Geopsy: Damping

Damping is an advanced signal processing toolbox aiming at computing the viscous damping ratio of an identified oscillating structure using the Random Decrement technique.

Background

Viscous damping ratio is a parameter representing the energy loss of an oscillating system. The loss can be either internal (material damping) or to another system (radiated damping). The computation of the viscous damping assumes the friction forces (energy loss) are proportional to the velocity of the system. For a single degree-of-freedom system, the solution of the differential equation (impulse response function in time) is then an exponentially decreasing sinus function of the form:

$h(t)=-{\frac {e^{-\xi \omega t}}{\omega '}}sin(\omega 't)$ with $\omega '=\omega {\sqrt {1-\xi ^{2}}}$

with \xi the damping ratio and \omega the angular frequency of resonance of the system. The assumption of viscous damping may not be appropriate in all cases but is common in civil engineering and seismology.

The Random Decrement technique ...

Practical Use

The Damping toolbox is used in Geopsy after detecting peaks in the Power Spectrum or the Structure spectrum. Computing the damping ratio is above all an indication on the origin of the peak. An undamped peak ($\xi <<1$) is produced by a self-entertaining source, generally an industrial machine. In an oscillating structure like a building, the damping ratio ranges between 1 and 10%. Slightly lower values are possible for slender structures. Higher damping cannot generally be detected in recordings because of too low energy.

Damping ratio toolbox

Starting the Damping toolbox found in the Menu Tools or using the Toolbar applies the Random Decrement technique to the signals in the active signal viewer.

The Damping toolbox is divided into 3 parts: Filter, Time Limits and Parameters of the Random Decrement technique. These parameters are automatically saved in a log file of the database name and can be restored clicking on Load Parameters

Filter

Applying a narrow band filter is generally necessary in order to select the frequency band of the interesting peak, since other peaks are generally existing in the spectrum. This may strongly affect the signals and is the major drawback of the random decrement technique. The available filtering options are detailed in Filter.

Time Limits

The time limits define the signal range on which the Random Decrement Technique is applied. Options for Time Limits are defined in the corresponding section.

Parameters of the Random Decrement technique

In Geopsy, two parameters can be customized to compute the damping ratio using the Random Decrement:

• Window length is size of the stacked windows to compute the random decrement. It should contain around 10 periods, i.e. ${\frac {10}{f_{0}}}$ seconds, with $f_{0}$ the resonance frequency of interest.
• Fitting length is the time length used for the fitting. It is therefore lower or equal to the window length. It should first be set to the window length and eventually decreased if the end of the response function is no more described by an exponentially decreasing sinus function.

Several window length should always be tested in order to check the robustness of the results.

Results

When clicking on start