse response functions (IRFs), which can be obtained through the inverse Fourier transform. These methods attempt to perform some fitting between measured and theoretical functions and employ different optimization procedures and different levels of simplification. Accordingly, they are usually classified according to the following criteria:

* Domain of application (time or frequency)

* Type of formulation (indirect or modal and direct)

* Number of modes analyzed (SDOF or MDOF - single degree of freedom or multi degree of freedom)

* Number of inputs and type of estimates (SISO, SIMO, MIMO, MISO - single input single output, single input multi output, multi input multi output, multi input single output).

Early methods of identification were developed for the frequency domain. For simple SDOF formulations (peak amplitude, curve-fit, inverse methods, for example), the fit between a measured and a theoretical FRF of a SDOF system in the vicinity of each resonant frequency is developed; neglecting the contribution of resonant modes. In more sophisticated MDOF methods - rational fraction polynomial (RFP), complex exponential frequency domain (CEFD), polyreference frequency domain (PRFD) - the fit between measured and theoretical FRFs is made globally for a wide range of frequencies.

Time-domain methods, which tend to provide the best results when a large frequency range or a large number of modes exist in the data, were developed because of limitations in the frequency resolution of spectral estimates and leakage errors in the estimates. The most widely known methods are either indirect - complex exponential (CE), least-squares complex exponential (LSCE), polyreference complex exponential (PRCE), Ibrahim time domain (ITD), eigen system realization algorithm (ERA), or direct autoregressive moving-average (ARMA).