Geopsy: Damping - Revision history

Pierre-Yves Bard at 15:22, 12 March 2010

2010-03-12T15:22:31Z

Pierre-Yves Bard at 15:19, 12 March 2010

2010-03-12T15:19:57Z

Pierre-Yves Bard at 15:19, 12 March 2010

2010-03-12T15:19:17Z

Pierre-Yves Bard at 15:18, 12 March 2010

2010-03-12T15:18:35Z

Pierre-Yves Bard at 15:04, 12 March 2010

2010-03-12T15:04:56Z

Pierre-Yves Bard: /* Parameters of the Random Decrement technique */

2010-03-12T14:42:52Z

Parameters of the Random Decrement technique

Pierre-Yves Bard: /* Practical Use */

2010-03-12T14:32:12Z

Practical Use

Pierre-Yves Bard: /* Practical Use */

2010-03-12T14:29:15Z

Practical Use

Pierre-Yves Bard: /* Practical Use */

2010-03-12T14:28:11Z

Practical Use

Pierre-Yves Bard: /* Background */

2010-03-12T14:27:37Z

Background

@@ Line 38: / Line 38: @@
 Several window lengths should always be tested in order to check the robustness of the results.
-[[Image:DampingToolboxRes.png|thumb|right|300px|Damping results in each direction of the building. This structure has particularly small damping ratios.]]
+[[Image:DampingToolboxRes.png|thumb|right|300px|Example damping results for a building : the two Randomdec signatures were derived from recordings at building top floor in each direction. This structure has particularly small damping ratios.]]
 [[Image:DampingToolboxRes1.png|thumb|center|300px|Example identification of an artifical source : this "RandomDec" signature was obtained from the vertical component of a noise recording:  the monochromatic component at 2.92 Hz with a very low damping (0.06%) witnesses an industrial origin ]]

← Older revision		Revision as of 15:19, 12 March 2010
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	[[Image:DampingToolboxRes.png\|thumb\|right\|300px\|Damping results in each direction of the building. This structure has particularly small damping ratios.]]		[[Image:DampingToolboxRes.png\|thumb\|right\|300px\|Damping results in each direction of the building. This structure has particularly small damping ratios.]]
−	[[Image:DampingToolboxRes1.png\|thumb\|~~left~~\|300px\|Example identification of an artifical source : this "RandomDec" signature was obtained from the vertical component of a noise recording: the monochromatic component at 2.92 Hz with a very low damping (0.06%) witnesses an industrial origin ]]	+	[[Image:DampingToolboxRes1.png\|thumb\|center\|300px\|Example identification of an artifical source : this "RandomDec" signature was obtained from the vertical component of a noise recording: the monochromatic component at 2.92 Hz with a very low damping (0.06%) witnesses an industrial origin ]]

← Older revision		Revision as of 15:19, 12 March 2010
Line 39:		Line 39:

	[[Image:DampingToolboxRes.png\|thumb\|right\|300px\|Damping results in each direction of the building. This structure has particularly small damping ratios.]]		[[Image:DampingToolboxRes.png\|thumb\|right\|300px\|Damping results in each direction of the building. This structure has particularly small damping ratios.]]
−	[[Image:DampingToolboxRes1.png\|thumb\|~~right~~\|300px\|Example identification of an artifical source : this "RandomDec" signature was obtained from the vertical component of a noise recording: the monochromatic component at 2.92 Hz with a very low damping (0.06%) witnesses an industrial origin ]]	+	[[Image:DampingToolboxRes1.png\|thumb\|left\|300px\|Example identification of an artifical source : this "RandomDec" signature was obtained from the vertical component of a noise recording: the monochromatic component at 2.92 Hz with a very low damping (0.06%) witnesses an industrial origin ]]

← Older revision		Revision as of 15:18, 12 March 2010
Line 39:		Line 39:

	[[Image:DampingToolboxRes.png\|thumb\|right\|300px\|Damping results in each direction of the building. This structure has particularly small damping ratios.]]		[[Image:DampingToolboxRes.png\|thumb\|right\|300px\|Damping results in each direction of the building. This structure has particularly small damping ratios.]]
−	[[Image:DampingToolboxRes1.png\|thumb\|right\|300px\|Example identification of an artifical source : this "RandomDec" signature was obtained from the vertical component of a noise recording: the very low damping (0.06%) witnesses an industrial origin ]]	+	[[Image:DampingToolboxRes1.png\|thumb\|right\|300px\|Example identification of an artifical source : this "RandomDec" signature was obtained from the vertical component of a noise recording: the monochromatic component at 2.92 Hz with a very low damping (0.06%) witnesses an industrial origin ]]

← Older revision		Revision as of 15:04, 12 March 2010
Line 39:		Line 39:

	[[Image:DampingToolboxRes.png\|thumb\|right\|300px\|Damping results in each direction of the building. This structure has particularly small damping ratios.]]		[[Image:DampingToolboxRes.png\|thumb\|right\|300px\|Damping results in each direction of the building. This structure has particularly small damping ratios.]]
		+	[[Image:DampingToolboxRes1.png\|thumb\|right\|300px\|Example identification of an artifical source : this "RandomDec" signature was obtained from the vertical component of a noise recording: the very low damping (0.06%) witnesses an industrial origin ]]
		+

	===Results===		===Results===

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 ===Parameters of the Random Decrement technique===
 In Geopsy, two parameters can be customized to compute the damping ratio using the Random Decrement technique:
-*''Window length'' is size of the stacked windows to compute the random decrement. It should contain at least 10 periods, i.e. <math>\frac{10}{f_0}</math> seconds, with <math>f_0</math> the resonance frequency of interest.
+*''Window length'' is the size of the stacked windows from the window origin coresponding to a zero-crossing with possitive derivative. It should contain at least 10 periods, i.e. <math>\frac{10}{f_1}</math> seconds, with <math>f_1</math> the frequency of interest.
-*''Fitting length'' is the time length of the resulting random decrement used for the fitting. It should therefore be 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 cosine function.
+*''Fitting length'' is the time length of the resulting random decrement used for the fitting. It should therefore be lower than or equal to the window length. It should first be set to the window length and eventually decreased in case the resulting response function exhibits a high-damping and cannot be described by an exponentially decreasing sine function after several periods.
 Several window lengths should always be tested in order to check the robustness of the results.
 [[Image:DampingToolboxRes.png|thumb|right|300px|Damping results in each direction of the building. This structure has particularly small damping ratios.]]
 ===Results===
 When clicking on start button, a results page appears with one [[SciFigs: Graph|graph]] per signal processed. Each graph includes 1 layer with 4 lines representing the mean (solid black line) and standard deviation (dashed black line) of the Random Decrement and the fitted exponentially decreasing function (solid red line). Next to each graph, the frequency f (in Hertz) and damping ratio z (in %) of this fitted function are displayed.

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 ==Practical Use==
 The Damping toolbox is used in Geopsy after detecting peaks in the [[Spectral amplitudes|Power Spectrum]] or the [[Geopsy: Structure spectrum|Structure spectrum]]. Computing the damping ratio is above all an indication on the origin of the peak. An undamped peak (<math>\xi<<1%</math>) is produced by a self-entertaining source, generally an industrial machine. In an oscillating structure like a building, the damping ratio generally 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.
-For ground ambient vibration recordings, oscillating structures (machines, buildings, trees...) may pollute the signals and lead to false interpretation, e.g. of the [[H/V spectral ratio|H/V spectral ratios]].
+For ground ambient vibration recordings, oscillating structures (machines, buildings, trees...) may pollute the signals and lead to false interpretation, e.g. of the [[H/V spectral ratio|H/V spectral ratios]]. The [Geopsy: damping|damping]] tool is mainly intended to identify pollution by continuous, monochromatic signals.
 [[Image:DampingToolbox.png|thumb|right|250px|Damping toolbox pop-up menu]]

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 ==Practical Use==
-The Damping toolbox is used in Geopsy after detecting peaks in the [[Spectral amplitudes|Power Spectrum]] or the [[Geopsy: Structure spectrum|Structure spectrum]]. Computing the damping ratio is above all an indication on the origin of the peak. An undamped peak (<math>\xi<<1</math>) 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.
+The Damping toolbox is used in Geopsy after detecting peaks in the [[Spectral amplitudes|Power Spectrum]] or the [[Geopsy: Structure spectrum|Structure spectrum]]. Computing the damping ratio is above all an indication on the origin of the peak. An undamped peak (<math>\xi<<1%</math>) 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.
 For ground ambient vibration recordings, oscillating structures (machines, buildings, trees...) may pollute the signals and lead to false interpretation, e.g. of the [[H/V spectral ratio|H/V spectral ratios]].
 [[Image:DampingToolbox.png|thumb|right|250px|Damping toolbox pop-up menu]]
 ==Damping ratio toolbox==
 Starting the ''Damping'' toolbox found in the [[Geopsy: Tools|Menu Tools]] or using the [[Geopsy: Toolbar|Toolbar]] applies the Random Decrement technique to the signals in the active [[Geopsy: Signal Viewer|signal viewer]].

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 ==Background==
 [[Image:DampingToolboxSpe.png|thumb|right|250px|Spectrum of recordings in a building for which the damping will be calculated]]
-[[Wikipedia:Damping ratio|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 in time (impulse response function) is then an exponentially decreasing sinus function of the form:
+[[Wikipedia:Damping ratio|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 in time (impulse response function) is then an exponentially decreasing sine function of the form:
 <math>
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 The Random Decrement technique is based on the assumption that at each time step, the signal is the sum of a random signal and the impulse response function of the study-system. Stacking many time windows with the same initial condition results in enhancing the impulse response function component with respect to  the zero-mean random part. The algorithm selects all the windows of the given length starting with a 0 amplitude and a positive derivative and averages them.
-Then, the Impulse response function is fitted by an exponentially decreasing cosine function (starting at 0) depending on an amplitude <math>\alpha</math>, the resonance frequency <math>f=\frac{\omega}{2\pi}</math> and the damping ratio <math>\xi</math>.
+Then, the Impulse response function is fitted by an exponentially decreasing sine function (starting at 0) depending on an amplitude <math>\alpha</math>, the resonance frequency <math>f=\frac{\omega}{2\pi}</math> and the damping ratio <math>\xi</math>.
 ==Practical Use==